| 1 | /* Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, |
| 2 | * 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, |
| 3 | * 2014 Free Software Foundation, Inc. |
| 4 | * |
| 5 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories |
| 6 | * and Bellcore. See scm_divide. |
| 7 | * |
| 8 | * |
| 9 | * This library is free software; you can redistribute it and/or |
| 10 | * modify it under the terms of the GNU Lesser General Public License |
| 11 | * as published by the Free Software Foundation; either version 3 of |
| 12 | * the License, or (at your option) any later version. |
| 13 | * |
| 14 | * This library is distributed in the hope that it will be useful, but |
| 15 | * WITHOUT ANY WARRANTY; without even the implied warranty of |
| 16 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| 17 | * Lesser General Public License for more details. |
| 18 | * |
| 19 | * You should have received a copy of the GNU Lesser General Public |
| 20 | * License along with this library; if not, write to the Free Software |
| 21 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
| 22 | * 02110-1301 USA |
| 23 | */ |
| 24 | |
| 25 | \f |
| 26 | /* General assumptions: |
| 27 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. |
| 28 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. |
| 29 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. |
| 30 | * XXX What about infinities? They are equal to their own floor! -mhw |
| 31 | * All objects satisfying SCM_FRACTIONP are never an integer. |
| 32 | */ |
| 33 | |
| 34 | /* TODO: |
| 35 | |
| 36 | - see if special casing bignums and reals in integer-exponent when |
| 37 | possible (to use mpz_pow and mpf_pow_ui) is faster. |
| 38 | |
| 39 | - look in to better short-circuiting of common cases in |
| 40 | integer-expt and elsewhere. |
| 41 | |
| 42 | - see if direct mpz operations can help in ash and elsewhere. |
| 43 | |
| 44 | */ |
| 45 | |
| 46 | #ifdef HAVE_CONFIG_H |
| 47 | # include <config.h> |
| 48 | #endif |
| 49 | |
| 50 | #include <verify.h> |
| 51 | #include <assert.h> |
| 52 | |
| 53 | #include <math.h> |
| 54 | #include <string.h> |
| 55 | #include <unicase.h> |
| 56 | #include <unictype.h> |
| 57 | |
| 58 | #if HAVE_COMPLEX_H |
| 59 | #include <complex.h> |
| 60 | #endif |
| 61 | |
| 62 | #include <stdarg.h> |
| 63 | |
| 64 | #include "libguile/_scm.h" |
| 65 | #include "libguile/feature.h" |
| 66 | #include "libguile/ports.h" |
| 67 | #include "libguile/root.h" |
| 68 | #include "libguile/smob.h" |
| 69 | #include "libguile/strings.h" |
| 70 | #include "libguile/bdw-gc.h" |
| 71 | |
| 72 | #include "libguile/validate.h" |
| 73 | #include "libguile/numbers.h" |
| 74 | #include "libguile/deprecation.h" |
| 75 | |
| 76 | #include "libguile/eq.h" |
| 77 | |
| 78 | /* values per glibc, if not already defined */ |
| 79 | #ifndef M_LOG10E |
| 80 | #define M_LOG10E 0.43429448190325182765 |
| 81 | #endif |
| 82 | #ifndef M_LN2 |
| 83 | #define M_LN2 0.69314718055994530942 |
| 84 | #endif |
| 85 | #ifndef M_PI |
| 86 | #define M_PI 3.14159265358979323846 |
| 87 | #endif |
| 88 | |
| 89 | /* FIXME: We assume that FLT_RADIX is 2 */ |
| 90 | verify (FLT_RADIX == 2); |
| 91 | |
| 92 | typedef scm_t_signed_bits scm_t_inum; |
| 93 | #define scm_from_inum(x) (scm_from_signed_integer (x)) |
| 94 | |
| 95 | /* Test an inum to see if it can be converted to a double without loss |
| 96 | of precision. Note that this will sometimes return 0 even when 1 |
| 97 | could have been returned, e.g. for large powers of 2. It is designed |
| 98 | to be a fast check to optimize common cases. */ |
| 99 | #define INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE(n) \ |
| 100 | (SCM_I_FIXNUM_BIT-1 <= DBL_MANT_DIG \ |
| 101 | || ((n) ^ ((n) >> (SCM_I_FIXNUM_BIT-1))) < (1L << DBL_MANT_DIG)) |
| 102 | |
| 103 | #if ! HAVE_DECL_MPZ_INITS |
| 104 | |
| 105 | /* GMP < 5.0.0 lacks `mpz_inits' and `mpz_clears'. Provide them. */ |
| 106 | |
| 107 | #define VARARG_MPZ_ITERATOR(func) \ |
| 108 | static void \ |
| 109 | func ## s (mpz_t x, ...) \ |
| 110 | { \ |
| 111 | va_list ap; \ |
| 112 | \ |
| 113 | va_start (ap, x); \ |
| 114 | while (x != NULL) \ |
| 115 | { \ |
| 116 | func (x); \ |
| 117 | x = va_arg (ap, mpz_ptr); \ |
| 118 | } \ |
| 119 | va_end (ap); \ |
| 120 | } |
| 121 | |
| 122 | VARARG_MPZ_ITERATOR (mpz_init) |
| 123 | VARARG_MPZ_ITERATOR (mpz_clear) |
| 124 | |
| 125 | #endif |
| 126 | |
| 127 | \f |
| 128 | |
| 129 | /* |
| 130 | Wonder if this might be faster for some of our code? A switch on |
| 131 | the numtag would jump directly to the right case, and the |
| 132 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... |
| 133 | |
| 134 | #define SCM_I_NUMTAG_NOTNUM 0 |
| 135 | #define SCM_I_NUMTAG_INUM 1 |
| 136 | #define SCM_I_NUMTAG_BIG scm_tc16_big |
| 137 | #define SCM_I_NUMTAG_REAL scm_tc16_real |
| 138 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex |
| 139 | #define SCM_I_NUMTAG(x) \ |
| 140 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
| 141 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
| 142 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
| 143 | : SCM_I_NUMTAG_NOTNUM))) |
| 144 | */ |
| 145 | /* the macro above will not work as is with fractions */ |
| 146 | |
| 147 | |
| 148 | /* Default to 1, because as we used to hard-code `free' as the |
| 149 | deallocator, we know that overriding these functions with |
| 150 | instrumented `malloc' / `free' is OK. */ |
| 151 | int scm_install_gmp_memory_functions = 1; |
| 152 | static SCM flo0; |
| 153 | static SCM exactly_one_half; |
| 154 | static SCM flo_log10e; |
| 155 | |
| 156 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
| 157 | |
| 158 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
| 159 | * printed or scm_string representation of an inexact number. |
| 160 | */ |
| 161 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
| 162 | |
| 163 | |
| 164 | #if !defined (HAVE_ASINH) |
| 165 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } |
| 166 | #endif |
| 167 | #if !defined (HAVE_ACOSH) |
| 168 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } |
| 169 | #endif |
| 170 | #if !defined (HAVE_ATANH) |
| 171 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } |
| 172 | #endif |
| 173 | |
| 174 | /* mpz_cmp_d in GMP before 4.2 didn't recognise infinities, so |
| 175 | xmpz_cmp_d uses an explicit check. Starting with GMP 4.2 (released |
| 176 | in March 2006), mpz_cmp_d now handles infinities properly. */ |
| 177 | #if 1 |
| 178 | #define xmpz_cmp_d(z, d) \ |
| 179 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
| 180 | #else |
| 181 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) |
| 182 | #endif |
| 183 | |
| 184 | |
| 185 | #if defined (GUILE_I) |
| 186 | #if defined HAVE_COMPLEX_DOUBLE |
| 187 | |
| 188 | /* For an SCM object Z which is a complex number (ie. satisfies |
| 189 | SCM_COMPLEXP), return its value as a C level "complex double". */ |
| 190 | #define SCM_COMPLEX_VALUE(z) \ |
| 191 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
| 192 | |
| 193 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
| 194 | |
| 195 | /* Convert a C "complex double" to an SCM value. */ |
| 196 | static inline SCM |
| 197 | scm_from_complex_double (complex double z) |
| 198 | { |
| 199 | return scm_c_make_rectangular (creal (z), cimag (z)); |
| 200 | } |
| 201 | |
| 202 | #endif /* HAVE_COMPLEX_DOUBLE */ |
| 203 | #endif /* GUILE_I */ |
| 204 | |
| 205 | \f |
| 206 | |
| 207 | static mpz_t z_negative_one; |
| 208 | |
| 209 | \f |
| 210 | |
| 211 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
| 212 | static void |
| 213 | finalize_bignum (void *ptr, void *data) |
| 214 | { |
| 215 | SCM bignum; |
| 216 | |
| 217 | bignum = PTR2SCM (ptr); |
| 218 | mpz_clear (SCM_I_BIG_MPZ (bignum)); |
| 219 | } |
| 220 | |
| 221 | /* The next three functions (custom_libgmp_*) are passed to |
| 222 | mp_set_memory_functions (in GMP) so that memory used by the digits |
| 223 | themselves is known to the garbage collector. This is needed so |
| 224 | that GC will be run at appropriate times. Otherwise, a program which |
| 225 | creates many large bignums would malloc a huge amount of memory |
| 226 | before the GC runs. */ |
| 227 | static void * |
| 228 | custom_gmp_malloc (size_t alloc_size) |
| 229 | { |
| 230 | return scm_malloc (alloc_size); |
| 231 | } |
| 232 | |
| 233 | static void * |
| 234 | custom_gmp_realloc (void *old_ptr, size_t old_size, size_t new_size) |
| 235 | { |
| 236 | return scm_realloc (old_ptr, new_size); |
| 237 | } |
| 238 | |
| 239 | static void |
| 240 | custom_gmp_free (void *ptr, size_t size) |
| 241 | { |
| 242 | free (ptr); |
| 243 | } |
| 244 | |
| 245 | |
| 246 | /* Return a new uninitialized bignum. */ |
| 247 | static inline SCM |
| 248 | make_bignum (void) |
| 249 | { |
| 250 | scm_t_bits *p; |
| 251 | |
| 252 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ |
| 253 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), |
| 254 | "bignum"); |
| 255 | p[0] = scm_tc16_big; |
| 256 | |
| 257 | scm_i_set_finalizer (p, finalize_bignum, NULL); |
| 258 | |
| 259 | return SCM_PACK (p); |
| 260 | } |
| 261 | |
| 262 | |
| 263 | SCM |
| 264 | scm_i_mkbig () |
| 265 | { |
| 266 | /* Return a newly created bignum. */ |
| 267 | SCM z = make_bignum (); |
| 268 | mpz_init (SCM_I_BIG_MPZ (z)); |
| 269 | return z; |
| 270 | } |
| 271 | |
| 272 | static SCM |
| 273 | scm_i_inum2big (scm_t_inum x) |
| 274 | { |
| 275 | /* Return a newly created bignum initialized to X. */ |
| 276 | SCM z = make_bignum (); |
| 277 | #if SIZEOF_VOID_P == SIZEOF_LONG |
| 278 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
| 279 | #else |
| 280 | /* Note that in this case, you'll also have to check all mpz_*_ui and |
| 281 | mpz_*_si invocations in Guile. */ |
| 282 | #error creation of mpz not implemented for this inum size |
| 283 | #endif |
| 284 | return z; |
| 285 | } |
| 286 | |
| 287 | SCM |
| 288 | scm_i_long2big (long x) |
| 289 | { |
| 290 | /* Return a newly created bignum initialized to X. */ |
| 291 | SCM z = make_bignum (); |
| 292 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
| 293 | return z; |
| 294 | } |
| 295 | |
| 296 | SCM |
| 297 | scm_i_ulong2big (unsigned long x) |
| 298 | { |
| 299 | /* Return a newly created bignum initialized to X. */ |
| 300 | SCM z = make_bignum (); |
| 301 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
| 302 | return z; |
| 303 | } |
| 304 | |
| 305 | SCM |
| 306 | scm_i_clonebig (SCM src_big, int same_sign_p) |
| 307 | { |
| 308 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ |
| 309 | SCM z = make_bignum (); |
| 310 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
| 311 | if (!same_sign_p) |
| 312 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); |
| 313 | return z; |
| 314 | } |
| 315 | |
| 316 | int |
| 317 | scm_i_bigcmp (SCM x, SCM y) |
| 318 | { |
| 319 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ |
| 320 | /* presume we already know x and y are bignums */ |
| 321 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 322 | scm_remember_upto_here_2 (x, y); |
| 323 | return result; |
| 324 | } |
| 325 | |
| 326 | SCM |
| 327 | scm_i_dbl2big (double d) |
| 328 | { |
| 329 | /* results are only defined if d is an integer */ |
| 330 | SCM z = make_bignum (); |
| 331 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
| 332 | return z; |
| 333 | } |
| 334 | |
| 335 | /* Convert a integer in double representation to a SCM number. */ |
| 336 | |
| 337 | SCM |
| 338 | scm_i_dbl2num (double u) |
| 339 | { |
| 340 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both |
| 341 | powers of 2, so there's no rounding when making "double" values |
| 342 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could |
| 343 | get rounded on a 64-bit machine, hence the "+1". |
| 344 | |
| 345 | The use of floor() to force to an integer value ensures we get a |
| 346 | "numerically closest" value without depending on how a |
| 347 | double->long cast or how mpz_set_d will round. For reference, |
| 348 | double->long probably follows the hardware rounding mode, |
| 349 | mpz_set_d truncates towards zero. */ |
| 350 | |
| 351 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not |
| 352 | representable as a double? */ |
| 353 | |
| 354 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) |
| 355 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) |
| 356 | return SCM_I_MAKINUM ((scm_t_inum) u); |
| 357 | else |
| 358 | return scm_i_dbl2big (u); |
| 359 | } |
| 360 | |
| 361 | static SCM round_right_shift_exact_integer (SCM n, long count); |
| 362 | |
| 363 | /* scm_i_big2dbl_2exp() is like frexp for bignums: it converts the |
| 364 | bignum b into a normalized significand and exponent such that |
| 365 | b = significand * 2^exponent and 1/2 <= abs(significand) < 1. |
| 366 | The return value is the significand rounded to the closest |
| 367 | representable double, and the exponent is placed into *expon_p. |
| 368 | If b is zero, then the returned exponent and significand are both |
| 369 | zero. */ |
| 370 | |
| 371 | static double |
| 372 | scm_i_big2dbl_2exp (SCM b, long *expon_p) |
| 373 | { |
| 374 | size_t bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); |
| 375 | size_t shift = 0; |
| 376 | |
| 377 | if (bits > DBL_MANT_DIG) |
| 378 | { |
| 379 | shift = bits - DBL_MANT_DIG; |
| 380 | b = round_right_shift_exact_integer (b, shift); |
| 381 | if (SCM_I_INUMP (b)) |
| 382 | { |
| 383 | int expon; |
| 384 | double signif = frexp (SCM_I_INUM (b), &expon); |
| 385 | *expon_p = expon + shift; |
| 386 | return signif; |
| 387 | } |
| 388 | } |
| 389 | |
| 390 | { |
| 391 | long expon; |
| 392 | double signif = mpz_get_d_2exp (&expon, SCM_I_BIG_MPZ (b)); |
| 393 | scm_remember_upto_here_1 (b); |
| 394 | *expon_p = expon + shift; |
| 395 | return signif; |
| 396 | } |
| 397 | } |
| 398 | |
| 399 | /* scm_i_big2dbl() rounds to the closest representable double, |
| 400 | in accordance with R5RS exact->inexact. */ |
| 401 | double |
| 402 | scm_i_big2dbl (SCM b) |
| 403 | { |
| 404 | long expon; |
| 405 | double signif = scm_i_big2dbl_2exp (b, &expon); |
| 406 | return ldexp (signif, expon); |
| 407 | } |
| 408 | |
| 409 | SCM |
| 410 | scm_i_normbig (SCM b) |
| 411 | { |
| 412 | /* convert a big back to a fixnum if it'll fit */ |
| 413 | /* presume b is a bignum */ |
| 414 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) |
| 415 | { |
| 416 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
| 417 | if (SCM_FIXABLE (val)) |
| 418 | b = SCM_I_MAKINUM (val); |
| 419 | } |
| 420 | return b; |
| 421 | } |
| 422 | |
| 423 | static SCM_C_INLINE_KEYWORD SCM |
| 424 | scm_i_mpz2num (mpz_t b) |
| 425 | { |
| 426 | /* convert a mpz number to a SCM number. */ |
| 427 | if (mpz_fits_slong_p (b)) |
| 428 | { |
| 429 | scm_t_inum val = mpz_get_si (b); |
| 430 | if (SCM_FIXABLE (val)) |
| 431 | return SCM_I_MAKINUM (val); |
| 432 | } |
| 433 | |
| 434 | { |
| 435 | SCM z = make_bignum (); |
| 436 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
| 437 | return z; |
| 438 | } |
| 439 | } |
| 440 | |
| 441 | /* Make the ratio NUMERATOR/DENOMINATOR, where: |
| 442 | 1. NUMERATOR and DENOMINATOR are exact integers |
| 443 | 2. NUMERATOR and DENOMINATOR are reduced to lowest terms: gcd(n,d) == 1 */ |
| 444 | static SCM |
| 445 | scm_i_make_ratio_already_reduced (SCM numerator, SCM denominator) |
| 446 | { |
| 447 | /* Flip signs so that the denominator is positive. */ |
| 448 | if (scm_is_false (scm_positive_p (denominator))) |
| 449 | { |
| 450 | if (SCM_UNLIKELY (scm_is_eq (denominator, SCM_INUM0))) |
| 451 | scm_num_overflow ("make-ratio"); |
| 452 | else |
| 453 | { |
| 454 | numerator = scm_difference (numerator, SCM_UNDEFINED); |
| 455 | denominator = scm_difference (denominator, SCM_UNDEFINED); |
| 456 | } |
| 457 | } |
| 458 | |
| 459 | /* Check for the integer case */ |
| 460 | if (scm_is_eq (denominator, SCM_INUM1)) |
| 461 | return numerator; |
| 462 | |
| 463 | return scm_double_cell (scm_tc16_fraction, |
| 464 | SCM_UNPACK (numerator), |
| 465 | SCM_UNPACK (denominator), 0); |
| 466 | } |
| 467 | |
| 468 | static SCM scm_exact_integer_quotient (SCM x, SCM y); |
| 469 | |
| 470 | /* Make the ratio NUMERATOR/DENOMINATOR */ |
| 471 | static SCM |
| 472 | scm_i_make_ratio (SCM numerator, SCM denominator) |
| 473 | #define FUNC_NAME "make-ratio" |
| 474 | { |
| 475 | /* Make sure the arguments are proper */ |
| 476 | if (!SCM_LIKELY (SCM_I_INUMP (numerator) || SCM_BIGP (numerator))) |
| 477 | SCM_WRONG_TYPE_ARG (1, numerator); |
| 478 | else if (!SCM_LIKELY (SCM_I_INUMP (denominator) || SCM_BIGP (denominator))) |
| 479 | SCM_WRONG_TYPE_ARG (2, denominator); |
| 480 | else |
| 481 | { |
| 482 | SCM the_gcd = scm_gcd (numerator, denominator); |
| 483 | if (!(scm_is_eq (the_gcd, SCM_INUM1))) |
| 484 | { |
| 485 | /* Reduce to lowest terms */ |
| 486 | numerator = scm_exact_integer_quotient (numerator, the_gcd); |
| 487 | denominator = scm_exact_integer_quotient (denominator, the_gcd); |
| 488 | } |
| 489 | return scm_i_make_ratio_already_reduced (numerator, denominator); |
| 490 | } |
| 491 | } |
| 492 | #undef FUNC_NAME |
| 493 | |
| 494 | static mpz_t scm_i_divide2double_lo2b; |
| 495 | |
| 496 | /* Return the double that is closest to the exact rational N/D, with |
| 497 | ties rounded toward even mantissas. N and D must be exact |
| 498 | integers. */ |
| 499 | static double |
| 500 | scm_i_divide2double (SCM n, SCM d) |
| 501 | { |
| 502 | int neg; |
| 503 | mpz_t nn, dd, lo, hi, x; |
| 504 | ssize_t e; |
| 505 | |
| 506 | if (SCM_LIKELY (SCM_I_INUMP (d))) |
| 507 | { |
| 508 | if (SCM_LIKELY |
| 509 | (SCM_I_INUMP (n) |
| 510 | && INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE (SCM_I_INUM (n)) |
| 511 | && INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE (SCM_I_INUM (d)))) |
| 512 | /* If both N and D can be losslessly converted to doubles, then |
| 513 | we can rely on IEEE floating point to do proper rounding much |
| 514 | faster than we can. */ |
| 515 | return ((double) SCM_I_INUM (n)) / ((double) SCM_I_INUM (d)); |
| 516 | |
| 517 | if (SCM_UNLIKELY (scm_is_eq (d, SCM_INUM0))) |
| 518 | { |
| 519 | if (scm_is_true (scm_positive_p (n))) |
| 520 | return 1.0 / 0.0; |
| 521 | else if (scm_is_true (scm_negative_p (n))) |
| 522 | return -1.0 / 0.0; |
| 523 | else |
| 524 | return 0.0 / 0.0; |
| 525 | } |
| 526 | |
| 527 | mpz_init_set_si (dd, SCM_I_INUM (d)); |
| 528 | } |
| 529 | else |
| 530 | mpz_init_set (dd, SCM_I_BIG_MPZ (d)); |
| 531 | |
| 532 | if (SCM_I_INUMP (n)) |
| 533 | mpz_init_set_si (nn, SCM_I_INUM (n)); |
| 534 | else |
| 535 | mpz_init_set (nn, SCM_I_BIG_MPZ (n)); |
| 536 | |
| 537 | neg = (mpz_sgn (nn) < 0) ^ (mpz_sgn (dd) < 0); |
| 538 | mpz_abs (nn, nn); |
| 539 | mpz_abs (dd, dd); |
| 540 | |
| 541 | /* Now we need to find the value of e such that: |
| 542 | |
| 543 | For e <= 0: |
| 544 | b^{p-1} - 1/2b <= b^-e n / d < b^p - 1/2 [1A] |
| 545 | (2 b^p - 1) <= 2 b b^-e n / d < (2 b^p - 1) b [2A] |
| 546 | (2 b^p - 1) d <= 2 b b^-e n < (2 b^p - 1) d b [3A] |
| 547 | |
| 548 | For e >= 0: |
| 549 | b^{p-1} - 1/2b <= n / b^e d < b^p - 1/2 [1B] |
| 550 | (2 b^p - 1) <= 2 b n / b^e d < (2 b^p - 1) b [2B] |
| 551 | (2 b^p - 1) d b^e <= 2 b n < (2 b^p - 1) d b b^e [3B] |
| 552 | |
| 553 | where: p = DBL_MANT_DIG |
| 554 | b = FLT_RADIX (here assumed to be 2) |
| 555 | |
| 556 | After rounding, the mantissa must be an integer between b^{p-1} and |
| 557 | (b^p - 1), except for subnormal numbers. In the inequations [1A] |
| 558 | and [1B], the middle expression represents the mantissa *before* |
| 559 | rounding, and therefore is bounded by the range of values that will |
| 560 | round to a floating-point number with the exponent e. The upper |
| 561 | bound is (b^p - 1 + 1/2) = (b^p - 1/2), and is exclusive because |
| 562 | ties will round up to the next power of b. The lower bound is |
| 563 | (b^{p-1} - 1/2b), and is inclusive because ties will round toward |
| 564 | this power of b. Here we subtract 1/2b instead of 1/2 because it |
| 565 | is in the range of the next smaller exponent, where the |
| 566 | representable numbers are closer together by a factor of b. |
| 567 | |
| 568 | Inequations [2A] and [2B] are derived from [1A] and [1B] by |
| 569 | multiplying by 2b, and in [3A] and [3B] we multiply by the |
| 570 | denominator of the middle value to obtain integer expressions. |
| 571 | |
| 572 | In the code below, we refer to the three expressions in [3A] or |
| 573 | [3B] as lo, x, and hi. If the number is normalizable, we will |
| 574 | achieve the goal: lo <= x < hi */ |
| 575 | |
| 576 | /* Make an initial guess for e */ |
| 577 | e = mpz_sizeinbase (nn, 2) - mpz_sizeinbase (dd, 2) - (DBL_MANT_DIG-1); |
| 578 | if (e < DBL_MIN_EXP - DBL_MANT_DIG) |
| 579 | e = DBL_MIN_EXP - DBL_MANT_DIG; |
| 580 | |
| 581 | /* Compute the initial values of lo, x, and hi |
| 582 | based on the initial guess of e */ |
| 583 | mpz_inits (lo, hi, x, NULL); |
| 584 | mpz_mul_2exp (x, nn, 2 + ((e < 0) ? -e : 0)); |
| 585 | mpz_mul (lo, dd, scm_i_divide2double_lo2b); |
| 586 | if (e > 0) |
| 587 | mpz_mul_2exp (lo, lo, e); |
| 588 | mpz_mul_2exp (hi, lo, 1); |
| 589 | |
| 590 | /* Adjust e as needed to satisfy the inequality lo <= x < hi, |
| 591 | (but without making e less then the minimum exponent) */ |
| 592 | while (mpz_cmp (x, lo) < 0 && e > DBL_MIN_EXP - DBL_MANT_DIG) |
| 593 | { |
| 594 | mpz_mul_2exp (x, x, 1); |
| 595 | e--; |
| 596 | } |
| 597 | while (mpz_cmp (x, hi) >= 0) |
| 598 | { |
| 599 | /* If we ever used lo's value again, |
| 600 | we would need to double lo here. */ |
| 601 | mpz_mul_2exp (hi, hi, 1); |
| 602 | e++; |
| 603 | } |
| 604 | |
| 605 | /* Now compute the rounded mantissa: |
| 606 | n / b^e d (if e >= 0) |
| 607 | n b^-e / d (if e <= 0) */ |
| 608 | { |
| 609 | int cmp; |
| 610 | double result; |
| 611 | |
| 612 | if (e < 0) |
| 613 | mpz_mul_2exp (nn, nn, -e); |
| 614 | else |
| 615 | mpz_mul_2exp (dd, dd, e); |
| 616 | |
| 617 | /* mpz does not directly support rounded right |
| 618 | shifts, so we have to do it the hard way. |
| 619 | For efficiency, we reuse lo and hi. |
| 620 | hi == quotient, lo == remainder */ |
| 621 | mpz_fdiv_qr (hi, lo, nn, dd); |
| 622 | |
| 623 | /* The fractional part of the unrounded mantissa would be |
| 624 | remainder/dividend, i.e. lo/dd. So we have a tie if |
| 625 | lo/dd = 1/2. Multiplying both sides by 2*dd yields the |
| 626 | integer expression 2*lo = dd. Here we do that comparison |
| 627 | to decide whether to round up or down. */ |
| 628 | mpz_mul_2exp (lo, lo, 1); |
| 629 | cmp = mpz_cmp (lo, dd); |
| 630 | if (cmp > 0 || (cmp == 0 && mpz_odd_p (hi))) |
| 631 | mpz_add_ui (hi, hi, 1); |
| 632 | |
| 633 | result = ldexp (mpz_get_d (hi), e); |
| 634 | if (neg) |
| 635 | result = -result; |
| 636 | |
| 637 | mpz_clears (nn, dd, lo, hi, x, NULL); |
| 638 | return result; |
| 639 | } |
| 640 | } |
| 641 | |
| 642 | double |
| 643 | scm_i_fraction2double (SCM z) |
| 644 | { |
| 645 | return scm_i_divide2double (SCM_FRACTION_NUMERATOR (z), |
| 646 | SCM_FRACTION_DENOMINATOR (z)); |
| 647 | } |
| 648 | |
| 649 | static SCM |
| 650 | scm_i_from_double (double val) |
| 651 | { |
| 652 | SCM z; |
| 653 | |
| 654 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); |
| 655 | |
| 656 | SCM_SET_CELL_TYPE (z, scm_tc16_real); |
| 657 | SCM_REAL_VALUE (z) = val; |
| 658 | |
| 659 | return z; |
| 660 | } |
| 661 | |
| 662 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
| 663 | (SCM x), |
| 664 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
| 665 | "otherwise.") |
| 666 | #define FUNC_NAME s_scm_exact_p |
| 667 | { |
| 668 | if (SCM_INEXACTP (x)) |
| 669 | return SCM_BOOL_F; |
| 670 | else if (SCM_NUMBERP (x)) |
| 671 | return SCM_BOOL_T; |
| 672 | else |
| 673 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
| 674 | } |
| 675 | #undef FUNC_NAME |
| 676 | |
| 677 | int |
| 678 | scm_is_exact (SCM val) |
| 679 | { |
| 680 | return scm_is_true (scm_exact_p (val)); |
| 681 | } |
| 682 | |
| 683 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
| 684 | (SCM x), |
| 685 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
| 686 | "else.") |
| 687 | #define FUNC_NAME s_scm_inexact_p |
| 688 | { |
| 689 | if (SCM_INEXACTP (x)) |
| 690 | return SCM_BOOL_T; |
| 691 | else if (SCM_NUMBERP (x)) |
| 692 | return SCM_BOOL_F; |
| 693 | else |
| 694 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
| 695 | } |
| 696 | #undef FUNC_NAME |
| 697 | |
| 698 | int |
| 699 | scm_is_inexact (SCM val) |
| 700 | { |
| 701 | return scm_is_true (scm_inexact_p (val)); |
| 702 | } |
| 703 | |
| 704 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
| 705 | (SCM n), |
| 706 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
| 707 | "otherwise.") |
| 708 | #define FUNC_NAME s_scm_odd_p |
| 709 | { |
| 710 | if (SCM_I_INUMP (n)) |
| 711 | { |
| 712 | scm_t_inum val = SCM_I_INUM (n); |
| 713 | return scm_from_bool ((val & 1L) != 0); |
| 714 | } |
| 715 | else if (SCM_BIGP (n)) |
| 716 | { |
| 717 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); |
| 718 | scm_remember_upto_here_1 (n); |
| 719 | return scm_from_bool (odd_p); |
| 720 | } |
| 721 | else if (SCM_REALP (n)) |
| 722 | { |
| 723 | double val = SCM_REAL_VALUE (n); |
| 724 | if (isfinite (val)) |
| 725 | { |
| 726 | double rem = fabs (fmod (val, 2.0)); |
| 727 | if (rem == 1.0) |
| 728 | return SCM_BOOL_T; |
| 729 | else if (rem == 0.0) |
| 730 | return SCM_BOOL_F; |
| 731 | } |
| 732 | } |
| 733 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
| 734 | } |
| 735 | #undef FUNC_NAME |
| 736 | |
| 737 | |
| 738 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
| 739 | (SCM n), |
| 740 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
| 741 | "otherwise.") |
| 742 | #define FUNC_NAME s_scm_even_p |
| 743 | { |
| 744 | if (SCM_I_INUMP (n)) |
| 745 | { |
| 746 | scm_t_inum val = SCM_I_INUM (n); |
| 747 | return scm_from_bool ((val & 1L) == 0); |
| 748 | } |
| 749 | else if (SCM_BIGP (n)) |
| 750 | { |
| 751 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); |
| 752 | scm_remember_upto_here_1 (n); |
| 753 | return scm_from_bool (even_p); |
| 754 | } |
| 755 | else if (SCM_REALP (n)) |
| 756 | { |
| 757 | double val = SCM_REAL_VALUE (n); |
| 758 | if (isfinite (val)) |
| 759 | { |
| 760 | double rem = fabs (fmod (val, 2.0)); |
| 761 | if (rem == 1.0) |
| 762 | return SCM_BOOL_F; |
| 763 | else if (rem == 0.0) |
| 764 | return SCM_BOOL_T; |
| 765 | } |
| 766 | } |
| 767 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
| 768 | } |
| 769 | #undef FUNC_NAME |
| 770 | |
| 771 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
| 772 | (SCM x), |
| 773 | "Return @code{#t} if the real number @var{x} is neither\n" |
| 774 | "infinite nor a NaN, @code{#f} otherwise.") |
| 775 | #define FUNC_NAME s_scm_finite_p |
| 776 | { |
| 777 | if (SCM_REALP (x)) |
| 778 | return scm_from_bool (isfinite (SCM_REAL_VALUE (x))); |
| 779 | else if (scm_is_real (x)) |
| 780 | return SCM_BOOL_T; |
| 781 | else |
| 782 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
| 783 | } |
| 784 | #undef FUNC_NAME |
| 785 | |
| 786 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
| 787 | (SCM x), |
| 788 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" |
| 789 | "@samp{-inf.0}. Otherwise return @code{#f}.") |
| 790 | #define FUNC_NAME s_scm_inf_p |
| 791 | { |
| 792 | if (SCM_REALP (x)) |
| 793 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
| 794 | else if (scm_is_real (x)) |
| 795 | return SCM_BOOL_F; |
| 796 | else |
| 797 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
| 798 | } |
| 799 | #undef FUNC_NAME |
| 800 | |
| 801 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
| 802 | (SCM x), |
| 803 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
| 804 | "or @code{#f} otherwise.") |
| 805 | #define FUNC_NAME s_scm_nan_p |
| 806 | { |
| 807 | if (SCM_REALP (x)) |
| 808 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); |
| 809 | else if (scm_is_real (x)) |
| 810 | return SCM_BOOL_F; |
| 811 | else |
| 812 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
| 813 | } |
| 814 | #undef FUNC_NAME |
| 815 | |
| 816 | /* Guile's idea of infinity. */ |
| 817 | static double guile_Inf; |
| 818 | |
| 819 | /* Guile's idea of not a number. */ |
| 820 | static double guile_NaN; |
| 821 | |
| 822 | static void |
| 823 | guile_ieee_init (void) |
| 824 | { |
| 825 | /* Some version of gcc on some old version of Linux used to crash when |
| 826 | trying to make Inf and NaN. */ |
| 827 | |
| 828 | #ifdef INFINITY |
| 829 | /* C99 INFINITY, when available. |
| 830 | FIXME: The standard allows for INFINITY to be something that overflows |
| 831 | at compile time. We ought to have a configure test to check for that |
| 832 | before trying to use it. (But in practice we believe this is not a |
| 833 | problem on any system guile is likely to target.) */ |
| 834 | guile_Inf = INFINITY; |
| 835 | #elif defined HAVE_DINFINITY |
| 836 | /* OSF */ |
| 837 | extern unsigned int DINFINITY[2]; |
| 838 | guile_Inf = (*((double *) (DINFINITY))); |
| 839 | #else |
| 840 | double tmp = 1e+10; |
| 841 | guile_Inf = tmp; |
| 842 | for (;;) |
| 843 | { |
| 844 | guile_Inf *= 1e+10; |
| 845 | if (guile_Inf == tmp) |
| 846 | break; |
| 847 | tmp = guile_Inf; |
| 848 | } |
| 849 | #endif |
| 850 | |
| 851 | #ifdef NAN |
| 852 | /* C99 NAN, when available */ |
| 853 | guile_NaN = NAN; |
| 854 | #elif defined HAVE_DQNAN |
| 855 | { |
| 856 | /* OSF */ |
| 857 | extern unsigned int DQNAN[2]; |
| 858 | guile_NaN = (*((double *)(DQNAN))); |
| 859 | } |
| 860 | #else |
| 861 | guile_NaN = guile_Inf / guile_Inf; |
| 862 | #endif |
| 863 | } |
| 864 | |
| 865 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, |
| 866 | (void), |
| 867 | "Return Inf.") |
| 868 | #define FUNC_NAME s_scm_inf |
| 869 | { |
| 870 | static int initialized = 0; |
| 871 | if (! initialized) |
| 872 | { |
| 873 | guile_ieee_init (); |
| 874 | initialized = 1; |
| 875 | } |
| 876 | return scm_i_from_double (guile_Inf); |
| 877 | } |
| 878 | #undef FUNC_NAME |
| 879 | |
| 880 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, |
| 881 | (void), |
| 882 | "Return NaN.") |
| 883 | #define FUNC_NAME s_scm_nan |
| 884 | { |
| 885 | static int initialized = 0; |
| 886 | if (!initialized) |
| 887 | { |
| 888 | guile_ieee_init (); |
| 889 | initialized = 1; |
| 890 | } |
| 891 | return scm_i_from_double (guile_NaN); |
| 892 | } |
| 893 | #undef FUNC_NAME |
| 894 | |
| 895 | |
| 896 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
| 897 | (SCM x), |
| 898 | "Return the absolute value of @var{x}.") |
| 899 | #define FUNC_NAME s_scm_abs |
| 900 | { |
| 901 | if (SCM_I_INUMP (x)) |
| 902 | { |
| 903 | scm_t_inum xx = SCM_I_INUM (x); |
| 904 | if (xx >= 0) |
| 905 | return x; |
| 906 | else if (SCM_POSFIXABLE (-xx)) |
| 907 | return SCM_I_MAKINUM (-xx); |
| 908 | else |
| 909 | return scm_i_inum2big (-xx); |
| 910 | } |
| 911 | else if (SCM_LIKELY (SCM_REALP (x))) |
| 912 | { |
| 913 | double xx = SCM_REAL_VALUE (x); |
| 914 | /* If x is a NaN then xx<0 is false so we return x unchanged */ |
| 915 | if (xx < 0.0) |
| 916 | return scm_i_from_double (-xx); |
| 917 | /* Handle signed zeroes properly */ |
| 918 | else if (SCM_UNLIKELY (xx == 0.0)) |
| 919 | return flo0; |
| 920 | else |
| 921 | return x; |
| 922 | } |
| 923 | else if (SCM_BIGP (x)) |
| 924 | { |
| 925 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 926 | if (sgn < 0) |
| 927 | return scm_i_clonebig (x, 0); |
| 928 | else |
| 929 | return x; |
| 930 | } |
| 931 | else if (SCM_FRACTIONP (x)) |
| 932 | { |
| 933 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
| 934 | return x; |
| 935 | return scm_i_make_ratio_already_reduced |
| 936 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
| 937 | SCM_FRACTION_DENOMINATOR (x)); |
| 938 | } |
| 939 | else |
| 940 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
| 941 | } |
| 942 | #undef FUNC_NAME |
| 943 | |
| 944 | |
| 945 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
| 946 | (SCM x, SCM y), |
| 947 | "Return the quotient of the numbers @var{x} and @var{y}.") |
| 948 | #define FUNC_NAME s_scm_quotient |
| 949 | { |
| 950 | if (SCM_LIKELY (scm_is_integer (x))) |
| 951 | { |
| 952 | if (SCM_LIKELY (scm_is_integer (y))) |
| 953 | return scm_truncate_quotient (x, y); |
| 954 | else |
| 955 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
| 956 | } |
| 957 | else |
| 958 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
| 959 | } |
| 960 | #undef FUNC_NAME |
| 961 | |
| 962 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
| 963 | (SCM x, SCM y), |
| 964 | "Return the remainder of the numbers @var{x} and @var{y}.\n" |
| 965 | "@lisp\n" |
| 966 | "(remainder 13 4) @result{} 1\n" |
| 967 | "(remainder -13 4) @result{} -1\n" |
| 968 | "@end lisp") |
| 969 | #define FUNC_NAME s_scm_remainder |
| 970 | { |
| 971 | if (SCM_LIKELY (scm_is_integer (x))) |
| 972 | { |
| 973 | if (SCM_LIKELY (scm_is_integer (y))) |
| 974 | return scm_truncate_remainder (x, y); |
| 975 | else |
| 976 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
| 977 | } |
| 978 | else |
| 979 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
| 980 | } |
| 981 | #undef FUNC_NAME |
| 982 | |
| 983 | |
| 984 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
| 985 | (SCM x, SCM y), |
| 986 | "Return the modulo of the numbers @var{x} and @var{y}.\n" |
| 987 | "@lisp\n" |
| 988 | "(modulo 13 4) @result{} 1\n" |
| 989 | "(modulo -13 4) @result{} 3\n" |
| 990 | "@end lisp") |
| 991 | #define FUNC_NAME s_scm_modulo |
| 992 | { |
| 993 | if (SCM_LIKELY (scm_is_integer (x))) |
| 994 | { |
| 995 | if (SCM_LIKELY (scm_is_integer (y))) |
| 996 | return scm_floor_remainder (x, y); |
| 997 | else |
| 998 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
| 999 | } |
| 1000 | else |
| 1001 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
| 1002 | } |
| 1003 | #undef FUNC_NAME |
| 1004 | |
| 1005 | /* Return the exact integer q such that n = q*d, for exact integers n |
| 1006 | and d, where d is known in advance to divide n evenly (with zero |
| 1007 | remainder). For large integers, this can be computed more |
| 1008 | efficiently than when the remainder is unknown. */ |
| 1009 | static SCM |
| 1010 | scm_exact_integer_quotient (SCM n, SCM d) |
| 1011 | #define FUNC_NAME "exact-integer-quotient" |
| 1012 | { |
| 1013 | if (SCM_LIKELY (SCM_I_INUMP (n))) |
| 1014 | { |
| 1015 | scm_t_inum nn = SCM_I_INUM (n); |
| 1016 | if (SCM_LIKELY (SCM_I_INUMP (d))) |
| 1017 | { |
| 1018 | scm_t_inum dd = SCM_I_INUM (d); |
| 1019 | if (SCM_UNLIKELY (dd == 0)) |
| 1020 | scm_num_overflow ("exact-integer-quotient"); |
| 1021 | else |
| 1022 | { |
| 1023 | scm_t_inum qq = nn / dd; |
| 1024 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 1025 | return SCM_I_MAKINUM (qq); |
| 1026 | else |
| 1027 | return scm_i_inum2big (qq); |
| 1028 | } |
| 1029 | } |
| 1030 | else if (SCM_LIKELY (SCM_BIGP (d))) |
| 1031 | { |
| 1032 | /* n is an inum and d is a bignum. Given that d is known to |
| 1033 | divide n evenly, there are only two possibilities: n is 0, |
| 1034 | or else n is fixnum-min and d is abs(fixnum-min). */ |
| 1035 | if (nn == 0) |
| 1036 | return SCM_INUM0; |
| 1037 | else |
| 1038 | return SCM_I_MAKINUM (-1); |
| 1039 | } |
| 1040 | else |
| 1041 | SCM_WRONG_TYPE_ARG (2, d); |
| 1042 | } |
| 1043 | else if (SCM_LIKELY (SCM_BIGP (n))) |
| 1044 | { |
| 1045 | if (SCM_LIKELY (SCM_I_INUMP (d))) |
| 1046 | { |
| 1047 | scm_t_inum dd = SCM_I_INUM (d); |
| 1048 | if (SCM_UNLIKELY (dd == 0)) |
| 1049 | scm_num_overflow ("exact-integer-quotient"); |
| 1050 | else if (SCM_UNLIKELY (dd == 1)) |
| 1051 | return n; |
| 1052 | else |
| 1053 | { |
| 1054 | SCM q = scm_i_mkbig (); |
| 1055 | if (dd > 0) |
| 1056 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), dd); |
| 1057 | else |
| 1058 | { |
| 1059 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), -dd); |
| 1060 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 1061 | } |
| 1062 | scm_remember_upto_here_1 (n); |
| 1063 | return scm_i_normbig (q); |
| 1064 | } |
| 1065 | } |
| 1066 | else if (SCM_LIKELY (SCM_BIGP (d))) |
| 1067 | { |
| 1068 | SCM q = scm_i_mkbig (); |
| 1069 | mpz_divexact (SCM_I_BIG_MPZ (q), |
| 1070 | SCM_I_BIG_MPZ (n), |
| 1071 | SCM_I_BIG_MPZ (d)); |
| 1072 | scm_remember_upto_here_2 (n, d); |
| 1073 | return scm_i_normbig (q); |
| 1074 | } |
| 1075 | else |
| 1076 | SCM_WRONG_TYPE_ARG (2, d); |
| 1077 | } |
| 1078 | else |
| 1079 | SCM_WRONG_TYPE_ARG (1, n); |
| 1080 | } |
| 1081 | #undef FUNC_NAME |
| 1082 | |
| 1083 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
| 1084 | two-valued functions. It is called from primitive generics that take |
| 1085 | two arguments and return two values, when the core procedure is |
| 1086 | unable to handle the given argument types. If there are GOOPS |
| 1087 | methods for this primitive generic, it dispatches to GOOPS and, if |
| 1088 | successful, expects two values to be returned, which are placed in |
| 1089 | *rp1 and *rp2. If there are no GOOPS methods, it throws a |
| 1090 | wrong-type-arg exception. |
| 1091 | |
| 1092 | FIXME: This obviously belongs somewhere else, but until we decide on |
| 1093 | the right API, it is here as a static function, because it is needed |
| 1094 | by the *_divide functions below. |
| 1095 | */ |
| 1096 | static void |
| 1097 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, |
| 1098 | const char *subr, SCM *rp1, SCM *rp2) |
| 1099 | { |
| 1100 | if (SCM_UNPACK (gf)) |
| 1101 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); |
| 1102 | else |
| 1103 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); |
| 1104 | } |
| 1105 | |
| 1106 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
| 1107 | (SCM x, SCM y), |
| 1108 | "Return the integer @var{q} such that\n" |
| 1109 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 1110 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" |
| 1111 | "@lisp\n" |
| 1112 | "(euclidean-quotient 123 10) @result{} 12\n" |
| 1113 | "(euclidean-quotient 123 -10) @result{} -12\n" |
| 1114 | "(euclidean-quotient -123 10) @result{} -13\n" |
| 1115 | "(euclidean-quotient -123 -10) @result{} 13\n" |
| 1116 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" |
| 1117 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" |
| 1118 | "@end lisp") |
| 1119 | #define FUNC_NAME s_scm_euclidean_quotient |
| 1120 | { |
| 1121 | if (scm_is_false (scm_negative_p (y))) |
| 1122 | return scm_floor_quotient (x, y); |
| 1123 | else |
| 1124 | return scm_ceiling_quotient (x, y); |
| 1125 | } |
| 1126 | #undef FUNC_NAME |
| 1127 | |
| 1128 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
| 1129 | (SCM x, SCM y), |
| 1130 | "Return the real number @var{r} such that\n" |
| 1131 | "@math{0 <= @var{r} < abs(@var{y})} and\n" |
| 1132 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 1133 | "for some integer @var{q}.\n" |
| 1134 | "@lisp\n" |
| 1135 | "(euclidean-remainder 123 10) @result{} 3\n" |
| 1136 | "(euclidean-remainder 123 -10) @result{} 3\n" |
| 1137 | "(euclidean-remainder -123 10) @result{} 7\n" |
| 1138 | "(euclidean-remainder -123 -10) @result{} 7\n" |
| 1139 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" |
| 1140 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" |
| 1141 | "@end lisp") |
| 1142 | #define FUNC_NAME s_scm_euclidean_remainder |
| 1143 | { |
| 1144 | if (scm_is_false (scm_negative_p (y))) |
| 1145 | return scm_floor_remainder (x, y); |
| 1146 | else |
| 1147 | return scm_ceiling_remainder (x, y); |
| 1148 | } |
| 1149 | #undef FUNC_NAME |
| 1150 | |
| 1151 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
| 1152 | (SCM x, SCM y), |
| 1153 | "Return the integer @var{q} and the real number @var{r}\n" |
| 1154 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 1155 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" |
| 1156 | "@lisp\n" |
| 1157 | "(euclidean/ 123 10) @result{} 12 and 3\n" |
| 1158 | "(euclidean/ 123 -10) @result{} -12 and 3\n" |
| 1159 | "(euclidean/ -123 10) @result{} -13 and 7\n" |
| 1160 | "(euclidean/ -123 -10) @result{} 13 and 7\n" |
| 1161 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" |
| 1162 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" |
| 1163 | "@end lisp") |
| 1164 | #define FUNC_NAME s_scm_i_euclidean_divide |
| 1165 | { |
| 1166 | if (scm_is_false (scm_negative_p (y))) |
| 1167 | return scm_i_floor_divide (x, y); |
| 1168 | else |
| 1169 | return scm_i_ceiling_divide (x, y); |
| 1170 | } |
| 1171 | #undef FUNC_NAME |
| 1172 | |
| 1173 | void |
| 1174 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 1175 | { |
| 1176 | if (scm_is_false (scm_negative_p (y))) |
| 1177 | return scm_floor_divide (x, y, qp, rp); |
| 1178 | else |
| 1179 | return scm_ceiling_divide (x, y, qp, rp); |
| 1180 | } |
| 1181 | |
| 1182 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
| 1183 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); |
| 1184 | |
| 1185 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, |
| 1186 | (SCM x, SCM y), |
| 1187 | "Return the floor of @math{@var{x} / @var{y}}.\n" |
| 1188 | "@lisp\n" |
| 1189 | "(floor-quotient 123 10) @result{} 12\n" |
| 1190 | "(floor-quotient 123 -10) @result{} -13\n" |
| 1191 | "(floor-quotient -123 10) @result{} -13\n" |
| 1192 | "(floor-quotient -123 -10) @result{} 12\n" |
| 1193 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" |
| 1194 | "(floor-quotient 16/3 -10/7) @result{} -4\n" |
| 1195 | "@end lisp") |
| 1196 | #define FUNC_NAME s_scm_floor_quotient |
| 1197 | { |
| 1198 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 1199 | { |
| 1200 | scm_t_inum xx = SCM_I_INUM (x); |
| 1201 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1202 | { |
| 1203 | scm_t_inum yy = SCM_I_INUM (y); |
| 1204 | scm_t_inum xx1 = xx; |
| 1205 | scm_t_inum qq; |
| 1206 | if (SCM_LIKELY (yy > 0)) |
| 1207 | { |
| 1208 | if (SCM_UNLIKELY (xx < 0)) |
| 1209 | xx1 = xx - yy + 1; |
| 1210 | } |
| 1211 | else if (SCM_UNLIKELY (yy == 0)) |
| 1212 | scm_num_overflow (s_scm_floor_quotient); |
| 1213 | else if (xx > 0) |
| 1214 | xx1 = xx - yy - 1; |
| 1215 | qq = xx1 / yy; |
| 1216 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 1217 | return SCM_I_MAKINUM (qq); |
| 1218 | else |
| 1219 | return scm_i_inum2big (qq); |
| 1220 | } |
| 1221 | else if (SCM_BIGP (y)) |
| 1222 | { |
| 1223 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 1224 | scm_remember_upto_here_1 (y); |
| 1225 | if (sign > 0) |
| 1226 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); |
| 1227 | else |
| 1228 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); |
| 1229 | } |
| 1230 | else if (SCM_REALP (y)) |
| 1231 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); |
| 1232 | else if (SCM_FRACTIONP (y)) |
| 1233 | return scm_i_exact_rational_floor_quotient (x, y); |
| 1234 | else |
| 1235 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
| 1236 | s_scm_floor_quotient); |
| 1237 | } |
| 1238 | else if (SCM_BIGP (x)) |
| 1239 | { |
| 1240 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1241 | { |
| 1242 | scm_t_inum yy = SCM_I_INUM (y); |
| 1243 | if (SCM_UNLIKELY (yy == 0)) |
| 1244 | scm_num_overflow (s_scm_floor_quotient); |
| 1245 | else if (SCM_UNLIKELY (yy == 1)) |
| 1246 | return x; |
| 1247 | else |
| 1248 | { |
| 1249 | SCM q = scm_i_mkbig (); |
| 1250 | if (yy > 0) |
| 1251 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); |
| 1252 | else |
| 1253 | { |
| 1254 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); |
| 1255 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 1256 | } |
| 1257 | scm_remember_upto_here_1 (x); |
| 1258 | return scm_i_normbig (q); |
| 1259 | } |
| 1260 | } |
| 1261 | else if (SCM_BIGP (y)) |
| 1262 | { |
| 1263 | SCM q = scm_i_mkbig (); |
| 1264 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), |
| 1265 | SCM_I_BIG_MPZ (x), |
| 1266 | SCM_I_BIG_MPZ (y)); |
| 1267 | scm_remember_upto_here_2 (x, y); |
| 1268 | return scm_i_normbig (q); |
| 1269 | } |
| 1270 | else if (SCM_REALP (y)) |
| 1271 | return scm_i_inexact_floor_quotient |
| 1272 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 1273 | else if (SCM_FRACTIONP (y)) |
| 1274 | return scm_i_exact_rational_floor_quotient (x, y); |
| 1275 | else |
| 1276 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
| 1277 | s_scm_floor_quotient); |
| 1278 | } |
| 1279 | else if (SCM_REALP (x)) |
| 1280 | { |
| 1281 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 1282 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1283 | return scm_i_inexact_floor_quotient |
| 1284 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 1285 | else |
| 1286 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
| 1287 | s_scm_floor_quotient); |
| 1288 | } |
| 1289 | else if (SCM_FRACTIONP (x)) |
| 1290 | { |
| 1291 | if (SCM_REALP (y)) |
| 1292 | return scm_i_inexact_floor_quotient |
| 1293 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 1294 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1295 | return scm_i_exact_rational_floor_quotient (x, y); |
| 1296 | else |
| 1297 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
| 1298 | s_scm_floor_quotient); |
| 1299 | } |
| 1300 | else |
| 1301 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, |
| 1302 | s_scm_floor_quotient); |
| 1303 | } |
| 1304 | #undef FUNC_NAME |
| 1305 | |
| 1306 | static SCM |
| 1307 | scm_i_inexact_floor_quotient (double x, double y) |
| 1308 | { |
| 1309 | if (SCM_UNLIKELY (y == 0)) |
| 1310 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ |
| 1311 | else |
| 1312 | return scm_i_from_double (floor (x / y)); |
| 1313 | } |
| 1314 | |
| 1315 | static SCM |
| 1316 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) |
| 1317 | { |
| 1318 | return scm_floor_quotient |
| 1319 | (scm_product (scm_numerator (x), scm_denominator (y)), |
| 1320 | scm_product (scm_numerator (y), scm_denominator (x))); |
| 1321 | } |
| 1322 | |
| 1323 | static SCM scm_i_inexact_floor_remainder (double x, double y); |
| 1324 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); |
| 1325 | |
| 1326 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, |
| 1327 | (SCM x, SCM y), |
| 1328 | "Return the real number @var{r} such that\n" |
| 1329 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 1330 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" |
| 1331 | "@lisp\n" |
| 1332 | "(floor-remainder 123 10) @result{} 3\n" |
| 1333 | "(floor-remainder 123 -10) @result{} -7\n" |
| 1334 | "(floor-remainder -123 10) @result{} 7\n" |
| 1335 | "(floor-remainder -123 -10) @result{} -3\n" |
| 1336 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" |
| 1337 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" |
| 1338 | "@end lisp") |
| 1339 | #define FUNC_NAME s_scm_floor_remainder |
| 1340 | { |
| 1341 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 1342 | { |
| 1343 | scm_t_inum xx = SCM_I_INUM (x); |
| 1344 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1345 | { |
| 1346 | scm_t_inum yy = SCM_I_INUM (y); |
| 1347 | if (SCM_UNLIKELY (yy == 0)) |
| 1348 | scm_num_overflow (s_scm_floor_remainder); |
| 1349 | else |
| 1350 | { |
| 1351 | scm_t_inum rr = xx % yy; |
| 1352 | int needs_adjustment; |
| 1353 | |
| 1354 | if (SCM_LIKELY (yy > 0)) |
| 1355 | needs_adjustment = (rr < 0); |
| 1356 | else |
| 1357 | needs_adjustment = (rr > 0); |
| 1358 | |
| 1359 | if (needs_adjustment) |
| 1360 | rr += yy; |
| 1361 | return SCM_I_MAKINUM (rr); |
| 1362 | } |
| 1363 | } |
| 1364 | else if (SCM_BIGP (y)) |
| 1365 | { |
| 1366 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 1367 | scm_remember_upto_here_1 (y); |
| 1368 | if (sign > 0) |
| 1369 | { |
| 1370 | if (xx < 0) |
| 1371 | { |
| 1372 | SCM r = scm_i_mkbig (); |
| 1373 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); |
| 1374 | scm_remember_upto_here_1 (y); |
| 1375 | return scm_i_normbig (r); |
| 1376 | } |
| 1377 | else |
| 1378 | return x; |
| 1379 | } |
| 1380 | else if (xx <= 0) |
| 1381 | return x; |
| 1382 | else |
| 1383 | { |
| 1384 | SCM r = scm_i_mkbig (); |
| 1385 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); |
| 1386 | scm_remember_upto_here_1 (y); |
| 1387 | return scm_i_normbig (r); |
| 1388 | } |
| 1389 | } |
| 1390 | else if (SCM_REALP (y)) |
| 1391 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); |
| 1392 | else if (SCM_FRACTIONP (y)) |
| 1393 | return scm_i_exact_rational_floor_remainder (x, y); |
| 1394 | else |
| 1395 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
| 1396 | s_scm_floor_remainder); |
| 1397 | } |
| 1398 | else if (SCM_BIGP (x)) |
| 1399 | { |
| 1400 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1401 | { |
| 1402 | scm_t_inum yy = SCM_I_INUM (y); |
| 1403 | if (SCM_UNLIKELY (yy == 0)) |
| 1404 | scm_num_overflow (s_scm_floor_remainder); |
| 1405 | else |
| 1406 | { |
| 1407 | scm_t_inum rr; |
| 1408 | if (yy > 0) |
| 1409 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); |
| 1410 | else |
| 1411 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); |
| 1412 | scm_remember_upto_here_1 (x); |
| 1413 | return SCM_I_MAKINUM (rr); |
| 1414 | } |
| 1415 | } |
| 1416 | else if (SCM_BIGP (y)) |
| 1417 | { |
| 1418 | SCM r = scm_i_mkbig (); |
| 1419 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), |
| 1420 | SCM_I_BIG_MPZ (x), |
| 1421 | SCM_I_BIG_MPZ (y)); |
| 1422 | scm_remember_upto_here_2 (x, y); |
| 1423 | return scm_i_normbig (r); |
| 1424 | } |
| 1425 | else if (SCM_REALP (y)) |
| 1426 | return scm_i_inexact_floor_remainder |
| 1427 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 1428 | else if (SCM_FRACTIONP (y)) |
| 1429 | return scm_i_exact_rational_floor_remainder (x, y); |
| 1430 | else |
| 1431 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
| 1432 | s_scm_floor_remainder); |
| 1433 | } |
| 1434 | else if (SCM_REALP (x)) |
| 1435 | { |
| 1436 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 1437 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1438 | return scm_i_inexact_floor_remainder |
| 1439 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 1440 | else |
| 1441 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
| 1442 | s_scm_floor_remainder); |
| 1443 | } |
| 1444 | else if (SCM_FRACTIONP (x)) |
| 1445 | { |
| 1446 | if (SCM_REALP (y)) |
| 1447 | return scm_i_inexact_floor_remainder |
| 1448 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 1449 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1450 | return scm_i_exact_rational_floor_remainder (x, y); |
| 1451 | else |
| 1452 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
| 1453 | s_scm_floor_remainder); |
| 1454 | } |
| 1455 | else |
| 1456 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, |
| 1457 | s_scm_floor_remainder); |
| 1458 | } |
| 1459 | #undef FUNC_NAME |
| 1460 | |
| 1461 | static SCM |
| 1462 | scm_i_inexact_floor_remainder (double x, double y) |
| 1463 | { |
| 1464 | /* Although it would be more efficient to use fmod here, we can't |
| 1465 | because it would in some cases produce results inconsistent with |
| 1466 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even |
| 1467 | close). In particular, when x is very close to a multiple of y, |
| 1468 | then r might be either 0.0 or y, but those two cases must |
| 1469 | correspond to different choices of q. If r = 0.0 then q must be |
| 1470 | x/y, and if r = y then q must be x/y-1. If quotient chooses one |
| 1471 | and remainder chooses the other, it would be bad. */ |
| 1472 | if (SCM_UNLIKELY (y == 0)) |
| 1473 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ |
| 1474 | else |
| 1475 | return scm_i_from_double (x - y * floor (x / y)); |
| 1476 | } |
| 1477 | |
| 1478 | static SCM |
| 1479 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) |
| 1480 | { |
| 1481 | SCM xd = scm_denominator (x); |
| 1482 | SCM yd = scm_denominator (y); |
| 1483 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), |
| 1484 | scm_product (scm_numerator (y), xd)); |
| 1485 | return scm_divide (r1, scm_product (xd, yd)); |
| 1486 | } |
| 1487 | |
| 1488 | |
| 1489 | static void scm_i_inexact_floor_divide (double x, double y, |
| 1490 | SCM *qp, SCM *rp); |
| 1491 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, |
| 1492 | SCM *qp, SCM *rp); |
| 1493 | |
| 1494 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, |
| 1495 | (SCM x, SCM y), |
| 1496 | "Return the integer @var{q} and the real number @var{r}\n" |
| 1497 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 1498 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" |
| 1499 | "@lisp\n" |
| 1500 | "(floor/ 123 10) @result{} 12 and 3\n" |
| 1501 | "(floor/ 123 -10) @result{} -13 and -7\n" |
| 1502 | "(floor/ -123 10) @result{} -13 and 7\n" |
| 1503 | "(floor/ -123 -10) @result{} 12 and -3\n" |
| 1504 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" |
| 1505 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" |
| 1506 | "@end lisp") |
| 1507 | #define FUNC_NAME s_scm_i_floor_divide |
| 1508 | { |
| 1509 | SCM q, r; |
| 1510 | |
| 1511 | scm_floor_divide(x, y, &q, &r); |
| 1512 | return scm_values (scm_list_2 (q, r)); |
| 1513 | } |
| 1514 | #undef FUNC_NAME |
| 1515 | |
| 1516 | #define s_scm_floor_divide s_scm_i_floor_divide |
| 1517 | #define g_scm_floor_divide g_scm_i_floor_divide |
| 1518 | |
| 1519 | void |
| 1520 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 1521 | { |
| 1522 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 1523 | { |
| 1524 | scm_t_inum xx = SCM_I_INUM (x); |
| 1525 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1526 | { |
| 1527 | scm_t_inum yy = SCM_I_INUM (y); |
| 1528 | if (SCM_UNLIKELY (yy == 0)) |
| 1529 | scm_num_overflow (s_scm_floor_divide); |
| 1530 | else |
| 1531 | { |
| 1532 | scm_t_inum qq = xx / yy; |
| 1533 | scm_t_inum rr = xx % yy; |
| 1534 | int needs_adjustment; |
| 1535 | |
| 1536 | if (SCM_LIKELY (yy > 0)) |
| 1537 | needs_adjustment = (rr < 0); |
| 1538 | else |
| 1539 | needs_adjustment = (rr > 0); |
| 1540 | |
| 1541 | if (needs_adjustment) |
| 1542 | { |
| 1543 | rr += yy; |
| 1544 | qq--; |
| 1545 | } |
| 1546 | |
| 1547 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 1548 | *qp = SCM_I_MAKINUM (qq); |
| 1549 | else |
| 1550 | *qp = scm_i_inum2big (qq); |
| 1551 | *rp = SCM_I_MAKINUM (rr); |
| 1552 | } |
| 1553 | return; |
| 1554 | } |
| 1555 | else if (SCM_BIGP (y)) |
| 1556 | { |
| 1557 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 1558 | scm_remember_upto_here_1 (y); |
| 1559 | if (sign > 0) |
| 1560 | { |
| 1561 | if (xx < 0) |
| 1562 | { |
| 1563 | SCM r = scm_i_mkbig (); |
| 1564 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); |
| 1565 | scm_remember_upto_here_1 (y); |
| 1566 | *qp = SCM_I_MAKINUM (-1); |
| 1567 | *rp = scm_i_normbig (r); |
| 1568 | } |
| 1569 | else |
| 1570 | { |
| 1571 | *qp = SCM_INUM0; |
| 1572 | *rp = x; |
| 1573 | } |
| 1574 | } |
| 1575 | else if (xx <= 0) |
| 1576 | { |
| 1577 | *qp = SCM_INUM0; |
| 1578 | *rp = x; |
| 1579 | } |
| 1580 | else |
| 1581 | { |
| 1582 | SCM r = scm_i_mkbig (); |
| 1583 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); |
| 1584 | scm_remember_upto_here_1 (y); |
| 1585 | *qp = SCM_I_MAKINUM (-1); |
| 1586 | *rp = scm_i_normbig (r); |
| 1587 | } |
| 1588 | return; |
| 1589 | } |
| 1590 | else if (SCM_REALP (y)) |
| 1591 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
| 1592 | else if (SCM_FRACTIONP (y)) |
| 1593 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); |
| 1594 | else |
| 1595 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, |
| 1596 | s_scm_floor_divide, qp, rp); |
| 1597 | } |
| 1598 | else if (SCM_BIGP (x)) |
| 1599 | { |
| 1600 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1601 | { |
| 1602 | scm_t_inum yy = SCM_I_INUM (y); |
| 1603 | if (SCM_UNLIKELY (yy == 0)) |
| 1604 | scm_num_overflow (s_scm_floor_divide); |
| 1605 | else |
| 1606 | { |
| 1607 | SCM q = scm_i_mkbig (); |
| 1608 | SCM r = scm_i_mkbig (); |
| 1609 | if (yy > 0) |
| 1610 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 1611 | SCM_I_BIG_MPZ (x), yy); |
| 1612 | else |
| 1613 | { |
| 1614 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 1615 | SCM_I_BIG_MPZ (x), -yy); |
| 1616 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 1617 | } |
| 1618 | scm_remember_upto_here_1 (x); |
| 1619 | *qp = scm_i_normbig (q); |
| 1620 | *rp = scm_i_normbig (r); |
| 1621 | } |
| 1622 | return; |
| 1623 | } |
| 1624 | else if (SCM_BIGP (y)) |
| 1625 | { |
| 1626 | SCM q = scm_i_mkbig (); |
| 1627 | SCM r = scm_i_mkbig (); |
| 1628 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 1629 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 1630 | scm_remember_upto_here_2 (x, y); |
| 1631 | *qp = scm_i_normbig (q); |
| 1632 | *rp = scm_i_normbig (r); |
| 1633 | return; |
| 1634 | } |
| 1635 | else if (SCM_REALP (y)) |
| 1636 | return scm_i_inexact_floor_divide |
| 1637 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
| 1638 | else if (SCM_FRACTIONP (y)) |
| 1639 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); |
| 1640 | else |
| 1641 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, |
| 1642 | s_scm_floor_divide, qp, rp); |
| 1643 | } |
| 1644 | else if (SCM_REALP (x)) |
| 1645 | { |
| 1646 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 1647 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1648 | return scm_i_inexact_floor_divide |
| 1649 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
| 1650 | else |
| 1651 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, |
| 1652 | s_scm_floor_divide, qp, rp); |
| 1653 | } |
| 1654 | else if (SCM_FRACTIONP (x)) |
| 1655 | { |
| 1656 | if (SCM_REALP (y)) |
| 1657 | return scm_i_inexact_floor_divide |
| 1658 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
| 1659 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1660 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); |
| 1661 | else |
| 1662 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, |
| 1663 | s_scm_floor_divide, qp, rp); |
| 1664 | } |
| 1665 | else |
| 1666 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, |
| 1667 | s_scm_floor_divide, qp, rp); |
| 1668 | } |
| 1669 | |
| 1670 | static void |
| 1671 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) |
| 1672 | { |
| 1673 | if (SCM_UNLIKELY (y == 0)) |
| 1674 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ |
| 1675 | else |
| 1676 | { |
| 1677 | double q = floor (x / y); |
| 1678 | double r = x - q * y; |
| 1679 | *qp = scm_i_from_double (q); |
| 1680 | *rp = scm_i_from_double (r); |
| 1681 | } |
| 1682 | } |
| 1683 | |
| 1684 | static void |
| 1685 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 1686 | { |
| 1687 | SCM r1; |
| 1688 | SCM xd = scm_denominator (x); |
| 1689 | SCM yd = scm_denominator (y); |
| 1690 | |
| 1691 | scm_floor_divide (scm_product (scm_numerator (x), yd), |
| 1692 | scm_product (scm_numerator (y), xd), |
| 1693 | qp, &r1); |
| 1694 | *rp = scm_divide (r1, scm_product (xd, yd)); |
| 1695 | } |
| 1696 | |
| 1697 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); |
| 1698 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); |
| 1699 | |
| 1700 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, |
| 1701 | (SCM x, SCM y), |
| 1702 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" |
| 1703 | "@lisp\n" |
| 1704 | "(ceiling-quotient 123 10) @result{} 13\n" |
| 1705 | "(ceiling-quotient 123 -10) @result{} -12\n" |
| 1706 | "(ceiling-quotient -123 10) @result{} -12\n" |
| 1707 | "(ceiling-quotient -123 -10) @result{} 13\n" |
| 1708 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" |
| 1709 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" |
| 1710 | "@end lisp") |
| 1711 | #define FUNC_NAME s_scm_ceiling_quotient |
| 1712 | { |
| 1713 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 1714 | { |
| 1715 | scm_t_inum xx = SCM_I_INUM (x); |
| 1716 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1717 | { |
| 1718 | scm_t_inum yy = SCM_I_INUM (y); |
| 1719 | if (SCM_UNLIKELY (yy == 0)) |
| 1720 | scm_num_overflow (s_scm_ceiling_quotient); |
| 1721 | else |
| 1722 | { |
| 1723 | scm_t_inum xx1 = xx; |
| 1724 | scm_t_inum qq; |
| 1725 | if (SCM_LIKELY (yy > 0)) |
| 1726 | { |
| 1727 | if (SCM_LIKELY (xx >= 0)) |
| 1728 | xx1 = xx + yy - 1; |
| 1729 | } |
| 1730 | else if (xx < 0) |
| 1731 | xx1 = xx + yy + 1; |
| 1732 | qq = xx1 / yy; |
| 1733 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 1734 | return SCM_I_MAKINUM (qq); |
| 1735 | else |
| 1736 | return scm_i_inum2big (qq); |
| 1737 | } |
| 1738 | } |
| 1739 | else if (SCM_BIGP (y)) |
| 1740 | { |
| 1741 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 1742 | scm_remember_upto_here_1 (y); |
| 1743 | if (SCM_LIKELY (sign > 0)) |
| 1744 | { |
| 1745 | if (SCM_LIKELY (xx > 0)) |
| 1746 | return SCM_INUM1; |
| 1747 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) |
| 1748 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
| 1749 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) |
| 1750 | { |
| 1751 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ |
| 1752 | scm_remember_upto_here_1 (y); |
| 1753 | return SCM_I_MAKINUM (-1); |
| 1754 | } |
| 1755 | else |
| 1756 | return SCM_INUM0; |
| 1757 | } |
| 1758 | else if (xx >= 0) |
| 1759 | return SCM_INUM0; |
| 1760 | else |
| 1761 | return SCM_INUM1; |
| 1762 | } |
| 1763 | else if (SCM_REALP (y)) |
| 1764 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); |
| 1765 | else if (SCM_FRACTIONP (y)) |
| 1766 | return scm_i_exact_rational_ceiling_quotient (x, y); |
| 1767 | else |
| 1768 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
| 1769 | s_scm_ceiling_quotient); |
| 1770 | } |
| 1771 | else if (SCM_BIGP (x)) |
| 1772 | { |
| 1773 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1774 | { |
| 1775 | scm_t_inum yy = SCM_I_INUM (y); |
| 1776 | if (SCM_UNLIKELY (yy == 0)) |
| 1777 | scm_num_overflow (s_scm_ceiling_quotient); |
| 1778 | else if (SCM_UNLIKELY (yy == 1)) |
| 1779 | return x; |
| 1780 | else |
| 1781 | { |
| 1782 | SCM q = scm_i_mkbig (); |
| 1783 | if (yy > 0) |
| 1784 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); |
| 1785 | else |
| 1786 | { |
| 1787 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); |
| 1788 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 1789 | } |
| 1790 | scm_remember_upto_here_1 (x); |
| 1791 | return scm_i_normbig (q); |
| 1792 | } |
| 1793 | } |
| 1794 | else if (SCM_BIGP (y)) |
| 1795 | { |
| 1796 | SCM q = scm_i_mkbig (); |
| 1797 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), |
| 1798 | SCM_I_BIG_MPZ (x), |
| 1799 | SCM_I_BIG_MPZ (y)); |
| 1800 | scm_remember_upto_here_2 (x, y); |
| 1801 | return scm_i_normbig (q); |
| 1802 | } |
| 1803 | else if (SCM_REALP (y)) |
| 1804 | return scm_i_inexact_ceiling_quotient |
| 1805 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 1806 | else if (SCM_FRACTIONP (y)) |
| 1807 | return scm_i_exact_rational_ceiling_quotient (x, y); |
| 1808 | else |
| 1809 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
| 1810 | s_scm_ceiling_quotient); |
| 1811 | } |
| 1812 | else if (SCM_REALP (x)) |
| 1813 | { |
| 1814 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 1815 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1816 | return scm_i_inexact_ceiling_quotient |
| 1817 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 1818 | else |
| 1819 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
| 1820 | s_scm_ceiling_quotient); |
| 1821 | } |
| 1822 | else if (SCM_FRACTIONP (x)) |
| 1823 | { |
| 1824 | if (SCM_REALP (y)) |
| 1825 | return scm_i_inexact_ceiling_quotient |
| 1826 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 1827 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1828 | return scm_i_exact_rational_ceiling_quotient (x, y); |
| 1829 | else |
| 1830 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
| 1831 | s_scm_ceiling_quotient); |
| 1832 | } |
| 1833 | else |
| 1834 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, |
| 1835 | s_scm_ceiling_quotient); |
| 1836 | } |
| 1837 | #undef FUNC_NAME |
| 1838 | |
| 1839 | static SCM |
| 1840 | scm_i_inexact_ceiling_quotient (double x, double y) |
| 1841 | { |
| 1842 | if (SCM_UNLIKELY (y == 0)) |
| 1843 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ |
| 1844 | else |
| 1845 | return scm_i_from_double (ceil (x / y)); |
| 1846 | } |
| 1847 | |
| 1848 | static SCM |
| 1849 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) |
| 1850 | { |
| 1851 | return scm_ceiling_quotient |
| 1852 | (scm_product (scm_numerator (x), scm_denominator (y)), |
| 1853 | scm_product (scm_numerator (y), scm_denominator (x))); |
| 1854 | } |
| 1855 | |
| 1856 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); |
| 1857 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); |
| 1858 | |
| 1859 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, |
| 1860 | (SCM x, SCM y), |
| 1861 | "Return the real number @var{r} such that\n" |
| 1862 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 1863 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" |
| 1864 | "@lisp\n" |
| 1865 | "(ceiling-remainder 123 10) @result{} -7\n" |
| 1866 | "(ceiling-remainder 123 -10) @result{} 3\n" |
| 1867 | "(ceiling-remainder -123 10) @result{} -3\n" |
| 1868 | "(ceiling-remainder -123 -10) @result{} 7\n" |
| 1869 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" |
| 1870 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" |
| 1871 | "@end lisp") |
| 1872 | #define FUNC_NAME s_scm_ceiling_remainder |
| 1873 | { |
| 1874 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 1875 | { |
| 1876 | scm_t_inum xx = SCM_I_INUM (x); |
| 1877 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1878 | { |
| 1879 | scm_t_inum yy = SCM_I_INUM (y); |
| 1880 | if (SCM_UNLIKELY (yy == 0)) |
| 1881 | scm_num_overflow (s_scm_ceiling_remainder); |
| 1882 | else |
| 1883 | { |
| 1884 | scm_t_inum rr = xx % yy; |
| 1885 | int needs_adjustment; |
| 1886 | |
| 1887 | if (SCM_LIKELY (yy > 0)) |
| 1888 | needs_adjustment = (rr > 0); |
| 1889 | else |
| 1890 | needs_adjustment = (rr < 0); |
| 1891 | |
| 1892 | if (needs_adjustment) |
| 1893 | rr -= yy; |
| 1894 | return SCM_I_MAKINUM (rr); |
| 1895 | } |
| 1896 | } |
| 1897 | else if (SCM_BIGP (y)) |
| 1898 | { |
| 1899 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 1900 | scm_remember_upto_here_1 (y); |
| 1901 | if (SCM_LIKELY (sign > 0)) |
| 1902 | { |
| 1903 | if (SCM_LIKELY (xx > 0)) |
| 1904 | { |
| 1905 | SCM r = scm_i_mkbig (); |
| 1906 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); |
| 1907 | scm_remember_upto_here_1 (y); |
| 1908 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); |
| 1909 | return scm_i_normbig (r); |
| 1910 | } |
| 1911 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) |
| 1912 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
| 1913 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) |
| 1914 | { |
| 1915 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ |
| 1916 | scm_remember_upto_here_1 (y); |
| 1917 | return SCM_INUM0; |
| 1918 | } |
| 1919 | else |
| 1920 | return x; |
| 1921 | } |
| 1922 | else if (xx >= 0) |
| 1923 | return x; |
| 1924 | else |
| 1925 | { |
| 1926 | SCM r = scm_i_mkbig (); |
| 1927 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); |
| 1928 | scm_remember_upto_here_1 (y); |
| 1929 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); |
| 1930 | return scm_i_normbig (r); |
| 1931 | } |
| 1932 | } |
| 1933 | else if (SCM_REALP (y)) |
| 1934 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); |
| 1935 | else if (SCM_FRACTIONP (y)) |
| 1936 | return scm_i_exact_rational_ceiling_remainder (x, y); |
| 1937 | else |
| 1938 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
| 1939 | s_scm_ceiling_remainder); |
| 1940 | } |
| 1941 | else if (SCM_BIGP (x)) |
| 1942 | { |
| 1943 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 1944 | { |
| 1945 | scm_t_inum yy = SCM_I_INUM (y); |
| 1946 | if (SCM_UNLIKELY (yy == 0)) |
| 1947 | scm_num_overflow (s_scm_ceiling_remainder); |
| 1948 | else |
| 1949 | { |
| 1950 | scm_t_inum rr; |
| 1951 | if (yy > 0) |
| 1952 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); |
| 1953 | else |
| 1954 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); |
| 1955 | scm_remember_upto_here_1 (x); |
| 1956 | return SCM_I_MAKINUM (rr); |
| 1957 | } |
| 1958 | } |
| 1959 | else if (SCM_BIGP (y)) |
| 1960 | { |
| 1961 | SCM r = scm_i_mkbig (); |
| 1962 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), |
| 1963 | SCM_I_BIG_MPZ (x), |
| 1964 | SCM_I_BIG_MPZ (y)); |
| 1965 | scm_remember_upto_here_2 (x, y); |
| 1966 | return scm_i_normbig (r); |
| 1967 | } |
| 1968 | else if (SCM_REALP (y)) |
| 1969 | return scm_i_inexact_ceiling_remainder |
| 1970 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 1971 | else if (SCM_FRACTIONP (y)) |
| 1972 | return scm_i_exact_rational_ceiling_remainder (x, y); |
| 1973 | else |
| 1974 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
| 1975 | s_scm_ceiling_remainder); |
| 1976 | } |
| 1977 | else if (SCM_REALP (x)) |
| 1978 | { |
| 1979 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 1980 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1981 | return scm_i_inexact_ceiling_remainder |
| 1982 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 1983 | else |
| 1984 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
| 1985 | s_scm_ceiling_remainder); |
| 1986 | } |
| 1987 | else if (SCM_FRACTIONP (x)) |
| 1988 | { |
| 1989 | if (SCM_REALP (y)) |
| 1990 | return scm_i_inexact_ceiling_remainder |
| 1991 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 1992 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 1993 | return scm_i_exact_rational_ceiling_remainder (x, y); |
| 1994 | else |
| 1995 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
| 1996 | s_scm_ceiling_remainder); |
| 1997 | } |
| 1998 | else |
| 1999 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, |
| 2000 | s_scm_ceiling_remainder); |
| 2001 | } |
| 2002 | #undef FUNC_NAME |
| 2003 | |
| 2004 | static SCM |
| 2005 | scm_i_inexact_ceiling_remainder (double x, double y) |
| 2006 | { |
| 2007 | /* Although it would be more efficient to use fmod here, we can't |
| 2008 | because it would in some cases produce results inconsistent with |
| 2009 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even |
| 2010 | close). In particular, when x is very close to a multiple of y, |
| 2011 | then r might be either 0.0 or -y, but those two cases must |
| 2012 | correspond to different choices of q. If r = 0.0 then q must be |
| 2013 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one |
| 2014 | and remainder chooses the other, it would be bad. */ |
| 2015 | if (SCM_UNLIKELY (y == 0)) |
| 2016 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ |
| 2017 | else |
| 2018 | return scm_i_from_double (x - y * ceil (x / y)); |
| 2019 | } |
| 2020 | |
| 2021 | static SCM |
| 2022 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) |
| 2023 | { |
| 2024 | SCM xd = scm_denominator (x); |
| 2025 | SCM yd = scm_denominator (y); |
| 2026 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), |
| 2027 | scm_product (scm_numerator (y), xd)); |
| 2028 | return scm_divide (r1, scm_product (xd, yd)); |
| 2029 | } |
| 2030 | |
| 2031 | static void scm_i_inexact_ceiling_divide (double x, double y, |
| 2032 | SCM *qp, SCM *rp); |
| 2033 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, |
| 2034 | SCM *qp, SCM *rp); |
| 2035 | |
| 2036 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, |
| 2037 | (SCM x, SCM y), |
| 2038 | "Return the integer @var{q} and the real number @var{r}\n" |
| 2039 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 2040 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" |
| 2041 | "@lisp\n" |
| 2042 | "(ceiling/ 123 10) @result{} 13 and -7\n" |
| 2043 | "(ceiling/ 123 -10) @result{} -12 and 3\n" |
| 2044 | "(ceiling/ -123 10) @result{} -12 and -3\n" |
| 2045 | "(ceiling/ -123 -10) @result{} 13 and 7\n" |
| 2046 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" |
| 2047 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" |
| 2048 | "@end lisp") |
| 2049 | #define FUNC_NAME s_scm_i_ceiling_divide |
| 2050 | { |
| 2051 | SCM q, r; |
| 2052 | |
| 2053 | scm_ceiling_divide(x, y, &q, &r); |
| 2054 | return scm_values (scm_list_2 (q, r)); |
| 2055 | } |
| 2056 | #undef FUNC_NAME |
| 2057 | |
| 2058 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide |
| 2059 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide |
| 2060 | |
| 2061 | void |
| 2062 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 2063 | { |
| 2064 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 2065 | { |
| 2066 | scm_t_inum xx = SCM_I_INUM (x); |
| 2067 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2068 | { |
| 2069 | scm_t_inum yy = SCM_I_INUM (y); |
| 2070 | if (SCM_UNLIKELY (yy == 0)) |
| 2071 | scm_num_overflow (s_scm_ceiling_divide); |
| 2072 | else |
| 2073 | { |
| 2074 | scm_t_inum qq = xx / yy; |
| 2075 | scm_t_inum rr = xx % yy; |
| 2076 | int needs_adjustment; |
| 2077 | |
| 2078 | if (SCM_LIKELY (yy > 0)) |
| 2079 | needs_adjustment = (rr > 0); |
| 2080 | else |
| 2081 | needs_adjustment = (rr < 0); |
| 2082 | |
| 2083 | if (needs_adjustment) |
| 2084 | { |
| 2085 | rr -= yy; |
| 2086 | qq++; |
| 2087 | } |
| 2088 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 2089 | *qp = SCM_I_MAKINUM (qq); |
| 2090 | else |
| 2091 | *qp = scm_i_inum2big (qq); |
| 2092 | *rp = SCM_I_MAKINUM (rr); |
| 2093 | } |
| 2094 | return; |
| 2095 | } |
| 2096 | else if (SCM_BIGP (y)) |
| 2097 | { |
| 2098 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 2099 | scm_remember_upto_here_1 (y); |
| 2100 | if (SCM_LIKELY (sign > 0)) |
| 2101 | { |
| 2102 | if (SCM_LIKELY (xx > 0)) |
| 2103 | { |
| 2104 | SCM r = scm_i_mkbig (); |
| 2105 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); |
| 2106 | scm_remember_upto_here_1 (y); |
| 2107 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); |
| 2108 | *qp = SCM_INUM1; |
| 2109 | *rp = scm_i_normbig (r); |
| 2110 | } |
| 2111 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) |
| 2112 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
| 2113 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) |
| 2114 | { |
| 2115 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ |
| 2116 | scm_remember_upto_here_1 (y); |
| 2117 | *qp = SCM_I_MAKINUM (-1); |
| 2118 | *rp = SCM_INUM0; |
| 2119 | } |
| 2120 | else |
| 2121 | { |
| 2122 | *qp = SCM_INUM0; |
| 2123 | *rp = x; |
| 2124 | } |
| 2125 | } |
| 2126 | else if (xx >= 0) |
| 2127 | { |
| 2128 | *qp = SCM_INUM0; |
| 2129 | *rp = x; |
| 2130 | } |
| 2131 | else |
| 2132 | { |
| 2133 | SCM r = scm_i_mkbig (); |
| 2134 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); |
| 2135 | scm_remember_upto_here_1 (y); |
| 2136 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); |
| 2137 | *qp = SCM_INUM1; |
| 2138 | *rp = scm_i_normbig (r); |
| 2139 | } |
| 2140 | return; |
| 2141 | } |
| 2142 | else if (SCM_REALP (y)) |
| 2143 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
| 2144 | else if (SCM_FRACTIONP (y)) |
| 2145 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); |
| 2146 | else |
| 2147 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, |
| 2148 | s_scm_ceiling_divide, qp, rp); |
| 2149 | } |
| 2150 | else if (SCM_BIGP (x)) |
| 2151 | { |
| 2152 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2153 | { |
| 2154 | scm_t_inum yy = SCM_I_INUM (y); |
| 2155 | if (SCM_UNLIKELY (yy == 0)) |
| 2156 | scm_num_overflow (s_scm_ceiling_divide); |
| 2157 | else |
| 2158 | { |
| 2159 | SCM q = scm_i_mkbig (); |
| 2160 | SCM r = scm_i_mkbig (); |
| 2161 | if (yy > 0) |
| 2162 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 2163 | SCM_I_BIG_MPZ (x), yy); |
| 2164 | else |
| 2165 | { |
| 2166 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 2167 | SCM_I_BIG_MPZ (x), -yy); |
| 2168 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 2169 | } |
| 2170 | scm_remember_upto_here_1 (x); |
| 2171 | *qp = scm_i_normbig (q); |
| 2172 | *rp = scm_i_normbig (r); |
| 2173 | } |
| 2174 | return; |
| 2175 | } |
| 2176 | else if (SCM_BIGP (y)) |
| 2177 | { |
| 2178 | SCM q = scm_i_mkbig (); |
| 2179 | SCM r = scm_i_mkbig (); |
| 2180 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 2181 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 2182 | scm_remember_upto_here_2 (x, y); |
| 2183 | *qp = scm_i_normbig (q); |
| 2184 | *rp = scm_i_normbig (r); |
| 2185 | return; |
| 2186 | } |
| 2187 | else if (SCM_REALP (y)) |
| 2188 | return scm_i_inexact_ceiling_divide |
| 2189 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
| 2190 | else if (SCM_FRACTIONP (y)) |
| 2191 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); |
| 2192 | else |
| 2193 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, |
| 2194 | s_scm_ceiling_divide, qp, rp); |
| 2195 | } |
| 2196 | else if (SCM_REALP (x)) |
| 2197 | { |
| 2198 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 2199 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2200 | return scm_i_inexact_ceiling_divide |
| 2201 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
| 2202 | else |
| 2203 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, |
| 2204 | s_scm_ceiling_divide, qp, rp); |
| 2205 | } |
| 2206 | else if (SCM_FRACTIONP (x)) |
| 2207 | { |
| 2208 | if (SCM_REALP (y)) |
| 2209 | return scm_i_inexact_ceiling_divide |
| 2210 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
| 2211 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2212 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); |
| 2213 | else |
| 2214 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, |
| 2215 | s_scm_ceiling_divide, qp, rp); |
| 2216 | } |
| 2217 | else |
| 2218 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, |
| 2219 | s_scm_ceiling_divide, qp, rp); |
| 2220 | } |
| 2221 | |
| 2222 | static void |
| 2223 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) |
| 2224 | { |
| 2225 | if (SCM_UNLIKELY (y == 0)) |
| 2226 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ |
| 2227 | else |
| 2228 | { |
| 2229 | double q = ceil (x / y); |
| 2230 | double r = x - q * y; |
| 2231 | *qp = scm_i_from_double (q); |
| 2232 | *rp = scm_i_from_double (r); |
| 2233 | } |
| 2234 | } |
| 2235 | |
| 2236 | static void |
| 2237 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 2238 | { |
| 2239 | SCM r1; |
| 2240 | SCM xd = scm_denominator (x); |
| 2241 | SCM yd = scm_denominator (y); |
| 2242 | |
| 2243 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), |
| 2244 | scm_product (scm_numerator (y), xd), |
| 2245 | qp, &r1); |
| 2246 | *rp = scm_divide (r1, scm_product (xd, yd)); |
| 2247 | } |
| 2248 | |
| 2249 | static SCM scm_i_inexact_truncate_quotient (double x, double y); |
| 2250 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); |
| 2251 | |
| 2252 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, |
| 2253 | (SCM x, SCM y), |
| 2254 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" |
| 2255 | "@lisp\n" |
| 2256 | "(truncate-quotient 123 10) @result{} 12\n" |
| 2257 | "(truncate-quotient 123 -10) @result{} -12\n" |
| 2258 | "(truncate-quotient -123 10) @result{} -12\n" |
| 2259 | "(truncate-quotient -123 -10) @result{} 12\n" |
| 2260 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" |
| 2261 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" |
| 2262 | "@end lisp") |
| 2263 | #define FUNC_NAME s_scm_truncate_quotient |
| 2264 | { |
| 2265 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 2266 | { |
| 2267 | scm_t_inum xx = SCM_I_INUM (x); |
| 2268 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2269 | { |
| 2270 | scm_t_inum yy = SCM_I_INUM (y); |
| 2271 | if (SCM_UNLIKELY (yy == 0)) |
| 2272 | scm_num_overflow (s_scm_truncate_quotient); |
| 2273 | else |
| 2274 | { |
| 2275 | scm_t_inum qq = xx / yy; |
| 2276 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 2277 | return SCM_I_MAKINUM (qq); |
| 2278 | else |
| 2279 | return scm_i_inum2big (qq); |
| 2280 | } |
| 2281 | } |
| 2282 | else if (SCM_BIGP (y)) |
| 2283 | { |
| 2284 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) |
| 2285 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
| 2286 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) |
| 2287 | { |
| 2288 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ |
| 2289 | scm_remember_upto_here_1 (y); |
| 2290 | return SCM_I_MAKINUM (-1); |
| 2291 | } |
| 2292 | else |
| 2293 | return SCM_INUM0; |
| 2294 | } |
| 2295 | else if (SCM_REALP (y)) |
| 2296 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); |
| 2297 | else if (SCM_FRACTIONP (y)) |
| 2298 | return scm_i_exact_rational_truncate_quotient (x, y); |
| 2299 | else |
| 2300 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
| 2301 | s_scm_truncate_quotient); |
| 2302 | } |
| 2303 | else if (SCM_BIGP (x)) |
| 2304 | { |
| 2305 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2306 | { |
| 2307 | scm_t_inum yy = SCM_I_INUM (y); |
| 2308 | if (SCM_UNLIKELY (yy == 0)) |
| 2309 | scm_num_overflow (s_scm_truncate_quotient); |
| 2310 | else if (SCM_UNLIKELY (yy == 1)) |
| 2311 | return x; |
| 2312 | else |
| 2313 | { |
| 2314 | SCM q = scm_i_mkbig (); |
| 2315 | if (yy > 0) |
| 2316 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); |
| 2317 | else |
| 2318 | { |
| 2319 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); |
| 2320 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 2321 | } |
| 2322 | scm_remember_upto_here_1 (x); |
| 2323 | return scm_i_normbig (q); |
| 2324 | } |
| 2325 | } |
| 2326 | else if (SCM_BIGP (y)) |
| 2327 | { |
| 2328 | SCM q = scm_i_mkbig (); |
| 2329 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), |
| 2330 | SCM_I_BIG_MPZ (x), |
| 2331 | SCM_I_BIG_MPZ (y)); |
| 2332 | scm_remember_upto_here_2 (x, y); |
| 2333 | return scm_i_normbig (q); |
| 2334 | } |
| 2335 | else if (SCM_REALP (y)) |
| 2336 | return scm_i_inexact_truncate_quotient |
| 2337 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 2338 | else if (SCM_FRACTIONP (y)) |
| 2339 | return scm_i_exact_rational_truncate_quotient (x, y); |
| 2340 | else |
| 2341 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
| 2342 | s_scm_truncate_quotient); |
| 2343 | } |
| 2344 | else if (SCM_REALP (x)) |
| 2345 | { |
| 2346 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 2347 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2348 | return scm_i_inexact_truncate_quotient |
| 2349 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 2350 | else |
| 2351 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
| 2352 | s_scm_truncate_quotient); |
| 2353 | } |
| 2354 | else if (SCM_FRACTIONP (x)) |
| 2355 | { |
| 2356 | if (SCM_REALP (y)) |
| 2357 | return scm_i_inexact_truncate_quotient |
| 2358 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 2359 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2360 | return scm_i_exact_rational_truncate_quotient (x, y); |
| 2361 | else |
| 2362 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
| 2363 | s_scm_truncate_quotient); |
| 2364 | } |
| 2365 | else |
| 2366 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, |
| 2367 | s_scm_truncate_quotient); |
| 2368 | } |
| 2369 | #undef FUNC_NAME |
| 2370 | |
| 2371 | static SCM |
| 2372 | scm_i_inexact_truncate_quotient (double x, double y) |
| 2373 | { |
| 2374 | if (SCM_UNLIKELY (y == 0)) |
| 2375 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ |
| 2376 | else |
| 2377 | return scm_i_from_double (trunc (x / y)); |
| 2378 | } |
| 2379 | |
| 2380 | static SCM |
| 2381 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) |
| 2382 | { |
| 2383 | return scm_truncate_quotient |
| 2384 | (scm_product (scm_numerator (x), scm_denominator (y)), |
| 2385 | scm_product (scm_numerator (y), scm_denominator (x))); |
| 2386 | } |
| 2387 | |
| 2388 | static SCM scm_i_inexact_truncate_remainder (double x, double y); |
| 2389 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); |
| 2390 | |
| 2391 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, |
| 2392 | (SCM x, SCM y), |
| 2393 | "Return the real number @var{r} such that\n" |
| 2394 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 2395 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" |
| 2396 | "@lisp\n" |
| 2397 | "(truncate-remainder 123 10) @result{} 3\n" |
| 2398 | "(truncate-remainder 123 -10) @result{} 3\n" |
| 2399 | "(truncate-remainder -123 10) @result{} -3\n" |
| 2400 | "(truncate-remainder -123 -10) @result{} -3\n" |
| 2401 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" |
| 2402 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" |
| 2403 | "@end lisp") |
| 2404 | #define FUNC_NAME s_scm_truncate_remainder |
| 2405 | { |
| 2406 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 2407 | { |
| 2408 | scm_t_inum xx = SCM_I_INUM (x); |
| 2409 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2410 | { |
| 2411 | scm_t_inum yy = SCM_I_INUM (y); |
| 2412 | if (SCM_UNLIKELY (yy == 0)) |
| 2413 | scm_num_overflow (s_scm_truncate_remainder); |
| 2414 | else |
| 2415 | return SCM_I_MAKINUM (xx % yy); |
| 2416 | } |
| 2417 | else if (SCM_BIGP (y)) |
| 2418 | { |
| 2419 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) |
| 2420 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
| 2421 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) |
| 2422 | { |
| 2423 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ |
| 2424 | scm_remember_upto_here_1 (y); |
| 2425 | return SCM_INUM0; |
| 2426 | } |
| 2427 | else |
| 2428 | return x; |
| 2429 | } |
| 2430 | else if (SCM_REALP (y)) |
| 2431 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); |
| 2432 | else if (SCM_FRACTIONP (y)) |
| 2433 | return scm_i_exact_rational_truncate_remainder (x, y); |
| 2434 | else |
| 2435 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
| 2436 | s_scm_truncate_remainder); |
| 2437 | } |
| 2438 | else if (SCM_BIGP (x)) |
| 2439 | { |
| 2440 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2441 | { |
| 2442 | scm_t_inum yy = SCM_I_INUM (y); |
| 2443 | if (SCM_UNLIKELY (yy == 0)) |
| 2444 | scm_num_overflow (s_scm_truncate_remainder); |
| 2445 | else |
| 2446 | { |
| 2447 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), |
| 2448 | (yy > 0) ? yy : -yy) |
| 2449 | * mpz_sgn (SCM_I_BIG_MPZ (x))); |
| 2450 | scm_remember_upto_here_1 (x); |
| 2451 | return SCM_I_MAKINUM (rr); |
| 2452 | } |
| 2453 | } |
| 2454 | else if (SCM_BIGP (y)) |
| 2455 | { |
| 2456 | SCM r = scm_i_mkbig (); |
| 2457 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), |
| 2458 | SCM_I_BIG_MPZ (x), |
| 2459 | SCM_I_BIG_MPZ (y)); |
| 2460 | scm_remember_upto_here_2 (x, y); |
| 2461 | return scm_i_normbig (r); |
| 2462 | } |
| 2463 | else if (SCM_REALP (y)) |
| 2464 | return scm_i_inexact_truncate_remainder |
| 2465 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 2466 | else if (SCM_FRACTIONP (y)) |
| 2467 | return scm_i_exact_rational_truncate_remainder (x, y); |
| 2468 | else |
| 2469 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
| 2470 | s_scm_truncate_remainder); |
| 2471 | } |
| 2472 | else if (SCM_REALP (x)) |
| 2473 | { |
| 2474 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 2475 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2476 | return scm_i_inexact_truncate_remainder |
| 2477 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 2478 | else |
| 2479 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
| 2480 | s_scm_truncate_remainder); |
| 2481 | } |
| 2482 | else if (SCM_FRACTIONP (x)) |
| 2483 | { |
| 2484 | if (SCM_REALP (y)) |
| 2485 | return scm_i_inexact_truncate_remainder |
| 2486 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 2487 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2488 | return scm_i_exact_rational_truncate_remainder (x, y); |
| 2489 | else |
| 2490 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
| 2491 | s_scm_truncate_remainder); |
| 2492 | } |
| 2493 | else |
| 2494 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, |
| 2495 | s_scm_truncate_remainder); |
| 2496 | } |
| 2497 | #undef FUNC_NAME |
| 2498 | |
| 2499 | static SCM |
| 2500 | scm_i_inexact_truncate_remainder (double x, double y) |
| 2501 | { |
| 2502 | /* Although it would be more efficient to use fmod here, we can't |
| 2503 | because it would in some cases produce results inconsistent with |
| 2504 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even |
| 2505 | close). In particular, when x is very close to a multiple of y, |
| 2506 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must |
| 2507 | correspond to different choices of q. If quotient chooses one and |
| 2508 | remainder chooses the other, it would be bad. */ |
| 2509 | if (SCM_UNLIKELY (y == 0)) |
| 2510 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ |
| 2511 | else |
| 2512 | return scm_i_from_double (x - y * trunc (x / y)); |
| 2513 | } |
| 2514 | |
| 2515 | static SCM |
| 2516 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) |
| 2517 | { |
| 2518 | SCM xd = scm_denominator (x); |
| 2519 | SCM yd = scm_denominator (y); |
| 2520 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), |
| 2521 | scm_product (scm_numerator (y), xd)); |
| 2522 | return scm_divide (r1, scm_product (xd, yd)); |
| 2523 | } |
| 2524 | |
| 2525 | |
| 2526 | static void scm_i_inexact_truncate_divide (double x, double y, |
| 2527 | SCM *qp, SCM *rp); |
| 2528 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, |
| 2529 | SCM *qp, SCM *rp); |
| 2530 | |
| 2531 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, |
| 2532 | (SCM x, SCM y), |
| 2533 | "Return the integer @var{q} and the real number @var{r}\n" |
| 2534 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 2535 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" |
| 2536 | "@lisp\n" |
| 2537 | "(truncate/ 123 10) @result{} 12 and 3\n" |
| 2538 | "(truncate/ 123 -10) @result{} -12 and 3\n" |
| 2539 | "(truncate/ -123 10) @result{} -12 and -3\n" |
| 2540 | "(truncate/ -123 -10) @result{} 12 and -3\n" |
| 2541 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" |
| 2542 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" |
| 2543 | "@end lisp") |
| 2544 | #define FUNC_NAME s_scm_i_truncate_divide |
| 2545 | { |
| 2546 | SCM q, r; |
| 2547 | |
| 2548 | scm_truncate_divide(x, y, &q, &r); |
| 2549 | return scm_values (scm_list_2 (q, r)); |
| 2550 | } |
| 2551 | #undef FUNC_NAME |
| 2552 | |
| 2553 | #define s_scm_truncate_divide s_scm_i_truncate_divide |
| 2554 | #define g_scm_truncate_divide g_scm_i_truncate_divide |
| 2555 | |
| 2556 | void |
| 2557 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 2558 | { |
| 2559 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 2560 | { |
| 2561 | scm_t_inum xx = SCM_I_INUM (x); |
| 2562 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2563 | { |
| 2564 | scm_t_inum yy = SCM_I_INUM (y); |
| 2565 | if (SCM_UNLIKELY (yy == 0)) |
| 2566 | scm_num_overflow (s_scm_truncate_divide); |
| 2567 | else |
| 2568 | { |
| 2569 | scm_t_inum qq = xx / yy; |
| 2570 | scm_t_inum rr = xx % yy; |
| 2571 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 2572 | *qp = SCM_I_MAKINUM (qq); |
| 2573 | else |
| 2574 | *qp = scm_i_inum2big (qq); |
| 2575 | *rp = SCM_I_MAKINUM (rr); |
| 2576 | } |
| 2577 | return; |
| 2578 | } |
| 2579 | else if (SCM_BIGP (y)) |
| 2580 | { |
| 2581 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) |
| 2582 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
| 2583 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) |
| 2584 | { |
| 2585 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ |
| 2586 | scm_remember_upto_here_1 (y); |
| 2587 | *qp = SCM_I_MAKINUM (-1); |
| 2588 | *rp = SCM_INUM0; |
| 2589 | } |
| 2590 | else |
| 2591 | { |
| 2592 | *qp = SCM_INUM0; |
| 2593 | *rp = x; |
| 2594 | } |
| 2595 | return; |
| 2596 | } |
| 2597 | else if (SCM_REALP (y)) |
| 2598 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
| 2599 | else if (SCM_FRACTIONP (y)) |
| 2600 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); |
| 2601 | else |
| 2602 | return two_valued_wta_dispatch_2 |
| 2603 | (g_scm_truncate_divide, x, y, SCM_ARG2, |
| 2604 | s_scm_truncate_divide, qp, rp); |
| 2605 | } |
| 2606 | else if (SCM_BIGP (x)) |
| 2607 | { |
| 2608 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2609 | { |
| 2610 | scm_t_inum yy = SCM_I_INUM (y); |
| 2611 | if (SCM_UNLIKELY (yy == 0)) |
| 2612 | scm_num_overflow (s_scm_truncate_divide); |
| 2613 | else |
| 2614 | { |
| 2615 | SCM q = scm_i_mkbig (); |
| 2616 | scm_t_inum rr; |
| 2617 | if (yy > 0) |
| 2618 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 2619 | SCM_I_BIG_MPZ (x), yy); |
| 2620 | else |
| 2621 | { |
| 2622 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 2623 | SCM_I_BIG_MPZ (x), -yy); |
| 2624 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 2625 | } |
| 2626 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 2627 | scm_remember_upto_here_1 (x); |
| 2628 | *qp = scm_i_normbig (q); |
| 2629 | *rp = SCM_I_MAKINUM (rr); |
| 2630 | } |
| 2631 | return; |
| 2632 | } |
| 2633 | else if (SCM_BIGP (y)) |
| 2634 | { |
| 2635 | SCM q = scm_i_mkbig (); |
| 2636 | SCM r = scm_i_mkbig (); |
| 2637 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 2638 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 2639 | scm_remember_upto_here_2 (x, y); |
| 2640 | *qp = scm_i_normbig (q); |
| 2641 | *rp = scm_i_normbig (r); |
| 2642 | } |
| 2643 | else if (SCM_REALP (y)) |
| 2644 | return scm_i_inexact_truncate_divide |
| 2645 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
| 2646 | else if (SCM_FRACTIONP (y)) |
| 2647 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); |
| 2648 | else |
| 2649 | return two_valued_wta_dispatch_2 |
| 2650 | (g_scm_truncate_divide, x, y, SCM_ARG2, |
| 2651 | s_scm_truncate_divide, qp, rp); |
| 2652 | } |
| 2653 | else if (SCM_REALP (x)) |
| 2654 | { |
| 2655 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 2656 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2657 | return scm_i_inexact_truncate_divide |
| 2658 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
| 2659 | else |
| 2660 | return two_valued_wta_dispatch_2 |
| 2661 | (g_scm_truncate_divide, x, y, SCM_ARG2, |
| 2662 | s_scm_truncate_divide, qp, rp); |
| 2663 | } |
| 2664 | else if (SCM_FRACTIONP (x)) |
| 2665 | { |
| 2666 | if (SCM_REALP (y)) |
| 2667 | return scm_i_inexact_truncate_divide |
| 2668 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
| 2669 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2670 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); |
| 2671 | else |
| 2672 | return two_valued_wta_dispatch_2 |
| 2673 | (g_scm_truncate_divide, x, y, SCM_ARG2, |
| 2674 | s_scm_truncate_divide, qp, rp); |
| 2675 | } |
| 2676 | else |
| 2677 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, |
| 2678 | s_scm_truncate_divide, qp, rp); |
| 2679 | } |
| 2680 | |
| 2681 | static void |
| 2682 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) |
| 2683 | { |
| 2684 | if (SCM_UNLIKELY (y == 0)) |
| 2685 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ |
| 2686 | else |
| 2687 | { |
| 2688 | double q = trunc (x / y); |
| 2689 | double r = x - q * y; |
| 2690 | *qp = scm_i_from_double (q); |
| 2691 | *rp = scm_i_from_double (r); |
| 2692 | } |
| 2693 | } |
| 2694 | |
| 2695 | static void |
| 2696 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 2697 | { |
| 2698 | SCM r1; |
| 2699 | SCM xd = scm_denominator (x); |
| 2700 | SCM yd = scm_denominator (y); |
| 2701 | |
| 2702 | scm_truncate_divide (scm_product (scm_numerator (x), yd), |
| 2703 | scm_product (scm_numerator (y), xd), |
| 2704 | qp, &r1); |
| 2705 | *rp = scm_divide (r1, scm_product (xd, yd)); |
| 2706 | } |
| 2707 | |
| 2708 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
| 2709 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); |
| 2710 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
| 2711 | |
| 2712 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
| 2713 | (SCM x, SCM y), |
| 2714 | "Return the integer @var{q} such that\n" |
| 2715 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" |
| 2716 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" |
| 2717 | "@lisp\n" |
| 2718 | "(centered-quotient 123 10) @result{} 12\n" |
| 2719 | "(centered-quotient 123 -10) @result{} -12\n" |
| 2720 | "(centered-quotient -123 10) @result{} -12\n" |
| 2721 | "(centered-quotient -123 -10) @result{} 12\n" |
| 2722 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" |
| 2723 | "(centered-quotient 16/3 -10/7) @result{} -4\n" |
| 2724 | "@end lisp") |
| 2725 | #define FUNC_NAME s_scm_centered_quotient |
| 2726 | { |
| 2727 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 2728 | { |
| 2729 | scm_t_inum xx = SCM_I_INUM (x); |
| 2730 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2731 | { |
| 2732 | scm_t_inum yy = SCM_I_INUM (y); |
| 2733 | if (SCM_UNLIKELY (yy == 0)) |
| 2734 | scm_num_overflow (s_scm_centered_quotient); |
| 2735 | else |
| 2736 | { |
| 2737 | scm_t_inum qq = xx / yy; |
| 2738 | scm_t_inum rr = xx % yy; |
| 2739 | if (SCM_LIKELY (xx > 0)) |
| 2740 | { |
| 2741 | if (SCM_LIKELY (yy > 0)) |
| 2742 | { |
| 2743 | if (rr >= (yy + 1) / 2) |
| 2744 | qq++; |
| 2745 | } |
| 2746 | else |
| 2747 | { |
| 2748 | if (rr >= (1 - yy) / 2) |
| 2749 | qq--; |
| 2750 | } |
| 2751 | } |
| 2752 | else |
| 2753 | { |
| 2754 | if (SCM_LIKELY (yy > 0)) |
| 2755 | { |
| 2756 | if (rr < -yy / 2) |
| 2757 | qq--; |
| 2758 | } |
| 2759 | else |
| 2760 | { |
| 2761 | if (rr < yy / 2) |
| 2762 | qq++; |
| 2763 | } |
| 2764 | } |
| 2765 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 2766 | return SCM_I_MAKINUM (qq); |
| 2767 | else |
| 2768 | return scm_i_inum2big (qq); |
| 2769 | } |
| 2770 | } |
| 2771 | else if (SCM_BIGP (y)) |
| 2772 | { |
| 2773 | /* Pass a denormalized bignum version of x (even though it |
| 2774 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ |
| 2775 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); |
| 2776 | } |
| 2777 | else if (SCM_REALP (y)) |
| 2778 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); |
| 2779 | else if (SCM_FRACTIONP (y)) |
| 2780 | return scm_i_exact_rational_centered_quotient (x, y); |
| 2781 | else |
| 2782 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
| 2783 | s_scm_centered_quotient); |
| 2784 | } |
| 2785 | else if (SCM_BIGP (x)) |
| 2786 | { |
| 2787 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2788 | { |
| 2789 | scm_t_inum yy = SCM_I_INUM (y); |
| 2790 | if (SCM_UNLIKELY (yy == 0)) |
| 2791 | scm_num_overflow (s_scm_centered_quotient); |
| 2792 | else if (SCM_UNLIKELY (yy == 1)) |
| 2793 | return x; |
| 2794 | else |
| 2795 | { |
| 2796 | SCM q = scm_i_mkbig (); |
| 2797 | scm_t_inum rr; |
| 2798 | /* Arrange for rr to initially be non-positive, |
| 2799 | because that simplifies the test to see |
| 2800 | if it is within the needed bounds. */ |
| 2801 | if (yy > 0) |
| 2802 | { |
| 2803 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 2804 | SCM_I_BIG_MPZ (x), yy); |
| 2805 | scm_remember_upto_here_1 (x); |
| 2806 | if (rr < -yy / 2) |
| 2807 | mpz_sub_ui (SCM_I_BIG_MPZ (q), |
| 2808 | SCM_I_BIG_MPZ (q), 1); |
| 2809 | } |
| 2810 | else |
| 2811 | { |
| 2812 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 2813 | SCM_I_BIG_MPZ (x), -yy); |
| 2814 | scm_remember_upto_here_1 (x); |
| 2815 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 2816 | if (rr < yy / 2) |
| 2817 | mpz_add_ui (SCM_I_BIG_MPZ (q), |
| 2818 | SCM_I_BIG_MPZ (q), 1); |
| 2819 | } |
| 2820 | return scm_i_normbig (q); |
| 2821 | } |
| 2822 | } |
| 2823 | else if (SCM_BIGP (y)) |
| 2824 | return scm_i_bigint_centered_quotient (x, y); |
| 2825 | else if (SCM_REALP (y)) |
| 2826 | return scm_i_inexact_centered_quotient |
| 2827 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 2828 | else if (SCM_FRACTIONP (y)) |
| 2829 | return scm_i_exact_rational_centered_quotient (x, y); |
| 2830 | else |
| 2831 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
| 2832 | s_scm_centered_quotient); |
| 2833 | } |
| 2834 | else if (SCM_REALP (x)) |
| 2835 | { |
| 2836 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 2837 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2838 | return scm_i_inexact_centered_quotient |
| 2839 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 2840 | else |
| 2841 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
| 2842 | s_scm_centered_quotient); |
| 2843 | } |
| 2844 | else if (SCM_FRACTIONP (x)) |
| 2845 | { |
| 2846 | if (SCM_REALP (y)) |
| 2847 | return scm_i_inexact_centered_quotient |
| 2848 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 2849 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 2850 | return scm_i_exact_rational_centered_quotient (x, y); |
| 2851 | else |
| 2852 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
| 2853 | s_scm_centered_quotient); |
| 2854 | } |
| 2855 | else |
| 2856 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, |
| 2857 | s_scm_centered_quotient); |
| 2858 | } |
| 2859 | #undef FUNC_NAME |
| 2860 | |
| 2861 | static SCM |
| 2862 | scm_i_inexact_centered_quotient (double x, double y) |
| 2863 | { |
| 2864 | if (SCM_LIKELY (y > 0)) |
| 2865 | return scm_i_from_double (floor (x/y + 0.5)); |
| 2866 | else if (SCM_LIKELY (y < 0)) |
| 2867 | return scm_i_from_double (ceil (x/y - 0.5)); |
| 2868 | else if (y == 0) |
| 2869 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ |
| 2870 | else |
| 2871 | return scm_nan (); |
| 2872 | } |
| 2873 | |
| 2874 | /* Assumes that both x and y are bigints, though |
| 2875 | x might be able to fit into a fixnum. */ |
| 2876 | static SCM |
| 2877 | scm_i_bigint_centered_quotient (SCM x, SCM y) |
| 2878 | { |
| 2879 | SCM q, r, min_r; |
| 2880 | |
| 2881 | /* Note that x might be small enough to fit into a |
| 2882 | fixnum, so we must not let it escape into the wild */ |
| 2883 | q = scm_i_mkbig (); |
| 2884 | r = scm_i_mkbig (); |
| 2885 | |
| 2886 | /* min_r will eventually become -abs(y)/2 */ |
| 2887 | min_r = scm_i_mkbig (); |
| 2888 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), |
| 2889 | SCM_I_BIG_MPZ (y), 1); |
| 2890 | |
| 2891 | /* Arrange for rr to initially be non-positive, |
| 2892 | because that simplifies the test to see |
| 2893 | if it is within the needed bounds. */ |
| 2894 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) |
| 2895 | { |
| 2896 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 2897 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 2898 | scm_remember_upto_here_2 (x, y); |
| 2899 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); |
| 2900 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) |
| 2901 | mpz_sub_ui (SCM_I_BIG_MPZ (q), |
| 2902 | SCM_I_BIG_MPZ (q), 1); |
| 2903 | } |
| 2904 | else |
| 2905 | { |
| 2906 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 2907 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 2908 | scm_remember_upto_here_2 (x, y); |
| 2909 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) |
| 2910 | mpz_add_ui (SCM_I_BIG_MPZ (q), |
| 2911 | SCM_I_BIG_MPZ (q), 1); |
| 2912 | } |
| 2913 | scm_remember_upto_here_2 (r, min_r); |
| 2914 | return scm_i_normbig (q); |
| 2915 | } |
| 2916 | |
| 2917 | static SCM |
| 2918 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) |
| 2919 | { |
| 2920 | return scm_centered_quotient |
| 2921 | (scm_product (scm_numerator (x), scm_denominator (y)), |
| 2922 | scm_product (scm_numerator (y), scm_denominator (x))); |
| 2923 | } |
| 2924 | |
| 2925 | static SCM scm_i_inexact_centered_remainder (double x, double y); |
| 2926 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); |
| 2927 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); |
| 2928 | |
| 2929 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, |
| 2930 | (SCM x, SCM y), |
| 2931 | "Return the real number @var{r} such that\n" |
| 2932 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" |
| 2933 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 2934 | "for some integer @var{q}.\n" |
| 2935 | "@lisp\n" |
| 2936 | "(centered-remainder 123 10) @result{} 3\n" |
| 2937 | "(centered-remainder 123 -10) @result{} 3\n" |
| 2938 | "(centered-remainder -123 10) @result{} -3\n" |
| 2939 | "(centered-remainder -123 -10) @result{} -3\n" |
| 2940 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" |
| 2941 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" |
| 2942 | "@end lisp") |
| 2943 | #define FUNC_NAME s_scm_centered_remainder |
| 2944 | { |
| 2945 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 2946 | { |
| 2947 | scm_t_inum xx = SCM_I_INUM (x); |
| 2948 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 2949 | { |
| 2950 | scm_t_inum yy = SCM_I_INUM (y); |
| 2951 | if (SCM_UNLIKELY (yy == 0)) |
| 2952 | scm_num_overflow (s_scm_centered_remainder); |
| 2953 | else |
| 2954 | { |
| 2955 | scm_t_inum rr = xx % yy; |
| 2956 | if (SCM_LIKELY (xx > 0)) |
| 2957 | { |
| 2958 | if (SCM_LIKELY (yy > 0)) |
| 2959 | { |
| 2960 | if (rr >= (yy + 1) / 2) |
| 2961 | rr -= yy; |
| 2962 | } |
| 2963 | else |
| 2964 | { |
| 2965 | if (rr >= (1 - yy) / 2) |
| 2966 | rr += yy; |
| 2967 | } |
| 2968 | } |
| 2969 | else |
| 2970 | { |
| 2971 | if (SCM_LIKELY (yy > 0)) |
| 2972 | { |
| 2973 | if (rr < -yy / 2) |
| 2974 | rr += yy; |
| 2975 | } |
| 2976 | else |
| 2977 | { |
| 2978 | if (rr < yy / 2) |
| 2979 | rr -= yy; |
| 2980 | } |
| 2981 | } |
| 2982 | return SCM_I_MAKINUM (rr); |
| 2983 | } |
| 2984 | } |
| 2985 | else if (SCM_BIGP (y)) |
| 2986 | { |
| 2987 | /* Pass a denormalized bignum version of x (even though it |
| 2988 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ |
| 2989 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); |
| 2990 | } |
| 2991 | else if (SCM_REALP (y)) |
| 2992 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); |
| 2993 | else if (SCM_FRACTIONP (y)) |
| 2994 | return scm_i_exact_rational_centered_remainder (x, y); |
| 2995 | else |
| 2996 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
| 2997 | s_scm_centered_remainder); |
| 2998 | } |
| 2999 | else if (SCM_BIGP (x)) |
| 3000 | { |
| 3001 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3002 | { |
| 3003 | scm_t_inum yy = SCM_I_INUM (y); |
| 3004 | if (SCM_UNLIKELY (yy == 0)) |
| 3005 | scm_num_overflow (s_scm_centered_remainder); |
| 3006 | else |
| 3007 | { |
| 3008 | scm_t_inum rr; |
| 3009 | /* Arrange for rr to initially be non-positive, |
| 3010 | because that simplifies the test to see |
| 3011 | if it is within the needed bounds. */ |
| 3012 | if (yy > 0) |
| 3013 | { |
| 3014 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); |
| 3015 | scm_remember_upto_here_1 (x); |
| 3016 | if (rr < -yy / 2) |
| 3017 | rr += yy; |
| 3018 | } |
| 3019 | else |
| 3020 | { |
| 3021 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); |
| 3022 | scm_remember_upto_here_1 (x); |
| 3023 | if (rr < yy / 2) |
| 3024 | rr -= yy; |
| 3025 | } |
| 3026 | return SCM_I_MAKINUM (rr); |
| 3027 | } |
| 3028 | } |
| 3029 | else if (SCM_BIGP (y)) |
| 3030 | return scm_i_bigint_centered_remainder (x, y); |
| 3031 | else if (SCM_REALP (y)) |
| 3032 | return scm_i_inexact_centered_remainder |
| 3033 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 3034 | else if (SCM_FRACTIONP (y)) |
| 3035 | return scm_i_exact_rational_centered_remainder (x, y); |
| 3036 | else |
| 3037 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
| 3038 | s_scm_centered_remainder); |
| 3039 | } |
| 3040 | else if (SCM_REALP (x)) |
| 3041 | { |
| 3042 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 3043 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3044 | return scm_i_inexact_centered_remainder |
| 3045 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 3046 | else |
| 3047 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
| 3048 | s_scm_centered_remainder); |
| 3049 | } |
| 3050 | else if (SCM_FRACTIONP (x)) |
| 3051 | { |
| 3052 | if (SCM_REALP (y)) |
| 3053 | return scm_i_inexact_centered_remainder |
| 3054 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 3055 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3056 | return scm_i_exact_rational_centered_remainder (x, y); |
| 3057 | else |
| 3058 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
| 3059 | s_scm_centered_remainder); |
| 3060 | } |
| 3061 | else |
| 3062 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, |
| 3063 | s_scm_centered_remainder); |
| 3064 | } |
| 3065 | #undef FUNC_NAME |
| 3066 | |
| 3067 | static SCM |
| 3068 | scm_i_inexact_centered_remainder (double x, double y) |
| 3069 | { |
| 3070 | double q; |
| 3071 | |
| 3072 | /* Although it would be more efficient to use fmod here, we can't |
| 3073 | because it would in some cases produce results inconsistent with |
| 3074 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even |
| 3075 | close). In particular, when x-y/2 is very close to a multiple of |
| 3076 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those |
| 3077 | two cases must correspond to different choices of q. If quotient |
| 3078 | chooses one and remainder chooses the other, it would be bad. */ |
| 3079 | if (SCM_LIKELY (y > 0)) |
| 3080 | q = floor (x/y + 0.5); |
| 3081 | else if (SCM_LIKELY (y < 0)) |
| 3082 | q = ceil (x/y - 0.5); |
| 3083 | else if (y == 0) |
| 3084 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ |
| 3085 | else |
| 3086 | return scm_nan (); |
| 3087 | return scm_i_from_double (x - q * y); |
| 3088 | } |
| 3089 | |
| 3090 | /* Assumes that both x and y are bigints, though |
| 3091 | x might be able to fit into a fixnum. */ |
| 3092 | static SCM |
| 3093 | scm_i_bigint_centered_remainder (SCM x, SCM y) |
| 3094 | { |
| 3095 | SCM r, min_r; |
| 3096 | |
| 3097 | /* Note that x might be small enough to fit into a |
| 3098 | fixnum, so we must not let it escape into the wild */ |
| 3099 | r = scm_i_mkbig (); |
| 3100 | |
| 3101 | /* min_r will eventually become -abs(y)/2 */ |
| 3102 | min_r = scm_i_mkbig (); |
| 3103 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), |
| 3104 | SCM_I_BIG_MPZ (y), 1); |
| 3105 | |
| 3106 | /* Arrange for rr to initially be non-positive, |
| 3107 | because that simplifies the test to see |
| 3108 | if it is within the needed bounds. */ |
| 3109 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) |
| 3110 | { |
| 3111 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), |
| 3112 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 3113 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); |
| 3114 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) |
| 3115 | mpz_add (SCM_I_BIG_MPZ (r), |
| 3116 | SCM_I_BIG_MPZ (r), |
| 3117 | SCM_I_BIG_MPZ (y)); |
| 3118 | } |
| 3119 | else |
| 3120 | { |
| 3121 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), |
| 3122 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 3123 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) |
| 3124 | mpz_sub (SCM_I_BIG_MPZ (r), |
| 3125 | SCM_I_BIG_MPZ (r), |
| 3126 | SCM_I_BIG_MPZ (y)); |
| 3127 | } |
| 3128 | scm_remember_upto_here_2 (x, y); |
| 3129 | return scm_i_normbig (r); |
| 3130 | } |
| 3131 | |
| 3132 | static SCM |
| 3133 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) |
| 3134 | { |
| 3135 | SCM xd = scm_denominator (x); |
| 3136 | SCM yd = scm_denominator (y); |
| 3137 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), |
| 3138 | scm_product (scm_numerator (y), xd)); |
| 3139 | return scm_divide (r1, scm_product (xd, yd)); |
| 3140 | } |
| 3141 | |
| 3142 | |
| 3143 | static void scm_i_inexact_centered_divide (double x, double y, |
| 3144 | SCM *qp, SCM *rp); |
| 3145 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); |
| 3146 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, |
| 3147 | SCM *qp, SCM *rp); |
| 3148 | |
| 3149 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, |
| 3150 | (SCM x, SCM y), |
| 3151 | "Return the integer @var{q} and the real number @var{r}\n" |
| 3152 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 3153 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" |
| 3154 | "@lisp\n" |
| 3155 | "(centered/ 123 10) @result{} 12 and 3\n" |
| 3156 | "(centered/ 123 -10) @result{} -12 and 3\n" |
| 3157 | "(centered/ -123 10) @result{} -12 and -3\n" |
| 3158 | "(centered/ -123 -10) @result{} 12 and -3\n" |
| 3159 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" |
| 3160 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" |
| 3161 | "@end lisp") |
| 3162 | #define FUNC_NAME s_scm_i_centered_divide |
| 3163 | { |
| 3164 | SCM q, r; |
| 3165 | |
| 3166 | scm_centered_divide(x, y, &q, &r); |
| 3167 | return scm_values (scm_list_2 (q, r)); |
| 3168 | } |
| 3169 | #undef FUNC_NAME |
| 3170 | |
| 3171 | #define s_scm_centered_divide s_scm_i_centered_divide |
| 3172 | #define g_scm_centered_divide g_scm_i_centered_divide |
| 3173 | |
| 3174 | void |
| 3175 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 3176 | { |
| 3177 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 3178 | { |
| 3179 | scm_t_inum xx = SCM_I_INUM (x); |
| 3180 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3181 | { |
| 3182 | scm_t_inum yy = SCM_I_INUM (y); |
| 3183 | if (SCM_UNLIKELY (yy == 0)) |
| 3184 | scm_num_overflow (s_scm_centered_divide); |
| 3185 | else |
| 3186 | { |
| 3187 | scm_t_inum qq = xx / yy; |
| 3188 | scm_t_inum rr = xx % yy; |
| 3189 | if (SCM_LIKELY (xx > 0)) |
| 3190 | { |
| 3191 | if (SCM_LIKELY (yy > 0)) |
| 3192 | { |
| 3193 | if (rr >= (yy + 1) / 2) |
| 3194 | { qq++; rr -= yy; } |
| 3195 | } |
| 3196 | else |
| 3197 | { |
| 3198 | if (rr >= (1 - yy) / 2) |
| 3199 | { qq--; rr += yy; } |
| 3200 | } |
| 3201 | } |
| 3202 | else |
| 3203 | { |
| 3204 | if (SCM_LIKELY (yy > 0)) |
| 3205 | { |
| 3206 | if (rr < -yy / 2) |
| 3207 | { qq--; rr += yy; } |
| 3208 | } |
| 3209 | else |
| 3210 | { |
| 3211 | if (rr < yy / 2) |
| 3212 | { qq++; rr -= yy; } |
| 3213 | } |
| 3214 | } |
| 3215 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 3216 | *qp = SCM_I_MAKINUM (qq); |
| 3217 | else |
| 3218 | *qp = scm_i_inum2big (qq); |
| 3219 | *rp = SCM_I_MAKINUM (rr); |
| 3220 | } |
| 3221 | return; |
| 3222 | } |
| 3223 | else if (SCM_BIGP (y)) |
| 3224 | { |
| 3225 | /* Pass a denormalized bignum version of x (even though it |
| 3226 | can fit in a fixnum) to scm_i_bigint_centered_divide */ |
| 3227 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); |
| 3228 | } |
| 3229 | else if (SCM_REALP (y)) |
| 3230 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
| 3231 | else if (SCM_FRACTIONP (y)) |
| 3232 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); |
| 3233 | else |
| 3234 | return two_valued_wta_dispatch_2 |
| 3235 | (g_scm_centered_divide, x, y, SCM_ARG2, |
| 3236 | s_scm_centered_divide, qp, rp); |
| 3237 | } |
| 3238 | else if (SCM_BIGP (x)) |
| 3239 | { |
| 3240 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3241 | { |
| 3242 | scm_t_inum yy = SCM_I_INUM (y); |
| 3243 | if (SCM_UNLIKELY (yy == 0)) |
| 3244 | scm_num_overflow (s_scm_centered_divide); |
| 3245 | else |
| 3246 | { |
| 3247 | SCM q = scm_i_mkbig (); |
| 3248 | scm_t_inum rr; |
| 3249 | /* Arrange for rr to initially be non-positive, |
| 3250 | because that simplifies the test to see |
| 3251 | if it is within the needed bounds. */ |
| 3252 | if (yy > 0) |
| 3253 | { |
| 3254 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3255 | SCM_I_BIG_MPZ (x), yy); |
| 3256 | scm_remember_upto_here_1 (x); |
| 3257 | if (rr < -yy / 2) |
| 3258 | { |
| 3259 | mpz_sub_ui (SCM_I_BIG_MPZ (q), |
| 3260 | SCM_I_BIG_MPZ (q), 1); |
| 3261 | rr += yy; |
| 3262 | } |
| 3263 | } |
| 3264 | else |
| 3265 | { |
| 3266 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3267 | SCM_I_BIG_MPZ (x), -yy); |
| 3268 | scm_remember_upto_here_1 (x); |
| 3269 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 3270 | if (rr < yy / 2) |
| 3271 | { |
| 3272 | mpz_add_ui (SCM_I_BIG_MPZ (q), |
| 3273 | SCM_I_BIG_MPZ (q), 1); |
| 3274 | rr -= yy; |
| 3275 | } |
| 3276 | } |
| 3277 | *qp = scm_i_normbig (q); |
| 3278 | *rp = SCM_I_MAKINUM (rr); |
| 3279 | } |
| 3280 | return; |
| 3281 | } |
| 3282 | else if (SCM_BIGP (y)) |
| 3283 | return scm_i_bigint_centered_divide (x, y, qp, rp); |
| 3284 | else if (SCM_REALP (y)) |
| 3285 | return scm_i_inexact_centered_divide |
| 3286 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
| 3287 | else if (SCM_FRACTIONP (y)) |
| 3288 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); |
| 3289 | else |
| 3290 | return two_valued_wta_dispatch_2 |
| 3291 | (g_scm_centered_divide, x, y, SCM_ARG2, |
| 3292 | s_scm_centered_divide, qp, rp); |
| 3293 | } |
| 3294 | else if (SCM_REALP (x)) |
| 3295 | { |
| 3296 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 3297 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3298 | return scm_i_inexact_centered_divide |
| 3299 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
| 3300 | else |
| 3301 | return two_valued_wta_dispatch_2 |
| 3302 | (g_scm_centered_divide, x, y, SCM_ARG2, |
| 3303 | s_scm_centered_divide, qp, rp); |
| 3304 | } |
| 3305 | else if (SCM_FRACTIONP (x)) |
| 3306 | { |
| 3307 | if (SCM_REALP (y)) |
| 3308 | return scm_i_inexact_centered_divide |
| 3309 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
| 3310 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3311 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); |
| 3312 | else |
| 3313 | return two_valued_wta_dispatch_2 |
| 3314 | (g_scm_centered_divide, x, y, SCM_ARG2, |
| 3315 | s_scm_centered_divide, qp, rp); |
| 3316 | } |
| 3317 | else |
| 3318 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
| 3319 | s_scm_centered_divide, qp, rp); |
| 3320 | } |
| 3321 | |
| 3322 | static void |
| 3323 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) |
| 3324 | { |
| 3325 | double q, r; |
| 3326 | |
| 3327 | if (SCM_LIKELY (y > 0)) |
| 3328 | q = floor (x/y + 0.5); |
| 3329 | else if (SCM_LIKELY (y < 0)) |
| 3330 | q = ceil (x/y - 0.5); |
| 3331 | else if (y == 0) |
| 3332 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ |
| 3333 | else |
| 3334 | q = guile_NaN; |
| 3335 | r = x - q * y; |
| 3336 | *qp = scm_i_from_double (q); |
| 3337 | *rp = scm_i_from_double (r); |
| 3338 | } |
| 3339 | |
| 3340 | /* Assumes that both x and y are bigints, though |
| 3341 | x might be able to fit into a fixnum. */ |
| 3342 | static void |
| 3343 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 3344 | { |
| 3345 | SCM q, r, min_r; |
| 3346 | |
| 3347 | /* Note that x might be small enough to fit into a |
| 3348 | fixnum, so we must not let it escape into the wild */ |
| 3349 | q = scm_i_mkbig (); |
| 3350 | r = scm_i_mkbig (); |
| 3351 | |
| 3352 | /* min_r will eventually become -abs(y/2) */ |
| 3353 | min_r = scm_i_mkbig (); |
| 3354 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), |
| 3355 | SCM_I_BIG_MPZ (y), 1); |
| 3356 | |
| 3357 | /* Arrange for rr to initially be non-positive, |
| 3358 | because that simplifies the test to see |
| 3359 | if it is within the needed bounds. */ |
| 3360 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) |
| 3361 | { |
| 3362 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 3363 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 3364 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); |
| 3365 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) |
| 3366 | { |
| 3367 | mpz_sub_ui (SCM_I_BIG_MPZ (q), |
| 3368 | SCM_I_BIG_MPZ (q), 1); |
| 3369 | mpz_add (SCM_I_BIG_MPZ (r), |
| 3370 | SCM_I_BIG_MPZ (r), |
| 3371 | SCM_I_BIG_MPZ (y)); |
| 3372 | } |
| 3373 | } |
| 3374 | else |
| 3375 | { |
| 3376 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 3377 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 3378 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) |
| 3379 | { |
| 3380 | mpz_add_ui (SCM_I_BIG_MPZ (q), |
| 3381 | SCM_I_BIG_MPZ (q), 1); |
| 3382 | mpz_sub (SCM_I_BIG_MPZ (r), |
| 3383 | SCM_I_BIG_MPZ (r), |
| 3384 | SCM_I_BIG_MPZ (y)); |
| 3385 | } |
| 3386 | } |
| 3387 | scm_remember_upto_here_2 (x, y); |
| 3388 | *qp = scm_i_normbig (q); |
| 3389 | *rp = scm_i_normbig (r); |
| 3390 | } |
| 3391 | |
| 3392 | static void |
| 3393 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 3394 | { |
| 3395 | SCM r1; |
| 3396 | SCM xd = scm_denominator (x); |
| 3397 | SCM yd = scm_denominator (y); |
| 3398 | |
| 3399 | scm_centered_divide (scm_product (scm_numerator (x), yd), |
| 3400 | scm_product (scm_numerator (y), xd), |
| 3401 | qp, &r1); |
| 3402 | *rp = scm_divide (r1, scm_product (xd, yd)); |
| 3403 | } |
| 3404 | |
| 3405 | static SCM scm_i_inexact_round_quotient (double x, double y); |
| 3406 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); |
| 3407 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); |
| 3408 | |
| 3409 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, |
| 3410 | (SCM x, SCM y), |
| 3411 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
| 3412 | "with ties going to the nearest even integer.\n" |
| 3413 | "@lisp\n" |
| 3414 | "(round-quotient 123 10) @result{} 12\n" |
| 3415 | "(round-quotient 123 -10) @result{} -12\n" |
| 3416 | "(round-quotient -123 10) @result{} -12\n" |
| 3417 | "(round-quotient -123 -10) @result{} 12\n" |
| 3418 | "(round-quotient 125 10) @result{} 12\n" |
| 3419 | "(round-quotient 127 10) @result{} 13\n" |
| 3420 | "(round-quotient 135 10) @result{} 14\n" |
| 3421 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" |
| 3422 | "(round-quotient 16/3 -10/7) @result{} -4\n" |
| 3423 | "@end lisp") |
| 3424 | #define FUNC_NAME s_scm_round_quotient |
| 3425 | { |
| 3426 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 3427 | { |
| 3428 | scm_t_inum xx = SCM_I_INUM (x); |
| 3429 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3430 | { |
| 3431 | scm_t_inum yy = SCM_I_INUM (y); |
| 3432 | if (SCM_UNLIKELY (yy == 0)) |
| 3433 | scm_num_overflow (s_scm_round_quotient); |
| 3434 | else |
| 3435 | { |
| 3436 | scm_t_inum qq = xx / yy; |
| 3437 | scm_t_inum rr = xx % yy; |
| 3438 | scm_t_inum ay = yy; |
| 3439 | scm_t_inum r2 = 2 * rr; |
| 3440 | |
| 3441 | if (SCM_LIKELY (yy < 0)) |
| 3442 | { |
| 3443 | ay = -ay; |
| 3444 | r2 = -r2; |
| 3445 | } |
| 3446 | |
| 3447 | if (qq & 1L) |
| 3448 | { |
| 3449 | if (r2 >= ay) |
| 3450 | qq++; |
| 3451 | else if (r2 <= -ay) |
| 3452 | qq--; |
| 3453 | } |
| 3454 | else |
| 3455 | { |
| 3456 | if (r2 > ay) |
| 3457 | qq++; |
| 3458 | else if (r2 < -ay) |
| 3459 | qq--; |
| 3460 | } |
| 3461 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 3462 | return SCM_I_MAKINUM (qq); |
| 3463 | else |
| 3464 | return scm_i_inum2big (qq); |
| 3465 | } |
| 3466 | } |
| 3467 | else if (SCM_BIGP (y)) |
| 3468 | { |
| 3469 | /* Pass a denormalized bignum version of x (even though it |
| 3470 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
| 3471 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); |
| 3472 | } |
| 3473 | else if (SCM_REALP (y)) |
| 3474 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
| 3475 | else if (SCM_FRACTIONP (y)) |
| 3476 | return scm_i_exact_rational_round_quotient (x, y); |
| 3477 | else |
| 3478 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
| 3479 | s_scm_round_quotient); |
| 3480 | } |
| 3481 | else if (SCM_BIGP (x)) |
| 3482 | { |
| 3483 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3484 | { |
| 3485 | scm_t_inum yy = SCM_I_INUM (y); |
| 3486 | if (SCM_UNLIKELY (yy == 0)) |
| 3487 | scm_num_overflow (s_scm_round_quotient); |
| 3488 | else if (SCM_UNLIKELY (yy == 1)) |
| 3489 | return x; |
| 3490 | else |
| 3491 | { |
| 3492 | SCM q = scm_i_mkbig (); |
| 3493 | scm_t_inum rr; |
| 3494 | int needs_adjustment; |
| 3495 | |
| 3496 | if (yy > 0) |
| 3497 | { |
| 3498 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3499 | SCM_I_BIG_MPZ (x), yy); |
| 3500 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3501 | needs_adjustment = (2*rr >= yy); |
| 3502 | else |
| 3503 | needs_adjustment = (2*rr > yy); |
| 3504 | } |
| 3505 | else |
| 3506 | { |
| 3507 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3508 | SCM_I_BIG_MPZ (x), -yy); |
| 3509 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 3510 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3511 | needs_adjustment = (2*rr <= yy); |
| 3512 | else |
| 3513 | needs_adjustment = (2*rr < yy); |
| 3514 | } |
| 3515 | scm_remember_upto_here_1 (x); |
| 3516 | if (needs_adjustment) |
| 3517 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
| 3518 | return scm_i_normbig (q); |
| 3519 | } |
| 3520 | } |
| 3521 | else if (SCM_BIGP (y)) |
| 3522 | return scm_i_bigint_round_quotient (x, y); |
| 3523 | else if (SCM_REALP (y)) |
| 3524 | return scm_i_inexact_round_quotient |
| 3525 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 3526 | else if (SCM_FRACTIONP (y)) |
| 3527 | return scm_i_exact_rational_round_quotient (x, y); |
| 3528 | else |
| 3529 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
| 3530 | s_scm_round_quotient); |
| 3531 | } |
| 3532 | else if (SCM_REALP (x)) |
| 3533 | { |
| 3534 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 3535 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3536 | return scm_i_inexact_round_quotient |
| 3537 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 3538 | else |
| 3539 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
| 3540 | s_scm_round_quotient); |
| 3541 | } |
| 3542 | else if (SCM_FRACTIONP (x)) |
| 3543 | { |
| 3544 | if (SCM_REALP (y)) |
| 3545 | return scm_i_inexact_round_quotient |
| 3546 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 3547 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3548 | return scm_i_exact_rational_round_quotient (x, y); |
| 3549 | else |
| 3550 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
| 3551 | s_scm_round_quotient); |
| 3552 | } |
| 3553 | else |
| 3554 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
| 3555 | s_scm_round_quotient); |
| 3556 | } |
| 3557 | #undef FUNC_NAME |
| 3558 | |
| 3559 | static SCM |
| 3560 | scm_i_inexact_round_quotient (double x, double y) |
| 3561 | { |
| 3562 | if (SCM_UNLIKELY (y == 0)) |
| 3563 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ |
| 3564 | else |
| 3565 | return scm_i_from_double (scm_c_round (x / y)); |
| 3566 | } |
| 3567 | |
| 3568 | /* Assumes that both x and y are bigints, though |
| 3569 | x might be able to fit into a fixnum. */ |
| 3570 | static SCM |
| 3571 | scm_i_bigint_round_quotient (SCM x, SCM y) |
| 3572 | { |
| 3573 | SCM q, r, r2; |
| 3574 | int cmp, needs_adjustment; |
| 3575 | |
| 3576 | /* Note that x might be small enough to fit into a |
| 3577 | fixnum, so we must not let it escape into the wild */ |
| 3578 | q = scm_i_mkbig (); |
| 3579 | r = scm_i_mkbig (); |
| 3580 | r2 = scm_i_mkbig (); |
| 3581 | |
| 3582 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 3583 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 3584 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ |
| 3585 | scm_remember_upto_here_2 (x, r); |
| 3586 | |
| 3587 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
| 3588 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3589 | needs_adjustment = (cmp >= 0); |
| 3590 | else |
| 3591 | needs_adjustment = (cmp > 0); |
| 3592 | scm_remember_upto_here_2 (r2, y); |
| 3593 | |
| 3594 | if (needs_adjustment) |
| 3595 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
| 3596 | |
| 3597 | return scm_i_normbig (q); |
| 3598 | } |
| 3599 | |
| 3600 | static SCM |
| 3601 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
| 3602 | { |
| 3603 | return scm_round_quotient |
| 3604 | (scm_product (scm_numerator (x), scm_denominator (y)), |
| 3605 | scm_product (scm_numerator (y), scm_denominator (x))); |
| 3606 | } |
| 3607 | |
| 3608 | static SCM scm_i_inexact_round_remainder (double x, double y); |
| 3609 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); |
| 3610 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); |
| 3611 | |
| 3612 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
| 3613 | (SCM x, SCM y), |
| 3614 | "Return the real number @var{r} such that\n" |
| 3615 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
| 3616 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
| 3617 | "nearest integer, with ties going to the nearest\n" |
| 3618 | "even integer.\n" |
| 3619 | "@lisp\n" |
| 3620 | "(round-remainder 123 10) @result{} 3\n" |
| 3621 | "(round-remainder 123 -10) @result{} 3\n" |
| 3622 | "(round-remainder -123 10) @result{} -3\n" |
| 3623 | "(round-remainder -123 -10) @result{} -3\n" |
| 3624 | "(round-remainder 125 10) @result{} 5\n" |
| 3625 | "(round-remainder 127 10) @result{} -3\n" |
| 3626 | "(round-remainder 135 10) @result{} -5\n" |
| 3627 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" |
| 3628 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" |
| 3629 | "@end lisp") |
| 3630 | #define FUNC_NAME s_scm_round_remainder |
| 3631 | { |
| 3632 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 3633 | { |
| 3634 | scm_t_inum xx = SCM_I_INUM (x); |
| 3635 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3636 | { |
| 3637 | scm_t_inum yy = SCM_I_INUM (y); |
| 3638 | if (SCM_UNLIKELY (yy == 0)) |
| 3639 | scm_num_overflow (s_scm_round_remainder); |
| 3640 | else |
| 3641 | { |
| 3642 | scm_t_inum qq = xx / yy; |
| 3643 | scm_t_inum rr = xx % yy; |
| 3644 | scm_t_inum ay = yy; |
| 3645 | scm_t_inum r2 = 2 * rr; |
| 3646 | |
| 3647 | if (SCM_LIKELY (yy < 0)) |
| 3648 | { |
| 3649 | ay = -ay; |
| 3650 | r2 = -r2; |
| 3651 | } |
| 3652 | |
| 3653 | if (qq & 1L) |
| 3654 | { |
| 3655 | if (r2 >= ay) |
| 3656 | rr -= yy; |
| 3657 | else if (r2 <= -ay) |
| 3658 | rr += yy; |
| 3659 | } |
| 3660 | else |
| 3661 | { |
| 3662 | if (r2 > ay) |
| 3663 | rr -= yy; |
| 3664 | else if (r2 < -ay) |
| 3665 | rr += yy; |
| 3666 | } |
| 3667 | return SCM_I_MAKINUM (rr); |
| 3668 | } |
| 3669 | } |
| 3670 | else if (SCM_BIGP (y)) |
| 3671 | { |
| 3672 | /* Pass a denormalized bignum version of x (even though it |
| 3673 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
| 3674 | return scm_i_bigint_round_remainder |
| 3675 | (scm_i_long2big (xx), y); |
| 3676 | } |
| 3677 | else if (SCM_REALP (y)) |
| 3678 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
| 3679 | else if (SCM_FRACTIONP (y)) |
| 3680 | return scm_i_exact_rational_round_remainder (x, y); |
| 3681 | else |
| 3682 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
| 3683 | s_scm_round_remainder); |
| 3684 | } |
| 3685 | else if (SCM_BIGP (x)) |
| 3686 | { |
| 3687 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3688 | { |
| 3689 | scm_t_inum yy = SCM_I_INUM (y); |
| 3690 | if (SCM_UNLIKELY (yy == 0)) |
| 3691 | scm_num_overflow (s_scm_round_remainder); |
| 3692 | else |
| 3693 | { |
| 3694 | SCM q = scm_i_mkbig (); |
| 3695 | scm_t_inum rr; |
| 3696 | int needs_adjustment; |
| 3697 | |
| 3698 | if (yy > 0) |
| 3699 | { |
| 3700 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3701 | SCM_I_BIG_MPZ (x), yy); |
| 3702 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3703 | needs_adjustment = (2*rr >= yy); |
| 3704 | else |
| 3705 | needs_adjustment = (2*rr > yy); |
| 3706 | } |
| 3707 | else |
| 3708 | { |
| 3709 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3710 | SCM_I_BIG_MPZ (x), -yy); |
| 3711 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3712 | needs_adjustment = (2*rr <= yy); |
| 3713 | else |
| 3714 | needs_adjustment = (2*rr < yy); |
| 3715 | } |
| 3716 | scm_remember_upto_here_2 (x, q); |
| 3717 | if (needs_adjustment) |
| 3718 | rr -= yy; |
| 3719 | return SCM_I_MAKINUM (rr); |
| 3720 | } |
| 3721 | } |
| 3722 | else if (SCM_BIGP (y)) |
| 3723 | return scm_i_bigint_round_remainder (x, y); |
| 3724 | else if (SCM_REALP (y)) |
| 3725 | return scm_i_inexact_round_remainder |
| 3726 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
| 3727 | else if (SCM_FRACTIONP (y)) |
| 3728 | return scm_i_exact_rational_round_remainder (x, y); |
| 3729 | else |
| 3730 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
| 3731 | s_scm_round_remainder); |
| 3732 | } |
| 3733 | else if (SCM_REALP (x)) |
| 3734 | { |
| 3735 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 3736 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3737 | return scm_i_inexact_round_remainder |
| 3738 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
| 3739 | else |
| 3740 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
| 3741 | s_scm_round_remainder); |
| 3742 | } |
| 3743 | else if (SCM_FRACTIONP (x)) |
| 3744 | { |
| 3745 | if (SCM_REALP (y)) |
| 3746 | return scm_i_inexact_round_remainder |
| 3747 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
| 3748 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3749 | return scm_i_exact_rational_round_remainder (x, y); |
| 3750 | else |
| 3751 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
| 3752 | s_scm_round_remainder); |
| 3753 | } |
| 3754 | else |
| 3755 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
| 3756 | s_scm_round_remainder); |
| 3757 | } |
| 3758 | #undef FUNC_NAME |
| 3759 | |
| 3760 | static SCM |
| 3761 | scm_i_inexact_round_remainder (double x, double y) |
| 3762 | { |
| 3763 | /* Although it would be more efficient to use fmod here, we can't |
| 3764 | because it would in some cases produce results inconsistent with |
| 3765 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
| 3766 | close). In particular, when x-y/2 is very close to a multiple of |
| 3767 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
| 3768 | cases must correspond to different choices of q. If quotient |
| 3769 | chooses one and remainder chooses the other, it would be bad. */ |
| 3770 | |
| 3771 | if (SCM_UNLIKELY (y == 0)) |
| 3772 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ |
| 3773 | else |
| 3774 | { |
| 3775 | double q = scm_c_round (x / y); |
| 3776 | return scm_i_from_double (x - q * y); |
| 3777 | } |
| 3778 | } |
| 3779 | |
| 3780 | /* Assumes that both x and y are bigints, though |
| 3781 | x might be able to fit into a fixnum. */ |
| 3782 | static SCM |
| 3783 | scm_i_bigint_round_remainder (SCM x, SCM y) |
| 3784 | { |
| 3785 | SCM q, r, r2; |
| 3786 | int cmp, needs_adjustment; |
| 3787 | |
| 3788 | /* Note that x might be small enough to fit into a |
| 3789 | fixnum, so we must not let it escape into the wild */ |
| 3790 | q = scm_i_mkbig (); |
| 3791 | r = scm_i_mkbig (); |
| 3792 | r2 = scm_i_mkbig (); |
| 3793 | |
| 3794 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 3795 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 3796 | scm_remember_upto_here_1 (x); |
| 3797 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ |
| 3798 | |
| 3799 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
| 3800 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3801 | needs_adjustment = (cmp >= 0); |
| 3802 | else |
| 3803 | needs_adjustment = (cmp > 0); |
| 3804 | scm_remember_upto_here_2 (q, r2); |
| 3805 | |
| 3806 | if (needs_adjustment) |
| 3807 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); |
| 3808 | |
| 3809 | scm_remember_upto_here_1 (y); |
| 3810 | return scm_i_normbig (r); |
| 3811 | } |
| 3812 | |
| 3813 | static SCM |
| 3814 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
| 3815 | { |
| 3816 | SCM xd = scm_denominator (x); |
| 3817 | SCM yd = scm_denominator (y); |
| 3818 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
| 3819 | scm_product (scm_numerator (y), xd)); |
| 3820 | return scm_divide (r1, scm_product (xd, yd)); |
| 3821 | } |
| 3822 | |
| 3823 | |
| 3824 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
| 3825 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); |
| 3826 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); |
| 3827 | |
| 3828 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
| 3829 | (SCM x, SCM y), |
| 3830 | "Return the integer @var{q} and the real number @var{r}\n" |
| 3831 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" |
| 3832 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
| 3833 | "nearest integer, with ties going to the nearest even integer.\n" |
| 3834 | "@lisp\n" |
| 3835 | "(round/ 123 10) @result{} 12 and 3\n" |
| 3836 | "(round/ 123 -10) @result{} -12 and 3\n" |
| 3837 | "(round/ -123 10) @result{} -12 and -3\n" |
| 3838 | "(round/ -123 -10) @result{} 12 and -3\n" |
| 3839 | "(round/ 125 10) @result{} 12 and 5\n" |
| 3840 | "(round/ 127 10) @result{} 13 and -3\n" |
| 3841 | "(round/ 135 10) @result{} 14 and -5\n" |
| 3842 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" |
| 3843 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" |
| 3844 | "@end lisp") |
| 3845 | #define FUNC_NAME s_scm_i_round_divide |
| 3846 | { |
| 3847 | SCM q, r; |
| 3848 | |
| 3849 | scm_round_divide(x, y, &q, &r); |
| 3850 | return scm_values (scm_list_2 (q, r)); |
| 3851 | } |
| 3852 | #undef FUNC_NAME |
| 3853 | |
| 3854 | #define s_scm_round_divide s_scm_i_round_divide |
| 3855 | #define g_scm_round_divide g_scm_i_round_divide |
| 3856 | |
| 3857 | void |
| 3858 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 3859 | { |
| 3860 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 3861 | { |
| 3862 | scm_t_inum xx = SCM_I_INUM (x); |
| 3863 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3864 | { |
| 3865 | scm_t_inum yy = SCM_I_INUM (y); |
| 3866 | if (SCM_UNLIKELY (yy == 0)) |
| 3867 | scm_num_overflow (s_scm_round_divide); |
| 3868 | else |
| 3869 | { |
| 3870 | scm_t_inum qq = xx / yy; |
| 3871 | scm_t_inum rr = xx % yy; |
| 3872 | scm_t_inum ay = yy; |
| 3873 | scm_t_inum r2 = 2 * rr; |
| 3874 | |
| 3875 | if (SCM_LIKELY (yy < 0)) |
| 3876 | { |
| 3877 | ay = -ay; |
| 3878 | r2 = -r2; |
| 3879 | } |
| 3880 | |
| 3881 | if (qq & 1L) |
| 3882 | { |
| 3883 | if (r2 >= ay) |
| 3884 | { qq++; rr -= yy; } |
| 3885 | else if (r2 <= -ay) |
| 3886 | { qq--; rr += yy; } |
| 3887 | } |
| 3888 | else |
| 3889 | { |
| 3890 | if (r2 > ay) |
| 3891 | { qq++; rr -= yy; } |
| 3892 | else if (r2 < -ay) |
| 3893 | { qq--; rr += yy; } |
| 3894 | } |
| 3895 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
| 3896 | *qp = SCM_I_MAKINUM (qq); |
| 3897 | else |
| 3898 | *qp = scm_i_inum2big (qq); |
| 3899 | *rp = SCM_I_MAKINUM (rr); |
| 3900 | } |
| 3901 | return; |
| 3902 | } |
| 3903 | else if (SCM_BIGP (y)) |
| 3904 | { |
| 3905 | /* Pass a denormalized bignum version of x (even though it |
| 3906 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
| 3907 | return scm_i_bigint_round_divide |
| 3908 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); |
| 3909 | } |
| 3910 | else if (SCM_REALP (y)) |
| 3911 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
| 3912 | else if (SCM_FRACTIONP (y)) |
| 3913 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
| 3914 | else |
| 3915 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
| 3916 | s_scm_round_divide, qp, rp); |
| 3917 | } |
| 3918 | else if (SCM_BIGP (x)) |
| 3919 | { |
| 3920 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 3921 | { |
| 3922 | scm_t_inum yy = SCM_I_INUM (y); |
| 3923 | if (SCM_UNLIKELY (yy == 0)) |
| 3924 | scm_num_overflow (s_scm_round_divide); |
| 3925 | else |
| 3926 | { |
| 3927 | SCM q = scm_i_mkbig (); |
| 3928 | scm_t_inum rr; |
| 3929 | int needs_adjustment; |
| 3930 | |
| 3931 | if (yy > 0) |
| 3932 | { |
| 3933 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3934 | SCM_I_BIG_MPZ (x), yy); |
| 3935 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3936 | needs_adjustment = (2*rr >= yy); |
| 3937 | else |
| 3938 | needs_adjustment = (2*rr > yy); |
| 3939 | } |
| 3940 | else |
| 3941 | { |
| 3942 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
| 3943 | SCM_I_BIG_MPZ (x), -yy); |
| 3944 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
| 3945 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 3946 | needs_adjustment = (2*rr <= yy); |
| 3947 | else |
| 3948 | needs_adjustment = (2*rr < yy); |
| 3949 | } |
| 3950 | scm_remember_upto_here_1 (x); |
| 3951 | if (needs_adjustment) |
| 3952 | { |
| 3953 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
| 3954 | rr -= yy; |
| 3955 | } |
| 3956 | *qp = scm_i_normbig (q); |
| 3957 | *rp = SCM_I_MAKINUM (rr); |
| 3958 | } |
| 3959 | return; |
| 3960 | } |
| 3961 | else if (SCM_BIGP (y)) |
| 3962 | return scm_i_bigint_round_divide (x, y, qp, rp); |
| 3963 | else if (SCM_REALP (y)) |
| 3964 | return scm_i_inexact_round_divide |
| 3965 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
| 3966 | else if (SCM_FRACTIONP (y)) |
| 3967 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
| 3968 | else |
| 3969 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
| 3970 | s_scm_round_divide, qp, rp); |
| 3971 | } |
| 3972 | else if (SCM_REALP (x)) |
| 3973 | { |
| 3974 | if (SCM_REALP (y) || SCM_I_INUMP (y) || |
| 3975 | SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3976 | return scm_i_inexact_round_divide |
| 3977 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
| 3978 | else |
| 3979 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
| 3980 | s_scm_round_divide, qp, rp); |
| 3981 | } |
| 3982 | else if (SCM_FRACTIONP (x)) |
| 3983 | { |
| 3984 | if (SCM_REALP (y)) |
| 3985 | return scm_i_inexact_round_divide |
| 3986 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
| 3987 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
| 3988 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
| 3989 | else |
| 3990 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
| 3991 | s_scm_round_divide, qp, rp); |
| 3992 | } |
| 3993 | else |
| 3994 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
| 3995 | s_scm_round_divide, qp, rp); |
| 3996 | } |
| 3997 | |
| 3998 | static void |
| 3999 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
| 4000 | { |
| 4001 | if (SCM_UNLIKELY (y == 0)) |
| 4002 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ |
| 4003 | else |
| 4004 | { |
| 4005 | double q = scm_c_round (x / y); |
| 4006 | double r = x - q * y; |
| 4007 | *qp = scm_i_from_double (q); |
| 4008 | *rp = scm_i_from_double (r); |
| 4009 | } |
| 4010 | } |
| 4011 | |
| 4012 | /* Assumes that both x and y are bigints, though |
| 4013 | x might be able to fit into a fixnum. */ |
| 4014 | static void |
| 4015 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 4016 | { |
| 4017 | SCM q, r, r2; |
| 4018 | int cmp, needs_adjustment; |
| 4019 | |
| 4020 | /* Note that x might be small enough to fit into a |
| 4021 | fixnum, so we must not let it escape into the wild */ |
| 4022 | q = scm_i_mkbig (); |
| 4023 | r = scm_i_mkbig (); |
| 4024 | r2 = scm_i_mkbig (); |
| 4025 | |
| 4026 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
| 4027 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 4028 | scm_remember_upto_here_1 (x); |
| 4029 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ |
| 4030 | |
| 4031 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
| 4032 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
| 4033 | needs_adjustment = (cmp >= 0); |
| 4034 | else |
| 4035 | needs_adjustment = (cmp > 0); |
| 4036 | |
| 4037 | if (needs_adjustment) |
| 4038 | { |
| 4039 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
| 4040 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); |
| 4041 | } |
| 4042 | |
| 4043 | scm_remember_upto_here_2 (r2, y); |
| 4044 | *qp = scm_i_normbig (q); |
| 4045 | *rp = scm_i_normbig (r); |
| 4046 | } |
| 4047 | |
| 4048 | static void |
| 4049 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
| 4050 | { |
| 4051 | SCM r1; |
| 4052 | SCM xd = scm_denominator (x); |
| 4053 | SCM yd = scm_denominator (y); |
| 4054 | |
| 4055 | scm_round_divide (scm_product (scm_numerator (x), yd), |
| 4056 | scm_product (scm_numerator (y), xd), |
| 4057 | qp, &r1); |
| 4058 | *rp = scm_divide (r1, scm_product (xd, yd)); |
| 4059 | } |
| 4060 | |
| 4061 | |
| 4062 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
| 4063 | (SCM x, SCM y, SCM rest), |
| 4064 | "Return the greatest common divisor of all parameter values.\n" |
| 4065 | "If called without arguments, 0 is returned.") |
| 4066 | #define FUNC_NAME s_scm_i_gcd |
| 4067 | { |
| 4068 | while (!scm_is_null (rest)) |
| 4069 | { x = scm_gcd (x, y); |
| 4070 | y = scm_car (rest); |
| 4071 | rest = scm_cdr (rest); |
| 4072 | } |
| 4073 | return scm_gcd (x, y); |
| 4074 | } |
| 4075 | #undef FUNC_NAME |
| 4076 | |
| 4077 | #define s_gcd s_scm_i_gcd |
| 4078 | #define g_gcd g_scm_i_gcd |
| 4079 | |
| 4080 | SCM |
| 4081 | scm_gcd (SCM x, SCM y) |
| 4082 | { |
| 4083 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
| 4084 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
| 4085 | |
| 4086 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 4087 | { |
| 4088 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 4089 | { |
| 4090 | scm_t_inum xx = SCM_I_INUM (x); |
| 4091 | scm_t_inum yy = SCM_I_INUM (y); |
| 4092 | scm_t_inum u = xx < 0 ? -xx : xx; |
| 4093 | scm_t_inum v = yy < 0 ? -yy : yy; |
| 4094 | scm_t_inum result; |
| 4095 | if (SCM_UNLIKELY (xx == 0)) |
| 4096 | result = v; |
| 4097 | else if (SCM_UNLIKELY (yy == 0)) |
| 4098 | result = u; |
| 4099 | else |
| 4100 | { |
| 4101 | int k = 0; |
| 4102 | /* Determine a common factor 2^k */ |
| 4103 | while (((u | v) & 1) == 0) |
| 4104 | { |
| 4105 | k++; |
| 4106 | u >>= 1; |
| 4107 | v >>= 1; |
| 4108 | } |
| 4109 | /* Now, any factor 2^n can be eliminated */ |
| 4110 | if ((u & 1) == 0) |
| 4111 | while ((u & 1) == 0) |
| 4112 | u >>= 1; |
| 4113 | else |
| 4114 | while ((v & 1) == 0) |
| 4115 | v >>= 1; |
| 4116 | /* Both u and v are now odd. Subtract the smaller one |
| 4117 | from the larger one to produce an even number, remove |
| 4118 | more factors of two, and repeat. */ |
| 4119 | while (u != v) |
| 4120 | { |
| 4121 | if (u > v) |
| 4122 | { |
| 4123 | u -= v; |
| 4124 | while ((u & 1) == 0) |
| 4125 | u >>= 1; |
| 4126 | } |
| 4127 | else |
| 4128 | { |
| 4129 | v -= u; |
| 4130 | while ((v & 1) == 0) |
| 4131 | v >>= 1; |
| 4132 | } |
| 4133 | } |
| 4134 | result = u << k; |
| 4135 | } |
| 4136 | return (SCM_POSFIXABLE (result) |
| 4137 | ? SCM_I_MAKINUM (result) |
| 4138 | : scm_i_inum2big (result)); |
| 4139 | } |
| 4140 | else if (SCM_BIGP (y)) |
| 4141 | { |
| 4142 | SCM_SWAP (x, y); |
| 4143 | goto big_inum; |
| 4144 | } |
| 4145 | else if (SCM_REALP (y) && scm_is_integer (y)) |
| 4146 | goto handle_inexacts; |
| 4147 | else |
| 4148 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
| 4149 | } |
| 4150 | else if (SCM_BIGP (x)) |
| 4151 | { |
| 4152 | if (SCM_I_INUMP (y)) |
| 4153 | { |
| 4154 | scm_t_bits result; |
| 4155 | scm_t_inum yy; |
| 4156 | big_inum: |
| 4157 | yy = SCM_I_INUM (y); |
| 4158 | if (yy == 0) |
| 4159 | return scm_abs (x); |
| 4160 | if (yy < 0) |
| 4161 | yy = -yy; |
| 4162 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
| 4163 | scm_remember_upto_here_1 (x); |
| 4164 | return (SCM_POSFIXABLE (result) |
| 4165 | ? SCM_I_MAKINUM (result) |
| 4166 | : scm_from_unsigned_integer (result)); |
| 4167 | } |
| 4168 | else if (SCM_BIGP (y)) |
| 4169 | { |
| 4170 | SCM result = scm_i_mkbig (); |
| 4171 | mpz_gcd (SCM_I_BIG_MPZ (result), |
| 4172 | SCM_I_BIG_MPZ (x), |
| 4173 | SCM_I_BIG_MPZ (y)); |
| 4174 | scm_remember_upto_here_2 (x, y); |
| 4175 | return scm_i_normbig (result); |
| 4176 | } |
| 4177 | else if (SCM_REALP (y) && scm_is_integer (y)) |
| 4178 | goto handle_inexacts; |
| 4179 | else |
| 4180 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
| 4181 | } |
| 4182 | else if (SCM_REALP (x) && scm_is_integer (x)) |
| 4183 | { |
| 4184 | if (SCM_I_INUMP (y) || SCM_BIGP (y) |
| 4185 | || (SCM_REALP (y) && scm_is_integer (y))) |
| 4186 | { |
| 4187 | handle_inexacts: |
| 4188 | return scm_exact_to_inexact (scm_gcd (scm_inexact_to_exact (x), |
| 4189 | scm_inexact_to_exact (y))); |
| 4190 | } |
| 4191 | else |
| 4192 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
| 4193 | } |
| 4194 | else |
| 4195 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
| 4196 | } |
| 4197 | |
| 4198 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
| 4199 | (SCM x, SCM y, SCM rest), |
| 4200 | "Return the least common multiple of the arguments.\n" |
| 4201 | "If called without arguments, 1 is returned.") |
| 4202 | #define FUNC_NAME s_scm_i_lcm |
| 4203 | { |
| 4204 | while (!scm_is_null (rest)) |
| 4205 | { x = scm_lcm (x, y); |
| 4206 | y = scm_car (rest); |
| 4207 | rest = scm_cdr (rest); |
| 4208 | } |
| 4209 | return scm_lcm (x, y); |
| 4210 | } |
| 4211 | #undef FUNC_NAME |
| 4212 | |
| 4213 | #define s_lcm s_scm_i_lcm |
| 4214 | #define g_lcm g_scm_i_lcm |
| 4215 | |
| 4216 | SCM |
| 4217 | scm_lcm (SCM n1, SCM n2) |
| 4218 | { |
| 4219 | if (SCM_UNLIKELY (SCM_UNBNDP (n2))) |
| 4220 | return SCM_UNBNDP (n1) ? SCM_INUM1 : scm_abs (n1); |
| 4221 | |
| 4222 | if (SCM_LIKELY (SCM_I_INUMP (n1))) |
| 4223 | { |
| 4224 | if (SCM_LIKELY (SCM_I_INUMP (n2))) |
| 4225 | { |
| 4226 | SCM d = scm_gcd (n1, n2); |
| 4227 | if (scm_is_eq (d, SCM_INUM0)) |
| 4228 | return d; |
| 4229 | else |
| 4230 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); |
| 4231 | } |
| 4232 | else if (SCM_LIKELY (SCM_BIGP (n2))) |
| 4233 | { |
| 4234 | /* inum n1, big n2 */ |
| 4235 | inumbig: |
| 4236 | { |
| 4237 | SCM result = scm_i_mkbig (); |
| 4238 | scm_t_inum nn1 = SCM_I_INUM (n1); |
| 4239 | if (nn1 == 0) return SCM_INUM0; |
| 4240 | if (nn1 < 0) nn1 = - nn1; |
| 4241 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); |
| 4242 | scm_remember_upto_here_1 (n2); |
| 4243 | return result; |
| 4244 | } |
| 4245 | } |
| 4246 | else if (SCM_REALP (n2) && scm_is_integer (n2)) |
| 4247 | goto handle_inexacts; |
| 4248 | else |
| 4249 | SCM_WTA_DISPATCH_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
| 4250 | } |
| 4251 | else if (SCM_LIKELY (SCM_BIGP (n1))) |
| 4252 | { |
| 4253 | /* big n1 */ |
| 4254 | if (SCM_I_INUMP (n2)) |
| 4255 | { |
| 4256 | SCM_SWAP (n1, n2); |
| 4257 | goto inumbig; |
| 4258 | } |
| 4259 | else if (SCM_LIKELY (SCM_BIGP (n2))) |
| 4260 | { |
| 4261 | SCM result = scm_i_mkbig (); |
| 4262 | mpz_lcm(SCM_I_BIG_MPZ (result), |
| 4263 | SCM_I_BIG_MPZ (n1), |
| 4264 | SCM_I_BIG_MPZ (n2)); |
| 4265 | scm_remember_upto_here_2(n1, n2); |
| 4266 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ |
| 4267 | return result; |
| 4268 | } |
| 4269 | else if (SCM_REALP (n2) && scm_is_integer (n2)) |
| 4270 | goto handle_inexacts; |
| 4271 | else |
| 4272 | SCM_WTA_DISPATCH_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
| 4273 | } |
| 4274 | else if (SCM_REALP (n1) && scm_is_integer (n1)) |
| 4275 | { |
| 4276 | if (SCM_I_INUMP (n2) || SCM_BIGP (n2) |
| 4277 | || (SCM_REALP (n2) && scm_is_integer (n2))) |
| 4278 | { |
| 4279 | handle_inexacts: |
| 4280 | return scm_exact_to_inexact (scm_lcm (scm_inexact_to_exact (n1), |
| 4281 | scm_inexact_to_exact (n2))); |
| 4282 | } |
| 4283 | else |
| 4284 | SCM_WTA_DISPATCH_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
| 4285 | } |
| 4286 | else |
| 4287 | SCM_WTA_DISPATCH_2 (g_lcm, n1, n2, SCM_ARG1, s_lcm); |
| 4288 | } |
| 4289 | |
| 4290 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
| 4291 | |
| 4292 | Logand: |
| 4293 | X Y Result Method: |
| 4294 | (len) |
| 4295 | + + + x (map digit:logand X Y) |
| 4296 | + - + x (map digit:logand X (lognot (+ -1 Y))) |
| 4297 | - + + y (map digit:logand (lognot (+ -1 X)) Y) |
| 4298 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) |
| 4299 | |
| 4300 | Logior: |
| 4301 | X Y Result Method: |
| 4302 | |
| 4303 | + + + (map digit:logior X Y) |
| 4304 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) |
| 4305 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) |
| 4306 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) |
| 4307 | |
| 4308 | Logxor: |
| 4309 | X Y Result Method: |
| 4310 | |
| 4311 | + + + (map digit:logxor X Y) |
| 4312 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) |
| 4313 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) |
| 4314 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) |
| 4315 | |
| 4316 | Logtest: |
| 4317 | X Y Result |
| 4318 | |
| 4319 | + + (any digit:logand X Y) |
| 4320 | + - (any digit:logand X (lognot (+ -1 Y))) |
| 4321 | - + (any digit:logand (lognot (+ -1 X)) Y) |
| 4322 | - - #t |
| 4323 | |
| 4324 | */ |
| 4325 | |
| 4326 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
| 4327 | (SCM x, SCM y, SCM rest), |
| 4328 | "Return the bitwise AND of the integer arguments.\n\n" |
| 4329 | "@lisp\n" |
| 4330 | "(logand) @result{} -1\n" |
| 4331 | "(logand 7) @result{} 7\n" |
| 4332 | "(logand #b111 #b011 #b001) @result{} 1\n" |
| 4333 | "@end lisp") |
| 4334 | #define FUNC_NAME s_scm_i_logand |
| 4335 | { |
| 4336 | while (!scm_is_null (rest)) |
| 4337 | { x = scm_logand (x, y); |
| 4338 | y = scm_car (rest); |
| 4339 | rest = scm_cdr (rest); |
| 4340 | } |
| 4341 | return scm_logand (x, y); |
| 4342 | } |
| 4343 | #undef FUNC_NAME |
| 4344 | |
| 4345 | #define s_scm_logand s_scm_i_logand |
| 4346 | |
| 4347 | SCM scm_logand (SCM n1, SCM n2) |
| 4348 | #define FUNC_NAME s_scm_logand |
| 4349 | { |
| 4350 | scm_t_inum nn1; |
| 4351 | |
| 4352 | if (SCM_UNBNDP (n2)) |
| 4353 | { |
| 4354 | if (SCM_UNBNDP (n1)) |
| 4355 | return SCM_I_MAKINUM (-1); |
| 4356 | else if (!SCM_NUMBERP (n1)) |
| 4357 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
| 4358 | else if (SCM_NUMBERP (n1)) |
| 4359 | return n1; |
| 4360 | else |
| 4361 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
| 4362 | } |
| 4363 | |
| 4364 | if (SCM_I_INUMP (n1)) |
| 4365 | { |
| 4366 | nn1 = SCM_I_INUM (n1); |
| 4367 | if (SCM_I_INUMP (n2)) |
| 4368 | { |
| 4369 | scm_t_inum nn2 = SCM_I_INUM (n2); |
| 4370 | return SCM_I_MAKINUM (nn1 & nn2); |
| 4371 | } |
| 4372 | else if SCM_BIGP (n2) |
| 4373 | { |
| 4374 | intbig: |
| 4375 | if (nn1 == 0) |
| 4376 | return SCM_INUM0; |
| 4377 | { |
| 4378 | SCM result_z = scm_i_mkbig (); |
| 4379 | mpz_t nn1_z; |
| 4380 | mpz_init_set_si (nn1_z, nn1); |
| 4381 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); |
| 4382 | scm_remember_upto_here_1 (n2); |
| 4383 | mpz_clear (nn1_z); |
| 4384 | return scm_i_normbig (result_z); |
| 4385 | } |
| 4386 | } |
| 4387 | else |
| 4388 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); |
| 4389 | } |
| 4390 | else if (SCM_BIGP (n1)) |
| 4391 | { |
| 4392 | if (SCM_I_INUMP (n2)) |
| 4393 | { |
| 4394 | SCM_SWAP (n1, n2); |
| 4395 | nn1 = SCM_I_INUM (n1); |
| 4396 | goto intbig; |
| 4397 | } |
| 4398 | else if (SCM_BIGP (n2)) |
| 4399 | { |
| 4400 | SCM result_z = scm_i_mkbig (); |
| 4401 | mpz_and (SCM_I_BIG_MPZ (result_z), |
| 4402 | SCM_I_BIG_MPZ (n1), |
| 4403 | SCM_I_BIG_MPZ (n2)); |
| 4404 | scm_remember_upto_here_2 (n1, n2); |
| 4405 | return scm_i_normbig (result_z); |
| 4406 | } |
| 4407 | else |
| 4408 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); |
| 4409 | } |
| 4410 | else |
| 4411 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
| 4412 | } |
| 4413 | #undef FUNC_NAME |
| 4414 | |
| 4415 | |
| 4416 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
| 4417 | (SCM x, SCM y, SCM rest), |
| 4418 | "Return the bitwise OR of the integer arguments.\n\n" |
| 4419 | "@lisp\n" |
| 4420 | "(logior) @result{} 0\n" |
| 4421 | "(logior 7) @result{} 7\n" |
| 4422 | "(logior #b000 #b001 #b011) @result{} 3\n" |
| 4423 | "@end lisp") |
| 4424 | #define FUNC_NAME s_scm_i_logior |
| 4425 | { |
| 4426 | while (!scm_is_null (rest)) |
| 4427 | { x = scm_logior (x, y); |
| 4428 | y = scm_car (rest); |
| 4429 | rest = scm_cdr (rest); |
| 4430 | } |
| 4431 | return scm_logior (x, y); |
| 4432 | } |
| 4433 | #undef FUNC_NAME |
| 4434 | |
| 4435 | #define s_scm_logior s_scm_i_logior |
| 4436 | |
| 4437 | SCM scm_logior (SCM n1, SCM n2) |
| 4438 | #define FUNC_NAME s_scm_logior |
| 4439 | { |
| 4440 | scm_t_inum nn1; |
| 4441 | |
| 4442 | if (SCM_UNBNDP (n2)) |
| 4443 | { |
| 4444 | if (SCM_UNBNDP (n1)) |
| 4445 | return SCM_INUM0; |
| 4446 | else if (SCM_NUMBERP (n1)) |
| 4447 | return n1; |
| 4448 | else |
| 4449 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
| 4450 | } |
| 4451 | |
| 4452 | if (SCM_I_INUMP (n1)) |
| 4453 | { |
| 4454 | nn1 = SCM_I_INUM (n1); |
| 4455 | if (SCM_I_INUMP (n2)) |
| 4456 | { |
| 4457 | long nn2 = SCM_I_INUM (n2); |
| 4458 | return SCM_I_MAKINUM (nn1 | nn2); |
| 4459 | } |
| 4460 | else if (SCM_BIGP (n2)) |
| 4461 | { |
| 4462 | intbig: |
| 4463 | if (nn1 == 0) |
| 4464 | return n2; |
| 4465 | { |
| 4466 | SCM result_z = scm_i_mkbig (); |
| 4467 | mpz_t nn1_z; |
| 4468 | mpz_init_set_si (nn1_z, nn1); |
| 4469 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); |
| 4470 | scm_remember_upto_here_1 (n2); |
| 4471 | mpz_clear (nn1_z); |
| 4472 | return scm_i_normbig (result_z); |
| 4473 | } |
| 4474 | } |
| 4475 | else |
| 4476 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); |
| 4477 | } |
| 4478 | else if (SCM_BIGP (n1)) |
| 4479 | { |
| 4480 | if (SCM_I_INUMP (n2)) |
| 4481 | { |
| 4482 | SCM_SWAP (n1, n2); |
| 4483 | nn1 = SCM_I_INUM (n1); |
| 4484 | goto intbig; |
| 4485 | } |
| 4486 | else if (SCM_BIGP (n2)) |
| 4487 | { |
| 4488 | SCM result_z = scm_i_mkbig (); |
| 4489 | mpz_ior (SCM_I_BIG_MPZ (result_z), |
| 4490 | SCM_I_BIG_MPZ (n1), |
| 4491 | SCM_I_BIG_MPZ (n2)); |
| 4492 | scm_remember_upto_here_2 (n1, n2); |
| 4493 | return scm_i_normbig (result_z); |
| 4494 | } |
| 4495 | else |
| 4496 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); |
| 4497 | } |
| 4498 | else |
| 4499 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
| 4500 | } |
| 4501 | #undef FUNC_NAME |
| 4502 | |
| 4503 | |
| 4504 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
| 4505 | (SCM x, SCM y, SCM rest), |
| 4506 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
| 4507 | "set in the result if it is set in an odd number of arguments.\n" |
| 4508 | "@lisp\n" |
| 4509 | "(logxor) @result{} 0\n" |
| 4510 | "(logxor 7) @result{} 7\n" |
| 4511 | "(logxor #b000 #b001 #b011) @result{} 2\n" |
| 4512 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" |
| 4513 | "@end lisp") |
| 4514 | #define FUNC_NAME s_scm_i_logxor |
| 4515 | { |
| 4516 | while (!scm_is_null (rest)) |
| 4517 | { x = scm_logxor (x, y); |
| 4518 | y = scm_car (rest); |
| 4519 | rest = scm_cdr (rest); |
| 4520 | } |
| 4521 | return scm_logxor (x, y); |
| 4522 | } |
| 4523 | #undef FUNC_NAME |
| 4524 | |
| 4525 | #define s_scm_logxor s_scm_i_logxor |
| 4526 | |
| 4527 | SCM scm_logxor (SCM n1, SCM n2) |
| 4528 | #define FUNC_NAME s_scm_logxor |
| 4529 | { |
| 4530 | scm_t_inum nn1; |
| 4531 | |
| 4532 | if (SCM_UNBNDP (n2)) |
| 4533 | { |
| 4534 | if (SCM_UNBNDP (n1)) |
| 4535 | return SCM_INUM0; |
| 4536 | else if (SCM_NUMBERP (n1)) |
| 4537 | return n1; |
| 4538 | else |
| 4539 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
| 4540 | } |
| 4541 | |
| 4542 | if (SCM_I_INUMP (n1)) |
| 4543 | { |
| 4544 | nn1 = SCM_I_INUM (n1); |
| 4545 | if (SCM_I_INUMP (n2)) |
| 4546 | { |
| 4547 | scm_t_inum nn2 = SCM_I_INUM (n2); |
| 4548 | return SCM_I_MAKINUM (nn1 ^ nn2); |
| 4549 | } |
| 4550 | else if (SCM_BIGP (n2)) |
| 4551 | { |
| 4552 | intbig: |
| 4553 | { |
| 4554 | SCM result_z = scm_i_mkbig (); |
| 4555 | mpz_t nn1_z; |
| 4556 | mpz_init_set_si (nn1_z, nn1); |
| 4557 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); |
| 4558 | scm_remember_upto_here_1 (n2); |
| 4559 | mpz_clear (nn1_z); |
| 4560 | return scm_i_normbig (result_z); |
| 4561 | } |
| 4562 | } |
| 4563 | else |
| 4564 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); |
| 4565 | } |
| 4566 | else if (SCM_BIGP (n1)) |
| 4567 | { |
| 4568 | if (SCM_I_INUMP (n2)) |
| 4569 | { |
| 4570 | SCM_SWAP (n1, n2); |
| 4571 | nn1 = SCM_I_INUM (n1); |
| 4572 | goto intbig; |
| 4573 | } |
| 4574 | else if (SCM_BIGP (n2)) |
| 4575 | { |
| 4576 | SCM result_z = scm_i_mkbig (); |
| 4577 | mpz_xor (SCM_I_BIG_MPZ (result_z), |
| 4578 | SCM_I_BIG_MPZ (n1), |
| 4579 | SCM_I_BIG_MPZ (n2)); |
| 4580 | scm_remember_upto_here_2 (n1, n2); |
| 4581 | return scm_i_normbig (result_z); |
| 4582 | } |
| 4583 | else |
| 4584 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); |
| 4585 | } |
| 4586 | else |
| 4587 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
| 4588 | } |
| 4589 | #undef FUNC_NAME |
| 4590 | |
| 4591 | |
| 4592 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
| 4593 | (SCM j, SCM k), |
| 4594 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
| 4595 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" |
| 4596 | "without actually calculating the @code{logand}, just testing\n" |
| 4597 | "for non-zero.\n" |
| 4598 | "\n" |
| 4599 | "@lisp\n" |
| 4600 | "(logtest #b0100 #b1011) @result{} #f\n" |
| 4601 | "(logtest #b0100 #b0111) @result{} #t\n" |
| 4602 | "@end lisp") |
| 4603 | #define FUNC_NAME s_scm_logtest |
| 4604 | { |
| 4605 | scm_t_inum nj; |
| 4606 | |
| 4607 | if (SCM_I_INUMP (j)) |
| 4608 | { |
| 4609 | nj = SCM_I_INUM (j); |
| 4610 | if (SCM_I_INUMP (k)) |
| 4611 | { |
| 4612 | scm_t_inum nk = SCM_I_INUM (k); |
| 4613 | return scm_from_bool (nj & nk); |
| 4614 | } |
| 4615 | else if (SCM_BIGP (k)) |
| 4616 | { |
| 4617 | intbig: |
| 4618 | if (nj == 0) |
| 4619 | return SCM_BOOL_F; |
| 4620 | { |
| 4621 | SCM result; |
| 4622 | mpz_t nj_z; |
| 4623 | mpz_init_set_si (nj_z, nj); |
| 4624 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); |
| 4625 | scm_remember_upto_here_1 (k); |
| 4626 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
| 4627 | mpz_clear (nj_z); |
| 4628 | return result; |
| 4629 | } |
| 4630 | } |
| 4631 | else |
| 4632 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); |
| 4633 | } |
| 4634 | else if (SCM_BIGP (j)) |
| 4635 | { |
| 4636 | if (SCM_I_INUMP (k)) |
| 4637 | { |
| 4638 | SCM_SWAP (j, k); |
| 4639 | nj = SCM_I_INUM (j); |
| 4640 | goto intbig; |
| 4641 | } |
| 4642 | else if (SCM_BIGP (k)) |
| 4643 | { |
| 4644 | SCM result; |
| 4645 | mpz_t result_z; |
| 4646 | mpz_init (result_z); |
| 4647 | mpz_and (result_z, |
| 4648 | SCM_I_BIG_MPZ (j), |
| 4649 | SCM_I_BIG_MPZ (k)); |
| 4650 | scm_remember_upto_here_2 (j, k); |
| 4651 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
| 4652 | mpz_clear (result_z); |
| 4653 | return result; |
| 4654 | } |
| 4655 | else |
| 4656 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); |
| 4657 | } |
| 4658 | else |
| 4659 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); |
| 4660 | } |
| 4661 | #undef FUNC_NAME |
| 4662 | |
| 4663 | |
| 4664 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
| 4665 | (SCM index, SCM j), |
| 4666 | "Test whether bit number @var{index} in @var{j} is set.\n" |
| 4667 | "@var{index} starts from 0 for the least significant bit.\n" |
| 4668 | "\n" |
| 4669 | "@lisp\n" |
| 4670 | "(logbit? 0 #b1101) @result{} #t\n" |
| 4671 | "(logbit? 1 #b1101) @result{} #f\n" |
| 4672 | "(logbit? 2 #b1101) @result{} #t\n" |
| 4673 | "(logbit? 3 #b1101) @result{} #t\n" |
| 4674 | "(logbit? 4 #b1101) @result{} #f\n" |
| 4675 | "@end lisp") |
| 4676 | #define FUNC_NAME s_scm_logbit_p |
| 4677 | { |
| 4678 | unsigned long int iindex; |
| 4679 | iindex = scm_to_ulong (index); |
| 4680 | |
| 4681 | if (SCM_I_INUMP (j)) |
| 4682 | { |
| 4683 | if (iindex < SCM_LONG_BIT - 1) |
| 4684 | /* Arrange for the number to be converted to unsigned before |
| 4685 | checking the bit, to ensure that we're testing the bit in a |
| 4686 | two's complement representation (regardless of the native |
| 4687 | representation. */ |
| 4688 | return scm_from_bool ((1UL << iindex) & SCM_I_INUM (j)); |
| 4689 | else |
| 4690 | /* Portably check the sign. */ |
| 4691 | return scm_from_bool (SCM_I_INUM (j) < 0); |
| 4692 | } |
| 4693 | else if (SCM_BIGP (j)) |
| 4694 | { |
| 4695 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); |
| 4696 | scm_remember_upto_here_1 (j); |
| 4697 | return scm_from_bool (val); |
| 4698 | } |
| 4699 | else |
| 4700 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
| 4701 | } |
| 4702 | #undef FUNC_NAME |
| 4703 | |
| 4704 | |
| 4705 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
| 4706 | (SCM n), |
| 4707 | "Return the integer which is the ones-complement of the integer\n" |
| 4708 | "argument.\n" |
| 4709 | "\n" |
| 4710 | "@lisp\n" |
| 4711 | "(number->string (lognot #b10000000) 2)\n" |
| 4712 | " @result{} \"-10000001\"\n" |
| 4713 | "(number->string (lognot #b0) 2)\n" |
| 4714 | " @result{} \"-1\"\n" |
| 4715 | "@end lisp") |
| 4716 | #define FUNC_NAME s_scm_lognot |
| 4717 | { |
| 4718 | if (SCM_I_INUMP (n)) { |
| 4719 | /* No overflow here, just need to toggle all the bits making up the inum. |
| 4720 | Enhancement: No need to strip the tag and add it back, could just xor |
| 4721 | a block of 1 bits, if that worked with the various debug versions of |
| 4722 | the SCM typedef. */ |
| 4723 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
| 4724 | |
| 4725 | } else if (SCM_BIGP (n)) { |
| 4726 | SCM result = scm_i_mkbig (); |
| 4727 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); |
| 4728 | scm_remember_upto_here_1 (n); |
| 4729 | return result; |
| 4730 | |
| 4731 | } else { |
| 4732 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
| 4733 | } |
| 4734 | } |
| 4735 | #undef FUNC_NAME |
| 4736 | |
| 4737 | /* returns 0 if IN is not an integer. OUT must already be |
| 4738 | initialized. */ |
| 4739 | static int |
| 4740 | coerce_to_big (SCM in, mpz_t out) |
| 4741 | { |
| 4742 | if (SCM_BIGP (in)) |
| 4743 | mpz_set (out, SCM_I_BIG_MPZ (in)); |
| 4744 | else if (SCM_I_INUMP (in)) |
| 4745 | mpz_set_si (out, SCM_I_INUM (in)); |
| 4746 | else |
| 4747 | return 0; |
| 4748 | |
| 4749 | return 1; |
| 4750 | } |
| 4751 | |
| 4752 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
| 4753 | (SCM n, SCM k, SCM m), |
| 4754 | "Return @var{n} raised to the integer exponent\n" |
| 4755 | "@var{k}, modulo @var{m}.\n" |
| 4756 | "\n" |
| 4757 | "@lisp\n" |
| 4758 | "(modulo-expt 2 3 5)\n" |
| 4759 | " @result{} 3\n" |
| 4760 | "@end lisp") |
| 4761 | #define FUNC_NAME s_scm_modulo_expt |
| 4762 | { |
| 4763 | mpz_t n_tmp; |
| 4764 | mpz_t k_tmp; |
| 4765 | mpz_t m_tmp; |
| 4766 | |
| 4767 | /* There are two classes of error we might encounter -- |
| 4768 | 1) Math errors, which we'll report by calling scm_num_overflow, |
| 4769 | and |
| 4770 | 2) wrong-type errors, which of course we'll report by calling |
| 4771 | SCM_WRONG_TYPE_ARG. |
| 4772 | We don't report those errors immediately, however; instead we do |
| 4773 | some cleanup first. These variables tell us which error (if |
| 4774 | any) we should report after cleaning up. |
| 4775 | */ |
| 4776 | int report_overflow = 0; |
| 4777 | |
| 4778 | int position_of_wrong_type = 0; |
| 4779 | SCM value_of_wrong_type = SCM_INUM0; |
| 4780 | |
| 4781 | SCM result = SCM_UNDEFINED; |
| 4782 | |
| 4783 | mpz_init (n_tmp); |
| 4784 | mpz_init (k_tmp); |
| 4785 | mpz_init (m_tmp); |
| 4786 | |
| 4787 | if (scm_is_eq (m, SCM_INUM0)) |
| 4788 | { |
| 4789 | report_overflow = 1; |
| 4790 | goto cleanup; |
| 4791 | } |
| 4792 | |
| 4793 | if (!coerce_to_big (n, n_tmp)) |
| 4794 | { |
| 4795 | value_of_wrong_type = n; |
| 4796 | position_of_wrong_type = 1; |
| 4797 | goto cleanup; |
| 4798 | } |
| 4799 | |
| 4800 | if (!coerce_to_big (k, k_tmp)) |
| 4801 | { |
| 4802 | value_of_wrong_type = k; |
| 4803 | position_of_wrong_type = 2; |
| 4804 | goto cleanup; |
| 4805 | } |
| 4806 | |
| 4807 | if (!coerce_to_big (m, m_tmp)) |
| 4808 | { |
| 4809 | value_of_wrong_type = m; |
| 4810 | position_of_wrong_type = 3; |
| 4811 | goto cleanup; |
| 4812 | } |
| 4813 | |
| 4814 | /* if the exponent K is negative, and we simply call mpz_powm, we |
| 4815 | will get a divide-by-zero exception when an inverse 1/n mod m |
| 4816 | doesn't exist (or is not unique). Since exceptions are hard to |
| 4817 | handle, we'll attempt the inversion "by hand" -- that way, we get |
| 4818 | a simple failure code, which is easy to handle. */ |
| 4819 | |
| 4820 | if (-1 == mpz_sgn (k_tmp)) |
| 4821 | { |
| 4822 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) |
| 4823 | { |
| 4824 | report_overflow = 1; |
| 4825 | goto cleanup; |
| 4826 | } |
| 4827 | mpz_neg (k_tmp, k_tmp); |
| 4828 | } |
| 4829 | |
| 4830 | result = scm_i_mkbig (); |
| 4831 | mpz_powm (SCM_I_BIG_MPZ (result), |
| 4832 | n_tmp, |
| 4833 | k_tmp, |
| 4834 | m_tmp); |
| 4835 | |
| 4836 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
| 4837 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); |
| 4838 | |
| 4839 | cleanup: |
| 4840 | mpz_clear (m_tmp); |
| 4841 | mpz_clear (k_tmp); |
| 4842 | mpz_clear (n_tmp); |
| 4843 | |
| 4844 | if (report_overflow) |
| 4845 | scm_num_overflow (FUNC_NAME); |
| 4846 | |
| 4847 | if (position_of_wrong_type) |
| 4848 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, |
| 4849 | value_of_wrong_type); |
| 4850 | |
| 4851 | return scm_i_normbig (result); |
| 4852 | } |
| 4853 | #undef FUNC_NAME |
| 4854 | |
| 4855 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
| 4856 | (SCM n, SCM k), |
| 4857 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
| 4858 | "exact integer, @var{n} can be any number.\n" |
| 4859 | "\n" |
| 4860 | "Negative @var{k} is supported, and results in\n" |
| 4861 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" |
| 4862 | "@math{@var{n}^0} is 1, as usual, and that\n" |
| 4863 | "includes @math{0^0} is 1.\n" |
| 4864 | "\n" |
| 4865 | "@lisp\n" |
| 4866 | "(integer-expt 2 5) @result{} 32\n" |
| 4867 | "(integer-expt -3 3) @result{} -27\n" |
| 4868 | "(integer-expt 5 -3) @result{} 1/125\n" |
| 4869 | "(integer-expt 0 0) @result{} 1\n" |
| 4870 | "@end lisp") |
| 4871 | #define FUNC_NAME s_scm_integer_expt |
| 4872 | { |
| 4873 | scm_t_inum i2 = 0; |
| 4874 | SCM z_i2 = SCM_BOOL_F; |
| 4875 | int i2_is_big = 0; |
| 4876 | SCM acc = SCM_I_MAKINUM (1L); |
| 4877 | |
| 4878 | /* Specifically refrain from checking the type of the first argument. |
| 4879 | This allows us to exponentiate any object that can be multiplied. |
| 4880 | If we must raise to a negative power, we must also be able to |
| 4881 | take its reciprocal. */ |
| 4882 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) |
| 4883 | SCM_WRONG_TYPE_ARG (2, k); |
| 4884 | |
| 4885 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
| 4886 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ |
| 4887 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) |
| 4888 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; |
| 4889 | /* The next check is necessary only because R6RS specifies different |
| 4890 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, |
| 4891 | we simply skip this case and move on. */ |
| 4892 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) |
| 4893 | { |
| 4894 | /* k cannot be 0 at this point, because we |
| 4895 | have already checked for that case above */ |
| 4896 | if (scm_is_true (scm_positive_p (k))) |
| 4897 | return n; |
| 4898 | else /* return NaN for (0 ^ k) for negative k per R6RS */ |
| 4899 | return scm_nan (); |
| 4900 | } |
| 4901 | else if (SCM_FRACTIONP (n)) |
| 4902 | { |
| 4903 | /* Optimize the fraction case by (a/b)^k ==> (a^k)/(b^k), to avoid |
| 4904 | needless reduction of intermediate products to lowest terms. |
| 4905 | If a and b have no common factors, then a^k and b^k have no |
| 4906 | common factors. Use 'scm_i_make_ratio_already_reduced' to |
| 4907 | construct the final result, so that no gcd computations are |
| 4908 | needed to exponentiate a fraction. */ |
| 4909 | if (scm_is_true (scm_positive_p (k))) |
| 4910 | return scm_i_make_ratio_already_reduced |
| 4911 | (scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k), |
| 4912 | scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k)); |
| 4913 | else |
| 4914 | { |
| 4915 | k = scm_difference (k, SCM_UNDEFINED); |
| 4916 | return scm_i_make_ratio_already_reduced |
| 4917 | (scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k), |
| 4918 | scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k)); |
| 4919 | } |
| 4920 | } |
| 4921 | |
| 4922 | if (SCM_I_INUMP (k)) |
| 4923 | i2 = SCM_I_INUM (k); |
| 4924 | else if (SCM_BIGP (k)) |
| 4925 | { |
| 4926 | z_i2 = scm_i_clonebig (k, 1); |
| 4927 | scm_remember_upto_here_1 (k); |
| 4928 | i2_is_big = 1; |
| 4929 | } |
| 4930 | else |
| 4931 | SCM_WRONG_TYPE_ARG (2, k); |
| 4932 | |
| 4933 | if (i2_is_big) |
| 4934 | { |
| 4935 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
| 4936 | { |
| 4937 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); |
| 4938 | n = scm_divide (n, SCM_UNDEFINED); |
| 4939 | } |
| 4940 | while (1) |
| 4941 | { |
| 4942 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) |
| 4943 | { |
| 4944 | return acc; |
| 4945 | } |
| 4946 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) |
| 4947 | { |
| 4948 | return scm_product (acc, n); |
| 4949 | } |
| 4950 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) |
| 4951 | acc = scm_product (acc, n); |
| 4952 | n = scm_product (n, n); |
| 4953 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); |
| 4954 | } |
| 4955 | } |
| 4956 | else |
| 4957 | { |
| 4958 | if (i2 < 0) |
| 4959 | { |
| 4960 | i2 = -i2; |
| 4961 | n = scm_divide (n, SCM_UNDEFINED); |
| 4962 | } |
| 4963 | while (1) |
| 4964 | { |
| 4965 | if (0 == i2) |
| 4966 | return acc; |
| 4967 | if (1 == i2) |
| 4968 | return scm_product (acc, n); |
| 4969 | if (i2 & 1) |
| 4970 | acc = scm_product (acc, n); |
| 4971 | n = scm_product (n, n); |
| 4972 | i2 >>= 1; |
| 4973 | } |
| 4974 | } |
| 4975 | } |
| 4976 | #undef FUNC_NAME |
| 4977 | |
| 4978 | /* Efficiently compute (N * 2^COUNT), |
| 4979 | where N is an exact integer, and COUNT > 0. */ |
| 4980 | static SCM |
| 4981 | left_shift_exact_integer (SCM n, long count) |
| 4982 | { |
| 4983 | if (SCM_I_INUMP (n)) |
| 4984 | { |
| 4985 | scm_t_inum nn = SCM_I_INUM (n); |
| 4986 | |
| 4987 | /* Left shift of count >= SCM_I_FIXNUM_BIT-1 will almost[*] always |
| 4988 | overflow a non-zero fixnum. For smaller shifts we check the |
| 4989 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're |
| 4990 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. |
| 4991 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - count)". |
| 4992 | |
| 4993 | [*] There's one exception: |
| 4994 | (-1) << SCM_I_FIXNUM_BIT-1 == SCM_MOST_NEGATIVE_FIXNUM */ |
| 4995 | |
| 4996 | if (nn == 0) |
| 4997 | return n; |
| 4998 | else if (count < SCM_I_FIXNUM_BIT-1 && |
| 4999 | ((scm_t_bits) (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - count)) + 1) |
| 5000 | <= 1)) |
| 5001 | return SCM_I_MAKINUM (nn < 0 ? -(-nn << count) : (nn << count)); |
| 5002 | else |
| 5003 | { |
| 5004 | SCM result = scm_i_inum2big (nn); |
| 5005 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
| 5006 | count); |
| 5007 | return scm_i_normbig (result); |
| 5008 | } |
| 5009 | } |
| 5010 | else if (SCM_BIGP (n)) |
| 5011 | { |
| 5012 | SCM result = scm_i_mkbig (); |
| 5013 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), count); |
| 5014 | scm_remember_upto_here_1 (n); |
| 5015 | return result; |
| 5016 | } |
| 5017 | else |
| 5018 | assert (0); |
| 5019 | } |
| 5020 | |
| 5021 | /* Efficiently compute floor (N / 2^COUNT), |
| 5022 | where N is an exact integer and COUNT > 0. */ |
| 5023 | static SCM |
| 5024 | floor_right_shift_exact_integer (SCM n, long count) |
| 5025 | { |
| 5026 | if (SCM_I_INUMP (n)) |
| 5027 | { |
| 5028 | scm_t_inum nn = SCM_I_INUM (n); |
| 5029 | |
| 5030 | if (count >= SCM_I_FIXNUM_BIT) |
| 5031 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM (-1)); |
| 5032 | else |
| 5033 | return SCM_I_MAKINUM (SCM_SRS (nn, count)); |
| 5034 | } |
| 5035 | else if (SCM_BIGP (n)) |
| 5036 | { |
| 5037 | SCM result = scm_i_mkbig (); |
| 5038 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), |
| 5039 | count); |
| 5040 | scm_remember_upto_here_1 (n); |
| 5041 | return scm_i_normbig (result); |
| 5042 | } |
| 5043 | else |
| 5044 | assert (0); |
| 5045 | } |
| 5046 | |
| 5047 | /* Efficiently compute round (N / 2^COUNT), |
| 5048 | where N is an exact integer and COUNT > 0. */ |
| 5049 | static SCM |
| 5050 | round_right_shift_exact_integer (SCM n, long count) |
| 5051 | { |
| 5052 | if (SCM_I_INUMP (n)) |
| 5053 | { |
| 5054 | if (count >= SCM_I_FIXNUM_BIT) |
| 5055 | return SCM_INUM0; |
| 5056 | else |
| 5057 | { |
| 5058 | scm_t_inum nn = SCM_I_INUM (n); |
| 5059 | scm_t_inum qq = SCM_SRS (nn, count); |
| 5060 | |
| 5061 | if (0 == (nn & (1L << (count-1)))) |
| 5062 | return SCM_I_MAKINUM (qq); /* round down */ |
| 5063 | else if (nn & ((1L << (count-1)) - 1)) |
| 5064 | return SCM_I_MAKINUM (qq + 1); /* round up */ |
| 5065 | else |
| 5066 | return SCM_I_MAKINUM ((~1L) & (qq + 1)); /* round to even */ |
| 5067 | } |
| 5068 | } |
| 5069 | else if (SCM_BIGP (n)) |
| 5070 | { |
| 5071 | SCM q = scm_i_mkbig (); |
| 5072 | |
| 5073 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), count); |
| 5074 | if (mpz_tstbit (SCM_I_BIG_MPZ (n), count-1) |
| 5075 | && (mpz_odd_p (SCM_I_BIG_MPZ (q)) |
| 5076 | || (mpz_scan1 (SCM_I_BIG_MPZ (n), 0) < count-1))) |
| 5077 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
| 5078 | scm_remember_upto_here_1 (n); |
| 5079 | return scm_i_normbig (q); |
| 5080 | } |
| 5081 | else |
| 5082 | assert (0); |
| 5083 | } |
| 5084 | |
| 5085 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
| 5086 | (SCM n, SCM count), |
| 5087 | "Return @math{floor(@var{n} * 2^@var{count})}.\n" |
| 5088 | "@var{n} and @var{count} must be exact integers.\n" |
| 5089 | "\n" |
| 5090 | "With @var{n} viewed as an infinite-precision twos-complement\n" |
| 5091 | "integer, @code{ash} means a left shift introducing zero bits\n" |
| 5092 | "when @var{count} is positive, or a right shift dropping bits\n" |
| 5093 | "when @var{count} is negative. This is an ``arithmetic'' shift.\n" |
| 5094 | "\n" |
| 5095 | "@lisp\n" |
| 5096 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
| 5097 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" |
| 5098 | "\n" |
| 5099 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" |
| 5100 | "(ash -23 -2) @result{} -6\n" |
| 5101 | "@end lisp") |
| 5102 | #define FUNC_NAME s_scm_ash |
| 5103 | { |
| 5104 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) |
| 5105 | { |
| 5106 | long bits_to_shift = scm_to_long (count); |
| 5107 | |
| 5108 | if (bits_to_shift > 0) |
| 5109 | return left_shift_exact_integer (n, bits_to_shift); |
| 5110 | else if (SCM_LIKELY (bits_to_shift < 0)) |
| 5111 | return floor_right_shift_exact_integer (n, -bits_to_shift); |
| 5112 | else |
| 5113 | return n; |
| 5114 | } |
| 5115 | else |
| 5116 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
| 5117 | } |
| 5118 | #undef FUNC_NAME |
| 5119 | |
| 5120 | SCM_DEFINE (scm_round_ash, "round-ash", 2, 0, 0, |
| 5121 | (SCM n, SCM count), |
| 5122 | "Return @math{round(@var{n} * 2^@var{count})}.\n" |
| 5123 | "@var{n} and @var{count} must be exact integers.\n" |
| 5124 | "\n" |
| 5125 | "With @var{n} viewed as an infinite-precision twos-complement\n" |
| 5126 | "integer, @code{round-ash} means a left shift introducing zero\n" |
| 5127 | "bits when @var{count} is positive, or a right shift rounding\n" |
| 5128 | "to the nearest integer (with ties going to the nearest even\n" |
| 5129 | "integer) when @var{count} is negative. This is a rounded\n" |
| 5130 | "``arithmetic'' shift.\n" |
| 5131 | "\n" |
| 5132 | "@lisp\n" |
| 5133 | "(number->string (round-ash #b1 3) 2) @result{} \"1000\"\n" |
| 5134 | "(number->string (round-ash #b1010 -1) 2) @result{} \"101\"\n" |
| 5135 | "(number->string (round-ash #b1010 -2) 2) @result{} \"10\"\n" |
| 5136 | "(number->string (round-ash #b1011 -2) 2) @result{} \"11\"\n" |
| 5137 | "(number->string (round-ash #b1101 -2) 2) @result{} \"11\"\n" |
| 5138 | "(number->string (round-ash #b1110 -2) 2) @result{} \"100\"\n" |
| 5139 | "@end lisp") |
| 5140 | #define FUNC_NAME s_scm_round_ash |
| 5141 | { |
| 5142 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) |
| 5143 | { |
| 5144 | long bits_to_shift = scm_to_long (count); |
| 5145 | |
| 5146 | if (bits_to_shift > 0) |
| 5147 | return left_shift_exact_integer (n, bits_to_shift); |
| 5148 | else if (SCM_LIKELY (bits_to_shift < 0)) |
| 5149 | return round_right_shift_exact_integer (n, -bits_to_shift); |
| 5150 | else |
| 5151 | return n; |
| 5152 | } |
| 5153 | else |
| 5154 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
| 5155 | } |
| 5156 | #undef FUNC_NAME |
| 5157 | |
| 5158 | |
| 5159 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
| 5160 | (SCM n, SCM start, SCM end), |
| 5161 | "Return the integer composed of the @var{start} (inclusive)\n" |
| 5162 | "through @var{end} (exclusive) bits of @var{n}. The\n" |
| 5163 | "@var{start}th bit becomes the 0-th bit in the result.\n" |
| 5164 | "\n" |
| 5165 | "@lisp\n" |
| 5166 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" |
| 5167 | " @result{} \"1010\"\n" |
| 5168 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" |
| 5169 | " @result{} \"10110\"\n" |
| 5170 | "@end lisp") |
| 5171 | #define FUNC_NAME s_scm_bit_extract |
| 5172 | { |
| 5173 | unsigned long int istart, iend, bits; |
| 5174 | istart = scm_to_ulong (start); |
| 5175 | iend = scm_to_ulong (end); |
| 5176 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
| 5177 | |
| 5178 | /* how many bits to keep */ |
| 5179 | bits = iend - istart; |
| 5180 | |
| 5181 | if (SCM_I_INUMP (n)) |
| 5182 | { |
| 5183 | scm_t_inum in = SCM_I_INUM (n); |
| 5184 | |
| 5185 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to |
| 5186 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
| 5187 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
| 5188 | |
| 5189 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
| 5190 | { |
| 5191 | /* Since we emulate two's complement encoded numbers, this |
| 5192 | * special case requires us to produce a result that has |
| 5193 | * more bits than can be stored in a fixnum. |
| 5194 | */ |
| 5195 | SCM result = scm_i_inum2big (in); |
| 5196 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
| 5197 | bits); |
| 5198 | return result; |
| 5199 | } |
| 5200 | |
| 5201 | /* mask down to requisite bits */ |
| 5202 | bits = min (bits, SCM_I_FIXNUM_BIT); |
| 5203 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
| 5204 | } |
| 5205 | else if (SCM_BIGP (n)) |
| 5206 | { |
| 5207 | SCM result; |
| 5208 | if (bits == 1) |
| 5209 | { |
| 5210 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
| 5211 | } |
| 5212 | else |
| 5213 | { |
| 5214 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when |
| 5215 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get |
| 5216 | such bits into a ulong. */ |
| 5217 | result = scm_i_mkbig (); |
| 5218 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); |
| 5219 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); |
| 5220 | result = scm_i_normbig (result); |
| 5221 | } |
| 5222 | scm_remember_upto_here_1 (n); |
| 5223 | return result; |
| 5224 | } |
| 5225 | else |
| 5226 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
| 5227 | } |
| 5228 | #undef FUNC_NAME |
| 5229 | |
| 5230 | |
| 5231 | static const char scm_logtab[] = { |
| 5232 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 |
| 5233 | }; |
| 5234 | |
| 5235 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
| 5236 | (SCM n), |
| 5237 | "Return the number of bits in integer @var{n}. If integer is\n" |
| 5238 | "positive, the 1-bits in its binary representation are counted.\n" |
| 5239 | "If negative, the 0-bits in its two's-complement binary\n" |
| 5240 | "representation are counted. If 0, 0 is returned.\n" |
| 5241 | "\n" |
| 5242 | "@lisp\n" |
| 5243 | "(logcount #b10101010)\n" |
| 5244 | " @result{} 4\n" |
| 5245 | "(logcount 0)\n" |
| 5246 | " @result{} 0\n" |
| 5247 | "(logcount -2)\n" |
| 5248 | " @result{} 1\n" |
| 5249 | "@end lisp") |
| 5250 | #define FUNC_NAME s_scm_logcount |
| 5251 | { |
| 5252 | if (SCM_I_INUMP (n)) |
| 5253 | { |
| 5254 | unsigned long c = 0; |
| 5255 | scm_t_inum nn = SCM_I_INUM (n); |
| 5256 | if (nn < 0) |
| 5257 | nn = -1 - nn; |
| 5258 | while (nn) |
| 5259 | { |
| 5260 | c += scm_logtab[15 & nn]; |
| 5261 | nn >>= 4; |
| 5262 | } |
| 5263 | return SCM_I_MAKINUM (c); |
| 5264 | } |
| 5265 | else if (SCM_BIGP (n)) |
| 5266 | { |
| 5267 | unsigned long count; |
| 5268 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
| 5269 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); |
| 5270 | else |
| 5271 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
| 5272 | scm_remember_upto_here_1 (n); |
| 5273 | return SCM_I_MAKINUM (count); |
| 5274 | } |
| 5275 | else |
| 5276 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
| 5277 | } |
| 5278 | #undef FUNC_NAME |
| 5279 | |
| 5280 | |
| 5281 | static const char scm_ilentab[] = { |
| 5282 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 |
| 5283 | }; |
| 5284 | |
| 5285 | |
| 5286 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
| 5287 | (SCM n), |
| 5288 | "Return the number of bits necessary to represent @var{n}.\n" |
| 5289 | "\n" |
| 5290 | "@lisp\n" |
| 5291 | "(integer-length #b10101010)\n" |
| 5292 | " @result{} 8\n" |
| 5293 | "(integer-length 0)\n" |
| 5294 | " @result{} 0\n" |
| 5295 | "(integer-length #b1111)\n" |
| 5296 | " @result{} 4\n" |
| 5297 | "@end lisp") |
| 5298 | #define FUNC_NAME s_scm_integer_length |
| 5299 | { |
| 5300 | if (SCM_I_INUMP (n)) |
| 5301 | { |
| 5302 | unsigned long c = 0; |
| 5303 | unsigned int l = 4; |
| 5304 | scm_t_inum nn = SCM_I_INUM (n); |
| 5305 | if (nn < 0) |
| 5306 | nn = -1 - nn; |
| 5307 | while (nn) |
| 5308 | { |
| 5309 | c += 4; |
| 5310 | l = scm_ilentab [15 & nn]; |
| 5311 | nn >>= 4; |
| 5312 | } |
| 5313 | return SCM_I_MAKINUM (c - 4 + l); |
| 5314 | } |
| 5315 | else if (SCM_BIGP (n)) |
| 5316 | { |
| 5317 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we |
| 5318 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is |
| 5319 | 1 too big, so check for that and adjust. */ |
| 5320 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); |
| 5321 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 |
| 5322 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ |
| 5323 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) |
| 5324 | size--; |
| 5325 | scm_remember_upto_here_1 (n); |
| 5326 | return SCM_I_MAKINUM (size); |
| 5327 | } |
| 5328 | else |
| 5329 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
| 5330 | } |
| 5331 | #undef FUNC_NAME |
| 5332 | |
| 5333 | /*** NUMBERS -> STRINGS ***/ |
| 5334 | #define SCM_MAX_DBL_RADIX 36 |
| 5335 | |
| 5336 | /* use this array as a way to generate a single digit */ |
| 5337 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
| 5338 | |
| 5339 | static mpz_t dbl_minimum_normal_mantissa; |
| 5340 | |
| 5341 | static size_t |
| 5342 | idbl2str (double dbl, char *a, int radix) |
| 5343 | { |
| 5344 | int ch = 0; |
| 5345 | |
| 5346 | if (radix < 2 || radix > SCM_MAX_DBL_RADIX) |
| 5347 | /* revert to existing behavior */ |
| 5348 | radix = 10; |
| 5349 | |
| 5350 | if (isinf (dbl)) |
| 5351 | { |
| 5352 | strcpy (a, (dbl > 0.0) ? "+inf.0" : "-inf.0"); |
| 5353 | return 6; |
| 5354 | } |
| 5355 | else if (dbl > 0.0) |
| 5356 | ; |
| 5357 | else if (dbl < 0.0) |
| 5358 | { |
| 5359 | dbl = -dbl; |
| 5360 | a[ch++] = '-'; |
| 5361 | } |
| 5362 | else if (dbl == 0.0) |
| 5363 | { |
| 5364 | if (copysign (1.0, dbl) < 0.0) |
| 5365 | a[ch++] = '-'; |
| 5366 | strcpy (a + ch, "0.0"); |
| 5367 | return ch + 3; |
| 5368 | } |
| 5369 | else if (isnan (dbl)) |
| 5370 | { |
| 5371 | strcpy (a, "+nan.0"); |
| 5372 | return 6; |
| 5373 | } |
| 5374 | |
| 5375 | /* Algorithm taken from "Printing Floating-Point Numbers Quickly and |
| 5376 | Accurately" by Robert G. Burger and R. Kent Dybvig */ |
| 5377 | { |
| 5378 | int e, k; |
| 5379 | mpz_t f, r, s, mplus, mminus, hi, digit; |
| 5380 | int f_is_even, f_is_odd; |
| 5381 | int expon; |
| 5382 | int show_exp = 0; |
| 5383 | |
| 5384 | mpz_inits (f, r, s, mplus, mminus, hi, digit, NULL); |
| 5385 | mpz_set_d (f, ldexp (frexp (dbl, &e), DBL_MANT_DIG)); |
| 5386 | if (e < DBL_MIN_EXP) |
| 5387 | { |
| 5388 | mpz_tdiv_q_2exp (f, f, DBL_MIN_EXP - e); |
| 5389 | e = DBL_MIN_EXP; |
| 5390 | } |
| 5391 | e -= DBL_MANT_DIG; |
| 5392 | |
| 5393 | f_is_even = !mpz_odd_p (f); |
| 5394 | f_is_odd = !f_is_even; |
| 5395 | |
| 5396 | /* Initialize r, s, mplus, and mminus according |
| 5397 | to Table 1 from the paper. */ |
| 5398 | if (e < 0) |
| 5399 | { |
| 5400 | mpz_set_ui (mminus, 1); |
| 5401 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0 |
| 5402 | || e == DBL_MIN_EXP - DBL_MANT_DIG) |
| 5403 | { |
| 5404 | mpz_set_ui (mplus, 1); |
| 5405 | mpz_mul_2exp (r, f, 1); |
| 5406 | mpz_mul_2exp (s, mminus, 1 - e); |
| 5407 | } |
| 5408 | else |
| 5409 | { |
| 5410 | mpz_set_ui (mplus, 2); |
| 5411 | mpz_mul_2exp (r, f, 2); |
| 5412 | mpz_mul_2exp (s, mminus, 2 - e); |
| 5413 | } |
| 5414 | } |
| 5415 | else |
| 5416 | { |
| 5417 | mpz_set_ui (mminus, 1); |
| 5418 | mpz_mul_2exp (mminus, mminus, e); |
| 5419 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0) |
| 5420 | { |
| 5421 | mpz_set (mplus, mminus); |
| 5422 | mpz_mul_2exp (r, f, 1 + e); |
| 5423 | mpz_set_ui (s, 2); |
| 5424 | } |
| 5425 | else |
| 5426 | { |
| 5427 | mpz_mul_2exp (mplus, mminus, 1); |
| 5428 | mpz_mul_2exp (r, f, 2 + e); |
| 5429 | mpz_set_ui (s, 4); |
| 5430 | } |
| 5431 | } |
| 5432 | |
| 5433 | /* Find the smallest k such that: |
| 5434 | (r + mplus) / s < radix^k (if f is even) |
| 5435 | (r + mplus) / s <= radix^k (if f is odd) */ |
| 5436 | { |
| 5437 | /* IMPROVE-ME: Make an initial guess to speed this up */ |
| 5438 | mpz_add (hi, r, mplus); |
| 5439 | k = 0; |
| 5440 | while (mpz_cmp (hi, s) >= f_is_odd) |
| 5441 | { |
| 5442 | mpz_mul_ui (s, s, radix); |
| 5443 | k++; |
| 5444 | } |
| 5445 | if (k == 0) |
| 5446 | { |
| 5447 | mpz_mul_ui (hi, hi, radix); |
| 5448 | while (mpz_cmp (hi, s) < f_is_odd) |
| 5449 | { |
| 5450 | mpz_mul_ui (r, r, radix); |
| 5451 | mpz_mul_ui (mplus, mplus, radix); |
| 5452 | mpz_mul_ui (mminus, mminus, radix); |
| 5453 | mpz_mul_ui (hi, hi, radix); |
| 5454 | k--; |
| 5455 | } |
| 5456 | } |
| 5457 | } |
| 5458 | |
| 5459 | expon = k - 1; |
| 5460 | if (k <= 0) |
| 5461 | { |
| 5462 | if (k <= -3) |
| 5463 | { |
| 5464 | /* Use scientific notation */ |
| 5465 | show_exp = 1; |
| 5466 | k = 1; |
| 5467 | } |
| 5468 | else |
| 5469 | { |
| 5470 | int i; |
| 5471 | |
| 5472 | /* Print leading zeroes */ |
| 5473 | a[ch++] = '0'; |
| 5474 | a[ch++] = '.'; |
| 5475 | for (i = 0; i > k; i--) |
| 5476 | a[ch++] = '0'; |
| 5477 | } |
| 5478 | } |
| 5479 | |
| 5480 | for (;;) |
| 5481 | { |
| 5482 | int end_1_p, end_2_p; |
| 5483 | int d; |
| 5484 | |
| 5485 | mpz_mul_ui (mplus, mplus, radix); |
| 5486 | mpz_mul_ui (mminus, mminus, radix); |
| 5487 | mpz_mul_ui (r, r, radix); |
| 5488 | mpz_fdiv_qr (digit, r, r, s); |
| 5489 | d = mpz_get_ui (digit); |
| 5490 | |
| 5491 | mpz_add (hi, r, mplus); |
| 5492 | end_1_p = (mpz_cmp (r, mminus) < f_is_even); |
| 5493 | end_2_p = (mpz_cmp (s, hi) < f_is_even); |
| 5494 | if (end_1_p || end_2_p) |
| 5495 | { |
| 5496 | mpz_mul_2exp (r, r, 1); |
| 5497 | if (!end_2_p) |
| 5498 | ; |
| 5499 | else if (!end_1_p) |
| 5500 | d++; |
| 5501 | else if (mpz_cmp (r, s) >= !(d & 1)) |
| 5502 | d++; |
| 5503 | a[ch++] = number_chars[d]; |
| 5504 | if (--k == 0) |
| 5505 | a[ch++] = '.'; |
| 5506 | break; |
| 5507 | } |
| 5508 | else |
| 5509 | { |
| 5510 | a[ch++] = number_chars[d]; |
| 5511 | if (--k == 0) |
| 5512 | a[ch++] = '.'; |
| 5513 | } |
| 5514 | } |
| 5515 | |
| 5516 | if (k > 0) |
| 5517 | { |
| 5518 | if (expon >= 7 && k >= 4 && expon >= k) |
| 5519 | { |
| 5520 | /* Here we would have to print more than three zeroes |
| 5521 | followed by a decimal point and another zero. It |
| 5522 | makes more sense to use scientific notation. */ |
| 5523 | |
| 5524 | /* Adjust k to what it would have been if we had chosen |
| 5525 | scientific notation from the beginning. */ |
| 5526 | k -= expon; |
| 5527 | |
| 5528 | /* k will now be <= 0, with magnitude equal to the number of |
| 5529 | digits that we printed which should now be put after the |
| 5530 | decimal point. */ |
| 5531 | |
| 5532 | /* Insert a decimal point */ |
| 5533 | memmove (a + ch + k + 1, a + ch + k, -k); |
| 5534 | a[ch + k] = '.'; |
| 5535 | ch++; |
| 5536 | |
| 5537 | show_exp = 1; |
| 5538 | } |
| 5539 | else |
| 5540 | { |
| 5541 | for (; k > 0; k--) |
| 5542 | a[ch++] = '0'; |
| 5543 | a[ch++] = '.'; |
| 5544 | } |
| 5545 | } |
| 5546 | |
| 5547 | if (k == 0) |
| 5548 | a[ch++] = '0'; |
| 5549 | |
| 5550 | if (show_exp) |
| 5551 | { |
| 5552 | a[ch++] = 'e'; |
| 5553 | ch += scm_iint2str (expon, radix, a + ch); |
| 5554 | } |
| 5555 | |
| 5556 | mpz_clears (f, r, s, mplus, mminus, hi, digit, NULL); |
| 5557 | } |
| 5558 | return ch; |
| 5559 | } |
| 5560 | |
| 5561 | |
| 5562 | static size_t |
| 5563 | icmplx2str (double real, double imag, char *str, int radix) |
| 5564 | { |
| 5565 | size_t i; |
| 5566 | double sgn; |
| 5567 | |
| 5568 | i = idbl2str (real, str, radix); |
| 5569 | #ifdef HAVE_COPYSIGN |
| 5570 | sgn = copysign (1.0, imag); |
| 5571 | #else |
| 5572 | sgn = imag; |
| 5573 | #endif |
| 5574 | /* Don't output a '+' for negative numbers or for Inf and |
| 5575 | NaN. They will provide their own sign. */ |
| 5576 | if (sgn >= 0 && isfinite (imag)) |
| 5577 | str[i++] = '+'; |
| 5578 | i += idbl2str (imag, &str[i], radix); |
| 5579 | str[i++] = 'i'; |
| 5580 | return i; |
| 5581 | } |
| 5582 | |
| 5583 | static size_t |
| 5584 | iflo2str (SCM flt, char *str, int radix) |
| 5585 | { |
| 5586 | size_t i; |
| 5587 | if (SCM_REALP (flt)) |
| 5588 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
| 5589 | else |
| 5590 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
| 5591 | str, radix); |
| 5592 | return i; |
| 5593 | } |
| 5594 | |
| 5595 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
| 5596 | characters in the result. |
| 5597 | rad is output base |
| 5598 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ |
| 5599 | size_t |
| 5600 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
| 5601 | { |
| 5602 | if (num < 0) |
| 5603 | { |
| 5604 | *p++ = '-'; |
| 5605 | return scm_iuint2str (-num, rad, p) + 1; |
| 5606 | } |
| 5607 | else |
| 5608 | return scm_iuint2str (num, rad, p); |
| 5609 | } |
| 5610 | |
| 5611 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
| 5612 | characters in the result. |
| 5613 | rad is output base |
| 5614 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ |
| 5615 | size_t |
| 5616 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) |
| 5617 | { |
| 5618 | size_t j = 1; |
| 5619 | size_t i; |
| 5620 | scm_t_uintmax n = num; |
| 5621 | |
| 5622 | if (rad < 2 || rad > 36) |
| 5623 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); |
| 5624 | |
| 5625 | for (n /= rad; n > 0; n /= rad) |
| 5626 | j++; |
| 5627 | |
| 5628 | i = j; |
| 5629 | n = num; |
| 5630 | while (i--) |
| 5631 | { |
| 5632 | int d = n % rad; |
| 5633 | |
| 5634 | n /= rad; |
| 5635 | p[i] = number_chars[d]; |
| 5636 | } |
| 5637 | return j; |
| 5638 | } |
| 5639 | |
| 5640 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
| 5641 | (SCM n, SCM radix), |
| 5642 | "Return a string holding the external representation of the\n" |
| 5643 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
| 5644 | "inexact, a radix of 10 will be used.") |
| 5645 | #define FUNC_NAME s_scm_number_to_string |
| 5646 | { |
| 5647 | int base; |
| 5648 | |
| 5649 | if (SCM_UNBNDP (radix)) |
| 5650 | base = 10; |
| 5651 | else |
| 5652 | base = scm_to_signed_integer (radix, 2, 36); |
| 5653 | |
| 5654 | if (SCM_I_INUMP (n)) |
| 5655 | { |
| 5656 | char num_buf [SCM_INTBUFLEN]; |
| 5657 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
| 5658 | return scm_from_locale_stringn (num_buf, length); |
| 5659 | } |
| 5660 | else if (SCM_BIGP (n)) |
| 5661 | { |
| 5662 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); |
| 5663 | size_t len = strlen (str); |
| 5664 | void (*freefunc) (void *, size_t); |
| 5665 | SCM ret; |
| 5666 | mp_get_memory_functions (NULL, NULL, &freefunc); |
| 5667 | scm_remember_upto_here_1 (n); |
| 5668 | ret = scm_from_latin1_stringn (str, len); |
| 5669 | freefunc (str, len + 1); |
| 5670 | return ret; |
| 5671 | } |
| 5672 | else if (SCM_FRACTIONP (n)) |
| 5673 | { |
| 5674 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
| 5675 | scm_from_locale_string ("/"), |
| 5676 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
| 5677 | } |
| 5678 | else if (SCM_INEXACTP (n)) |
| 5679 | { |
| 5680 | char num_buf [FLOBUFLEN]; |
| 5681 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
| 5682 | } |
| 5683 | else |
| 5684 | SCM_WRONG_TYPE_ARG (1, n); |
| 5685 | } |
| 5686 | #undef FUNC_NAME |
| 5687 | |
| 5688 | |
| 5689 | /* These print routines used to be stubbed here so that scm_repl.c |
| 5690 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ |
| 5691 | |
| 5692 | int |
| 5693 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
| 5694 | { |
| 5695 | char num_buf[FLOBUFLEN]; |
| 5696 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
| 5697 | return !0; |
| 5698 | } |
| 5699 | |
| 5700 | void |
| 5701 | scm_i_print_double (double val, SCM port) |
| 5702 | { |
| 5703 | char num_buf[FLOBUFLEN]; |
| 5704 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); |
| 5705 | } |
| 5706 | |
| 5707 | int |
| 5708 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
| 5709 | |
| 5710 | { |
| 5711 | char num_buf[FLOBUFLEN]; |
| 5712 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
| 5713 | return !0; |
| 5714 | } |
| 5715 | |
| 5716 | void |
| 5717 | scm_i_print_complex (double real, double imag, SCM port) |
| 5718 | { |
| 5719 | char num_buf[FLOBUFLEN]; |
| 5720 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); |
| 5721 | } |
| 5722 | |
| 5723 | int |
| 5724 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
| 5725 | { |
| 5726 | SCM str; |
| 5727 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
| 5728 | scm_display (str, port); |
| 5729 | scm_remember_upto_here_1 (str); |
| 5730 | return !0; |
| 5731 | } |
| 5732 | |
| 5733 | int |
| 5734 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
| 5735 | { |
| 5736 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
| 5737 | size_t len = strlen (str); |
| 5738 | void (*freefunc) (void *, size_t); |
| 5739 | mp_get_memory_functions (NULL, NULL, &freefunc); |
| 5740 | scm_remember_upto_here_1 (exp); |
| 5741 | scm_lfwrite (str, len, port); |
| 5742 | freefunc (str, len + 1); |
| 5743 | return !0; |
| 5744 | } |
| 5745 | /*** END nums->strs ***/ |
| 5746 | |
| 5747 | |
| 5748 | /*** STRINGS -> NUMBERS ***/ |
| 5749 | |
| 5750 | /* The following functions implement the conversion from strings to numbers. |
| 5751 | * The implementation somehow follows the grammar for numbers as it is given |
| 5752 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, |
| 5753 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some |
| 5754 | * points should be noted about the implementation: |
| 5755 | * |
| 5756 | * * Each function keeps a local index variable 'idx' that points at the |
| 5757 | * current position within the parsed string. The global index is only |
| 5758 | * updated if the function could parse the corresponding syntactic unit |
| 5759 | * successfully. |
| 5760 | * |
| 5761 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
| 5762 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
| 5763 | * |
| 5764 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
| 5765 | * Only if these fixnums would overflow, the result variables are updated |
| 5766 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, |
| 5767 | * the temporary variables holding the fixnums are cleared, and the process |
| 5768 | * starts over again. If for example fixnums were able to store five decimal |
| 5769 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, |
| 5770 | * and the result was computed as 12345 * 100000 + 67890. In other words, |
| 5771 | * only every five digits two bignum operations were performed. |
| 5772 | * |
| 5773 | * Notes on the handling of exactness specifiers: |
| 5774 | * |
| 5775 | * When parsing non-real complex numbers, we apply exactness specifiers on |
| 5776 | * per-component basis, as is done in PLT Scheme. For complex numbers |
| 5777 | * written in rectangular form, exactness specifiers are applied to the |
| 5778 | * real and imaginary parts before calling scm_make_rectangular. For |
| 5779 | * complex numbers written in polar form, exactness specifiers are applied |
| 5780 | * to the magnitude and angle before calling scm_make_polar. |
| 5781 | * |
| 5782 | * There are two kinds of exactness specifiers: forced and implicit. A |
| 5783 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of |
| 5784 | * the entire number, and applies to both components of a complex number. |
| 5785 | * "#e" causes each component to be made exact, and "#i" causes each |
| 5786 | * component to be made inexact. If no forced exactness specifier is |
| 5787 | * present, then the exactness of each component is determined |
| 5788 | * independently by the presence or absence of a decimal point or hash mark |
| 5789 | * within that component. If a decimal point or hash mark is present, the |
| 5790 | * component is made inexact, otherwise it is made exact. |
| 5791 | * |
| 5792 | * After the exactness specifiers have been applied to each component, they |
| 5793 | * are passed to either scm_make_rectangular or scm_make_polar to produce |
| 5794 | * the final result. Note that this will result in a real number if the |
| 5795 | * imaginary part, magnitude, or angle is an exact 0. |
| 5796 | * |
| 5797 | * For example, (string->number "#i5.0+0i") does the equivalent of: |
| 5798 | * |
| 5799 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) |
| 5800 | */ |
| 5801 | |
| 5802 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; |
| 5803 | |
| 5804 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ |
| 5805 | |
| 5806 | /* Caller is responsible for checking that the return value is in range |
| 5807 | for the given radix, which should be <= 36. */ |
| 5808 | static unsigned int |
| 5809 | char_decimal_value (scm_t_uint32 c) |
| 5810 | { |
| 5811 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, |
| 5812 | that's certainly above any valid decimal, so we take advantage of |
| 5813 | that to elide some tests. */ |
| 5814 | unsigned int d = (unsigned int) uc_decimal_value (c); |
| 5815 | |
| 5816 | /* If that failed, try extended hexadecimals, then. Only accept ascii |
| 5817 | hexadecimals. */ |
| 5818 | if (d >= 10U) |
| 5819 | { |
| 5820 | c = uc_tolower (c); |
| 5821 | if (c >= (scm_t_uint32) 'a') |
| 5822 | d = c - (scm_t_uint32)'a' + 10U; |
| 5823 | } |
| 5824 | return d; |
| 5825 | } |
| 5826 | |
| 5827 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
| 5828 | in base RADIX. Upon success, return the unsigned integer and update |
| 5829 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ |
| 5830 | static SCM |
| 5831 | mem2uinteger (SCM mem, unsigned int *p_idx, |
| 5832 | unsigned int radix, enum t_exactness *p_exactness) |
| 5833 | { |
| 5834 | unsigned int idx = *p_idx; |
| 5835 | unsigned int hash_seen = 0; |
| 5836 | scm_t_bits shift = 1; |
| 5837 | scm_t_bits add = 0; |
| 5838 | unsigned int digit_value; |
| 5839 | SCM result; |
| 5840 | char c; |
| 5841 | size_t len = scm_i_string_length (mem); |
| 5842 | |
| 5843 | if (idx == len) |
| 5844 | return SCM_BOOL_F; |
| 5845 | |
| 5846 | c = scm_i_string_ref (mem, idx); |
| 5847 | digit_value = char_decimal_value (c); |
| 5848 | if (digit_value >= radix) |
| 5849 | return SCM_BOOL_F; |
| 5850 | |
| 5851 | idx++; |
| 5852 | result = SCM_I_MAKINUM (digit_value); |
| 5853 | while (idx != len) |
| 5854 | { |
| 5855 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
| 5856 | if (c == '#') |
| 5857 | { |
| 5858 | hash_seen = 1; |
| 5859 | digit_value = 0; |
| 5860 | } |
| 5861 | else if (hash_seen) |
| 5862 | break; |
| 5863 | else |
| 5864 | { |
| 5865 | digit_value = char_decimal_value (c); |
| 5866 | /* This check catches non-decimals in addition to out-of-range |
| 5867 | decimals. */ |
| 5868 | if (digit_value >= radix) |
| 5869 | break; |
| 5870 | } |
| 5871 | |
| 5872 | idx++; |
| 5873 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) |
| 5874 | { |
| 5875 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
| 5876 | if (add > 0) |
| 5877 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
| 5878 | |
| 5879 | shift = radix; |
| 5880 | add = digit_value; |
| 5881 | } |
| 5882 | else |
| 5883 | { |
| 5884 | shift = shift * radix; |
| 5885 | add = add * radix + digit_value; |
| 5886 | } |
| 5887 | }; |
| 5888 | |
| 5889 | if (shift > 1) |
| 5890 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
| 5891 | if (add > 0) |
| 5892 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
| 5893 | |
| 5894 | *p_idx = idx; |
| 5895 | if (hash_seen) |
| 5896 | *p_exactness = INEXACT; |
| 5897 | |
| 5898 | return result; |
| 5899 | } |
| 5900 | |
| 5901 | |
| 5902 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
| 5903 | * covers the parts of the rules that start at a potential point. The value |
| 5904 | * of the digits up to the point have been parsed by the caller and are given |
| 5905 | * in variable result. The content of *p_exactness indicates, whether a hash |
| 5906 | * has already been seen in the digits before the point. |
| 5907 | */ |
| 5908 | |
| 5909 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
| 5910 | |
| 5911 | static SCM |
| 5912 | mem2decimal_from_point (SCM result, SCM mem, |
| 5913 | unsigned int *p_idx, enum t_exactness *p_exactness) |
| 5914 | { |
| 5915 | unsigned int idx = *p_idx; |
| 5916 | enum t_exactness x = *p_exactness; |
| 5917 | size_t len = scm_i_string_length (mem); |
| 5918 | |
| 5919 | if (idx == len) |
| 5920 | return result; |
| 5921 | |
| 5922 | if (scm_i_string_ref (mem, idx) == '.') |
| 5923 | { |
| 5924 | scm_t_bits shift = 1; |
| 5925 | scm_t_bits add = 0; |
| 5926 | unsigned int digit_value; |
| 5927 | SCM big_shift = SCM_INUM1; |
| 5928 | |
| 5929 | idx++; |
| 5930 | while (idx != len) |
| 5931 | { |
| 5932 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
| 5933 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) |
| 5934 | { |
| 5935 | if (x == INEXACT) |
| 5936 | return SCM_BOOL_F; |
| 5937 | else |
| 5938 | digit_value = DIGIT2UINT (c); |
| 5939 | } |
| 5940 | else if (c == '#') |
| 5941 | { |
| 5942 | x = INEXACT; |
| 5943 | digit_value = 0; |
| 5944 | } |
| 5945 | else |
| 5946 | break; |
| 5947 | |
| 5948 | idx++; |
| 5949 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) |
| 5950 | { |
| 5951 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
| 5952 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
| 5953 | if (add > 0) |
| 5954 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
| 5955 | |
| 5956 | shift = 10; |
| 5957 | add = digit_value; |
| 5958 | } |
| 5959 | else |
| 5960 | { |
| 5961 | shift = shift * 10; |
| 5962 | add = add * 10 + digit_value; |
| 5963 | } |
| 5964 | }; |
| 5965 | |
| 5966 | if (add > 0) |
| 5967 | { |
| 5968 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
| 5969 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
| 5970 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
| 5971 | } |
| 5972 | |
| 5973 | result = scm_divide (result, big_shift); |
| 5974 | |
| 5975 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
| 5976 | x = INEXACT; |
| 5977 | } |
| 5978 | |
| 5979 | if (idx != len) |
| 5980 | { |
| 5981 | int sign = 1; |
| 5982 | unsigned int start; |
| 5983 | scm_t_wchar c; |
| 5984 | int exponent; |
| 5985 | SCM e; |
| 5986 | |
| 5987 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ |
| 5988 | |
| 5989 | switch (scm_i_string_ref (mem, idx)) |
| 5990 | { |
| 5991 | case 'd': case 'D': |
| 5992 | case 'e': case 'E': |
| 5993 | case 'f': case 'F': |
| 5994 | case 'l': case 'L': |
| 5995 | case 's': case 'S': |
| 5996 | idx++; |
| 5997 | if (idx == len) |
| 5998 | return SCM_BOOL_F; |
| 5999 | |
| 6000 | start = idx; |
| 6001 | c = scm_i_string_ref (mem, idx); |
| 6002 | if (c == '-') |
| 6003 | { |
| 6004 | idx++; |
| 6005 | if (idx == len) |
| 6006 | return SCM_BOOL_F; |
| 6007 | |
| 6008 | sign = -1; |
| 6009 | c = scm_i_string_ref (mem, idx); |
| 6010 | } |
| 6011 | else if (c == '+') |
| 6012 | { |
| 6013 | idx++; |
| 6014 | if (idx == len) |
| 6015 | return SCM_BOOL_F; |
| 6016 | |
| 6017 | sign = 1; |
| 6018 | c = scm_i_string_ref (mem, idx); |
| 6019 | } |
| 6020 | else |
| 6021 | sign = 1; |
| 6022 | |
| 6023 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
| 6024 | return SCM_BOOL_F; |
| 6025 | |
| 6026 | idx++; |
| 6027 | exponent = DIGIT2UINT (c); |
| 6028 | while (idx != len) |
| 6029 | { |
| 6030 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
| 6031 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) |
| 6032 | { |
| 6033 | idx++; |
| 6034 | if (exponent <= SCM_MAXEXP) |
| 6035 | exponent = exponent * 10 + DIGIT2UINT (c); |
| 6036 | } |
| 6037 | else |
| 6038 | break; |
| 6039 | } |
| 6040 | |
| 6041 | if (exponent > ((sign == 1) ? SCM_MAXEXP : SCM_MAXEXP + DBL_DIG + 1)) |
| 6042 | { |
| 6043 | size_t exp_len = idx - start; |
| 6044 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
| 6045 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
| 6046 | scm_out_of_range ("string->number", exp_num); |
| 6047 | } |
| 6048 | |
| 6049 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
| 6050 | if (sign == 1) |
| 6051 | result = scm_product (result, e); |
| 6052 | else |
| 6053 | result = scm_divide (result, e); |
| 6054 | |
| 6055 | /* We've seen an exponent, thus the value is implicitly inexact. */ |
| 6056 | x = INEXACT; |
| 6057 | |
| 6058 | break; |
| 6059 | |
| 6060 | default: |
| 6061 | break; |
| 6062 | } |
| 6063 | } |
| 6064 | |
| 6065 | *p_idx = idx; |
| 6066 | if (x == INEXACT) |
| 6067 | *p_exactness = x; |
| 6068 | |
| 6069 | return result; |
| 6070 | } |
| 6071 | |
| 6072 | |
| 6073 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ |
| 6074 | |
| 6075 | static SCM |
| 6076 | mem2ureal (SCM mem, unsigned int *p_idx, |
| 6077 | unsigned int radix, enum t_exactness forced_x, |
| 6078 | int allow_inf_or_nan) |
| 6079 | { |
| 6080 | unsigned int idx = *p_idx; |
| 6081 | SCM result; |
| 6082 | size_t len = scm_i_string_length (mem); |
| 6083 | |
| 6084 | /* Start off believing that the number will be exact. This changes |
| 6085 | to INEXACT if we see a decimal point or a hash. */ |
| 6086 | enum t_exactness implicit_x = EXACT; |
| 6087 | |
| 6088 | if (idx == len) |
| 6089 | return SCM_BOOL_F; |
| 6090 | |
| 6091 | if (allow_inf_or_nan && forced_x != EXACT && idx+5 <= len) |
| 6092 | switch (scm_i_string_ref (mem, idx)) |
| 6093 | { |
| 6094 | case 'i': case 'I': |
| 6095 | switch (scm_i_string_ref (mem, idx + 1)) |
| 6096 | { |
| 6097 | case 'n': case 'N': |
| 6098 | switch (scm_i_string_ref (mem, idx + 2)) |
| 6099 | { |
| 6100 | case 'f': case 'F': |
| 6101 | if (scm_i_string_ref (mem, idx + 3) == '.' |
| 6102 | && scm_i_string_ref (mem, idx + 4) == '0') |
| 6103 | { |
| 6104 | *p_idx = idx+5; |
| 6105 | return scm_inf (); |
| 6106 | } |
| 6107 | } |
| 6108 | } |
| 6109 | case 'n': case 'N': |
| 6110 | switch (scm_i_string_ref (mem, idx + 1)) |
| 6111 | { |
| 6112 | case 'a': case 'A': |
| 6113 | switch (scm_i_string_ref (mem, idx + 2)) |
| 6114 | { |
| 6115 | case 'n': case 'N': |
| 6116 | if (scm_i_string_ref (mem, idx + 3) == '.') |
| 6117 | { |
| 6118 | /* Cobble up the fractional part. We might want to |
| 6119 | set the NaN's mantissa from it. */ |
| 6120 | idx += 4; |
| 6121 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), |
| 6122 | SCM_INUM0)) |
| 6123 | { |
| 6124 | #if SCM_ENABLE_DEPRECATED == 1 |
| 6125 | scm_c_issue_deprecation_warning |
| 6126 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); |
| 6127 | #else |
| 6128 | return SCM_BOOL_F; |
| 6129 | #endif |
| 6130 | } |
| 6131 | |
| 6132 | *p_idx = idx; |
| 6133 | return scm_nan (); |
| 6134 | } |
| 6135 | } |
| 6136 | } |
| 6137 | } |
| 6138 | |
| 6139 | if (scm_i_string_ref (mem, idx) == '.') |
| 6140 | { |
| 6141 | if (radix != 10) |
| 6142 | return SCM_BOOL_F; |
| 6143 | else if (idx + 1 == len) |
| 6144 | return SCM_BOOL_F; |
| 6145 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
| 6146 | return SCM_BOOL_F; |
| 6147 | else |
| 6148 | result = mem2decimal_from_point (SCM_INUM0, mem, |
| 6149 | p_idx, &implicit_x); |
| 6150 | } |
| 6151 | else |
| 6152 | { |
| 6153 | SCM uinteger; |
| 6154 | |
| 6155 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
| 6156 | if (scm_is_false (uinteger)) |
| 6157 | return SCM_BOOL_F; |
| 6158 | |
| 6159 | if (idx == len) |
| 6160 | result = uinteger; |
| 6161 | else if (scm_i_string_ref (mem, idx) == '/') |
| 6162 | { |
| 6163 | SCM divisor; |
| 6164 | |
| 6165 | idx++; |
| 6166 | if (idx == len) |
| 6167 | return SCM_BOOL_F; |
| 6168 | |
| 6169 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
| 6170 | if (scm_is_false (divisor) || scm_is_eq (divisor, SCM_INUM0)) |
| 6171 | return SCM_BOOL_F; |
| 6172 | |
| 6173 | /* both are int/big here, I assume */ |
| 6174 | result = scm_i_make_ratio (uinteger, divisor); |
| 6175 | } |
| 6176 | else if (radix == 10) |
| 6177 | { |
| 6178 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
| 6179 | if (scm_is_false (result)) |
| 6180 | return SCM_BOOL_F; |
| 6181 | } |
| 6182 | else |
| 6183 | result = uinteger; |
| 6184 | |
| 6185 | *p_idx = idx; |
| 6186 | } |
| 6187 | |
| 6188 | switch (forced_x) |
| 6189 | { |
| 6190 | case EXACT: |
| 6191 | if (SCM_INEXACTP (result)) |
| 6192 | return scm_inexact_to_exact (result); |
| 6193 | else |
| 6194 | return result; |
| 6195 | case INEXACT: |
| 6196 | if (SCM_INEXACTP (result)) |
| 6197 | return result; |
| 6198 | else |
| 6199 | return scm_exact_to_inexact (result); |
| 6200 | case NO_EXACTNESS: |
| 6201 | if (implicit_x == INEXACT) |
| 6202 | { |
| 6203 | if (SCM_INEXACTP (result)) |
| 6204 | return result; |
| 6205 | else |
| 6206 | return scm_exact_to_inexact (result); |
| 6207 | } |
| 6208 | else |
| 6209 | return result; |
| 6210 | } |
| 6211 | |
| 6212 | /* We should never get here */ |
| 6213 | assert (0); |
| 6214 | } |
| 6215 | |
| 6216 | |
| 6217 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
| 6218 | |
| 6219 | static SCM |
| 6220 | mem2complex (SCM mem, unsigned int idx, |
| 6221 | unsigned int radix, enum t_exactness forced_x) |
| 6222 | { |
| 6223 | scm_t_wchar c; |
| 6224 | int sign = 0; |
| 6225 | SCM ureal; |
| 6226 | size_t len = scm_i_string_length (mem); |
| 6227 | |
| 6228 | if (idx == len) |
| 6229 | return SCM_BOOL_F; |
| 6230 | |
| 6231 | c = scm_i_string_ref (mem, idx); |
| 6232 | if (c == '+') |
| 6233 | { |
| 6234 | idx++; |
| 6235 | sign = 1; |
| 6236 | } |
| 6237 | else if (c == '-') |
| 6238 | { |
| 6239 | idx++; |
| 6240 | sign = -1; |
| 6241 | } |
| 6242 | |
| 6243 | if (idx == len) |
| 6244 | return SCM_BOOL_F; |
| 6245 | |
| 6246 | ureal = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
| 6247 | if (scm_is_false (ureal)) |
| 6248 | { |
| 6249 | /* input must be either +i or -i */ |
| 6250 | |
| 6251 | if (sign == 0) |
| 6252 | return SCM_BOOL_F; |
| 6253 | |
| 6254 | if (scm_i_string_ref (mem, idx) == 'i' |
| 6255 | || scm_i_string_ref (mem, idx) == 'I') |
| 6256 | { |
| 6257 | idx++; |
| 6258 | if (idx != len) |
| 6259 | return SCM_BOOL_F; |
| 6260 | |
| 6261 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
| 6262 | } |
| 6263 | else |
| 6264 | return SCM_BOOL_F; |
| 6265 | } |
| 6266 | else |
| 6267 | { |
| 6268 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
| 6269 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
| 6270 | |
| 6271 | if (idx == len) |
| 6272 | return ureal; |
| 6273 | |
| 6274 | c = scm_i_string_ref (mem, idx); |
| 6275 | switch (c) |
| 6276 | { |
| 6277 | case 'i': case 'I': |
| 6278 | /* either +<ureal>i or -<ureal>i */ |
| 6279 | |
| 6280 | idx++; |
| 6281 | if (sign == 0) |
| 6282 | return SCM_BOOL_F; |
| 6283 | if (idx != len) |
| 6284 | return SCM_BOOL_F; |
| 6285 | return scm_make_rectangular (SCM_INUM0, ureal); |
| 6286 | |
| 6287 | case '@': |
| 6288 | /* polar input: <real>@<real>. */ |
| 6289 | |
| 6290 | idx++; |
| 6291 | if (idx == len) |
| 6292 | return SCM_BOOL_F; |
| 6293 | else |
| 6294 | { |
| 6295 | int sign; |
| 6296 | SCM angle; |
| 6297 | SCM result; |
| 6298 | |
| 6299 | c = scm_i_string_ref (mem, idx); |
| 6300 | if (c == '+') |
| 6301 | { |
| 6302 | idx++; |
| 6303 | if (idx == len) |
| 6304 | return SCM_BOOL_F; |
| 6305 | sign = 1; |
| 6306 | } |
| 6307 | else if (c == '-') |
| 6308 | { |
| 6309 | idx++; |
| 6310 | if (idx == len) |
| 6311 | return SCM_BOOL_F; |
| 6312 | sign = -1; |
| 6313 | } |
| 6314 | else |
| 6315 | sign = 0; |
| 6316 | |
| 6317 | angle = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
| 6318 | if (scm_is_false (angle)) |
| 6319 | return SCM_BOOL_F; |
| 6320 | if (idx != len) |
| 6321 | return SCM_BOOL_F; |
| 6322 | |
| 6323 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
| 6324 | angle = scm_difference (angle, SCM_UNDEFINED); |
| 6325 | |
| 6326 | result = scm_make_polar (ureal, angle); |
| 6327 | return result; |
| 6328 | } |
| 6329 | case '+': |
| 6330 | case '-': |
| 6331 | /* expecting input matching <real>[+-]<ureal>?i */ |
| 6332 | |
| 6333 | idx++; |
| 6334 | if (idx == len) |
| 6335 | return SCM_BOOL_F; |
| 6336 | else |
| 6337 | { |
| 6338 | int sign = (c == '+') ? 1 : -1; |
| 6339 | SCM imag = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
| 6340 | |
| 6341 | if (scm_is_false (imag)) |
| 6342 | imag = SCM_I_MAKINUM (sign); |
| 6343 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
| 6344 | imag = scm_difference (imag, SCM_UNDEFINED); |
| 6345 | |
| 6346 | if (idx == len) |
| 6347 | return SCM_BOOL_F; |
| 6348 | if (scm_i_string_ref (mem, idx) != 'i' |
| 6349 | && scm_i_string_ref (mem, idx) != 'I') |
| 6350 | return SCM_BOOL_F; |
| 6351 | |
| 6352 | idx++; |
| 6353 | if (idx != len) |
| 6354 | return SCM_BOOL_F; |
| 6355 | |
| 6356 | return scm_make_rectangular (ureal, imag); |
| 6357 | } |
| 6358 | default: |
| 6359 | return SCM_BOOL_F; |
| 6360 | } |
| 6361 | } |
| 6362 | } |
| 6363 | |
| 6364 | |
| 6365 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
| 6366 | |
| 6367 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; |
| 6368 | |
| 6369 | SCM |
| 6370 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
| 6371 | { |
| 6372 | unsigned int idx = 0; |
| 6373 | unsigned int radix = NO_RADIX; |
| 6374 | enum t_exactness forced_x = NO_EXACTNESS; |
| 6375 | size_t len = scm_i_string_length (mem); |
| 6376 | |
| 6377 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ |
| 6378 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
| 6379 | { |
| 6380 | switch (scm_i_string_ref (mem, idx + 1)) |
| 6381 | { |
| 6382 | case 'b': case 'B': |
| 6383 | if (radix != NO_RADIX) |
| 6384 | return SCM_BOOL_F; |
| 6385 | radix = DUAL; |
| 6386 | break; |
| 6387 | case 'd': case 'D': |
| 6388 | if (radix != NO_RADIX) |
| 6389 | return SCM_BOOL_F; |
| 6390 | radix = DEC; |
| 6391 | break; |
| 6392 | case 'i': case 'I': |
| 6393 | if (forced_x != NO_EXACTNESS) |
| 6394 | return SCM_BOOL_F; |
| 6395 | forced_x = INEXACT; |
| 6396 | break; |
| 6397 | case 'e': case 'E': |
| 6398 | if (forced_x != NO_EXACTNESS) |
| 6399 | return SCM_BOOL_F; |
| 6400 | forced_x = EXACT; |
| 6401 | break; |
| 6402 | case 'o': case 'O': |
| 6403 | if (radix != NO_RADIX) |
| 6404 | return SCM_BOOL_F; |
| 6405 | radix = OCT; |
| 6406 | break; |
| 6407 | case 'x': case 'X': |
| 6408 | if (radix != NO_RADIX) |
| 6409 | return SCM_BOOL_F; |
| 6410 | radix = HEX; |
| 6411 | break; |
| 6412 | default: |
| 6413 | return SCM_BOOL_F; |
| 6414 | } |
| 6415 | idx += 2; |
| 6416 | } |
| 6417 | |
| 6418 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
| 6419 | if (radix == NO_RADIX) |
| 6420 | radix = default_radix; |
| 6421 | |
| 6422 | return mem2complex (mem, idx, radix, forced_x); |
| 6423 | } |
| 6424 | |
| 6425 | SCM |
| 6426 | scm_c_locale_stringn_to_number (const char* mem, size_t len, |
| 6427 | unsigned int default_radix) |
| 6428 | { |
| 6429 | SCM str = scm_from_locale_stringn (mem, len); |
| 6430 | |
| 6431 | return scm_i_string_to_number (str, default_radix); |
| 6432 | } |
| 6433 | |
| 6434 | |
| 6435 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
| 6436 | (SCM string, SCM radix), |
| 6437 | "Return a number of the maximally precise representation\n" |
| 6438 | "expressed by the given @var{string}. @var{radix} must be an\n" |
| 6439 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
| 6440 | "is a default radix that may be overridden by an explicit radix\n" |
| 6441 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" |
| 6442 | "supplied, then the default radix is 10. If string is not a\n" |
| 6443 | "syntactically valid notation for a number, then\n" |
| 6444 | "@code{string->number} returns @code{#f}.") |
| 6445 | #define FUNC_NAME s_scm_string_to_number |
| 6446 | { |
| 6447 | SCM answer; |
| 6448 | unsigned int base; |
| 6449 | SCM_VALIDATE_STRING (1, string); |
| 6450 | |
| 6451 | if (SCM_UNBNDP (radix)) |
| 6452 | base = 10; |
| 6453 | else |
| 6454 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); |
| 6455 | |
| 6456 | answer = scm_i_string_to_number (string, base); |
| 6457 | scm_remember_upto_here_1 (string); |
| 6458 | return answer; |
| 6459 | } |
| 6460 | #undef FUNC_NAME |
| 6461 | |
| 6462 | |
| 6463 | /*** END strs->nums ***/ |
| 6464 | |
| 6465 | |
| 6466 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
| 6467 | (SCM x), |
| 6468 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" |
| 6469 | "otherwise.") |
| 6470 | #define FUNC_NAME s_scm_number_p |
| 6471 | { |
| 6472 | return scm_from_bool (SCM_NUMBERP (x)); |
| 6473 | } |
| 6474 | #undef FUNC_NAME |
| 6475 | |
| 6476 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, |
| 6477 | (SCM x), |
| 6478 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
| 6479 | "otherwise. Note that the sets of real, rational and integer\n" |
| 6480 | "values form subsets of the set of complex numbers, i. e. the\n" |
| 6481 | "predicate will also be fulfilled if @var{x} is a real,\n" |
| 6482 | "rational or integer number.") |
| 6483 | #define FUNC_NAME s_scm_complex_p |
| 6484 | { |
| 6485 | /* all numbers are complex. */ |
| 6486 | return scm_number_p (x); |
| 6487 | } |
| 6488 | #undef FUNC_NAME |
| 6489 | |
| 6490 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
| 6491 | (SCM x), |
| 6492 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" |
| 6493 | "otherwise. Note that the set of integer values forms a subset of\n" |
| 6494 | "the set of real numbers, i. e. the predicate will also be\n" |
| 6495 | "fulfilled if @var{x} is an integer number.") |
| 6496 | #define FUNC_NAME s_scm_real_p |
| 6497 | { |
| 6498 | return scm_from_bool |
| 6499 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); |
| 6500 | } |
| 6501 | #undef FUNC_NAME |
| 6502 | |
| 6503 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, |
| 6504 | (SCM x), |
| 6505 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
| 6506 | "otherwise. Note that the set of integer values forms a subset of\n" |
| 6507 | "the set of rational numbers, i. e. the predicate will also be\n" |
| 6508 | "fulfilled if @var{x} is an integer number.") |
| 6509 | #define FUNC_NAME s_scm_rational_p |
| 6510 | { |
| 6511 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
| 6512 | return SCM_BOOL_T; |
| 6513 | else if (SCM_REALP (x)) |
| 6514 | /* due to their limited precision, finite floating point numbers are |
| 6515 | rational as well. (finite means neither infinity nor a NaN) */ |
| 6516 | return scm_from_bool (isfinite (SCM_REAL_VALUE (x))); |
| 6517 | else |
| 6518 | return SCM_BOOL_F; |
| 6519 | } |
| 6520 | #undef FUNC_NAME |
| 6521 | |
| 6522 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
| 6523 | (SCM x), |
| 6524 | "Return @code{#t} if @var{x} is an integer number,\n" |
| 6525 | "else return @code{#f}.") |
| 6526 | #define FUNC_NAME s_scm_integer_p |
| 6527 | { |
| 6528 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
| 6529 | return SCM_BOOL_T; |
| 6530 | else if (SCM_REALP (x)) |
| 6531 | { |
| 6532 | double val = SCM_REAL_VALUE (x); |
| 6533 | return scm_from_bool (!isinf (val) && (val == floor (val))); |
| 6534 | } |
| 6535 | else |
| 6536 | return SCM_BOOL_F; |
| 6537 | } |
| 6538 | #undef FUNC_NAME |
| 6539 | |
| 6540 | SCM_DEFINE (scm_exact_integer_p, "exact-integer?", 1, 0, 0, |
| 6541 | (SCM x), |
| 6542 | "Return @code{#t} if @var{x} is an exact integer number,\n" |
| 6543 | "else return @code{#f}.") |
| 6544 | #define FUNC_NAME s_scm_exact_integer_p |
| 6545 | { |
| 6546 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
| 6547 | return SCM_BOOL_T; |
| 6548 | else |
| 6549 | return SCM_BOOL_F; |
| 6550 | } |
| 6551 | #undef FUNC_NAME |
| 6552 | |
| 6553 | |
| 6554 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
| 6555 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, |
| 6556 | (SCM x, SCM y, SCM rest), |
| 6557 | "Return @code{#t} if all parameters are numerically equal.") |
| 6558 | #define FUNC_NAME s_scm_i_num_eq_p |
| 6559 | { |
| 6560 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) |
| 6561 | return SCM_BOOL_T; |
| 6562 | while (!scm_is_null (rest)) |
| 6563 | { |
| 6564 | if (scm_is_false (scm_num_eq_p (x, y))) |
| 6565 | return SCM_BOOL_F; |
| 6566 | x = y; |
| 6567 | y = scm_car (rest); |
| 6568 | rest = scm_cdr (rest); |
| 6569 | } |
| 6570 | return scm_num_eq_p (x, y); |
| 6571 | } |
| 6572 | #undef FUNC_NAME |
| 6573 | SCM |
| 6574 | scm_num_eq_p (SCM x, SCM y) |
| 6575 | { |
| 6576 | again: |
| 6577 | if (SCM_I_INUMP (x)) |
| 6578 | { |
| 6579 | scm_t_signed_bits xx = SCM_I_INUM (x); |
| 6580 | if (SCM_I_INUMP (y)) |
| 6581 | { |
| 6582 | scm_t_signed_bits yy = SCM_I_INUM (y); |
| 6583 | return scm_from_bool (xx == yy); |
| 6584 | } |
| 6585 | else if (SCM_BIGP (y)) |
| 6586 | return SCM_BOOL_F; |
| 6587 | else if (SCM_REALP (y)) |
| 6588 | { |
| 6589 | /* On a 32-bit system an inum fits a double, we can cast the inum |
| 6590 | to a double and compare. |
| 6591 | |
| 6592 | But on a 64-bit system an inum is bigger than a double and |
| 6593 | casting it to a double (call that dxx) will round. |
| 6594 | Although dxx will not in general be equal to xx, dxx will |
| 6595 | always be an integer and within a factor of 2 of xx, so if |
| 6596 | dxx==yy, we know that yy is an integer and fits in |
| 6597 | scm_t_signed_bits. So we cast yy to scm_t_signed_bits and |
| 6598 | compare with plain xx. |
| 6599 | |
| 6600 | An alternative (for any size system actually) would be to check |
| 6601 | yy is an integer (with floor) and is in range of an inum |
| 6602 | (compare against appropriate powers of 2) then test |
| 6603 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
| 6604 | casts/comparisons might be fastest or easiest for the cpu. */ |
| 6605 | |
| 6606 | double yy = SCM_REAL_VALUE (y); |
| 6607 | return scm_from_bool ((double) xx == yy |
| 6608 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 |
| 6609 | || xx == (scm_t_signed_bits) yy)); |
| 6610 | } |
| 6611 | else if (SCM_COMPLEXP (y)) |
| 6612 | { |
| 6613 | /* see comments with inum/real above */ |
| 6614 | double ry = SCM_COMPLEX_REAL (y); |
| 6615 | return scm_from_bool ((double) xx == ry |
| 6616 | && 0.0 == SCM_COMPLEX_IMAG (y) |
| 6617 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 |
| 6618 | || xx == (scm_t_signed_bits) ry)); |
| 6619 | } |
| 6620 | else if (SCM_FRACTIONP (y)) |
| 6621 | return SCM_BOOL_F; |
| 6622 | else |
| 6623 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
| 6624 | } |
| 6625 | else if (SCM_BIGP (x)) |
| 6626 | { |
| 6627 | if (SCM_I_INUMP (y)) |
| 6628 | return SCM_BOOL_F; |
| 6629 | else if (SCM_BIGP (y)) |
| 6630 | { |
| 6631 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 6632 | scm_remember_upto_here_2 (x, y); |
| 6633 | return scm_from_bool (0 == cmp); |
| 6634 | } |
| 6635 | else if (SCM_REALP (y)) |
| 6636 | { |
| 6637 | int cmp; |
| 6638 | if (isnan (SCM_REAL_VALUE (y))) |
| 6639 | return SCM_BOOL_F; |
| 6640 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); |
| 6641 | scm_remember_upto_here_1 (x); |
| 6642 | return scm_from_bool (0 == cmp); |
| 6643 | } |
| 6644 | else if (SCM_COMPLEXP (y)) |
| 6645 | { |
| 6646 | int cmp; |
| 6647 | if (0.0 != SCM_COMPLEX_IMAG (y)) |
| 6648 | return SCM_BOOL_F; |
| 6649 | if (isnan (SCM_COMPLEX_REAL (y))) |
| 6650 | return SCM_BOOL_F; |
| 6651 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); |
| 6652 | scm_remember_upto_here_1 (x); |
| 6653 | return scm_from_bool (0 == cmp); |
| 6654 | } |
| 6655 | else if (SCM_FRACTIONP (y)) |
| 6656 | return SCM_BOOL_F; |
| 6657 | else |
| 6658 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
| 6659 | } |
| 6660 | else if (SCM_REALP (x)) |
| 6661 | { |
| 6662 | double xx = SCM_REAL_VALUE (x); |
| 6663 | if (SCM_I_INUMP (y)) |
| 6664 | { |
| 6665 | /* see comments with inum/real above */ |
| 6666 | scm_t_signed_bits yy = SCM_I_INUM (y); |
| 6667 | return scm_from_bool (xx == (double) yy |
| 6668 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 |
| 6669 | || (scm_t_signed_bits) xx == yy)); |
| 6670 | } |
| 6671 | else if (SCM_BIGP (y)) |
| 6672 | { |
| 6673 | int cmp; |
| 6674 | if (isnan (xx)) |
| 6675 | return SCM_BOOL_F; |
| 6676 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx); |
| 6677 | scm_remember_upto_here_1 (y); |
| 6678 | return scm_from_bool (0 == cmp); |
| 6679 | } |
| 6680 | else if (SCM_REALP (y)) |
| 6681 | return scm_from_bool (xx == SCM_REAL_VALUE (y)); |
| 6682 | else if (SCM_COMPLEXP (y)) |
| 6683 | return scm_from_bool ((xx == SCM_COMPLEX_REAL (y)) |
| 6684 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
| 6685 | else if (SCM_FRACTIONP (y)) |
| 6686 | { |
| 6687 | if (isnan (xx) || isinf (xx)) |
| 6688 | return SCM_BOOL_F; |
| 6689 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
| 6690 | goto again; |
| 6691 | } |
| 6692 | else |
| 6693 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
| 6694 | } |
| 6695 | else if (SCM_COMPLEXP (x)) |
| 6696 | { |
| 6697 | if (SCM_I_INUMP (y)) |
| 6698 | { |
| 6699 | /* see comments with inum/real above */ |
| 6700 | double rx = SCM_COMPLEX_REAL (x); |
| 6701 | scm_t_signed_bits yy = SCM_I_INUM (y); |
| 6702 | return scm_from_bool (rx == (double) yy |
| 6703 | && 0.0 == SCM_COMPLEX_IMAG (x) |
| 6704 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 |
| 6705 | || (scm_t_signed_bits) rx == yy)); |
| 6706 | } |
| 6707 | else if (SCM_BIGP (y)) |
| 6708 | { |
| 6709 | int cmp; |
| 6710 | if (0.0 != SCM_COMPLEX_IMAG (x)) |
| 6711 | return SCM_BOOL_F; |
| 6712 | if (isnan (SCM_COMPLEX_REAL (x))) |
| 6713 | return SCM_BOOL_F; |
| 6714 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); |
| 6715 | scm_remember_upto_here_1 (y); |
| 6716 | return scm_from_bool (0 == cmp); |
| 6717 | } |
| 6718 | else if (SCM_REALP (y)) |
| 6719 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
| 6720 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
| 6721 | else if (SCM_COMPLEXP (y)) |
| 6722 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
| 6723 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
| 6724 | else if (SCM_FRACTIONP (y)) |
| 6725 | { |
| 6726 | double xx; |
| 6727 | if (SCM_COMPLEX_IMAG (x) != 0.0) |
| 6728 | return SCM_BOOL_F; |
| 6729 | xx = SCM_COMPLEX_REAL (x); |
| 6730 | if (isnan (xx) || isinf (xx)) |
| 6731 | return SCM_BOOL_F; |
| 6732 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
| 6733 | goto again; |
| 6734 | } |
| 6735 | else |
| 6736 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
| 6737 | } |
| 6738 | else if (SCM_FRACTIONP (x)) |
| 6739 | { |
| 6740 | if (SCM_I_INUMP (y)) |
| 6741 | return SCM_BOOL_F; |
| 6742 | else if (SCM_BIGP (y)) |
| 6743 | return SCM_BOOL_F; |
| 6744 | else if (SCM_REALP (y)) |
| 6745 | { |
| 6746 | double yy = SCM_REAL_VALUE (y); |
| 6747 | if (isnan (yy) || isinf (yy)) |
| 6748 | return SCM_BOOL_F; |
| 6749 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
| 6750 | goto again; |
| 6751 | } |
| 6752 | else if (SCM_COMPLEXP (y)) |
| 6753 | { |
| 6754 | double yy; |
| 6755 | if (SCM_COMPLEX_IMAG (y) != 0.0) |
| 6756 | return SCM_BOOL_F; |
| 6757 | yy = SCM_COMPLEX_REAL (y); |
| 6758 | if (isnan (yy) || isinf(yy)) |
| 6759 | return SCM_BOOL_F; |
| 6760 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
| 6761 | goto again; |
| 6762 | } |
| 6763 | else if (SCM_FRACTIONP (y)) |
| 6764 | return scm_i_fraction_equalp (x, y); |
| 6765 | else |
| 6766 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
| 6767 | } |
| 6768 | else |
| 6769 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
| 6770 | } |
| 6771 | |
| 6772 | |
| 6773 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
| 6774 | done are good for inums, but for bignums an answer can almost always be |
| 6775 | had by just examining a few high bits of the operands, as done by GMP in |
| 6776 | mpq_cmp. flonum/frac compares likewise, but with the slight complication |
| 6777 | of the float exponent to take into account. */ |
| 6778 | |
| 6779 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
| 6780 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
| 6781 | (SCM x, SCM y, SCM rest), |
| 6782 | "Return @code{#t} if the list of parameters is monotonically\n" |
| 6783 | "increasing.") |
| 6784 | #define FUNC_NAME s_scm_i_num_less_p |
| 6785 | { |
| 6786 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) |
| 6787 | return SCM_BOOL_T; |
| 6788 | while (!scm_is_null (rest)) |
| 6789 | { |
| 6790 | if (scm_is_false (scm_less_p (x, y))) |
| 6791 | return SCM_BOOL_F; |
| 6792 | x = y; |
| 6793 | y = scm_car (rest); |
| 6794 | rest = scm_cdr (rest); |
| 6795 | } |
| 6796 | return scm_less_p (x, y); |
| 6797 | } |
| 6798 | #undef FUNC_NAME |
| 6799 | SCM |
| 6800 | scm_less_p (SCM x, SCM y) |
| 6801 | { |
| 6802 | again: |
| 6803 | if (SCM_I_INUMP (x)) |
| 6804 | { |
| 6805 | scm_t_inum xx = SCM_I_INUM (x); |
| 6806 | if (SCM_I_INUMP (y)) |
| 6807 | { |
| 6808 | scm_t_inum yy = SCM_I_INUM (y); |
| 6809 | return scm_from_bool (xx < yy); |
| 6810 | } |
| 6811 | else if (SCM_BIGP (y)) |
| 6812 | { |
| 6813 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 6814 | scm_remember_upto_here_1 (y); |
| 6815 | return scm_from_bool (sgn > 0); |
| 6816 | } |
| 6817 | else if (SCM_REALP (y)) |
| 6818 | { |
| 6819 | /* We can safely take the ceiling of y without changing the |
| 6820 | result of x<y, given that x is an integer. */ |
| 6821 | double yy = ceil (SCM_REAL_VALUE (y)); |
| 6822 | |
| 6823 | /* In the following comparisons, it's important that the right |
| 6824 | hand side always be a power of 2, so that it can be |
| 6825 | losslessly converted to a double even on 64-bit |
| 6826 | machines. */ |
| 6827 | if (yy >= (double) (SCM_MOST_POSITIVE_FIXNUM+1)) |
| 6828 | return SCM_BOOL_T; |
| 6829 | else if (!(yy > (double) SCM_MOST_NEGATIVE_FIXNUM)) |
| 6830 | /* The condition above is carefully written to include the |
| 6831 | case where yy==NaN. */ |
| 6832 | return SCM_BOOL_F; |
| 6833 | else |
| 6834 | /* yy is a finite integer that fits in an inum. */ |
| 6835 | return scm_from_bool (xx < (scm_t_inum) yy); |
| 6836 | } |
| 6837 | else if (SCM_FRACTIONP (y)) |
| 6838 | { |
| 6839 | /* "x < a/b" becomes "x*b < a" */ |
| 6840 | int_frac: |
| 6841 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); |
| 6842 | y = SCM_FRACTION_NUMERATOR (y); |
| 6843 | goto again; |
| 6844 | } |
| 6845 | else |
| 6846 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
| 6847 | } |
| 6848 | else if (SCM_BIGP (x)) |
| 6849 | { |
| 6850 | if (SCM_I_INUMP (y)) |
| 6851 | { |
| 6852 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 6853 | scm_remember_upto_here_1 (x); |
| 6854 | return scm_from_bool (sgn < 0); |
| 6855 | } |
| 6856 | else if (SCM_BIGP (y)) |
| 6857 | { |
| 6858 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 6859 | scm_remember_upto_here_2 (x, y); |
| 6860 | return scm_from_bool (cmp < 0); |
| 6861 | } |
| 6862 | else if (SCM_REALP (y)) |
| 6863 | { |
| 6864 | int cmp; |
| 6865 | if (isnan (SCM_REAL_VALUE (y))) |
| 6866 | return SCM_BOOL_F; |
| 6867 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); |
| 6868 | scm_remember_upto_here_1 (x); |
| 6869 | return scm_from_bool (cmp < 0); |
| 6870 | } |
| 6871 | else if (SCM_FRACTIONP (y)) |
| 6872 | goto int_frac; |
| 6873 | else |
| 6874 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
| 6875 | } |
| 6876 | else if (SCM_REALP (x)) |
| 6877 | { |
| 6878 | if (SCM_I_INUMP (y)) |
| 6879 | { |
| 6880 | /* We can safely take the floor of x without changing the |
| 6881 | result of x<y, given that y is an integer. */ |
| 6882 | double xx = floor (SCM_REAL_VALUE (x)); |
| 6883 | |
| 6884 | /* In the following comparisons, it's important that the right |
| 6885 | hand side always be a power of 2, so that it can be |
| 6886 | losslessly converted to a double even on 64-bit |
| 6887 | machines. */ |
| 6888 | if (xx < (double) SCM_MOST_NEGATIVE_FIXNUM) |
| 6889 | return SCM_BOOL_T; |
| 6890 | else if (!(xx < (double) (SCM_MOST_POSITIVE_FIXNUM+1))) |
| 6891 | /* The condition above is carefully written to include the |
| 6892 | case where xx==NaN. */ |
| 6893 | return SCM_BOOL_F; |
| 6894 | else |
| 6895 | /* xx is a finite integer that fits in an inum. */ |
| 6896 | return scm_from_bool ((scm_t_inum) xx < SCM_I_INUM (y)); |
| 6897 | } |
| 6898 | else if (SCM_BIGP (y)) |
| 6899 | { |
| 6900 | int cmp; |
| 6901 | if (isnan (SCM_REAL_VALUE (x))) |
| 6902 | return SCM_BOOL_F; |
| 6903 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); |
| 6904 | scm_remember_upto_here_1 (y); |
| 6905 | return scm_from_bool (cmp > 0); |
| 6906 | } |
| 6907 | else if (SCM_REALP (y)) |
| 6908 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
| 6909 | else if (SCM_FRACTIONP (y)) |
| 6910 | { |
| 6911 | double xx = SCM_REAL_VALUE (x); |
| 6912 | if (isnan (xx)) |
| 6913 | return SCM_BOOL_F; |
| 6914 | if (isinf (xx)) |
| 6915 | return scm_from_bool (xx < 0.0); |
| 6916 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
| 6917 | goto again; |
| 6918 | } |
| 6919 | else |
| 6920 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
| 6921 | } |
| 6922 | else if (SCM_FRACTIONP (x)) |
| 6923 | { |
| 6924 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
| 6925 | { |
| 6926 | /* "a/b < y" becomes "a < y*b" */ |
| 6927 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); |
| 6928 | x = SCM_FRACTION_NUMERATOR (x); |
| 6929 | goto again; |
| 6930 | } |
| 6931 | else if (SCM_REALP (y)) |
| 6932 | { |
| 6933 | double yy = SCM_REAL_VALUE (y); |
| 6934 | if (isnan (yy)) |
| 6935 | return SCM_BOOL_F; |
| 6936 | if (isinf (yy)) |
| 6937 | return scm_from_bool (0.0 < yy); |
| 6938 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
| 6939 | goto again; |
| 6940 | } |
| 6941 | else if (SCM_FRACTIONP (y)) |
| 6942 | { |
| 6943 | /* "a/b < c/d" becomes "a*d < c*b" */ |
| 6944 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), |
| 6945 | SCM_FRACTION_DENOMINATOR (y)); |
| 6946 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), |
| 6947 | SCM_FRACTION_DENOMINATOR (x)); |
| 6948 | x = new_x; |
| 6949 | y = new_y; |
| 6950 | goto again; |
| 6951 | } |
| 6952 | else |
| 6953 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
| 6954 | } |
| 6955 | else |
| 6956 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
| 6957 | } |
| 6958 | |
| 6959 | |
| 6960 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
| 6961 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, |
| 6962 | (SCM x, SCM y, SCM rest), |
| 6963 | "Return @code{#t} if the list of parameters is monotonically\n" |
| 6964 | "decreasing.") |
| 6965 | #define FUNC_NAME s_scm_i_num_gr_p |
| 6966 | { |
| 6967 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) |
| 6968 | return SCM_BOOL_T; |
| 6969 | while (!scm_is_null (rest)) |
| 6970 | { |
| 6971 | if (scm_is_false (scm_gr_p (x, y))) |
| 6972 | return SCM_BOOL_F; |
| 6973 | x = y; |
| 6974 | y = scm_car (rest); |
| 6975 | rest = scm_cdr (rest); |
| 6976 | } |
| 6977 | return scm_gr_p (x, y); |
| 6978 | } |
| 6979 | #undef FUNC_NAME |
| 6980 | #define FUNC_NAME s_scm_i_num_gr_p |
| 6981 | SCM |
| 6982 | scm_gr_p (SCM x, SCM y) |
| 6983 | { |
| 6984 | if (!SCM_NUMBERP (x)) |
| 6985 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
| 6986 | else if (!SCM_NUMBERP (y)) |
| 6987 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
| 6988 | else |
| 6989 | return scm_less_p (y, x); |
| 6990 | } |
| 6991 | #undef FUNC_NAME |
| 6992 | |
| 6993 | |
| 6994 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
| 6995 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, |
| 6996 | (SCM x, SCM y, SCM rest), |
| 6997 | "Return @code{#t} if the list of parameters is monotonically\n" |
| 6998 | "non-decreasing.") |
| 6999 | #define FUNC_NAME s_scm_i_num_leq_p |
| 7000 | { |
| 7001 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) |
| 7002 | return SCM_BOOL_T; |
| 7003 | while (!scm_is_null (rest)) |
| 7004 | { |
| 7005 | if (scm_is_false (scm_leq_p (x, y))) |
| 7006 | return SCM_BOOL_F; |
| 7007 | x = y; |
| 7008 | y = scm_car (rest); |
| 7009 | rest = scm_cdr (rest); |
| 7010 | } |
| 7011 | return scm_leq_p (x, y); |
| 7012 | } |
| 7013 | #undef FUNC_NAME |
| 7014 | #define FUNC_NAME s_scm_i_num_leq_p |
| 7015 | SCM |
| 7016 | scm_leq_p (SCM x, SCM y) |
| 7017 | { |
| 7018 | if (!SCM_NUMBERP (x)) |
| 7019 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
| 7020 | else if (!SCM_NUMBERP (y)) |
| 7021 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
| 7022 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
| 7023 | return SCM_BOOL_F; |
| 7024 | else |
| 7025 | return scm_not (scm_less_p (y, x)); |
| 7026 | } |
| 7027 | #undef FUNC_NAME |
| 7028 | |
| 7029 | |
| 7030 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
| 7031 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, |
| 7032 | (SCM x, SCM y, SCM rest), |
| 7033 | "Return @code{#t} if the list of parameters is monotonically\n" |
| 7034 | "non-increasing.") |
| 7035 | #define FUNC_NAME s_scm_i_num_geq_p |
| 7036 | { |
| 7037 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) |
| 7038 | return SCM_BOOL_T; |
| 7039 | while (!scm_is_null (rest)) |
| 7040 | { |
| 7041 | if (scm_is_false (scm_geq_p (x, y))) |
| 7042 | return SCM_BOOL_F; |
| 7043 | x = y; |
| 7044 | y = scm_car (rest); |
| 7045 | rest = scm_cdr (rest); |
| 7046 | } |
| 7047 | return scm_geq_p (x, y); |
| 7048 | } |
| 7049 | #undef FUNC_NAME |
| 7050 | #define FUNC_NAME s_scm_i_num_geq_p |
| 7051 | SCM |
| 7052 | scm_geq_p (SCM x, SCM y) |
| 7053 | { |
| 7054 | if (!SCM_NUMBERP (x)) |
| 7055 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
| 7056 | else if (!SCM_NUMBERP (y)) |
| 7057 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
| 7058 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
| 7059 | return SCM_BOOL_F; |
| 7060 | else |
| 7061 | return scm_not (scm_less_p (x, y)); |
| 7062 | } |
| 7063 | #undef FUNC_NAME |
| 7064 | |
| 7065 | |
| 7066 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
| 7067 | (SCM z), |
| 7068 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
| 7069 | "zero.") |
| 7070 | #define FUNC_NAME s_scm_zero_p |
| 7071 | { |
| 7072 | if (SCM_I_INUMP (z)) |
| 7073 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
| 7074 | else if (SCM_BIGP (z)) |
| 7075 | return SCM_BOOL_F; |
| 7076 | else if (SCM_REALP (z)) |
| 7077 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
| 7078 | else if (SCM_COMPLEXP (z)) |
| 7079 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
| 7080 | && SCM_COMPLEX_IMAG (z) == 0.0); |
| 7081 | else if (SCM_FRACTIONP (z)) |
| 7082 | return SCM_BOOL_F; |
| 7083 | else |
| 7084 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
| 7085 | } |
| 7086 | #undef FUNC_NAME |
| 7087 | |
| 7088 | |
| 7089 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
| 7090 | (SCM x), |
| 7091 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
| 7092 | "zero.") |
| 7093 | #define FUNC_NAME s_scm_positive_p |
| 7094 | { |
| 7095 | if (SCM_I_INUMP (x)) |
| 7096 | return scm_from_bool (SCM_I_INUM (x) > 0); |
| 7097 | else if (SCM_BIGP (x)) |
| 7098 | { |
| 7099 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7100 | scm_remember_upto_here_1 (x); |
| 7101 | return scm_from_bool (sgn > 0); |
| 7102 | } |
| 7103 | else if (SCM_REALP (x)) |
| 7104 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
| 7105 | else if (SCM_FRACTIONP (x)) |
| 7106 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); |
| 7107 | else |
| 7108 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
| 7109 | } |
| 7110 | #undef FUNC_NAME |
| 7111 | |
| 7112 | |
| 7113 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
| 7114 | (SCM x), |
| 7115 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
| 7116 | "zero.") |
| 7117 | #define FUNC_NAME s_scm_negative_p |
| 7118 | { |
| 7119 | if (SCM_I_INUMP (x)) |
| 7120 | return scm_from_bool (SCM_I_INUM (x) < 0); |
| 7121 | else if (SCM_BIGP (x)) |
| 7122 | { |
| 7123 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7124 | scm_remember_upto_here_1 (x); |
| 7125 | return scm_from_bool (sgn < 0); |
| 7126 | } |
| 7127 | else if (SCM_REALP (x)) |
| 7128 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
| 7129 | else if (SCM_FRACTIONP (x)) |
| 7130 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); |
| 7131 | else |
| 7132 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
| 7133 | } |
| 7134 | #undef FUNC_NAME |
| 7135 | |
| 7136 | |
| 7137 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
| 7138 | required by r5rs. On that basis, for exact/inexact combinations the |
| 7139 | exact is converted to inexact to compare and possibly return. This is |
| 7140 | unlike scm_less_p above which takes some trouble to preserve all bits in |
| 7141 | its test, such trouble is not required for min and max. */ |
| 7142 | |
| 7143 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
| 7144 | (SCM x, SCM y, SCM rest), |
| 7145 | "Return the maximum of all parameter values.") |
| 7146 | #define FUNC_NAME s_scm_i_max |
| 7147 | { |
| 7148 | while (!scm_is_null (rest)) |
| 7149 | { x = scm_max (x, y); |
| 7150 | y = scm_car (rest); |
| 7151 | rest = scm_cdr (rest); |
| 7152 | } |
| 7153 | return scm_max (x, y); |
| 7154 | } |
| 7155 | #undef FUNC_NAME |
| 7156 | |
| 7157 | #define s_max s_scm_i_max |
| 7158 | #define g_max g_scm_i_max |
| 7159 | |
| 7160 | SCM |
| 7161 | scm_max (SCM x, SCM y) |
| 7162 | { |
| 7163 | if (SCM_UNBNDP (y)) |
| 7164 | { |
| 7165 | if (SCM_UNBNDP (x)) |
| 7166 | SCM_WTA_DISPATCH_0 (g_max, s_max); |
| 7167 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
| 7168 | return x; |
| 7169 | else |
| 7170 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); |
| 7171 | } |
| 7172 | |
| 7173 | if (SCM_I_INUMP (x)) |
| 7174 | { |
| 7175 | scm_t_inum xx = SCM_I_INUM (x); |
| 7176 | if (SCM_I_INUMP (y)) |
| 7177 | { |
| 7178 | scm_t_inum yy = SCM_I_INUM (y); |
| 7179 | return (xx < yy) ? y : x; |
| 7180 | } |
| 7181 | else if (SCM_BIGP (y)) |
| 7182 | { |
| 7183 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 7184 | scm_remember_upto_here_1 (y); |
| 7185 | return (sgn < 0) ? x : y; |
| 7186 | } |
| 7187 | else if (SCM_REALP (y)) |
| 7188 | { |
| 7189 | double xxd = xx; |
| 7190 | double yyd = SCM_REAL_VALUE (y); |
| 7191 | |
| 7192 | if (xxd > yyd) |
| 7193 | return scm_i_from_double (xxd); |
| 7194 | /* If y is a NaN, then "==" is false and we return the NaN */ |
| 7195 | else if (SCM_LIKELY (!(xxd == yyd))) |
| 7196 | return y; |
| 7197 | /* Handle signed zeroes properly */ |
| 7198 | else if (xx == 0) |
| 7199 | return flo0; |
| 7200 | else |
| 7201 | return y; |
| 7202 | } |
| 7203 | else if (SCM_FRACTIONP (y)) |
| 7204 | { |
| 7205 | use_less: |
| 7206 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
| 7207 | } |
| 7208 | else |
| 7209 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); |
| 7210 | } |
| 7211 | else if (SCM_BIGP (x)) |
| 7212 | { |
| 7213 | if (SCM_I_INUMP (y)) |
| 7214 | { |
| 7215 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7216 | scm_remember_upto_here_1 (x); |
| 7217 | return (sgn < 0) ? y : x; |
| 7218 | } |
| 7219 | else if (SCM_BIGP (y)) |
| 7220 | { |
| 7221 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 7222 | scm_remember_upto_here_2 (x, y); |
| 7223 | return (cmp > 0) ? x : y; |
| 7224 | } |
| 7225 | else if (SCM_REALP (y)) |
| 7226 | { |
| 7227 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
| 7228 | double xx, yy; |
| 7229 | big_real: |
| 7230 | xx = scm_i_big2dbl (x); |
| 7231 | yy = SCM_REAL_VALUE (y); |
| 7232 | return (xx > yy ? scm_i_from_double (xx) : y); |
| 7233 | } |
| 7234 | else if (SCM_FRACTIONP (y)) |
| 7235 | { |
| 7236 | goto use_less; |
| 7237 | } |
| 7238 | else |
| 7239 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); |
| 7240 | } |
| 7241 | else if (SCM_REALP (x)) |
| 7242 | { |
| 7243 | if (SCM_I_INUMP (y)) |
| 7244 | { |
| 7245 | scm_t_inum yy = SCM_I_INUM (y); |
| 7246 | double xxd = SCM_REAL_VALUE (x); |
| 7247 | double yyd = yy; |
| 7248 | |
| 7249 | if (yyd > xxd) |
| 7250 | return scm_i_from_double (yyd); |
| 7251 | /* If x is a NaN, then "==" is false and we return the NaN */ |
| 7252 | else if (SCM_LIKELY (!(xxd == yyd))) |
| 7253 | return x; |
| 7254 | /* Handle signed zeroes properly */ |
| 7255 | else if (yy == 0) |
| 7256 | return flo0; |
| 7257 | else |
| 7258 | return x; |
| 7259 | } |
| 7260 | else if (SCM_BIGP (y)) |
| 7261 | { |
| 7262 | SCM_SWAP (x, y); |
| 7263 | goto big_real; |
| 7264 | } |
| 7265 | else if (SCM_REALP (y)) |
| 7266 | { |
| 7267 | double xx = SCM_REAL_VALUE (x); |
| 7268 | double yy = SCM_REAL_VALUE (y); |
| 7269 | |
| 7270 | /* For purposes of max: nan > +inf.0 > everything else, |
| 7271 | per the R6RS errata */ |
| 7272 | if (xx > yy) |
| 7273 | return x; |
| 7274 | else if (SCM_LIKELY (xx < yy)) |
| 7275 | return y; |
| 7276 | /* If neither (xx > yy) nor (xx < yy), then |
| 7277 | either they're equal or one is a NaN */ |
| 7278 | else if (SCM_UNLIKELY (xx != yy)) |
| 7279 | return (xx != xx) ? x : y; /* Return the NaN */ |
| 7280 | /* xx == yy, but handle signed zeroes properly */ |
| 7281 | else if (copysign (1.0, yy) < 0.0) |
| 7282 | return x; |
| 7283 | else |
| 7284 | return y; |
| 7285 | } |
| 7286 | else if (SCM_FRACTIONP (y)) |
| 7287 | { |
| 7288 | double yy = scm_i_fraction2double (y); |
| 7289 | double xx = SCM_REAL_VALUE (x); |
| 7290 | return (xx < yy) ? scm_i_from_double (yy) : x; |
| 7291 | } |
| 7292 | else |
| 7293 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); |
| 7294 | } |
| 7295 | else if (SCM_FRACTIONP (x)) |
| 7296 | { |
| 7297 | if (SCM_I_INUMP (y)) |
| 7298 | { |
| 7299 | goto use_less; |
| 7300 | } |
| 7301 | else if (SCM_BIGP (y)) |
| 7302 | { |
| 7303 | goto use_less; |
| 7304 | } |
| 7305 | else if (SCM_REALP (y)) |
| 7306 | { |
| 7307 | double xx = scm_i_fraction2double (x); |
| 7308 | /* if y==NaN then ">" is false, so we return the NaN y */ |
| 7309 | return (xx > SCM_REAL_VALUE (y)) ? scm_i_from_double (xx) : y; |
| 7310 | } |
| 7311 | else if (SCM_FRACTIONP (y)) |
| 7312 | { |
| 7313 | goto use_less; |
| 7314 | } |
| 7315 | else |
| 7316 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); |
| 7317 | } |
| 7318 | else |
| 7319 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
| 7320 | } |
| 7321 | |
| 7322 | |
| 7323 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
| 7324 | (SCM x, SCM y, SCM rest), |
| 7325 | "Return the minimum of all parameter values.") |
| 7326 | #define FUNC_NAME s_scm_i_min |
| 7327 | { |
| 7328 | while (!scm_is_null (rest)) |
| 7329 | { x = scm_min (x, y); |
| 7330 | y = scm_car (rest); |
| 7331 | rest = scm_cdr (rest); |
| 7332 | } |
| 7333 | return scm_min (x, y); |
| 7334 | } |
| 7335 | #undef FUNC_NAME |
| 7336 | |
| 7337 | #define s_min s_scm_i_min |
| 7338 | #define g_min g_scm_i_min |
| 7339 | |
| 7340 | SCM |
| 7341 | scm_min (SCM x, SCM y) |
| 7342 | { |
| 7343 | if (SCM_UNBNDP (y)) |
| 7344 | { |
| 7345 | if (SCM_UNBNDP (x)) |
| 7346 | SCM_WTA_DISPATCH_0 (g_min, s_min); |
| 7347 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
| 7348 | return x; |
| 7349 | else |
| 7350 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); |
| 7351 | } |
| 7352 | |
| 7353 | if (SCM_I_INUMP (x)) |
| 7354 | { |
| 7355 | scm_t_inum xx = SCM_I_INUM (x); |
| 7356 | if (SCM_I_INUMP (y)) |
| 7357 | { |
| 7358 | scm_t_inum yy = SCM_I_INUM (y); |
| 7359 | return (xx < yy) ? x : y; |
| 7360 | } |
| 7361 | else if (SCM_BIGP (y)) |
| 7362 | { |
| 7363 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 7364 | scm_remember_upto_here_1 (y); |
| 7365 | return (sgn < 0) ? y : x; |
| 7366 | } |
| 7367 | else if (SCM_REALP (y)) |
| 7368 | { |
| 7369 | double z = xx; |
| 7370 | /* if y==NaN then "<" is false and we return NaN */ |
| 7371 | return (z < SCM_REAL_VALUE (y)) ? scm_i_from_double (z) : y; |
| 7372 | } |
| 7373 | else if (SCM_FRACTIONP (y)) |
| 7374 | { |
| 7375 | use_less: |
| 7376 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
| 7377 | } |
| 7378 | else |
| 7379 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
| 7380 | } |
| 7381 | else if (SCM_BIGP (x)) |
| 7382 | { |
| 7383 | if (SCM_I_INUMP (y)) |
| 7384 | { |
| 7385 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7386 | scm_remember_upto_here_1 (x); |
| 7387 | return (sgn < 0) ? x : y; |
| 7388 | } |
| 7389 | else if (SCM_BIGP (y)) |
| 7390 | { |
| 7391 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
| 7392 | scm_remember_upto_here_2 (x, y); |
| 7393 | return (cmp > 0) ? y : x; |
| 7394 | } |
| 7395 | else if (SCM_REALP (y)) |
| 7396 | { |
| 7397 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
| 7398 | double xx, yy; |
| 7399 | big_real: |
| 7400 | xx = scm_i_big2dbl (x); |
| 7401 | yy = SCM_REAL_VALUE (y); |
| 7402 | return (xx < yy ? scm_i_from_double (xx) : y); |
| 7403 | } |
| 7404 | else if (SCM_FRACTIONP (y)) |
| 7405 | { |
| 7406 | goto use_less; |
| 7407 | } |
| 7408 | else |
| 7409 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
| 7410 | } |
| 7411 | else if (SCM_REALP (x)) |
| 7412 | { |
| 7413 | if (SCM_I_INUMP (y)) |
| 7414 | { |
| 7415 | double z = SCM_I_INUM (y); |
| 7416 | /* if x==NaN then "<" is false and we return NaN */ |
| 7417 | return (z < SCM_REAL_VALUE (x)) ? scm_i_from_double (z) : x; |
| 7418 | } |
| 7419 | else if (SCM_BIGP (y)) |
| 7420 | { |
| 7421 | SCM_SWAP (x, y); |
| 7422 | goto big_real; |
| 7423 | } |
| 7424 | else if (SCM_REALP (y)) |
| 7425 | { |
| 7426 | double xx = SCM_REAL_VALUE (x); |
| 7427 | double yy = SCM_REAL_VALUE (y); |
| 7428 | |
| 7429 | /* For purposes of min: nan < -inf.0 < everything else, |
| 7430 | per the R6RS errata */ |
| 7431 | if (xx < yy) |
| 7432 | return x; |
| 7433 | else if (SCM_LIKELY (xx > yy)) |
| 7434 | return y; |
| 7435 | /* If neither (xx < yy) nor (xx > yy), then |
| 7436 | either they're equal or one is a NaN */ |
| 7437 | else if (SCM_UNLIKELY (xx != yy)) |
| 7438 | return (xx != xx) ? x : y; /* Return the NaN */ |
| 7439 | /* xx == yy, but handle signed zeroes properly */ |
| 7440 | else if (copysign (1.0, xx) < 0.0) |
| 7441 | return x; |
| 7442 | else |
| 7443 | return y; |
| 7444 | } |
| 7445 | else if (SCM_FRACTIONP (y)) |
| 7446 | { |
| 7447 | double yy = scm_i_fraction2double (y); |
| 7448 | double xx = SCM_REAL_VALUE (x); |
| 7449 | return (yy < xx) ? scm_i_from_double (yy) : x; |
| 7450 | } |
| 7451 | else |
| 7452 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
| 7453 | } |
| 7454 | else if (SCM_FRACTIONP (x)) |
| 7455 | { |
| 7456 | if (SCM_I_INUMP (y)) |
| 7457 | { |
| 7458 | goto use_less; |
| 7459 | } |
| 7460 | else if (SCM_BIGP (y)) |
| 7461 | { |
| 7462 | goto use_less; |
| 7463 | } |
| 7464 | else if (SCM_REALP (y)) |
| 7465 | { |
| 7466 | double xx = scm_i_fraction2double (x); |
| 7467 | /* if y==NaN then "<" is false, so we return the NaN y */ |
| 7468 | return (xx < SCM_REAL_VALUE (y)) ? scm_i_from_double (xx) : y; |
| 7469 | } |
| 7470 | else if (SCM_FRACTIONP (y)) |
| 7471 | { |
| 7472 | goto use_less; |
| 7473 | } |
| 7474 | else |
| 7475 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
| 7476 | } |
| 7477 | else |
| 7478 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
| 7479 | } |
| 7480 | |
| 7481 | |
| 7482 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
| 7483 | (SCM x, SCM y, SCM rest), |
| 7484 | "Return the sum of all parameter values. Return 0 if called without\n" |
| 7485 | "any parameters." ) |
| 7486 | #define FUNC_NAME s_scm_i_sum |
| 7487 | { |
| 7488 | while (!scm_is_null (rest)) |
| 7489 | { x = scm_sum (x, y); |
| 7490 | y = scm_car (rest); |
| 7491 | rest = scm_cdr (rest); |
| 7492 | } |
| 7493 | return scm_sum (x, y); |
| 7494 | } |
| 7495 | #undef FUNC_NAME |
| 7496 | |
| 7497 | #define s_sum s_scm_i_sum |
| 7498 | #define g_sum g_scm_i_sum |
| 7499 | |
| 7500 | SCM |
| 7501 | scm_sum (SCM x, SCM y) |
| 7502 | { |
| 7503 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
| 7504 | { |
| 7505 | if (SCM_NUMBERP (x)) return x; |
| 7506 | if (SCM_UNBNDP (x)) return SCM_INUM0; |
| 7507 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
| 7508 | } |
| 7509 | |
| 7510 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 7511 | { |
| 7512 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 7513 | { |
| 7514 | scm_t_inum xx = SCM_I_INUM (x); |
| 7515 | scm_t_inum yy = SCM_I_INUM (y); |
| 7516 | scm_t_inum z = xx + yy; |
| 7517 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); |
| 7518 | } |
| 7519 | else if (SCM_BIGP (y)) |
| 7520 | { |
| 7521 | SCM_SWAP (x, y); |
| 7522 | goto add_big_inum; |
| 7523 | } |
| 7524 | else if (SCM_REALP (y)) |
| 7525 | { |
| 7526 | scm_t_inum xx = SCM_I_INUM (x); |
| 7527 | return scm_i_from_double (xx + SCM_REAL_VALUE (y)); |
| 7528 | } |
| 7529 | else if (SCM_COMPLEXP (y)) |
| 7530 | { |
| 7531 | scm_t_inum xx = SCM_I_INUM (x); |
| 7532 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
| 7533 | SCM_COMPLEX_IMAG (y)); |
| 7534 | } |
| 7535 | else if (SCM_FRACTIONP (y)) |
| 7536 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
| 7537 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
| 7538 | SCM_FRACTION_DENOMINATOR (y)); |
| 7539 | else |
| 7540 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); |
| 7541 | } else if (SCM_BIGP (x)) |
| 7542 | { |
| 7543 | if (SCM_I_INUMP (y)) |
| 7544 | { |
| 7545 | scm_t_inum inum; |
| 7546 | int bigsgn; |
| 7547 | add_big_inum: |
| 7548 | inum = SCM_I_INUM (y); |
| 7549 | if (inum == 0) |
| 7550 | return x; |
| 7551 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7552 | if (inum < 0) |
| 7553 | { |
| 7554 | SCM result = scm_i_mkbig (); |
| 7555 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); |
| 7556 | scm_remember_upto_here_1 (x); |
| 7557 | /* we know the result will have to be a bignum */ |
| 7558 | if (bigsgn == -1) |
| 7559 | return result; |
| 7560 | return scm_i_normbig (result); |
| 7561 | } |
| 7562 | else |
| 7563 | { |
| 7564 | SCM result = scm_i_mkbig (); |
| 7565 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); |
| 7566 | scm_remember_upto_here_1 (x); |
| 7567 | /* we know the result will have to be a bignum */ |
| 7568 | if (bigsgn == 1) |
| 7569 | return result; |
| 7570 | return scm_i_normbig (result); |
| 7571 | } |
| 7572 | } |
| 7573 | else if (SCM_BIGP (y)) |
| 7574 | { |
| 7575 | SCM result = scm_i_mkbig (); |
| 7576 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7577 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 7578 | mpz_add (SCM_I_BIG_MPZ (result), |
| 7579 | SCM_I_BIG_MPZ (x), |
| 7580 | SCM_I_BIG_MPZ (y)); |
| 7581 | scm_remember_upto_here_2 (x, y); |
| 7582 | /* we know the result will have to be a bignum */ |
| 7583 | if (sgn_x == sgn_y) |
| 7584 | return result; |
| 7585 | return scm_i_normbig (result); |
| 7586 | } |
| 7587 | else if (SCM_REALP (y)) |
| 7588 | { |
| 7589 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); |
| 7590 | scm_remember_upto_here_1 (x); |
| 7591 | return scm_i_from_double (result); |
| 7592 | } |
| 7593 | else if (SCM_COMPLEXP (y)) |
| 7594 | { |
| 7595 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) |
| 7596 | + SCM_COMPLEX_REAL (y)); |
| 7597 | scm_remember_upto_here_1 (x); |
| 7598 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
| 7599 | } |
| 7600 | else if (SCM_FRACTIONP (y)) |
| 7601 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
| 7602 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
| 7603 | SCM_FRACTION_DENOMINATOR (y)); |
| 7604 | else |
| 7605 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); |
| 7606 | } |
| 7607 | else if (SCM_REALP (x)) |
| 7608 | { |
| 7609 | if (SCM_I_INUMP (y)) |
| 7610 | return scm_i_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
| 7611 | else if (SCM_BIGP (y)) |
| 7612 | { |
| 7613 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); |
| 7614 | scm_remember_upto_here_1 (y); |
| 7615 | return scm_i_from_double (result); |
| 7616 | } |
| 7617 | else if (SCM_REALP (y)) |
| 7618 | return scm_i_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
| 7619 | else if (SCM_COMPLEXP (y)) |
| 7620 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
| 7621 | SCM_COMPLEX_IMAG (y)); |
| 7622 | else if (SCM_FRACTIONP (y)) |
| 7623 | return scm_i_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
| 7624 | else |
| 7625 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); |
| 7626 | } |
| 7627 | else if (SCM_COMPLEXP (x)) |
| 7628 | { |
| 7629 | if (SCM_I_INUMP (y)) |
| 7630 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
| 7631 | SCM_COMPLEX_IMAG (x)); |
| 7632 | else if (SCM_BIGP (y)) |
| 7633 | { |
| 7634 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) |
| 7635 | + SCM_COMPLEX_REAL (x)); |
| 7636 | scm_remember_upto_here_1 (y); |
| 7637 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
| 7638 | } |
| 7639 | else if (SCM_REALP (y)) |
| 7640 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
| 7641 | SCM_COMPLEX_IMAG (x)); |
| 7642 | else if (SCM_COMPLEXP (y)) |
| 7643 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
| 7644 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
| 7645 | else if (SCM_FRACTIONP (y)) |
| 7646 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
| 7647 | SCM_COMPLEX_IMAG (x)); |
| 7648 | else |
| 7649 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); |
| 7650 | } |
| 7651 | else if (SCM_FRACTIONP (x)) |
| 7652 | { |
| 7653 | if (SCM_I_INUMP (y)) |
| 7654 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
| 7655 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
| 7656 | SCM_FRACTION_DENOMINATOR (x)); |
| 7657 | else if (SCM_BIGP (y)) |
| 7658 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
| 7659 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
| 7660 | SCM_FRACTION_DENOMINATOR (x)); |
| 7661 | else if (SCM_REALP (y)) |
| 7662 | return scm_i_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
| 7663 | else if (SCM_COMPLEXP (y)) |
| 7664 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
| 7665 | SCM_COMPLEX_IMAG (y)); |
| 7666 | else if (SCM_FRACTIONP (y)) |
| 7667 | /* a/b + c/d = (ad + bc) / bd */ |
| 7668 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
| 7669 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
| 7670 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); |
| 7671 | else |
| 7672 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); |
| 7673 | } |
| 7674 | else |
| 7675 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
| 7676 | } |
| 7677 | |
| 7678 | |
| 7679 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
| 7680 | (SCM x), |
| 7681 | "Return @math{@var{x}+1}.") |
| 7682 | #define FUNC_NAME s_scm_oneplus |
| 7683 | { |
| 7684 | return scm_sum (x, SCM_INUM1); |
| 7685 | } |
| 7686 | #undef FUNC_NAME |
| 7687 | |
| 7688 | |
| 7689 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
| 7690 | (SCM x, SCM y, SCM rest), |
| 7691 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" |
| 7692 | "the sum of all but the first argument are subtracted from the first\n" |
| 7693 | "argument.") |
| 7694 | #define FUNC_NAME s_scm_i_difference |
| 7695 | { |
| 7696 | while (!scm_is_null (rest)) |
| 7697 | { x = scm_difference (x, y); |
| 7698 | y = scm_car (rest); |
| 7699 | rest = scm_cdr (rest); |
| 7700 | } |
| 7701 | return scm_difference (x, y); |
| 7702 | } |
| 7703 | #undef FUNC_NAME |
| 7704 | |
| 7705 | #define s_difference s_scm_i_difference |
| 7706 | #define g_difference g_scm_i_difference |
| 7707 | |
| 7708 | SCM |
| 7709 | scm_difference (SCM x, SCM y) |
| 7710 | #define FUNC_NAME s_difference |
| 7711 | { |
| 7712 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
| 7713 | { |
| 7714 | if (SCM_UNBNDP (x)) |
| 7715 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); |
| 7716 | else |
| 7717 | if (SCM_I_INUMP (x)) |
| 7718 | { |
| 7719 | scm_t_inum xx = -SCM_I_INUM (x); |
| 7720 | if (SCM_FIXABLE (xx)) |
| 7721 | return SCM_I_MAKINUM (xx); |
| 7722 | else |
| 7723 | return scm_i_inum2big (xx); |
| 7724 | } |
| 7725 | else if (SCM_BIGP (x)) |
| 7726 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
| 7727 | bignum, but negating that gives a fixnum. */ |
| 7728 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
| 7729 | else if (SCM_REALP (x)) |
| 7730 | return scm_i_from_double (-SCM_REAL_VALUE (x)); |
| 7731 | else if (SCM_COMPLEXP (x)) |
| 7732 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
| 7733 | -SCM_COMPLEX_IMAG (x)); |
| 7734 | else if (SCM_FRACTIONP (x)) |
| 7735 | return scm_i_make_ratio_already_reduced |
| 7736 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
| 7737 | SCM_FRACTION_DENOMINATOR (x)); |
| 7738 | else |
| 7739 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); |
| 7740 | } |
| 7741 | |
| 7742 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 7743 | { |
| 7744 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 7745 | { |
| 7746 | scm_t_inum xx = SCM_I_INUM (x); |
| 7747 | scm_t_inum yy = SCM_I_INUM (y); |
| 7748 | scm_t_inum z = xx - yy; |
| 7749 | if (SCM_FIXABLE (z)) |
| 7750 | return SCM_I_MAKINUM (z); |
| 7751 | else |
| 7752 | return scm_i_inum2big (z); |
| 7753 | } |
| 7754 | else if (SCM_BIGP (y)) |
| 7755 | { |
| 7756 | /* inum-x - big-y */ |
| 7757 | scm_t_inum xx = SCM_I_INUM (x); |
| 7758 | |
| 7759 | if (xx == 0) |
| 7760 | { |
| 7761 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
| 7762 | bignum, but negating that gives a fixnum. */ |
| 7763 | return scm_i_normbig (scm_i_clonebig (y, 0)); |
| 7764 | } |
| 7765 | else |
| 7766 | { |
| 7767 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 7768 | SCM result = scm_i_mkbig (); |
| 7769 | |
| 7770 | if (xx >= 0) |
| 7771 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); |
| 7772 | else |
| 7773 | { |
| 7774 | /* x - y == -(y + -x) */ |
| 7775 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); |
| 7776 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); |
| 7777 | } |
| 7778 | scm_remember_upto_here_1 (y); |
| 7779 | |
| 7780 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
| 7781 | /* we know the result will have to be a bignum */ |
| 7782 | return result; |
| 7783 | else |
| 7784 | return scm_i_normbig (result); |
| 7785 | } |
| 7786 | } |
| 7787 | else if (SCM_REALP (y)) |
| 7788 | { |
| 7789 | scm_t_inum xx = SCM_I_INUM (x); |
| 7790 | |
| 7791 | /* |
| 7792 | * We need to handle x == exact 0 |
| 7793 | * specially because R6RS states that: |
| 7794 | * (- 0.0) ==> -0.0 and |
| 7795 | * (- 0.0 0.0) ==> 0.0 |
| 7796 | * and the scheme compiler changes |
| 7797 | * (- 0.0) into (- 0 0.0) |
| 7798 | * So we need to treat (- 0 0.0) like (- 0.0). |
| 7799 | * At the C level, (-x) is different than (0.0 - x). |
| 7800 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. |
| 7801 | */ |
| 7802 | if (xx == 0) |
| 7803 | return scm_i_from_double (- SCM_REAL_VALUE (y)); |
| 7804 | else |
| 7805 | return scm_i_from_double (xx - SCM_REAL_VALUE (y)); |
| 7806 | } |
| 7807 | else if (SCM_COMPLEXP (y)) |
| 7808 | { |
| 7809 | scm_t_inum xx = SCM_I_INUM (x); |
| 7810 | |
| 7811 | /* We need to handle x == exact 0 specially. |
| 7812 | See the comment above (for SCM_REALP (y)) */ |
| 7813 | if (xx == 0) |
| 7814 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), |
| 7815 | - SCM_COMPLEX_IMAG (y)); |
| 7816 | else |
| 7817 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
| 7818 | - SCM_COMPLEX_IMAG (y)); |
| 7819 | } |
| 7820 | else if (SCM_FRACTIONP (y)) |
| 7821 | /* a - b/c = (ac - b) / c */ |
| 7822 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
| 7823 | SCM_FRACTION_NUMERATOR (y)), |
| 7824 | SCM_FRACTION_DENOMINATOR (y)); |
| 7825 | else |
| 7826 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
| 7827 | } |
| 7828 | else if (SCM_BIGP (x)) |
| 7829 | { |
| 7830 | if (SCM_I_INUMP (y)) |
| 7831 | { |
| 7832 | /* big-x - inum-y */ |
| 7833 | scm_t_inum yy = SCM_I_INUM (y); |
| 7834 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7835 | |
| 7836 | scm_remember_upto_here_1 (x); |
| 7837 | if (sgn_x == 0) |
| 7838 | return (SCM_FIXABLE (-yy) ? |
| 7839 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
| 7840 | else |
| 7841 | { |
| 7842 | SCM result = scm_i_mkbig (); |
| 7843 | |
| 7844 | if (yy >= 0) |
| 7845 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); |
| 7846 | else |
| 7847 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); |
| 7848 | scm_remember_upto_here_1 (x); |
| 7849 | |
| 7850 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
| 7851 | /* we know the result will have to be a bignum */ |
| 7852 | return result; |
| 7853 | else |
| 7854 | return scm_i_normbig (result); |
| 7855 | } |
| 7856 | } |
| 7857 | else if (SCM_BIGP (y)) |
| 7858 | { |
| 7859 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 7860 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); |
| 7861 | SCM result = scm_i_mkbig (); |
| 7862 | mpz_sub (SCM_I_BIG_MPZ (result), |
| 7863 | SCM_I_BIG_MPZ (x), |
| 7864 | SCM_I_BIG_MPZ (y)); |
| 7865 | scm_remember_upto_here_2 (x, y); |
| 7866 | /* we know the result will have to be a bignum */ |
| 7867 | if ((sgn_x == 1) && (sgn_y == -1)) |
| 7868 | return result; |
| 7869 | if ((sgn_x == -1) && (sgn_y == 1)) |
| 7870 | return result; |
| 7871 | return scm_i_normbig (result); |
| 7872 | } |
| 7873 | else if (SCM_REALP (y)) |
| 7874 | { |
| 7875 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); |
| 7876 | scm_remember_upto_here_1 (x); |
| 7877 | return scm_i_from_double (result); |
| 7878 | } |
| 7879 | else if (SCM_COMPLEXP (y)) |
| 7880 | { |
| 7881 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) |
| 7882 | - SCM_COMPLEX_REAL (y)); |
| 7883 | scm_remember_upto_here_1 (x); |
| 7884 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
| 7885 | } |
| 7886 | else if (SCM_FRACTIONP (y)) |
| 7887 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
| 7888 | SCM_FRACTION_NUMERATOR (y)), |
| 7889 | SCM_FRACTION_DENOMINATOR (y)); |
| 7890 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
| 7891 | } |
| 7892 | else if (SCM_REALP (x)) |
| 7893 | { |
| 7894 | if (SCM_I_INUMP (y)) |
| 7895 | return scm_i_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
| 7896 | else if (SCM_BIGP (y)) |
| 7897 | { |
| 7898 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); |
| 7899 | scm_remember_upto_here_1 (x); |
| 7900 | return scm_i_from_double (result); |
| 7901 | } |
| 7902 | else if (SCM_REALP (y)) |
| 7903 | return scm_i_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
| 7904 | else if (SCM_COMPLEXP (y)) |
| 7905 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
| 7906 | -SCM_COMPLEX_IMAG (y)); |
| 7907 | else if (SCM_FRACTIONP (y)) |
| 7908 | return scm_i_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
| 7909 | else |
| 7910 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
| 7911 | } |
| 7912 | else if (SCM_COMPLEXP (x)) |
| 7913 | { |
| 7914 | if (SCM_I_INUMP (y)) |
| 7915 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
| 7916 | SCM_COMPLEX_IMAG (x)); |
| 7917 | else if (SCM_BIGP (y)) |
| 7918 | { |
| 7919 | double real_part = (SCM_COMPLEX_REAL (x) |
| 7920 | - mpz_get_d (SCM_I_BIG_MPZ (y))); |
| 7921 | scm_remember_upto_here_1 (x); |
| 7922 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
| 7923 | } |
| 7924 | else if (SCM_REALP (y)) |
| 7925 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
| 7926 | SCM_COMPLEX_IMAG (x)); |
| 7927 | else if (SCM_COMPLEXP (y)) |
| 7928 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
| 7929 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
| 7930 | else if (SCM_FRACTIONP (y)) |
| 7931 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
| 7932 | SCM_COMPLEX_IMAG (x)); |
| 7933 | else |
| 7934 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
| 7935 | } |
| 7936 | else if (SCM_FRACTIONP (x)) |
| 7937 | { |
| 7938 | if (SCM_I_INUMP (y)) |
| 7939 | /* a/b - c = (a - cb) / b */ |
| 7940 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
| 7941 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
| 7942 | SCM_FRACTION_DENOMINATOR (x)); |
| 7943 | else if (SCM_BIGP (y)) |
| 7944 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
| 7945 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
| 7946 | SCM_FRACTION_DENOMINATOR (x)); |
| 7947 | else if (SCM_REALP (y)) |
| 7948 | return scm_i_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
| 7949 | else if (SCM_COMPLEXP (y)) |
| 7950 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
| 7951 | -SCM_COMPLEX_IMAG (y)); |
| 7952 | else if (SCM_FRACTIONP (y)) |
| 7953 | /* a/b - c/d = (ad - bc) / bd */ |
| 7954 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
| 7955 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
| 7956 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); |
| 7957 | else |
| 7958 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
| 7959 | } |
| 7960 | else |
| 7961 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
| 7962 | } |
| 7963 | #undef FUNC_NAME |
| 7964 | |
| 7965 | |
| 7966 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
| 7967 | (SCM x), |
| 7968 | "Return @math{@var{x}-1}.") |
| 7969 | #define FUNC_NAME s_scm_oneminus |
| 7970 | { |
| 7971 | return scm_difference (x, SCM_INUM1); |
| 7972 | } |
| 7973 | #undef FUNC_NAME |
| 7974 | |
| 7975 | |
| 7976 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
| 7977 | (SCM x, SCM y, SCM rest), |
| 7978 | "Return the product of all arguments. If called without arguments,\n" |
| 7979 | "1 is returned.") |
| 7980 | #define FUNC_NAME s_scm_i_product |
| 7981 | { |
| 7982 | while (!scm_is_null (rest)) |
| 7983 | { x = scm_product (x, y); |
| 7984 | y = scm_car (rest); |
| 7985 | rest = scm_cdr (rest); |
| 7986 | } |
| 7987 | return scm_product (x, y); |
| 7988 | } |
| 7989 | #undef FUNC_NAME |
| 7990 | |
| 7991 | #define s_product s_scm_i_product |
| 7992 | #define g_product g_scm_i_product |
| 7993 | |
| 7994 | SCM |
| 7995 | scm_product (SCM x, SCM y) |
| 7996 | { |
| 7997 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
| 7998 | { |
| 7999 | if (SCM_UNBNDP (x)) |
| 8000 | return SCM_I_MAKINUM (1L); |
| 8001 | else if (SCM_NUMBERP (x)) |
| 8002 | return x; |
| 8003 | else |
| 8004 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); |
| 8005 | } |
| 8006 | |
| 8007 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 8008 | { |
| 8009 | scm_t_inum xx; |
| 8010 | |
| 8011 | xinum: |
| 8012 | xx = SCM_I_INUM (x); |
| 8013 | |
| 8014 | switch (xx) |
| 8015 | { |
| 8016 | case 1: |
| 8017 | /* exact1 is the universal multiplicative identity */ |
| 8018 | return y; |
| 8019 | break; |
| 8020 | case 0: |
| 8021 | /* exact0 times a fixnum is exact0: optimize this case */ |
| 8022 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 8023 | return SCM_INUM0; |
| 8024 | /* if the other argument is inexact, the result is inexact, |
| 8025 | and we must do the multiplication in order to handle |
| 8026 | infinities and NaNs properly. */ |
| 8027 | else if (SCM_REALP (y)) |
| 8028 | return scm_i_from_double (0.0 * SCM_REAL_VALUE (y)); |
| 8029 | else if (SCM_COMPLEXP (y)) |
| 8030 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), |
| 8031 | 0.0 * SCM_COMPLEX_IMAG (y)); |
| 8032 | /* we've already handled inexact numbers, |
| 8033 | so y must be exact, and we return exact0 */ |
| 8034 | else if (SCM_NUMP (y)) |
| 8035 | return SCM_INUM0; |
| 8036 | else |
| 8037 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); |
| 8038 | break; |
| 8039 | case -1: |
| 8040 | /* |
| 8041 | * This case is important for more than just optimization. |
| 8042 | * It handles the case of negating |
| 8043 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
| 8044 | * which is a bignum that must be changed back into a fixnum. |
| 8045 | * Failure to do so will cause the following to return #f: |
| 8046 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) |
| 8047 | */ |
| 8048 | return scm_difference(y, SCM_UNDEFINED); |
| 8049 | break; |
| 8050 | } |
| 8051 | |
| 8052 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 8053 | { |
| 8054 | scm_t_inum yy = SCM_I_INUM (y); |
| 8055 | #if SCM_I_FIXNUM_BIT < 32 && SCM_HAVE_T_INT64 |
| 8056 | scm_t_int64 kk = xx * (scm_t_int64) yy; |
| 8057 | if (SCM_FIXABLE (kk)) |
| 8058 | return SCM_I_MAKINUM (kk); |
| 8059 | #else |
| 8060 | scm_t_inum axx = (xx > 0) ? xx : -xx; |
| 8061 | scm_t_inum ayy = (yy > 0) ? yy : -yy; |
| 8062 | if (SCM_MOST_POSITIVE_FIXNUM / axx >= ayy) |
| 8063 | return SCM_I_MAKINUM (xx * yy); |
| 8064 | #endif |
| 8065 | else |
| 8066 | { |
| 8067 | SCM result = scm_i_inum2big (xx); |
| 8068 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
| 8069 | return scm_i_normbig (result); |
| 8070 | } |
| 8071 | } |
| 8072 | else if (SCM_BIGP (y)) |
| 8073 | { |
| 8074 | SCM result = scm_i_mkbig (); |
| 8075 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); |
| 8076 | scm_remember_upto_here_1 (y); |
| 8077 | return result; |
| 8078 | } |
| 8079 | else if (SCM_REALP (y)) |
| 8080 | return scm_i_from_double (xx * SCM_REAL_VALUE (y)); |
| 8081 | else if (SCM_COMPLEXP (y)) |
| 8082 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
| 8083 | xx * SCM_COMPLEX_IMAG (y)); |
| 8084 | else if (SCM_FRACTIONP (y)) |
| 8085 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
| 8086 | SCM_FRACTION_DENOMINATOR (y)); |
| 8087 | else |
| 8088 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); |
| 8089 | } |
| 8090 | else if (SCM_BIGP (x)) |
| 8091 | { |
| 8092 | if (SCM_I_INUMP (y)) |
| 8093 | { |
| 8094 | SCM_SWAP (x, y); |
| 8095 | goto xinum; |
| 8096 | } |
| 8097 | else if (SCM_BIGP (y)) |
| 8098 | { |
| 8099 | SCM result = scm_i_mkbig (); |
| 8100 | mpz_mul (SCM_I_BIG_MPZ (result), |
| 8101 | SCM_I_BIG_MPZ (x), |
| 8102 | SCM_I_BIG_MPZ (y)); |
| 8103 | scm_remember_upto_here_2 (x, y); |
| 8104 | return result; |
| 8105 | } |
| 8106 | else if (SCM_REALP (y)) |
| 8107 | { |
| 8108 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); |
| 8109 | scm_remember_upto_here_1 (x); |
| 8110 | return scm_i_from_double (result); |
| 8111 | } |
| 8112 | else if (SCM_COMPLEXP (y)) |
| 8113 | { |
| 8114 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); |
| 8115 | scm_remember_upto_here_1 (x); |
| 8116 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
| 8117 | z * SCM_COMPLEX_IMAG (y)); |
| 8118 | } |
| 8119 | else if (SCM_FRACTIONP (y)) |
| 8120 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
| 8121 | SCM_FRACTION_DENOMINATOR (y)); |
| 8122 | else |
| 8123 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); |
| 8124 | } |
| 8125 | else if (SCM_REALP (x)) |
| 8126 | { |
| 8127 | if (SCM_I_INUMP (y)) |
| 8128 | { |
| 8129 | SCM_SWAP (x, y); |
| 8130 | goto xinum; |
| 8131 | } |
| 8132 | else if (SCM_BIGP (y)) |
| 8133 | { |
| 8134 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); |
| 8135 | scm_remember_upto_here_1 (y); |
| 8136 | return scm_i_from_double (result); |
| 8137 | } |
| 8138 | else if (SCM_REALP (y)) |
| 8139 | return scm_i_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
| 8140 | else if (SCM_COMPLEXP (y)) |
| 8141 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
| 8142 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
| 8143 | else if (SCM_FRACTIONP (y)) |
| 8144 | return scm_i_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
| 8145 | else |
| 8146 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); |
| 8147 | } |
| 8148 | else if (SCM_COMPLEXP (x)) |
| 8149 | { |
| 8150 | if (SCM_I_INUMP (y)) |
| 8151 | { |
| 8152 | SCM_SWAP (x, y); |
| 8153 | goto xinum; |
| 8154 | } |
| 8155 | else if (SCM_BIGP (y)) |
| 8156 | { |
| 8157 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); |
| 8158 | scm_remember_upto_here_1 (y); |
| 8159 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
| 8160 | z * SCM_COMPLEX_IMAG (x)); |
| 8161 | } |
| 8162 | else if (SCM_REALP (y)) |
| 8163 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
| 8164 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
| 8165 | else if (SCM_COMPLEXP (y)) |
| 8166 | { |
| 8167 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
| 8168 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
| 8169 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) |
| 8170 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); |
| 8171 | } |
| 8172 | else if (SCM_FRACTIONP (y)) |
| 8173 | { |
| 8174 | double yy = scm_i_fraction2double (y); |
| 8175 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
| 8176 | yy * SCM_COMPLEX_IMAG (x)); |
| 8177 | } |
| 8178 | else |
| 8179 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); |
| 8180 | } |
| 8181 | else if (SCM_FRACTIONP (x)) |
| 8182 | { |
| 8183 | if (SCM_I_INUMP (y)) |
| 8184 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
| 8185 | SCM_FRACTION_DENOMINATOR (x)); |
| 8186 | else if (SCM_BIGP (y)) |
| 8187 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
| 8188 | SCM_FRACTION_DENOMINATOR (x)); |
| 8189 | else if (SCM_REALP (y)) |
| 8190 | return scm_i_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
| 8191 | else if (SCM_COMPLEXP (y)) |
| 8192 | { |
| 8193 | double xx = scm_i_fraction2double (x); |
| 8194 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
| 8195 | xx * SCM_COMPLEX_IMAG (y)); |
| 8196 | } |
| 8197 | else if (SCM_FRACTIONP (y)) |
| 8198 | /* a/b * c/d = ac / bd */ |
| 8199 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
| 8200 | SCM_FRACTION_NUMERATOR (y)), |
| 8201 | scm_product (SCM_FRACTION_DENOMINATOR (x), |
| 8202 | SCM_FRACTION_DENOMINATOR (y))); |
| 8203 | else |
| 8204 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); |
| 8205 | } |
| 8206 | else |
| 8207 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
| 8208 | } |
| 8209 | |
| 8210 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
| 8211 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) |
| 8212 | #define ALLOW_DIVIDE_BY_ZERO |
| 8213 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ |
| 8214 | #endif |
| 8215 | |
| 8216 | /* The code below for complex division is adapted from the GNU |
| 8217 | libstdc++, which adapted it from f2c's libF77, and is subject to |
| 8218 | this copyright: */ |
| 8219 | |
| 8220 | /**************************************************************** |
| 8221 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. |
| 8222 | |
| 8223 | Permission to use, copy, modify, and distribute this software |
| 8224 | and its documentation for any purpose and without fee is hereby |
| 8225 | granted, provided that the above copyright notice appear in all |
| 8226 | copies and that both that the copyright notice and this |
| 8227 | permission notice and warranty disclaimer appear in supporting |
| 8228 | documentation, and that the names of AT&T Bell Laboratories or |
| 8229 | Bellcore or any of their entities not be used in advertising or |
| 8230 | publicity pertaining to distribution of the software without |
| 8231 | specific, written prior permission. |
| 8232 | |
| 8233 | AT&T and Bellcore disclaim all warranties with regard to this |
| 8234 | software, including all implied warranties of merchantability |
| 8235 | and fitness. In no event shall AT&T or Bellcore be liable for |
| 8236 | any special, indirect or consequential damages or any damages |
| 8237 | whatsoever resulting from loss of use, data or profits, whether |
| 8238 | in an action of contract, negligence or other tortious action, |
| 8239 | arising out of or in connection with the use or performance of |
| 8240 | this software. |
| 8241 | ****************************************************************/ |
| 8242 | |
| 8243 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
| 8244 | (SCM x, SCM y, SCM rest), |
| 8245 | "Divide the first argument by the product of the remaining\n" |
| 8246 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" |
| 8247 | "returned.") |
| 8248 | #define FUNC_NAME s_scm_i_divide |
| 8249 | { |
| 8250 | while (!scm_is_null (rest)) |
| 8251 | { x = scm_divide (x, y); |
| 8252 | y = scm_car (rest); |
| 8253 | rest = scm_cdr (rest); |
| 8254 | } |
| 8255 | return scm_divide (x, y); |
| 8256 | } |
| 8257 | #undef FUNC_NAME |
| 8258 | |
| 8259 | #define s_divide s_scm_i_divide |
| 8260 | #define g_divide g_scm_i_divide |
| 8261 | |
| 8262 | SCM |
| 8263 | scm_divide (SCM x, SCM y) |
| 8264 | #define FUNC_NAME s_divide |
| 8265 | { |
| 8266 | double a; |
| 8267 | |
| 8268 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
| 8269 | { |
| 8270 | if (SCM_UNBNDP (x)) |
| 8271 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); |
| 8272 | else if (SCM_I_INUMP (x)) |
| 8273 | { |
| 8274 | scm_t_inum xx = SCM_I_INUM (x); |
| 8275 | if (xx == 1 || xx == -1) |
| 8276 | return x; |
| 8277 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 8278 | else if (xx == 0) |
| 8279 | scm_num_overflow (s_divide); |
| 8280 | #endif |
| 8281 | else |
| 8282 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
| 8283 | } |
| 8284 | else if (SCM_BIGP (x)) |
| 8285 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
| 8286 | else if (SCM_REALP (x)) |
| 8287 | { |
| 8288 | double xx = SCM_REAL_VALUE (x); |
| 8289 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8290 | if (xx == 0.0) |
| 8291 | scm_num_overflow (s_divide); |
| 8292 | else |
| 8293 | #endif |
| 8294 | return scm_i_from_double (1.0 / xx); |
| 8295 | } |
| 8296 | else if (SCM_COMPLEXP (x)) |
| 8297 | { |
| 8298 | double r = SCM_COMPLEX_REAL (x); |
| 8299 | double i = SCM_COMPLEX_IMAG (x); |
| 8300 | if (fabs(r) <= fabs(i)) |
| 8301 | { |
| 8302 | double t = r / i; |
| 8303 | double d = i * (1.0 + t * t); |
| 8304 | return scm_c_make_rectangular (t / d, -1.0 / d); |
| 8305 | } |
| 8306 | else |
| 8307 | { |
| 8308 | double t = i / r; |
| 8309 | double d = r * (1.0 + t * t); |
| 8310 | return scm_c_make_rectangular (1.0 / d, -t / d); |
| 8311 | } |
| 8312 | } |
| 8313 | else if (SCM_FRACTIONP (x)) |
| 8314 | return scm_i_make_ratio_already_reduced (SCM_FRACTION_DENOMINATOR (x), |
| 8315 | SCM_FRACTION_NUMERATOR (x)); |
| 8316 | else |
| 8317 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); |
| 8318 | } |
| 8319 | |
| 8320 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
| 8321 | { |
| 8322 | scm_t_inum xx = SCM_I_INUM (x); |
| 8323 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
| 8324 | { |
| 8325 | scm_t_inum yy = SCM_I_INUM (y); |
| 8326 | if (yy == 0) |
| 8327 | { |
| 8328 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 8329 | scm_num_overflow (s_divide); |
| 8330 | #else |
| 8331 | return scm_i_from_double ((double) xx / (double) yy); |
| 8332 | #endif |
| 8333 | } |
| 8334 | else if (xx % yy != 0) |
| 8335 | return scm_i_make_ratio (x, y); |
| 8336 | else |
| 8337 | { |
| 8338 | scm_t_inum z = xx / yy; |
| 8339 | if (SCM_FIXABLE (z)) |
| 8340 | return SCM_I_MAKINUM (z); |
| 8341 | else |
| 8342 | return scm_i_inum2big (z); |
| 8343 | } |
| 8344 | } |
| 8345 | else if (SCM_BIGP (y)) |
| 8346 | return scm_i_make_ratio (x, y); |
| 8347 | else if (SCM_REALP (y)) |
| 8348 | { |
| 8349 | double yy = SCM_REAL_VALUE (y); |
| 8350 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8351 | if (yy == 0.0) |
| 8352 | scm_num_overflow (s_divide); |
| 8353 | else |
| 8354 | #endif |
| 8355 | /* FIXME: Precision may be lost here due to: |
| 8356 | (1) The cast from 'scm_t_inum' to 'double' |
| 8357 | (2) Double rounding */ |
| 8358 | return scm_i_from_double ((double) xx / yy); |
| 8359 | } |
| 8360 | else if (SCM_COMPLEXP (y)) |
| 8361 | { |
| 8362 | a = xx; |
| 8363 | complex_div: /* y _must_ be a complex number */ |
| 8364 | { |
| 8365 | double r = SCM_COMPLEX_REAL (y); |
| 8366 | double i = SCM_COMPLEX_IMAG (y); |
| 8367 | if (fabs(r) <= fabs(i)) |
| 8368 | { |
| 8369 | double t = r / i; |
| 8370 | double d = i * (1.0 + t * t); |
| 8371 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
| 8372 | } |
| 8373 | else |
| 8374 | { |
| 8375 | double t = i / r; |
| 8376 | double d = r * (1.0 + t * t); |
| 8377 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
| 8378 | } |
| 8379 | } |
| 8380 | } |
| 8381 | else if (SCM_FRACTIONP (y)) |
| 8382 | /* a / b/c = ac / b */ |
| 8383 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
| 8384 | SCM_FRACTION_NUMERATOR (y)); |
| 8385 | else |
| 8386 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); |
| 8387 | } |
| 8388 | else if (SCM_BIGP (x)) |
| 8389 | { |
| 8390 | if (SCM_I_INUMP (y)) |
| 8391 | { |
| 8392 | scm_t_inum yy = SCM_I_INUM (y); |
| 8393 | if (yy == 0) |
| 8394 | { |
| 8395 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 8396 | scm_num_overflow (s_divide); |
| 8397 | #else |
| 8398 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
| 8399 | scm_remember_upto_here_1 (x); |
| 8400 | return (sgn == 0) ? scm_nan () : scm_inf (); |
| 8401 | #endif |
| 8402 | } |
| 8403 | else if (yy == 1) |
| 8404 | return x; |
| 8405 | else |
| 8406 | { |
| 8407 | /* FIXME: HMM, what are the relative performance issues here? |
| 8408 | We need to test. Is it faster on average to test |
| 8409 | divisible_p, then perform whichever operation, or is it |
| 8410 | faster to perform the integer div opportunistically and |
| 8411 | switch to real if there's a remainder? For now we take the |
| 8412 | middle ground: test, then if divisible, use the faster div |
| 8413 | func. */ |
| 8414 | |
| 8415 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
| 8416 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
| 8417 | |
| 8418 | if (divisible_p) |
| 8419 | { |
| 8420 | SCM result = scm_i_mkbig (); |
| 8421 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); |
| 8422 | scm_remember_upto_here_1 (x); |
| 8423 | if (yy < 0) |
| 8424 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); |
| 8425 | return scm_i_normbig (result); |
| 8426 | } |
| 8427 | else |
| 8428 | return scm_i_make_ratio (x, y); |
| 8429 | } |
| 8430 | } |
| 8431 | else if (SCM_BIGP (y)) |
| 8432 | { |
| 8433 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
| 8434 | SCM_I_BIG_MPZ (y)); |
| 8435 | if (divisible_p) |
| 8436 | { |
| 8437 | SCM result = scm_i_mkbig (); |
| 8438 | mpz_divexact (SCM_I_BIG_MPZ (result), |
| 8439 | SCM_I_BIG_MPZ (x), |
| 8440 | SCM_I_BIG_MPZ (y)); |
| 8441 | scm_remember_upto_here_2 (x, y); |
| 8442 | return scm_i_normbig (result); |
| 8443 | } |
| 8444 | else |
| 8445 | return scm_i_make_ratio (x, y); |
| 8446 | } |
| 8447 | else if (SCM_REALP (y)) |
| 8448 | { |
| 8449 | double yy = SCM_REAL_VALUE (y); |
| 8450 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8451 | if (yy == 0.0) |
| 8452 | scm_num_overflow (s_divide); |
| 8453 | else |
| 8454 | #endif |
| 8455 | /* FIXME: Precision may be lost here due to: |
| 8456 | (1) scm_i_big2dbl (2) Double rounding */ |
| 8457 | return scm_i_from_double (scm_i_big2dbl (x) / yy); |
| 8458 | } |
| 8459 | else if (SCM_COMPLEXP (y)) |
| 8460 | { |
| 8461 | a = scm_i_big2dbl (x); |
| 8462 | goto complex_div; |
| 8463 | } |
| 8464 | else if (SCM_FRACTIONP (y)) |
| 8465 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
| 8466 | SCM_FRACTION_NUMERATOR (y)); |
| 8467 | else |
| 8468 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); |
| 8469 | } |
| 8470 | else if (SCM_REALP (x)) |
| 8471 | { |
| 8472 | double rx = SCM_REAL_VALUE (x); |
| 8473 | if (SCM_I_INUMP (y)) |
| 8474 | { |
| 8475 | scm_t_inum yy = SCM_I_INUM (y); |
| 8476 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 8477 | if (yy == 0) |
| 8478 | scm_num_overflow (s_divide); |
| 8479 | else |
| 8480 | #endif |
| 8481 | /* FIXME: Precision may be lost here due to: |
| 8482 | (1) The cast from 'scm_t_inum' to 'double' |
| 8483 | (2) Double rounding */ |
| 8484 | return scm_i_from_double (rx / (double) yy); |
| 8485 | } |
| 8486 | else if (SCM_BIGP (y)) |
| 8487 | { |
| 8488 | /* FIXME: Precision may be lost here due to: |
| 8489 | (1) The conversion from bignum to double |
| 8490 | (2) Double rounding */ |
| 8491 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
| 8492 | scm_remember_upto_here_1 (y); |
| 8493 | return scm_i_from_double (rx / dby); |
| 8494 | } |
| 8495 | else if (SCM_REALP (y)) |
| 8496 | { |
| 8497 | double yy = SCM_REAL_VALUE (y); |
| 8498 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8499 | if (yy == 0.0) |
| 8500 | scm_num_overflow (s_divide); |
| 8501 | else |
| 8502 | #endif |
| 8503 | return scm_i_from_double (rx / yy); |
| 8504 | } |
| 8505 | else if (SCM_COMPLEXP (y)) |
| 8506 | { |
| 8507 | a = rx; |
| 8508 | goto complex_div; |
| 8509 | } |
| 8510 | else if (SCM_FRACTIONP (y)) |
| 8511 | return scm_i_from_double (rx / scm_i_fraction2double (y)); |
| 8512 | else |
| 8513 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); |
| 8514 | } |
| 8515 | else if (SCM_COMPLEXP (x)) |
| 8516 | { |
| 8517 | double rx = SCM_COMPLEX_REAL (x); |
| 8518 | double ix = SCM_COMPLEX_IMAG (x); |
| 8519 | if (SCM_I_INUMP (y)) |
| 8520 | { |
| 8521 | scm_t_inum yy = SCM_I_INUM (y); |
| 8522 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 8523 | if (yy == 0) |
| 8524 | scm_num_overflow (s_divide); |
| 8525 | else |
| 8526 | #endif |
| 8527 | { |
| 8528 | /* FIXME: Precision may be lost here due to: |
| 8529 | (1) The conversion from 'scm_t_inum' to double |
| 8530 | (2) Double rounding */ |
| 8531 | double d = yy; |
| 8532 | return scm_c_make_rectangular (rx / d, ix / d); |
| 8533 | } |
| 8534 | } |
| 8535 | else if (SCM_BIGP (y)) |
| 8536 | { |
| 8537 | /* FIXME: Precision may be lost here due to: |
| 8538 | (1) The conversion from bignum to double |
| 8539 | (2) Double rounding */ |
| 8540 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
| 8541 | scm_remember_upto_here_1 (y); |
| 8542 | return scm_c_make_rectangular (rx / dby, ix / dby); |
| 8543 | } |
| 8544 | else if (SCM_REALP (y)) |
| 8545 | { |
| 8546 | double yy = SCM_REAL_VALUE (y); |
| 8547 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8548 | if (yy == 0.0) |
| 8549 | scm_num_overflow (s_divide); |
| 8550 | else |
| 8551 | #endif |
| 8552 | return scm_c_make_rectangular (rx / yy, ix / yy); |
| 8553 | } |
| 8554 | else if (SCM_COMPLEXP (y)) |
| 8555 | { |
| 8556 | double ry = SCM_COMPLEX_REAL (y); |
| 8557 | double iy = SCM_COMPLEX_IMAG (y); |
| 8558 | if (fabs(ry) <= fabs(iy)) |
| 8559 | { |
| 8560 | double t = ry / iy; |
| 8561 | double d = iy * (1.0 + t * t); |
| 8562 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
| 8563 | } |
| 8564 | else |
| 8565 | { |
| 8566 | double t = iy / ry; |
| 8567 | double d = ry * (1.0 + t * t); |
| 8568 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
| 8569 | } |
| 8570 | } |
| 8571 | else if (SCM_FRACTIONP (y)) |
| 8572 | { |
| 8573 | /* FIXME: Precision may be lost here due to: |
| 8574 | (1) The conversion from fraction to double |
| 8575 | (2) Double rounding */ |
| 8576 | double yy = scm_i_fraction2double (y); |
| 8577 | return scm_c_make_rectangular (rx / yy, ix / yy); |
| 8578 | } |
| 8579 | else |
| 8580 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); |
| 8581 | } |
| 8582 | else if (SCM_FRACTIONP (x)) |
| 8583 | { |
| 8584 | if (SCM_I_INUMP (y)) |
| 8585 | { |
| 8586 | scm_t_inum yy = SCM_I_INUM (y); |
| 8587 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 8588 | if (yy == 0) |
| 8589 | scm_num_overflow (s_divide); |
| 8590 | else |
| 8591 | #endif |
| 8592 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
| 8593 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
| 8594 | } |
| 8595 | else if (SCM_BIGP (y)) |
| 8596 | { |
| 8597 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
| 8598 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
| 8599 | } |
| 8600 | else if (SCM_REALP (y)) |
| 8601 | { |
| 8602 | double yy = SCM_REAL_VALUE (y); |
| 8603 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8604 | if (yy == 0.0) |
| 8605 | scm_num_overflow (s_divide); |
| 8606 | else |
| 8607 | #endif |
| 8608 | /* FIXME: Precision may be lost here due to: |
| 8609 | (1) The conversion from fraction to double |
| 8610 | (2) Double rounding */ |
| 8611 | return scm_i_from_double (scm_i_fraction2double (x) / yy); |
| 8612 | } |
| 8613 | else if (SCM_COMPLEXP (y)) |
| 8614 | { |
| 8615 | /* FIXME: Precision may be lost here due to: |
| 8616 | (1) The conversion from fraction to double |
| 8617 | (2) Double rounding */ |
| 8618 | a = scm_i_fraction2double (x); |
| 8619 | goto complex_div; |
| 8620 | } |
| 8621 | else if (SCM_FRACTIONP (y)) |
| 8622 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
| 8623 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
| 8624 | else |
| 8625 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); |
| 8626 | } |
| 8627 | else |
| 8628 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
| 8629 | } |
| 8630 | #undef FUNC_NAME |
| 8631 | |
| 8632 | |
| 8633 | double |
| 8634 | scm_c_truncate (double x) |
| 8635 | { |
| 8636 | return trunc (x); |
| 8637 | } |
| 8638 | |
| 8639 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
| 8640 | half-way case (ie. when x is an integer plus 0.5) going upwards. |
| 8641 | Then half-way cases are identified and adjusted down if the |
| 8642 | round-upwards didn't give the desired even integer. |
| 8643 | |
| 8644 | "plus_half == result" identifies a half-way case. If plus_half, which is |
| 8645 | x + 0.5, is an integer then x must be an integer plus 0.5. |
| 8646 | |
| 8647 | An odd "result" value is identified with result/2 != floor(result/2). |
| 8648 | This is done with plus_half, since that value is ready for use sooner in |
| 8649 | a pipelined cpu, and we're already requiring plus_half == result. |
| 8650 | |
| 8651 | Note however that we need to be careful when x is big and already an |
| 8652 | integer. In that case "x+0.5" may round to an adjacent integer, causing |
| 8653 | us to return such a value, incorrectly. For instance if the hardware is |
| 8654 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF |
| 8655 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value |
| 8656 | returned. Or if the hardware is in round-upwards mode, then other bigger |
| 8657 | values like say x == 2^128 will see x+0.5 rounding up to the next higher |
| 8658 | representable value, 2^128+2^76 (or whatever), again incorrect. |
| 8659 | |
| 8660 | These bad roundings of x+0.5 are avoided by testing at the start whether |
| 8661 | x is already an integer. If it is then clearly that's the desired result |
| 8662 | already. And if it's not then the exponent must be small enough to allow |
| 8663 | an 0.5 to be represented, and hence added without a bad rounding. */ |
| 8664 | |
| 8665 | double |
| 8666 | scm_c_round (double x) |
| 8667 | { |
| 8668 | double plus_half, result; |
| 8669 | |
| 8670 | if (x == floor (x)) |
| 8671 | return x; |
| 8672 | |
| 8673 | plus_half = x + 0.5; |
| 8674 | result = floor (plus_half); |
| 8675 | /* Adjust so that the rounding is towards even. */ |
| 8676 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
| 8677 | ? result - 1 |
| 8678 | : result); |
| 8679 | } |
| 8680 | |
| 8681 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
| 8682 | (SCM x), |
| 8683 | "Round the number @var{x} towards zero.") |
| 8684 | #define FUNC_NAME s_scm_truncate_number |
| 8685 | { |
| 8686 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
| 8687 | return x; |
| 8688 | else if (SCM_REALP (x)) |
| 8689 | return scm_i_from_double (trunc (SCM_REAL_VALUE (x))); |
| 8690 | else if (SCM_FRACTIONP (x)) |
| 8691 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), |
| 8692 | SCM_FRACTION_DENOMINATOR (x)); |
| 8693 | else |
| 8694 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
| 8695 | s_scm_truncate_number); |
| 8696 | } |
| 8697 | #undef FUNC_NAME |
| 8698 | |
| 8699 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
| 8700 | (SCM x), |
| 8701 | "Round the number @var{x} towards the nearest integer. " |
| 8702 | "When it is exactly halfway between two integers, " |
| 8703 | "round towards the even one.") |
| 8704 | #define FUNC_NAME s_scm_round_number |
| 8705 | { |
| 8706 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
| 8707 | return x; |
| 8708 | else if (SCM_REALP (x)) |
| 8709 | return scm_i_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
| 8710 | else if (SCM_FRACTIONP (x)) |
| 8711 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), |
| 8712 | SCM_FRACTION_DENOMINATOR (x)); |
| 8713 | else |
| 8714 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
| 8715 | s_scm_round_number); |
| 8716 | } |
| 8717 | #undef FUNC_NAME |
| 8718 | |
| 8719 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, |
| 8720 | (SCM x), |
| 8721 | "Round the number @var{x} towards minus infinity.") |
| 8722 | #define FUNC_NAME s_scm_floor |
| 8723 | { |
| 8724 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
| 8725 | return x; |
| 8726 | else if (SCM_REALP (x)) |
| 8727 | return scm_i_from_double (floor (SCM_REAL_VALUE (x))); |
| 8728 | else if (SCM_FRACTIONP (x)) |
| 8729 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
| 8730 | SCM_FRACTION_DENOMINATOR (x)); |
| 8731 | else |
| 8732 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); |
| 8733 | } |
| 8734 | #undef FUNC_NAME |
| 8735 | |
| 8736 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, |
| 8737 | (SCM x), |
| 8738 | "Round the number @var{x} towards infinity.") |
| 8739 | #define FUNC_NAME s_scm_ceiling |
| 8740 | { |
| 8741 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
| 8742 | return x; |
| 8743 | else if (SCM_REALP (x)) |
| 8744 | return scm_i_from_double (ceil (SCM_REAL_VALUE (x))); |
| 8745 | else if (SCM_FRACTIONP (x)) |
| 8746 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
| 8747 | SCM_FRACTION_DENOMINATOR (x)); |
| 8748 | else |
| 8749 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); |
| 8750 | } |
| 8751 | #undef FUNC_NAME |
| 8752 | |
| 8753 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
| 8754 | (SCM x, SCM y), |
| 8755 | "Return @var{x} raised to the power of @var{y}.") |
| 8756 | #define FUNC_NAME s_scm_expt |
| 8757 | { |
| 8758 | if (scm_is_integer (y)) |
| 8759 | { |
| 8760 | if (scm_is_true (scm_exact_p (y))) |
| 8761 | return scm_integer_expt (x, y); |
| 8762 | else |
| 8763 | { |
| 8764 | /* Here we handle the case where the exponent is an inexact |
| 8765 | integer. We make the exponent exact in order to use |
| 8766 | scm_integer_expt, and thus avoid the spurious imaginary |
| 8767 | parts that may result from round-off errors in the general |
| 8768 | e^(y log x) method below (for example when squaring a large |
| 8769 | negative number). In this case, we must return an inexact |
| 8770 | result for correctness. We also make the base inexact so |
| 8771 | that scm_integer_expt will use fast inexact arithmetic |
| 8772 | internally. Note that making the base inexact is not |
| 8773 | sufficient to guarantee an inexact result, because |
| 8774 | scm_integer_expt will return an exact 1 when the exponent |
| 8775 | is 0, even if the base is inexact. */ |
| 8776 | return scm_exact_to_inexact |
| 8777 | (scm_integer_expt (scm_exact_to_inexact (x), |
| 8778 | scm_inexact_to_exact (y))); |
| 8779 | } |
| 8780 | } |
| 8781 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
| 8782 | { |
| 8783 | return scm_i_from_double (pow (scm_to_double (x), scm_to_double (y))); |
| 8784 | } |
| 8785 | else if (scm_is_complex (x) && scm_is_complex (y)) |
| 8786 | return scm_exp (scm_product (scm_log (x), y)); |
| 8787 | else if (scm_is_complex (x)) |
| 8788 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); |
| 8789 | else |
| 8790 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); |
| 8791 | } |
| 8792 | #undef FUNC_NAME |
| 8793 | |
| 8794 | /* sin/cos/tan/asin/acos/atan |
| 8795 | sinh/cosh/tanh/asinh/acosh/atanh |
| 8796 | Derived from "Transcen.scm", Complex trancendental functions for SCM. |
| 8797 | Written by Jerry D. Hedden, (C) FSF. |
| 8798 | See the file `COPYING' for terms applying to this program. */ |
| 8799 | |
| 8800 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
| 8801 | (SCM z), |
| 8802 | "Compute the sine of @var{z}.") |
| 8803 | #define FUNC_NAME s_scm_sin |
| 8804 | { |
| 8805 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 8806 | return z; /* sin(exact0) = exact0 */ |
| 8807 | else if (scm_is_real (z)) |
| 8808 | return scm_i_from_double (sin (scm_to_double (z))); |
| 8809 | else if (SCM_COMPLEXP (z)) |
| 8810 | { double x, y; |
| 8811 | x = SCM_COMPLEX_REAL (z); |
| 8812 | y = SCM_COMPLEX_IMAG (z); |
| 8813 | return scm_c_make_rectangular (sin (x) * cosh (y), |
| 8814 | cos (x) * sinh (y)); |
| 8815 | } |
| 8816 | else |
| 8817 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); |
| 8818 | } |
| 8819 | #undef FUNC_NAME |
| 8820 | |
| 8821 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
| 8822 | (SCM z), |
| 8823 | "Compute the cosine of @var{z}.") |
| 8824 | #define FUNC_NAME s_scm_cos |
| 8825 | { |
| 8826 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 8827 | return SCM_INUM1; /* cos(exact0) = exact1 */ |
| 8828 | else if (scm_is_real (z)) |
| 8829 | return scm_i_from_double (cos (scm_to_double (z))); |
| 8830 | else if (SCM_COMPLEXP (z)) |
| 8831 | { double x, y; |
| 8832 | x = SCM_COMPLEX_REAL (z); |
| 8833 | y = SCM_COMPLEX_IMAG (z); |
| 8834 | return scm_c_make_rectangular (cos (x) * cosh (y), |
| 8835 | -sin (x) * sinh (y)); |
| 8836 | } |
| 8837 | else |
| 8838 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); |
| 8839 | } |
| 8840 | #undef FUNC_NAME |
| 8841 | |
| 8842 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, |
| 8843 | (SCM z), |
| 8844 | "Compute the tangent of @var{z}.") |
| 8845 | #define FUNC_NAME s_scm_tan |
| 8846 | { |
| 8847 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 8848 | return z; /* tan(exact0) = exact0 */ |
| 8849 | else if (scm_is_real (z)) |
| 8850 | return scm_i_from_double (tan (scm_to_double (z))); |
| 8851 | else if (SCM_COMPLEXP (z)) |
| 8852 | { double x, y, w; |
| 8853 | x = 2.0 * SCM_COMPLEX_REAL (z); |
| 8854 | y = 2.0 * SCM_COMPLEX_IMAG (z); |
| 8855 | w = cos (x) + cosh (y); |
| 8856 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8857 | if (w == 0.0) |
| 8858 | scm_num_overflow (s_scm_tan); |
| 8859 | #endif |
| 8860 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); |
| 8861 | } |
| 8862 | else |
| 8863 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); |
| 8864 | } |
| 8865 | #undef FUNC_NAME |
| 8866 | |
| 8867 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, |
| 8868 | (SCM z), |
| 8869 | "Compute the hyperbolic sine of @var{z}.") |
| 8870 | #define FUNC_NAME s_scm_sinh |
| 8871 | { |
| 8872 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 8873 | return z; /* sinh(exact0) = exact0 */ |
| 8874 | else if (scm_is_real (z)) |
| 8875 | return scm_i_from_double (sinh (scm_to_double (z))); |
| 8876 | else if (SCM_COMPLEXP (z)) |
| 8877 | { double x, y; |
| 8878 | x = SCM_COMPLEX_REAL (z); |
| 8879 | y = SCM_COMPLEX_IMAG (z); |
| 8880 | return scm_c_make_rectangular (sinh (x) * cos (y), |
| 8881 | cosh (x) * sin (y)); |
| 8882 | } |
| 8883 | else |
| 8884 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); |
| 8885 | } |
| 8886 | #undef FUNC_NAME |
| 8887 | |
| 8888 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, |
| 8889 | (SCM z), |
| 8890 | "Compute the hyperbolic cosine of @var{z}.") |
| 8891 | #define FUNC_NAME s_scm_cosh |
| 8892 | { |
| 8893 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 8894 | return SCM_INUM1; /* cosh(exact0) = exact1 */ |
| 8895 | else if (scm_is_real (z)) |
| 8896 | return scm_i_from_double (cosh (scm_to_double (z))); |
| 8897 | else if (SCM_COMPLEXP (z)) |
| 8898 | { double x, y; |
| 8899 | x = SCM_COMPLEX_REAL (z); |
| 8900 | y = SCM_COMPLEX_IMAG (z); |
| 8901 | return scm_c_make_rectangular (cosh (x) * cos (y), |
| 8902 | sinh (x) * sin (y)); |
| 8903 | } |
| 8904 | else |
| 8905 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); |
| 8906 | } |
| 8907 | #undef FUNC_NAME |
| 8908 | |
| 8909 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, |
| 8910 | (SCM z), |
| 8911 | "Compute the hyperbolic tangent of @var{z}.") |
| 8912 | #define FUNC_NAME s_scm_tanh |
| 8913 | { |
| 8914 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 8915 | return z; /* tanh(exact0) = exact0 */ |
| 8916 | else if (scm_is_real (z)) |
| 8917 | return scm_i_from_double (tanh (scm_to_double (z))); |
| 8918 | else if (SCM_COMPLEXP (z)) |
| 8919 | { double x, y, w; |
| 8920 | x = 2.0 * SCM_COMPLEX_REAL (z); |
| 8921 | y = 2.0 * SCM_COMPLEX_IMAG (z); |
| 8922 | w = cosh (x) + cos (y); |
| 8923 | #ifndef ALLOW_DIVIDE_BY_ZERO |
| 8924 | if (w == 0.0) |
| 8925 | scm_num_overflow (s_scm_tanh); |
| 8926 | #endif |
| 8927 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); |
| 8928 | } |
| 8929 | else |
| 8930 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); |
| 8931 | } |
| 8932 | #undef FUNC_NAME |
| 8933 | |
| 8934 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, |
| 8935 | (SCM z), |
| 8936 | "Compute the arc sine of @var{z}.") |
| 8937 | #define FUNC_NAME s_scm_asin |
| 8938 | { |
| 8939 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 8940 | return z; /* asin(exact0) = exact0 */ |
| 8941 | else if (scm_is_real (z)) |
| 8942 | { |
| 8943 | double w = scm_to_double (z); |
| 8944 | if (w >= -1.0 && w <= 1.0) |
| 8945 | return scm_i_from_double (asin (w)); |
| 8946 | else |
| 8947 | return scm_product (scm_c_make_rectangular (0, -1), |
| 8948 | scm_sys_asinh (scm_c_make_rectangular (0, w))); |
| 8949 | } |
| 8950 | else if (SCM_COMPLEXP (z)) |
| 8951 | { double x, y; |
| 8952 | x = SCM_COMPLEX_REAL (z); |
| 8953 | y = SCM_COMPLEX_IMAG (z); |
| 8954 | return scm_product (scm_c_make_rectangular (0, -1), |
| 8955 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); |
| 8956 | } |
| 8957 | else |
| 8958 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); |
| 8959 | } |
| 8960 | #undef FUNC_NAME |
| 8961 | |
| 8962 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, |
| 8963 | (SCM z), |
| 8964 | "Compute the arc cosine of @var{z}.") |
| 8965 | #define FUNC_NAME s_scm_acos |
| 8966 | { |
| 8967 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
| 8968 | return SCM_INUM0; /* acos(exact1) = exact0 */ |
| 8969 | else if (scm_is_real (z)) |
| 8970 | { |
| 8971 | double w = scm_to_double (z); |
| 8972 | if (w >= -1.0 && w <= 1.0) |
| 8973 | return scm_i_from_double (acos (w)); |
| 8974 | else |
| 8975 | return scm_sum (scm_i_from_double (acos (0.0)), |
| 8976 | scm_product (scm_c_make_rectangular (0, 1), |
| 8977 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); |
| 8978 | } |
| 8979 | else if (SCM_COMPLEXP (z)) |
| 8980 | { double x, y; |
| 8981 | x = SCM_COMPLEX_REAL (z); |
| 8982 | y = SCM_COMPLEX_IMAG (z); |
| 8983 | return scm_sum (scm_i_from_double (acos (0.0)), |
| 8984 | scm_product (scm_c_make_rectangular (0, 1), |
| 8985 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); |
| 8986 | } |
| 8987 | else |
| 8988 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); |
| 8989 | } |
| 8990 | #undef FUNC_NAME |
| 8991 | |
| 8992 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, |
| 8993 | (SCM z, SCM y), |
| 8994 | "With one argument, compute the arc tangent of @var{z}.\n" |
| 8995 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" |
| 8996 | "using the sign of @var{z} and @var{y} to determine the quadrant.") |
| 8997 | #define FUNC_NAME s_scm_atan |
| 8998 | { |
| 8999 | if (SCM_UNBNDP (y)) |
| 9000 | { |
| 9001 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 9002 | return z; /* atan(exact0) = exact0 */ |
| 9003 | else if (scm_is_real (z)) |
| 9004 | return scm_i_from_double (atan (scm_to_double (z))); |
| 9005 | else if (SCM_COMPLEXP (z)) |
| 9006 | { |
| 9007 | double v, w; |
| 9008 | v = SCM_COMPLEX_REAL (z); |
| 9009 | w = SCM_COMPLEX_IMAG (z); |
| 9010 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), |
| 9011 | scm_c_make_rectangular (v, w + 1.0))), |
| 9012 | scm_c_make_rectangular (0, 2)); |
| 9013 | } |
| 9014 | else |
| 9015 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
| 9016 | } |
| 9017 | else if (scm_is_real (z)) |
| 9018 | { |
| 9019 | if (scm_is_real (y)) |
| 9020 | return scm_i_from_double (atan2 (scm_to_double (z), scm_to_double (y))); |
| 9021 | else |
| 9022 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); |
| 9023 | } |
| 9024 | else |
| 9025 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); |
| 9026 | } |
| 9027 | #undef FUNC_NAME |
| 9028 | |
| 9029 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, |
| 9030 | (SCM z), |
| 9031 | "Compute the inverse hyperbolic sine of @var{z}.") |
| 9032 | #define FUNC_NAME s_scm_sys_asinh |
| 9033 | { |
| 9034 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 9035 | return z; /* asinh(exact0) = exact0 */ |
| 9036 | else if (scm_is_real (z)) |
| 9037 | return scm_i_from_double (asinh (scm_to_double (z))); |
| 9038 | else if (scm_is_number (z)) |
| 9039 | return scm_log (scm_sum (z, |
| 9040 | scm_sqrt (scm_sum (scm_product (z, z), |
| 9041 | SCM_INUM1)))); |
| 9042 | else |
| 9043 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); |
| 9044 | } |
| 9045 | #undef FUNC_NAME |
| 9046 | |
| 9047 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, |
| 9048 | (SCM z), |
| 9049 | "Compute the inverse hyperbolic cosine of @var{z}.") |
| 9050 | #define FUNC_NAME s_scm_sys_acosh |
| 9051 | { |
| 9052 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
| 9053 | return SCM_INUM0; /* acosh(exact1) = exact0 */ |
| 9054 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) |
| 9055 | return scm_i_from_double (acosh (scm_to_double (z))); |
| 9056 | else if (scm_is_number (z)) |
| 9057 | return scm_log (scm_sum (z, |
| 9058 | scm_sqrt (scm_difference (scm_product (z, z), |
| 9059 | SCM_INUM1)))); |
| 9060 | else |
| 9061 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); |
| 9062 | } |
| 9063 | #undef FUNC_NAME |
| 9064 | |
| 9065 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, |
| 9066 | (SCM z), |
| 9067 | "Compute the inverse hyperbolic tangent of @var{z}.") |
| 9068 | #define FUNC_NAME s_scm_sys_atanh |
| 9069 | { |
| 9070 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
| 9071 | return z; /* atanh(exact0) = exact0 */ |
| 9072 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) |
| 9073 | return scm_i_from_double (atanh (scm_to_double (z))); |
| 9074 | else if (scm_is_number (z)) |
| 9075 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
| 9076 | scm_difference (SCM_INUM1, z))), |
| 9077 | SCM_I_MAKINUM (2)); |
| 9078 | else |
| 9079 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); |
| 9080 | } |
| 9081 | #undef FUNC_NAME |
| 9082 | |
| 9083 | SCM |
| 9084 | scm_c_make_rectangular (double re, double im) |
| 9085 | { |
| 9086 | SCM z; |
| 9087 | |
| 9088 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
| 9089 | "complex")); |
| 9090 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); |
| 9091 | SCM_COMPLEX_REAL (z) = re; |
| 9092 | SCM_COMPLEX_IMAG (z) = im; |
| 9093 | return z; |
| 9094 | } |
| 9095 | |
| 9096 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
| 9097 | (SCM real_part, SCM imaginary_part), |
| 9098 | "Return a complex number constructed of the given @var{real_part} " |
| 9099 | "and @var{imaginary_part} parts.") |
| 9100 | #define FUNC_NAME s_scm_make_rectangular |
| 9101 | { |
| 9102 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
| 9103 | SCM_ARG1, FUNC_NAME, "real"); |
| 9104 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, |
| 9105 | SCM_ARG2, FUNC_NAME, "real"); |
| 9106 | |
| 9107 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ |
| 9108 | if (scm_is_eq (imaginary_part, SCM_INUM0)) |
| 9109 | return real_part; |
| 9110 | else |
| 9111 | return scm_c_make_rectangular (scm_to_double (real_part), |
| 9112 | scm_to_double (imaginary_part)); |
| 9113 | } |
| 9114 | #undef FUNC_NAME |
| 9115 | |
| 9116 | SCM |
| 9117 | scm_c_make_polar (double mag, double ang) |
| 9118 | { |
| 9119 | double s, c; |
| 9120 | |
| 9121 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only |
| 9122 | use it on Glibc-based systems that have it (it's a GNU extension). See |
| 9123 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for |
| 9124 | details. */ |
| 9125 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) |
| 9126 | sincos (ang, &s, &c); |
| 9127 | #else |
| 9128 | s = sin (ang); |
| 9129 | c = cos (ang); |
| 9130 | #endif |
| 9131 | |
| 9132 | /* If s and c are NaNs, this indicates that the angle is a NaN, |
| 9133 | infinite, or perhaps simply too large to determine its value |
| 9134 | mod 2*pi. However, we know something that the floating-point |
| 9135 | implementation doesn't know: We know that s and c are finite. |
| 9136 | Therefore, if the magnitude is zero, return a complex zero. |
| 9137 | |
| 9138 | The reason we check for the NaNs instead of using this case |
| 9139 | whenever mag == 0.0 is because when the angle is known, we'd |
| 9140 | like to return the correct kind of non-real complex zero: |
| 9141 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending |
| 9142 | on which quadrant the angle is in. |
| 9143 | */ |
| 9144 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) |
| 9145 | return scm_c_make_rectangular (0.0, 0.0); |
| 9146 | else |
| 9147 | return scm_c_make_rectangular (mag * c, mag * s); |
| 9148 | } |
| 9149 | |
| 9150 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
| 9151 | (SCM mag, SCM ang), |
| 9152 | "Return the complex number @var{mag} * e^(i * @var{ang}).") |
| 9153 | #define FUNC_NAME s_scm_make_polar |
| 9154 | { |
| 9155 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
| 9156 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); |
| 9157 | |
| 9158 | /* If mag is exact0, return exact0 */ |
| 9159 | if (scm_is_eq (mag, SCM_INUM0)) |
| 9160 | return SCM_INUM0; |
| 9161 | /* Return a real if ang is exact0 */ |
| 9162 | else if (scm_is_eq (ang, SCM_INUM0)) |
| 9163 | return mag; |
| 9164 | else |
| 9165 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); |
| 9166 | } |
| 9167 | #undef FUNC_NAME |
| 9168 | |
| 9169 | |
| 9170 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
| 9171 | (SCM z), |
| 9172 | "Return the real part of the number @var{z}.") |
| 9173 | #define FUNC_NAME s_scm_real_part |
| 9174 | { |
| 9175 | if (SCM_COMPLEXP (z)) |
| 9176 | return scm_i_from_double (SCM_COMPLEX_REAL (z)); |
| 9177 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
| 9178 | return z; |
| 9179 | else |
| 9180 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
| 9181 | } |
| 9182 | #undef FUNC_NAME |
| 9183 | |
| 9184 | |
| 9185 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
| 9186 | (SCM z), |
| 9187 | "Return the imaginary part of the number @var{z}.") |
| 9188 | #define FUNC_NAME s_scm_imag_part |
| 9189 | { |
| 9190 | if (SCM_COMPLEXP (z)) |
| 9191 | return scm_i_from_double (SCM_COMPLEX_IMAG (z)); |
| 9192 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
| 9193 | return SCM_INUM0; |
| 9194 | else |
| 9195 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
| 9196 | } |
| 9197 | #undef FUNC_NAME |
| 9198 | |
| 9199 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
| 9200 | (SCM z), |
| 9201 | "Return the numerator of the number @var{z}.") |
| 9202 | #define FUNC_NAME s_scm_numerator |
| 9203 | { |
| 9204 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
| 9205 | return z; |
| 9206 | else if (SCM_FRACTIONP (z)) |
| 9207 | return SCM_FRACTION_NUMERATOR (z); |
| 9208 | else if (SCM_REALP (z)) |
| 9209 | { |
| 9210 | double zz = SCM_REAL_VALUE (z); |
| 9211 | if (zz == floor (zz)) |
| 9212 | /* Handle -0.0 and infinities in accordance with R6RS |
| 9213 | flnumerator, and optimize handling of integers. */ |
| 9214 | return z; |
| 9215 | else |
| 9216 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); |
| 9217 | } |
| 9218 | else |
| 9219 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
| 9220 | } |
| 9221 | #undef FUNC_NAME |
| 9222 | |
| 9223 | |
| 9224 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
| 9225 | (SCM z), |
| 9226 | "Return the denominator of the number @var{z}.") |
| 9227 | #define FUNC_NAME s_scm_denominator |
| 9228 | { |
| 9229 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
| 9230 | return SCM_INUM1; |
| 9231 | else if (SCM_FRACTIONP (z)) |
| 9232 | return SCM_FRACTION_DENOMINATOR (z); |
| 9233 | else if (SCM_REALP (z)) |
| 9234 | { |
| 9235 | double zz = SCM_REAL_VALUE (z); |
| 9236 | if (zz == floor (zz)) |
| 9237 | /* Handle infinities in accordance with R6RS fldenominator, and |
| 9238 | optimize handling of integers. */ |
| 9239 | return scm_i_from_double (1.0); |
| 9240 | else |
| 9241 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); |
| 9242 | } |
| 9243 | else |
| 9244 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
| 9245 | } |
| 9246 | #undef FUNC_NAME |
| 9247 | |
| 9248 | |
| 9249 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, |
| 9250 | (SCM z), |
| 9251 | "Return the magnitude of the number @var{z}. This is the same as\n" |
| 9252 | "@code{abs} for real arguments, but also allows complex numbers.") |
| 9253 | #define FUNC_NAME s_scm_magnitude |
| 9254 | { |
| 9255 | if (SCM_I_INUMP (z)) |
| 9256 | { |
| 9257 | scm_t_inum zz = SCM_I_INUM (z); |
| 9258 | if (zz >= 0) |
| 9259 | return z; |
| 9260 | else if (SCM_POSFIXABLE (-zz)) |
| 9261 | return SCM_I_MAKINUM (-zz); |
| 9262 | else |
| 9263 | return scm_i_inum2big (-zz); |
| 9264 | } |
| 9265 | else if (SCM_BIGP (z)) |
| 9266 | { |
| 9267 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); |
| 9268 | scm_remember_upto_here_1 (z); |
| 9269 | if (sgn < 0) |
| 9270 | return scm_i_clonebig (z, 0); |
| 9271 | else |
| 9272 | return z; |
| 9273 | } |
| 9274 | else if (SCM_REALP (z)) |
| 9275 | return scm_i_from_double (fabs (SCM_REAL_VALUE (z))); |
| 9276 | else if (SCM_COMPLEXP (z)) |
| 9277 | return scm_i_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
| 9278 | else if (SCM_FRACTIONP (z)) |
| 9279 | { |
| 9280 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
| 9281 | return z; |
| 9282 | return scm_i_make_ratio_already_reduced |
| 9283 | (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
| 9284 | SCM_FRACTION_DENOMINATOR (z)); |
| 9285 | } |
| 9286 | else |
| 9287 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
| 9288 | } |
| 9289 | #undef FUNC_NAME |
| 9290 | |
| 9291 | |
| 9292 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
| 9293 | (SCM z), |
| 9294 | "Return the angle of the complex number @var{z}.") |
| 9295 | #define FUNC_NAME s_scm_angle |
| 9296 | { |
| 9297 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
| 9298 | flo0 to save allocating a new flonum with scm_i_from_double each time. |
| 9299 | But if atan2 follows the floating point rounding mode, then the value |
| 9300 | is not a constant. Maybe it'd be close enough though. */ |
| 9301 | if (SCM_I_INUMP (z)) |
| 9302 | { |
| 9303 | if (SCM_I_INUM (z) >= 0) |
| 9304 | return flo0; |
| 9305 | else |
| 9306 | return scm_i_from_double (atan2 (0.0, -1.0)); |
| 9307 | } |
| 9308 | else if (SCM_BIGP (z)) |
| 9309 | { |
| 9310 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); |
| 9311 | scm_remember_upto_here_1 (z); |
| 9312 | if (sgn < 0) |
| 9313 | return scm_i_from_double (atan2 (0.0, -1.0)); |
| 9314 | else |
| 9315 | return flo0; |
| 9316 | } |
| 9317 | else if (SCM_REALP (z)) |
| 9318 | { |
| 9319 | double x = SCM_REAL_VALUE (z); |
| 9320 | if (copysign (1.0, x) > 0.0) |
| 9321 | return flo0; |
| 9322 | else |
| 9323 | return scm_i_from_double (atan2 (0.0, -1.0)); |
| 9324 | } |
| 9325 | else if (SCM_COMPLEXP (z)) |
| 9326 | return scm_i_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
| 9327 | else if (SCM_FRACTIONP (z)) |
| 9328 | { |
| 9329 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
| 9330 | return flo0; |
| 9331 | else return scm_i_from_double (atan2 (0.0, -1.0)); |
| 9332 | } |
| 9333 | else |
| 9334 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
| 9335 | } |
| 9336 | #undef FUNC_NAME |
| 9337 | |
| 9338 | |
| 9339 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
| 9340 | (SCM z), |
| 9341 | "Convert the number @var{z} to its inexact representation.\n") |
| 9342 | #define FUNC_NAME s_scm_exact_to_inexact |
| 9343 | { |
| 9344 | if (SCM_I_INUMP (z)) |
| 9345 | return scm_i_from_double ((double) SCM_I_INUM (z)); |
| 9346 | else if (SCM_BIGP (z)) |
| 9347 | return scm_i_from_double (scm_i_big2dbl (z)); |
| 9348 | else if (SCM_FRACTIONP (z)) |
| 9349 | return scm_i_from_double (scm_i_fraction2double (z)); |
| 9350 | else if (SCM_INEXACTP (z)) |
| 9351 | return z; |
| 9352 | else |
| 9353 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
| 9354 | } |
| 9355 | #undef FUNC_NAME |
| 9356 | |
| 9357 | |
| 9358 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
| 9359 | (SCM z), |
| 9360 | "Return an exact number that is numerically closest to @var{z}.") |
| 9361 | #define FUNC_NAME s_scm_inexact_to_exact |
| 9362 | { |
| 9363 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
| 9364 | return z; |
| 9365 | else |
| 9366 | { |
| 9367 | double val; |
| 9368 | |
| 9369 | if (SCM_REALP (z)) |
| 9370 | val = SCM_REAL_VALUE (z); |
| 9371 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) |
| 9372 | val = SCM_COMPLEX_REAL (z); |
| 9373 | else |
| 9374 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); |
| 9375 | |
| 9376 | if (!SCM_LIKELY (isfinite (val))) |
| 9377 | SCM_OUT_OF_RANGE (1, z); |
| 9378 | else if (val == 0.0) |
| 9379 | return SCM_INUM0; |
| 9380 | else |
| 9381 | { |
| 9382 | int expon; |
| 9383 | SCM numerator; |
| 9384 | |
| 9385 | numerator = scm_i_dbl2big (ldexp (frexp (val, &expon), |
| 9386 | DBL_MANT_DIG)); |
| 9387 | expon -= DBL_MANT_DIG; |
| 9388 | if (expon < 0) |
| 9389 | { |
| 9390 | int shift = mpz_scan1 (SCM_I_BIG_MPZ (numerator), 0); |
| 9391 | |
| 9392 | if (shift > -expon) |
| 9393 | shift = -expon; |
| 9394 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (numerator), |
| 9395 | SCM_I_BIG_MPZ (numerator), |
| 9396 | shift); |
| 9397 | expon += shift; |
| 9398 | } |
| 9399 | numerator = scm_i_normbig (numerator); |
| 9400 | if (expon < 0) |
| 9401 | return scm_i_make_ratio_already_reduced |
| 9402 | (numerator, left_shift_exact_integer (SCM_INUM1, -expon)); |
| 9403 | else if (expon > 0) |
| 9404 | return left_shift_exact_integer (numerator, expon); |
| 9405 | else |
| 9406 | return numerator; |
| 9407 | } |
| 9408 | } |
| 9409 | } |
| 9410 | #undef FUNC_NAME |
| 9411 | |
| 9412 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
| 9413 | (SCM x, SCM eps), |
| 9414 | "Returns the @emph{simplest} rational number differing\n" |
| 9415 | "from @var{x} by no more than @var{eps}.\n" |
| 9416 | "\n" |
| 9417 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" |
| 9418 | "exact result when both its arguments are exact. Thus, you might need\n" |
| 9419 | "to use @code{inexact->exact} on the arguments.\n" |
| 9420 | "\n" |
| 9421 | "@lisp\n" |
| 9422 | "(rationalize (inexact->exact 1.2) 1/100)\n" |
| 9423 | "@result{} 6/5\n" |
| 9424 | "@end lisp") |
| 9425 | #define FUNC_NAME s_scm_rationalize |
| 9426 | { |
| 9427 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
| 9428 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); |
| 9429 | |
| 9430 | if (SCM_UNLIKELY (!scm_is_exact (eps) || !scm_is_exact (x))) |
| 9431 | { |
| 9432 | if (SCM_UNLIKELY (scm_is_false (scm_finite_p (eps)))) |
| 9433 | { |
| 9434 | if (scm_is_false (scm_nan_p (eps)) && scm_is_true (scm_finite_p (x))) |
| 9435 | return flo0; |
| 9436 | else |
| 9437 | return scm_nan (); |
| 9438 | } |
| 9439 | else if (SCM_UNLIKELY (scm_is_false (scm_finite_p (x)))) |
| 9440 | return x; |
| 9441 | else |
| 9442 | return scm_exact_to_inexact |
| 9443 | (scm_rationalize (scm_inexact_to_exact (x), |
| 9444 | scm_inexact_to_exact (eps))); |
| 9445 | } |
| 9446 | else |
| 9447 | { |
| 9448 | /* X and EPS are exact rationals. |
| 9449 | |
| 9450 | The code that follows is equivalent to the following Scheme code: |
| 9451 | |
| 9452 | (define (exact-rationalize x eps) |
| 9453 | (let ((n1 (if (negative? x) -1 1)) |
| 9454 | (x (abs x)) |
| 9455 | (eps (abs eps))) |
| 9456 | (let ((lo (- x eps)) |
| 9457 | (hi (+ x eps))) |
| 9458 | (if (<= lo 0) |
| 9459 | 0 |
| 9460 | (let loop ((nlo (numerator lo)) (dlo (denominator lo)) |
| 9461 | (nhi (numerator hi)) (dhi (denominator hi)) |
| 9462 | (n1 n1) (d1 0) (n2 0) (d2 1)) |
| 9463 | (let-values (((qlo rlo) (floor/ nlo dlo)) |
| 9464 | ((qhi rhi) (floor/ nhi dhi))) |
| 9465 | (let ((n0 (+ n2 (* n1 qlo))) |
| 9466 | (d0 (+ d2 (* d1 qlo)))) |
| 9467 | (cond ((zero? rlo) (/ n0 d0)) |
| 9468 | ((< qlo qhi) (/ (+ n0 n1) (+ d0 d1))) |
| 9469 | (else (loop dhi rhi dlo rlo n0 d0 n1 d1)))))))))) |
| 9470 | */ |
| 9471 | |
| 9472 | int n1_init = 1; |
| 9473 | SCM lo, hi; |
| 9474 | |
| 9475 | eps = scm_abs (eps); |
| 9476 | if (scm_is_true (scm_negative_p (x))) |
| 9477 | { |
| 9478 | n1_init = -1; |
| 9479 | x = scm_difference (x, SCM_UNDEFINED); |
| 9480 | } |
| 9481 | |
| 9482 | /* X and EPS are non-negative exact rationals. */ |
| 9483 | |
| 9484 | lo = scm_difference (x, eps); |
| 9485 | hi = scm_sum (x, eps); |
| 9486 | |
| 9487 | if (scm_is_false (scm_positive_p (lo))) |
| 9488 | /* If zero is included in the interval, return it. |
| 9489 | It is the simplest rational of all. */ |
| 9490 | return SCM_INUM0; |
| 9491 | else |
| 9492 | { |
| 9493 | SCM result; |
| 9494 | mpz_t n0, d0, n1, d1, n2, d2; |
| 9495 | mpz_t nlo, dlo, nhi, dhi; |
| 9496 | mpz_t qlo, rlo, qhi, rhi; |
| 9497 | |
| 9498 | /* LO and HI are positive exact rationals. */ |
| 9499 | |
| 9500 | /* Our approach here follows the method described by Alan |
| 9501 | Bawden in a message entitled "(rationalize x y)" on the |
| 9502 | rrrs-authors mailing list, dated 16 Feb 1988 14:08:28 EST: |
| 9503 | |
| 9504 | http://groups.csail.mit.edu/mac/ftpdir/scheme-mail/HTML/rrrs-1988/msg00063.html |
| 9505 | |
| 9506 | In brief, we compute the continued fractions of the two |
| 9507 | endpoints of the interval (LO and HI). The continued |
| 9508 | fraction of the result consists of the common prefix of the |
| 9509 | continued fractions of LO and HI, plus one final term. The |
| 9510 | final term of the result is the smallest integer contained |
| 9511 | in the interval between the remainders of LO and HI after |
| 9512 | the common prefix has been removed. |
| 9513 | |
| 9514 | The following code lazily computes the continued fraction |
| 9515 | representations of LO and HI, and simultaneously converts |
| 9516 | the continued fraction of the result into a rational |
| 9517 | number. We use MPZ functions directly to avoid type |
| 9518 | dispatch and GC allocation during the loop. */ |
| 9519 | |
| 9520 | mpz_inits (n0, d0, n1, d1, n2, d2, |
| 9521 | nlo, dlo, nhi, dhi, |
| 9522 | qlo, rlo, qhi, rhi, |
| 9523 | NULL); |
| 9524 | |
| 9525 | /* The variables N1, D1, N2 and D2 are used to compute the |
| 9526 | resulting rational from its continued fraction. At each |
| 9527 | step, N2/D2 and N1/D1 are the last two convergents. They |
| 9528 | are normally initialized to 0/1 and 1/0, respectively. |
| 9529 | However, if we negated X then we must negate the result as |
| 9530 | well, and we do that by initializing N1/D1 to -1/0. */ |
| 9531 | mpz_set_si (n1, n1_init); |
| 9532 | mpz_set_ui (d1, 0); |
| 9533 | mpz_set_ui (n2, 0); |
| 9534 | mpz_set_ui (d2, 1); |
| 9535 | |
| 9536 | /* The variables NLO, DLO, NHI, and DHI are used to lazily |
| 9537 | compute the continued fraction representations of LO and HI |
| 9538 | using Euclid's algorithm. Initially, NLO/DLO == LO and |
| 9539 | NHI/DHI == HI. */ |
| 9540 | scm_to_mpz (scm_numerator (lo), nlo); |
| 9541 | scm_to_mpz (scm_denominator (lo), dlo); |
| 9542 | scm_to_mpz (scm_numerator (hi), nhi); |
| 9543 | scm_to_mpz (scm_denominator (hi), dhi); |
| 9544 | |
| 9545 | /* As long as we're using exact arithmetic, the following loop |
| 9546 | is guaranteed to terminate. */ |
| 9547 | for (;;) |
| 9548 | { |
| 9549 | /* Compute the next terms (QLO and QHI) of the continued |
| 9550 | fractions of LO and HI. */ |
| 9551 | mpz_fdiv_qr (qlo, rlo, nlo, dlo); /* QLO <-- floor (NLO/DLO), RLO <-- NLO - QLO * DLO */ |
| 9552 | mpz_fdiv_qr (qhi, rhi, nhi, dhi); /* QHI <-- floor (NHI/DHI), RHI <-- NHI - QHI * DHI */ |
| 9553 | |
| 9554 | /* The next term of the result will be either QLO or |
| 9555 | QLO+1. Here we compute the next convergent of the |
| 9556 | result based on the assumption that QLO is the next |
| 9557 | term. If that turns out to be wrong, we'll adjust |
| 9558 | these later by adding N1 to N0 and D1 to D0. */ |
| 9559 | mpz_set (n0, n2); mpz_addmul (n0, n1, qlo); /* N0 <-- N2 + (QLO * N1) */ |
| 9560 | mpz_set (d0, d2); mpz_addmul (d0, d1, qlo); /* D0 <-- D2 + (QLO * D1) */ |
| 9561 | |
| 9562 | /* We stop iterating when an integer is contained in the |
| 9563 | interval between the remainders NLO/DLO and NHI/DHI. |
| 9564 | There are two cases to consider: either NLO/DLO == QLO |
| 9565 | is an integer (indicated by RLO == 0), or QLO < QHI. */ |
| 9566 | if (mpz_sgn (rlo) == 0 || mpz_cmp (qlo, qhi) != 0) |
| 9567 | break; |
| 9568 | |
| 9569 | /* Efficiently shuffle variables around for the next |
| 9570 | iteration. First we shift the recent convergents. */ |
| 9571 | mpz_swap (n2, n1); mpz_swap (n1, n0); /* N2 <-- N1 <-- N0 */ |
| 9572 | mpz_swap (d2, d1); mpz_swap (d1, d0); /* D2 <-- D1 <-- D0 */ |
| 9573 | |
| 9574 | /* The following shuffling is a bit confusing, so some |
| 9575 | explanation is in order. Conceptually, we're doing a |
| 9576 | couple of things here. After substracting the floor of |
| 9577 | NLO/DLO, the remainder is RLO/DLO. The rest of the |
| 9578 | continued fraction will represent the remainder's |
| 9579 | reciprocal DLO/RLO. Similarly for the HI endpoint. |
| 9580 | So in the next iteration, the new endpoints will be |
| 9581 | DLO/RLO and DHI/RHI. However, when we take the |
| 9582 | reciprocals of these endpoints, their order is |
| 9583 | switched. So in summary, we want NLO/DLO <-- DHI/RHI |
| 9584 | and NHI/DHI <-- DLO/RLO. */ |
| 9585 | mpz_swap (nlo, dhi); mpz_swap (dhi, rlo); /* NLO <-- DHI <-- RLO */ |
| 9586 | mpz_swap (nhi, dlo); mpz_swap (dlo, rhi); /* NHI <-- DLO <-- RHI */ |
| 9587 | } |
| 9588 | |
| 9589 | /* There is now an integer in the interval [NLO/DLO NHI/DHI]. |
| 9590 | The last term of the result will be the smallest integer in |
| 9591 | that interval, which is ceiling(NLO/DLO). We have already |
| 9592 | computed floor(NLO/DLO) in QLO, so now we adjust QLO to be |
| 9593 | equal to the ceiling. */ |
| 9594 | if (mpz_sgn (rlo) != 0) |
| 9595 | { |
| 9596 | /* If RLO is non-zero, then NLO/DLO is not an integer and |
| 9597 | the next term will be QLO+1. QLO was used in the |
| 9598 | computation of N0 and D0 above. Here we adjust N0 and |
| 9599 | D0 to be based on QLO+1 instead of QLO. */ |
| 9600 | mpz_add (n0, n0, n1); /* N0 <-- N0 + N1 */ |
| 9601 | mpz_add (d0, d0, d1); /* D0 <-- D0 + D1 */ |
| 9602 | } |
| 9603 | |
| 9604 | /* The simplest rational in the interval is N0/D0 */ |
| 9605 | result = scm_i_make_ratio_already_reduced (scm_from_mpz (n0), |
| 9606 | scm_from_mpz (d0)); |
| 9607 | mpz_clears (n0, d0, n1, d1, n2, d2, |
| 9608 | nlo, dlo, nhi, dhi, |
| 9609 | qlo, rlo, qhi, rhi, |
| 9610 | NULL); |
| 9611 | return result; |
| 9612 | } |
| 9613 | } |
| 9614 | } |
| 9615 | #undef FUNC_NAME |
| 9616 | |
| 9617 | /* conversion functions */ |
| 9618 | |
| 9619 | int |
| 9620 | scm_is_integer (SCM val) |
| 9621 | { |
| 9622 | return scm_is_true (scm_integer_p (val)); |
| 9623 | } |
| 9624 | |
| 9625 | int |
| 9626 | scm_is_exact_integer (SCM val) |
| 9627 | { |
| 9628 | return scm_is_true (scm_exact_integer_p (val)); |
| 9629 | } |
| 9630 | |
| 9631 | int |
| 9632 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) |
| 9633 | { |
| 9634 | if (SCM_I_INUMP (val)) |
| 9635 | { |
| 9636 | scm_t_signed_bits n = SCM_I_INUM (val); |
| 9637 | return n >= min && n <= max; |
| 9638 | } |
| 9639 | else if (SCM_BIGP (val)) |
| 9640 | { |
| 9641 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) |
| 9642 | return 0; |
| 9643 | else if (min >= LONG_MIN && max <= LONG_MAX) |
| 9644 | { |
| 9645 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) |
| 9646 | { |
| 9647 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); |
| 9648 | return n >= min && n <= max; |
| 9649 | } |
| 9650 | else |
| 9651 | return 0; |
| 9652 | } |
| 9653 | else |
| 9654 | { |
| 9655 | scm_t_intmax n; |
| 9656 | size_t count; |
| 9657 | |
| 9658 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
| 9659 | > CHAR_BIT*sizeof (scm_t_uintmax)) |
| 9660 | return 0; |
| 9661 | |
| 9662 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, |
| 9663 | SCM_I_BIG_MPZ (val)); |
| 9664 | |
| 9665 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
| 9666 | { |
| 9667 | if (n < 0) |
| 9668 | return 0; |
| 9669 | } |
| 9670 | else |
| 9671 | { |
| 9672 | n = -n; |
| 9673 | if (n >= 0) |
| 9674 | return 0; |
| 9675 | } |
| 9676 | |
| 9677 | return n >= min && n <= max; |
| 9678 | } |
| 9679 | } |
| 9680 | else |
| 9681 | return 0; |
| 9682 | } |
| 9683 | |
| 9684 | int |
| 9685 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) |
| 9686 | { |
| 9687 | if (SCM_I_INUMP (val)) |
| 9688 | { |
| 9689 | scm_t_signed_bits n = SCM_I_INUM (val); |
| 9690 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
| 9691 | } |
| 9692 | else if (SCM_BIGP (val)) |
| 9693 | { |
| 9694 | if (max <= SCM_MOST_POSITIVE_FIXNUM) |
| 9695 | return 0; |
| 9696 | else if (max <= ULONG_MAX) |
| 9697 | { |
| 9698 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) |
| 9699 | { |
| 9700 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); |
| 9701 | return n >= min && n <= max; |
| 9702 | } |
| 9703 | else |
| 9704 | return 0; |
| 9705 | } |
| 9706 | else |
| 9707 | { |
| 9708 | scm_t_uintmax n; |
| 9709 | size_t count; |
| 9710 | |
| 9711 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
| 9712 | return 0; |
| 9713 | |
| 9714 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
| 9715 | > CHAR_BIT*sizeof (scm_t_uintmax)) |
| 9716 | return 0; |
| 9717 | |
| 9718 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, |
| 9719 | SCM_I_BIG_MPZ (val)); |
| 9720 | |
| 9721 | return n >= min && n <= max; |
| 9722 | } |
| 9723 | } |
| 9724 | else |
| 9725 | return 0; |
| 9726 | } |
| 9727 | |
| 9728 | static void |
| 9729 | scm_i_range_error (SCM bad_val, SCM min, SCM max) |
| 9730 | { |
| 9731 | scm_error (scm_out_of_range_key, |
| 9732 | NULL, |
| 9733 | "Value out of range ~S to ~S: ~S", |
| 9734 | scm_list_3 (min, max, bad_val), |
| 9735 | scm_list_1 (bad_val)); |
| 9736 | } |
| 9737 | |
| 9738 | #define TYPE scm_t_intmax |
| 9739 | #define TYPE_MIN min |
| 9740 | #define TYPE_MAX max |
| 9741 | #define SIZEOF_TYPE 0 |
| 9742 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) |
| 9743 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) |
| 9744 | #include "libguile/conv-integer.i.c" |
| 9745 | |
| 9746 | #define TYPE scm_t_uintmax |
| 9747 | #define TYPE_MIN min |
| 9748 | #define TYPE_MAX max |
| 9749 | #define SIZEOF_TYPE 0 |
| 9750 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) |
| 9751 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) |
| 9752 | #include "libguile/conv-uinteger.i.c" |
| 9753 | |
| 9754 | #define TYPE scm_t_int8 |
| 9755 | #define TYPE_MIN SCM_T_INT8_MIN |
| 9756 | #define TYPE_MAX SCM_T_INT8_MAX |
| 9757 | #define SIZEOF_TYPE 1 |
| 9758 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) |
| 9759 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) |
| 9760 | #include "libguile/conv-integer.i.c" |
| 9761 | |
| 9762 | #define TYPE scm_t_uint8 |
| 9763 | #define TYPE_MIN 0 |
| 9764 | #define TYPE_MAX SCM_T_UINT8_MAX |
| 9765 | #define SIZEOF_TYPE 1 |
| 9766 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) |
| 9767 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) |
| 9768 | #include "libguile/conv-uinteger.i.c" |
| 9769 | |
| 9770 | #define TYPE scm_t_int16 |
| 9771 | #define TYPE_MIN SCM_T_INT16_MIN |
| 9772 | #define TYPE_MAX SCM_T_INT16_MAX |
| 9773 | #define SIZEOF_TYPE 2 |
| 9774 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) |
| 9775 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) |
| 9776 | #include "libguile/conv-integer.i.c" |
| 9777 | |
| 9778 | #define TYPE scm_t_uint16 |
| 9779 | #define TYPE_MIN 0 |
| 9780 | #define TYPE_MAX SCM_T_UINT16_MAX |
| 9781 | #define SIZEOF_TYPE 2 |
| 9782 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) |
| 9783 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) |
| 9784 | #include "libguile/conv-uinteger.i.c" |
| 9785 | |
| 9786 | #define TYPE scm_t_int32 |
| 9787 | #define TYPE_MIN SCM_T_INT32_MIN |
| 9788 | #define TYPE_MAX SCM_T_INT32_MAX |
| 9789 | #define SIZEOF_TYPE 4 |
| 9790 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) |
| 9791 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) |
| 9792 | #include "libguile/conv-integer.i.c" |
| 9793 | |
| 9794 | #define TYPE scm_t_uint32 |
| 9795 | #define TYPE_MIN 0 |
| 9796 | #define TYPE_MAX SCM_T_UINT32_MAX |
| 9797 | #define SIZEOF_TYPE 4 |
| 9798 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) |
| 9799 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) |
| 9800 | #include "libguile/conv-uinteger.i.c" |
| 9801 | |
| 9802 | #define TYPE scm_t_wchar |
| 9803 | #define TYPE_MIN (scm_t_int32)-1 |
| 9804 | #define TYPE_MAX (scm_t_int32)0x10ffff |
| 9805 | #define SIZEOF_TYPE 4 |
| 9806 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) |
| 9807 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) |
| 9808 | #include "libguile/conv-integer.i.c" |
| 9809 | |
| 9810 | #define TYPE scm_t_int64 |
| 9811 | #define TYPE_MIN SCM_T_INT64_MIN |
| 9812 | #define TYPE_MAX SCM_T_INT64_MAX |
| 9813 | #define SIZEOF_TYPE 8 |
| 9814 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) |
| 9815 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) |
| 9816 | #include "libguile/conv-integer.i.c" |
| 9817 | |
| 9818 | #define TYPE scm_t_uint64 |
| 9819 | #define TYPE_MIN 0 |
| 9820 | #define TYPE_MAX SCM_T_UINT64_MAX |
| 9821 | #define SIZEOF_TYPE 8 |
| 9822 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) |
| 9823 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) |
| 9824 | #include "libguile/conv-uinteger.i.c" |
| 9825 | |
| 9826 | void |
| 9827 | scm_to_mpz (SCM val, mpz_t rop) |
| 9828 | { |
| 9829 | if (SCM_I_INUMP (val)) |
| 9830 | mpz_set_si (rop, SCM_I_INUM (val)); |
| 9831 | else if (SCM_BIGP (val)) |
| 9832 | mpz_set (rop, SCM_I_BIG_MPZ (val)); |
| 9833 | else |
| 9834 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); |
| 9835 | } |
| 9836 | |
| 9837 | SCM |
| 9838 | scm_from_mpz (mpz_t val) |
| 9839 | { |
| 9840 | return scm_i_mpz2num (val); |
| 9841 | } |
| 9842 | |
| 9843 | int |
| 9844 | scm_is_real (SCM val) |
| 9845 | { |
| 9846 | return scm_is_true (scm_real_p (val)); |
| 9847 | } |
| 9848 | |
| 9849 | int |
| 9850 | scm_is_rational (SCM val) |
| 9851 | { |
| 9852 | return scm_is_true (scm_rational_p (val)); |
| 9853 | } |
| 9854 | |
| 9855 | double |
| 9856 | scm_to_double (SCM val) |
| 9857 | { |
| 9858 | if (SCM_I_INUMP (val)) |
| 9859 | return SCM_I_INUM (val); |
| 9860 | else if (SCM_BIGP (val)) |
| 9861 | return scm_i_big2dbl (val); |
| 9862 | else if (SCM_FRACTIONP (val)) |
| 9863 | return scm_i_fraction2double (val); |
| 9864 | else if (SCM_REALP (val)) |
| 9865 | return SCM_REAL_VALUE (val); |
| 9866 | else |
| 9867 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
| 9868 | } |
| 9869 | |
| 9870 | SCM |
| 9871 | scm_from_double (double val) |
| 9872 | { |
| 9873 | return scm_i_from_double (val); |
| 9874 | } |
| 9875 | |
| 9876 | #if SCM_ENABLE_DEPRECATED == 1 |
| 9877 | |
| 9878 | float |
| 9879 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
| 9880 | { |
| 9881 | scm_c_issue_deprecation_warning |
| 9882 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); |
| 9883 | |
| 9884 | if (SCM_BIGP (num)) |
| 9885 | { |
| 9886 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); |
| 9887 | if (!isinf (res)) |
| 9888 | return res; |
| 9889 | else |
| 9890 | scm_out_of_range (NULL, num); |
| 9891 | } |
| 9892 | else |
| 9893 | return scm_to_double (num); |
| 9894 | } |
| 9895 | |
| 9896 | double |
| 9897 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
| 9898 | { |
| 9899 | scm_c_issue_deprecation_warning |
| 9900 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); |
| 9901 | |
| 9902 | if (SCM_BIGP (num)) |
| 9903 | { |
| 9904 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); |
| 9905 | if (!isinf (res)) |
| 9906 | return res; |
| 9907 | else |
| 9908 | scm_out_of_range (NULL, num); |
| 9909 | } |
| 9910 | else |
| 9911 | return scm_to_double (num); |
| 9912 | } |
| 9913 | |
| 9914 | #endif |
| 9915 | |
| 9916 | int |
| 9917 | scm_is_complex (SCM val) |
| 9918 | { |
| 9919 | return scm_is_true (scm_complex_p (val)); |
| 9920 | } |
| 9921 | |
| 9922 | double |
| 9923 | scm_c_real_part (SCM z) |
| 9924 | { |
| 9925 | if (SCM_COMPLEXP (z)) |
| 9926 | return SCM_COMPLEX_REAL (z); |
| 9927 | else |
| 9928 | { |
| 9929 | /* Use the scm_real_part to get proper error checking and |
| 9930 | dispatching. |
| 9931 | */ |
| 9932 | return scm_to_double (scm_real_part (z)); |
| 9933 | } |
| 9934 | } |
| 9935 | |
| 9936 | double |
| 9937 | scm_c_imag_part (SCM z) |
| 9938 | { |
| 9939 | if (SCM_COMPLEXP (z)) |
| 9940 | return SCM_COMPLEX_IMAG (z); |
| 9941 | else |
| 9942 | { |
| 9943 | /* Use the scm_imag_part to get proper error checking and |
| 9944 | dispatching. The result will almost always be 0.0, but not |
| 9945 | always. |
| 9946 | */ |
| 9947 | return scm_to_double (scm_imag_part (z)); |
| 9948 | } |
| 9949 | } |
| 9950 | |
| 9951 | double |
| 9952 | scm_c_magnitude (SCM z) |
| 9953 | { |
| 9954 | return scm_to_double (scm_magnitude (z)); |
| 9955 | } |
| 9956 | |
| 9957 | double |
| 9958 | scm_c_angle (SCM z) |
| 9959 | { |
| 9960 | return scm_to_double (scm_angle (z)); |
| 9961 | } |
| 9962 | |
| 9963 | int |
| 9964 | scm_is_number (SCM z) |
| 9965 | { |
| 9966 | return scm_is_true (scm_number_p (z)); |
| 9967 | } |
| 9968 | |
| 9969 | |
| 9970 | /* Returns log(x * 2^shift) */ |
| 9971 | static SCM |
| 9972 | log_of_shifted_double (double x, long shift) |
| 9973 | { |
| 9974 | double ans = log (fabs (x)) + shift * M_LN2; |
| 9975 | |
| 9976 | if (copysign (1.0, x) > 0.0) |
| 9977 | return scm_i_from_double (ans); |
| 9978 | else |
| 9979 | return scm_c_make_rectangular (ans, M_PI); |
| 9980 | } |
| 9981 | |
| 9982 | /* Returns log(n), for exact integer n */ |
| 9983 | static SCM |
| 9984 | log_of_exact_integer (SCM n) |
| 9985 | { |
| 9986 | if (SCM_I_INUMP (n)) |
| 9987 | return log_of_shifted_double (SCM_I_INUM (n), 0); |
| 9988 | else if (SCM_BIGP (n)) |
| 9989 | { |
| 9990 | long expon; |
| 9991 | double signif = scm_i_big2dbl_2exp (n, &expon); |
| 9992 | return log_of_shifted_double (signif, expon); |
| 9993 | } |
| 9994 | else |
| 9995 | scm_wrong_type_arg ("log_of_exact_integer", SCM_ARG1, n); |
| 9996 | } |
| 9997 | |
| 9998 | /* Returns log(n/d), for exact non-zero integers n and d */ |
| 9999 | static SCM |
| 10000 | log_of_fraction (SCM n, SCM d) |
| 10001 | { |
| 10002 | long n_size = scm_to_long (scm_integer_length (n)); |
| 10003 | long d_size = scm_to_long (scm_integer_length (d)); |
| 10004 | |
| 10005 | if (abs (n_size - d_size) > 1) |
| 10006 | return (scm_difference (log_of_exact_integer (n), |
| 10007 | log_of_exact_integer (d))); |
| 10008 | else if (scm_is_false (scm_negative_p (n))) |
| 10009 | return scm_i_from_double |
| 10010 | (log1p (scm_i_divide2double (scm_difference (n, d), d))); |
| 10011 | else |
| 10012 | return scm_c_make_rectangular |
| 10013 | (log1p (scm_i_divide2double (scm_difference (scm_abs (n), d), |
| 10014 | d)), |
| 10015 | M_PI); |
| 10016 | } |
| 10017 | |
| 10018 | |
| 10019 | /* In the following functions we dispatch to the real-arg funcs like log() |
| 10020 | when we know the arg is real, instead of just handing everything to |
| 10021 | clog() for instance. This is in case clog() doesn't optimize for a |
| 10022 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as |
| 10023 | well use it to go straight to the applicable C func. */ |
| 10024 | |
| 10025 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
| 10026 | (SCM z), |
| 10027 | "Return the natural logarithm of @var{z}.") |
| 10028 | #define FUNC_NAME s_scm_log |
| 10029 | { |
| 10030 | if (SCM_COMPLEXP (z)) |
| 10031 | { |
| 10032 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
| 10033 | && defined (SCM_COMPLEX_VALUE) |
| 10034 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
| 10035 | #else |
| 10036 | double re = SCM_COMPLEX_REAL (z); |
| 10037 | double im = SCM_COMPLEX_IMAG (z); |
| 10038 | return scm_c_make_rectangular (log (hypot (re, im)), |
| 10039 | atan2 (im, re)); |
| 10040 | #endif |
| 10041 | } |
| 10042 | else if (SCM_REALP (z)) |
| 10043 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); |
| 10044 | else if (SCM_I_INUMP (z)) |
| 10045 | { |
| 10046 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 10047 | if (scm_is_eq (z, SCM_INUM0)) |
| 10048 | scm_num_overflow (s_scm_log); |
| 10049 | #endif |
| 10050 | return log_of_shifted_double (SCM_I_INUM (z), 0); |
| 10051 | } |
| 10052 | else if (SCM_BIGP (z)) |
| 10053 | return log_of_exact_integer (z); |
| 10054 | else if (SCM_FRACTIONP (z)) |
| 10055 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), |
| 10056 | SCM_FRACTION_DENOMINATOR (z)); |
| 10057 | else |
| 10058 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); |
| 10059 | } |
| 10060 | #undef FUNC_NAME |
| 10061 | |
| 10062 | |
| 10063 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
| 10064 | (SCM z), |
| 10065 | "Return the base 10 logarithm of @var{z}.") |
| 10066 | #define FUNC_NAME s_scm_log10 |
| 10067 | { |
| 10068 | if (SCM_COMPLEXP (z)) |
| 10069 | { |
| 10070 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using |
| 10071 | clog() and a multiply by M_LOG10E, rather than the fallback |
| 10072 | log10+hypot+atan2.) */ |
| 10073 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
| 10074 | && defined SCM_COMPLEX_VALUE |
| 10075 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
| 10076 | #else |
| 10077 | double re = SCM_COMPLEX_REAL (z); |
| 10078 | double im = SCM_COMPLEX_IMAG (z); |
| 10079 | return scm_c_make_rectangular (log10 (hypot (re, im)), |
| 10080 | M_LOG10E * atan2 (im, re)); |
| 10081 | #endif |
| 10082 | } |
| 10083 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
| 10084 | { |
| 10085 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
| 10086 | if (scm_is_eq (z, SCM_INUM0)) |
| 10087 | scm_num_overflow (s_scm_log10); |
| 10088 | #endif |
| 10089 | { |
| 10090 | double re = scm_to_double (z); |
| 10091 | double l = log10 (fabs (re)); |
| 10092 | if (copysign (1.0, re) > 0.0) |
| 10093 | return scm_i_from_double (l); |
| 10094 | else |
| 10095 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); |
| 10096 | } |
| 10097 | } |
| 10098 | else if (SCM_BIGP (z)) |
| 10099 | return scm_product (flo_log10e, log_of_exact_integer (z)); |
| 10100 | else if (SCM_FRACTIONP (z)) |
| 10101 | return scm_product (flo_log10e, |
| 10102 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), |
| 10103 | SCM_FRACTION_DENOMINATOR (z))); |
| 10104 | else |
| 10105 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); |
| 10106 | } |
| 10107 | #undef FUNC_NAME |
| 10108 | |
| 10109 | |
| 10110 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
| 10111 | (SCM z), |
| 10112 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" |
| 10113 | "base of natural logarithms (2.71828@dots{}).") |
| 10114 | #define FUNC_NAME s_scm_exp |
| 10115 | { |
| 10116 | if (SCM_COMPLEXP (z)) |
| 10117 | { |
| 10118 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
| 10119 | && defined (SCM_COMPLEX_VALUE) |
| 10120 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
| 10121 | #else |
| 10122 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), |
| 10123 | SCM_COMPLEX_IMAG (z)); |
| 10124 | #endif |
| 10125 | } |
| 10126 | else if (SCM_NUMBERP (z)) |
| 10127 | { |
| 10128 | /* When z is a negative bignum the conversion to double overflows, |
| 10129 | giving -infinity, but that's ok, the exp is still 0.0. */ |
| 10130 | return scm_i_from_double (exp (scm_to_double (z))); |
| 10131 | } |
| 10132 | else |
| 10133 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); |
| 10134 | } |
| 10135 | #undef FUNC_NAME |
| 10136 | |
| 10137 | |
| 10138 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
| 10139 | (SCM k), |
| 10140 | "Return two exact non-negative integers @var{s} and @var{r}\n" |
| 10141 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" |
| 10142 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" |
| 10143 | "An error is raised if @var{k} is not an exact non-negative integer.\n" |
| 10144 | "\n" |
| 10145 | "@lisp\n" |
| 10146 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" |
| 10147 | "@end lisp") |
| 10148 | #define FUNC_NAME s_scm_i_exact_integer_sqrt |
| 10149 | { |
| 10150 | SCM s, r; |
| 10151 | |
| 10152 | scm_exact_integer_sqrt (k, &s, &r); |
| 10153 | return scm_values (scm_list_2 (s, r)); |
| 10154 | } |
| 10155 | #undef FUNC_NAME |
| 10156 | |
| 10157 | void |
| 10158 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) |
| 10159 | { |
| 10160 | if (SCM_LIKELY (SCM_I_INUMP (k))) |
| 10161 | { |
| 10162 | mpz_t kk, ss, rr; |
| 10163 | |
| 10164 | if (SCM_I_INUM (k) < 0) |
| 10165 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, |
| 10166 | "exact non-negative integer"); |
| 10167 | mpz_init_set_ui (kk, SCM_I_INUM (k)); |
| 10168 | mpz_inits (ss, rr, NULL); |
| 10169 | mpz_sqrtrem (ss, rr, kk); |
| 10170 | *sp = SCM_I_MAKINUM (mpz_get_ui (ss)); |
| 10171 | *rp = SCM_I_MAKINUM (mpz_get_ui (rr)); |
| 10172 | mpz_clears (kk, ss, rr, NULL); |
| 10173 | } |
| 10174 | else if (SCM_LIKELY (SCM_BIGP (k))) |
| 10175 | { |
| 10176 | SCM s, r; |
| 10177 | |
| 10178 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) |
| 10179 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, |
| 10180 | "exact non-negative integer"); |
| 10181 | s = scm_i_mkbig (); |
| 10182 | r = scm_i_mkbig (); |
| 10183 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); |
| 10184 | scm_remember_upto_here_1 (k); |
| 10185 | *sp = scm_i_normbig (s); |
| 10186 | *rp = scm_i_normbig (r); |
| 10187 | } |
| 10188 | else |
| 10189 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, |
| 10190 | "exact non-negative integer"); |
| 10191 | } |
| 10192 | |
| 10193 | /* Return true iff K is a perfect square. |
| 10194 | K must be an exact integer. */ |
| 10195 | static int |
| 10196 | exact_integer_is_perfect_square (SCM k) |
| 10197 | { |
| 10198 | int result; |
| 10199 | |
| 10200 | if (SCM_LIKELY (SCM_I_INUMP (k))) |
| 10201 | { |
| 10202 | mpz_t kk; |
| 10203 | |
| 10204 | mpz_init_set_si (kk, SCM_I_INUM (k)); |
| 10205 | result = mpz_perfect_square_p (kk); |
| 10206 | mpz_clear (kk); |
| 10207 | } |
| 10208 | else |
| 10209 | { |
| 10210 | result = mpz_perfect_square_p (SCM_I_BIG_MPZ (k)); |
| 10211 | scm_remember_upto_here_1 (k); |
| 10212 | } |
| 10213 | return result; |
| 10214 | } |
| 10215 | |
| 10216 | /* Return the floor of the square root of K. |
| 10217 | K must be an exact integer. */ |
| 10218 | static SCM |
| 10219 | exact_integer_floor_square_root (SCM k) |
| 10220 | { |
| 10221 | if (SCM_LIKELY (SCM_I_INUMP (k))) |
| 10222 | { |
| 10223 | mpz_t kk; |
| 10224 | scm_t_inum ss; |
| 10225 | |
| 10226 | mpz_init_set_ui (kk, SCM_I_INUM (k)); |
| 10227 | mpz_sqrt (kk, kk); |
| 10228 | ss = mpz_get_ui (kk); |
| 10229 | mpz_clear (kk); |
| 10230 | return SCM_I_MAKINUM (ss); |
| 10231 | } |
| 10232 | else |
| 10233 | { |
| 10234 | SCM s; |
| 10235 | |
| 10236 | s = scm_i_mkbig (); |
| 10237 | mpz_sqrt (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (k)); |
| 10238 | scm_remember_upto_here_1 (k); |
| 10239 | return scm_i_normbig (s); |
| 10240 | } |
| 10241 | } |
| 10242 | |
| 10243 | |
| 10244 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
| 10245 | (SCM z), |
| 10246 | "Return the square root of @var{z}. Of the two possible roots\n" |
| 10247 | "(positive and negative), the one with positive real part\n" |
| 10248 | "is returned, or if that's zero then a positive imaginary part.\n" |
| 10249 | "Thus,\n" |
| 10250 | "\n" |
| 10251 | "@example\n" |
| 10252 | "(sqrt 9.0) @result{} 3.0\n" |
| 10253 | "(sqrt -9.0) @result{} 0.0+3.0i\n" |
| 10254 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" |
| 10255 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" |
| 10256 | "@end example") |
| 10257 | #define FUNC_NAME s_scm_sqrt |
| 10258 | { |
| 10259 | if (SCM_COMPLEXP (z)) |
| 10260 | { |
| 10261 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
| 10262 | && defined SCM_COMPLEX_VALUE |
| 10263 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
| 10264 | #else |
| 10265 | double re = SCM_COMPLEX_REAL (z); |
| 10266 | double im = SCM_COMPLEX_IMAG (z); |
| 10267 | return scm_c_make_polar (sqrt (hypot (re, im)), |
| 10268 | 0.5 * atan2 (im, re)); |
| 10269 | #endif |
| 10270 | } |
| 10271 | else if (SCM_NUMBERP (z)) |
| 10272 | { |
| 10273 | if (SCM_I_INUMP (z)) |
| 10274 | { |
| 10275 | scm_t_inum x = SCM_I_INUM (z); |
| 10276 | |
| 10277 | if (SCM_LIKELY (x >= 0)) |
| 10278 | { |
| 10279 | if (SCM_LIKELY (SCM_I_FIXNUM_BIT < DBL_MANT_DIG |
| 10280 | || x < (1L << (DBL_MANT_DIG - 1)))) |
| 10281 | { |
| 10282 | double root = sqrt (x); |
| 10283 | |
| 10284 | /* If 0 <= x < 2^(DBL_MANT_DIG-1) and sqrt(x) is an |
| 10285 | integer, then the result is exact. */ |
| 10286 | if (root == floor (root)) |
| 10287 | return SCM_I_MAKINUM ((scm_t_inum) root); |
| 10288 | else |
| 10289 | return scm_i_from_double (root); |
| 10290 | } |
| 10291 | else |
| 10292 | { |
| 10293 | mpz_t xx; |
| 10294 | scm_t_inum root; |
| 10295 | |
| 10296 | mpz_init_set_ui (xx, x); |
| 10297 | if (mpz_perfect_square_p (xx)) |
| 10298 | { |
| 10299 | mpz_sqrt (xx, xx); |
| 10300 | root = mpz_get_ui (xx); |
| 10301 | mpz_clear (xx); |
| 10302 | return SCM_I_MAKINUM (root); |
| 10303 | } |
| 10304 | else |
| 10305 | mpz_clear (xx); |
| 10306 | } |
| 10307 | } |
| 10308 | } |
| 10309 | else if (SCM_BIGP (z)) |
| 10310 | { |
| 10311 | if (mpz_perfect_square_p (SCM_I_BIG_MPZ (z))) |
| 10312 | { |
| 10313 | SCM root = scm_i_mkbig (); |
| 10314 | |
| 10315 | mpz_sqrt (SCM_I_BIG_MPZ (root), SCM_I_BIG_MPZ (z)); |
| 10316 | scm_remember_upto_here_1 (z); |
| 10317 | return scm_i_normbig (root); |
| 10318 | } |
| 10319 | else |
| 10320 | { |
| 10321 | long expon; |
| 10322 | double signif = scm_i_big2dbl_2exp (z, &expon); |
| 10323 | |
| 10324 | if (expon & 1) |
| 10325 | { |
| 10326 | signif *= 2; |
| 10327 | expon--; |
| 10328 | } |
| 10329 | if (signif < 0) |
| 10330 | return scm_c_make_rectangular |
| 10331 | (0.0, ldexp (sqrt (-signif), expon / 2)); |
| 10332 | else |
| 10333 | return scm_i_from_double (ldexp (sqrt (signif), expon / 2)); |
| 10334 | } |
| 10335 | } |
| 10336 | else if (SCM_FRACTIONP (z)) |
| 10337 | { |
| 10338 | SCM n = SCM_FRACTION_NUMERATOR (z); |
| 10339 | SCM d = SCM_FRACTION_DENOMINATOR (z); |
| 10340 | |
| 10341 | if (exact_integer_is_perfect_square (n) |
| 10342 | && exact_integer_is_perfect_square (d)) |
| 10343 | return scm_i_make_ratio_already_reduced |
| 10344 | (exact_integer_floor_square_root (n), |
| 10345 | exact_integer_floor_square_root (d)); |
| 10346 | else |
| 10347 | { |
| 10348 | double xx = scm_i_divide2double (n, d); |
| 10349 | double abs_xx = fabs (xx); |
| 10350 | long shift = 0; |
| 10351 | |
| 10352 | if (SCM_UNLIKELY (abs_xx > DBL_MAX || abs_xx < DBL_MIN)) |
| 10353 | { |
| 10354 | shift = (scm_to_long (scm_integer_length (n)) |
| 10355 | - scm_to_long (scm_integer_length (d))) / 2; |
| 10356 | if (shift > 0) |
| 10357 | d = left_shift_exact_integer (d, 2 * shift); |
| 10358 | else |
| 10359 | n = left_shift_exact_integer (n, -2 * shift); |
| 10360 | xx = scm_i_divide2double (n, d); |
| 10361 | } |
| 10362 | |
| 10363 | if (xx < 0) |
| 10364 | return scm_c_make_rectangular (0.0, ldexp (sqrt (-xx), shift)); |
| 10365 | else |
| 10366 | return scm_i_from_double (ldexp (sqrt (xx), shift)); |
| 10367 | } |
| 10368 | } |
| 10369 | |
| 10370 | /* Fallback method, when the cases above do not apply. */ |
| 10371 | { |
| 10372 | double xx = scm_to_double (z); |
| 10373 | if (xx < 0) |
| 10374 | return scm_c_make_rectangular (0.0, sqrt (-xx)); |
| 10375 | else |
| 10376 | return scm_i_from_double (sqrt (xx)); |
| 10377 | } |
| 10378 | } |
| 10379 | else |
| 10380 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); |
| 10381 | } |
| 10382 | #undef FUNC_NAME |
| 10383 | |
| 10384 | |
| 10385 | |
| 10386 | void |
| 10387 | scm_init_numbers () |
| 10388 | { |
| 10389 | if (scm_install_gmp_memory_functions) |
| 10390 | mp_set_memory_functions (custom_gmp_malloc, |
| 10391 | custom_gmp_realloc, |
| 10392 | custom_gmp_free); |
| 10393 | |
| 10394 | mpz_init_set_si (z_negative_one, -1); |
| 10395 | |
| 10396 | /* It may be possible to tune the performance of some algorithms by using |
| 10397 | * the following constants to avoid the creation of bignums. Please, before |
| 10398 | * using these values, remember the two rules of program optimization: |
| 10399 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ |
| 10400 | scm_c_define ("most-positive-fixnum", |
| 10401 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
| 10402 | scm_c_define ("most-negative-fixnum", |
| 10403 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
| 10404 | |
| 10405 | scm_add_feature ("complex"); |
| 10406 | scm_add_feature ("inexact"); |
| 10407 | flo0 = scm_i_from_double (0.0); |
| 10408 | flo_log10e = scm_i_from_double (M_LOG10E); |
| 10409 | |
| 10410 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
| 10411 | |
| 10412 | { |
| 10413 | /* Set scm_i_divide2double_lo2b to (2 b^p - 1) */ |
| 10414 | mpz_init_set_ui (scm_i_divide2double_lo2b, 1); |
| 10415 | mpz_mul_2exp (scm_i_divide2double_lo2b, |
| 10416 | scm_i_divide2double_lo2b, |
| 10417 | DBL_MANT_DIG + 1); /* 2 b^p */ |
| 10418 | mpz_sub_ui (scm_i_divide2double_lo2b, scm_i_divide2double_lo2b, 1); |
| 10419 | } |
| 10420 | |
| 10421 | { |
| 10422 | /* Set dbl_minimum_normal_mantissa to b^{p-1} */ |
| 10423 | mpz_init_set_ui (dbl_minimum_normal_mantissa, 1); |
| 10424 | mpz_mul_2exp (dbl_minimum_normal_mantissa, |
| 10425 | dbl_minimum_normal_mantissa, |
| 10426 | DBL_MANT_DIG - 1); |
| 10427 | } |
| 10428 | |
| 10429 | #include "libguile/numbers.x" |
| 10430 | } |
| 10431 | |
| 10432 | /* |
| 10433 | Local Variables: |
| 10434 | c-file-style: "gnu" |
| 10435 | End: |
| 10436 | */ |