Commit | Line | Data |
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2b829bbb | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e MV |
7 | * This library is free software; you can redistribute it and/or |
8 | * modify it under the terms of the GNU Lesser General Public | |
9 | * License as published by the Free Software Foundation; either | |
10 | * version 2.1 of the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
73be1d9e MV |
12 | * This library is distributed in the hope that it will be useful, |
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
92205699 | 19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
73be1d9e | 20 | */ |
1bbd0b84 | 21 | |
0f2d19dd | 22 | \f |
ca46fb90 RB |
23 | /* General assumptions: |
24 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. | |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
f92e85f7 | 28 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
29 | */ |
30 | ||
31 | /* TODO: | |
32 | ||
33 | - see if special casing bignums and reals in integer-exponent when | |
34 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
35 | ||
36 | - look in to better short-circuiting of common cases in | |
37 | integer-expt and elsewhere. | |
38 | ||
39 | - see if direct mpz operations can help in ash and elsewhere. | |
40 | ||
41 | */ | |
0f2d19dd | 42 | |
8ab3d8a0 | 43 | /* tell glibc (2.3) to give prototype for C99 trunc(), csqrt(), etc */ |
fa605590 KR |
44 | #define _GNU_SOURCE |
45 | ||
ee33d62a RB |
46 | #if HAVE_CONFIG_H |
47 | # include <config.h> | |
48 | #endif | |
49 | ||
0f2d19dd | 50 | #include <math.h> |
3c9a524f | 51 | #include <ctype.h> |
fc194577 | 52 | #include <string.h> |
f92e85f7 | 53 | |
8ab3d8a0 KR |
54 | #if HAVE_COMPLEX_H |
55 | #include <complex.h> | |
56 | #endif | |
57 | ||
a0599745 | 58 | #include "libguile/_scm.h" |
a0599745 MD |
59 | #include "libguile/feature.h" |
60 | #include "libguile/ports.h" | |
61 | #include "libguile/root.h" | |
62 | #include "libguile/smob.h" | |
63 | #include "libguile/strings.h" | |
a0599745 MD |
64 | |
65 | #include "libguile/validate.h" | |
66 | #include "libguile/numbers.h" | |
1be6b49c | 67 | #include "libguile/deprecation.h" |
f4c627b3 | 68 | |
f92e85f7 MV |
69 | #include "libguile/eq.h" |
70 | ||
55f26379 MV |
71 | #include "libguile/discouraged.h" |
72 | ||
8ab3d8a0 KR |
73 | /* values per glibc, if not already defined */ |
74 | #ifndef M_LOG10E | |
75 | #define M_LOG10E 0.43429448190325182765 | |
76 | #endif | |
77 | #ifndef M_PI | |
78 | #define M_PI 3.14159265358979323846 | |
79 | #endif | |
80 | ||
0f2d19dd | 81 | \f |
f4c627b3 | 82 | |
ca46fb90 RB |
83 | /* |
84 | Wonder if this might be faster for some of our code? A switch on | |
85 | the numtag would jump directly to the right case, and the | |
86 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
87 | ||
88 | #define SCM_I_NUMTAG_NOTNUM 0 | |
89 | #define SCM_I_NUMTAG_INUM 1 | |
90 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
91 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
92 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
93 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 94 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 95 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 96 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
97 | : SCM_I_NUMTAG_NOTNUM))) |
98 | */ | |
f92e85f7 | 99 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
100 | |
101 | ||
34d19ef6 | 102 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 103 | |
56e55ac7 | 104 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
105 | * printed or scm_string representation of an inexact number. |
106 | */ | |
0b799eea | 107 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 108 | |
7351e207 MV |
109 | #if defined (SCO) |
110 | #if ! defined (HAVE_ISNAN) | |
111 | #define HAVE_ISNAN | |
112 | static int | |
113 | isnan (double x) | |
114 | { | |
115 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
116 | } | |
0f2d19dd | 117 | #endif |
7351e207 MV |
118 | #if ! defined (HAVE_ISINF) |
119 | #define HAVE_ISINF | |
120 | static int | |
121 | isinf (double x) | |
122 | { | |
123 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
124 | } | |
0f2d19dd | 125 | |
7351e207 | 126 | #endif |
e6f3ef58 MD |
127 | #endif |
128 | ||
b127c712 | 129 | |
f8a8200b KR |
130 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
131 | an explicit check. In some future gmp (don't know what version number), | |
132 | mpz_cmp_d is supposed to do this itself. */ | |
133 | #if 1 | |
b127c712 KR |
134 | #define xmpz_cmp_d(z, d) \ |
135 | (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) | |
136 | #else | |
137 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
138 | #endif | |
139 | ||
a98ce907 KR |
140 | /* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have |
141 | isinf. It does have finite and isnan though, hence the use of those. | |
142 | fpclass would be a possibility on that system too. */ | |
f92e85f7 MV |
143 | static int |
144 | xisinf (double x) | |
145 | { | |
146 | #if defined (HAVE_ISINF) | |
147 | return isinf (x); | |
148 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
149 | return (! (finite (x) || isnan (x))); | |
150 | #else | |
151 | return 0; | |
152 | #endif | |
153 | } | |
154 | ||
155 | static int | |
156 | xisnan (double x) | |
157 | { | |
158 | #if defined (HAVE_ISNAN) | |
159 | return isnan (x); | |
160 | #else | |
161 | return 0; | |
162 | #endif | |
163 | } | |
164 | ||
8ab3d8a0 KR |
165 | |
166 | /* For an SCM object Z which is a complex number (ie. satisfies | |
167 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
168 | #define SCM_COMPLEX_VALUE(z) \ | |
169 | (SCM_COMPLEX_REAL (z) + _Complex_I * SCM_COMPLEX_IMAG (z)) | |
170 | ||
171 | /* Convert a C "complex double" to an SCM value. */ | |
172 | #if HAVE_COMPLEX_DOUBLE | |
173 | static SCM | |
174 | scm_from_complex_double (complex double z) | |
175 | { | |
176 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
177 | } | |
178 | #endif /* HAVE_COMPLEX_DOUBLE */ | |
179 | ||
0f2d19dd JB |
180 | \f |
181 | ||
713a4259 | 182 | static mpz_t z_negative_one; |
ac0c002c DH |
183 | |
184 | \f | |
185 | ||
570b6821 | 186 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
187 | scm_i_mkbig () |
188 | { | |
189 | /* Return a newly created bignum. */ | |
190 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
191 | mpz_init (SCM_I_BIG_MPZ (z)); | |
192 | return z; | |
193 | } | |
194 | ||
c71b0706 MV |
195 | SCM_C_INLINE_KEYWORD SCM |
196 | scm_i_long2big (long x) | |
197 | { | |
198 | /* Return a newly created bignum initialized to X. */ | |
199 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
200 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
201 | return z; | |
202 | } | |
203 | ||
204 | SCM_C_INLINE_KEYWORD SCM | |
205 | scm_i_ulong2big (unsigned long x) | |
206 | { | |
207 | /* Return a newly created bignum initialized to X. */ | |
208 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
209 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); | |
210 | return z; | |
211 | } | |
212 | ||
23c3b605 | 213 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
214 | scm_i_clonebig (SCM src_big, int same_sign_p) |
215 | { | |
216 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
217 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
218 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); | |
0aacf84e MD |
219 | if (!same_sign_p) |
220 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
221 | return z; |
222 | } | |
223 | ||
570b6821 | 224 | SCM_C_INLINE_KEYWORD int |
ca46fb90 RB |
225 | scm_i_bigcmp (SCM x, SCM y) |
226 | { | |
227 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
228 | /* presume we already know x and y are bignums */ | |
229 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
230 | scm_remember_upto_here_2 (x, y); | |
231 | return result; | |
232 | } | |
233 | ||
570b6821 | 234 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
235 | scm_i_dbl2big (double d) |
236 | { | |
237 | /* results are only defined if d is an integer */ | |
238 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
239 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); | |
240 | return z; | |
241 | } | |
242 | ||
f92e85f7 MV |
243 | /* Convert a integer in double representation to a SCM number. */ |
244 | ||
245 | SCM_C_INLINE_KEYWORD SCM | |
246 | scm_i_dbl2num (double u) | |
247 | { | |
248 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
249 | powers of 2, so there's no rounding when making "double" values | |
250 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
251 | get rounded on a 64-bit machine, hence the "+1". | |
252 | ||
253 | The use of floor() to force to an integer value ensures we get a | |
254 | "numerically closest" value without depending on how a | |
255 | double->long cast or how mpz_set_d will round. For reference, | |
256 | double->long probably follows the hardware rounding mode, | |
257 | mpz_set_d truncates towards zero. */ | |
258 | ||
259 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
260 | representable as a double? */ | |
261 | ||
262 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
263 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
d956fa6f | 264 | return SCM_I_MAKINUM ((long) u); |
f92e85f7 MV |
265 | else |
266 | return scm_i_dbl2big (u); | |
267 | } | |
268 | ||
089c9a59 KR |
269 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
270 | with R5RS exact->inexact. | |
271 | ||
272 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
273 | (ie. truncate towards zero), then adjust to get the closest double by |
274 | examining the next lower bit and adding 1 (to the absolute value) if | |
275 | necessary. | |
276 | ||
277 | Bignums exactly half way between representable doubles are rounded to the | |
278 | next higher absolute value (ie. away from zero). This seems like an | |
279 | adequate interpretation of R5RS "numerically closest", and it's easier | |
280 | and faster than a full "nearest-even" style. | |
281 | ||
282 | The bit test must be done on the absolute value of the mpz_t, which means | |
283 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
284 | negatives as twos complement. | |
285 | ||
286 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
287 | following the hardware rounding mode, but applied to the absolute value | |
288 | of the mpz_t operand. This is not what we want so we put the high | |
289 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
290 | mpz_get_d is supposed to always truncate towards zero. | |
291 | ||
292 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
293 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
294 | mpz_getlimbn if we could be bothered coding that, and if the new | |
295 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
296 | |
297 | double | |
ca46fb90 RB |
298 | scm_i_big2dbl (SCM b) |
299 | { | |
089c9a59 KR |
300 | double result; |
301 | size_t bits; | |
302 | ||
303 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
304 | ||
f8a8200b | 305 | #if 1 |
089c9a59 | 306 | { |
f8a8200b | 307 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
308 | mpz_t tmp; |
309 | if (bits > DBL_MANT_DIG) | |
310 | { | |
311 | size_t shift = bits - DBL_MANT_DIG; | |
312 | mpz_init2 (tmp, DBL_MANT_DIG); | |
313 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
314 | result = ldexp (mpz_get_d (tmp), shift); | |
315 | mpz_clear (tmp); | |
316 | } | |
317 | else | |
318 | { | |
319 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
320 | } | |
321 | } | |
322 | #else | |
f8a8200b | 323 | /* Future GMP */ |
089c9a59 KR |
324 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
325 | #endif | |
326 | ||
327 | if (bits > DBL_MANT_DIG) | |
328 | { | |
329 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
330 | /* test bit number "pos" in absolute value */ | |
331 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
332 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
333 | { | |
334 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
335 | } | |
336 | } | |
337 | ||
ca46fb90 RB |
338 | scm_remember_upto_here_1 (b); |
339 | return result; | |
340 | } | |
341 | ||
570b6821 | 342 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
343 | scm_i_normbig (SCM b) |
344 | { | |
345 | /* convert a big back to a fixnum if it'll fit */ | |
346 | /* presume b is a bignum */ | |
347 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
348 | { | |
349 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
350 | if (SCM_FIXABLE (val)) | |
d956fa6f | 351 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
352 | } |
353 | return b; | |
354 | } | |
f872b822 | 355 | |
f92e85f7 MV |
356 | static SCM_C_INLINE_KEYWORD SCM |
357 | scm_i_mpz2num (mpz_t b) | |
358 | { | |
359 | /* convert a mpz number to a SCM number. */ | |
360 | if (mpz_fits_slong_p (b)) | |
361 | { | |
362 | long val = mpz_get_si (b); | |
363 | if (SCM_FIXABLE (val)) | |
d956fa6f | 364 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
365 | } |
366 | ||
367 | { | |
368 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
369 | mpz_init_set (SCM_I_BIG_MPZ (z), b); | |
370 | return z; | |
371 | } | |
372 | } | |
373 | ||
374 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
375 | static SCM scm_divide2real (SCM x, SCM y); | |
376 | ||
cba42c93 MV |
377 | static SCM |
378 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 379 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 380 | { |
c60e130c MV |
381 | /* First make sure the arguments are proper. |
382 | */ | |
e11e83f3 | 383 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 384 | { |
bc36d050 | 385 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 386 | scm_num_overflow ("make-ratio"); |
bc36d050 | 387 | if (scm_is_eq (denominator, SCM_I_MAKINUM(1))) |
f92e85f7 MV |
388 | return numerator; |
389 | } | |
390 | else | |
391 | { | |
392 | if (!(SCM_BIGP(denominator))) | |
393 | SCM_WRONG_TYPE_ARG (2, denominator); | |
394 | } | |
e11e83f3 | 395 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
396 | SCM_WRONG_TYPE_ARG (1, numerator); |
397 | ||
398 | /* Then flip signs so that the denominator is positive. | |
399 | */ | |
73e4de09 | 400 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
401 | { |
402 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
403 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
404 | } | |
405 | ||
406 | /* Now consider for each of the four fixnum/bignum combinations | |
407 | whether the rational number is really an integer. | |
408 | */ | |
e11e83f3 | 409 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 410 | { |
e11e83f3 | 411 | long x = SCM_I_INUM (numerator); |
bc36d050 | 412 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 413 | return SCM_INUM0; |
e11e83f3 | 414 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 415 | { |
dd5130ca | 416 | long y; |
e11e83f3 | 417 | y = SCM_I_INUM (denominator); |
f92e85f7 | 418 | if (x == y) |
d956fa6f | 419 | return SCM_I_MAKINUM(1); |
f92e85f7 | 420 | if ((x % y) == 0) |
d956fa6f | 421 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 422 | } |
dd5130ca KR |
423 | else |
424 | { | |
425 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
426 | of that value for the denominator, as a bignum. Apart from |
427 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
428 | integer. */ | |
429 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
430 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
431 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 432 | return SCM_I_MAKINUM(-1); |
dd5130ca | 433 | } |
f92e85f7 | 434 | } |
c60e130c | 435 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 436 | { |
e11e83f3 | 437 | if (SCM_I_INUMP (denominator)) |
c60e130c | 438 | { |
e11e83f3 | 439 | long yy = SCM_I_INUM (denominator); |
c60e130c MV |
440 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
441 | return scm_divide (numerator, denominator); | |
442 | } | |
443 | else | |
f92e85f7 | 444 | { |
bc36d050 | 445 | if (scm_is_eq (numerator, denominator)) |
d956fa6f | 446 | return SCM_I_MAKINUM(1); |
c60e130c MV |
447 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
448 | SCM_I_BIG_MPZ (denominator))) | |
449 | return scm_divide(numerator, denominator); | |
f92e85f7 | 450 | } |
f92e85f7 | 451 | } |
c60e130c MV |
452 | |
453 | /* No, it's a proper fraction. | |
454 | */ | |
e2bf3b19 HWN |
455 | { |
456 | SCM divisor = scm_gcd (numerator, denominator); | |
457 | if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1)))) | |
458 | { | |
459 | numerator = scm_divide (numerator, divisor); | |
460 | denominator = scm_divide (denominator, divisor); | |
461 | } | |
462 | ||
463 | return scm_double_cell (scm_tc16_fraction, | |
464 | SCM_UNPACK (numerator), | |
465 | SCM_UNPACK (denominator), 0); | |
466 | } | |
f92e85f7 | 467 | } |
c60e130c | 468 | #undef FUNC_NAME |
f92e85f7 | 469 | |
f92e85f7 MV |
470 | double |
471 | scm_i_fraction2double (SCM z) | |
472 | { | |
55f26379 MV |
473 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
474 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
475 | } |
476 | ||
a1ec6916 | 477 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 478 | (SCM x), |
942e5b91 MG |
479 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
480 | "otherwise.") | |
1bbd0b84 | 481 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 482 | { |
e11e83f3 | 483 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
484 | return SCM_BOOL_T; |
485 | if (SCM_BIGP (x)) | |
486 | return SCM_BOOL_T; | |
f92e85f7 MV |
487 | if (SCM_FRACTIONP (x)) |
488 | return SCM_BOOL_T; | |
eb927cb9 MV |
489 | if (SCM_NUMBERP (x)) |
490 | return SCM_BOOL_F; | |
491 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 492 | } |
1bbd0b84 | 493 | #undef FUNC_NAME |
0f2d19dd | 494 | |
4219f20d | 495 | |
a1ec6916 | 496 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 497 | (SCM n), |
942e5b91 MG |
498 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
499 | "otherwise.") | |
1bbd0b84 | 500 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 501 | { |
e11e83f3 | 502 | if (SCM_I_INUMP (n)) |
0aacf84e | 503 | { |
e11e83f3 | 504 | long val = SCM_I_INUM (n); |
73e4de09 | 505 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
506 | } |
507 | else if (SCM_BIGP (n)) | |
508 | { | |
509 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
510 | scm_remember_upto_here_1 (n); | |
73e4de09 | 511 | return scm_from_bool (odd_p); |
0aacf84e | 512 | } |
73e4de09 | 513 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 514 | return SCM_BOOL_T; |
f92e85f7 MV |
515 | else if (SCM_REALP (n)) |
516 | { | |
517 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
518 | if (rem == 1.0) | |
519 | return SCM_BOOL_T; | |
520 | else if (rem == 0.0) | |
521 | return SCM_BOOL_F; | |
522 | else | |
523 | SCM_WRONG_TYPE_ARG (1, n); | |
524 | } | |
0aacf84e | 525 | else |
a1a33b0f | 526 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 527 | } |
1bbd0b84 | 528 | #undef FUNC_NAME |
0f2d19dd | 529 | |
4219f20d | 530 | |
a1ec6916 | 531 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 532 | (SCM n), |
942e5b91 MG |
533 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
534 | "otherwise.") | |
1bbd0b84 | 535 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 536 | { |
e11e83f3 | 537 | if (SCM_I_INUMP (n)) |
0aacf84e | 538 | { |
e11e83f3 | 539 | long val = SCM_I_INUM (n); |
73e4de09 | 540 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
541 | } |
542 | else if (SCM_BIGP (n)) | |
543 | { | |
544 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
545 | scm_remember_upto_here_1 (n); | |
73e4de09 | 546 | return scm_from_bool (even_p); |
0aacf84e | 547 | } |
73e4de09 | 548 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 549 | return SCM_BOOL_T; |
f92e85f7 MV |
550 | else if (SCM_REALP (n)) |
551 | { | |
552 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
553 | if (rem == 1.0) | |
554 | return SCM_BOOL_F; | |
555 | else if (rem == 0.0) | |
556 | return SCM_BOOL_T; | |
557 | else | |
558 | SCM_WRONG_TYPE_ARG (1, n); | |
559 | } | |
0aacf84e | 560 | else |
a1a33b0f | 561 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 562 | } |
1bbd0b84 | 563 | #undef FUNC_NAME |
0f2d19dd | 564 | |
7351e207 | 565 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a MV |
566 | (SCM x), |
567 | "Return @code{#t} if @var{x} is either @samp{+inf.0}\n" | |
568 | "or @samp{-inf.0}, @code{#f} otherwise.") | |
7351e207 MV |
569 | #define FUNC_NAME s_scm_inf_p |
570 | { | |
b1092b3a MV |
571 | if (SCM_REALP (x)) |
572 | return scm_from_bool (xisinf (SCM_REAL_VALUE (x))); | |
573 | else if (SCM_COMPLEXP (x)) | |
574 | return scm_from_bool (xisinf (SCM_COMPLEX_REAL (x)) | |
575 | || xisinf (SCM_COMPLEX_IMAG (x))); | |
0aacf84e | 576 | else |
7351e207 | 577 | return SCM_BOOL_F; |
7351e207 MV |
578 | } |
579 | #undef FUNC_NAME | |
580 | ||
581 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
582 | (SCM n), | |
583 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
584 | "otherwise.") | |
585 | #define FUNC_NAME s_scm_nan_p | |
586 | { | |
0aacf84e | 587 | if (SCM_REALP (n)) |
73e4de09 | 588 | return scm_from_bool (xisnan (SCM_REAL_VALUE (n))); |
0aacf84e | 589 | else if (SCM_COMPLEXP (n)) |
73e4de09 | 590 | return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n)) |
7351e207 | 591 | || xisnan (SCM_COMPLEX_IMAG (n))); |
0aacf84e | 592 | else |
7351e207 | 593 | return SCM_BOOL_F; |
7351e207 MV |
594 | } |
595 | #undef FUNC_NAME | |
596 | ||
597 | /* Guile's idea of infinity. */ | |
598 | static double guile_Inf; | |
599 | ||
600 | /* Guile's idea of not a number. */ | |
601 | static double guile_NaN; | |
602 | ||
603 | static void | |
604 | guile_ieee_init (void) | |
605 | { | |
606 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
607 | ||
608 | /* Some version of gcc on some old version of Linux used to crash when | |
609 | trying to make Inf and NaN. */ | |
610 | ||
240a27d2 KR |
611 | #ifdef INFINITY |
612 | /* C99 INFINITY, when available. | |
613 | FIXME: The standard allows for INFINITY to be something that overflows | |
614 | at compile time. We ought to have a configure test to check for that | |
615 | before trying to use it. (But in practice we believe this is not a | |
616 | problem on any system guile is likely to target.) */ | |
617 | guile_Inf = INFINITY; | |
618 | #elif HAVE_DINFINITY | |
619 | /* OSF */ | |
7351e207 | 620 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 621 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
622 | #else |
623 | double tmp = 1e+10; | |
624 | guile_Inf = tmp; | |
625 | for (;;) | |
626 | { | |
627 | guile_Inf *= 1e+10; | |
628 | if (guile_Inf == tmp) | |
629 | break; | |
630 | tmp = guile_Inf; | |
631 | } | |
632 | #endif | |
633 | ||
634 | #endif | |
635 | ||
636 | #if defined (HAVE_ISNAN) | |
637 | ||
240a27d2 KR |
638 | #ifdef NAN |
639 | /* C99 NAN, when available */ | |
640 | guile_NaN = NAN; | |
641 | #elif HAVE_DQNAN | |
eaa94eaa LC |
642 | { |
643 | /* OSF */ | |
644 | extern unsigned int DQNAN[2]; | |
645 | guile_NaN = (*((double *)(DQNAN))); | |
646 | } | |
7351e207 MV |
647 | #else |
648 | guile_NaN = guile_Inf / guile_Inf; | |
649 | #endif | |
650 | ||
651 | #endif | |
652 | } | |
653 | ||
654 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
655 | (void), | |
656 | "Return Inf.") | |
657 | #define FUNC_NAME s_scm_inf | |
658 | { | |
659 | static int initialized = 0; | |
660 | if (! initialized) | |
661 | { | |
662 | guile_ieee_init (); | |
663 | initialized = 1; | |
664 | } | |
55f26379 | 665 | return scm_from_double (guile_Inf); |
7351e207 MV |
666 | } |
667 | #undef FUNC_NAME | |
668 | ||
669 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
670 | (void), | |
671 | "Return NaN.") | |
672 | #define FUNC_NAME s_scm_nan | |
673 | { | |
674 | static int initialized = 0; | |
0aacf84e | 675 | if (!initialized) |
7351e207 MV |
676 | { |
677 | guile_ieee_init (); | |
678 | initialized = 1; | |
679 | } | |
55f26379 | 680 | return scm_from_double (guile_NaN); |
7351e207 MV |
681 | } |
682 | #undef FUNC_NAME | |
683 | ||
4219f20d | 684 | |
a48d60b1 MD |
685 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
686 | (SCM x), | |
687 | "Return the absolute value of @var{x}.") | |
688 | #define FUNC_NAME | |
0f2d19dd | 689 | { |
e11e83f3 | 690 | if (SCM_I_INUMP (x)) |
0aacf84e | 691 | { |
e11e83f3 | 692 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
693 | if (xx >= 0) |
694 | return x; | |
695 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 696 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
697 | else |
698 | return scm_i_long2big (-xx); | |
4219f20d | 699 | } |
0aacf84e MD |
700 | else if (SCM_BIGP (x)) |
701 | { | |
702 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
703 | if (sgn < 0) | |
704 | return scm_i_clonebig (x, 0); | |
705 | else | |
706 | return x; | |
4219f20d | 707 | } |
0aacf84e | 708 | else if (SCM_REALP (x)) |
ae38324d KR |
709 | { |
710 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
711 | double xx = SCM_REAL_VALUE (x); | |
712 | if (xx < 0.0) | |
55f26379 | 713 | return scm_from_double (-xx); |
ae38324d KR |
714 | else |
715 | return x; | |
716 | } | |
f92e85f7 MV |
717 | else if (SCM_FRACTIONP (x)) |
718 | { | |
73e4de09 | 719 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 720 | return x; |
cba42c93 | 721 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
722 | SCM_FRACTION_DENOMINATOR (x)); |
723 | } | |
0aacf84e | 724 | else |
a48d60b1 | 725 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 726 | } |
a48d60b1 | 727 | #undef FUNC_NAME |
0f2d19dd | 728 | |
4219f20d | 729 | |
9de33deb | 730 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
731 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
732 | */ | |
0f2d19dd | 733 | SCM |
6e8d25a6 | 734 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 735 | { |
e11e83f3 | 736 | if (SCM_I_INUMP (x)) |
0aacf84e | 737 | { |
e11e83f3 MV |
738 | long xx = SCM_I_INUM (x); |
739 | if (SCM_I_INUMP (y)) | |
0aacf84e | 740 | { |
e11e83f3 | 741 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
742 | if (yy == 0) |
743 | scm_num_overflow (s_quotient); | |
744 | else | |
745 | { | |
746 | long z = xx / yy; | |
747 | if (SCM_FIXABLE (z)) | |
d956fa6f | 748 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
749 | else |
750 | return scm_i_long2big (z); | |
751 | } | |
828865c3 | 752 | } |
0aacf84e | 753 | else if (SCM_BIGP (y)) |
ac0c002c | 754 | { |
e11e83f3 | 755 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
756 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
757 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
758 | { | |
759 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
760 | scm_remember_upto_here_1 (y); | |
d956fa6f | 761 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 762 | } |
0aacf84e | 763 | else |
d956fa6f | 764 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
765 | } |
766 | else | |
0aacf84e | 767 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 768 | } |
0aacf84e MD |
769 | else if (SCM_BIGP (x)) |
770 | { | |
e11e83f3 | 771 | if (SCM_I_INUMP (y)) |
0aacf84e | 772 | { |
e11e83f3 | 773 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
774 | if (yy == 0) |
775 | scm_num_overflow (s_quotient); | |
776 | else if (yy == 1) | |
777 | return x; | |
778 | else | |
779 | { | |
780 | SCM result = scm_i_mkbig (); | |
781 | if (yy < 0) | |
782 | { | |
783 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
784 | SCM_I_BIG_MPZ (x), | |
785 | - yy); | |
786 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
787 | } | |
788 | else | |
789 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
790 | scm_remember_upto_here_1 (x); | |
791 | return scm_i_normbig (result); | |
792 | } | |
793 | } | |
794 | else if (SCM_BIGP (y)) | |
795 | { | |
796 | SCM result = scm_i_mkbig (); | |
797 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
798 | SCM_I_BIG_MPZ (x), | |
799 | SCM_I_BIG_MPZ (y)); | |
800 | scm_remember_upto_here_2 (x, y); | |
801 | return scm_i_normbig (result); | |
802 | } | |
803 | else | |
804 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 805 | } |
0aacf84e | 806 | else |
89a7e495 | 807 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
808 | } |
809 | ||
9de33deb | 810 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
811 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
812 | * "@lisp\n" | |
813 | * "(remainder 13 4) @result{} 1\n" | |
814 | * "(remainder -13 4) @result{} -1\n" | |
815 | * "@end lisp" | |
816 | */ | |
0f2d19dd | 817 | SCM |
6e8d25a6 | 818 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 819 | { |
e11e83f3 | 820 | if (SCM_I_INUMP (x)) |
0aacf84e | 821 | { |
e11e83f3 | 822 | if (SCM_I_INUMP (y)) |
0aacf84e | 823 | { |
e11e83f3 | 824 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
825 | if (yy == 0) |
826 | scm_num_overflow (s_remainder); | |
827 | else | |
828 | { | |
e11e83f3 | 829 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 830 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
831 | } |
832 | } | |
833 | else if (SCM_BIGP (y)) | |
ac0c002c | 834 | { |
e11e83f3 | 835 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
836 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
837 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
838 | { | |
839 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
840 | scm_remember_upto_here_1 (y); | |
d956fa6f | 841 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 842 | } |
0aacf84e MD |
843 | else |
844 | return x; | |
ac0c002c DH |
845 | } |
846 | else | |
0aacf84e | 847 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 848 | } |
0aacf84e MD |
849 | else if (SCM_BIGP (x)) |
850 | { | |
e11e83f3 | 851 | if (SCM_I_INUMP (y)) |
0aacf84e | 852 | { |
e11e83f3 | 853 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
854 | if (yy == 0) |
855 | scm_num_overflow (s_remainder); | |
856 | else | |
857 | { | |
858 | SCM result = scm_i_mkbig (); | |
859 | if (yy < 0) | |
860 | yy = - yy; | |
861 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
862 | scm_remember_upto_here_1 (x); | |
863 | return scm_i_normbig (result); | |
864 | } | |
865 | } | |
866 | else if (SCM_BIGP (y)) | |
867 | { | |
868 | SCM result = scm_i_mkbig (); | |
869 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
870 | SCM_I_BIG_MPZ (x), | |
871 | SCM_I_BIG_MPZ (y)); | |
872 | scm_remember_upto_here_2 (x, y); | |
873 | return scm_i_normbig (result); | |
874 | } | |
875 | else | |
876 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 877 | } |
0aacf84e | 878 | else |
89a7e495 | 879 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
880 | } |
881 | ||
89a7e495 | 882 | |
9de33deb | 883 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
884 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
885 | * "@lisp\n" | |
886 | * "(modulo 13 4) @result{} 1\n" | |
887 | * "(modulo -13 4) @result{} 3\n" | |
888 | * "@end lisp" | |
889 | */ | |
0f2d19dd | 890 | SCM |
6e8d25a6 | 891 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 892 | { |
e11e83f3 | 893 | if (SCM_I_INUMP (x)) |
0aacf84e | 894 | { |
e11e83f3 MV |
895 | long xx = SCM_I_INUM (x); |
896 | if (SCM_I_INUMP (y)) | |
0aacf84e | 897 | { |
e11e83f3 | 898 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
899 | if (yy == 0) |
900 | scm_num_overflow (s_modulo); | |
901 | else | |
902 | { | |
66b1c775 KR |
903 | /* C99 specifies that "%" is the remainder corresponding to a |
904 | quotient rounded towards zero, and that's also traditional | |
905 | for machine division, so z here should be well defined. */ | |
0aacf84e MD |
906 | long z = xx % yy; |
907 | long result; | |
908 | ||
909 | if (yy < 0) | |
910 | { | |
911 | if (z > 0) | |
912 | result = z + yy; | |
913 | else | |
914 | result = z; | |
915 | } | |
916 | else | |
917 | { | |
918 | if (z < 0) | |
919 | result = z + yy; | |
920 | else | |
921 | result = z; | |
922 | } | |
d956fa6f | 923 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
924 | } |
925 | } | |
926 | else if (SCM_BIGP (y)) | |
927 | { | |
928 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
929 | { |
930 | mpz_t z_x; | |
931 | SCM result; | |
932 | ||
933 | if (sgn_y < 0) | |
934 | { | |
935 | SCM pos_y = scm_i_clonebig (y, 0); | |
936 | /* do this after the last scm_op */ | |
937 | mpz_init_set_si (z_x, xx); | |
938 | result = pos_y; /* re-use this bignum */ | |
939 | mpz_mod (SCM_I_BIG_MPZ (result), | |
940 | z_x, | |
941 | SCM_I_BIG_MPZ (pos_y)); | |
942 | scm_remember_upto_here_1 (pos_y); | |
943 | } | |
944 | else | |
945 | { | |
946 | result = scm_i_mkbig (); | |
947 | /* do this after the last scm_op */ | |
948 | mpz_init_set_si (z_x, xx); | |
949 | mpz_mod (SCM_I_BIG_MPZ (result), | |
950 | z_x, | |
951 | SCM_I_BIG_MPZ (y)); | |
952 | scm_remember_upto_here_1 (y); | |
953 | } | |
ca46fb90 | 954 | |
0aacf84e MD |
955 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
956 | mpz_add (SCM_I_BIG_MPZ (result), | |
957 | SCM_I_BIG_MPZ (y), | |
958 | SCM_I_BIG_MPZ (result)); | |
959 | scm_remember_upto_here_1 (y); | |
960 | /* and do this before the next one */ | |
961 | mpz_clear (z_x); | |
962 | return scm_i_normbig (result); | |
963 | } | |
964 | } | |
965 | else | |
966 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 967 | } |
0aacf84e MD |
968 | else if (SCM_BIGP (x)) |
969 | { | |
e11e83f3 | 970 | if (SCM_I_INUMP (y)) |
0aacf84e | 971 | { |
e11e83f3 | 972 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
973 | if (yy == 0) |
974 | scm_num_overflow (s_modulo); | |
975 | else | |
976 | { | |
977 | SCM result = scm_i_mkbig (); | |
978 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
979 | SCM_I_BIG_MPZ (x), | |
980 | (yy < 0) ? - yy : yy); | |
981 | scm_remember_upto_here_1 (x); | |
982 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
983 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
984 | SCM_I_BIG_MPZ (result), | |
985 | - yy); | |
986 | return scm_i_normbig (result); | |
987 | } | |
988 | } | |
989 | else if (SCM_BIGP (y)) | |
990 | { | |
0aacf84e MD |
991 | { |
992 | SCM result = scm_i_mkbig (); | |
993 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
994 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
995 | mpz_mod (SCM_I_BIG_MPZ (result), | |
996 | SCM_I_BIG_MPZ (x), | |
997 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 998 | |
0aacf84e MD |
999 | scm_remember_upto_here_1 (x); |
1000 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1001 | mpz_add (SCM_I_BIG_MPZ (result), | |
1002 | SCM_I_BIG_MPZ (y), | |
1003 | SCM_I_BIG_MPZ (result)); | |
1004 | scm_remember_upto_here_2 (y, pos_y); | |
1005 | return scm_i_normbig (result); | |
1006 | } | |
1007 | } | |
1008 | else | |
1009 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 1010 | } |
0aacf84e | 1011 | else |
09fb7599 | 1012 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
1013 | } |
1014 | ||
9de33deb | 1015 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
1016 | /* "Return the greatest common divisor of all arguments.\n" |
1017 | * "If called without arguments, 0 is returned." | |
1018 | */ | |
0f2d19dd | 1019 | SCM |
6e8d25a6 | 1020 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1021 | { |
ca46fb90 | 1022 | if (SCM_UNBNDP (y)) |
0aacf84e | 1023 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 | 1024 | |
e11e83f3 | 1025 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1026 | { |
e11e83f3 | 1027 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1028 | { |
e11e83f3 MV |
1029 | long xx = SCM_I_INUM (x); |
1030 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1031 | long u = xx < 0 ? -xx : xx; |
1032 | long v = yy < 0 ? -yy : yy; | |
1033 | long result; | |
0aacf84e MD |
1034 | if (xx == 0) |
1035 | result = v; | |
1036 | else if (yy == 0) | |
1037 | result = u; | |
1038 | else | |
1039 | { | |
1040 | long k = 1; | |
1041 | long t; | |
1042 | /* Determine a common factor 2^k */ | |
1043 | while (!(1 & (u | v))) | |
1044 | { | |
1045 | k <<= 1; | |
1046 | u >>= 1; | |
1047 | v >>= 1; | |
1048 | } | |
1049 | /* Now, any factor 2^n can be eliminated */ | |
1050 | if (u & 1) | |
1051 | t = -v; | |
1052 | else | |
1053 | { | |
1054 | t = u; | |
1055 | b3: | |
1056 | t = SCM_SRS (t, 1); | |
1057 | } | |
1058 | if (!(1 & t)) | |
1059 | goto b3; | |
1060 | if (t > 0) | |
1061 | u = t; | |
1062 | else | |
1063 | v = -t; | |
1064 | t = u - v; | |
1065 | if (t != 0) | |
1066 | goto b3; | |
1067 | result = u * k; | |
1068 | } | |
1069 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1070 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1071 | : scm_i_long2big (result)); |
ca46fb90 RB |
1072 | } |
1073 | else if (SCM_BIGP (y)) | |
1074 | { | |
0bff4dce KR |
1075 | SCM_SWAP (x, y); |
1076 | goto big_inum; | |
ca46fb90 RB |
1077 | } |
1078 | else | |
1079 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1080 | } |
ca46fb90 RB |
1081 | else if (SCM_BIGP (x)) |
1082 | { | |
e11e83f3 | 1083 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1084 | { |
1085 | unsigned long result; | |
0bff4dce KR |
1086 | long yy; |
1087 | big_inum: | |
e11e83f3 | 1088 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1089 | if (yy == 0) |
1090 | return scm_abs (x); | |
0aacf84e MD |
1091 | if (yy < 0) |
1092 | yy = -yy; | |
ca46fb90 RB |
1093 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1094 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1095 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1096 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1097 | : scm_from_ulong (result)); |
ca46fb90 RB |
1098 | } |
1099 | else if (SCM_BIGP (y)) | |
1100 | { | |
1101 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1102 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1103 | SCM_I_BIG_MPZ (x), | |
1104 | SCM_I_BIG_MPZ (y)); | |
1105 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1106 | return scm_i_normbig (result); |
1107 | } | |
1108 | else | |
1109 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1110 | } |
ca46fb90 | 1111 | else |
09fb7599 | 1112 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1113 | } |
1114 | ||
9de33deb | 1115 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1116 | /* "Return the least common multiple of the arguments.\n" |
1117 | * "If called without arguments, 1 is returned." | |
1118 | */ | |
0f2d19dd | 1119 | SCM |
6e8d25a6 | 1120 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1121 | { |
ca46fb90 RB |
1122 | if (SCM_UNBNDP (n2)) |
1123 | { | |
1124 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1125 | return SCM_I_MAKINUM (1L); |
1126 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1127 | } |
09fb7599 | 1128 | |
e11e83f3 | 1129 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1130 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1131 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1132 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1133 | |
e11e83f3 | 1134 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1135 | { |
e11e83f3 | 1136 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1137 | { |
1138 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1139 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1140 | return d; |
1141 | else | |
1142 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1143 | } | |
1144 | else | |
1145 | { | |
1146 | /* inum n1, big n2 */ | |
1147 | inumbig: | |
1148 | { | |
1149 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1150 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1151 | if (nn1 == 0) return SCM_INUM0; |
1152 | if (nn1 < 0) nn1 = - nn1; | |
1153 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1154 | scm_remember_upto_here_1 (n2); | |
1155 | return result; | |
1156 | } | |
1157 | } | |
1158 | } | |
1159 | else | |
1160 | { | |
1161 | /* big n1 */ | |
e11e83f3 | 1162 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1163 | { |
1164 | SCM_SWAP (n1, n2); | |
1165 | goto inumbig; | |
1166 | } | |
1167 | else | |
1168 | { | |
1169 | SCM result = scm_i_mkbig (); | |
1170 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1171 | SCM_I_BIG_MPZ (n1), | |
1172 | SCM_I_BIG_MPZ (n2)); | |
1173 | scm_remember_upto_here_2(n1, n2); | |
1174 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1175 | return result; | |
1176 | } | |
f872b822 | 1177 | } |
0f2d19dd JB |
1178 | } |
1179 | ||
8a525303 GB |
1180 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1181 | ||
1182 | Logand: | |
1183 | X Y Result Method: | |
1184 | (len) | |
1185 | + + + x (map digit:logand X Y) | |
1186 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1187 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1188 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1189 | ||
1190 | Logior: | |
1191 | X Y Result Method: | |
1192 | ||
1193 | + + + (map digit:logior X Y) | |
1194 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1195 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1196 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1197 | ||
1198 | Logxor: | |
1199 | X Y Result Method: | |
1200 | ||
1201 | + + + (map digit:logxor X Y) | |
1202 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1203 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1204 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1205 | ||
1206 | Logtest: | |
1207 | X Y Result | |
1208 | ||
1209 | + + (any digit:logand X Y) | |
1210 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1211 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1212 | - - #t | |
1213 | ||
1214 | */ | |
1215 | ||
c3ee7520 | 1216 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1217 | (SCM n1, SCM n2), |
3c3db128 GH |
1218 | "Return the bitwise AND of the integer arguments.\n\n" |
1219 | "@lisp\n" | |
1220 | "(logand) @result{} -1\n" | |
1221 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1222 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1223 | "@end lisp") |
1bbd0b84 | 1224 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1225 | { |
9a00c9fc DH |
1226 | long int nn1; |
1227 | ||
0aacf84e MD |
1228 | if (SCM_UNBNDP (n2)) |
1229 | { | |
1230 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1231 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1232 | else if (!SCM_NUMBERP (n1)) |
1233 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1234 | else if (SCM_NUMBERP (n1)) | |
1235 | return n1; | |
1236 | else | |
1237 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1238 | } |
09fb7599 | 1239 | |
e11e83f3 | 1240 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1241 | { |
e11e83f3 MV |
1242 | nn1 = SCM_I_INUM (n1); |
1243 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1244 | { |
e11e83f3 | 1245 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1246 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1247 | } |
1248 | else if SCM_BIGP (n2) | |
1249 | { | |
1250 | intbig: | |
1251 | if (n1 == 0) | |
1252 | return SCM_INUM0; | |
1253 | { | |
1254 | SCM result_z = scm_i_mkbig (); | |
1255 | mpz_t nn1_z; | |
1256 | mpz_init_set_si (nn1_z, nn1); | |
1257 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1258 | scm_remember_upto_here_1 (n2); | |
1259 | mpz_clear (nn1_z); | |
1260 | return scm_i_normbig (result_z); | |
1261 | } | |
1262 | } | |
1263 | else | |
1264 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1265 | } | |
1266 | else if (SCM_BIGP (n1)) | |
1267 | { | |
e11e83f3 | 1268 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1269 | { |
1270 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1271 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1272 | goto intbig; |
1273 | } | |
1274 | else if (SCM_BIGP (n2)) | |
1275 | { | |
1276 | SCM result_z = scm_i_mkbig (); | |
1277 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1278 | SCM_I_BIG_MPZ (n1), | |
1279 | SCM_I_BIG_MPZ (n2)); | |
1280 | scm_remember_upto_here_2 (n1, n2); | |
1281 | return scm_i_normbig (result_z); | |
1282 | } | |
1283 | else | |
1284 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1285 | } |
0aacf84e | 1286 | else |
09fb7599 | 1287 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1288 | } |
1bbd0b84 | 1289 | #undef FUNC_NAME |
0f2d19dd | 1290 | |
09fb7599 | 1291 | |
c3ee7520 | 1292 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1293 | (SCM n1, SCM n2), |
3c3db128 GH |
1294 | "Return the bitwise OR of the integer arguments.\n\n" |
1295 | "@lisp\n" | |
1296 | "(logior) @result{} 0\n" | |
1297 | "(logior 7) @result{} 7\n" | |
1298 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1299 | "@end lisp") |
1bbd0b84 | 1300 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1301 | { |
9a00c9fc DH |
1302 | long int nn1; |
1303 | ||
0aacf84e MD |
1304 | if (SCM_UNBNDP (n2)) |
1305 | { | |
1306 | if (SCM_UNBNDP (n1)) | |
1307 | return SCM_INUM0; | |
1308 | else if (SCM_NUMBERP (n1)) | |
1309 | return n1; | |
1310 | else | |
1311 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1312 | } |
09fb7599 | 1313 | |
e11e83f3 | 1314 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1315 | { |
e11e83f3 MV |
1316 | nn1 = SCM_I_INUM (n1); |
1317 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1318 | { |
e11e83f3 | 1319 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1320 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1321 | } |
1322 | else if (SCM_BIGP (n2)) | |
1323 | { | |
1324 | intbig: | |
1325 | if (nn1 == 0) | |
1326 | return n2; | |
1327 | { | |
1328 | SCM result_z = scm_i_mkbig (); | |
1329 | mpz_t nn1_z; | |
1330 | mpz_init_set_si (nn1_z, nn1); | |
1331 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1332 | scm_remember_upto_here_1 (n2); | |
1333 | mpz_clear (nn1_z); | |
9806de0d | 1334 | return scm_i_normbig (result_z); |
0aacf84e MD |
1335 | } |
1336 | } | |
1337 | else | |
1338 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1339 | } | |
1340 | else if (SCM_BIGP (n1)) | |
1341 | { | |
e11e83f3 | 1342 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1343 | { |
1344 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1345 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1346 | goto intbig; |
1347 | } | |
1348 | else if (SCM_BIGP (n2)) | |
1349 | { | |
1350 | SCM result_z = scm_i_mkbig (); | |
1351 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1352 | SCM_I_BIG_MPZ (n1), | |
1353 | SCM_I_BIG_MPZ (n2)); | |
1354 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1355 | return scm_i_normbig (result_z); |
0aacf84e MD |
1356 | } |
1357 | else | |
1358 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1359 | } |
0aacf84e | 1360 | else |
09fb7599 | 1361 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1362 | } |
1bbd0b84 | 1363 | #undef FUNC_NAME |
0f2d19dd | 1364 | |
09fb7599 | 1365 | |
c3ee7520 | 1366 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1367 | (SCM n1, SCM n2), |
3c3db128 GH |
1368 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1369 | "set in the result if it is set in an odd number of arguments.\n" | |
1370 | "@lisp\n" | |
1371 | "(logxor) @result{} 0\n" | |
1372 | "(logxor 7) @result{} 7\n" | |
1373 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1374 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1375 | "@end lisp") |
1bbd0b84 | 1376 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1377 | { |
9a00c9fc DH |
1378 | long int nn1; |
1379 | ||
0aacf84e MD |
1380 | if (SCM_UNBNDP (n2)) |
1381 | { | |
1382 | if (SCM_UNBNDP (n1)) | |
1383 | return SCM_INUM0; | |
1384 | else if (SCM_NUMBERP (n1)) | |
1385 | return n1; | |
1386 | else | |
1387 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1388 | } |
09fb7599 | 1389 | |
e11e83f3 | 1390 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1391 | { |
e11e83f3 MV |
1392 | nn1 = SCM_I_INUM (n1); |
1393 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1394 | { |
e11e83f3 | 1395 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1396 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1397 | } |
1398 | else if (SCM_BIGP (n2)) | |
1399 | { | |
1400 | intbig: | |
1401 | { | |
1402 | SCM result_z = scm_i_mkbig (); | |
1403 | mpz_t nn1_z; | |
1404 | mpz_init_set_si (nn1_z, nn1); | |
1405 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1406 | scm_remember_upto_here_1 (n2); | |
1407 | mpz_clear (nn1_z); | |
1408 | return scm_i_normbig (result_z); | |
1409 | } | |
1410 | } | |
1411 | else | |
1412 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1413 | } | |
1414 | else if (SCM_BIGP (n1)) | |
1415 | { | |
e11e83f3 | 1416 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1417 | { |
1418 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1419 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1420 | goto intbig; |
1421 | } | |
1422 | else if (SCM_BIGP (n2)) | |
1423 | { | |
1424 | SCM result_z = scm_i_mkbig (); | |
1425 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1426 | SCM_I_BIG_MPZ (n1), | |
1427 | SCM_I_BIG_MPZ (n2)); | |
1428 | scm_remember_upto_here_2 (n1, n2); | |
1429 | return scm_i_normbig (result_z); | |
1430 | } | |
1431 | else | |
1432 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1433 | } |
0aacf84e | 1434 | else |
09fb7599 | 1435 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1436 | } |
1bbd0b84 | 1437 | #undef FUNC_NAME |
0f2d19dd | 1438 | |
09fb7599 | 1439 | |
a1ec6916 | 1440 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1441 | (SCM j, SCM k), |
ba6e7231 KR |
1442 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1443 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1444 | "without actually calculating the @code{logand}, just testing\n" | |
1445 | "for non-zero.\n" | |
1446 | "\n" | |
1e6808ea | 1447 | "@lisp\n" |
b380b885 MD |
1448 | "(logtest #b0100 #b1011) @result{} #f\n" |
1449 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1450 | "@end lisp") |
1bbd0b84 | 1451 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1452 | { |
1e6808ea | 1453 | long int nj; |
9a00c9fc | 1454 | |
e11e83f3 | 1455 | if (SCM_I_INUMP (j)) |
0aacf84e | 1456 | { |
e11e83f3 MV |
1457 | nj = SCM_I_INUM (j); |
1458 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1459 | { |
e11e83f3 | 1460 | long nk = SCM_I_INUM (k); |
73e4de09 | 1461 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1462 | } |
1463 | else if (SCM_BIGP (k)) | |
1464 | { | |
1465 | intbig: | |
1466 | if (nj == 0) | |
1467 | return SCM_BOOL_F; | |
1468 | { | |
1469 | SCM result; | |
1470 | mpz_t nj_z; | |
1471 | mpz_init_set_si (nj_z, nj); | |
1472 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1473 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1474 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1475 | mpz_clear (nj_z); |
1476 | return result; | |
1477 | } | |
1478 | } | |
1479 | else | |
1480 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1481 | } | |
1482 | else if (SCM_BIGP (j)) | |
1483 | { | |
e11e83f3 | 1484 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1485 | { |
1486 | SCM_SWAP (j, k); | |
e11e83f3 | 1487 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1488 | goto intbig; |
1489 | } | |
1490 | else if (SCM_BIGP (k)) | |
1491 | { | |
1492 | SCM result; | |
1493 | mpz_t result_z; | |
1494 | mpz_init (result_z); | |
1495 | mpz_and (result_z, | |
1496 | SCM_I_BIG_MPZ (j), | |
1497 | SCM_I_BIG_MPZ (k)); | |
1498 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1499 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1500 | mpz_clear (result_z); |
1501 | return result; | |
1502 | } | |
1503 | else | |
1504 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1505 | } | |
1506 | else | |
1507 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1508 | } |
1bbd0b84 | 1509 | #undef FUNC_NAME |
0f2d19dd | 1510 | |
c1bfcf60 | 1511 | |
a1ec6916 | 1512 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1513 | (SCM index, SCM j), |
ba6e7231 KR |
1514 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1515 | "@var{index} starts from 0 for the least significant bit.\n" | |
1516 | "\n" | |
1e6808ea | 1517 | "@lisp\n" |
b380b885 MD |
1518 | "(logbit? 0 #b1101) @result{} #t\n" |
1519 | "(logbit? 1 #b1101) @result{} #f\n" | |
1520 | "(logbit? 2 #b1101) @result{} #t\n" | |
1521 | "(logbit? 3 #b1101) @result{} #t\n" | |
1522 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1523 | "@end lisp") |
1bbd0b84 | 1524 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1525 | { |
78166ad5 | 1526 | unsigned long int iindex; |
5efd3c7d | 1527 | iindex = scm_to_ulong (index); |
78166ad5 | 1528 | |
e11e83f3 | 1529 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1530 | { |
1531 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1532 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1533 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1534 | } |
0aacf84e MD |
1535 | else if (SCM_BIGP (j)) |
1536 | { | |
1537 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1538 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1539 | return scm_from_bool (val); |
0aacf84e MD |
1540 | } |
1541 | else | |
78166ad5 | 1542 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1543 | } |
1bbd0b84 | 1544 | #undef FUNC_NAME |
0f2d19dd | 1545 | |
78166ad5 | 1546 | |
a1ec6916 | 1547 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1548 | (SCM n), |
4d814788 | 1549 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1550 | "argument.\n" |
1551 | "\n" | |
b380b885 MD |
1552 | "@lisp\n" |
1553 | "(number->string (lognot #b10000000) 2)\n" | |
1554 | " @result{} \"-10000001\"\n" | |
1555 | "(number->string (lognot #b0) 2)\n" | |
1556 | " @result{} \"-1\"\n" | |
1e6808ea | 1557 | "@end lisp") |
1bbd0b84 | 1558 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1559 | { |
e11e83f3 | 1560 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1561 | /* No overflow here, just need to toggle all the bits making up the inum. |
1562 | Enhancement: No need to strip the tag and add it back, could just xor | |
1563 | a block of 1 bits, if that worked with the various debug versions of | |
1564 | the SCM typedef. */ | |
e11e83f3 | 1565 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1566 | |
1567 | } else if (SCM_BIGP (n)) { | |
1568 | SCM result = scm_i_mkbig (); | |
1569 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1570 | scm_remember_upto_here_1 (n); | |
1571 | return result; | |
1572 | ||
1573 | } else { | |
1574 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1575 | } | |
0f2d19dd | 1576 | } |
1bbd0b84 | 1577 | #undef FUNC_NAME |
0f2d19dd | 1578 | |
518b7508 KR |
1579 | /* returns 0 if IN is not an integer. OUT must already be |
1580 | initialized. */ | |
1581 | static int | |
1582 | coerce_to_big (SCM in, mpz_t out) | |
1583 | { | |
1584 | if (SCM_BIGP (in)) | |
1585 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1586 | else if (SCM_I_INUMP (in)) |
1587 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1588 | else |
1589 | return 0; | |
1590 | ||
1591 | return 1; | |
1592 | } | |
1593 | ||
d885e204 | 1594 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1595 | (SCM n, SCM k, SCM m), |
1596 | "Return @var{n} raised to the integer exponent\n" | |
1597 | "@var{k}, modulo @var{m}.\n" | |
1598 | "\n" | |
1599 | "@lisp\n" | |
1600 | "(modulo-expt 2 3 5)\n" | |
1601 | " @result{} 3\n" | |
1602 | "@end lisp") | |
d885e204 | 1603 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1604 | { |
1605 | mpz_t n_tmp; | |
1606 | mpz_t k_tmp; | |
1607 | mpz_t m_tmp; | |
1608 | ||
1609 | /* There are two classes of error we might encounter -- | |
1610 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1611 | and | |
1612 | 2) wrong-type errors, which of course we'll report by calling | |
1613 | SCM_WRONG_TYPE_ARG. | |
1614 | We don't report those errors immediately, however; instead we do | |
1615 | some cleanup first. These variables tell us which error (if | |
1616 | any) we should report after cleaning up. | |
1617 | */ | |
1618 | int report_overflow = 0; | |
1619 | ||
1620 | int position_of_wrong_type = 0; | |
1621 | SCM value_of_wrong_type = SCM_INUM0; | |
1622 | ||
1623 | SCM result = SCM_UNDEFINED; | |
1624 | ||
1625 | mpz_init (n_tmp); | |
1626 | mpz_init (k_tmp); | |
1627 | mpz_init (m_tmp); | |
1628 | ||
bc36d050 | 1629 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1630 | { |
1631 | report_overflow = 1; | |
1632 | goto cleanup; | |
1633 | } | |
1634 | ||
1635 | if (!coerce_to_big (n, n_tmp)) | |
1636 | { | |
1637 | value_of_wrong_type = n; | |
1638 | position_of_wrong_type = 1; | |
1639 | goto cleanup; | |
1640 | } | |
1641 | ||
1642 | if (!coerce_to_big (k, k_tmp)) | |
1643 | { | |
1644 | value_of_wrong_type = k; | |
1645 | position_of_wrong_type = 2; | |
1646 | goto cleanup; | |
1647 | } | |
1648 | ||
1649 | if (!coerce_to_big (m, m_tmp)) | |
1650 | { | |
1651 | value_of_wrong_type = m; | |
1652 | position_of_wrong_type = 3; | |
1653 | goto cleanup; | |
1654 | } | |
1655 | ||
1656 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1657 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1658 | doesn't exist (or is not unique). Since exceptions are hard to | |
1659 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1660 | a simple failure code, which is easy to handle. */ | |
1661 | ||
1662 | if (-1 == mpz_sgn (k_tmp)) | |
1663 | { | |
1664 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1665 | { | |
1666 | report_overflow = 1; | |
1667 | goto cleanup; | |
1668 | } | |
1669 | mpz_neg (k_tmp, k_tmp); | |
1670 | } | |
1671 | ||
1672 | result = scm_i_mkbig (); | |
1673 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1674 | n_tmp, | |
1675 | k_tmp, | |
1676 | m_tmp); | |
b7b8c575 KR |
1677 | |
1678 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1679 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1680 | ||
518b7508 KR |
1681 | cleanup: |
1682 | mpz_clear (m_tmp); | |
1683 | mpz_clear (k_tmp); | |
1684 | mpz_clear (n_tmp); | |
1685 | ||
1686 | if (report_overflow) | |
1687 | scm_num_overflow (FUNC_NAME); | |
1688 | ||
1689 | if (position_of_wrong_type) | |
1690 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1691 | value_of_wrong_type); | |
1692 | ||
1693 | return scm_i_normbig (result); | |
1694 | } | |
1695 | #undef FUNC_NAME | |
1696 | ||
a1ec6916 | 1697 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1698 | (SCM n, SCM k), |
ba6e7231 KR |
1699 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1700 | "exact integer, @var{n} can be any number.\n" | |
1701 | "\n" | |
1702 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1703 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1704 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1705 | "\n" |
b380b885 | 1706 | "@lisp\n" |
ba6e7231 KR |
1707 | "(integer-expt 2 5) @result{} 32\n" |
1708 | "(integer-expt -3 3) @result{} -27\n" | |
1709 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1710 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1711 | "@end lisp") |
1bbd0b84 | 1712 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1713 | { |
1c35cb19 RB |
1714 | long i2 = 0; |
1715 | SCM z_i2 = SCM_BOOL_F; | |
1716 | int i2_is_big = 0; | |
d956fa6f | 1717 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1718 | |
d57ed702 | 1719 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1720 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1721 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1722 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1723 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1724 | |
e11e83f3 MV |
1725 | if (SCM_I_INUMP (k)) |
1726 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1727 | else if (SCM_BIGP (k)) |
1728 | { | |
1729 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1730 | scm_remember_upto_here_1 (k); |
1731 | i2_is_big = 1; | |
1732 | } | |
2830fd91 | 1733 | else |
ca46fb90 RB |
1734 | SCM_WRONG_TYPE_ARG (2, k); |
1735 | ||
1736 | if (i2_is_big) | |
f872b822 | 1737 | { |
ca46fb90 RB |
1738 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1739 | { | |
1740 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1741 | n = scm_divide (n, SCM_UNDEFINED); | |
1742 | } | |
1743 | while (1) | |
1744 | { | |
1745 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1746 | { | |
ca46fb90 RB |
1747 | return acc; |
1748 | } | |
1749 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1750 | { | |
ca46fb90 RB |
1751 | return scm_product (acc, n); |
1752 | } | |
1753 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1754 | acc = scm_product (acc, n); | |
1755 | n = scm_product (n, n); | |
1756 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1757 | } | |
f872b822 | 1758 | } |
ca46fb90 | 1759 | else |
f872b822 | 1760 | { |
ca46fb90 RB |
1761 | if (i2 < 0) |
1762 | { | |
1763 | i2 = -i2; | |
1764 | n = scm_divide (n, SCM_UNDEFINED); | |
1765 | } | |
1766 | while (1) | |
1767 | { | |
1768 | if (0 == i2) | |
1769 | return acc; | |
1770 | if (1 == i2) | |
1771 | return scm_product (acc, n); | |
1772 | if (i2 & 1) | |
1773 | acc = scm_product (acc, n); | |
1774 | n = scm_product (n, n); | |
1775 | i2 >>= 1; | |
1776 | } | |
f872b822 | 1777 | } |
0f2d19dd | 1778 | } |
1bbd0b84 | 1779 | #undef FUNC_NAME |
0f2d19dd | 1780 | |
a1ec6916 | 1781 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1782 | (SCM n, SCM cnt), |
32f19569 KR |
1783 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1784 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1785 | "\n" |
e7644cb2 | 1786 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1787 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1788 | "infinity. (Note that this is not the same rounding as\n" | |
1789 | "@code{quotient} does.)\n" | |
1790 | "\n" | |
1791 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1792 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1793 | "shift dropping bits.\n" | |
1e6808ea | 1794 | "\n" |
b380b885 | 1795 | "@lisp\n" |
1e6808ea MG |
1796 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1797 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1798 | "\n" |
1799 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1800 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1801 | "@end lisp") |
1bbd0b84 | 1802 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1803 | { |
3ab9f56e | 1804 | long bits_to_shift; |
5efd3c7d | 1805 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1806 | |
788aca27 KR |
1807 | if (SCM_I_INUMP (n)) |
1808 | { | |
1809 | long nn = SCM_I_INUM (n); | |
1810 | ||
1811 | if (bits_to_shift > 0) | |
1812 | { | |
1813 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1814 | overflow a non-zero fixnum. For smaller shifts we check the | |
1815 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1816 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1817 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1818 | bits_to_shift)". */ | |
1819 | ||
1820 | if (nn == 0) | |
1821 | return n; | |
1822 | ||
1823 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
1824 | && ((unsigned long) | |
1825 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) | |
1826 | <= 1)) | |
1827 | { | |
1828 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1829 | } | |
1830 | else | |
1831 | { | |
1832 | SCM result = scm_i_long2big (nn); | |
1833 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1834 | bits_to_shift); | |
1835 | return result; | |
1836 | } | |
1837 | } | |
1838 | else | |
1839 | { | |
1840 | bits_to_shift = -bits_to_shift; | |
1841 | if (bits_to_shift >= SCM_LONG_BIT) | |
1842 | return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1)); | |
1843 | else | |
1844 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1845 | } | |
1846 | ||
1847 | } | |
1848 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1849 | { |
788aca27 KR |
1850 | SCM result; |
1851 | ||
1852 | if (bits_to_shift == 0) | |
1853 | return n; | |
1854 | ||
1855 | result = scm_i_mkbig (); | |
1856 | if (bits_to_shift >= 0) | |
1857 | { | |
1858 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1859 | bits_to_shift); | |
1860 | return result; | |
1861 | } | |
ca46fb90 | 1862 | else |
788aca27 KR |
1863 | { |
1864 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1865 | we have to allocate a bignum even if the result is going to be a | |
1866 | fixnum. */ | |
1867 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1868 | -bits_to_shift); | |
1869 | return scm_i_normbig (result); | |
1870 | } | |
1871 | ||
ca46fb90 RB |
1872 | } |
1873 | else | |
788aca27 KR |
1874 | { |
1875 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1876 | } | |
0f2d19dd | 1877 | } |
1bbd0b84 | 1878 | #undef FUNC_NAME |
0f2d19dd | 1879 | |
3c9f20f8 | 1880 | |
a1ec6916 | 1881 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1882 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1883 | "Return the integer composed of the @var{start} (inclusive)\n" |
1884 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1885 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1886 | "\n" | |
b380b885 MD |
1887 | "@lisp\n" |
1888 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1889 | " @result{} \"1010\"\n" | |
1890 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1891 | " @result{} \"10110\"\n" | |
1892 | "@end lisp") | |
1bbd0b84 | 1893 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1894 | { |
7f848242 | 1895 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1896 | istart = scm_to_ulong (start); |
1897 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1898 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1899 | |
7f848242 KR |
1900 | /* how many bits to keep */ |
1901 | bits = iend - istart; | |
1902 | ||
e11e83f3 | 1903 | if (SCM_I_INUMP (n)) |
0aacf84e | 1904 | { |
e11e83f3 | 1905 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1906 | |
1907 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1908 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1909 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1910 | |
0aacf84e MD |
1911 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1912 | { | |
1913 | /* Since we emulate two's complement encoded numbers, this | |
1914 | * special case requires us to produce a result that has | |
7f848242 | 1915 | * more bits than can be stored in a fixnum. |
0aacf84e | 1916 | */ |
7f848242 KR |
1917 | SCM result = scm_i_long2big (in); |
1918 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1919 | bits); | |
1920 | return result; | |
0aacf84e | 1921 | } |
ac0c002c | 1922 | |
7f848242 | 1923 | /* mask down to requisite bits */ |
857ae6af | 1924 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1925 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1926 | } |
1927 | else if (SCM_BIGP (n)) | |
ac0c002c | 1928 | { |
7f848242 KR |
1929 | SCM result; |
1930 | if (bits == 1) | |
1931 | { | |
d956fa6f | 1932 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1933 | } |
1934 | else | |
1935 | { | |
1936 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1937 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1938 | such bits into a ulong. */ | |
1939 | result = scm_i_mkbig (); | |
1940 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1941 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1942 | result = scm_i_normbig (result); | |
1943 | } | |
1944 | scm_remember_upto_here_1 (n); | |
1945 | return result; | |
ac0c002c | 1946 | } |
0aacf84e | 1947 | else |
78166ad5 | 1948 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1949 | } |
1bbd0b84 | 1950 | #undef FUNC_NAME |
0f2d19dd | 1951 | |
7f848242 | 1952 | |
e4755e5c JB |
1953 | static const char scm_logtab[] = { |
1954 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1955 | }; | |
1cc91f1b | 1956 | |
a1ec6916 | 1957 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1958 | (SCM n), |
1e6808ea MG |
1959 | "Return the number of bits in integer @var{n}. If integer is\n" |
1960 | "positive, the 1-bits in its binary representation are counted.\n" | |
1961 | "If negative, the 0-bits in its two's-complement binary\n" | |
1962 | "representation are counted. If 0, 0 is returned.\n" | |
1963 | "\n" | |
b380b885 MD |
1964 | "@lisp\n" |
1965 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1966 | " @result{} 4\n" |
1967 | "(logcount 0)\n" | |
1968 | " @result{} 0\n" | |
1969 | "(logcount -2)\n" | |
1970 | " @result{} 1\n" | |
1971 | "@end lisp") | |
1972 | #define FUNC_NAME s_scm_logcount | |
1973 | { | |
e11e83f3 | 1974 | if (SCM_I_INUMP (n)) |
f872b822 | 1975 | { |
ca46fb90 | 1976 | unsigned long int c = 0; |
e11e83f3 | 1977 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
1978 | if (nn < 0) |
1979 | nn = -1 - nn; | |
1980 | while (nn) | |
1981 | { | |
1982 | c += scm_logtab[15 & nn]; | |
1983 | nn >>= 4; | |
1984 | } | |
d956fa6f | 1985 | return SCM_I_MAKINUM (c); |
f872b822 | 1986 | } |
ca46fb90 | 1987 | else if (SCM_BIGP (n)) |
f872b822 | 1988 | { |
ca46fb90 | 1989 | unsigned long count; |
713a4259 KR |
1990 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1991 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1992 | else |
713a4259 KR |
1993 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1994 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1995 | return SCM_I_MAKINUM (count); |
f872b822 | 1996 | } |
ca46fb90 RB |
1997 | else |
1998 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 1999 | } |
ca46fb90 | 2000 | #undef FUNC_NAME |
0f2d19dd JB |
2001 | |
2002 | ||
ca46fb90 RB |
2003 | static const char scm_ilentab[] = { |
2004 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
2005 | }; | |
2006 | ||
0f2d19dd | 2007 | |
ca46fb90 RB |
2008 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
2009 | (SCM n), | |
2010 | "Return the number of bits necessary to represent @var{n}.\n" | |
2011 | "\n" | |
2012 | "@lisp\n" | |
2013 | "(integer-length #b10101010)\n" | |
2014 | " @result{} 8\n" | |
2015 | "(integer-length 0)\n" | |
2016 | " @result{} 0\n" | |
2017 | "(integer-length #b1111)\n" | |
2018 | " @result{} 4\n" | |
2019 | "@end lisp") | |
2020 | #define FUNC_NAME s_scm_integer_length | |
2021 | { | |
e11e83f3 | 2022 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2023 | { |
2024 | unsigned long int c = 0; | |
2025 | unsigned int l = 4; | |
e11e83f3 | 2026 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
2027 | if (nn < 0) |
2028 | nn = -1 - nn; | |
2029 | while (nn) | |
2030 | { | |
2031 | c += 4; | |
2032 | l = scm_ilentab [15 & nn]; | |
2033 | nn >>= 4; | |
2034 | } | |
d956fa6f | 2035 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2036 | } |
2037 | else if (SCM_BIGP (n)) | |
2038 | { | |
2039 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2040 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2041 | 1 too big, so check for that and adjust. */ | |
2042 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2043 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2044 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2045 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2046 | size--; | |
2047 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2048 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2049 | } |
2050 | else | |
ca46fb90 | 2051 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2052 | } |
2053 | #undef FUNC_NAME | |
0f2d19dd JB |
2054 | |
2055 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2056 | #define SCM_MAX_DBL_PREC 60 |
2057 | #define SCM_MAX_DBL_RADIX 36 | |
2058 | ||
2059 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2060 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2061 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2062 | ||
2063 | static | |
2064 | void init_dblprec(int *prec, int radix) { | |
2065 | /* determine floating point precision by adding successively | |
2066 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2067 | double f = ((double)1.0)/radix; | |
2068 | double fsum = 1.0 + f; | |
2069 | ||
2070 | *prec = 0; | |
2071 | while (fsum != 1.0) | |
2072 | { | |
2073 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2074 | fsum = 1.0; | |
2075 | else | |
2076 | { | |
2077 | f /= radix; | |
2078 | fsum = f + 1.0; | |
2079 | } | |
2080 | } | |
2081 | (*prec) -= 1; | |
2082 | } | |
2083 | ||
2084 | static | |
2085 | void init_fx_radix(double *fx_list, int radix) | |
2086 | { | |
2087 | /* initialize a per-radix list of tolerances. When added | |
2088 | to a number < 1.0, we can determine if we should raund | |
2089 | up and quit converting a number to a string. */ | |
2090 | int i; | |
2091 | fx_list[0] = 0.0; | |
2092 | fx_list[1] = 0.5; | |
2093 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2094 | fx_list[i] = (fx_list[i-1] / radix); | |
2095 | } | |
2096 | ||
2097 | /* use this array as a way to generate a single digit */ | |
2098 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2099 | |
1be6b49c | 2100 | static size_t |
0b799eea | 2101 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2102 | { |
0b799eea MV |
2103 | int efmt, dpt, d, i, wp; |
2104 | double *fx; | |
2105 | #ifdef DBL_MIN_10_EXP | |
2106 | double f_cpy; | |
2107 | int exp_cpy; | |
2108 | #endif /* DBL_MIN_10_EXP */ | |
2109 | size_t ch = 0; | |
2110 | int exp = 0; | |
2111 | ||
2112 | if(radix < 2 || | |
2113 | radix > SCM_MAX_DBL_RADIX) | |
2114 | { | |
2115 | /* revert to existing behavior */ | |
2116 | radix = 10; | |
2117 | } | |
2118 | ||
2119 | wp = scm_dblprec[radix-2]; | |
2120 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2121 | |
f872b822 | 2122 | if (f == 0.0) |
abb7e44d MV |
2123 | { |
2124 | #ifdef HAVE_COPYSIGN | |
2125 | double sgn = copysign (1.0, f); | |
2126 | ||
2127 | if (sgn < 0.0) | |
2128 | a[ch++] = '-'; | |
2129 | #endif | |
abb7e44d MV |
2130 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2131 | } | |
7351e207 MV |
2132 | |
2133 | if (xisinf (f)) | |
2134 | { | |
2135 | if (f < 0) | |
2136 | strcpy (a, "-inf.0"); | |
2137 | else | |
2138 | strcpy (a, "+inf.0"); | |
2139 | return ch+6; | |
2140 | } | |
2141 | else if (xisnan (f)) | |
2142 | { | |
2143 | strcpy (a, "+nan.0"); | |
2144 | return ch+6; | |
2145 | } | |
2146 | ||
f872b822 MD |
2147 | if (f < 0.0) |
2148 | { | |
2149 | f = -f; | |
2150 | a[ch++] = '-'; | |
2151 | } | |
7351e207 | 2152 | |
f872b822 MD |
2153 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2154 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2155 | /* just do the checking...if it passes, we do the conversion for our |
2156 | radix again below */ | |
2157 | f_cpy = f; | |
2158 | exp_cpy = exp; | |
2159 | ||
2160 | while (f_cpy < 1.0) | |
f872b822 | 2161 | { |
0b799eea MV |
2162 | f_cpy *= 10.0; |
2163 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2164 | { |
2165 | a[ch++] = '#'; | |
2166 | a[ch++] = '.'; | |
2167 | a[ch++] = '#'; | |
2168 | return ch; | |
2169 | } | |
f872b822 | 2170 | } |
0b799eea | 2171 | while (f_cpy > 10.0) |
f872b822 | 2172 | { |
0b799eea MV |
2173 | f_cpy *= 0.10; |
2174 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2175 | { |
2176 | a[ch++] = '#'; | |
2177 | a[ch++] = '.'; | |
2178 | a[ch++] = '#'; | |
2179 | return ch; | |
2180 | } | |
f872b822 | 2181 | } |
0b799eea MV |
2182 | #endif |
2183 | ||
f872b822 MD |
2184 | while (f < 1.0) |
2185 | { | |
0b799eea | 2186 | f *= radix; |
f872b822 MD |
2187 | exp--; |
2188 | } | |
0b799eea | 2189 | while (f > radix) |
f872b822 | 2190 | { |
0b799eea | 2191 | f /= radix; |
f872b822 MD |
2192 | exp++; |
2193 | } | |
0b799eea MV |
2194 | |
2195 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2196 | { |
2197 | f = 1.0; | |
2198 | exp++; | |
2199 | } | |
0f2d19dd | 2200 | zero: |
0b799eea MV |
2201 | #ifdef ENGNOT |
2202 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2203 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2204 | exp -= dpt++; |
2205 | efmt = 1; | |
f872b822 MD |
2206 | #else |
2207 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2208 | if (!efmt) |
cda139a7 MD |
2209 | { |
2210 | if (exp < 0) | |
2211 | { | |
2212 | a[ch++] = '0'; | |
2213 | a[ch++] = '.'; | |
2214 | dpt = exp; | |
f872b822 MD |
2215 | while (++dpt) |
2216 | a[ch++] = '0'; | |
cda139a7 MD |
2217 | } |
2218 | else | |
f872b822 | 2219 | dpt = exp + 1; |
cda139a7 | 2220 | } |
0f2d19dd JB |
2221 | else |
2222 | dpt = 1; | |
f872b822 MD |
2223 | #endif |
2224 | ||
2225 | do | |
2226 | { | |
2227 | d = f; | |
2228 | f -= d; | |
0b799eea | 2229 | a[ch++] = number_chars[d]; |
f872b822 MD |
2230 | if (f < fx[wp]) |
2231 | break; | |
2232 | if (f + fx[wp] >= 1.0) | |
2233 | { | |
0b799eea | 2234 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2235 | break; |
2236 | } | |
0b799eea | 2237 | f *= radix; |
f872b822 MD |
2238 | if (!(--dpt)) |
2239 | a[ch++] = '.'; | |
0f2d19dd | 2240 | } |
f872b822 | 2241 | while (wp--); |
0f2d19dd JB |
2242 | |
2243 | if (dpt > 0) | |
cda139a7 | 2244 | { |
f872b822 | 2245 | #ifndef ENGNOT |
cda139a7 MD |
2246 | if ((dpt > 4) && (exp > 6)) |
2247 | { | |
f872b822 | 2248 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2249 | for (i = ch++; i > d; i--) |
f872b822 | 2250 | a[i] = a[i - 1]; |
cda139a7 MD |
2251 | a[d] = '.'; |
2252 | efmt = 1; | |
2253 | } | |
2254 | else | |
f872b822 | 2255 | #endif |
cda139a7 | 2256 | { |
f872b822 MD |
2257 | while (--dpt) |
2258 | a[ch++] = '0'; | |
cda139a7 MD |
2259 | a[ch++] = '.'; |
2260 | } | |
2261 | } | |
f872b822 MD |
2262 | if (a[ch - 1] == '.') |
2263 | a[ch++] = '0'; /* trailing zero */ | |
2264 | if (efmt && exp) | |
2265 | { | |
2266 | a[ch++] = 'e'; | |
2267 | if (exp < 0) | |
2268 | { | |
2269 | exp = -exp; | |
2270 | a[ch++] = '-'; | |
2271 | } | |
0b799eea MV |
2272 | for (i = radix; i <= exp; i *= radix); |
2273 | for (i /= radix; i; i /= radix) | |
f872b822 | 2274 | { |
0b799eea | 2275 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2276 | exp %= i; |
2277 | } | |
0f2d19dd | 2278 | } |
0f2d19dd JB |
2279 | return ch; |
2280 | } | |
2281 | ||
7a1aba42 MV |
2282 | |
2283 | static size_t | |
2284 | icmplx2str (double real, double imag, char *str, int radix) | |
2285 | { | |
2286 | size_t i; | |
2287 | ||
2288 | i = idbl2str (real, str, radix); | |
2289 | if (imag != 0.0) | |
2290 | { | |
2291 | /* Don't output a '+' for negative numbers or for Inf and | |
2292 | NaN. They will provide their own sign. */ | |
2293 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
2294 | str[i++] = '+'; | |
2295 | i += idbl2str (imag, &str[i], radix); | |
2296 | str[i++] = 'i'; | |
2297 | } | |
2298 | return i; | |
2299 | } | |
2300 | ||
1be6b49c | 2301 | static size_t |
0b799eea | 2302 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2303 | { |
1be6b49c | 2304 | size_t i; |
3c9a524f | 2305 | if (SCM_REALP (flt)) |
0b799eea | 2306 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2307 | else |
7a1aba42 MV |
2308 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2309 | str, radix); | |
0f2d19dd JB |
2310 | return i; |
2311 | } | |
0f2d19dd | 2312 | |
2881e77b | 2313 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2314 | characters in the result. |
2315 | rad is output base | |
2316 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2317 | size_t |
2881e77b MV |
2318 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2319 | { | |
2320 | if (num < 0) | |
2321 | { | |
2322 | *p++ = '-'; | |
2323 | return scm_iuint2str (-num, rad, p) + 1; | |
2324 | } | |
2325 | else | |
2326 | return scm_iuint2str (num, rad, p); | |
2327 | } | |
2328 | ||
2329 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2330 | characters in the result. | |
2331 | rad is output base | |
2332 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2333 | size_t | |
2334 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2335 | { |
1be6b49c ML |
2336 | size_t j = 1; |
2337 | size_t i; | |
2881e77b | 2338 | scm_t_uintmax n = num; |
5c11cc9d | 2339 | |
f872b822 | 2340 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2341 | j++; |
2342 | ||
2343 | i = j; | |
2881e77b | 2344 | n = num; |
f872b822 MD |
2345 | while (i--) |
2346 | { | |
5c11cc9d GH |
2347 | int d = n % rad; |
2348 | ||
f872b822 MD |
2349 | n /= rad; |
2350 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2351 | } | |
0f2d19dd JB |
2352 | return j; |
2353 | } | |
2354 | ||
a1ec6916 | 2355 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2356 | (SCM n, SCM radix), |
2357 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2358 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2359 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2360 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2361 | { |
1bbd0b84 | 2362 | int base; |
98cb6e75 | 2363 | |
0aacf84e | 2364 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2365 | base = 10; |
0aacf84e | 2366 | else |
5efd3c7d | 2367 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2368 | |
e11e83f3 | 2369 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2370 | { |
2371 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2372 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2373 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2374 | } |
2375 | else if (SCM_BIGP (n)) | |
2376 | { | |
2377 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2378 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2379 | return scm_take_locale_string (str); |
0aacf84e | 2380 | } |
f92e85f7 MV |
2381 | else if (SCM_FRACTIONP (n)) |
2382 | { | |
f92e85f7 | 2383 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 2384 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2385 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2386 | } | |
0aacf84e MD |
2387 | else if (SCM_INEXACTP (n)) |
2388 | { | |
2389 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2390 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2391 | } |
2392 | else | |
bb628794 | 2393 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2394 | } |
1bbd0b84 | 2395 | #undef FUNC_NAME |
0f2d19dd JB |
2396 | |
2397 | ||
ca46fb90 RB |
2398 | /* These print routines used to be stubbed here so that scm_repl.c |
2399 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2400 | |
0f2d19dd | 2401 | int |
e81d98ec | 2402 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2403 | { |
56e55ac7 | 2404 | char num_buf[FLOBUFLEN]; |
0b799eea | 2405 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2406 | return !0; |
2407 | } | |
2408 | ||
b479fe9a MV |
2409 | void |
2410 | scm_i_print_double (double val, SCM port) | |
2411 | { | |
2412 | char num_buf[FLOBUFLEN]; | |
2413 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2414 | } | |
2415 | ||
f3ae5d60 | 2416 | int |
e81d98ec | 2417 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2418 | |
f3ae5d60 | 2419 | { |
56e55ac7 | 2420 | char num_buf[FLOBUFLEN]; |
0b799eea | 2421 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2422 | return !0; |
2423 | } | |
1cc91f1b | 2424 | |
7a1aba42 MV |
2425 | void |
2426 | scm_i_print_complex (double real, double imag, SCM port) | |
2427 | { | |
2428 | char num_buf[FLOBUFLEN]; | |
2429 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2430 | } | |
2431 | ||
f92e85f7 MV |
2432 | int |
2433 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2434 | { | |
2435 | SCM str; | |
f92e85f7 | 2436 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
cc95e00a | 2437 | scm_lfwrite (scm_i_string_chars (str), scm_i_string_length (str), port); |
f92e85f7 MV |
2438 | scm_remember_upto_here_1 (str); |
2439 | return !0; | |
2440 | } | |
2441 | ||
0f2d19dd | 2442 | int |
e81d98ec | 2443 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2444 | { |
ca46fb90 RB |
2445 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2446 | scm_remember_upto_here_1 (exp); | |
2447 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2448 | free (str); | |
0f2d19dd JB |
2449 | return !0; |
2450 | } | |
2451 | /*** END nums->strs ***/ | |
2452 | ||
3c9a524f | 2453 | |
0f2d19dd | 2454 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2455 | |
3c9a524f DH |
2456 | /* The following functions implement the conversion from strings to numbers. |
2457 | * The implementation somehow follows the grammar for numbers as it is given | |
2458 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2459 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2460 | * points should be noted about the implementation: | |
2461 | * * Each function keeps a local index variable 'idx' that points at the | |
2462 | * current position within the parsed string. The global index is only | |
2463 | * updated if the function could parse the corresponding syntactic unit | |
2464 | * successfully. | |
2465 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2466 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2467 | * global exactness information is only updated after each part has been | |
2468 | * successfully parsed. | |
2469 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2470 | * Only if these fixnums would overflow, the result variables are updated | |
2471 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2472 | * the temporary variables holding the fixnums are cleared, and the process | |
2473 | * starts over again. If for example fixnums were able to store five decimal | |
2474 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2475 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2476 | * only every five digits two bignum operations were performed. | |
2477 | */ | |
2478 | ||
2479 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2480 | ||
2481 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2482 | ||
2483 | /* In non ASCII-style encodings the following macro might not work. */ | |
71df73ac KR |
2484 | #define XDIGIT2UINT(d) \ |
2485 | (isdigit ((int) (unsigned char) d) \ | |
2486 | ? (d) - '0' \ | |
2487 | : tolower ((int) (unsigned char) d) - 'a' + 10) | |
3c9a524f | 2488 | |
2a8fecee | 2489 | static SCM |
3c9a524f DH |
2490 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2491 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2492 | { |
3c9a524f DH |
2493 | unsigned int idx = *p_idx; |
2494 | unsigned int hash_seen = 0; | |
2495 | scm_t_bits shift = 1; | |
2496 | scm_t_bits add = 0; | |
2497 | unsigned int digit_value; | |
2498 | SCM result; | |
2499 | char c; | |
2500 | ||
2501 | if (idx == len) | |
2502 | return SCM_BOOL_F; | |
2a8fecee | 2503 | |
3c9a524f | 2504 | c = mem[idx]; |
71df73ac | 2505 | if (!isxdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2506 | return SCM_BOOL_F; |
2507 | digit_value = XDIGIT2UINT (c); | |
2508 | if (digit_value >= radix) | |
2509 | return SCM_BOOL_F; | |
2510 | ||
2511 | idx++; | |
d956fa6f | 2512 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2513 | while (idx != len) |
f872b822 | 2514 | { |
3c9a524f | 2515 | char c = mem[idx]; |
71df73ac | 2516 | if (isxdigit ((int) (unsigned char) c)) |
f872b822 | 2517 | { |
3c9a524f | 2518 | if (hash_seen) |
1fe5e088 | 2519 | break; |
3c9a524f DH |
2520 | digit_value = XDIGIT2UINT (c); |
2521 | if (digit_value >= radix) | |
1fe5e088 | 2522 | break; |
f872b822 | 2523 | } |
3c9a524f DH |
2524 | else if (c == '#') |
2525 | { | |
2526 | hash_seen = 1; | |
2527 | digit_value = 0; | |
2528 | } | |
2529 | else | |
2530 | break; | |
2531 | ||
2532 | idx++; | |
2533 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2534 | { | |
d956fa6f | 2535 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2536 | if (add > 0) |
d956fa6f | 2537 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2538 | |
2539 | shift = radix; | |
2540 | add = digit_value; | |
2541 | } | |
2542 | else | |
2543 | { | |
2544 | shift = shift * radix; | |
2545 | add = add * radix + digit_value; | |
2546 | } | |
2547 | }; | |
2548 | ||
2549 | if (shift > 1) | |
d956fa6f | 2550 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2551 | if (add > 0) |
d956fa6f | 2552 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2553 | |
2554 | *p_idx = idx; | |
2555 | if (hash_seen) | |
2556 | *p_exactness = INEXACT; | |
2557 | ||
2558 | return result; | |
2a8fecee JB |
2559 | } |
2560 | ||
2561 | ||
3c9a524f DH |
2562 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2563 | * covers the parts of the rules that start at a potential point. The value | |
2564 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2565 | * in variable result. The content of *p_exactness indicates, whether a hash |
2566 | * has already been seen in the digits before the point. | |
3c9a524f | 2567 | */ |
1cc91f1b | 2568 | |
3c9a524f DH |
2569 | /* In non ASCII-style encodings the following macro might not work. */ |
2570 | #define DIGIT2UINT(d) ((d) - '0') | |
2571 | ||
2572 | static SCM | |
79d34f68 | 2573 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2574 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2575 | { |
3c9a524f DH |
2576 | unsigned int idx = *p_idx; |
2577 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2578 | |
2579 | if (idx == len) | |
79d34f68 | 2580 | return result; |
3c9a524f DH |
2581 | |
2582 | if (mem[idx] == '.') | |
2583 | { | |
2584 | scm_t_bits shift = 1; | |
2585 | scm_t_bits add = 0; | |
2586 | unsigned int digit_value; | |
d956fa6f | 2587 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2588 | |
2589 | idx++; | |
2590 | while (idx != len) | |
2591 | { | |
2592 | char c = mem[idx]; | |
71df73ac | 2593 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2594 | { |
2595 | if (x == INEXACT) | |
2596 | return SCM_BOOL_F; | |
2597 | else | |
2598 | digit_value = DIGIT2UINT (c); | |
2599 | } | |
2600 | else if (c == '#') | |
2601 | { | |
2602 | x = INEXACT; | |
2603 | digit_value = 0; | |
2604 | } | |
2605 | else | |
2606 | break; | |
2607 | ||
2608 | idx++; | |
2609 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2610 | { | |
d956fa6f MV |
2611 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2612 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2613 | if (add > 0) |
d956fa6f | 2614 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2615 | |
2616 | shift = 10; | |
2617 | add = digit_value; | |
2618 | } | |
2619 | else | |
2620 | { | |
2621 | shift = shift * 10; | |
2622 | add = add * 10 + digit_value; | |
2623 | } | |
2624 | }; | |
2625 | ||
2626 | if (add > 0) | |
2627 | { | |
d956fa6f MV |
2628 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2629 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2630 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2631 | } |
2632 | ||
d8592269 | 2633 | result = scm_divide (result, big_shift); |
79d34f68 | 2634 | |
3c9a524f DH |
2635 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2636 | x = INEXACT; | |
f872b822 | 2637 | } |
3c9a524f | 2638 | |
3c9a524f | 2639 | if (idx != len) |
f872b822 | 2640 | { |
3c9a524f DH |
2641 | int sign = 1; |
2642 | unsigned int start; | |
2643 | char c; | |
2644 | int exponent; | |
2645 | SCM e; | |
2646 | ||
2647 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2648 | ||
2649 | switch (mem[idx]) | |
f872b822 | 2650 | { |
3c9a524f DH |
2651 | case 'd': case 'D': |
2652 | case 'e': case 'E': | |
2653 | case 'f': case 'F': | |
2654 | case 'l': case 'L': | |
2655 | case 's': case 'S': | |
2656 | idx++; | |
2657 | start = idx; | |
2658 | c = mem[idx]; | |
2659 | if (c == '-') | |
2660 | { | |
2661 | idx++; | |
2662 | sign = -1; | |
2663 | c = mem[idx]; | |
2664 | } | |
2665 | else if (c == '+') | |
2666 | { | |
2667 | idx++; | |
2668 | sign = 1; | |
2669 | c = mem[idx]; | |
2670 | } | |
2671 | else | |
2672 | sign = 1; | |
2673 | ||
71df73ac | 2674 | if (!isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2675 | return SCM_BOOL_F; |
2676 | ||
2677 | idx++; | |
2678 | exponent = DIGIT2UINT (c); | |
2679 | while (idx != len) | |
f872b822 | 2680 | { |
3c9a524f | 2681 | char c = mem[idx]; |
71df73ac | 2682 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2683 | { |
2684 | idx++; | |
2685 | if (exponent <= SCM_MAXEXP) | |
2686 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2687 | } | |
2688 | else | |
2689 | break; | |
f872b822 | 2690 | } |
3c9a524f DH |
2691 | |
2692 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2693 | { |
3c9a524f | 2694 | size_t exp_len = idx - start; |
cc95e00a | 2695 | SCM exp_string = scm_from_locale_stringn (&mem[start], exp_len); |
3c9a524f DH |
2696 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2697 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2698 | } |
3c9a524f | 2699 | |
d956fa6f | 2700 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2701 | if (sign == 1) |
2702 | result = scm_product (result, e); | |
2703 | else | |
f92e85f7 | 2704 | result = scm_divide2real (result, e); |
3c9a524f DH |
2705 | |
2706 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2707 | x = INEXACT; | |
2708 | ||
f872b822 | 2709 | break; |
3c9a524f | 2710 | |
f872b822 | 2711 | default: |
3c9a524f | 2712 | break; |
f872b822 | 2713 | } |
0f2d19dd | 2714 | } |
3c9a524f DH |
2715 | |
2716 | *p_idx = idx; | |
2717 | if (x == INEXACT) | |
2718 | *p_exactness = x; | |
2719 | ||
2720 | return result; | |
0f2d19dd | 2721 | } |
0f2d19dd | 2722 | |
3c9a524f DH |
2723 | |
2724 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2725 | ||
2726 | static SCM | |
2727 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2728 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2729 | { |
3c9a524f | 2730 | unsigned int idx = *p_idx; |
164d2481 | 2731 | SCM result; |
3c9a524f DH |
2732 | |
2733 | if (idx == len) | |
2734 | return SCM_BOOL_F; | |
2735 | ||
7351e207 MV |
2736 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2737 | { | |
2738 | *p_idx = idx+5; | |
2739 | return scm_inf (); | |
2740 | } | |
2741 | ||
2742 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2743 | { | |
2744 | enum t_exactness x = EXACT; | |
2745 | ||
d8592269 MV |
2746 | /* Cobble up the fractional part. We might want to set the |
2747 | NaN's mantissa from it. */ | |
7351e207 MV |
2748 | idx += 4; |
2749 | mem2uinteger (mem, len, &idx, 10, &x); | |
2750 | *p_idx = idx; | |
2751 | return scm_nan (); | |
2752 | } | |
2753 | ||
3c9a524f DH |
2754 | if (mem[idx] == '.') |
2755 | { | |
2756 | if (radix != 10) | |
2757 | return SCM_BOOL_F; | |
2758 | else if (idx + 1 == len) | |
2759 | return SCM_BOOL_F; | |
71df73ac | 2760 | else if (!isdigit ((int) (unsigned char) mem[idx + 1])) |
3c9a524f DH |
2761 | return SCM_BOOL_F; |
2762 | else | |
d956fa6f | 2763 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len, |
164d2481 | 2764 | p_idx, p_exactness); |
f872b822 | 2765 | } |
3c9a524f DH |
2766 | else |
2767 | { | |
2768 | enum t_exactness x = EXACT; | |
2769 | SCM uinteger; | |
3c9a524f DH |
2770 | |
2771 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2772 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2773 | return SCM_BOOL_F; |
2774 | ||
2775 | if (idx == len) | |
2776 | result = uinteger; | |
2777 | else if (mem[idx] == '/') | |
f872b822 | 2778 | { |
3c9a524f DH |
2779 | SCM divisor; |
2780 | ||
2781 | idx++; | |
2782 | ||
2783 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2784 | if (scm_is_false (divisor)) |
3c9a524f DH |
2785 | return SCM_BOOL_F; |
2786 | ||
f92e85f7 | 2787 | /* both are int/big here, I assume */ |
cba42c93 | 2788 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2789 | } |
3c9a524f DH |
2790 | else if (radix == 10) |
2791 | { | |
2792 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
73e4de09 | 2793 | if (scm_is_false (result)) |
3c9a524f DH |
2794 | return SCM_BOOL_F; |
2795 | } | |
2796 | else | |
2797 | result = uinteger; | |
2798 | ||
2799 | *p_idx = idx; | |
2800 | if (x == INEXACT) | |
2801 | *p_exactness = x; | |
f872b822 | 2802 | } |
164d2481 MV |
2803 | |
2804 | /* When returning an inexact zero, make sure it is represented as a | |
2805 | floating point value so that we can change its sign. | |
2806 | */ | |
bc36d050 | 2807 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2808 | result = scm_from_double (0.0); |
164d2481 MV |
2809 | |
2810 | return result; | |
3c9a524f | 2811 | } |
0f2d19dd | 2812 | |
0f2d19dd | 2813 | |
3c9a524f | 2814 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2815 | |
3c9a524f DH |
2816 | static SCM |
2817 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2818 | unsigned int radix, enum t_exactness *p_exactness) | |
2819 | { | |
2820 | char c; | |
2821 | int sign = 0; | |
2822 | SCM ureal; | |
2823 | ||
2824 | if (idx == len) | |
2825 | return SCM_BOOL_F; | |
2826 | ||
2827 | c = mem[idx]; | |
2828 | if (c == '+') | |
2829 | { | |
2830 | idx++; | |
2831 | sign = 1; | |
2832 | } | |
2833 | else if (c == '-') | |
2834 | { | |
2835 | idx++; | |
2836 | sign = -1; | |
0f2d19dd | 2837 | } |
0f2d19dd | 2838 | |
3c9a524f DH |
2839 | if (idx == len) |
2840 | return SCM_BOOL_F; | |
2841 | ||
2842 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2843 | if (scm_is_false (ureal)) |
f872b822 | 2844 | { |
3c9a524f DH |
2845 | /* input must be either +i or -i */ |
2846 | ||
2847 | if (sign == 0) | |
2848 | return SCM_BOOL_F; | |
2849 | ||
2850 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2851 | { |
3c9a524f DH |
2852 | idx++; |
2853 | if (idx != len) | |
2854 | return SCM_BOOL_F; | |
2855 | ||
d956fa6f | 2856 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2857 | } |
3c9a524f DH |
2858 | else |
2859 | return SCM_BOOL_F; | |
0f2d19dd | 2860 | } |
3c9a524f DH |
2861 | else |
2862 | { | |
73e4de09 | 2863 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2864 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2865 | |
3c9a524f DH |
2866 | if (idx == len) |
2867 | return ureal; | |
2868 | ||
2869 | c = mem[idx]; | |
2870 | switch (c) | |
f872b822 | 2871 | { |
3c9a524f DH |
2872 | case 'i': case 'I': |
2873 | /* either +<ureal>i or -<ureal>i */ | |
2874 | ||
2875 | idx++; | |
2876 | if (sign == 0) | |
2877 | return SCM_BOOL_F; | |
2878 | if (idx != len) | |
2879 | return SCM_BOOL_F; | |
d956fa6f | 2880 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2881 | |
2882 | case '@': | |
2883 | /* polar input: <real>@<real>. */ | |
2884 | ||
2885 | idx++; | |
2886 | if (idx == len) | |
2887 | return SCM_BOOL_F; | |
2888 | else | |
f872b822 | 2889 | { |
3c9a524f DH |
2890 | int sign; |
2891 | SCM angle; | |
2892 | SCM result; | |
2893 | ||
2894 | c = mem[idx]; | |
2895 | if (c == '+') | |
2896 | { | |
2897 | idx++; | |
2898 | sign = 1; | |
2899 | } | |
2900 | else if (c == '-') | |
2901 | { | |
2902 | idx++; | |
2903 | sign = -1; | |
2904 | } | |
2905 | else | |
2906 | sign = 1; | |
2907 | ||
2908 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2909 | if (scm_is_false (angle)) |
3c9a524f DH |
2910 | return SCM_BOOL_F; |
2911 | if (idx != len) | |
2912 | return SCM_BOOL_F; | |
2913 | ||
73e4de09 | 2914 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
2915 | angle = scm_difference (angle, SCM_UNDEFINED); |
2916 | ||
2917 | result = scm_make_polar (ureal, angle); | |
2918 | return result; | |
f872b822 | 2919 | } |
3c9a524f DH |
2920 | case '+': |
2921 | case '-': | |
2922 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2923 | |
3c9a524f DH |
2924 | idx++; |
2925 | if (idx == len) | |
2926 | return SCM_BOOL_F; | |
2927 | else | |
2928 | { | |
2929 | int sign = (c == '+') ? 1 : -1; | |
2930 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2931 | |
73e4de09 | 2932 | if (scm_is_false (imag)) |
d956fa6f | 2933 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 2934 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 2935 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2936 | |
3c9a524f DH |
2937 | if (idx == len) |
2938 | return SCM_BOOL_F; | |
2939 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2940 | return SCM_BOOL_F; | |
0f2d19dd | 2941 | |
3c9a524f DH |
2942 | idx++; |
2943 | if (idx != len) | |
2944 | return SCM_BOOL_F; | |
0f2d19dd | 2945 | |
1fe5e088 | 2946 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2947 | } |
2948 | default: | |
2949 | return SCM_BOOL_F; | |
2950 | } | |
2951 | } | |
0f2d19dd | 2952 | } |
0f2d19dd JB |
2953 | |
2954 | ||
3c9a524f DH |
2955 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2956 | ||
2957 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2958 | |
0f2d19dd | 2959 | SCM |
2b829bbb KR |
2960 | scm_c_locale_stringn_to_number (const char* mem, size_t len, |
2961 | unsigned int default_radix) | |
0f2d19dd | 2962 | { |
3c9a524f DH |
2963 | unsigned int idx = 0; |
2964 | unsigned int radix = NO_RADIX; | |
2965 | enum t_exactness forced_x = NO_EXACTNESS; | |
2966 | enum t_exactness implicit_x = EXACT; | |
2967 | SCM result; | |
2968 | ||
2969 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2970 | while (idx + 2 < len && mem[idx] == '#') | |
2971 | { | |
2972 | switch (mem[idx + 1]) | |
2973 | { | |
2974 | case 'b': case 'B': | |
2975 | if (radix != NO_RADIX) | |
2976 | return SCM_BOOL_F; | |
2977 | radix = DUAL; | |
2978 | break; | |
2979 | case 'd': case 'D': | |
2980 | if (radix != NO_RADIX) | |
2981 | return SCM_BOOL_F; | |
2982 | radix = DEC; | |
2983 | break; | |
2984 | case 'i': case 'I': | |
2985 | if (forced_x != NO_EXACTNESS) | |
2986 | return SCM_BOOL_F; | |
2987 | forced_x = INEXACT; | |
2988 | break; | |
2989 | case 'e': case 'E': | |
2990 | if (forced_x != NO_EXACTNESS) | |
2991 | return SCM_BOOL_F; | |
2992 | forced_x = EXACT; | |
2993 | break; | |
2994 | case 'o': case 'O': | |
2995 | if (radix != NO_RADIX) | |
2996 | return SCM_BOOL_F; | |
2997 | radix = OCT; | |
2998 | break; | |
2999 | case 'x': case 'X': | |
3000 | if (radix != NO_RADIX) | |
3001 | return SCM_BOOL_F; | |
3002 | radix = HEX; | |
3003 | break; | |
3004 | default: | |
f872b822 | 3005 | return SCM_BOOL_F; |
3c9a524f DH |
3006 | } |
3007 | idx += 2; | |
3008 | } | |
3009 | ||
3010 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
3011 | if (radix == NO_RADIX) | |
3012 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
3013 | else | |
3014 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
3015 | ||
73e4de09 | 3016 | if (scm_is_false (result)) |
3c9a524f | 3017 | return SCM_BOOL_F; |
f872b822 | 3018 | |
3c9a524f | 3019 | switch (forced_x) |
f872b822 | 3020 | { |
3c9a524f DH |
3021 | case EXACT: |
3022 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3023 | return scm_inexact_to_exact (result); |
3024 | else | |
3025 | return result; | |
3026 | case INEXACT: | |
3027 | if (SCM_INEXACTP (result)) | |
3028 | return result; | |
3029 | else | |
3030 | return scm_exact_to_inexact (result); | |
3031 | case NO_EXACTNESS: | |
3032 | default: | |
3033 | if (implicit_x == INEXACT) | |
3034 | { | |
3035 | if (SCM_INEXACTP (result)) | |
3036 | return result; | |
3037 | else | |
3038 | return scm_exact_to_inexact (result); | |
3039 | } | |
3040 | else | |
3041 | return result; | |
f872b822 | 3042 | } |
0f2d19dd JB |
3043 | } |
3044 | ||
3045 | ||
a1ec6916 | 3046 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3047 | (SCM string, SCM radix), |
1e6808ea | 3048 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3049 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3050 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3051 | "is a default radix that may be overridden by an explicit radix\n" | |
3052 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3053 | "supplied, then the default radix is 10. If string is not a\n" | |
3054 | "syntactically valid notation for a number, then\n" | |
3055 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3056 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3057 | { |
3058 | SCM answer; | |
5efd3c7d | 3059 | unsigned int base; |
a6d9e5ab | 3060 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3061 | |
3062 | if (SCM_UNBNDP (radix)) | |
3063 | base = 10; | |
3064 | else | |
3065 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3066 | ||
2b829bbb KR |
3067 | answer = scm_c_locale_stringn_to_number (scm_i_string_chars (string), |
3068 | scm_i_string_length (string), | |
3069 | base); | |
8824ac88 MV |
3070 | scm_remember_upto_here_1 (string); |
3071 | return answer; | |
0f2d19dd | 3072 | } |
1bbd0b84 | 3073 | #undef FUNC_NAME |
3c9a524f DH |
3074 | |
3075 | ||
0f2d19dd JB |
3076 | /*** END strs->nums ***/ |
3077 | ||
5986c47d | 3078 | |
0f2d19dd | 3079 | SCM |
1bbd0b84 | 3080 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3081 | { |
47ae1f0e | 3082 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3083 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3084 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3085 | } |
3086 | ||
0f2d19dd | 3087 | SCM |
f3ae5d60 | 3088 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3089 | { |
73e4de09 | 3090 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3091 | } |
3092 | ||
f3ae5d60 MD |
3093 | SCM |
3094 | scm_complex_equalp (SCM x, SCM y) | |
3095 | { | |
73e4de09 | 3096 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3097 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3098 | } | |
0f2d19dd | 3099 | |
f92e85f7 MV |
3100 | SCM |
3101 | scm_i_fraction_equalp (SCM x, SCM y) | |
3102 | { | |
73e4de09 | 3103 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3104 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3105 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3106 | SCM_FRACTION_DENOMINATOR (y)))) |
3107 | return SCM_BOOL_F; | |
3108 | else | |
3109 | return SCM_BOOL_T; | |
f92e85f7 | 3110 | } |
0f2d19dd JB |
3111 | |
3112 | ||
8507ec80 MV |
3113 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3114 | (SCM x), | |
3115 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3116 | "otherwise.") | |
3117 | #define FUNC_NAME s_scm_number_p | |
3118 | { | |
3119 | return scm_from_bool (SCM_NUMBERP (x)); | |
3120 | } | |
3121 | #undef FUNC_NAME | |
3122 | ||
3123 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3124 | (SCM x), |
942e5b91 | 3125 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3126 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3127 | "values form subsets of the set of complex numbers, i. e. the\n" |
3128 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3129 | "rational or integer number.") | |
8507ec80 | 3130 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3131 | { |
8507ec80 MV |
3132 | /* all numbers are complex. */ |
3133 | return scm_number_p (x); | |
0f2d19dd | 3134 | } |
1bbd0b84 | 3135 | #undef FUNC_NAME |
0f2d19dd | 3136 | |
f92e85f7 MV |
3137 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3138 | (SCM x), | |
3139 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3140 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3141 | "the set of real numbers, i. e. the predicate will also be\n" | |
3142 | "fulfilled if @var{x} is an integer number.") | |
3143 | #define FUNC_NAME s_scm_real_p | |
3144 | { | |
3145 | /* we can't represent irrational numbers. */ | |
3146 | return scm_rational_p (x); | |
3147 | } | |
3148 | #undef FUNC_NAME | |
3149 | ||
3150 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3151 | (SCM x), |
942e5b91 | 3152 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3153 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3154 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3155 | "fulfilled if @var{x} is an integer number.") |
3156 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3157 | { |
e11e83f3 | 3158 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3159 | return SCM_BOOL_T; |
0aacf84e | 3160 | else if (SCM_IMP (x)) |
0f2d19dd | 3161 | return SCM_BOOL_F; |
0aacf84e | 3162 | else if (SCM_BIGP (x)) |
0f2d19dd | 3163 | return SCM_BOOL_T; |
f92e85f7 MV |
3164 | else if (SCM_FRACTIONP (x)) |
3165 | return SCM_BOOL_T; | |
3166 | else if (SCM_REALP (x)) | |
3167 | /* due to their limited precision, all floating point numbers are | |
3168 | rational as well. */ | |
3169 | return SCM_BOOL_T; | |
0aacf84e | 3170 | else |
bb628794 | 3171 | return SCM_BOOL_F; |
0f2d19dd | 3172 | } |
1bbd0b84 | 3173 | #undef FUNC_NAME |
0f2d19dd | 3174 | |
a1ec6916 | 3175 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3176 | (SCM x), |
942e5b91 MG |
3177 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3178 | "else.") | |
1bbd0b84 | 3179 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3180 | { |
3181 | double r; | |
e11e83f3 | 3182 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3183 | return SCM_BOOL_T; |
3184 | if (SCM_IMP (x)) | |
3185 | return SCM_BOOL_F; | |
f872b822 MD |
3186 | if (SCM_BIGP (x)) |
3187 | return SCM_BOOL_T; | |
3c9a524f | 3188 | if (!SCM_INEXACTP (x)) |
f872b822 | 3189 | return SCM_BOOL_F; |
3c9a524f | 3190 | if (SCM_COMPLEXP (x)) |
f872b822 | 3191 | return SCM_BOOL_F; |
5986c47d | 3192 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3193 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3194 | if (r == floor (r)) |
3195 | return SCM_BOOL_T; | |
0f2d19dd JB |
3196 | return SCM_BOOL_F; |
3197 | } | |
1bbd0b84 | 3198 | #undef FUNC_NAME |
0f2d19dd JB |
3199 | |
3200 | ||
a1ec6916 | 3201 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3202 | (SCM x), |
942e5b91 MG |
3203 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3204 | "else.") | |
1bbd0b84 | 3205 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3206 | { |
eb927cb9 MV |
3207 | if (SCM_INEXACTP (x)) |
3208 | return SCM_BOOL_T; | |
3209 | if (SCM_NUMBERP (x)) | |
3210 | return SCM_BOOL_F; | |
3211 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3212 | } |
1bbd0b84 | 3213 | #undef FUNC_NAME |
0f2d19dd JB |
3214 | |
3215 | ||
152f82bf | 3216 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3217 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3218 | SCM |
6e8d25a6 | 3219 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3220 | { |
d8b95e27 | 3221 | again: |
e11e83f3 | 3222 | if (SCM_I_INUMP (x)) |
0aacf84e | 3223 | { |
e11e83f3 MV |
3224 | long xx = SCM_I_INUM (x); |
3225 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3226 | { |
e11e83f3 | 3227 | long yy = SCM_I_INUM (y); |
73e4de09 | 3228 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3229 | } |
3230 | else if (SCM_BIGP (y)) | |
3231 | return SCM_BOOL_F; | |
3232 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3233 | { |
3234 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3235 | to a double and compare. | |
3236 | ||
3237 | But on a 64-bit system an inum is bigger than a double and | |
3238 | casting it to a double (call that dxx) will round. dxx is at | |
3239 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3240 | an integer and fits a long. So we cast yy to a long and | |
3241 | compare with plain xx. | |
3242 | ||
3243 | An alternative (for any size system actually) would be to check | |
3244 | yy is an integer (with floor) and is in range of an inum | |
3245 | (compare against appropriate powers of 2) then test | |
3246 | xx==(long)yy. It's just a matter of which casts/comparisons | |
3247 | might be fastest or easiest for the cpu. */ | |
3248 | ||
3249 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3250 | return scm_from_bool ((double) xx == yy |
3251 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3252 | || xx == (long) yy)); | |
e8c5b1f2 | 3253 | } |
0aacf84e | 3254 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3255 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3256 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3257 | else if (SCM_FRACTIONP (y)) |
3258 | return SCM_BOOL_F; | |
0aacf84e MD |
3259 | else |
3260 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3261 | } |
0aacf84e MD |
3262 | else if (SCM_BIGP (x)) |
3263 | { | |
e11e83f3 | 3264 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3265 | return SCM_BOOL_F; |
3266 | else if (SCM_BIGP (y)) | |
3267 | { | |
3268 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3269 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3270 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3271 | } |
3272 | else if (SCM_REALP (y)) | |
3273 | { | |
3274 | int cmp; | |
3275 | if (xisnan (SCM_REAL_VALUE (y))) | |
3276 | return SCM_BOOL_F; | |
3277 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3278 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3279 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3280 | } |
3281 | else if (SCM_COMPLEXP (y)) | |
3282 | { | |
3283 | int cmp; | |
3284 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3285 | return SCM_BOOL_F; | |
3286 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3287 | return SCM_BOOL_F; | |
3288 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3289 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3290 | return scm_from_bool (0 == cmp); |
0aacf84e | 3291 | } |
f92e85f7 MV |
3292 | else if (SCM_FRACTIONP (y)) |
3293 | return SCM_BOOL_F; | |
0aacf84e MD |
3294 | else |
3295 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3296 | } |
0aacf84e MD |
3297 | else if (SCM_REALP (x)) |
3298 | { | |
e8c5b1f2 | 3299 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3300 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3301 | { |
3302 | /* see comments with inum/real above */ | |
3303 | long yy = SCM_I_INUM (y); | |
3a1b45fd MV |
3304 | return scm_from_bool (xx == (double) yy |
3305 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3306 | || (long) xx == yy)); | |
e8c5b1f2 | 3307 | } |
0aacf84e MD |
3308 | else if (SCM_BIGP (y)) |
3309 | { | |
3310 | int cmp; | |
3311 | if (xisnan (SCM_REAL_VALUE (x))) | |
3312 | return SCM_BOOL_F; | |
3313 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3314 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3315 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3316 | } |
3317 | else if (SCM_REALP (y)) | |
73e4de09 | 3318 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3319 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3320 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3321 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3322 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3323 | { |
3324 | double xx = SCM_REAL_VALUE (x); | |
3325 | if (xisnan (xx)) | |
3326 | return SCM_BOOL_F; | |
3327 | if (xisinf (xx)) | |
73e4de09 | 3328 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3329 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3330 | goto again; | |
3331 | } | |
0aacf84e MD |
3332 | else |
3333 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3334 | } |
0aacf84e MD |
3335 | else if (SCM_COMPLEXP (x)) |
3336 | { | |
e11e83f3 MV |
3337 | if (SCM_I_INUMP (y)) |
3338 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3339 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3340 | else if (SCM_BIGP (y)) | |
3341 | { | |
3342 | int cmp; | |
3343 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3344 | return SCM_BOOL_F; | |
3345 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3346 | return SCM_BOOL_F; | |
3347 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3348 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3349 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3350 | } |
3351 | else if (SCM_REALP (y)) | |
73e4de09 | 3352 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3353 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3354 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3355 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3356 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3357 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3358 | { |
3359 | double xx; | |
3360 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3361 | return SCM_BOOL_F; | |
3362 | xx = SCM_COMPLEX_REAL (x); | |
3363 | if (xisnan (xx)) | |
3364 | return SCM_BOOL_F; | |
3365 | if (xisinf (xx)) | |
73e4de09 | 3366 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3367 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3368 | goto again; | |
3369 | } | |
f92e85f7 MV |
3370 | else |
3371 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3372 | } | |
3373 | else if (SCM_FRACTIONP (x)) | |
3374 | { | |
e11e83f3 | 3375 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3376 | return SCM_BOOL_F; |
3377 | else if (SCM_BIGP (y)) | |
3378 | return SCM_BOOL_F; | |
3379 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3380 | { |
3381 | double yy = SCM_REAL_VALUE (y); | |
3382 | if (xisnan (yy)) | |
3383 | return SCM_BOOL_F; | |
3384 | if (xisinf (yy)) | |
73e4de09 | 3385 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3386 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3387 | goto again; | |
3388 | } | |
f92e85f7 | 3389 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3390 | { |
3391 | double yy; | |
3392 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3393 | return SCM_BOOL_F; | |
3394 | yy = SCM_COMPLEX_REAL (y); | |
3395 | if (xisnan (yy)) | |
3396 | return SCM_BOOL_F; | |
3397 | if (xisinf (yy)) | |
73e4de09 | 3398 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3399 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3400 | goto again; | |
3401 | } | |
f92e85f7 MV |
3402 | else if (SCM_FRACTIONP (y)) |
3403 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3404 | else |
3405 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3406 | } |
0aacf84e | 3407 | else |
f4c627b3 | 3408 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3409 | } |
3410 | ||
3411 | ||
a5f0b599 KR |
3412 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3413 | done are good for inums, but for bignums an answer can almost always be | |
3414 | had by just examining a few high bits of the operands, as done by GMP in | |
3415 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3416 | of the float exponent to take into account. */ | |
3417 | ||
152f82bf | 3418 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3419 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3420 | * "increasing." | |
3421 | */ | |
0f2d19dd | 3422 | SCM |
6e8d25a6 | 3423 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3424 | { |
a5f0b599 | 3425 | again: |
e11e83f3 | 3426 | if (SCM_I_INUMP (x)) |
0aacf84e | 3427 | { |
e11e83f3 MV |
3428 | long xx = SCM_I_INUM (x); |
3429 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3430 | { |
e11e83f3 | 3431 | long yy = SCM_I_INUM (y); |
73e4de09 | 3432 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3433 | } |
3434 | else if (SCM_BIGP (y)) | |
3435 | { | |
3436 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3437 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3438 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3439 | } |
3440 | else if (SCM_REALP (y)) | |
73e4de09 | 3441 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3442 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3443 | { |
3444 | /* "x < a/b" becomes "x*b < a" */ | |
3445 | int_frac: | |
3446 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3447 | y = SCM_FRACTION_NUMERATOR (y); | |
3448 | goto again; | |
3449 | } | |
0aacf84e MD |
3450 | else |
3451 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3452 | } |
0aacf84e MD |
3453 | else if (SCM_BIGP (x)) |
3454 | { | |
e11e83f3 | 3455 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3456 | { |
3457 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3458 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3459 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3460 | } |
3461 | else if (SCM_BIGP (y)) | |
3462 | { | |
3463 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3464 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3465 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3466 | } |
3467 | else if (SCM_REALP (y)) | |
3468 | { | |
3469 | int cmp; | |
3470 | if (xisnan (SCM_REAL_VALUE (y))) | |
3471 | return SCM_BOOL_F; | |
3472 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3473 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3474 | return scm_from_bool (cmp < 0); |
0aacf84e | 3475 | } |
f92e85f7 | 3476 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3477 | goto int_frac; |
0aacf84e MD |
3478 | else |
3479 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3480 | } |
0aacf84e MD |
3481 | else if (SCM_REALP (x)) |
3482 | { | |
e11e83f3 MV |
3483 | if (SCM_I_INUMP (y)) |
3484 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3485 | else if (SCM_BIGP (y)) |
3486 | { | |
3487 | int cmp; | |
3488 | if (xisnan (SCM_REAL_VALUE (x))) | |
3489 | return SCM_BOOL_F; | |
3490 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3491 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3492 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3493 | } |
3494 | else if (SCM_REALP (y)) | |
73e4de09 | 3495 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3496 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3497 | { |
3498 | double xx = SCM_REAL_VALUE (x); | |
3499 | if (xisnan (xx)) | |
3500 | return SCM_BOOL_F; | |
3501 | if (xisinf (xx)) | |
73e4de09 | 3502 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3503 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3504 | goto again; | |
3505 | } | |
f92e85f7 MV |
3506 | else |
3507 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3508 | } | |
3509 | else if (SCM_FRACTIONP (x)) | |
3510 | { | |
e11e83f3 | 3511 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3512 | { |
3513 | /* "a/b < y" becomes "a < y*b" */ | |
3514 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3515 | x = SCM_FRACTION_NUMERATOR (x); | |
3516 | goto again; | |
3517 | } | |
f92e85f7 | 3518 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3519 | { |
3520 | double yy = SCM_REAL_VALUE (y); | |
3521 | if (xisnan (yy)) | |
3522 | return SCM_BOOL_F; | |
3523 | if (xisinf (yy)) | |
73e4de09 | 3524 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3525 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3526 | goto again; | |
3527 | } | |
f92e85f7 | 3528 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3529 | { |
3530 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3531 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3532 | SCM_FRACTION_DENOMINATOR (y)); | |
3533 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3534 | SCM_FRACTION_DENOMINATOR (x)); | |
3535 | x = new_x; | |
3536 | y = new_y; | |
3537 | goto again; | |
3538 | } | |
0aacf84e MD |
3539 | else |
3540 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3541 | } |
0aacf84e | 3542 | else |
f4c627b3 | 3543 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3544 | } |
3545 | ||
3546 | ||
c76b1eaf | 3547 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3548 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3549 | * "decreasing." | |
c76b1eaf | 3550 | */ |
1bbd0b84 | 3551 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3552 | SCM |
3553 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3554 | { |
c76b1eaf MD |
3555 | if (!SCM_NUMBERP (x)) |
3556 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3557 | else if (!SCM_NUMBERP (y)) | |
3558 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3559 | else | |
3560 | return scm_less_p (y, x); | |
0f2d19dd | 3561 | } |
1bbd0b84 | 3562 | #undef FUNC_NAME |
0f2d19dd JB |
3563 | |
3564 | ||
c76b1eaf | 3565 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3566 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3567 | * "non-decreasing." |
3568 | */ | |
1bbd0b84 | 3569 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3570 | SCM |
3571 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3572 | { |
c76b1eaf MD |
3573 | if (!SCM_NUMBERP (x)) |
3574 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3575 | else if (!SCM_NUMBERP (y)) | |
3576 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3577 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3578 | return SCM_BOOL_F; |
c76b1eaf | 3579 | else |
73e4de09 | 3580 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3581 | } |
1bbd0b84 | 3582 | #undef FUNC_NAME |
0f2d19dd JB |
3583 | |
3584 | ||
c76b1eaf | 3585 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3586 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3587 | * "non-increasing." |
3588 | */ | |
1bbd0b84 | 3589 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3590 | SCM |
3591 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3592 | { |
c76b1eaf MD |
3593 | if (!SCM_NUMBERP (x)) |
3594 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3595 | else if (!SCM_NUMBERP (y)) | |
3596 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3597 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3598 | return SCM_BOOL_F; |
c76b1eaf | 3599 | else |
73e4de09 | 3600 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3601 | } |
1bbd0b84 | 3602 | #undef FUNC_NAME |
0f2d19dd JB |
3603 | |
3604 | ||
152f82bf | 3605 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3606 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3607 | * "zero." | |
3608 | */ | |
0f2d19dd | 3609 | SCM |
6e8d25a6 | 3610 | scm_zero_p (SCM z) |
0f2d19dd | 3611 | { |
e11e83f3 | 3612 | if (SCM_I_INUMP (z)) |
bc36d050 | 3613 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3614 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3615 | return SCM_BOOL_F; |
0aacf84e | 3616 | else if (SCM_REALP (z)) |
73e4de09 | 3617 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3618 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3619 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3620 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3621 | else if (SCM_FRACTIONP (z)) |
3622 | return SCM_BOOL_F; | |
0aacf84e | 3623 | else |
c2ff8ab0 | 3624 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3625 | } |
3626 | ||
3627 | ||
152f82bf | 3628 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3629 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3630 | * "zero." | |
3631 | */ | |
0f2d19dd | 3632 | SCM |
6e8d25a6 | 3633 | scm_positive_p (SCM x) |
0f2d19dd | 3634 | { |
e11e83f3 MV |
3635 | if (SCM_I_INUMP (x)) |
3636 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3637 | else if (SCM_BIGP (x)) |
3638 | { | |
3639 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3640 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3641 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3642 | } |
3643 | else if (SCM_REALP (x)) | |
73e4de09 | 3644 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3645 | else if (SCM_FRACTIONP (x)) |
3646 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3647 | else |
c2ff8ab0 | 3648 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3649 | } |
3650 | ||
3651 | ||
152f82bf | 3652 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3653 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3654 | * "zero." | |
3655 | */ | |
0f2d19dd | 3656 | SCM |
6e8d25a6 | 3657 | scm_negative_p (SCM x) |
0f2d19dd | 3658 | { |
e11e83f3 MV |
3659 | if (SCM_I_INUMP (x)) |
3660 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3661 | else if (SCM_BIGP (x)) |
3662 | { | |
3663 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3664 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3665 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3666 | } |
3667 | else if (SCM_REALP (x)) | |
73e4de09 | 3668 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3669 | else if (SCM_FRACTIONP (x)) |
3670 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3671 | else |
c2ff8ab0 | 3672 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3673 | } |
3674 | ||
3675 | ||
2a06f791 KR |
3676 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3677 | required by r5rs. On that basis, for exact/inexact combinations the | |
3678 | exact is converted to inexact to compare and possibly return. This is | |
3679 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3680 | its test, such trouble is not required for min and max. */ | |
3681 | ||
9de33deb | 3682 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3683 | /* "Return the maximum of all parameter values." |
3684 | */ | |
0f2d19dd | 3685 | SCM |
6e8d25a6 | 3686 | scm_max (SCM x, SCM y) |
0f2d19dd | 3687 | { |
0aacf84e MD |
3688 | if (SCM_UNBNDP (y)) |
3689 | { | |
3690 | if (SCM_UNBNDP (x)) | |
3691 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3692 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3693 | return x; |
3694 | else | |
3695 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3696 | } |
f4c627b3 | 3697 | |
e11e83f3 | 3698 | if (SCM_I_INUMP (x)) |
0aacf84e | 3699 | { |
e11e83f3 MV |
3700 | long xx = SCM_I_INUM (x); |
3701 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3702 | { |
e11e83f3 | 3703 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3704 | return (xx < yy) ? y : x; |
3705 | } | |
3706 | else if (SCM_BIGP (y)) | |
3707 | { | |
3708 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3709 | scm_remember_upto_here_1 (y); | |
3710 | return (sgn < 0) ? x : y; | |
3711 | } | |
3712 | else if (SCM_REALP (y)) | |
3713 | { | |
3714 | double z = xx; | |
3715 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3716 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3717 | } |
f92e85f7 MV |
3718 | else if (SCM_FRACTIONP (y)) |
3719 | { | |
e4bc5d6c | 3720 | use_less: |
73e4de09 | 3721 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3722 | } |
0aacf84e MD |
3723 | else |
3724 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3725 | } |
0aacf84e MD |
3726 | else if (SCM_BIGP (x)) |
3727 | { | |
e11e83f3 | 3728 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3729 | { |
3730 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3731 | scm_remember_upto_here_1 (x); | |
3732 | return (sgn < 0) ? y : x; | |
3733 | } | |
3734 | else if (SCM_BIGP (y)) | |
3735 | { | |
3736 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3737 | scm_remember_upto_here_2 (x, y); | |
3738 | return (cmp > 0) ? x : y; | |
3739 | } | |
3740 | else if (SCM_REALP (y)) | |
3741 | { | |
2a06f791 KR |
3742 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3743 | double xx, yy; | |
3744 | big_real: | |
3745 | xx = scm_i_big2dbl (x); | |
3746 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3747 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3748 | } |
f92e85f7 MV |
3749 | else if (SCM_FRACTIONP (y)) |
3750 | { | |
e4bc5d6c | 3751 | goto use_less; |
f92e85f7 | 3752 | } |
0aacf84e MD |
3753 | else |
3754 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3755 | } |
0aacf84e MD |
3756 | else if (SCM_REALP (x)) |
3757 | { | |
e11e83f3 | 3758 | if (SCM_I_INUMP (y)) |
0aacf84e | 3759 | { |
e11e83f3 | 3760 | double z = SCM_I_INUM (y); |
0aacf84e | 3761 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3762 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3763 | } |
3764 | else if (SCM_BIGP (y)) | |
3765 | { | |
b6f8f763 | 3766 | SCM_SWAP (x, y); |
2a06f791 | 3767 | goto big_real; |
0aacf84e MD |
3768 | } |
3769 | else if (SCM_REALP (y)) | |
3770 | { | |
3771 | /* if x==NaN then our explicit check means we return NaN | |
3772 | if y==NaN then ">" is false and we return NaN | |
3773 | calling isnan is unavoidable, since it's the only way to know | |
3774 | which of x or y causes any compares to be false */ | |
3775 | double xx = SCM_REAL_VALUE (x); | |
3776 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3777 | } | |
f92e85f7 MV |
3778 | else if (SCM_FRACTIONP (y)) |
3779 | { | |
3780 | double yy = scm_i_fraction2double (y); | |
3781 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3782 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3783 | } |
3784 | else | |
3785 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3786 | } | |
3787 | else if (SCM_FRACTIONP (x)) | |
3788 | { | |
e11e83f3 | 3789 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3790 | { |
e4bc5d6c | 3791 | goto use_less; |
f92e85f7 MV |
3792 | } |
3793 | else if (SCM_BIGP (y)) | |
3794 | { | |
e4bc5d6c | 3795 | goto use_less; |
f92e85f7 MV |
3796 | } |
3797 | else if (SCM_REALP (y)) | |
3798 | { | |
3799 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3800 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3801 | } |
3802 | else if (SCM_FRACTIONP (y)) | |
3803 | { | |
e4bc5d6c | 3804 | goto use_less; |
f92e85f7 | 3805 | } |
0aacf84e MD |
3806 | else |
3807 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3808 | } |
0aacf84e | 3809 | else |
f4c627b3 | 3810 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3811 | } |
3812 | ||
3813 | ||
9de33deb | 3814 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3815 | /* "Return the minium of all parameter values." |
3816 | */ | |
0f2d19dd | 3817 | SCM |
6e8d25a6 | 3818 | scm_min (SCM x, SCM y) |
0f2d19dd | 3819 | { |
0aacf84e MD |
3820 | if (SCM_UNBNDP (y)) |
3821 | { | |
3822 | if (SCM_UNBNDP (x)) | |
3823 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3824 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3825 | return x; |
3826 | else | |
3827 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3828 | } |
f4c627b3 | 3829 | |
e11e83f3 | 3830 | if (SCM_I_INUMP (x)) |
0aacf84e | 3831 | { |
e11e83f3 MV |
3832 | long xx = SCM_I_INUM (x); |
3833 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3834 | { |
e11e83f3 | 3835 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3836 | return (xx < yy) ? x : y; |
3837 | } | |
3838 | else if (SCM_BIGP (y)) | |
3839 | { | |
3840 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3841 | scm_remember_upto_here_1 (y); | |
3842 | return (sgn < 0) ? y : x; | |
3843 | } | |
3844 | else if (SCM_REALP (y)) | |
3845 | { | |
3846 | double z = xx; | |
3847 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3848 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3849 | } |
f92e85f7 MV |
3850 | else if (SCM_FRACTIONP (y)) |
3851 | { | |
e4bc5d6c | 3852 | use_less: |
73e4de09 | 3853 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 3854 | } |
0aacf84e MD |
3855 | else |
3856 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3857 | } |
0aacf84e MD |
3858 | else if (SCM_BIGP (x)) |
3859 | { | |
e11e83f3 | 3860 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3861 | { |
3862 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3863 | scm_remember_upto_here_1 (x); | |
3864 | return (sgn < 0) ? x : y; | |
3865 | } | |
3866 | else if (SCM_BIGP (y)) | |
3867 | { | |
3868 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3869 | scm_remember_upto_here_2 (x, y); | |
3870 | return (cmp > 0) ? y : x; | |
3871 | } | |
3872 | else if (SCM_REALP (y)) | |
3873 | { | |
2a06f791 KR |
3874 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
3875 | double xx, yy; | |
3876 | big_real: | |
3877 | xx = scm_i_big2dbl (x); | |
3878 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3879 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 3880 | } |
f92e85f7 MV |
3881 | else if (SCM_FRACTIONP (y)) |
3882 | { | |
e4bc5d6c | 3883 | goto use_less; |
f92e85f7 | 3884 | } |
0aacf84e MD |
3885 | else |
3886 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3887 | } |
0aacf84e MD |
3888 | else if (SCM_REALP (x)) |
3889 | { | |
e11e83f3 | 3890 | if (SCM_I_INUMP (y)) |
0aacf84e | 3891 | { |
e11e83f3 | 3892 | double z = SCM_I_INUM (y); |
0aacf84e | 3893 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3894 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
3895 | } |
3896 | else if (SCM_BIGP (y)) | |
3897 | { | |
b6f8f763 | 3898 | SCM_SWAP (x, y); |
2a06f791 | 3899 | goto big_real; |
0aacf84e MD |
3900 | } |
3901 | else if (SCM_REALP (y)) | |
3902 | { | |
3903 | /* if x==NaN then our explicit check means we return NaN | |
3904 | if y==NaN then "<" is false and we return NaN | |
3905 | calling isnan is unavoidable, since it's the only way to know | |
3906 | which of x or y causes any compares to be false */ | |
3907 | double xx = SCM_REAL_VALUE (x); | |
3908 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3909 | } | |
f92e85f7 MV |
3910 | else if (SCM_FRACTIONP (y)) |
3911 | { | |
3912 | double yy = scm_i_fraction2double (y); | |
3913 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3914 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 3915 | } |
0aacf84e MD |
3916 | else |
3917 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3918 | } |
f92e85f7 MV |
3919 | else if (SCM_FRACTIONP (x)) |
3920 | { | |
e11e83f3 | 3921 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3922 | { |
e4bc5d6c | 3923 | goto use_less; |
f92e85f7 MV |
3924 | } |
3925 | else if (SCM_BIGP (y)) | |
3926 | { | |
e4bc5d6c | 3927 | goto use_less; |
f92e85f7 MV |
3928 | } |
3929 | else if (SCM_REALP (y)) | |
3930 | { | |
3931 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3932 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
3933 | } |
3934 | else if (SCM_FRACTIONP (y)) | |
3935 | { | |
e4bc5d6c | 3936 | goto use_less; |
f92e85f7 MV |
3937 | } |
3938 | else | |
3939 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3940 | } | |
0aacf84e | 3941 | else |
f4c627b3 | 3942 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3943 | } |
3944 | ||
3945 | ||
9de33deb | 3946 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3947 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3948 | * "any parameters." | |
3949 | */ | |
0f2d19dd | 3950 | SCM |
6e8d25a6 | 3951 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3952 | { |
ca46fb90 RB |
3953 | if (SCM_UNBNDP (y)) |
3954 | { | |
3955 | if (SCM_NUMBERP (x)) return x; | |
3956 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3957 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3958 | } |
c209c88e | 3959 | |
e11e83f3 | 3960 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3961 | { |
e11e83f3 | 3962 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3963 | { |
e11e83f3 MV |
3964 | long xx = SCM_I_INUM (x); |
3965 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 3966 | long int z = xx + yy; |
d956fa6f | 3967 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
3968 | } |
3969 | else if (SCM_BIGP (y)) | |
3970 | { | |
3971 | SCM_SWAP (x, y); | |
3972 | goto add_big_inum; | |
3973 | } | |
3974 | else if (SCM_REALP (y)) | |
3975 | { | |
e11e83f3 | 3976 | long int xx = SCM_I_INUM (x); |
55f26379 | 3977 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
3978 | } |
3979 | else if (SCM_COMPLEXP (y)) | |
3980 | { | |
e11e83f3 | 3981 | long int xx = SCM_I_INUM (x); |
8507ec80 | 3982 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
3983 | SCM_COMPLEX_IMAG (y)); |
3984 | } | |
f92e85f7 | 3985 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3986 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3987 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3988 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3989 | else |
3990 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3991 | } else if (SCM_BIGP (x)) |
3992 | { | |
e11e83f3 | 3993 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3994 | { |
3995 | long int inum; | |
3996 | int bigsgn; | |
3997 | add_big_inum: | |
e11e83f3 | 3998 | inum = SCM_I_INUM (y); |
0aacf84e MD |
3999 | if (inum == 0) |
4000 | return x; | |
4001 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4002 | if (inum < 0) | |
4003 | { | |
4004 | SCM result = scm_i_mkbig (); | |
4005 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
4006 | scm_remember_upto_here_1 (x); | |
4007 | /* we know the result will have to be a bignum */ | |
4008 | if (bigsgn == -1) | |
4009 | return result; | |
4010 | return scm_i_normbig (result); | |
4011 | } | |
4012 | else | |
4013 | { | |
4014 | SCM result = scm_i_mkbig (); | |
4015 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4016 | scm_remember_upto_here_1 (x); | |
4017 | /* we know the result will have to be a bignum */ | |
4018 | if (bigsgn == 1) | |
4019 | return result; | |
4020 | return scm_i_normbig (result); | |
4021 | } | |
4022 | } | |
4023 | else if (SCM_BIGP (y)) | |
4024 | { | |
4025 | SCM result = scm_i_mkbig (); | |
4026 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4027 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4028 | mpz_add (SCM_I_BIG_MPZ (result), | |
4029 | SCM_I_BIG_MPZ (x), | |
4030 | SCM_I_BIG_MPZ (y)); | |
4031 | scm_remember_upto_here_2 (x, y); | |
4032 | /* we know the result will have to be a bignum */ | |
4033 | if (sgn_x == sgn_y) | |
4034 | return result; | |
4035 | return scm_i_normbig (result); | |
4036 | } | |
4037 | else if (SCM_REALP (y)) | |
4038 | { | |
4039 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4040 | scm_remember_upto_here_1 (x); | |
55f26379 | 4041 | return scm_from_double (result); |
0aacf84e MD |
4042 | } |
4043 | else if (SCM_COMPLEXP (y)) | |
4044 | { | |
4045 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4046 | + SCM_COMPLEX_REAL (y)); | |
4047 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4048 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4049 | } |
f92e85f7 | 4050 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4051 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4052 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4053 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4054 | else |
4055 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4056 | } |
0aacf84e MD |
4057 | else if (SCM_REALP (x)) |
4058 | { | |
e11e83f3 | 4059 | if (SCM_I_INUMP (y)) |
55f26379 | 4060 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4061 | else if (SCM_BIGP (y)) |
4062 | { | |
4063 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4064 | scm_remember_upto_here_1 (y); | |
55f26379 | 4065 | return scm_from_double (result); |
0aacf84e MD |
4066 | } |
4067 | else if (SCM_REALP (y)) | |
55f26379 | 4068 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4069 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4070 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4071 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4072 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4073 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4074 | else |
4075 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4076 | } |
0aacf84e MD |
4077 | else if (SCM_COMPLEXP (x)) |
4078 | { | |
e11e83f3 | 4079 | if (SCM_I_INUMP (y)) |
8507ec80 | 4080 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4081 | SCM_COMPLEX_IMAG (x)); |
4082 | else if (SCM_BIGP (y)) | |
4083 | { | |
4084 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4085 | + SCM_COMPLEX_REAL (x)); | |
4086 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4087 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4088 | } |
4089 | else if (SCM_REALP (y)) | |
8507ec80 | 4090 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4091 | SCM_COMPLEX_IMAG (x)); |
4092 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4093 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4094 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4095 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4096 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4097 | SCM_COMPLEX_IMAG (x)); |
4098 | else | |
4099 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4100 | } | |
4101 | else if (SCM_FRACTIONP (x)) | |
4102 | { | |
e11e83f3 | 4103 | if (SCM_I_INUMP (y)) |
cba42c93 | 4104 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4105 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4106 | SCM_FRACTION_DENOMINATOR (x)); | |
4107 | else if (SCM_BIGP (y)) | |
cba42c93 | 4108 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4109 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4110 | SCM_FRACTION_DENOMINATOR (x)); | |
4111 | else if (SCM_REALP (y)) | |
55f26379 | 4112 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4113 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4114 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4115 | SCM_COMPLEX_IMAG (y)); |
4116 | else if (SCM_FRACTIONP (y)) | |
4117 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4118 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4119 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4120 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4121 | else |
4122 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4123 | } |
0aacf84e | 4124 | else |
98cb6e75 | 4125 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4126 | } |
4127 | ||
4128 | ||
40882e3d KR |
4129 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4130 | (SCM x), | |
4131 | "Return @math{@var{x}+1}.") | |
4132 | #define FUNC_NAME s_scm_oneplus | |
4133 | { | |
4134 | return scm_sum (x, SCM_I_MAKINUM (1)); | |
4135 | } | |
4136 | #undef FUNC_NAME | |
4137 | ||
4138 | ||
9de33deb | 4139 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
4140 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
4141 | * the sum of all but the first argument are subtracted from the first | |
4142 | * argument. */ | |
c05e97b7 | 4143 | #define FUNC_NAME s_difference |
0f2d19dd | 4144 | SCM |
6e8d25a6 | 4145 | scm_difference (SCM x, SCM y) |
0f2d19dd | 4146 | { |
ca46fb90 RB |
4147 | if (SCM_UNBNDP (y)) |
4148 | { | |
4149 | if (SCM_UNBNDP (x)) | |
4150 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4151 | else | |
e11e83f3 | 4152 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4153 | { |
e11e83f3 | 4154 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4155 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4156 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4157 | else |
4158 | return scm_i_long2big (xx); | |
4159 | } | |
4160 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4161 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4162 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4163 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4164 | else if (SCM_REALP (x)) | |
55f26379 | 4165 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4166 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4167 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4168 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4169 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4170 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4171 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4172 | else |
4173 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4174 | } |
ca46fb90 | 4175 | |
e11e83f3 | 4176 | if (SCM_I_INUMP (x)) |
0aacf84e | 4177 | { |
e11e83f3 | 4178 | if (SCM_I_INUMP (y)) |
0aacf84e | 4179 | { |
e11e83f3 MV |
4180 | long int xx = SCM_I_INUM (x); |
4181 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4182 | long int z = xx - yy; |
4183 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4184 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4185 | else |
4186 | return scm_i_long2big (z); | |
4187 | } | |
4188 | else if (SCM_BIGP (y)) | |
4189 | { | |
4190 | /* inum-x - big-y */ | |
e11e83f3 | 4191 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4192 | |
0aacf84e MD |
4193 | if (xx == 0) |
4194 | return scm_i_clonebig (y, 0); | |
4195 | else | |
4196 | { | |
4197 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4198 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4199 | |
0aacf84e MD |
4200 | if (xx >= 0) |
4201 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4202 | else | |
4203 | { | |
4204 | /* x - y == -(y + -x) */ | |
4205 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4206 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4207 | } | |
4208 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4209 | |
0aacf84e MD |
4210 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4211 | /* we know the result will have to be a bignum */ | |
4212 | return result; | |
4213 | else | |
4214 | return scm_i_normbig (result); | |
4215 | } | |
4216 | } | |
4217 | else if (SCM_REALP (y)) | |
4218 | { | |
e11e83f3 | 4219 | long int xx = SCM_I_INUM (x); |
55f26379 | 4220 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4221 | } |
4222 | else if (SCM_COMPLEXP (y)) | |
4223 | { | |
e11e83f3 | 4224 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4225 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4226 | - SCM_COMPLEX_IMAG (y)); |
4227 | } | |
f92e85f7 MV |
4228 | else if (SCM_FRACTIONP (y)) |
4229 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4230 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4231 | SCM_FRACTION_NUMERATOR (y)), |
4232 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4233 | else |
4234 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4235 | } |
0aacf84e MD |
4236 | else if (SCM_BIGP (x)) |
4237 | { | |
e11e83f3 | 4238 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4239 | { |
4240 | /* big-x - inum-y */ | |
e11e83f3 | 4241 | long yy = SCM_I_INUM (y); |
0aacf84e | 4242 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4243 | |
0aacf84e MD |
4244 | scm_remember_upto_here_1 (x); |
4245 | if (sgn_x == 0) | |
c71b0706 MV |
4246 | return (SCM_FIXABLE (-yy) ? |
4247 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4248 | else |
4249 | { | |
4250 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4251 | |
708f22c6 KR |
4252 | if (yy >= 0) |
4253 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4254 | else | |
4255 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4256 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4257 | |
0aacf84e MD |
4258 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4259 | /* we know the result will have to be a bignum */ | |
4260 | return result; | |
4261 | else | |
4262 | return scm_i_normbig (result); | |
4263 | } | |
4264 | } | |
4265 | else if (SCM_BIGP (y)) | |
4266 | { | |
4267 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4268 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4269 | SCM result = scm_i_mkbig (); | |
4270 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4271 | SCM_I_BIG_MPZ (x), | |
4272 | SCM_I_BIG_MPZ (y)); | |
4273 | scm_remember_upto_here_2 (x, y); | |
4274 | /* we know the result will have to be a bignum */ | |
4275 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4276 | return result; | |
4277 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4278 | return result; | |
4279 | return scm_i_normbig (result); | |
4280 | } | |
4281 | else if (SCM_REALP (y)) | |
4282 | { | |
4283 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4284 | scm_remember_upto_here_1 (x); | |
55f26379 | 4285 | return scm_from_double (result); |
0aacf84e MD |
4286 | } |
4287 | else if (SCM_COMPLEXP (y)) | |
4288 | { | |
4289 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4290 | - SCM_COMPLEX_REAL (y)); | |
4291 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4292 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4293 | } |
f92e85f7 | 4294 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4295 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4296 | SCM_FRACTION_NUMERATOR (y)), |
4297 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4298 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4299 | } |
0aacf84e MD |
4300 | else if (SCM_REALP (x)) |
4301 | { | |
e11e83f3 | 4302 | if (SCM_I_INUMP (y)) |
55f26379 | 4303 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4304 | else if (SCM_BIGP (y)) |
4305 | { | |
4306 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4307 | scm_remember_upto_here_1 (x); | |
55f26379 | 4308 | return scm_from_double (result); |
0aacf84e MD |
4309 | } |
4310 | else if (SCM_REALP (y)) | |
55f26379 | 4311 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4312 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4313 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4314 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4315 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4316 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4317 | else |
4318 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4319 | } |
0aacf84e MD |
4320 | else if (SCM_COMPLEXP (x)) |
4321 | { | |
e11e83f3 | 4322 | if (SCM_I_INUMP (y)) |
8507ec80 | 4323 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4324 | SCM_COMPLEX_IMAG (x)); |
4325 | else if (SCM_BIGP (y)) | |
4326 | { | |
4327 | double real_part = (SCM_COMPLEX_REAL (x) | |
4328 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4329 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4330 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4331 | } |
4332 | else if (SCM_REALP (y)) | |
8507ec80 | 4333 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4334 | SCM_COMPLEX_IMAG (x)); |
4335 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4336 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4337 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4338 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4339 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4340 | SCM_COMPLEX_IMAG (x)); |
4341 | else | |
4342 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4343 | } | |
4344 | else if (SCM_FRACTIONP (x)) | |
4345 | { | |
e11e83f3 | 4346 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4347 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4348 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4349 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4350 | SCM_FRACTION_DENOMINATOR (x)); | |
4351 | else if (SCM_BIGP (y)) | |
cba42c93 | 4352 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4353 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4354 | SCM_FRACTION_DENOMINATOR (x)); | |
4355 | else if (SCM_REALP (y)) | |
55f26379 | 4356 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4357 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4358 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4359 | -SCM_COMPLEX_IMAG (y)); |
4360 | else if (SCM_FRACTIONP (y)) | |
4361 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4362 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4363 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4364 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4365 | else |
4366 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4367 | } |
0aacf84e | 4368 | else |
98cb6e75 | 4369 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4370 | } |
c05e97b7 | 4371 | #undef FUNC_NAME |
0f2d19dd | 4372 | |
ca46fb90 | 4373 | |
40882e3d KR |
4374 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4375 | (SCM x), | |
4376 | "Return @math{@var{x}-1}.") | |
4377 | #define FUNC_NAME s_scm_oneminus | |
4378 | { | |
4379 | return scm_difference (x, SCM_I_MAKINUM (1)); | |
4380 | } | |
4381 | #undef FUNC_NAME | |
4382 | ||
4383 | ||
9de33deb | 4384 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4385 | /* "Return the product of all arguments. If called without arguments,\n" |
4386 | * "1 is returned." | |
4387 | */ | |
0f2d19dd | 4388 | SCM |
6e8d25a6 | 4389 | scm_product (SCM x, SCM y) |
0f2d19dd | 4390 | { |
0aacf84e MD |
4391 | if (SCM_UNBNDP (y)) |
4392 | { | |
4393 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4394 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4395 | else if (SCM_NUMBERP (x)) |
4396 | return x; | |
4397 | else | |
4398 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4399 | } |
ca46fb90 | 4400 | |
e11e83f3 | 4401 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
4402 | { |
4403 | long xx; | |
f4c627b3 | 4404 | |
0aacf84e | 4405 | intbig: |
e11e83f3 | 4406 | xx = SCM_I_INUM (x); |
f4c627b3 | 4407 | |
0aacf84e MD |
4408 | switch (xx) |
4409 | { | |
ca46fb90 RB |
4410 | case 0: return x; break; |
4411 | case 1: return y; break; | |
0aacf84e | 4412 | } |
f4c627b3 | 4413 | |
e11e83f3 | 4414 | if (SCM_I_INUMP (y)) |
0aacf84e | 4415 | { |
e11e83f3 | 4416 | long yy = SCM_I_INUM (y); |
0aacf84e | 4417 | long kk = xx * yy; |
d956fa6f | 4418 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4419 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4420 | return k; |
4421 | else | |
4422 | { | |
4423 | SCM result = scm_i_long2big (xx); | |
4424 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4425 | return scm_i_normbig (result); | |
4426 | } | |
4427 | } | |
4428 | else if (SCM_BIGP (y)) | |
4429 | { | |
4430 | SCM result = scm_i_mkbig (); | |
4431 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4432 | scm_remember_upto_here_1 (y); | |
4433 | return result; | |
4434 | } | |
4435 | else if (SCM_REALP (y)) | |
55f26379 | 4436 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4437 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4438 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4439 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4440 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4441 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4442 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4443 | else |
4444 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4445 | } |
0aacf84e MD |
4446 | else if (SCM_BIGP (x)) |
4447 | { | |
e11e83f3 | 4448 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4449 | { |
4450 | SCM_SWAP (x, y); | |
4451 | goto intbig; | |
4452 | } | |
4453 | else if (SCM_BIGP (y)) | |
4454 | { | |
4455 | SCM result = scm_i_mkbig (); | |
4456 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4457 | SCM_I_BIG_MPZ (x), | |
4458 | SCM_I_BIG_MPZ (y)); | |
4459 | scm_remember_upto_here_2 (x, y); | |
4460 | return result; | |
4461 | } | |
4462 | else if (SCM_REALP (y)) | |
4463 | { | |
4464 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4465 | scm_remember_upto_here_1 (x); | |
55f26379 | 4466 | return scm_from_double (result); |
0aacf84e MD |
4467 | } |
4468 | else if (SCM_COMPLEXP (y)) | |
4469 | { | |
4470 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4471 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4472 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4473 | z * SCM_COMPLEX_IMAG (y)); |
4474 | } | |
f92e85f7 | 4475 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4476 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4477 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4478 | else |
4479 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4480 | } |
0aacf84e MD |
4481 | else if (SCM_REALP (x)) |
4482 | { | |
e11e83f3 | 4483 | if (SCM_I_INUMP (y)) |
55f26379 | 4484 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); |
0aacf84e MD |
4485 | else if (SCM_BIGP (y)) |
4486 | { | |
4487 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4488 | scm_remember_upto_here_1 (y); | |
55f26379 | 4489 | return scm_from_double (result); |
0aacf84e MD |
4490 | } |
4491 | else if (SCM_REALP (y)) | |
55f26379 | 4492 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4493 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4494 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4495 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4496 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4497 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4498 | else |
4499 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4500 | } |
0aacf84e MD |
4501 | else if (SCM_COMPLEXP (x)) |
4502 | { | |
e11e83f3 | 4503 | if (SCM_I_INUMP (y)) |
8507ec80 | 4504 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), |
e11e83f3 | 4505 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4506 | else if (SCM_BIGP (y)) |
4507 | { | |
4508 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4509 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4510 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4511 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4512 | } |
4513 | else if (SCM_REALP (y)) | |
8507ec80 | 4514 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4515 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4516 | else if (SCM_COMPLEXP (y)) | |
4517 | { | |
8507ec80 | 4518 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4519 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4520 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4521 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4522 | } | |
f92e85f7 MV |
4523 | else if (SCM_FRACTIONP (y)) |
4524 | { | |
4525 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4526 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4527 | yy * SCM_COMPLEX_IMAG (x)); |
4528 | } | |
4529 | else | |
4530 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4531 | } | |
4532 | else if (SCM_FRACTIONP (x)) | |
4533 | { | |
e11e83f3 | 4534 | if (SCM_I_INUMP (y)) |
cba42c93 | 4535 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4536 | SCM_FRACTION_DENOMINATOR (x)); |
4537 | else if (SCM_BIGP (y)) | |
cba42c93 | 4538 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4539 | SCM_FRACTION_DENOMINATOR (x)); |
4540 | else if (SCM_REALP (y)) | |
55f26379 | 4541 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4542 | else if (SCM_COMPLEXP (y)) |
4543 | { | |
4544 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4545 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4546 | xx * SCM_COMPLEX_IMAG (y)); |
4547 | } | |
4548 | else if (SCM_FRACTIONP (y)) | |
4549 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4550 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4551 | SCM_FRACTION_NUMERATOR (y)), |
4552 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4553 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4554 | else |
4555 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4556 | } |
0aacf84e | 4557 | else |
f4c627b3 | 4558 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4559 | } |
4560 | ||
7351e207 MV |
4561 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4562 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4563 | #define ALLOW_DIVIDE_BY_ZERO | |
4564 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4565 | #endif | |
0f2d19dd | 4566 | |
ba74ef4e MV |
4567 | /* The code below for complex division is adapted from the GNU |
4568 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4569 | this copyright: */ | |
4570 | ||
4571 | /**************************************************************** | |
4572 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4573 | ||
4574 | Permission to use, copy, modify, and distribute this software | |
4575 | and its documentation for any purpose and without fee is hereby | |
4576 | granted, provided that the above copyright notice appear in all | |
4577 | copies and that both that the copyright notice and this | |
4578 | permission notice and warranty disclaimer appear in supporting | |
4579 | documentation, and that the names of AT&T Bell Laboratories or | |
4580 | Bellcore or any of their entities not be used in advertising or | |
4581 | publicity pertaining to distribution of the software without | |
4582 | specific, written prior permission. | |
4583 | ||
4584 | AT&T and Bellcore disclaim all warranties with regard to this | |
4585 | software, including all implied warranties of merchantability | |
4586 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4587 | any special, indirect or consequential damages or any damages | |
4588 | whatsoever resulting from loss of use, data or profits, whether | |
4589 | in an action of contract, negligence or other tortious action, | |
4590 | arising out of or in connection with the use or performance of | |
4591 | this software. | |
4592 | ****************************************************************/ | |
4593 | ||
9de33deb | 4594 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4595 | /* Divide the first argument by the product of the remaining |
4596 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4597 | returned. */ | |
c05e97b7 | 4598 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4599 | static SCM |
4600 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4601 | { |
f8de44c1 DH |
4602 | double a; |
4603 | ||
0aacf84e MD |
4604 | if (SCM_UNBNDP (y)) |
4605 | { | |
4606 | if (SCM_UNBNDP (x)) | |
4607 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4608 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4609 | { |
e11e83f3 | 4610 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4611 | if (xx == 1 || xx == -1) |
4612 | return x; | |
7351e207 | 4613 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4614 | else if (xx == 0) |
4615 | scm_num_overflow (s_divide); | |
7351e207 | 4616 | #endif |
0aacf84e | 4617 | else |
f92e85f7 MV |
4618 | { |
4619 | if (inexact) | |
55f26379 | 4620 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4621 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4622 | } |
0aacf84e MD |
4623 | } |
4624 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4625 | { |
4626 | if (inexact) | |
55f26379 | 4627 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4628 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4629 | } |
0aacf84e MD |
4630 | else if (SCM_REALP (x)) |
4631 | { | |
4632 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4633 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4634 | if (xx == 0.0) |
4635 | scm_num_overflow (s_divide); | |
4636 | else | |
7351e207 | 4637 | #endif |
55f26379 | 4638 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4639 | } |
4640 | else if (SCM_COMPLEXP (x)) | |
4641 | { | |
4642 | double r = SCM_COMPLEX_REAL (x); | |
4643 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4644 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4645 | { |
4646 | double t = r / i; | |
4647 | double d = i * (1.0 + t * t); | |
8507ec80 | 4648 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4649 | } |
4650 | else | |
4651 | { | |
4652 | double t = i / r; | |
4653 | double d = r * (1.0 + t * t); | |
8507ec80 | 4654 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4655 | } |
4656 | } | |
f92e85f7 | 4657 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4658 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4659 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4660 | else |
4661 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4662 | } |
f8de44c1 | 4663 | |
e11e83f3 | 4664 | if (SCM_I_INUMP (x)) |
0aacf84e | 4665 | { |
e11e83f3 MV |
4666 | long xx = SCM_I_INUM (x); |
4667 | if (SCM_I_INUMP (y)) | |
0aacf84e | 4668 | { |
e11e83f3 | 4669 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4670 | if (yy == 0) |
4671 | { | |
7351e207 | 4672 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4673 | scm_num_overflow (s_divide); |
7351e207 | 4674 | #else |
55f26379 | 4675 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4676 | #endif |
0aacf84e MD |
4677 | } |
4678 | else if (xx % yy != 0) | |
f92e85f7 MV |
4679 | { |
4680 | if (inexact) | |
55f26379 | 4681 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4682 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4683 | } |
0aacf84e MD |
4684 | else |
4685 | { | |
4686 | long z = xx / yy; | |
4687 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4688 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4689 | else |
4690 | return scm_i_long2big (z); | |
4691 | } | |
f872b822 | 4692 | } |
0aacf84e | 4693 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4694 | { |
4695 | if (inexact) | |
55f26379 | 4696 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4697 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4698 | } |
0aacf84e MD |
4699 | else if (SCM_REALP (y)) |
4700 | { | |
4701 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4702 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4703 | if (yy == 0.0) |
4704 | scm_num_overflow (s_divide); | |
4705 | else | |
7351e207 | 4706 | #endif |
55f26379 | 4707 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4708 | } |
0aacf84e MD |
4709 | else if (SCM_COMPLEXP (y)) |
4710 | { | |
4711 | a = xx; | |
4712 | complex_div: /* y _must_ be a complex number */ | |
4713 | { | |
4714 | double r = SCM_COMPLEX_REAL (y); | |
4715 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4716 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4717 | { |
4718 | double t = r / i; | |
4719 | double d = i * (1.0 + t * t); | |
8507ec80 | 4720 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4721 | } |
4722 | else | |
4723 | { | |
4724 | double t = i / r; | |
4725 | double d = r * (1.0 + t * t); | |
8507ec80 | 4726 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4727 | } |
4728 | } | |
4729 | } | |
f92e85f7 MV |
4730 | else if (SCM_FRACTIONP (y)) |
4731 | /* a / b/c = ac / b */ | |
cba42c93 | 4732 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4733 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4734 | else |
4735 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4736 | } |
0aacf84e MD |
4737 | else if (SCM_BIGP (x)) |
4738 | { | |
e11e83f3 | 4739 | if (SCM_I_INUMP (y)) |
0aacf84e | 4740 | { |
e11e83f3 | 4741 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4742 | if (yy == 0) |
4743 | { | |
7351e207 | 4744 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4745 | scm_num_overflow (s_divide); |
7351e207 | 4746 | #else |
0aacf84e MD |
4747 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4748 | scm_remember_upto_here_1 (x); | |
4749 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4750 | #endif |
0aacf84e MD |
4751 | } |
4752 | else if (yy == 1) | |
4753 | return x; | |
4754 | else | |
4755 | { | |
4756 | /* FIXME: HMM, what are the relative performance issues here? | |
4757 | We need to test. Is it faster on average to test | |
4758 | divisible_p, then perform whichever operation, or is it | |
4759 | faster to perform the integer div opportunistically and | |
4760 | switch to real if there's a remainder? For now we take the | |
4761 | middle ground: test, then if divisible, use the faster div | |
4762 | func. */ | |
4763 | ||
4764 | long abs_yy = yy < 0 ? -yy : yy; | |
4765 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4766 | ||
4767 | if (divisible_p) | |
4768 | { | |
4769 | SCM result = scm_i_mkbig (); | |
4770 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4771 | scm_remember_upto_here_1 (x); | |
4772 | if (yy < 0) | |
4773 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4774 | return scm_i_normbig (result); | |
4775 | } | |
4776 | else | |
f92e85f7 MV |
4777 | { |
4778 | if (inexact) | |
55f26379 | 4779 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4780 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4781 | } |
0aacf84e MD |
4782 | } |
4783 | } | |
4784 | else if (SCM_BIGP (y)) | |
4785 | { | |
4786 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4787 | if (y_is_zero) | |
4788 | { | |
ca46fb90 | 4789 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4790 | scm_num_overflow (s_divide); |
f872b822 | 4791 | #else |
0aacf84e MD |
4792 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4793 | scm_remember_upto_here_1 (x); | |
4794 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4795 | #endif |
0aacf84e MD |
4796 | } |
4797 | else | |
4798 | { | |
4799 | /* big_x / big_y */ | |
23f2b9a3 KR |
4800 | if (inexact) |
4801 | { | |
4802 | /* It's easily possible for the ratio x/y to fit a double | |
4803 | but one or both x and y be too big to fit a double, | |
4804 | hence the use of mpq_get_d rather than converting and | |
4805 | dividing. */ | |
4806 | mpq_t q; | |
4807 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
4808 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
4809 | return scm_from_double (mpq_get_d (q)); | |
4810 | } | |
4811 | else | |
4812 | { | |
4813 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4814 | SCM_I_BIG_MPZ (y)); | |
4815 | if (divisible_p) | |
4816 | { | |
4817 | SCM result = scm_i_mkbig (); | |
4818 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4819 | SCM_I_BIG_MPZ (x), | |
4820 | SCM_I_BIG_MPZ (y)); | |
4821 | scm_remember_upto_here_2 (x, y); | |
4822 | return scm_i_normbig (result); | |
4823 | } | |
4824 | else | |
4825 | return scm_i_make_ratio (x, y); | |
4826 | } | |
0aacf84e MD |
4827 | } |
4828 | } | |
4829 | else if (SCM_REALP (y)) | |
4830 | { | |
4831 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4832 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4833 | if (yy == 0.0) |
4834 | scm_num_overflow (s_divide); | |
4835 | else | |
7351e207 | 4836 | #endif |
55f26379 | 4837 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
4838 | } |
4839 | else if (SCM_COMPLEXP (y)) | |
4840 | { | |
4841 | a = scm_i_big2dbl (x); | |
4842 | goto complex_div; | |
4843 | } | |
f92e85f7 | 4844 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4845 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4846 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4847 | else |
4848 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4849 | } |
0aacf84e MD |
4850 | else if (SCM_REALP (x)) |
4851 | { | |
4852 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 4853 | if (SCM_I_INUMP (y)) |
0aacf84e | 4854 | { |
e11e83f3 | 4855 | long int yy = SCM_I_INUM (y); |
7351e207 | 4856 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4857 | if (yy == 0) |
4858 | scm_num_overflow (s_divide); | |
4859 | else | |
7351e207 | 4860 | #endif |
55f26379 | 4861 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
4862 | } |
4863 | else if (SCM_BIGP (y)) | |
4864 | { | |
4865 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4866 | scm_remember_upto_here_1 (y); | |
55f26379 | 4867 | return scm_from_double (rx / dby); |
0aacf84e MD |
4868 | } |
4869 | else if (SCM_REALP (y)) | |
4870 | { | |
4871 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4872 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4873 | if (yy == 0.0) |
4874 | scm_num_overflow (s_divide); | |
4875 | else | |
7351e207 | 4876 | #endif |
55f26379 | 4877 | return scm_from_double (rx / yy); |
0aacf84e MD |
4878 | } |
4879 | else if (SCM_COMPLEXP (y)) | |
4880 | { | |
4881 | a = rx; | |
4882 | goto complex_div; | |
4883 | } | |
f92e85f7 | 4884 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4885 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
4886 | else |
4887 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4888 | } |
0aacf84e MD |
4889 | else if (SCM_COMPLEXP (x)) |
4890 | { | |
4891 | double rx = SCM_COMPLEX_REAL (x); | |
4892 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 4893 | if (SCM_I_INUMP (y)) |
0aacf84e | 4894 | { |
e11e83f3 | 4895 | long int yy = SCM_I_INUM (y); |
7351e207 | 4896 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4897 | if (yy == 0) |
4898 | scm_num_overflow (s_divide); | |
4899 | else | |
7351e207 | 4900 | #endif |
0aacf84e MD |
4901 | { |
4902 | double d = yy; | |
8507ec80 | 4903 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
4904 | } |
4905 | } | |
4906 | else if (SCM_BIGP (y)) | |
4907 | { | |
4908 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4909 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4910 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
4911 | } |
4912 | else if (SCM_REALP (y)) | |
4913 | { | |
4914 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4915 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4916 | if (yy == 0.0) |
4917 | scm_num_overflow (s_divide); | |
4918 | else | |
7351e207 | 4919 | #endif |
8507ec80 | 4920 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
4921 | } |
4922 | else if (SCM_COMPLEXP (y)) | |
4923 | { | |
4924 | double ry = SCM_COMPLEX_REAL (y); | |
4925 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4926 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
4927 | { |
4928 | double t = ry / iy; | |
4929 | double d = iy * (1.0 + t * t); | |
8507ec80 | 4930 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
4931 | } |
4932 | else | |
4933 | { | |
4934 | double t = iy / ry; | |
4935 | double d = ry * (1.0 + t * t); | |
8507ec80 | 4936 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
4937 | } |
4938 | } | |
f92e85f7 MV |
4939 | else if (SCM_FRACTIONP (y)) |
4940 | { | |
4941 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4942 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 4943 | } |
0aacf84e MD |
4944 | else |
4945 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4946 | } |
f92e85f7 MV |
4947 | else if (SCM_FRACTIONP (x)) |
4948 | { | |
e11e83f3 | 4949 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4950 | { |
e11e83f3 | 4951 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
4952 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4953 | if (yy == 0) | |
4954 | scm_num_overflow (s_divide); | |
4955 | else | |
4956 | #endif | |
cba42c93 | 4957 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4958 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4959 | } | |
4960 | else if (SCM_BIGP (y)) | |
4961 | { | |
cba42c93 | 4962 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4963 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4964 | } | |
4965 | else if (SCM_REALP (y)) | |
4966 | { | |
4967 | double yy = SCM_REAL_VALUE (y); | |
4968 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4969 | if (yy == 0.0) | |
4970 | scm_num_overflow (s_divide); | |
4971 | else | |
4972 | #endif | |
55f26379 | 4973 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
4974 | } |
4975 | else if (SCM_COMPLEXP (y)) | |
4976 | { | |
4977 | a = scm_i_fraction2double (x); | |
4978 | goto complex_div; | |
4979 | } | |
4980 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 4981 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4982 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
4983 | else | |
4984 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4985 | } | |
0aacf84e | 4986 | else |
f8de44c1 | 4987 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 4988 | } |
f92e85f7 MV |
4989 | |
4990 | SCM | |
4991 | scm_divide (SCM x, SCM y) | |
4992 | { | |
4993 | return scm_i_divide (x, y, 0); | |
4994 | } | |
4995 | ||
4996 | static SCM scm_divide2real (SCM x, SCM y) | |
4997 | { | |
4998 | return scm_i_divide (x, y, 1); | |
4999 | } | |
c05e97b7 | 5000 | #undef FUNC_NAME |
0f2d19dd | 5001 | |
fa605590 | 5002 | |
0f2d19dd | 5003 | double |
6e8d25a6 | 5004 | scm_asinh (double x) |
0f2d19dd | 5005 | { |
fa605590 KR |
5006 | #if HAVE_ASINH |
5007 | return asinh (x); | |
5008 | #else | |
5009 | #define asinh scm_asinh | |
f872b822 | 5010 | return log (x + sqrt (x * x + 1)); |
fa605590 | 5011 | #endif |
0f2d19dd | 5012 | } |
fa605590 KR |
5013 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
5014 | /* "Return the inverse hyperbolic sine of @var{x}." | |
5015 | */ | |
0f2d19dd JB |
5016 | |
5017 | ||
0f2d19dd | 5018 | double |
6e8d25a6 | 5019 | scm_acosh (double x) |
0f2d19dd | 5020 | { |
fa605590 KR |
5021 | #if HAVE_ACOSH |
5022 | return acosh (x); | |
5023 | #else | |
5024 | #define acosh scm_acosh | |
f872b822 | 5025 | return log (x + sqrt (x * x - 1)); |
fa605590 | 5026 | #endif |
0f2d19dd | 5027 | } |
fa605590 KR |
5028 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
5029 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
5030 | */ | |
0f2d19dd JB |
5031 | |
5032 | ||
0f2d19dd | 5033 | double |
6e8d25a6 | 5034 | scm_atanh (double x) |
0f2d19dd | 5035 | { |
fa605590 KR |
5036 | #if HAVE_ATANH |
5037 | return atanh (x); | |
5038 | #else | |
5039 | #define atanh scm_atanh | |
f872b822 | 5040 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 5041 | #endif |
0f2d19dd | 5042 | } |
fa605590 KR |
5043 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
5044 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
5045 | */ | |
0f2d19dd JB |
5046 | |
5047 | ||
0f2d19dd | 5048 | double |
3101f40f | 5049 | scm_c_truncate (double x) |
0f2d19dd | 5050 | { |
fa605590 KR |
5051 | #if HAVE_TRUNC |
5052 | return trunc (x); | |
5053 | #else | |
f872b822 MD |
5054 | if (x < 0.0) |
5055 | return -floor (-x); | |
5056 | return floor (x); | |
fa605590 | 5057 | #endif |
0f2d19dd | 5058 | } |
0f2d19dd | 5059 | |
3101f40f MV |
5060 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5061 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5062 | Then half-way cases are identified and adjusted down if the | |
5063 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5064 | |
5065 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5066 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5067 | ||
5068 | An odd "result" value is identified with result/2 != floor(result/2). | |
5069 | This is done with plus_half, since that value is ready for use sooner in | |
5070 | a pipelined cpu, and we're already requiring plus_half == result. | |
5071 | ||
5072 | Note however that we need to be careful when x is big and already an | |
5073 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5074 | us to return such a value, incorrectly. For instance if the hardware is | |
5075 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5076 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5077 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5078 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5079 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5080 | ||
5081 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5082 | x is already an integer. If it is then clearly that's the desired result | |
5083 | already. And if it's not then the exponent must be small enough to allow | |
5084 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5085 | ||
0f2d19dd | 5086 | double |
3101f40f | 5087 | scm_c_round (double x) |
0f2d19dd | 5088 | { |
6187f48b KR |
5089 | double plus_half, result; |
5090 | ||
5091 | if (x == floor (x)) | |
5092 | return x; | |
5093 | ||
5094 | plus_half = x + 0.5; | |
5095 | result = floor (plus_half); | |
3101f40f | 5096 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5097 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5098 | ? result - 1 | |
5099 | : result); | |
0f2d19dd JB |
5100 | } |
5101 | ||
f92e85f7 MV |
5102 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5103 | (SCM x), | |
5104 | "Round the number @var{x} towards zero.") | |
5105 | #define FUNC_NAME s_scm_truncate_number | |
5106 | { | |
73e4de09 | 5107 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5108 | return scm_floor (x); |
5109 | else | |
5110 | return scm_ceiling (x); | |
5111 | } | |
5112 | #undef FUNC_NAME | |
5113 | ||
5114 | static SCM exactly_one_half; | |
5115 | ||
5116 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5117 | (SCM x), | |
5118 | "Round the number @var{x} towards the nearest integer. " | |
5119 | "When it is exactly halfway between two integers, " | |
5120 | "round towards the even one.") | |
5121 | #define FUNC_NAME s_scm_round_number | |
5122 | { | |
e11e83f3 | 5123 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5124 | return x; |
5125 | else if (SCM_REALP (x)) | |
3101f40f | 5126 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5127 | else |
bae30667 KR |
5128 | { |
5129 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5130 | single quotient+remainder division then examining to see which way | |
5131 | the rounding should go. */ | |
5132 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5133 | SCM result = scm_floor (plus_half); | |
3101f40f | 5134 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5135 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5136 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 5137 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
5138 | else |
5139 | return result; | |
5140 | } | |
f92e85f7 MV |
5141 | } |
5142 | #undef FUNC_NAME | |
5143 | ||
5144 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5145 | (SCM x), | |
5146 | "Round the number @var{x} towards minus infinity.") | |
5147 | #define FUNC_NAME s_scm_floor | |
5148 | { | |
e11e83f3 | 5149 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5150 | return x; |
5151 | else if (SCM_REALP (x)) | |
55f26379 | 5152 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5153 | else if (SCM_FRACTIONP (x)) |
5154 | { | |
5155 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5156 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5157 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5158 | { |
5159 | /* For positive x, rounding towards zero is correct. */ | |
5160 | return q; | |
5161 | } | |
5162 | else | |
5163 | { | |
5164 | /* For negative x, we need to return q-1 unless x is an | |
5165 | integer. But fractions are never integer, per our | |
5166 | assumptions. */ | |
d956fa6f | 5167 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5168 | } |
5169 | } | |
5170 | else | |
5171 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5172 | } | |
5173 | #undef FUNC_NAME | |
5174 | ||
5175 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5176 | (SCM x), | |
5177 | "Round the number @var{x} towards infinity.") | |
5178 | #define FUNC_NAME s_scm_ceiling | |
5179 | { | |
e11e83f3 | 5180 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5181 | return x; |
5182 | else if (SCM_REALP (x)) | |
55f26379 | 5183 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5184 | else if (SCM_FRACTIONP (x)) |
5185 | { | |
5186 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5187 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5188 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5189 | { |
5190 | /* For negative x, rounding towards zero is correct. */ | |
5191 | return q; | |
5192 | } | |
5193 | else | |
5194 | { | |
5195 | /* For positive x, we need to return q+1 unless x is an | |
5196 | integer. But fractions are never integer, per our | |
5197 | assumptions. */ | |
d956fa6f | 5198 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5199 | } |
5200 | } | |
5201 | else | |
5202 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5203 | } | |
5204 | #undef FUNC_NAME | |
0f2d19dd | 5205 | |
14b18ed6 | 5206 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
5207 | /* "Return the square root of the real number @var{x}." |
5208 | */ | |
14b18ed6 | 5209 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
5210 | /* "Return the absolute value of the real number @var{x}." |
5211 | */ | |
14b18ed6 | 5212 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
5213 | /* "Return the @var{x}th power of e." |
5214 | */ | |
14b18ed6 | 5215 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 5216 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 5217 | */ |
14b18ed6 | 5218 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
5219 | /* "Return the sine of the real number @var{x}." |
5220 | */ | |
14b18ed6 | 5221 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
5222 | /* "Return the cosine of the real number @var{x}." |
5223 | */ | |
14b18ed6 | 5224 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
5225 | /* "Return the tangent of the real number @var{x}." |
5226 | */ | |
14b18ed6 | 5227 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
5228 | /* "Return the arc sine of the real number @var{x}." |
5229 | */ | |
14b18ed6 | 5230 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
5231 | /* "Return the arc cosine of the real number @var{x}." |
5232 | */ | |
14b18ed6 | 5233 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
5234 | /* "Return the arc tangent of the real number @var{x}." |
5235 | */ | |
14b18ed6 | 5236 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
5237 | /* "Return the hyperbolic sine of the real number @var{x}." |
5238 | */ | |
14b18ed6 | 5239 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
5240 | /* "Return the hyperbolic cosine of the real number @var{x}." |
5241 | */ | |
14b18ed6 | 5242 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
5243 | /* "Return the hyperbolic tangent of the real number @var{x}." |
5244 | */ | |
f872b822 MD |
5245 | |
5246 | struct dpair | |
5247 | { | |
5248 | double x, y; | |
5249 | }; | |
5250 | ||
27c37006 NJ |
5251 | static void scm_two_doubles (SCM x, |
5252 | SCM y, | |
3eeba8d4 JB |
5253 | const char *sstring, |
5254 | struct dpair * xy); | |
f872b822 MD |
5255 | |
5256 | static void | |
27c37006 NJ |
5257 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
5258 | { | |
e11e83f3 MV |
5259 | if (SCM_I_INUMP (x)) |
5260 | xy->x = SCM_I_INUM (x); | |
0aacf84e | 5261 | else if (SCM_BIGP (x)) |
1be6b49c | 5262 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 5263 | else if (SCM_REALP (x)) |
27c37006 | 5264 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
5265 | else if (SCM_FRACTIONP (x)) |
5266 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 5267 | else |
27c37006 | 5268 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 5269 | |
e11e83f3 MV |
5270 | if (SCM_I_INUMP (y)) |
5271 | xy->y = SCM_I_INUM (y); | |
0aacf84e | 5272 | else if (SCM_BIGP (y)) |
1be6b49c | 5273 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 5274 | else if (SCM_REALP (y)) |
27c37006 | 5275 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
5276 | else if (SCM_FRACTIONP (y)) |
5277 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 5278 | else |
27c37006 | 5279 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
5280 | } |
5281 | ||
5282 | ||
a1ec6916 | 5283 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
5284 | (SCM x, SCM y), |
5285 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 5286 | "procedure does not accept complex arguments.") |
1bbd0b84 | 5287 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
5288 | { |
5289 | struct dpair xy; | |
27c37006 | 5290 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5291 | return scm_from_double (pow (xy.x, xy.y)); |
0f2d19dd | 5292 | } |
1bbd0b84 | 5293 | #undef FUNC_NAME |
0f2d19dd JB |
5294 | |
5295 | ||
a1ec6916 | 5296 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
5297 | (SCM x, SCM y), |
5298 | "Return the arc tangent of the two arguments @var{x} and\n" | |
5299 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
5300 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
5301 | "are used to determine the quadrant of the result. This\n" |
5302 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 5303 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
5304 | { |
5305 | struct dpair xy; | |
27c37006 | 5306 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5307 | return scm_from_double (atan2 (xy.x, xy.y)); |
0f2d19dd | 5308 | } |
1bbd0b84 | 5309 | #undef FUNC_NAME |
0f2d19dd | 5310 | |
8507ec80 MV |
5311 | SCM |
5312 | scm_c_make_rectangular (double re, double im) | |
5313 | { | |
5314 | if (im == 0.0) | |
5315 | return scm_from_double (re); | |
5316 | else | |
5317 | { | |
5318 | SCM z; | |
5319 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), | |
5320 | "complex")); | |
5321 | SCM_COMPLEX_REAL (z) = re; | |
5322 | SCM_COMPLEX_IMAG (z) = im; | |
5323 | return z; | |
5324 | } | |
5325 | } | |
0f2d19dd | 5326 | |
a1ec6916 | 5327 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 5328 | (SCM real, SCM imaginary), |
942e5b91 MG |
5329 | "Return a complex number constructed of the given @var{real} and\n" |
5330 | "@var{imaginary} parts.") | |
1bbd0b84 | 5331 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5332 | { |
5333 | struct dpair xy; | |
bb628794 | 5334 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
8507ec80 | 5335 | return scm_c_make_rectangular (xy.x, xy.y); |
0f2d19dd | 5336 | } |
1bbd0b84 | 5337 | #undef FUNC_NAME |
0f2d19dd | 5338 | |
8507ec80 MV |
5339 | SCM |
5340 | scm_c_make_polar (double mag, double ang) | |
5341 | { | |
5342 | double s, c; | |
5343 | #if HAVE_SINCOS | |
5344 | sincos (ang, &s, &c); | |
5345 | #else | |
5346 | s = sin (ang); | |
5347 | c = cos (ang); | |
5348 | #endif | |
5349 | return scm_c_make_rectangular (mag * c, mag * s); | |
5350 | } | |
0f2d19dd | 5351 | |
a1ec6916 | 5352 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5353 | (SCM x, SCM y), |
942e5b91 | 5354 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5355 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5356 | { |
5357 | struct dpair xy; | |
27c37006 | 5358 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
8507ec80 | 5359 | return scm_c_make_polar (xy.x, xy.y); |
0f2d19dd | 5360 | } |
1bbd0b84 | 5361 | #undef FUNC_NAME |
0f2d19dd JB |
5362 | |
5363 | ||
152f82bf | 5364 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5365 | /* "Return the real part of the number @var{z}." |
5366 | */ | |
0f2d19dd | 5367 | SCM |
6e8d25a6 | 5368 | scm_real_part (SCM z) |
0f2d19dd | 5369 | { |
e11e83f3 | 5370 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5371 | return z; |
0aacf84e | 5372 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5373 | return z; |
0aacf84e | 5374 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5375 | return z; |
0aacf84e | 5376 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5377 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5378 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5379 | return z; |
0aacf84e | 5380 | else |
c2ff8ab0 | 5381 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5382 | } |
5383 | ||
5384 | ||
152f82bf | 5385 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5386 | /* "Return the imaginary part of the number @var{z}." |
5387 | */ | |
0f2d19dd | 5388 | SCM |
6e8d25a6 | 5389 | scm_imag_part (SCM z) |
0f2d19dd | 5390 | { |
e11e83f3 | 5391 | if (SCM_I_INUMP (z)) |
f872b822 | 5392 | return SCM_INUM0; |
0aacf84e | 5393 | else if (SCM_BIGP (z)) |
f872b822 | 5394 | return SCM_INUM0; |
0aacf84e | 5395 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5396 | return scm_flo0; |
0aacf84e | 5397 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5398 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5399 | else if (SCM_FRACTIONP (z)) |
5400 | return SCM_INUM0; | |
0aacf84e | 5401 | else |
c2ff8ab0 | 5402 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5403 | } |
5404 | ||
f92e85f7 MV |
5405 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5406 | /* "Return the numerator of the number @var{z}." | |
5407 | */ | |
5408 | SCM | |
5409 | scm_numerator (SCM z) | |
5410 | { | |
e11e83f3 | 5411 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5412 | return z; |
5413 | else if (SCM_BIGP (z)) | |
5414 | return z; | |
5415 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 5416 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
5417 | else if (SCM_REALP (z)) |
5418 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5419 | else | |
5420 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5421 | } | |
5422 | ||
5423 | ||
5424 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5425 | /* "Return the denominator of the number @var{z}." | |
5426 | */ | |
5427 | SCM | |
5428 | scm_denominator (SCM z) | |
5429 | { | |
e11e83f3 | 5430 | if (SCM_I_INUMP (z)) |
d956fa6f | 5431 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5432 | else if (SCM_BIGP (z)) |
d956fa6f | 5433 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5434 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 5435 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
5436 | else if (SCM_REALP (z)) |
5437 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5438 | else | |
5439 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5440 | } | |
0f2d19dd | 5441 | |
9de33deb | 5442 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5443 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5444 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5445 | */ | |
0f2d19dd | 5446 | SCM |
6e8d25a6 | 5447 | scm_magnitude (SCM z) |
0f2d19dd | 5448 | { |
e11e83f3 | 5449 | if (SCM_I_INUMP (z)) |
0aacf84e | 5450 | { |
e11e83f3 | 5451 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5452 | if (zz >= 0) |
5453 | return z; | |
5454 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5455 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5456 | else |
5457 | return scm_i_long2big (-zz); | |
5986c47d | 5458 | } |
0aacf84e MD |
5459 | else if (SCM_BIGP (z)) |
5460 | { | |
5461 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5462 | scm_remember_upto_here_1 (z); | |
5463 | if (sgn < 0) | |
5464 | return scm_i_clonebig (z, 0); | |
5465 | else | |
5466 | return z; | |
5986c47d | 5467 | } |
0aacf84e | 5468 | else if (SCM_REALP (z)) |
55f26379 | 5469 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5470 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5471 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5472 | else if (SCM_FRACTIONP (z)) |
5473 | { | |
73e4de09 | 5474 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5475 | return z; |
cba42c93 | 5476 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5477 | SCM_FRACTION_DENOMINATOR (z)); |
5478 | } | |
0aacf84e | 5479 | else |
c2ff8ab0 | 5480 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5481 | } |
5482 | ||
5483 | ||
9de33deb | 5484 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5485 | /* "Return the angle of the complex number @var{z}." |
5486 | */ | |
0f2d19dd | 5487 | SCM |
6e8d25a6 | 5488 | scm_angle (SCM z) |
0f2d19dd | 5489 | { |
c8ae173e | 5490 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5491 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5492 | But if atan2 follows the floating point rounding mode, then the value |
5493 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5494 | if (SCM_I_INUMP (z)) |
0aacf84e | 5495 | { |
e11e83f3 | 5496 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5497 | return scm_flo0; |
0aacf84e | 5498 | else |
55f26379 | 5499 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5500 | } |
0aacf84e MD |
5501 | else if (SCM_BIGP (z)) |
5502 | { | |
5503 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5504 | scm_remember_upto_here_1 (z); | |
5505 | if (sgn < 0) | |
55f26379 | 5506 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5507 | else |
c8ae173e | 5508 | return scm_flo0; |
0f2d19dd | 5509 | } |
0aacf84e | 5510 | else if (SCM_REALP (z)) |
c8ae173e KR |
5511 | { |
5512 | if (SCM_REAL_VALUE (z) >= 0) | |
5513 | return scm_flo0; | |
5514 | else | |
55f26379 | 5515 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5516 | } |
0aacf84e | 5517 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5518 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5519 | else if (SCM_FRACTIONP (z)) |
5520 | { | |
73e4de09 | 5521 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5522 | return scm_flo0; |
55f26379 | 5523 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5524 | } |
0aacf84e | 5525 | else |
f4c627b3 | 5526 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5527 | } |
5528 | ||
5529 | ||
3c9a524f DH |
5530 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5531 | /* Convert the number @var{x} to its inexact representation.\n" | |
5532 | */ | |
5533 | SCM | |
5534 | scm_exact_to_inexact (SCM z) | |
5535 | { | |
e11e83f3 | 5536 | if (SCM_I_INUMP (z)) |
55f26379 | 5537 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5538 | else if (SCM_BIGP (z)) |
55f26379 | 5539 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5540 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5541 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5542 | else if (SCM_INEXACTP (z)) |
5543 | return z; | |
5544 | else | |
5545 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5546 | } | |
5547 | ||
5548 | ||
a1ec6916 | 5549 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5550 | (SCM z), |
1e6808ea | 5551 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5552 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5553 | { |
e11e83f3 | 5554 | if (SCM_I_INUMP (z)) |
f872b822 | 5555 | return z; |
0aacf84e | 5556 | else if (SCM_BIGP (z)) |
f872b822 | 5557 | return z; |
0aacf84e MD |
5558 | else if (SCM_REALP (z)) |
5559 | { | |
f92e85f7 MV |
5560 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5561 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5562 | else |
f92e85f7 MV |
5563 | { |
5564 | mpq_t frac; | |
5565 | SCM q; | |
5566 | ||
5567 | mpq_init (frac); | |
5568 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5569 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5570 | scm_i_mpz2num (mpq_denref (frac))); |
5571 | ||
cba42c93 | 5572 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5573 | for frac... |
5574 | */ | |
5575 | mpq_clear (frac); | |
5576 | return q; | |
5577 | } | |
c2ff8ab0 | 5578 | } |
f92e85f7 MV |
5579 | else if (SCM_FRACTIONP (z)) |
5580 | return z; | |
0aacf84e | 5581 | else |
c2ff8ab0 | 5582 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5583 | } |
1bbd0b84 | 5584 | #undef FUNC_NAME |
0f2d19dd | 5585 | |
f92e85f7 MV |
5586 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
5587 | (SCM x, SCM err), | |
5588 | "Return an exact number that is within @var{err} of @var{x}.") | |
5589 | #define FUNC_NAME s_scm_rationalize | |
5590 | { | |
e11e83f3 | 5591 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5592 | return x; |
5593 | else if (SCM_BIGP (x)) | |
5594 | return x; | |
5595 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5596 | { | |
5597 | /* Use continued fractions to find closest ratio. All | |
5598 | arithmetic is done with exact numbers. | |
5599 | */ | |
5600 | ||
5601 | SCM ex = scm_inexact_to_exact (x); | |
5602 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5603 | SCM tt = SCM_I_MAKINUM (1); |
5604 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5605 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5606 | SCM rx; |
5607 | int i = 0; | |
5608 | ||
73e4de09 | 5609 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5610 | return ex; |
5611 | ||
5612 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5613 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5614 | ||
5615 | /* We stop after a million iterations just to be absolutely sure | |
5616 | that we don't go into an infinite loop. The process normally | |
5617 | converges after less than a dozen iterations. | |
5618 | */ | |
5619 | ||
5620 | err = scm_abs (err); | |
5621 | while (++i < 1000000) | |
5622 | { | |
5623 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5624 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5625 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5626 | scm_is_false | |
f92e85f7 MV |
5627 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
5628 | err))) /* abs(x-a/b) <= err */ | |
02164269 MV |
5629 | { |
5630 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 MV |
5631 | if (scm_is_false (scm_exact_p (x)) |
5632 | || scm_is_false (scm_exact_p (err))) | |
02164269 MV |
5633 | return scm_exact_to_inexact (res); |
5634 | else | |
5635 | return res; | |
5636 | } | |
f92e85f7 MV |
5637 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5638 | SCM_UNDEFINED); | |
5639 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5640 | a2 = a1; | |
5641 | b2 = b1; | |
5642 | a1 = a; | |
5643 | b1 = b; | |
5644 | } | |
5645 | scm_num_overflow (s_scm_rationalize); | |
5646 | } | |
5647 | else | |
5648 | SCM_WRONG_TYPE_ARG (1, x); | |
5649 | } | |
5650 | #undef FUNC_NAME | |
5651 | ||
73e4de09 MV |
5652 | /* conversion functions */ |
5653 | ||
5654 | int | |
5655 | scm_is_integer (SCM val) | |
5656 | { | |
5657 | return scm_is_true (scm_integer_p (val)); | |
5658 | } | |
5659 | ||
5660 | int | |
5661 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
5662 | { | |
e11e83f3 | 5663 | if (SCM_I_INUMP (val)) |
73e4de09 | 5664 | { |
e11e83f3 | 5665 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5666 | return n >= min && n <= max; |
5667 | } | |
5668 | else if (SCM_BIGP (val)) | |
5669 | { | |
5670 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
5671 | return 0; | |
5672 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
5673 | { |
5674 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
5675 | { | |
5676 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
5677 | return n >= min && n <= max; | |
5678 | } | |
5679 | else | |
5680 | return 0; | |
5681 | } | |
73e4de09 MV |
5682 | else |
5683 | { | |
d956fa6f MV |
5684 | scm_t_intmax n; |
5685 | size_t count; | |
73e4de09 | 5686 | |
d956fa6f MV |
5687 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5688 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
5689 | return 0; | |
5690 | ||
5691 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5692 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5693 | |
d956fa6f | 5694 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 5695 | { |
d956fa6f MV |
5696 | if (n < 0) |
5697 | return 0; | |
73e4de09 | 5698 | } |
73e4de09 MV |
5699 | else |
5700 | { | |
d956fa6f MV |
5701 | n = -n; |
5702 | if (n >= 0) | |
5703 | return 0; | |
73e4de09 | 5704 | } |
d956fa6f MV |
5705 | |
5706 | return n >= min && n <= max; | |
73e4de09 MV |
5707 | } |
5708 | } | |
73e4de09 MV |
5709 | else |
5710 | return 0; | |
5711 | } | |
5712 | ||
5713 | int | |
5714 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
5715 | { | |
e11e83f3 | 5716 | if (SCM_I_INUMP (val)) |
73e4de09 | 5717 | { |
e11e83f3 | 5718 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5719 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
5720 | } | |
5721 | else if (SCM_BIGP (val)) | |
5722 | { | |
5723 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
5724 | return 0; | |
5725 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
5726 | { |
5727 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
5728 | { | |
5729 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
5730 | return n >= min && n <= max; | |
5731 | } | |
5732 | else | |
5733 | return 0; | |
5734 | } | |
73e4de09 MV |
5735 | else |
5736 | { | |
d956fa6f MV |
5737 | scm_t_uintmax n; |
5738 | size_t count; | |
73e4de09 | 5739 | |
d956fa6f MV |
5740 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
5741 | return 0; | |
73e4de09 | 5742 | |
d956fa6f MV |
5743 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5744 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 5745 | return 0; |
d956fa6f MV |
5746 | |
5747 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5748 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5749 | |
d956fa6f | 5750 | return n >= min && n <= max; |
73e4de09 MV |
5751 | } |
5752 | } | |
73e4de09 MV |
5753 | else |
5754 | return 0; | |
5755 | } | |
5756 | ||
1713d319 MV |
5757 | static void |
5758 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
5759 | { | |
5760 | scm_error (scm_out_of_range_key, | |
5761 | NULL, | |
5762 | "Value out of range ~S to ~S: ~S", | |
5763 | scm_list_3 (min, max, bad_val), | |
5764 | scm_list_1 (bad_val)); | |
5765 | } | |
5766 | ||
bfd7932e MV |
5767 | #define TYPE scm_t_intmax |
5768 | #define TYPE_MIN min | |
5769 | #define TYPE_MAX max | |
5770 | #define SIZEOF_TYPE 0 | |
5771 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
5772 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
5773 | #include "libguile/conv-integer.i.c" | |
5774 | ||
5775 | #define TYPE scm_t_uintmax | |
5776 | #define TYPE_MIN min | |
5777 | #define TYPE_MAX max | |
5778 | #define SIZEOF_TYPE 0 | |
5779 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
5780 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
5781 | #include "libguile/conv-uinteger.i.c" | |
5782 | ||
5783 | #define TYPE scm_t_int8 | |
5784 | #define TYPE_MIN SCM_T_INT8_MIN | |
5785 | #define TYPE_MAX SCM_T_INT8_MAX | |
5786 | #define SIZEOF_TYPE 1 | |
5787 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
5788 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
5789 | #include "libguile/conv-integer.i.c" | |
5790 | ||
5791 | #define TYPE scm_t_uint8 | |
5792 | #define TYPE_MIN 0 | |
5793 | #define TYPE_MAX SCM_T_UINT8_MAX | |
5794 | #define SIZEOF_TYPE 1 | |
5795 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
5796 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
5797 | #include "libguile/conv-uinteger.i.c" | |
5798 | ||
5799 | #define TYPE scm_t_int16 | |
5800 | #define TYPE_MIN SCM_T_INT16_MIN | |
5801 | #define TYPE_MAX SCM_T_INT16_MAX | |
5802 | #define SIZEOF_TYPE 2 | |
5803 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
5804 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
5805 | #include "libguile/conv-integer.i.c" | |
5806 | ||
5807 | #define TYPE scm_t_uint16 | |
5808 | #define TYPE_MIN 0 | |
5809 | #define TYPE_MAX SCM_T_UINT16_MAX | |
5810 | #define SIZEOF_TYPE 2 | |
5811 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
5812 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
5813 | #include "libguile/conv-uinteger.i.c" | |
5814 | ||
5815 | #define TYPE scm_t_int32 | |
5816 | #define TYPE_MIN SCM_T_INT32_MIN | |
5817 | #define TYPE_MAX SCM_T_INT32_MAX | |
5818 | #define SIZEOF_TYPE 4 | |
5819 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
5820 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
5821 | #include "libguile/conv-integer.i.c" | |
5822 | ||
5823 | #define TYPE scm_t_uint32 | |
5824 | #define TYPE_MIN 0 | |
5825 | #define TYPE_MAX SCM_T_UINT32_MAX | |
5826 | #define SIZEOF_TYPE 4 | |
5827 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
5828 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
5829 | #include "libguile/conv-uinteger.i.c" | |
5830 | ||
5831 | #if SCM_HAVE_T_INT64 | |
5832 | ||
5833 | #define TYPE scm_t_int64 | |
5834 | #define TYPE_MIN SCM_T_INT64_MIN | |
5835 | #define TYPE_MAX SCM_T_INT64_MAX | |
5836 | #define SIZEOF_TYPE 8 | |
5837 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
5838 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
5839 | #include "libguile/conv-integer.i.c" | |
5840 | ||
5841 | #define TYPE scm_t_uint64 | |
5842 | #define TYPE_MIN 0 | |
5843 | #define TYPE_MAX SCM_T_UINT64_MAX | |
5844 | #define SIZEOF_TYPE 8 | |
5845 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
5846 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
5847 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 5848 | |
bfd7932e | 5849 | #endif |
73e4de09 | 5850 | |
cd036260 MV |
5851 | void |
5852 | scm_to_mpz (SCM val, mpz_t rop) | |
5853 | { | |
5854 | if (SCM_I_INUMP (val)) | |
5855 | mpz_set_si (rop, SCM_I_INUM (val)); | |
5856 | else if (SCM_BIGP (val)) | |
5857 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
5858 | else | |
5859 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
5860 | } | |
5861 | ||
5862 | SCM | |
5863 | scm_from_mpz (mpz_t val) | |
5864 | { | |
5865 | return scm_i_mpz2num (val); | |
5866 | } | |
5867 | ||
73e4de09 MV |
5868 | int |
5869 | scm_is_real (SCM val) | |
5870 | { | |
5871 | return scm_is_true (scm_real_p (val)); | |
5872 | } | |
5873 | ||
55f26379 MV |
5874 | int |
5875 | scm_is_rational (SCM val) | |
5876 | { | |
5877 | return scm_is_true (scm_rational_p (val)); | |
5878 | } | |
5879 | ||
73e4de09 MV |
5880 | double |
5881 | scm_to_double (SCM val) | |
5882 | { | |
55f26379 MV |
5883 | if (SCM_I_INUMP (val)) |
5884 | return SCM_I_INUM (val); | |
5885 | else if (SCM_BIGP (val)) | |
5886 | return scm_i_big2dbl (val); | |
5887 | else if (SCM_FRACTIONP (val)) | |
5888 | return scm_i_fraction2double (val); | |
5889 | else if (SCM_REALP (val)) | |
5890 | return SCM_REAL_VALUE (val); | |
5891 | else | |
7a1aba42 | 5892 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
5893 | } |
5894 | ||
5895 | SCM | |
5896 | scm_from_double (double val) | |
5897 | { | |
55f26379 MV |
5898 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
5899 | SCM_REAL_VALUE (z) = val; | |
5900 | return z; | |
73e4de09 MV |
5901 | } |
5902 | ||
55f26379 MV |
5903 | #if SCM_ENABLE_DISCOURAGED == 1 |
5904 | ||
5905 | float | |
5906 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
5907 | { | |
5908 | if (SCM_BIGP (num)) | |
5909 | { | |
5910 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5911 | if (!xisinf (res)) | |
5912 | return res; | |
5913 | else | |
5914 | scm_out_of_range (NULL, num); | |
5915 | } | |
5916 | else | |
5917 | return scm_to_double (num); | |
5918 | } | |
5919 | ||
5920 | double | |
5921 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
5922 | { | |
5923 | if (SCM_BIGP (num)) | |
5924 | { | |
5925 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5926 | if (!xisinf (res)) | |
5927 | return res; | |
5928 | else | |
5929 | scm_out_of_range (NULL, num); | |
5930 | } | |
5931 | else | |
5932 | return scm_to_double (num); | |
5933 | } | |
5934 | ||
5935 | #endif | |
5936 | ||
8507ec80 MV |
5937 | int |
5938 | scm_is_complex (SCM val) | |
5939 | { | |
5940 | return scm_is_true (scm_complex_p (val)); | |
5941 | } | |
5942 | ||
5943 | double | |
5944 | scm_c_real_part (SCM z) | |
5945 | { | |
5946 | if (SCM_COMPLEXP (z)) | |
5947 | return SCM_COMPLEX_REAL (z); | |
5948 | else | |
5949 | { | |
5950 | /* Use the scm_real_part to get proper error checking and | |
5951 | dispatching. | |
5952 | */ | |
5953 | return scm_to_double (scm_real_part (z)); | |
5954 | } | |
5955 | } | |
5956 | ||
5957 | double | |
5958 | scm_c_imag_part (SCM z) | |
5959 | { | |
5960 | if (SCM_COMPLEXP (z)) | |
5961 | return SCM_COMPLEX_IMAG (z); | |
5962 | else | |
5963 | { | |
5964 | /* Use the scm_imag_part to get proper error checking and | |
5965 | dispatching. The result will almost always be 0.0, but not | |
5966 | always. | |
5967 | */ | |
5968 | return scm_to_double (scm_imag_part (z)); | |
5969 | } | |
5970 | } | |
5971 | ||
5972 | double | |
5973 | scm_c_magnitude (SCM z) | |
5974 | { | |
5975 | return scm_to_double (scm_magnitude (z)); | |
5976 | } | |
5977 | ||
5978 | double | |
5979 | scm_c_angle (SCM z) | |
5980 | { | |
5981 | return scm_to_double (scm_angle (z)); | |
5982 | } | |
5983 | ||
5984 | int | |
5985 | scm_is_number (SCM z) | |
5986 | { | |
5987 | return scm_is_true (scm_number_p (z)); | |
5988 | } | |
5989 | ||
8ab3d8a0 KR |
5990 | |
5991 | /* In the following functions we dispatch to the real-arg funcs like log() | |
5992 | when we know the arg is real, instead of just handing everything to | |
5993 | clog() for instance. This is in case clog() doesn't optimize for a | |
5994 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
5995 | well use it to go straight to the applicable C func. */ | |
5996 | ||
5997 | SCM_DEFINE (scm_log, "log", 1, 0, 0, | |
5998 | (SCM z), | |
5999 | "Return the natural logarithm of @var{z}.") | |
6000 | #define FUNC_NAME s_scm_log | |
6001 | { | |
6002 | if (SCM_COMPLEXP (z)) | |
6003 | { | |
6004 | #if HAVE_COMPLEX_DOUBLE | |
6005 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); | |
6006 | #else | |
6007 | double re = SCM_COMPLEX_REAL (z); | |
6008 | double im = SCM_COMPLEX_IMAG (z); | |
6009 | return scm_c_make_rectangular (log (hypot (re, im)), | |
6010 | atan2 (im, re)); | |
6011 | #endif | |
6012 | } | |
6013 | else | |
6014 | { | |
6015 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6016 | although the value itself overflows. */ | |
6017 | double re = scm_to_double (z); | |
6018 | double l = log (fabs (re)); | |
6019 | if (re >= 0.0) | |
6020 | return scm_from_double (l); | |
6021 | else | |
6022 | return scm_c_make_rectangular (l, M_PI); | |
6023 | } | |
6024 | } | |
6025 | #undef FUNC_NAME | |
6026 | ||
6027 | ||
6028 | SCM_DEFINE (scm_log10, "log10", 1, 0, 0, | |
6029 | (SCM z), | |
6030 | "Return the base 10 logarithm of @var{z}.") | |
6031 | #define FUNC_NAME s_scm_log10 | |
6032 | { | |
6033 | if (SCM_COMPLEXP (z)) | |
6034 | { | |
6035 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
6036 | clog() and a multiply by M_LOG10E, rather than the fallback | |
6037 | log10+hypot+atan2.) */ | |
6038 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG10 | |
6039 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); | |
6040 | #else | |
6041 | double re = SCM_COMPLEX_REAL (z); | |
6042 | double im = SCM_COMPLEX_IMAG (z); | |
6043 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
6044 | M_LOG10E * atan2 (im, re)); | |
6045 | #endif | |
6046 | } | |
6047 | else | |
6048 | { | |
6049 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6050 | although the value itself overflows. */ | |
6051 | double re = scm_to_double (z); | |
6052 | double l = log10 (fabs (re)); | |
6053 | if (re >= 0.0) | |
6054 | return scm_from_double (l); | |
6055 | else | |
6056 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
6057 | } | |
6058 | } | |
6059 | #undef FUNC_NAME | |
6060 | ||
6061 | ||
6062 | SCM_DEFINE (scm_exp, "exp", 1, 0, 0, | |
6063 | (SCM z), | |
6064 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
6065 | "base of natural logarithms (2.71828@dots{}).") | |
6066 | #define FUNC_NAME s_scm_exp | |
6067 | { | |
6068 | if (SCM_COMPLEXP (z)) | |
6069 | { | |
6070 | #if HAVE_COMPLEX_DOUBLE | |
6071 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); | |
6072 | #else | |
6073 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
6074 | SCM_COMPLEX_IMAG (z)); | |
6075 | #endif | |
6076 | } | |
6077 | else | |
6078 | { | |
6079 | /* When z is a negative bignum the conversion to double overflows, | |
6080 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
6081 | return scm_from_double (exp (scm_to_double (z))); | |
6082 | } | |
6083 | } | |
6084 | #undef FUNC_NAME | |
6085 | ||
6086 | ||
6087 | SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0, | |
6088 | (SCM x), | |
6089 | "Return the square root of @var{z}. Of the two possible roots\n" | |
6090 | "(positive and negative), the one with the a positive real part\n" | |
6091 | "is returned, or if that's zero then a positive imaginary part.\n" | |
6092 | "Thus,\n" | |
6093 | "\n" | |
6094 | "@example\n" | |
6095 | "(sqrt 9.0) @result{} 3.0\n" | |
6096 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
6097 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
6098 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
6099 | "@end example") | |
6100 | #define FUNC_NAME s_scm_sqrt | |
6101 | { | |
6102 | if (SCM_COMPLEXP (x)) | |
6103 | { | |
6104 | #if HAVE_COMPLEX_DOUBLE && HAVE_USABLE_CSQRT | |
6105 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x))); | |
6106 | #else | |
6107 | double re = SCM_COMPLEX_REAL (x); | |
6108 | double im = SCM_COMPLEX_IMAG (x); | |
6109 | return scm_c_make_polar (sqrt (hypot (re, im)), | |
6110 | 0.5 * atan2 (im, re)); | |
6111 | #endif | |
6112 | } | |
6113 | else | |
6114 | { | |
6115 | double xx = scm_to_double (x); | |
6116 | if (xx < 0) | |
6117 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
6118 | else | |
6119 | return scm_from_double (sqrt (xx)); | |
6120 | } | |
6121 | } | |
6122 | #undef FUNC_NAME | |
6123 | ||
6124 | ||
6125 | ||
0f2d19dd JB |
6126 | void |
6127 | scm_init_numbers () | |
0f2d19dd | 6128 | { |
0b799eea MV |
6129 | int i; |
6130 | ||
713a4259 KR |
6131 | mpz_init_set_si (z_negative_one, -1); |
6132 | ||
a261c0e9 DH |
6133 | /* It may be possible to tune the performance of some algorithms by using |
6134 | * the following constants to avoid the creation of bignums. Please, before | |
6135 | * using these values, remember the two rules of program optimization: | |
6136 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 6137 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 6138 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 6139 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 6140 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 6141 | |
f3ae5d60 MD |
6142 | scm_add_feature ("complex"); |
6143 | scm_add_feature ("inexact"); | |
55f26379 | 6144 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
6145 | |
6146 | /* determine floating point precision */ | |
55f26379 | 6147 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6148 | { |
6149 | init_dblprec(&scm_dblprec[i-2],i); | |
6150 | init_fx_radix(fx_per_radix[i-2],i); | |
6151 | } | |
f872b822 | 6152 | #ifdef DBL_DIG |
0b799eea MV |
6153 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
6154 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
6155 | #endif | |
1be6b49c | 6156 | |
d956fa6f MV |
6157 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
6158 | SCM_I_MAKINUM (2))); | |
a0599745 | 6159 | #include "libguile/numbers.x" |
0f2d19dd | 6160 | } |
89e00824 ML |
6161 | |
6162 | /* | |
6163 | Local Variables: | |
6164 | c-file-style: "gnu" | |
6165 | End: | |
6166 | */ |