1 /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004 Free Software Foundation, Inc.
3 * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories
4 * and Bellcore. See scm_divide.
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.
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.
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
19 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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.
28 * All objects satisfying SCM_FRACTIONP are never an integer.
33 - see if special casing bignums and reals in integer-exponent when
34 possible (to use mpz_pow and mpf_pow_ui) is faster.
36 - look in to better short-circuiting of common cases in
37 integer-expt and elsewhere.
39 - see if direct mpz operations can help in ash and elsewhere.
43 /* tell glibc (2.3) to give prototype for C99 trunc() */
54 #include "libguile/_scm.h"
55 #include "libguile/feature.h"
56 #include "libguile/ports.h"
57 #include "libguile/root.h"
58 #include "libguile/smob.h"
59 #include "libguile/strings.h"
61 #include "libguile/validate.h"
62 #include "libguile/numbers.h"
63 #include "libguile/deprecation.h"
65 #include "libguile/eq.h"
67 #include "libguile/discouraged.h"
72 Wonder if this might be faster for some of our code? A switch on
73 the numtag would jump directly to the right case, and the
74 SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests...
76 #define SCM_I_NUMTAG_NOTNUM 0
77 #define SCM_I_NUMTAG_INUM 1
78 #define SCM_I_NUMTAG_BIG scm_tc16_big
79 #define SCM_I_NUMTAG_REAL scm_tc16_real
80 #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex
81 #define SCM_I_NUMTAG(x) \
82 (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \
83 : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \
84 : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \
85 : SCM_I_NUMTAG_NOTNUM)))
87 /* the macro above will not work as is with fractions */
90 #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0)
92 /* FLOBUFLEN is the maximum number of characters neccessary for the
93 * printed or scm_string representation of an inexact number.
95 #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10)
98 #if ! defined (HAVE_ISNAN)
103 return (IsNANorINF (x
) && NaN (x
) && ! IsINF (x
)) ? 1 : 0;
106 #if ! defined (HAVE_ISINF)
111 return (IsNANorINF (x
) && IsINF (x
)) ? 1 : 0;
118 /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses
119 an explicit check. In some future gmp (don't know what version number),
120 mpz_cmp_d is supposed to do this itself. */
122 #define xmpz_cmp_d(z, d) \
123 (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d))
125 #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d)
128 /* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have
129 isinf. It does have finite and isnan though, hence the use of those.
130 fpclass would be a possibility on that system too. */
134 #if defined (HAVE_ISINF)
136 #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN)
137 return (! (finite (x
) || isnan (x
)));
146 #if defined (HAVE_ISNAN)
155 static mpz_t z_negative_one
;
159 SCM_C_INLINE_KEYWORD SCM
162 /* Return a newly created bignum. */
163 SCM z
= scm_double_cell (scm_tc16_big
, 0, 0, 0);
164 mpz_init (SCM_I_BIG_MPZ (z
));
168 SCM_C_INLINE_KEYWORD SCM
169 scm_i_long2big (long x
)
171 /* Return a newly created bignum initialized to X. */
172 SCM z
= scm_double_cell (scm_tc16_big
, 0, 0, 0);
173 mpz_init_set_si (SCM_I_BIG_MPZ (z
), x
);
177 SCM_C_INLINE_KEYWORD SCM
178 scm_i_ulong2big (unsigned long x
)
180 /* Return a newly created bignum initialized to X. */
181 SCM z
= scm_double_cell (scm_tc16_big
, 0, 0, 0);
182 mpz_init_set_ui (SCM_I_BIG_MPZ (z
), x
);
186 SCM_C_INLINE_KEYWORD
static SCM
187 scm_i_clonebig (SCM src_big
, int same_sign_p
)
189 /* Copy src_big's value, negate it if same_sign_p is false, and return. */
190 SCM z
= scm_double_cell (scm_tc16_big
, 0, 0, 0);
191 mpz_init_set (SCM_I_BIG_MPZ (z
), SCM_I_BIG_MPZ (src_big
));
193 mpz_neg (SCM_I_BIG_MPZ (z
), SCM_I_BIG_MPZ (z
));
197 SCM_C_INLINE_KEYWORD
int
198 scm_i_bigcmp (SCM x
, SCM y
)
200 /* Return neg if x < y, pos if x > y, and 0 if x == y */
201 /* presume we already know x and y are bignums */
202 int result
= mpz_cmp (SCM_I_BIG_MPZ (x
), SCM_I_BIG_MPZ (y
));
203 scm_remember_upto_here_2 (x
, y
);
207 SCM_C_INLINE_KEYWORD SCM
208 scm_i_dbl2big (double d
)
210 /* results are only defined if d is an integer */
211 SCM z
= scm_double_cell (scm_tc16_big
, 0, 0, 0);
212 mpz_init_set_d (SCM_I_BIG_MPZ (z
), d
);
216 /* Convert a integer in double representation to a SCM number. */
218 SCM_C_INLINE_KEYWORD SCM
219 scm_i_dbl2num (double u
)
221 /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both
222 powers of 2, so there's no rounding when making "double" values
223 from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could
224 get rounded on a 64-bit machine, hence the "+1".
226 The use of floor() to force to an integer value ensures we get a
227 "numerically closest" value without depending on how a
228 double->long cast or how mpz_set_d will round. For reference,
229 double->long probably follows the hardware rounding mode,
230 mpz_set_d truncates towards zero. */
232 /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not
233 representable as a double? */
235 if (u
< (double) (SCM_MOST_POSITIVE_FIXNUM
+1)
236 && u
>= (double) SCM_MOST_NEGATIVE_FIXNUM
)
237 return SCM_I_MAKINUM ((long) u
);
239 return scm_i_dbl2big (u
);
242 /* scm_i_big2dbl() rounds to the closest representable double, in accordance
243 with R5RS exact->inexact.
245 The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits
246 (ie. truncate towards zero), then adjust to get the closest double by
247 examining the next lower bit and adding 1 (to the absolute value) if
250 Bignums exactly half way between representable doubles are rounded to the
251 next higher absolute value (ie. away from zero). This seems like an
252 adequate interpretation of R5RS "numerically closest", and it's easier
253 and faster than a full "nearest-even" style.
255 The bit test must be done on the absolute value of the mpz_t, which means
256 we need to use mpz_getlimbn. mpz_tstbit is not right, it treats
257 negatives as twos complement.
259 In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up
260 following the hardware rounding mode, but applied to the absolute value
261 of the mpz_t operand. This is not what we want so we put the high
262 DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when,
263 mpz_get_d is supposed to always truncate towards zero.
265 ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3
266 is a slowdown. It'd be faster to pick out the relevant high bits with
267 mpz_getlimbn if we could be bothered coding that, and if the new
268 truncating gmp doesn't come out. */
271 scm_i_big2dbl (SCM b
)
276 bits
= mpz_sizeinbase (SCM_I_BIG_MPZ (b
), 2);
280 /* Current GMP, eg. 4.1.3, force truncation towards zero */
282 if (bits
> DBL_MANT_DIG
)
284 size_t shift
= bits
- DBL_MANT_DIG
;
285 mpz_init2 (tmp
, DBL_MANT_DIG
);
286 mpz_tdiv_q_2exp (tmp
, SCM_I_BIG_MPZ (b
), shift
);
287 result
= ldexp (mpz_get_d (tmp
), shift
);
292 result
= mpz_get_d (SCM_I_BIG_MPZ (b
));
297 result
= mpz_get_d (SCM_I_BIG_MPZ (b
));
300 if (bits
> DBL_MANT_DIG
)
302 unsigned long pos
= bits
- DBL_MANT_DIG
- 1;
303 /* test bit number "pos" in absolute value */
304 if (mpz_getlimbn (SCM_I_BIG_MPZ (b
), pos
/ GMP_NUMB_BITS
)
305 & ((mp_limb_t
) 1 << (pos
% GMP_NUMB_BITS
)))
307 result
+= ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b
)), pos
+ 1);
311 scm_remember_upto_here_1 (b
);
315 SCM_C_INLINE_KEYWORD SCM
316 scm_i_normbig (SCM b
)
318 /* convert a big back to a fixnum if it'll fit */
319 /* presume b is a bignum */
320 if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b
)))
322 long val
= mpz_get_si (SCM_I_BIG_MPZ (b
));
323 if (SCM_FIXABLE (val
))
324 b
= SCM_I_MAKINUM (val
);
329 static SCM_C_INLINE_KEYWORD SCM
330 scm_i_mpz2num (mpz_t b
)
332 /* convert a mpz number to a SCM number. */
333 if (mpz_fits_slong_p (b
))
335 long val
= mpz_get_si (b
);
336 if (SCM_FIXABLE (val
))
337 return SCM_I_MAKINUM (val
);
341 SCM z
= scm_double_cell (scm_tc16_big
, 0, 0, 0);
342 mpz_init_set (SCM_I_BIG_MPZ (z
), b
);
347 /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */
348 static SCM
scm_divide2real (SCM x
, SCM y
);
351 scm_i_make_ratio (SCM numerator
, SCM denominator
)
352 #define FUNC_NAME "make-ratio"
354 /* First make sure the arguments are proper.
356 if (SCM_I_INUMP (denominator
))
358 if (scm_is_eq (denominator
, SCM_INUM0
))
359 scm_num_overflow ("make-ratio");
360 if (scm_is_eq (denominator
, SCM_I_MAKINUM(1)))
365 if (!(SCM_BIGP(denominator
)))
366 SCM_WRONG_TYPE_ARG (2, denominator
);
368 if (!SCM_I_INUMP (numerator
) && !SCM_BIGP (numerator
))
369 SCM_WRONG_TYPE_ARG (1, numerator
);
371 /* Then flip signs so that the denominator is positive.
373 if (scm_is_true (scm_negative_p (denominator
)))
375 numerator
= scm_difference (numerator
, SCM_UNDEFINED
);
376 denominator
= scm_difference (denominator
, SCM_UNDEFINED
);
379 /* Now consider for each of the four fixnum/bignum combinations
380 whether the rational number is really an integer.
382 if (SCM_I_INUMP (numerator
))
384 long x
= SCM_I_INUM (numerator
);
385 if (scm_is_eq (numerator
, SCM_INUM0
))
387 if (SCM_I_INUMP (denominator
))
390 y
= SCM_I_INUM (denominator
);
392 return SCM_I_MAKINUM(1);
394 return SCM_I_MAKINUM (x
/ y
);
398 /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative
399 of that value for the denominator, as a bignum. Apart from
400 that case, abs(bignum) > abs(inum) so inum/bignum is not an
402 if (x
== SCM_MOST_NEGATIVE_FIXNUM
403 && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator
),
404 - SCM_MOST_NEGATIVE_FIXNUM
) == 0)
405 return SCM_I_MAKINUM(-1);
408 else if (SCM_BIGP (numerator
))
410 if (SCM_I_INUMP (denominator
))
412 long yy
= SCM_I_INUM (denominator
);
413 if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator
), yy
))
414 return scm_divide (numerator
, denominator
);
418 if (scm_is_eq (numerator
, denominator
))
419 return SCM_I_MAKINUM(1);
420 if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator
),
421 SCM_I_BIG_MPZ (denominator
)))
422 return scm_divide(numerator
, denominator
);
426 /* No, it's a proper fraction.
428 return scm_double_cell (scm_tc16_fraction
,
429 SCM_UNPACK (numerator
),
430 SCM_UNPACK (denominator
), 0);
434 static void scm_i_fraction_reduce (SCM z
)
436 if (!(SCM_FRACTION_REDUCED (z
)))
439 divisor
= scm_gcd (SCM_FRACTION_NUMERATOR (z
), SCM_FRACTION_DENOMINATOR (z
));
440 if (!(scm_is_eq (divisor
, SCM_I_MAKINUM(1))))
443 SCM_FRACTION_SET_NUMERATOR (z
, scm_divide (SCM_FRACTION_NUMERATOR (z
), divisor
));
444 SCM_FRACTION_SET_DENOMINATOR (z
, scm_divide (SCM_FRACTION_DENOMINATOR (z
), divisor
));
446 SCM_FRACTION_REDUCED_SET (z
);
451 scm_i_fraction2double (SCM z
)
453 return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z
),
454 SCM_FRACTION_DENOMINATOR (z
)));
457 SCM_DEFINE (scm_exact_p
, "exact?", 1, 0, 0,
459 "Return @code{#t} if @var{x} is an exact number, @code{#f}\n"
461 #define FUNC_NAME s_scm_exact_p
467 if (SCM_FRACTIONP (x
))
471 SCM_WRONG_TYPE_ARG (1, x
);
476 SCM_DEFINE (scm_odd_p
, "odd?", 1, 0, 0,
478 "Return @code{#t} if @var{n} is an odd number, @code{#f}\n"
480 #define FUNC_NAME s_scm_odd_p
484 long val
= SCM_I_INUM (n
);
485 return scm_from_bool ((val
& 1L) != 0);
487 else if (SCM_BIGP (n
))
489 int odd_p
= mpz_odd_p (SCM_I_BIG_MPZ (n
));
490 scm_remember_upto_here_1 (n
);
491 return scm_from_bool (odd_p
);
493 else if (scm_is_true (scm_inf_p (n
)))
495 else if (SCM_REALP (n
))
497 double rem
= fabs (fmod (SCM_REAL_VALUE(n
), 2.0));
503 SCM_WRONG_TYPE_ARG (1, n
);
506 SCM_WRONG_TYPE_ARG (1, n
);
511 SCM_DEFINE (scm_even_p
, "even?", 1, 0, 0,
513 "Return @code{#t} if @var{n} is an even number, @code{#f}\n"
515 #define FUNC_NAME s_scm_even_p
519 long val
= SCM_I_INUM (n
);
520 return scm_from_bool ((val
& 1L) == 0);
522 else if (SCM_BIGP (n
))
524 int even_p
= mpz_even_p (SCM_I_BIG_MPZ (n
));
525 scm_remember_upto_here_1 (n
);
526 return scm_from_bool (even_p
);
528 else if (scm_is_true (scm_inf_p (n
)))
530 else if (SCM_REALP (n
))
532 double rem
= fabs (fmod (SCM_REAL_VALUE(n
), 2.0));
538 SCM_WRONG_TYPE_ARG (1, n
);
541 SCM_WRONG_TYPE_ARG (1, n
);
545 SCM_DEFINE (scm_inf_p
, "inf?", 1, 0, 0,
547 "Return @code{#t} if @var{x} is either @samp{+inf.0}\n"
548 "or @samp{-inf.0}, @code{#f} otherwise.")
549 #define FUNC_NAME s_scm_inf_p
552 return scm_from_bool (xisinf (SCM_REAL_VALUE (x
)));
553 else if (SCM_COMPLEXP (x
))
554 return scm_from_bool (xisinf (SCM_COMPLEX_REAL (x
))
555 || xisinf (SCM_COMPLEX_IMAG (x
)));
561 SCM_DEFINE (scm_nan_p
, "nan?", 1, 0, 0,
563 "Return @code{#t} if @var{n} is a NaN, @code{#f}\n"
565 #define FUNC_NAME s_scm_nan_p
568 return scm_from_bool (xisnan (SCM_REAL_VALUE (n
)));
569 else if (SCM_COMPLEXP (n
))
570 return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n
))
571 || xisnan (SCM_COMPLEX_IMAG (n
)));
577 /* Guile's idea of infinity. */
578 static double guile_Inf
;
580 /* Guile's idea of not a number. */
581 static double guile_NaN
;
584 guile_ieee_init (void)
586 #if defined (HAVE_ISINF) || defined (HAVE_FINITE)
588 /* Some version of gcc on some old version of Linux used to crash when
589 trying to make Inf and NaN. */
592 /* C99 INFINITY, when available.
593 FIXME: The standard allows for INFINITY to be something that overflows
594 at compile time. We ought to have a configure test to check for that
595 before trying to use it. (But in practice we believe this is not a
596 problem on any system guile is likely to target.) */
597 guile_Inf
= INFINITY
;
600 extern unsigned int DINFINITY
[2];
601 guile_Inf
= (*(X_CAST(double *, DINFINITY
)));
608 if (guile_Inf
== tmp
)
616 #if defined (HAVE_ISNAN)
619 /* C99 NAN, when available */
623 extern unsigned int DQNAN
[2];
624 guile_NaN
= (*(X_CAST(double *, DQNAN
)));
626 guile_NaN
= guile_Inf
/ guile_Inf
;
632 SCM_DEFINE (scm_inf
, "inf", 0, 0, 0,
635 #define FUNC_NAME s_scm_inf
637 static int initialized
= 0;
643 return scm_from_double (guile_Inf
);
647 SCM_DEFINE (scm_nan
, "nan", 0, 0, 0,
650 #define FUNC_NAME s_scm_nan
652 static int initialized
= 0;
658 return scm_from_double (guile_NaN
);
663 SCM_PRIMITIVE_GENERIC (scm_abs
, "abs", 1, 0, 0,
665 "Return the absolute value of @var{x}.")
670 long int xx
= SCM_I_INUM (x
);
673 else if (SCM_POSFIXABLE (-xx
))
674 return SCM_I_MAKINUM (-xx
);
676 return scm_i_long2big (-xx
);
678 else if (SCM_BIGP (x
))
680 const int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
682 return scm_i_clonebig (x
, 0);
686 else if (SCM_REALP (x
))
688 /* note that if x is a NaN then xx<0 is false so we return x unchanged */
689 double xx
= SCM_REAL_VALUE (x
);
691 return scm_from_double (-xx
);
695 else if (SCM_FRACTIONP (x
))
697 if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x
))))
699 return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x
), SCM_UNDEFINED
),
700 SCM_FRACTION_DENOMINATOR (x
));
703 SCM_WTA_DISPATCH_1 (g_scm_abs
, x
, 1, s_scm_abs
);
708 SCM_GPROC (s_quotient
, "quotient", 2, 0, 0, scm_quotient
, g_quotient
);
709 /* "Return the quotient of the numbers @var{x} and @var{y}."
712 scm_quotient (SCM x
, SCM y
)
716 long xx
= SCM_I_INUM (x
);
719 long yy
= SCM_I_INUM (y
);
721 scm_num_overflow (s_quotient
);
726 return SCM_I_MAKINUM (z
);
728 return scm_i_long2big (z
);
731 else if (SCM_BIGP (y
))
733 if ((SCM_I_INUM (x
) == SCM_MOST_NEGATIVE_FIXNUM
)
734 && (mpz_cmp_ui (SCM_I_BIG_MPZ (y
),
735 - SCM_MOST_NEGATIVE_FIXNUM
) == 0))
737 /* Special case: x == fixnum-min && y == abs (fixnum-min) */
738 scm_remember_upto_here_1 (y
);
739 return SCM_I_MAKINUM (-1);
742 return SCM_I_MAKINUM (0);
745 SCM_WTA_DISPATCH_2 (g_quotient
, x
, y
, SCM_ARG2
, s_quotient
);
747 else if (SCM_BIGP (x
))
751 long yy
= SCM_I_INUM (y
);
753 scm_num_overflow (s_quotient
);
758 SCM result
= scm_i_mkbig ();
761 mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result
),
764 mpz_neg (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (result
));
767 mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (x
), yy
);
768 scm_remember_upto_here_1 (x
);
769 return scm_i_normbig (result
);
772 else if (SCM_BIGP (y
))
774 SCM result
= scm_i_mkbig ();
775 mpz_tdiv_q (SCM_I_BIG_MPZ (result
),
778 scm_remember_upto_here_2 (x
, y
);
779 return scm_i_normbig (result
);
782 SCM_WTA_DISPATCH_2 (g_quotient
, x
, y
, SCM_ARG2
, s_quotient
);
785 SCM_WTA_DISPATCH_2 (g_quotient
, x
, y
, SCM_ARG1
, s_quotient
);
788 SCM_GPROC (s_remainder
, "remainder", 2, 0, 0, scm_remainder
, g_remainder
);
789 /* "Return the remainder of the numbers @var{x} and @var{y}.\n"
791 * "(remainder 13 4) @result{} 1\n"
792 * "(remainder -13 4) @result{} -1\n"
796 scm_remainder (SCM x
, SCM y
)
802 long yy
= SCM_I_INUM (y
);
804 scm_num_overflow (s_remainder
);
807 long z
= SCM_I_INUM (x
) % yy
;
808 return SCM_I_MAKINUM (z
);
811 else if (SCM_BIGP (y
))
813 if ((SCM_I_INUM (x
) == SCM_MOST_NEGATIVE_FIXNUM
)
814 && (mpz_cmp_ui (SCM_I_BIG_MPZ (y
),
815 - SCM_MOST_NEGATIVE_FIXNUM
) == 0))
817 /* Special case: x == fixnum-min && y == abs (fixnum-min) */
818 scm_remember_upto_here_1 (y
);
819 return SCM_I_MAKINUM (0);
825 SCM_WTA_DISPATCH_2 (g_remainder
, x
, y
, SCM_ARG2
, s_remainder
);
827 else if (SCM_BIGP (x
))
831 long yy
= SCM_I_INUM (y
);
833 scm_num_overflow (s_remainder
);
836 SCM result
= scm_i_mkbig ();
839 mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ(x
), yy
);
840 scm_remember_upto_here_1 (x
);
841 return scm_i_normbig (result
);
844 else if (SCM_BIGP (y
))
846 SCM result
= scm_i_mkbig ();
847 mpz_tdiv_r (SCM_I_BIG_MPZ (result
),
850 scm_remember_upto_here_2 (x
, y
);
851 return scm_i_normbig (result
);
854 SCM_WTA_DISPATCH_2 (g_remainder
, x
, y
, SCM_ARG2
, s_remainder
);
857 SCM_WTA_DISPATCH_2 (g_remainder
, x
, y
, SCM_ARG1
, s_remainder
);
861 SCM_GPROC (s_modulo
, "modulo", 2, 0, 0, scm_modulo
, g_modulo
);
862 /* "Return the modulo of the numbers @var{x} and @var{y}.\n"
864 * "(modulo 13 4) @result{} 1\n"
865 * "(modulo -13 4) @result{} 3\n"
869 scm_modulo (SCM x
, SCM y
)
873 long xx
= SCM_I_INUM (x
);
876 long yy
= SCM_I_INUM (y
);
878 scm_num_overflow (s_modulo
);
881 /* C99 specifies that "%" is the remainder corresponding to a
882 quotient rounded towards zero, and that's also traditional
883 for machine division, so z here should be well defined. */
901 return SCM_I_MAKINUM (result
);
904 else if (SCM_BIGP (y
))
906 int sgn_y
= mpz_sgn (SCM_I_BIG_MPZ (y
));
913 SCM pos_y
= scm_i_clonebig (y
, 0);
914 /* do this after the last scm_op */
915 mpz_init_set_si (z_x
, xx
);
916 result
= pos_y
; /* re-use this bignum */
917 mpz_mod (SCM_I_BIG_MPZ (result
),
919 SCM_I_BIG_MPZ (pos_y
));
920 scm_remember_upto_here_1 (pos_y
);
924 result
= scm_i_mkbig ();
925 /* do this after the last scm_op */
926 mpz_init_set_si (z_x
, xx
);
927 mpz_mod (SCM_I_BIG_MPZ (result
),
930 scm_remember_upto_here_1 (y
);
933 if ((sgn_y
< 0) && mpz_sgn (SCM_I_BIG_MPZ (result
)) != 0)
934 mpz_add (SCM_I_BIG_MPZ (result
),
936 SCM_I_BIG_MPZ (result
));
937 scm_remember_upto_here_1 (y
);
938 /* and do this before the next one */
940 return scm_i_normbig (result
);
944 SCM_WTA_DISPATCH_2 (g_modulo
, x
, y
, SCM_ARG2
, s_modulo
);
946 else if (SCM_BIGP (x
))
950 long yy
= SCM_I_INUM (y
);
952 scm_num_overflow (s_modulo
);
955 SCM result
= scm_i_mkbig ();
956 mpz_mod_ui (SCM_I_BIG_MPZ (result
),
958 (yy
< 0) ? - yy
: yy
);
959 scm_remember_upto_here_1 (x
);
960 if ((yy
< 0) && (mpz_sgn (SCM_I_BIG_MPZ (result
)) != 0))
961 mpz_sub_ui (SCM_I_BIG_MPZ (result
),
962 SCM_I_BIG_MPZ (result
),
964 return scm_i_normbig (result
);
967 else if (SCM_BIGP (y
))
970 SCM result
= scm_i_mkbig ();
971 int y_sgn
= mpz_sgn (SCM_I_BIG_MPZ (y
));
972 SCM pos_y
= scm_i_clonebig (y
, y_sgn
>= 0);
973 mpz_mod (SCM_I_BIG_MPZ (result
),
975 SCM_I_BIG_MPZ (pos_y
));
977 scm_remember_upto_here_1 (x
);
978 if ((y_sgn
< 0) && (mpz_sgn (SCM_I_BIG_MPZ (result
)) != 0))
979 mpz_add (SCM_I_BIG_MPZ (result
),
981 SCM_I_BIG_MPZ (result
));
982 scm_remember_upto_here_2 (y
, pos_y
);
983 return scm_i_normbig (result
);
987 SCM_WTA_DISPATCH_2 (g_modulo
, x
, y
, SCM_ARG2
, s_modulo
);
990 SCM_WTA_DISPATCH_2 (g_modulo
, x
, y
, SCM_ARG1
, s_modulo
);
993 SCM_GPROC1 (s_gcd
, "gcd", scm_tc7_asubr
, scm_gcd
, g_gcd
);
994 /* "Return the greatest common divisor of all arguments.\n"
995 * "If called without arguments, 0 is returned."
998 scm_gcd (SCM x
, SCM y
)
1001 return SCM_UNBNDP (x
) ? SCM_INUM0
: x
;
1003 if (SCM_I_INUMP (x
))
1005 if (SCM_I_INUMP (y
))
1007 long xx
= SCM_I_INUM (x
);
1008 long yy
= SCM_I_INUM (y
);
1009 long u
= xx
< 0 ? -xx
: xx
;
1010 long v
= yy
< 0 ? -yy
: yy
;
1020 /* Determine a common factor 2^k */
1021 while (!(1 & (u
| v
)))
1027 /* Now, any factor 2^n can be eliminated */
1047 return (SCM_POSFIXABLE (result
)
1048 ? SCM_I_MAKINUM (result
)
1049 : scm_i_long2big (result
));
1051 else if (SCM_BIGP (y
))
1057 SCM_WTA_DISPATCH_2 (g_gcd
, x
, y
, SCM_ARG2
, s_gcd
);
1059 else if (SCM_BIGP (x
))
1061 if (SCM_I_INUMP (y
))
1063 unsigned long result
;
1066 yy
= SCM_I_INUM (y
);
1071 result
= mpz_gcd_ui (NULL
, SCM_I_BIG_MPZ (x
), yy
);
1072 scm_remember_upto_here_1 (x
);
1073 return (SCM_POSFIXABLE (result
)
1074 ? SCM_I_MAKINUM (result
)
1075 : scm_from_ulong (result
));
1077 else if (SCM_BIGP (y
))
1079 SCM result
= scm_i_mkbig ();
1080 mpz_gcd (SCM_I_BIG_MPZ (result
),
1083 scm_remember_upto_here_2 (x
, y
);
1084 return scm_i_normbig (result
);
1087 SCM_WTA_DISPATCH_2 (g_gcd
, x
, y
, SCM_ARG2
, s_gcd
);
1090 SCM_WTA_DISPATCH_2 (g_gcd
, x
, y
, SCM_ARG1
, s_gcd
);
1093 SCM_GPROC1 (s_lcm
, "lcm", scm_tc7_asubr
, scm_lcm
, g_lcm
);
1094 /* "Return the least common multiple of the arguments.\n"
1095 * "If called without arguments, 1 is returned."
1098 scm_lcm (SCM n1
, SCM n2
)
1100 if (SCM_UNBNDP (n2
))
1102 if (SCM_UNBNDP (n1
))
1103 return SCM_I_MAKINUM (1L);
1104 n2
= SCM_I_MAKINUM (1L);
1107 SCM_GASSERT2 (SCM_I_INUMP (n1
) || SCM_BIGP (n1
),
1108 g_lcm
, n1
, n2
, SCM_ARG1
, s_lcm
);
1109 SCM_GASSERT2 (SCM_I_INUMP (n2
) || SCM_BIGP (n2
),
1110 g_lcm
, n1
, n2
, SCM_ARGn
, s_lcm
);
1112 if (SCM_I_INUMP (n1
))
1114 if (SCM_I_INUMP (n2
))
1116 SCM d
= scm_gcd (n1
, n2
);
1117 if (scm_is_eq (d
, SCM_INUM0
))
1120 return scm_abs (scm_product (n1
, scm_quotient (n2
, d
)));
1124 /* inum n1, big n2 */
1127 SCM result
= scm_i_mkbig ();
1128 long nn1
= SCM_I_INUM (n1
);
1129 if (nn1
== 0) return SCM_INUM0
;
1130 if (nn1
< 0) nn1
= - nn1
;
1131 mpz_lcm_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (n2
), nn1
);
1132 scm_remember_upto_here_1 (n2
);
1140 if (SCM_I_INUMP (n2
))
1147 SCM result
= scm_i_mkbig ();
1148 mpz_lcm(SCM_I_BIG_MPZ (result
),
1150 SCM_I_BIG_MPZ (n2
));
1151 scm_remember_upto_here_2(n1
, n2
);
1152 /* shouldn't need to normalize b/c lcm of 2 bigs should be big */
1158 /* Emulating 2's complement bignums with sign magnitude arithmetic:
1163 + + + x (map digit:logand X Y)
1164 + - + x (map digit:logand X (lognot (+ -1 Y)))
1165 - + + y (map digit:logand (lognot (+ -1 X)) Y)
1166 - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y)))
1171 + + + (map digit:logior X Y)
1172 + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y)))
1173 - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y)))
1174 - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y)))
1179 + + + (map digit:logxor X Y)
1180 + - - (+ 1 (map digit:logxor X (+ -1 Y)))
1181 - + - (+ 1 (map digit:logxor (+ -1 X) Y))
1182 - - + (map digit:logxor (+ -1 X) (+ -1 Y))
1187 + + (any digit:logand X Y)
1188 + - (any digit:logand X (lognot (+ -1 Y)))
1189 - + (any digit:logand (lognot (+ -1 X)) Y)
1194 SCM_DEFINE1 (scm_logand
, "logand", scm_tc7_asubr
,
1196 "Return the bitwise AND of the integer arguments.\n\n"
1198 "(logand) @result{} -1\n"
1199 "(logand 7) @result{} 7\n"
1200 "(logand #b111 #b011 #b001) @result{} 1\n"
1202 #define FUNC_NAME s_scm_logand
1206 if (SCM_UNBNDP (n2
))
1208 if (SCM_UNBNDP (n1
))
1209 return SCM_I_MAKINUM (-1);
1210 else if (!SCM_NUMBERP (n1
))
1211 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n1
);
1212 else if (SCM_NUMBERP (n1
))
1215 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n1
);
1218 if (SCM_I_INUMP (n1
))
1220 nn1
= SCM_I_INUM (n1
);
1221 if (SCM_I_INUMP (n2
))
1223 long nn2
= SCM_I_INUM (n2
);
1224 return SCM_I_MAKINUM (nn1
& nn2
);
1226 else if SCM_BIGP (n2
)
1232 SCM result_z
= scm_i_mkbig ();
1234 mpz_init_set_si (nn1_z
, nn1
);
1235 mpz_and (SCM_I_BIG_MPZ (result_z
), nn1_z
, SCM_I_BIG_MPZ (n2
));
1236 scm_remember_upto_here_1 (n2
);
1238 return scm_i_normbig (result_z
);
1242 SCM_WRONG_TYPE_ARG (SCM_ARG2
, n2
);
1244 else if (SCM_BIGP (n1
))
1246 if (SCM_I_INUMP (n2
))
1249 nn1
= SCM_I_INUM (n1
);
1252 else if (SCM_BIGP (n2
))
1254 SCM result_z
= scm_i_mkbig ();
1255 mpz_and (SCM_I_BIG_MPZ (result_z
),
1257 SCM_I_BIG_MPZ (n2
));
1258 scm_remember_upto_here_2 (n1
, n2
);
1259 return scm_i_normbig (result_z
);
1262 SCM_WRONG_TYPE_ARG (SCM_ARG2
, n2
);
1265 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n1
);
1270 SCM_DEFINE1 (scm_logior
, "logior", scm_tc7_asubr
,
1272 "Return the bitwise OR of the integer arguments.\n\n"
1274 "(logior) @result{} 0\n"
1275 "(logior 7) @result{} 7\n"
1276 "(logior #b000 #b001 #b011) @result{} 3\n"
1278 #define FUNC_NAME s_scm_logior
1282 if (SCM_UNBNDP (n2
))
1284 if (SCM_UNBNDP (n1
))
1286 else if (SCM_NUMBERP (n1
))
1289 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n1
);
1292 if (SCM_I_INUMP (n1
))
1294 nn1
= SCM_I_INUM (n1
);
1295 if (SCM_I_INUMP (n2
))
1297 long nn2
= SCM_I_INUM (n2
);
1298 return SCM_I_MAKINUM (nn1
| nn2
);
1300 else if (SCM_BIGP (n2
))
1306 SCM result_z
= scm_i_mkbig ();
1308 mpz_init_set_si (nn1_z
, nn1
);
1309 mpz_ior (SCM_I_BIG_MPZ (result_z
), nn1_z
, SCM_I_BIG_MPZ (n2
));
1310 scm_remember_upto_here_1 (n2
);
1316 SCM_WRONG_TYPE_ARG (SCM_ARG2
, n2
);
1318 else if (SCM_BIGP (n1
))
1320 if (SCM_I_INUMP (n2
))
1323 nn1
= SCM_I_INUM (n1
);
1326 else if (SCM_BIGP (n2
))
1328 SCM result_z
= scm_i_mkbig ();
1329 mpz_ior (SCM_I_BIG_MPZ (result_z
),
1331 SCM_I_BIG_MPZ (n2
));
1332 scm_remember_upto_here_2 (n1
, n2
);
1336 SCM_WRONG_TYPE_ARG (SCM_ARG2
, n2
);
1339 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n1
);
1344 SCM_DEFINE1 (scm_logxor
, "logxor", scm_tc7_asubr
,
1346 "Return the bitwise XOR of the integer arguments. A bit is\n"
1347 "set in the result if it is set in an odd number of arguments.\n"
1349 "(logxor) @result{} 0\n"
1350 "(logxor 7) @result{} 7\n"
1351 "(logxor #b000 #b001 #b011) @result{} 2\n"
1352 "(logxor #b000 #b001 #b011 #b011) @result{} 1\n"
1354 #define FUNC_NAME s_scm_logxor
1358 if (SCM_UNBNDP (n2
))
1360 if (SCM_UNBNDP (n1
))
1362 else if (SCM_NUMBERP (n1
))
1365 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n1
);
1368 if (SCM_I_INUMP (n1
))
1370 nn1
= SCM_I_INUM (n1
);
1371 if (SCM_I_INUMP (n2
))
1373 long nn2
= SCM_I_INUM (n2
);
1374 return SCM_I_MAKINUM (nn1
^ nn2
);
1376 else if (SCM_BIGP (n2
))
1380 SCM result_z
= scm_i_mkbig ();
1382 mpz_init_set_si (nn1_z
, nn1
);
1383 mpz_xor (SCM_I_BIG_MPZ (result_z
), nn1_z
, SCM_I_BIG_MPZ (n2
));
1384 scm_remember_upto_here_1 (n2
);
1386 return scm_i_normbig (result_z
);
1390 SCM_WRONG_TYPE_ARG (SCM_ARG2
, n2
);
1392 else if (SCM_BIGP (n1
))
1394 if (SCM_I_INUMP (n2
))
1397 nn1
= SCM_I_INUM (n1
);
1400 else if (SCM_BIGP (n2
))
1402 SCM result_z
= scm_i_mkbig ();
1403 mpz_xor (SCM_I_BIG_MPZ (result_z
),
1405 SCM_I_BIG_MPZ (n2
));
1406 scm_remember_upto_here_2 (n1
, n2
);
1407 return scm_i_normbig (result_z
);
1410 SCM_WRONG_TYPE_ARG (SCM_ARG2
, n2
);
1413 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n1
);
1418 SCM_DEFINE (scm_logtest
, "logtest", 2, 0, 0,
1420 "Test whether @var{j} and @var{k} have any 1 bits in common.\n"
1421 "This is equivalent to @code{(not (zero? (logand j k)))}, but\n"
1422 "without actually calculating the @code{logand}, just testing\n"
1426 "(logtest #b0100 #b1011) @result{} #f\n"
1427 "(logtest #b0100 #b0111) @result{} #t\n"
1429 #define FUNC_NAME s_scm_logtest
1433 if (SCM_I_INUMP (j
))
1435 nj
= SCM_I_INUM (j
);
1436 if (SCM_I_INUMP (k
))
1438 long nk
= SCM_I_INUM (k
);
1439 return scm_from_bool (nj
& nk
);
1441 else if (SCM_BIGP (k
))
1449 mpz_init_set_si (nj_z
, nj
);
1450 mpz_and (nj_z
, nj_z
, SCM_I_BIG_MPZ (k
));
1451 scm_remember_upto_here_1 (k
);
1452 result
= scm_from_bool (mpz_sgn (nj_z
) != 0);
1458 SCM_WRONG_TYPE_ARG (SCM_ARG2
, k
);
1460 else if (SCM_BIGP (j
))
1462 if (SCM_I_INUMP (k
))
1465 nj
= SCM_I_INUM (j
);
1468 else if (SCM_BIGP (k
))
1472 mpz_init (result_z
);
1476 scm_remember_upto_here_2 (j
, k
);
1477 result
= scm_from_bool (mpz_sgn (result_z
) != 0);
1478 mpz_clear (result_z
);
1482 SCM_WRONG_TYPE_ARG (SCM_ARG2
, k
);
1485 SCM_WRONG_TYPE_ARG (SCM_ARG1
, j
);
1490 SCM_DEFINE (scm_logbit_p
, "logbit?", 2, 0, 0,
1492 "Test whether bit number @var{index} in @var{j} is set.\n"
1493 "@var{index} starts from 0 for the least significant bit.\n"
1496 "(logbit? 0 #b1101) @result{} #t\n"
1497 "(logbit? 1 #b1101) @result{} #f\n"
1498 "(logbit? 2 #b1101) @result{} #t\n"
1499 "(logbit? 3 #b1101) @result{} #t\n"
1500 "(logbit? 4 #b1101) @result{} #f\n"
1502 #define FUNC_NAME s_scm_logbit_p
1504 unsigned long int iindex
;
1505 iindex
= scm_to_ulong (index
);
1507 if (SCM_I_INUMP (j
))
1509 /* bits above what's in an inum follow the sign bit */
1510 iindex
= min (iindex
, SCM_LONG_BIT
- 1);
1511 return scm_from_bool ((1L << iindex
) & SCM_I_INUM (j
));
1513 else if (SCM_BIGP (j
))
1515 int val
= mpz_tstbit (SCM_I_BIG_MPZ (j
), iindex
);
1516 scm_remember_upto_here_1 (j
);
1517 return scm_from_bool (val
);
1520 SCM_WRONG_TYPE_ARG (SCM_ARG2
, j
);
1525 SCM_DEFINE (scm_lognot
, "lognot", 1, 0, 0,
1527 "Return the integer which is the ones-complement of the integer\n"
1531 "(number->string (lognot #b10000000) 2)\n"
1532 " @result{} \"-10000001\"\n"
1533 "(number->string (lognot #b0) 2)\n"
1534 " @result{} \"-1\"\n"
1536 #define FUNC_NAME s_scm_lognot
1538 if (SCM_I_INUMP (n
)) {
1539 /* No overflow here, just need to toggle all the bits making up the inum.
1540 Enhancement: No need to strip the tag and add it back, could just xor
1541 a block of 1 bits, if that worked with the various debug versions of
1543 return SCM_I_MAKINUM (~ SCM_I_INUM (n
));
1545 } else if (SCM_BIGP (n
)) {
1546 SCM result
= scm_i_mkbig ();
1547 mpz_com (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (n
));
1548 scm_remember_upto_here_1 (n
);
1552 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n
);
1557 /* returns 0 if IN is not an integer. OUT must already be
1560 coerce_to_big (SCM in
, mpz_t out
)
1563 mpz_set (out
, SCM_I_BIG_MPZ (in
));
1564 else if (SCM_I_INUMP (in
))
1565 mpz_set_si (out
, SCM_I_INUM (in
));
1572 SCM_DEFINE (scm_modulo_expt
, "modulo-expt", 3, 0, 0,
1573 (SCM n
, SCM k
, SCM m
),
1574 "Return @var{n} raised to the integer exponent\n"
1575 "@var{k}, modulo @var{m}.\n"
1578 "(modulo-expt 2 3 5)\n"
1581 #define FUNC_NAME s_scm_modulo_expt
1587 /* There are two classes of error we might encounter --
1588 1) Math errors, which we'll report by calling scm_num_overflow,
1590 2) wrong-type errors, which of course we'll report by calling
1592 We don't report those errors immediately, however; instead we do
1593 some cleanup first. These variables tell us which error (if
1594 any) we should report after cleaning up.
1596 int report_overflow
= 0;
1598 int position_of_wrong_type
= 0;
1599 SCM value_of_wrong_type
= SCM_INUM0
;
1601 SCM result
= SCM_UNDEFINED
;
1607 if (scm_is_eq (m
, SCM_INUM0
))
1609 report_overflow
= 1;
1613 if (!coerce_to_big (n
, n_tmp
))
1615 value_of_wrong_type
= n
;
1616 position_of_wrong_type
= 1;
1620 if (!coerce_to_big (k
, k_tmp
))
1622 value_of_wrong_type
= k
;
1623 position_of_wrong_type
= 2;
1627 if (!coerce_to_big (m
, m_tmp
))
1629 value_of_wrong_type
= m
;
1630 position_of_wrong_type
= 3;
1634 /* if the exponent K is negative, and we simply call mpz_powm, we
1635 will get a divide-by-zero exception when an inverse 1/n mod m
1636 doesn't exist (or is not unique). Since exceptions are hard to
1637 handle, we'll attempt the inversion "by hand" -- that way, we get
1638 a simple failure code, which is easy to handle. */
1640 if (-1 == mpz_sgn (k_tmp
))
1642 if (!mpz_invert (n_tmp
, n_tmp
, m_tmp
))
1644 report_overflow
= 1;
1647 mpz_neg (k_tmp
, k_tmp
);
1650 result
= scm_i_mkbig ();
1651 mpz_powm (SCM_I_BIG_MPZ (result
),
1656 if (mpz_sgn (m_tmp
) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result
)) != 0)
1657 mpz_add (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (result
), m_tmp
);
1664 if (report_overflow
)
1665 scm_num_overflow (FUNC_NAME
);
1667 if (position_of_wrong_type
)
1668 SCM_WRONG_TYPE_ARG (position_of_wrong_type
,
1669 value_of_wrong_type
);
1671 return scm_i_normbig (result
);
1675 SCM_DEFINE (scm_integer_expt
, "integer-expt", 2, 0, 0,
1677 "Return @var{n} raised to the power @var{k}. @var{k} must be an\n"
1678 "exact integer, @var{n} can be any number.\n"
1680 "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n"
1681 "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n"
1682 "includes @math{0^0} is 1.\n"
1685 "(integer-expt 2 5) @result{} 32\n"
1686 "(integer-expt -3 3) @result{} -27\n"
1687 "(integer-expt 5 -3) @result{} 1/125\n"
1688 "(integer-expt 0 0) @result{} 1\n"
1690 #define FUNC_NAME s_scm_integer_expt
1693 SCM z_i2
= SCM_BOOL_F
;
1695 SCM acc
= SCM_I_MAKINUM (1L);
1697 /* 0^0 == 1 according to R5RS */
1698 if (scm_is_eq (n
, SCM_INUM0
) || scm_is_eq (n
, acc
))
1699 return scm_is_false (scm_zero_p(k
)) ? n
: acc
;
1700 else if (scm_is_eq (n
, SCM_I_MAKINUM (-1L)))
1701 return scm_is_false (scm_even_p (k
)) ? n
: acc
;
1703 if (SCM_I_INUMP (k
))
1704 i2
= SCM_I_INUM (k
);
1705 else if (SCM_BIGP (k
))
1707 z_i2
= scm_i_clonebig (k
, 1);
1708 scm_remember_upto_here_1 (k
);
1712 SCM_WRONG_TYPE_ARG (2, k
);
1716 if (mpz_sgn(SCM_I_BIG_MPZ (z_i2
)) == -1)
1718 mpz_neg (SCM_I_BIG_MPZ (z_i2
), SCM_I_BIG_MPZ (z_i2
));
1719 n
= scm_divide (n
, SCM_UNDEFINED
);
1723 if (mpz_sgn(SCM_I_BIG_MPZ (z_i2
)) == 0)
1727 if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2
), 1) == 0)
1729 return scm_product (acc
, n
);
1731 if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2
), 0))
1732 acc
= scm_product (acc
, n
);
1733 n
= scm_product (n
, n
);
1734 mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2
), SCM_I_BIG_MPZ (z_i2
), 1);
1742 n
= scm_divide (n
, SCM_UNDEFINED
);
1749 return scm_product (acc
, n
);
1751 acc
= scm_product (acc
, n
);
1752 n
= scm_product (n
, n
);
1759 SCM_DEFINE (scm_ash
, "ash", 2, 0, 0,
1761 "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n"
1762 "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n"
1764 "This is effectively a multiplication by 2^@var{cnt}, and when\n"
1765 "@var{cnt} is negative it's a division, rounded towards negative\n"
1766 "infinity. (Note that this is not the same rounding as\n"
1767 "@code{quotient} does.)\n"
1769 "With @var{n} viewed as an infinite precision twos complement,\n"
1770 "@code{ash} means a left shift introducing zero bits, or a right\n"
1771 "shift dropping bits.\n"
1774 "(number->string (ash #b1 3) 2) @result{} \"1000\"\n"
1775 "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n"
1777 ";; -23 is bits ...11101001, -6 is bits ...111010\n"
1778 "(ash -23 -2) @result{} -6\n"
1780 #define FUNC_NAME s_scm_ash
1783 bits_to_shift
= scm_to_long (cnt
);
1785 if (SCM_I_INUMP (n
))
1787 long nn
= SCM_I_INUM (n
);
1789 if (bits_to_shift
> 0)
1791 /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always
1792 overflow a non-zero fixnum. For smaller shifts we check the
1793 bits going into positions above SCM_I_FIXNUM_BIT-1. If they're
1794 all 0s for nn>=0, or all 1s for nn<0 then there's no overflow.
1795 Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 -
1801 if (bits_to_shift
< SCM_I_FIXNUM_BIT
-1
1803 (SCM_SRS (nn
, (SCM_I_FIXNUM_BIT
-1 - bits_to_shift
)) + 1)
1806 return SCM_I_MAKINUM (nn
<< bits_to_shift
);
1810 SCM result
= scm_i_long2big (nn
);
1811 mpz_mul_2exp (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (result
),
1818 bits_to_shift
= -bits_to_shift
;
1819 if (bits_to_shift
>= SCM_LONG_BIT
)
1820 return (nn
>= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1));
1822 return SCM_I_MAKINUM (SCM_SRS (nn
, bits_to_shift
));
1826 else if (SCM_BIGP (n
))
1830 if (bits_to_shift
== 0)
1833 result
= scm_i_mkbig ();
1834 if (bits_to_shift
>= 0)
1836 mpz_mul_2exp (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (n
),
1842 /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so
1843 we have to allocate a bignum even if the result is going to be a
1845 mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (n
),
1847 return scm_i_normbig (result
);
1853 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n
);
1859 SCM_DEFINE (scm_bit_extract
, "bit-extract", 3, 0, 0,
1860 (SCM n
, SCM start
, SCM end
),
1861 "Return the integer composed of the @var{start} (inclusive)\n"
1862 "through @var{end} (exclusive) bits of @var{n}. The\n"
1863 "@var{start}th bit becomes the 0-th bit in the result.\n"
1866 "(number->string (bit-extract #b1101101010 0 4) 2)\n"
1867 " @result{} \"1010\"\n"
1868 "(number->string (bit-extract #b1101101010 4 9) 2)\n"
1869 " @result{} \"10110\"\n"
1871 #define FUNC_NAME s_scm_bit_extract
1873 unsigned long int istart
, iend
, bits
;
1874 istart
= scm_to_ulong (start
);
1875 iend
= scm_to_ulong (end
);
1876 SCM_ASSERT_RANGE (3, end
, (iend
>= istart
));
1878 /* how many bits to keep */
1879 bits
= iend
- istart
;
1881 if (SCM_I_INUMP (n
))
1883 long int in
= SCM_I_INUM (n
);
1885 /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to
1886 SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */
1887 in
= SCM_SRS (in
, min (istart
, SCM_I_FIXNUM_BIT
-1));
1889 if (in
< 0 && bits
>= SCM_I_FIXNUM_BIT
)
1891 /* Since we emulate two's complement encoded numbers, this
1892 * special case requires us to produce a result that has
1893 * more bits than can be stored in a fixnum.
1895 SCM result
= scm_i_long2big (in
);
1896 mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (result
),
1901 /* mask down to requisite bits */
1902 bits
= min (bits
, SCM_I_FIXNUM_BIT
);
1903 return SCM_I_MAKINUM (in
& ((1L << bits
) - 1));
1905 else if (SCM_BIGP (n
))
1910 result
= SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n
), istart
));
1914 /* ENHANCE-ME: It'd be nice not to allocate a new bignum when
1915 bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get
1916 such bits into a ulong. */
1917 result
= scm_i_mkbig ();
1918 mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result
), SCM_I_BIG_MPZ(n
), istart
);
1919 mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result
), SCM_I_BIG_MPZ(result
), bits
);
1920 result
= scm_i_normbig (result
);
1922 scm_remember_upto_here_1 (n
);
1926 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n
);
1931 static const char scm_logtab
[] = {
1932 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
1935 SCM_DEFINE (scm_logcount
, "logcount", 1, 0, 0,
1937 "Return the number of bits in integer @var{n}. If integer is\n"
1938 "positive, the 1-bits in its binary representation are counted.\n"
1939 "If negative, the 0-bits in its two's-complement binary\n"
1940 "representation are counted. If 0, 0 is returned.\n"
1943 "(logcount #b10101010)\n"
1950 #define FUNC_NAME s_scm_logcount
1952 if (SCM_I_INUMP (n
))
1954 unsigned long int c
= 0;
1955 long int nn
= SCM_I_INUM (n
);
1960 c
+= scm_logtab
[15 & nn
];
1963 return SCM_I_MAKINUM (c
);
1965 else if (SCM_BIGP (n
))
1967 unsigned long count
;
1968 if (mpz_sgn (SCM_I_BIG_MPZ (n
)) >= 0)
1969 count
= mpz_popcount (SCM_I_BIG_MPZ (n
));
1971 count
= mpz_hamdist (SCM_I_BIG_MPZ (n
), z_negative_one
);
1972 scm_remember_upto_here_1 (n
);
1973 return SCM_I_MAKINUM (count
);
1976 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n
);
1981 static const char scm_ilentab
[] = {
1982 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4
1986 SCM_DEFINE (scm_integer_length
, "integer-length", 1, 0, 0,
1988 "Return the number of bits necessary to represent @var{n}.\n"
1991 "(integer-length #b10101010)\n"
1993 "(integer-length 0)\n"
1995 "(integer-length #b1111)\n"
1998 #define FUNC_NAME s_scm_integer_length
2000 if (SCM_I_INUMP (n
))
2002 unsigned long int c
= 0;
2004 long int nn
= SCM_I_INUM (n
);
2010 l
= scm_ilentab
[15 & nn
];
2013 return SCM_I_MAKINUM (c
- 4 + l
);
2015 else if (SCM_BIGP (n
))
2017 /* mpz_sizeinbase looks at the absolute value of negatives, whereas we
2018 want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is
2019 1 too big, so check for that and adjust. */
2020 size_t size
= mpz_sizeinbase (SCM_I_BIG_MPZ (n
), 2);
2021 if (mpz_sgn (SCM_I_BIG_MPZ (n
)) < 0
2022 && mpz_scan0 (SCM_I_BIG_MPZ (n
), /* no 0 bits above the lowest 1 */
2023 mpz_scan1 (SCM_I_BIG_MPZ (n
), 0)) == ULONG_MAX
)
2025 scm_remember_upto_here_1 (n
);
2026 return SCM_I_MAKINUM (size
);
2029 SCM_WRONG_TYPE_ARG (SCM_ARG1
, n
);
2033 /*** NUMBERS -> STRINGS ***/
2034 #define SCM_MAX_DBL_PREC 60
2035 #define SCM_MAX_DBL_RADIX 36
2037 /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */
2038 static int scm_dblprec
[SCM_MAX_DBL_RADIX
- 1];
2039 static double fx_per_radix
[SCM_MAX_DBL_RADIX
- 1][SCM_MAX_DBL_PREC
];
2042 void init_dblprec(int *prec
, int radix
) {
2043 /* determine floating point precision by adding successively
2044 smaller increments to 1.0 until it is considered == 1.0 */
2045 double f
= ((double)1.0)/radix
;
2046 double fsum
= 1.0 + f
;
2051 if (++(*prec
) > SCM_MAX_DBL_PREC
)
2063 void init_fx_radix(double *fx_list
, int radix
)
2065 /* initialize a per-radix list of tolerances. When added
2066 to a number < 1.0, we can determine if we should raund
2067 up and quit converting a number to a string. */
2071 for( i
= 2 ; i
< SCM_MAX_DBL_PREC
; ++i
)
2072 fx_list
[i
] = (fx_list
[i
-1] / radix
);
2075 /* use this array as a way to generate a single digit */
2076 static const char*number_chars
="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
2079 idbl2str (double f
, char *a
, int radix
)
2081 int efmt
, dpt
, d
, i
, wp
;
2083 #ifdef DBL_MIN_10_EXP
2086 #endif /* DBL_MIN_10_EXP */
2091 radix
> SCM_MAX_DBL_RADIX
)
2093 /* revert to existing behavior */
2097 wp
= scm_dblprec
[radix
-2];
2098 fx
= fx_per_radix
[radix
-2];
2102 #ifdef HAVE_COPYSIGN
2103 double sgn
= copysign (1.0, f
);
2108 goto zero
; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */
2114 strcpy (a
, "-inf.0");
2116 strcpy (a
, "+inf.0");
2119 else if (xisnan (f
))
2121 strcpy (a
, "+nan.0");
2131 #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from
2132 make-uniform-vector, from causing infinite loops. */
2133 /* just do the checking...if it passes, we do the conversion for our
2134 radix again below */
2141 if (exp_cpy
-- < DBL_MIN_10_EXP
)
2149 while (f_cpy
> 10.0)
2152 if (exp_cpy
++ > DBL_MAX_10_EXP
)
2173 if (f
+ fx
[wp
] >= radix
)
2180 /* adding 9999 makes this equivalent to abs(x) % 3 */
2181 dpt
= (exp
+ 9999) % 3;
2185 efmt
= (exp
< -3) || (exp
> wp
+ 2);
2207 a
[ch
++] = number_chars
[d
];
2210 if (f
+ fx
[wp
] >= 1.0)
2212 a
[ch
- 1] = number_chars
[d
+1];
2224 if ((dpt
> 4) && (exp
> 6))
2226 d
= (a
[0] == '-' ? 2 : 1);
2227 for (i
= ch
++; i
> d
; i
--)
2240 if (a
[ch
- 1] == '.')
2241 a
[ch
++] = '0'; /* trailing zero */
2250 for (i
= radix
; i
<= exp
; i
*= radix
);
2251 for (i
/= radix
; i
; i
/= radix
)
2253 a
[ch
++] = number_chars
[exp
/ i
];
2262 icmplx2str (double real
, double imag
, char *str
, int radix
)
2266 i
= idbl2str (real
, str
, radix
);
2269 /* Don't output a '+' for negative numbers or for Inf and
2270 NaN. They will provide their own sign. */
2271 if (0 <= imag
&& !xisinf (imag
) && !xisnan (imag
))
2273 i
+= idbl2str (imag
, &str
[i
], radix
);
2280 iflo2str (SCM flt
, char *str
, int radix
)
2283 if (SCM_REALP (flt
))
2284 i
= idbl2str (SCM_REAL_VALUE (flt
), str
, radix
);
2286 i
= icmplx2str (SCM_COMPLEX_REAL (flt
), SCM_COMPLEX_IMAG (flt
),
2291 /* convert a scm_t_intmax to a string (unterminated). returns the number of
2292 characters in the result.
2294 p is destination: worst case (base 2) is SCM_INTBUFLEN */
2296 scm_iint2str (scm_t_intmax num
, int rad
, char *p
)
2301 return scm_iuint2str (-num
, rad
, p
) + 1;
2304 return scm_iuint2str (num
, rad
, p
);
2307 /* convert a scm_t_intmax to a string (unterminated). returns the number of
2308 characters in the result.
2310 p is destination: worst case (base 2) is SCM_INTBUFLEN */
2312 scm_iuint2str (scm_t_uintmax num
, int rad
, char *p
)
2316 scm_t_uintmax n
= num
;
2318 for (n
/= rad
; n
> 0; n
/= rad
)
2328 p
[i
] = d
+ ((d
< 10) ? '0' : 'a' - 10);
2333 SCM_DEFINE (scm_number_to_string
, "number->string", 1, 1, 0,
2335 "Return a string holding the external representation of the\n"
2336 "number @var{n} in the given @var{radix}. If @var{n} is\n"
2337 "inexact, a radix of 10 will be used.")
2338 #define FUNC_NAME s_scm_number_to_string
2342 if (SCM_UNBNDP (radix
))
2345 base
= scm_to_signed_integer (radix
, 2, 36);
2347 if (SCM_I_INUMP (n
))
2349 char num_buf
[SCM_INTBUFLEN
];
2350 size_t length
= scm_iint2str (SCM_I_INUM (n
), base
, num_buf
);
2351 return scm_from_locale_stringn (num_buf
, length
);
2353 else if (SCM_BIGP (n
))
2355 char *str
= mpz_get_str (NULL
, base
, SCM_I_BIG_MPZ (n
));
2356 scm_remember_upto_here_1 (n
);
2357 return scm_take_locale_string (str
);
2359 else if (SCM_FRACTIONP (n
))
2361 scm_i_fraction_reduce (n
);
2362 return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n
), radix
),
2363 scm_from_locale_string ("/"),
2364 scm_number_to_string (SCM_FRACTION_DENOMINATOR (n
), radix
)));
2366 else if (SCM_INEXACTP (n
))
2368 char num_buf
[FLOBUFLEN
];
2369 return scm_from_locale_stringn (num_buf
, iflo2str (n
, num_buf
, base
));
2372 SCM_WRONG_TYPE_ARG (1, n
);
2377 /* These print routines used to be stubbed here so that scm_repl.c
2378 wouldn't need SCM_BIGDIG conditionals (pre GMP) */
2381 scm_print_real (SCM sexp
, SCM port
, scm_print_state
*pstate SCM_UNUSED
)
2383 char num_buf
[FLOBUFLEN
];
2384 scm_lfwrite (num_buf
, iflo2str (sexp
, num_buf
, 10), port
);
2389 scm_i_print_double (double val
, SCM port
)
2391 char num_buf
[FLOBUFLEN
];
2392 scm_lfwrite (num_buf
, idbl2str (val
, num_buf
, 10), port
);
2396 scm_print_complex (SCM sexp
, SCM port
, scm_print_state
*pstate SCM_UNUSED
)
2399 char num_buf
[FLOBUFLEN
];
2400 scm_lfwrite (num_buf
, iflo2str (sexp
, num_buf
, 10), port
);
2405 scm_i_print_complex (double real
, double imag
, SCM port
)
2407 char num_buf
[FLOBUFLEN
];
2408 scm_lfwrite (num_buf
, icmplx2str (real
, imag
, num_buf
, 10), port
);
2412 scm_i_print_fraction (SCM sexp
, SCM port
, scm_print_state
*pstate SCM_UNUSED
)
2415 scm_i_fraction_reduce (sexp
);
2416 str
= scm_number_to_string (sexp
, SCM_UNDEFINED
);
2417 scm_lfwrite (scm_i_string_chars (str
), scm_i_string_length (str
), port
);
2418 scm_remember_upto_here_1 (str
);
2423 scm_bigprint (SCM exp
, SCM port
, scm_print_state
*pstate SCM_UNUSED
)
2425 char *str
= mpz_get_str (NULL
, 10, SCM_I_BIG_MPZ (exp
));
2426 scm_remember_upto_here_1 (exp
);
2427 scm_lfwrite (str
, (size_t) strlen (str
), port
);
2431 /*** END nums->strs ***/
2434 /*** STRINGS -> NUMBERS ***/
2436 /* The following functions implement the conversion from strings to numbers.
2437 * The implementation somehow follows the grammar for numbers as it is given
2438 * in R5RS. Thus, the functions resemble syntactic units (<ureal R>,
2439 * <uinteger R>, ...) that are used to build up numbers in the grammar. Some
2440 * points should be noted about the implementation:
2441 * * Each function keeps a local index variable 'idx' that points at the
2442 * current position within the parsed string. The global index is only
2443 * updated if the function could parse the corresponding syntactic unit
2445 * * Similarly, the functions keep track of indicators of inexactness ('#',
2446 * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the
2447 * global exactness information is only updated after each part has been
2448 * successfully parsed.
2449 * * Sequences of digits are parsed into temporary variables holding fixnums.
2450 * Only if these fixnums would overflow, the result variables are updated
2451 * using the standard functions scm_add, scm_product, scm_divide etc. Then,
2452 * the temporary variables holding the fixnums are cleared, and the process
2453 * starts over again. If for example fixnums were able to store five decimal
2454 * digits, a number 1234567890 would be parsed in two parts 12345 and 67890,
2455 * and the result was computed as 12345 * 100000 + 67890. In other words,
2456 * only every five digits two bignum operations were performed.
2459 enum t_exactness
{NO_EXACTNESS
, INEXACT
, EXACT
};
2461 /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */
2463 /* In non ASCII-style encodings the following macro might not work. */
2464 #define XDIGIT2UINT(d) \
2465 (isdigit ((int) (unsigned char) d) \
2467 : tolower ((int) (unsigned char) d) - 'a' + 10)
2470 mem2uinteger (const char* mem
, size_t len
, unsigned int *p_idx
,
2471 unsigned int radix
, enum t_exactness
*p_exactness
)
2473 unsigned int idx
= *p_idx
;
2474 unsigned int hash_seen
= 0;
2475 scm_t_bits shift
= 1;
2477 unsigned int digit_value
;
2485 if (!isxdigit ((int) (unsigned char) c
))
2487 digit_value
= XDIGIT2UINT (c
);
2488 if (digit_value
>= radix
)
2492 result
= SCM_I_MAKINUM (digit_value
);
2496 if (isxdigit ((int) (unsigned char) c
))
2500 digit_value
= XDIGIT2UINT (c
);
2501 if (digit_value
>= radix
)
2513 if (SCM_MOST_POSITIVE_FIXNUM
/ radix
< shift
)
2515 result
= scm_product (result
, SCM_I_MAKINUM (shift
));
2517 result
= scm_sum (result
, SCM_I_MAKINUM (add
));
2524 shift
= shift
* radix
;
2525 add
= add
* radix
+ digit_value
;
2530 result
= scm_product (result
, SCM_I_MAKINUM (shift
));
2532 result
= scm_sum (result
, SCM_I_MAKINUM (add
));
2536 *p_exactness
= INEXACT
;
2542 /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only
2543 * covers the parts of the rules that start at a potential point. The value
2544 * of the digits up to the point have been parsed by the caller and are given
2545 * in variable result. The content of *p_exactness indicates, whether a hash
2546 * has already been seen in the digits before the point.
2549 /* In non ASCII-style encodings the following macro might not work. */
2550 #define DIGIT2UINT(d) ((d) - '0')
2553 mem2decimal_from_point (SCM result
, const char* mem
, size_t len
,
2554 unsigned int *p_idx
, enum t_exactness
*p_exactness
)
2556 unsigned int idx
= *p_idx
;
2557 enum t_exactness x
= *p_exactness
;
2562 if (mem
[idx
] == '.')
2564 scm_t_bits shift
= 1;
2566 unsigned int digit_value
;
2567 SCM big_shift
= SCM_I_MAKINUM (1);
2573 if (isdigit ((int) (unsigned char) c
))
2578 digit_value
= DIGIT2UINT (c
);
2589 if (SCM_MOST_POSITIVE_FIXNUM
/ 10 < shift
)
2591 big_shift
= scm_product (big_shift
, SCM_I_MAKINUM (shift
));
2592 result
= scm_product (result
, SCM_I_MAKINUM (shift
));
2594 result
= scm_sum (result
, SCM_I_MAKINUM (add
));
2602 add
= add
* 10 + digit_value
;
2608 big_shift
= scm_product (big_shift
, SCM_I_MAKINUM (shift
));
2609 result
= scm_product (result
, SCM_I_MAKINUM (shift
));
2610 result
= scm_sum (result
, SCM_I_MAKINUM (add
));
2613 result
= scm_divide (result
, big_shift
);
2615 /* We've seen a decimal point, thus the value is implicitly inexact. */
2627 /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */
2654 if (!isdigit ((int) (unsigned char) c
))
2658 exponent
= DIGIT2UINT (c
);
2662 if (isdigit ((int) (unsigned char) c
))
2665 if (exponent
<= SCM_MAXEXP
)
2666 exponent
= exponent
* 10 + DIGIT2UINT (c
);
2672 if (exponent
> SCM_MAXEXP
)
2674 size_t exp_len
= idx
- start
;
2675 SCM exp_string
= scm_from_locale_stringn (&mem
[start
], exp_len
);
2676 SCM exp_num
= scm_string_to_number (exp_string
, SCM_UNDEFINED
);
2677 scm_out_of_range ("string->number", exp_num
);
2680 e
= scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent
));
2682 result
= scm_product (result
, e
);
2684 result
= scm_divide2real (result
, e
);
2686 /* We've seen an exponent, thus the value is implicitly inexact. */
2704 /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */
2707 mem2ureal (const char* mem
, size_t len
, unsigned int *p_idx
,
2708 unsigned int radix
, enum t_exactness
*p_exactness
)
2710 unsigned int idx
= *p_idx
;
2716 if (idx
+5 <= len
&& !strncmp (mem
+idx
, "inf.0", 5))
2722 if (idx
+4 < len
&& !strncmp (mem
+idx
, "nan.", 4))
2724 enum t_exactness x
= EXACT
;
2726 /* Cobble up the fractional part. We might want to set the
2727 NaN's mantissa from it. */
2729 mem2uinteger (mem
, len
, &idx
, 10, &x
);
2734 if (mem
[idx
] == '.')
2738 else if (idx
+ 1 == len
)
2740 else if (!isdigit ((int) (unsigned char) mem
[idx
+ 1]))
2743 result
= mem2decimal_from_point (SCM_I_MAKINUM (0), mem
, len
,
2744 p_idx
, p_exactness
);
2748 enum t_exactness x
= EXACT
;
2751 uinteger
= mem2uinteger (mem
, len
, &idx
, radix
, &x
);
2752 if (scm_is_false (uinteger
))
2757 else if (mem
[idx
] == '/')
2763 divisor
= mem2uinteger (mem
, len
, &idx
, radix
, &x
);
2764 if (scm_is_false (divisor
))
2767 /* both are int/big here, I assume */
2768 result
= scm_i_make_ratio (uinteger
, divisor
);
2770 else if (radix
== 10)
2772 result
= mem2decimal_from_point (uinteger
, mem
, len
, &idx
, &x
);
2773 if (scm_is_false (result
))
2784 /* When returning an inexact zero, make sure it is represented as a
2785 floating point value so that we can change its sign.
2787 if (scm_is_eq (result
, SCM_I_MAKINUM(0)) && *p_exactness
== INEXACT
)
2788 result
= scm_from_double (0.0);
2794 /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */
2797 mem2complex (const char* mem
, size_t len
, unsigned int idx
,
2798 unsigned int radix
, enum t_exactness
*p_exactness
)
2822 ureal
= mem2ureal (mem
, len
, &idx
, radix
, p_exactness
);
2823 if (scm_is_false (ureal
))
2825 /* input must be either +i or -i */
2830 if (mem
[idx
] == 'i' || mem
[idx
] == 'I')
2836 return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign
));
2843 if (sign
== -1 && scm_is_false (scm_nan_p (ureal
)))
2844 ureal
= scm_difference (ureal
, SCM_UNDEFINED
);
2853 /* either +<ureal>i or -<ureal>i */
2860 return scm_make_rectangular (SCM_I_MAKINUM (0), ureal
);
2863 /* polar input: <real>@<real>. */
2888 angle
= mem2ureal (mem
, len
, &idx
, radix
, p_exactness
);
2889 if (scm_is_false (angle
))
2894 if (sign
== -1 && scm_is_false (scm_nan_p (ureal
)))
2895 angle
= scm_difference (angle
, SCM_UNDEFINED
);
2897 result
= scm_make_polar (ureal
, angle
);
2902 /* expecting input matching <real>[+-]<ureal>?i */
2909 int sign
= (c
== '+') ? 1 : -1;
2910 SCM imag
= mem2ureal (mem
, len
, &idx
, radix
, p_exactness
);
2912 if (scm_is_false (imag
))
2913 imag
= SCM_I_MAKINUM (sign
);
2914 else if (sign
== -1 && scm_is_false (scm_nan_p (ureal
)))
2915 imag
= scm_difference (imag
, SCM_UNDEFINED
);
2919 if (mem
[idx
] != 'i' && mem
[idx
] != 'I')
2926 return scm_make_rectangular (ureal
, imag
);
2935 /* R5RS, section 7.1.1, lexical structure of numbers: <number> */
2937 enum t_radix
{NO_RADIX
=0, DUAL
=2, OCT
=8, DEC
=10, HEX
=16};
2940 scm_i_mem2number (const char* mem
, size_t len
, unsigned int default_radix
)
2942 unsigned int idx
= 0;
2943 unsigned int radix
= NO_RADIX
;
2944 enum t_exactness forced_x
= NO_EXACTNESS
;
2945 enum t_exactness implicit_x
= EXACT
;
2948 /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */
2949 while (idx
+ 2 < len
&& mem
[idx
] == '#')
2951 switch (mem
[idx
+ 1])
2954 if (radix
!= NO_RADIX
)
2959 if (radix
!= NO_RADIX
)
2964 if (forced_x
!= NO_EXACTNESS
)
2969 if (forced_x
!= NO_EXACTNESS
)
2974 if (radix
!= NO_RADIX
)
2979 if (radix
!= NO_RADIX
)
2989 /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */
2990 if (radix
== NO_RADIX
)
2991 result
= mem2complex (mem
, len
, idx
, default_radix
, &implicit_x
);
2993 result
= mem2complex (mem
, len
, idx
, (unsigned int) radix
, &implicit_x
);
2995 if (scm_is_false (result
))
3001 if (SCM_INEXACTP (result
))
3002 return scm_inexact_to_exact (result
);
3006 if (SCM_INEXACTP (result
))
3009 return scm_exact_to_inexact (result
);
3012 if (implicit_x
== INEXACT
)
3014 if (SCM_INEXACTP (result
))
3017 return scm_exact_to_inexact (result
);
3025 SCM_DEFINE (scm_string_to_number
, "string->number", 1, 1, 0,
3026 (SCM string
, SCM radix
),
3027 "Return a number of the maximally precise representation\n"
3028 "expressed by the given @var{string}. @var{radix} must be an\n"
3029 "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n"
3030 "is a default radix that may be overridden by an explicit radix\n"
3031 "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n"
3032 "supplied, then the default radix is 10. If string is not a\n"
3033 "syntactically valid notation for a number, then\n"
3034 "@code{string->number} returns @code{#f}.")
3035 #define FUNC_NAME s_scm_string_to_number
3039 SCM_VALIDATE_STRING (1, string
);
3041 if (SCM_UNBNDP (radix
))
3044 base
= scm_to_unsigned_integer (radix
, 2, INT_MAX
);
3046 answer
= scm_i_mem2number (scm_i_string_chars (string
),
3047 scm_i_string_length (string
),
3049 scm_remember_upto_here_1 (string
);
3055 /*** END strs->nums ***/
3059 scm_bigequal (SCM x
, SCM y
)
3061 int result
= mpz_cmp (SCM_I_BIG_MPZ (x
), SCM_I_BIG_MPZ (y
));
3062 scm_remember_upto_here_2 (x
, y
);
3063 return scm_from_bool (0 == result
);
3067 scm_real_equalp (SCM x
, SCM y
)
3069 return scm_from_bool (SCM_REAL_VALUE (x
) == SCM_REAL_VALUE (y
));
3073 scm_complex_equalp (SCM x
, SCM y
)
3075 return scm_from_bool (SCM_COMPLEX_REAL (x
) == SCM_COMPLEX_REAL (y
)
3076 && SCM_COMPLEX_IMAG (x
) == SCM_COMPLEX_IMAG (y
));
3080 scm_i_fraction_equalp (SCM x
, SCM y
)
3082 scm_i_fraction_reduce (x
);
3083 scm_i_fraction_reduce (y
);
3084 if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x
),
3085 SCM_FRACTION_NUMERATOR (y
)))
3086 || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x
),
3087 SCM_FRACTION_DENOMINATOR (y
))))
3094 SCM_DEFINE (scm_number_p
, "number?", 1, 0, 0,
3096 "Return @code{#t} if @var{x} is a number, @code{#f}\n"
3098 #define FUNC_NAME s_scm_number_p
3100 return scm_from_bool (SCM_NUMBERP (x
));
3104 SCM_DEFINE (scm_complex_p
, "complex?", 1, 0, 0,
3106 "Return @code{#t} if @var{x} is a complex number, @code{#f}\n"
3107 "otherwise. Note that the sets of real, rational and integer\n"
3108 "values form subsets of the set of complex numbers, i. e. the\n"
3109 "predicate will also be fulfilled if @var{x} is a real,\n"
3110 "rational or integer number.")
3111 #define FUNC_NAME s_scm_complex_p
3113 /* all numbers are complex. */
3114 return scm_number_p (x
);
3118 SCM_DEFINE (scm_real_p
, "real?", 1, 0, 0,
3120 "Return @code{#t} if @var{x} is a real number, @code{#f}\n"
3121 "otherwise. Note that the set of integer values forms a subset of\n"
3122 "the set of real numbers, i. e. the predicate will also be\n"
3123 "fulfilled if @var{x} is an integer number.")
3124 #define FUNC_NAME s_scm_real_p
3126 /* we can't represent irrational numbers. */
3127 return scm_rational_p (x
);
3131 SCM_DEFINE (scm_rational_p
, "rational?", 1, 0, 0,
3133 "Return @code{#t} if @var{x} is a rational number, @code{#f}\n"
3134 "otherwise. Note that the set of integer values forms a subset of\n"
3135 "the set of rational numbers, i. e. the predicate will also be\n"
3136 "fulfilled if @var{x} is an integer number.")
3137 #define FUNC_NAME s_scm_rational_p
3139 if (SCM_I_INUMP (x
))
3141 else if (SCM_IMP (x
))
3143 else if (SCM_BIGP (x
))
3145 else if (SCM_FRACTIONP (x
))
3147 else if (SCM_REALP (x
))
3148 /* due to their limited precision, all floating point numbers are
3149 rational as well. */
3156 SCM_DEFINE (scm_integer_p
, "integer?", 1, 0, 0,
3158 "Return @code{#t} if @var{x} is an integer number, @code{#f}\n"
3160 #define FUNC_NAME s_scm_integer_p
3163 if (SCM_I_INUMP (x
))
3169 if (!SCM_INEXACTP (x
))
3171 if (SCM_COMPLEXP (x
))
3173 r
= SCM_REAL_VALUE (x
);
3174 /* +/-inf passes r==floor(r), making those #t */
3182 SCM_DEFINE (scm_inexact_p
, "inexact?", 1, 0, 0,
3184 "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n"
3186 #define FUNC_NAME s_scm_inexact_p
3188 if (SCM_INEXACTP (x
))
3190 if (SCM_NUMBERP (x
))
3192 SCM_WRONG_TYPE_ARG (1, x
);
3197 SCM_GPROC1 (s_eq_p
, "=", scm_tc7_rpsubr
, scm_num_eq_p
, g_eq_p
);
3198 /* "Return @code{#t} if all parameters are numerically equal." */
3200 scm_num_eq_p (SCM x
, SCM y
)
3203 if (SCM_I_INUMP (x
))
3205 long xx
= SCM_I_INUM (x
);
3206 if (SCM_I_INUMP (y
))
3208 long yy
= SCM_I_INUM (y
);
3209 return scm_from_bool (xx
== yy
);
3211 else if (SCM_BIGP (y
))
3213 else if (SCM_REALP (y
))
3214 return scm_from_bool ((double) xx
== SCM_REAL_VALUE (y
));
3215 else if (SCM_COMPLEXP (y
))
3216 return scm_from_bool (((double) xx
== SCM_COMPLEX_REAL (y
))
3217 && (0.0 == SCM_COMPLEX_IMAG (y
)));
3218 else if (SCM_FRACTIONP (y
))
3221 SCM_WTA_DISPATCH_2 (g_eq_p
, x
, y
, SCM_ARGn
, s_eq_p
);
3223 else if (SCM_BIGP (x
))
3225 if (SCM_I_INUMP (y
))
3227 else if (SCM_BIGP (y
))
3229 int cmp
= mpz_cmp (SCM_I_BIG_MPZ (x
), SCM_I_BIG_MPZ (y
));
3230 scm_remember_upto_here_2 (x
, y
);
3231 return scm_from_bool (0 == cmp
);
3233 else if (SCM_REALP (y
))
3236 if (xisnan (SCM_REAL_VALUE (y
)))
3238 cmp
= xmpz_cmp_d (SCM_I_BIG_MPZ (x
), SCM_REAL_VALUE (y
));
3239 scm_remember_upto_here_1 (x
);
3240 return scm_from_bool (0 == cmp
);
3242 else if (SCM_COMPLEXP (y
))
3245 if (0.0 != SCM_COMPLEX_IMAG (y
))
3247 if (xisnan (SCM_COMPLEX_REAL (y
)))
3249 cmp
= xmpz_cmp_d (SCM_I_BIG_MPZ (x
), SCM_COMPLEX_REAL (y
));
3250 scm_remember_upto_here_1 (x
);
3251 return scm_from_bool (0 == cmp
);
3253 else if (SCM_FRACTIONP (y
))
3256 SCM_WTA_DISPATCH_2 (g_eq_p
, x
, y
, SCM_ARGn
, s_eq_p
);
3258 else if (SCM_REALP (x
))
3260 if (SCM_I_INUMP (y
))
3261 return scm_from_bool (SCM_REAL_VALUE (x
) == (double) SCM_I_INUM (y
));
3262 else if (SCM_BIGP (y
))
3265 if (xisnan (SCM_REAL_VALUE (x
)))
3267 cmp
= xmpz_cmp_d (SCM_I_BIG_MPZ (y
), SCM_REAL_VALUE (x
));
3268 scm_remember_upto_here_1 (y
);
3269 return scm_from_bool (0 == cmp
);
3271 else if (SCM_REALP (y
))
3272 return scm_from_bool (SCM_REAL_VALUE (x
) == SCM_REAL_VALUE (y
));
3273 else if (SCM_COMPLEXP (y
))
3274 return scm_from_bool ((SCM_REAL_VALUE (x
) == SCM_COMPLEX_REAL (y
))
3275 && (0.0 == SCM_COMPLEX_IMAG (y
)));
3276 else if (SCM_FRACTIONP (y
))
3278 double xx
= SCM_REAL_VALUE (x
);
3282 return scm_from_bool (xx
< 0.0);
3283 x
= scm_inexact_to_exact (x
); /* with x as frac or int */
3287 SCM_WTA_DISPATCH_2 (g_eq_p
, x
, y
, SCM_ARGn
, s_eq_p
);
3289 else if (SCM_COMPLEXP (x
))
3291 if (SCM_I_INUMP (y
))
3292 return scm_from_bool ((SCM_COMPLEX_REAL (x
) == (double) SCM_I_INUM (y
))
3293 && (SCM_COMPLEX_IMAG (x
) == 0.0));
3294 else if (SCM_BIGP (y
))
3297 if (0.0 != SCM_COMPLEX_IMAG (x
))
3299 if (xisnan (SCM_COMPLEX_REAL (x
)))
3301 cmp
= xmpz_cmp_d (SCM_I_BIG_MPZ (y
), SCM_COMPLEX_REAL (x
));
3302 scm_remember_upto_here_1 (y
);
3303 return scm_from_bool (0 == cmp
);
3305 else if (SCM_REALP (y
))
3306 return scm_from_bool ((SCM_COMPLEX_REAL (x
) == SCM_REAL_VALUE (y
))
3307 && (SCM_COMPLEX_IMAG (x
) == 0.0));
3308 else if (SCM_COMPLEXP (y
))
3309 return scm_from_bool ((SCM_COMPLEX_REAL (x
) == SCM_COMPLEX_REAL (y
))
3310 && (SCM_COMPLEX_IMAG (x
) == SCM_COMPLEX_IMAG (y
)));
3311 else if (SCM_FRACTIONP (y
))
3314 if (SCM_COMPLEX_IMAG (x
) != 0.0)
3316 xx
= SCM_COMPLEX_REAL (x
);
3320 return scm_from_bool (xx
< 0.0);
3321 x
= scm_inexact_to_exact (x
); /* with x as frac or int */
3325 SCM_WTA_DISPATCH_2 (g_eq_p
, x
, y
, SCM_ARGn
, s_eq_p
);
3327 else if (SCM_FRACTIONP (x
))
3329 if (SCM_I_INUMP (y
))
3331 else if (SCM_BIGP (y
))
3333 else if (SCM_REALP (y
))
3335 double yy
= SCM_REAL_VALUE (y
);
3339 return scm_from_bool (0.0 < yy
);
3340 y
= scm_inexact_to_exact (y
); /* with y as frac or int */
3343 else if (SCM_COMPLEXP (y
))
3346 if (SCM_COMPLEX_IMAG (y
) != 0.0)
3348 yy
= SCM_COMPLEX_REAL (y
);
3352 return scm_from_bool (0.0 < yy
);
3353 y
= scm_inexact_to_exact (y
); /* with y as frac or int */
3356 else if (SCM_FRACTIONP (y
))
3357 return scm_i_fraction_equalp (x
, y
);
3359 SCM_WTA_DISPATCH_2 (g_eq_p
, x
, y
, SCM_ARGn
, s_eq_p
);
3362 SCM_WTA_DISPATCH_2 (g_eq_p
, x
, y
, SCM_ARG1
, s_eq_p
);
3366 /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications
3367 done are good for inums, but for bignums an answer can almost always be
3368 had by just examining a few high bits of the operands, as done by GMP in
3369 mpq_cmp. flonum/frac compares likewise, but with the slight complication
3370 of the float exponent to take into account. */
3372 SCM_GPROC1 (s_less_p
, "<", scm_tc7_rpsubr
, scm_less_p
, g_less_p
);
3373 /* "Return @code{#t} if the list of parameters is monotonically\n"
3377 scm_less_p (SCM x
, SCM y
)
3380 if (SCM_I_INUMP (x
))
3382 long xx
= SCM_I_INUM (x
);
3383 if (SCM_I_INUMP (y
))
3385 long yy
= SCM_I_INUM (y
);
3386 return scm_from_bool (xx
< yy
);
3388 else if (SCM_BIGP (y
))
3390 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (y
));
3391 scm_remember_upto_here_1 (y
);
3392 return scm_from_bool (sgn
> 0);
3394 else if (SCM_REALP (y
))
3395 return scm_from_bool ((double) xx
< SCM_REAL_VALUE (y
));
3396 else if (SCM_FRACTIONP (y
))
3398 /* "x < a/b" becomes "x*b < a" */
3400 x
= scm_product (x
, SCM_FRACTION_DENOMINATOR (y
));
3401 y
= SCM_FRACTION_NUMERATOR (y
);
3405 SCM_WTA_DISPATCH_2 (g_less_p
, x
, y
, SCM_ARGn
, s_less_p
);
3407 else if (SCM_BIGP (x
))
3409 if (SCM_I_INUMP (y
))
3411 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
3412 scm_remember_upto_here_1 (x
);
3413 return scm_from_bool (sgn
< 0);
3415 else if (SCM_BIGP (y
))
3417 int cmp
= mpz_cmp (SCM_I_BIG_MPZ (x
), SCM_I_BIG_MPZ (y
));
3418 scm_remember_upto_here_2 (x
, y
);
3419 return scm_from_bool (cmp
< 0);
3421 else if (SCM_REALP (y
))
3424 if (xisnan (SCM_REAL_VALUE (y
)))
3426 cmp
= xmpz_cmp_d (SCM_I_BIG_MPZ (x
), SCM_REAL_VALUE (y
));
3427 scm_remember_upto_here_1 (x
);
3428 return scm_from_bool (cmp
< 0);
3430 else if (SCM_FRACTIONP (y
))
3433 SCM_WTA_DISPATCH_2 (g_less_p
, x
, y
, SCM_ARGn
, s_less_p
);
3435 else if (SCM_REALP (x
))
3437 if (SCM_I_INUMP (y
))
3438 return scm_from_bool (SCM_REAL_VALUE (x
) < (double) SCM_I_INUM (y
));
3439 else if (SCM_BIGP (y
))
3442 if (xisnan (SCM_REAL_VALUE (x
)))
3444 cmp
= xmpz_cmp_d (SCM_I_BIG_MPZ (y
), SCM_REAL_VALUE (x
));
3445 scm_remember_upto_here_1 (y
);
3446 return scm_from_bool (cmp
> 0);
3448 else if (SCM_REALP (y
))
3449 return scm_from_bool (SCM_REAL_VALUE (x
) < SCM_REAL_VALUE (y
));
3450 else if (SCM_FRACTIONP (y
))
3452 double xx
= SCM_REAL_VALUE (x
);
3456 return scm_from_bool (xx
< 0.0);
3457 x
= scm_inexact_to_exact (x
); /* with x as frac or int */
3461 SCM_WTA_DISPATCH_2 (g_less_p
, x
, y
, SCM_ARGn
, s_less_p
);
3463 else if (SCM_FRACTIONP (x
))
3465 if (SCM_I_INUMP (y
) || SCM_BIGP (y
))
3467 /* "a/b < y" becomes "a < y*b" */
3468 y
= scm_product (y
, SCM_FRACTION_DENOMINATOR (x
));
3469 x
= SCM_FRACTION_NUMERATOR (x
);
3472 else if (SCM_REALP (y
))
3474 double yy
= SCM_REAL_VALUE (y
);
3478 return scm_from_bool (0.0 < yy
);
3479 y
= scm_inexact_to_exact (y
); /* with y as frac or int */
3482 else if (SCM_FRACTIONP (y
))
3484 /* "a/b < c/d" becomes "a*d < c*b" */
3485 SCM new_x
= scm_product (SCM_FRACTION_NUMERATOR (x
),
3486 SCM_FRACTION_DENOMINATOR (y
));
3487 SCM new_y
= scm_product (SCM_FRACTION_NUMERATOR (y
),
3488 SCM_FRACTION_DENOMINATOR (x
));
3494 SCM_WTA_DISPATCH_2 (g_less_p
, x
, y
, SCM_ARGn
, s_less_p
);
3497 SCM_WTA_DISPATCH_2 (g_less_p
, x
, y
, SCM_ARG1
, s_less_p
);
3501 SCM_GPROC1 (s_scm_gr_p
, ">", scm_tc7_rpsubr
, scm_gr_p
, g_gr_p
);
3502 /* "Return @code{#t} if the list of parameters is monotonically\n"
3505 #define FUNC_NAME s_scm_gr_p
3507 scm_gr_p (SCM x
, SCM y
)
3509 if (!SCM_NUMBERP (x
))
3510 SCM_WTA_DISPATCH_2 (g_gr_p
, x
, y
, SCM_ARG1
, FUNC_NAME
);
3511 else if (!SCM_NUMBERP (y
))
3512 SCM_WTA_DISPATCH_2 (g_gr_p
, x
, y
, SCM_ARG2
, FUNC_NAME
);
3514 return scm_less_p (y
, x
);
3519 SCM_GPROC1 (s_scm_leq_p
, "<=", scm_tc7_rpsubr
, scm_leq_p
, g_leq_p
);
3520 /* "Return @code{#t} if the list of parameters is monotonically\n"
3523 #define FUNC_NAME s_scm_leq_p
3525 scm_leq_p (SCM x
, SCM y
)
3527 if (!SCM_NUMBERP (x
))
3528 SCM_WTA_DISPATCH_2 (g_leq_p
, x
, y
, SCM_ARG1
, FUNC_NAME
);
3529 else if (!SCM_NUMBERP (y
))
3530 SCM_WTA_DISPATCH_2 (g_leq_p
, x
, y
, SCM_ARG2
, FUNC_NAME
);
3531 else if (scm_is_true (scm_nan_p (x
)) || scm_is_true (scm_nan_p (y
)))
3534 return scm_not (scm_less_p (y
, x
));
3539 SCM_GPROC1 (s_scm_geq_p
, ">=", scm_tc7_rpsubr
, scm_geq_p
, g_geq_p
);
3540 /* "Return @code{#t} if the list of parameters is monotonically\n"
3543 #define FUNC_NAME s_scm_geq_p
3545 scm_geq_p (SCM x
, SCM y
)
3547 if (!SCM_NUMBERP (x
))
3548 SCM_WTA_DISPATCH_2 (g_geq_p
, x
, y
, SCM_ARG1
, FUNC_NAME
);
3549 else if (!SCM_NUMBERP (y
))
3550 SCM_WTA_DISPATCH_2 (g_geq_p
, x
, y
, SCM_ARG2
, FUNC_NAME
);
3551 else if (scm_is_true (scm_nan_p (x
)) || scm_is_true (scm_nan_p (y
)))
3554 return scm_not (scm_less_p (x
, y
));
3559 SCM_GPROC (s_zero_p
, "zero?", 1, 0, 0, scm_zero_p
, g_zero_p
);
3560 /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n"
3566 if (SCM_I_INUMP (z
))
3567 return scm_from_bool (scm_is_eq (z
, SCM_INUM0
));
3568 else if (SCM_BIGP (z
))
3570 else if (SCM_REALP (z
))
3571 return scm_from_bool (SCM_REAL_VALUE (z
) == 0.0);
3572 else if (SCM_COMPLEXP (z
))
3573 return scm_from_bool (SCM_COMPLEX_REAL (z
) == 0.0
3574 && SCM_COMPLEX_IMAG (z
) == 0.0);
3575 else if (SCM_FRACTIONP (z
))
3578 SCM_WTA_DISPATCH_1 (g_zero_p
, z
, SCM_ARG1
, s_zero_p
);
3582 SCM_GPROC (s_positive_p
, "positive?", 1, 0, 0, scm_positive_p
, g_positive_p
);
3583 /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n"
3587 scm_positive_p (SCM x
)
3589 if (SCM_I_INUMP (x
))
3590 return scm_from_bool (SCM_I_INUM (x
) > 0);
3591 else if (SCM_BIGP (x
))
3593 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
3594 scm_remember_upto_here_1 (x
);
3595 return scm_from_bool (sgn
> 0);
3597 else if (SCM_REALP (x
))
3598 return scm_from_bool(SCM_REAL_VALUE (x
) > 0.0);
3599 else if (SCM_FRACTIONP (x
))
3600 return scm_positive_p (SCM_FRACTION_NUMERATOR (x
));
3602 SCM_WTA_DISPATCH_1 (g_positive_p
, x
, SCM_ARG1
, s_positive_p
);
3606 SCM_GPROC (s_negative_p
, "negative?", 1, 0, 0, scm_negative_p
, g_negative_p
);
3607 /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n"
3611 scm_negative_p (SCM x
)
3613 if (SCM_I_INUMP (x
))
3614 return scm_from_bool (SCM_I_INUM (x
) < 0);
3615 else if (SCM_BIGP (x
))
3617 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
3618 scm_remember_upto_here_1 (x
);
3619 return scm_from_bool (sgn
< 0);
3621 else if (SCM_REALP (x
))
3622 return scm_from_bool(SCM_REAL_VALUE (x
) < 0.0);
3623 else if (SCM_FRACTIONP (x
))
3624 return scm_negative_p (SCM_FRACTION_NUMERATOR (x
));
3626 SCM_WTA_DISPATCH_1 (g_negative_p
, x
, SCM_ARG1
, s_negative_p
);
3630 /* scm_min and scm_max return an inexact when either argument is inexact, as
3631 required by r5rs. On that basis, for exact/inexact combinations the
3632 exact is converted to inexact to compare and possibly return. This is
3633 unlike scm_less_p above which takes some trouble to preserve all bits in
3634 its test, such trouble is not required for min and max. */
3636 SCM_GPROC1 (s_max
, "max", scm_tc7_asubr
, scm_max
, g_max
);
3637 /* "Return the maximum of all parameter values."
3640 scm_max (SCM x
, SCM y
)
3645 SCM_WTA_DISPATCH_0 (g_max
, s_max
);
3646 else if (SCM_I_INUMP(x
) || SCM_BIGP(x
) || SCM_REALP(x
) || SCM_FRACTIONP(x
))
3649 SCM_WTA_DISPATCH_1 (g_max
, x
, SCM_ARG1
, s_max
);
3652 if (SCM_I_INUMP (x
))
3654 long xx
= SCM_I_INUM (x
);
3655 if (SCM_I_INUMP (y
))
3657 long yy
= SCM_I_INUM (y
);
3658 return (xx
< yy
) ? y
: x
;
3660 else if (SCM_BIGP (y
))
3662 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (y
));
3663 scm_remember_upto_here_1 (y
);
3664 return (sgn
< 0) ? x
: y
;
3666 else if (SCM_REALP (y
))
3669 /* if y==NaN then ">" is false and we return NaN */
3670 return (z
> SCM_REAL_VALUE (y
)) ? scm_from_double (z
) : y
;
3672 else if (SCM_FRACTIONP (y
))
3675 return (scm_is_false (scm_less_p (x
, y
)) ? x
: y
);
3678 SCM_WTA_DISPATCH_2 (g_max
, x
, y
, SCM_ARGn
, s_max
);
3680 else if (SCM_BIGP (x
))
3682 if (SCM_I_INUMP (y
))
3684 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
3685 scm_remember_upto_here_1 (x
);
3686 return (sgn
< 0) ? y
: x
;
3688 else if (SCM_BIGP (y
))
3690 int cmp
= mpz_cmp (SCM_I_BIG_MPZ (x
), SCM_I_BIG_MPZ (y
));
3691 scm_remember_upto_here_2 (x
, y
);
3692 return (cmp
> 0) ? x
: y
;
3694 else if (SCM_REALP (y
))
3696 /* if y==NaN then xx>yy is false, so we return the NaN y */
3699 xx
= scm_i_big2dbl (x
);
3700 yy
= SCM_REAL_VALUE (y
);
3701 return (xx
> yy
? scm_from_double (xx
) : y
);
3703 else if (SCM_FRACTIONP (y
))
3708 SCM_WTA_DISPATCH_2 (g_max
, x
, y
, SCM_ARGn
, s_max
);
3710 else if (SCM_REALP (x
))
3712 if (SCM_I_INUMP (y
))
3714 double z
= SCM_I_INUM (y
);
3715 /* if x==NaN then "<" is false and we return NaN */
3716 return (SCM_REAL_VALUE (x
) < z
) ? scm_from_double (z
) : x
;
3718 else if (SCM_BIGP (y
))
3723 else if (SCM_REALP (y
))
3725 /* if x==NaN then our explicit check means we return NaN
3726 if y==NaN then ">" is false and we return NaN
3727 calling isnan is unavoidable, since it's the only way to know
3728 which of x or y causes any compares to be false */
3729 double xx
= SCM_REAL_VALUE (x
);
3730 return (xisnan (xx
) || xx
> SCM_REAL_VALUE (y
)) ? x
: y
;
3732 else if (SCM_FRACTIONP (y
))
3734 double yy
= scm_i_fraction2double (y
);
3735 double xx
= SCM_REAL_VALUE (x
);
3736 return (xx
< yy
) ? scm_from_double (yy
) : x
;
3739 SCM_WTA_DISPATCH_2 (g_max
, x
, y
, SCM_ARGn
, s_max
);
3741 else if (SCM_FRACTIONP (x
))
3743 if (SCM_I_INUMP (y
))
3747 else if (SCM_BIGP (y
))
3751 else if (SCM_REALP (y
))
3753 double xx
= scm_i_fraction2double (x
);
3754 return (xx
< SCM_REAL_VALUE (y
)) ? y
: scm_from_double (xx
);
3756 else if (SCM_FRACTIONP (y
))
3761 SCM_WTA_DISPATCH_2 (g_max
, x
, y
, SCM_ARGn
, s_max
);
3764 SCM_WTA_DISPATCH_2 (g_max
, x
, y
, SCM_ARG1
, s_max
);
3768 SCM_GPROC1 (s_min
, "min", scm_tc7_asubr
, scm_min
, g_min
);
3769 /* "Return the minium of all parameter values."
3772 scm_min (SCM x
, SCM y
)
3777 SCM_WTA_DISPATCH_0 (g_min
, s_min
);
3778 else if (SCM_I_INUMP(x
) || SCM_BIGP(x
) || SCM_REALP(x
) || SCM_FRACTIONP(x
))
3781 SCM_WTA_DISPATCH_1 (g_min
, x
, SCM_ARG1
, s_min
);
3784 if (SCM_I_INUMP (x
))
3786 long xx
= SCM_I_INUM (x
);
3787 if (SCM_I_INUMP (y
))
3789 long yy
= SCM_I_INUM (y
);
3790 return (xx
< yy
) ? x
: y
;
3792 else if (SCM_BIGP (y
))
3794 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (y
));
3795 scm_remember_upto_here_1 (y
);
3796 return (sgn
< 0) ? y
: x
;
3798 else if (SCM_REALP (y
))
3801 /* if y==NaN then "<" is false and we return NaN */
3802 return (z
< SCM_REAL_VALUE (y
)) ? scm_from_double (z
) : y
;
3804 else if (SCM_FRACTIONP (y
))
3807 return (scm_is_false (scm_less_p (x
, y
)) ? y
: x
);
3810 SCM_WTA_DISPATCH_2 (g_min
, x
, y
, SCM_ARGn
, s_min
);
3812 else if (SCM_BIGP (x
))
3814 if (SCM_I_INUMP (y
))
3816 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
3817 scm_remember_upto_here_1 (x
);
3818 return (sgn
< 0) ? x
: y
;
3820 else if (SCM_BIGP (y
))
3822 int cmp
= mpz_cmp (SCM_I_BIG_MPZ (x
), SCM_I_BIG_MPZ (y
));
3823 scm_remember_upto_here_2 (x
, y
);
3824 return (cmp
> 0) ? y
: x
;
3826 else if (SCM_REALP (y
))
3828 /* if y==NaN then xx<yy is false, so we return the NaN y */
3831 xx
= scm_i_big2dbl (x
);
3832 yy
= SCM_REAL_VALUE (y
);
3833 return (xx
< yy
? scm_from_double (xx
) : y
);
3835 else if (SCM_FRACTIONP (y
))
3840 SCM_WTA_DISPATCH_2 (g_min
, x
, y
, SCM_ARGn
, s_min
);
3842 else if (SCM_REALP (x
))
3844 if (SCM_I_INUMP (y
))
3846 double z
= SCM_I_INUM (y
);
3847 /* if x==NaN then "<" is false and we return NaN */
3848 return (z
< SCM_REAL_VALUE (x
)) ? scm_from_double (z
) : x
;
3850 else if (SCM_BIGP (y
))
3855 else if (SCM_REALP (y
))
3857 /* if x==NaN then our explicit check means we return NaN
3858 if y==NaN then "<" is false and we return NaN
3859 calling isnan is unavoidable, since it's the only way to know
3860 which of x or y causes any compares to be false */
3861 double xx
= SCM_REAL_VALUE (x
);
3862 return (xisnan (xx
) || xx
< SCM_REAL_VALUE (y
)) ? x
: y
;
3864 else if (SCM_FRACTIONP (y
))
3866 double yy
= scm_i_fraction2double (y
);
3867 double xx
= SCM_REAL_VALUE (x
);
3868 return (yy
< xx
) ? scm_from_double (yy
) : x
;
3871 SCM_WTA_DISPATCH_2 (g_min
, x
, y
, SCM_ARGn
, s_min
);
3873 else if (SCM_FRACTIONP (x
))
3875 if (SCM_I_INUMP (y
))
3879 else if (SCM_BIGP (y
))
3883 else if (SCM_REALP (y
))
3885 double xx
= scm_i_fraction2double (x
);
3886 return (SCM_REAL_VALUE (y
) < xx
) ? y
: scm_from_double (xx
);
3888 else if (SCM_FRACTIONP (y
))
3893 SCM_WTA_DISPATCH_2 (g_max
, x
, y
, SCM_ARGn
, s_max
);
3896 SCM_WTA_DISPATCH_2 (g_min
, x
, y
, SCM_ARG1
, s_min
);
3900 SCM_GPROC1 (s_sum
, "+", scm_tc7_asubr
, scm_sum
, g_sum
);
3901 /* "Return the sum of all parameter values. Return 0 if called without\n"
3905 scm_sum (SCM x
, SCM y
)
3909 if (SCM_NUMBERP (x
)) return x
;
3910 if (SCM_UNBNDP (x
)) return SCM_INUM0
;
3911 SCM_WTA_DISPATCH_1 (g_sum
, x
, SCM_ARG1
, s_sum
);
3914 if (SCM_I_INUMP (x
))
3916 if (SCM_I_INUMP (y
))
3918 long xx
= SCM_I_INUM (x
);
3919 long yy
= SCM_I_INUM (y
);
3920 long int z
= xx
+ yy
;
3921 return SCM_FIXABLE (z
) ? SCM_I_MAKINUM (z
) : scm_i_long2big (z
);
3923 else if (SCM_BIGP (y
))
3928 else if (SCM_REALP (y
))
3930 long int xx
= SCM_I_INUM (x
);
3931 return scm_from_double (xx
+ SCM_REAL_VALUE (y
));
3933 else if (SCM_COMPLEXP (y
))
3935 long int xx
= SCM_I_INUM (x
);
3936 return scm_c_make_rectangular (xx
+ SCM_COMPLEX_REAL (y
),
3937 SCM_COMPLEX_IMAG (y
));
3939 else if (SCM_FRACTIONP (y
))
3940 return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y
),
3941 scm_product (x
, SCM_FRACTION_DENOMINATOR (y
))),
3942 SCM_FRACTION_DENOMINATOR (y
));
3944 SCM_WTA_DISPATCH_2 (g_sum
, x
, y
, SCM_ARGn
, s_sum
);
3945 } else if (SCM_BIGP (x
))
3947 if (SCM_I_INUMP (y
))
3952 inum
= SCM_I_INUM (y
);
3955 bigsgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
3958 SCM result
= scm_i_mkbig ();
3959 mpz_sub_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (x
), - inum
);
3960 scm_remember_upto_here_1 (x
);
3961 /* we know the result will have to be a bignum */
3964 return scm_i_normbig (result
);
3968 SCM result
= scm_i_mkbig ();
3969 mpz_add_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (x
), inum
);
3970 scm_remember_upto_here_1 (x
);
3971 /* we know the result will have to be a bignum */
3974 return scm_i_normbig (result
);
3977 else if (SCM_BIGP (y
))
3979 SCM result
= scm_i_mkbig ();
3980 int sgn_x
= mpz_sgn (SCM_I_BIG_MPZ (x
));
3981 int sgn_y
= mpz_sgn (SCM_I_BIG_MPZ (y
));
3982 mpz_add (SCM_I_BIG_MPZ (result
),
3985 scm_remember_upto_here_2 (x
, y
);
3986 /* we know the result will have to be a bignum */
3989 return scm_i_normbig (result
);
3991 else if (SCM_REALP (y
))
3993 double result
= mpz_get_d (SCM_I_BIG_MPZ (x
)) + SCM_REAL_VALUE (y
);
3994 scm_remember_upto_here_1 (x
);
3995 return scm_from_double (result
);
3997 else if (SCM_COMPLEXP (y
))
3999 double real_part
= (mpz_get_d (SCM_I_BIG_MPZ (x
))
4000 + SCM_COMPLEX_REAL (y
));
4001 scm_remember_upto_here_1 (x
);
4002 return scm_c_make_rectangular (real_part
, SCM_COMPLEX_IMAG (y
));
4004 else if (SCM_FRACTIONP (y
))
4005 return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y
),
4006 scm_product (x
, SCM_FRACTION_DENOMINATOR (y
))),
4007 SCM_FRACTION_DENOMINATOR (y
));
4009 SCM_WTA_DISPATCH_2 (g_sum
, x
, y
, SCM_ARGn
, s_sum
);
4011 else if (SCM_REALP (x
))
4013 if (SCM_I_INUMP (y
))
4014 return scm_from_double (SCM_REAL_VALUE (x
) + SCM_I_INUM (y
));
4015 else if (SCM_BIGP (y
))
4017 double result
= mpz_get_d (SCM_I_BIG_MPZ (y
)) + SCM_REAL_VALUE (x
);
4018 scm_remember_upto_here_1 (y
);
4019 return scm_from_double (result
);
4021 else if (SCM_REALP (y
))
4022 return scm_from_double (SCM_REAL_VALUE (x
) + SCM_REAL_VALUE (y
));
4023 else if (SCM_COMPLEXP (y
))
4024 return scm_c_make_rectangular (SCM_REAL_VALUE (x
) + SCM_COMPLEX_REAL (y
),
4025 SCM_COMPLEX_IMAG (y
));
4026 else if (SCM_FRACTIONP (y
))
4027 return scm_from_double (SCM_REAL_VALUE (x
) + scm_i_fraction2double (y
));
4029 SCM_WTA_DISPATCH_2 (g_sum
, x
, y
, SCM_ARGn
, s_sum
);
4031 else if (SCM_COMPLEXP (x
))
4033 if (SCM_I_INUMP (y
))
4034 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) + SCM_I_INUM (y
),
4035 SCM_COMPLEX_IMAG (x
));
4036 else if (SCM_BIGP (y
))
4038 double real_part
= (mpz_get_d (SCM_I_BIG_MPZ (y
))
4039 + SCM_COMPLEX_REAL (x
));
4040 scm_remember_upto_here_1 (y
);
4041 return scm_c_make_rectangular (real_part
, SCM_COMPLEX_IMAG (x
));
4043 else if (SCM_REALP (y
))
4044 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) + SCM_REAL_VALUE (y
),
4045 SCM_COMPLEX_IMAG (x
));
4046 else if (SCM_COMPLEXP (y
))
4047 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) + SCM_COMPLEX_REAL (y
),
4048 SCM_COMPLEX_IMAG (x
) + SCM_COMPLEX_IMAG (y
));
4049 else if (SCM_FRACTIONP (y
))
4050 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) + scm_i_fraction2double (y
),
4051 SCM_COMPLEX_IMAG (x
));
4053 SCM_WTA_DISPATCH_2 (g_sum
, x
, y
, SCM_ARGn
, s_sum
);
4055 else if (SCM_FRACTIONP (x
))
4057 if (SCM_I_INUMP (y
))
4058 return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x
),
4059 scm_product (y
, SCM_FRACTION_DENOMINATOR (x
))),
4060 SCM_FRACTION_DENOMINATOR (x
));
4061 else if (SCM_BIGP (y
))
4062 return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x
),
4063 scm_product (y
, SCM_FRACTION_DENOMINATOR (x
))),
4064 SCM_FRACTION_DENOMINATOR (x
));
4065 else if (SCM_REALP (y
))
4066 return scm_from_double (SCM_REAL_VALUE (y
) + scm_i_fraction2double (x
));
4067 else if (SCM_COMPLEXP (y
))
4068 return scm_c_make_rectangular (SCM_COMPLEX_REAL (y
) + scm_i_fraction2double (x
),
4069 SCM_COMPLEX_IMAG (y
));
4070 else if (SCM_FRACTIONP (y
))
4071 /* a/b + c/d = (ad + bc) / bd */
4072 return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x
), SCM_FRACTION_DENOMINATOR (y
)),
4073 scm_product (SCM_FRACTION_NUMERATOR (y
), SCM_FRACTION_DENOMINATOR (x
))),
4074 scm_product (SCM_FRACTION_DENOMINATOR (x
), SCM_FRACTION_DENOMINATOR (y
)));
4076 SCM_WTA_DISPATCH_2 (g_sum
, x
, y
, SCM_ARGn
, s_sum
);
4079 SCM_WTA_DISPATCH_2 (g_sum
, x
, y
, SCM_ARG1
, s_sum
);
4083 SCM_GPROC1 (s_difference
, "-", scm_tc7_asubr
, scm_difference
, g_difference
);
4084 /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise
4085 * the sum of all but the first argument are subtracted from the first
4087 #define FUNC_NAME s_difference
4089 scm_difference (SCM x
, SCM y
)
4094 SCM_WTA_DISPATCH_0 (g_difference
, s_difference
);
4096 if (SCM_I_INUMP (x
))
4098 long xx
= -SCM_I_INUM (x
);
4099 if (SCM_FIXABLE (xx
))
4100 return SCM_I_MAKINUM (xx
);
4102 return scm_i_long2big (xx
);
4104 else if (SCM_BIGP (x
))
4105 /* FIXME: do we really need to normalize here? */
4106 return scm_i_normbig (scm_i_clonebig (x
, 0));
4107 else if (SCM_REALP (x
))
4108 return scm_from_double (-SCM_REAL_VALUE (x
));
4109 else if (SCM_COMPLEXP (x
))
4110 return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x
),
4111 -SCM_COMPLEX_IMAG (x
));
4112 else if (SCM_FRACTIONP (x
))
4113 return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x
), SCM_UNDEFINED
),
4114 SCM_FRACTION_DENOMINATOR (x
));
4116 SCM_WTA_DISPATCH_1 (g_difference
, x
, SCM_ARG1
, s_difference
);
4119 if (SCM_I_INUMP (x
))
4121 if (SCM_I_INUMP (y
))
4123 long int xx
= SCM_I_INUM (x
);
4124 long int yy
= SCM_I_INUM (y
);
4125 long int z
= xx
- yy
;
4126 if (SCM_FIXABLE (z
))
4127 return SCM_I_MAKINUM (z
);
4129 return scm_i_long2big (z
);
4131 else if (SCM_BIGP (y
))
4133 /* inum-x - big-y */
4134 long xx
= SCM_I_INUM (x
);
4137 return scm_i_clonebig (y
, 0);
4140 int sgn_y
= mpz_sgn (SCM_I_BIG_MPZ (y
));
4141 SCM result
= scm_i_mkbig ();
4144 mpz_ui_sub (SCM_I_BIG_MPZ (result
), xx
, SCM_I_BIG_MPZ (y
));
4147 /* x - y == -(y + -x) */
4148 mpz_add_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (y
), -xx
);
4149 mpz_neg (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (result
));
4151 scm_remember_upto_here_1 (y
);
4153 if ((xx
< 0 && (sgn_y
> 0)) || ((xx
> 0) && sgn_y
< 0))
4154 /* we know the result will have to be a bignum */
4157 return scm_i_normbig (result
);
4160 else if (SCM_REALP (y
))
4162 long int xx
= SCM_I_INUM (x
);
4163 return scm_from_double (xx
- SCM_REAL_VALUE (y
));
4165 else if (SCM_COMPLEXP (y
))
4167 long int xx
= SCM_I_INUM (x
);
4168 return scm_c_make_rectangular (xx
- SCM_COMPLEX_REAL (y
),
4169 - SCM_COMPLEX_IMAG (y
));
4171 else if (SCM_FRACTIONP (y
))
4172 /* a - b/c = (ac - b) / c */
4173 return scm_i_make_ratio (scm_difference (scm_product (x
, SCM_FRACTION_DENOMINATOR (y
)),
4174 SCM_FRACTION_NUMERATOR (y
)),
4175 SCM_FRACTION_DENOMINATOR (y
));
4177 SCM_WTA_DISPATCH_2 (g_difference
, x
, y
, SCM_ARGn
, s_difference
);
4179 else if (SCM_BIGP (x
))
4181 if (SCM_I_INUMP (y
))
4183 /* big-x - inum-y */
4184 long yy
= SCM_I_INUM (y
);
4185 int sgn_x
= mpz_sgn (SCM_I_BIG_MPZ (x
));
4187 scm_remember_upto_here_1 (x
);
4189 return (SCM_FIXABLE (-yy
) ?
4190 SCM_I_MAKINUM (-yy
) : scm_from_long (-yy
));
4193 SCM result
= scm_i_mkbig ();
4196 mpz_sub_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (x
), yy
);
4198 mpz_add_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (x
), -yy
);
4199 scm_remember_upto_here_1 (x
);
4201 if ((sgn_x
< 0 && (yy
> 0)) || ((sgn_x
> 0) && yy
< 0))
4202 /* we know the result will have to be a bignum */
4205 return scm_i_normbig (result
);
4208 else if (SCM_BIGP (y
))
4210 int sgn_x
= mpz_sgn (SCM_I_BIG_MPZ (x
));
4211 int sgn_y
= mpz_sgn (SCM_I_BIG_MPZ (y
));
4212 SCM result
= scm_i_mkbig ();
4213 mpz_sub (SCM_I_BIG_MPZ (result
),
4216 scm_remember_upto_here_2 (x
, y
);
4217 /* we know the result will have to be a bignum */
4218 if ((sgn_x
== 1) && (sgn_y
== -1))
4220 if ((sgn_x
== -1) && (sgn_y
== 1))
4222 return scm_i_normbig (result
);
4224 else if (SCM_REALP (y
))
4226 double result
= mpz_get_d (SCM_I_BIG_MPZ (x
)) - SCM_REAL_VALUE (y
);
4227 scm_remember_upto_here_1 (x
);
4228 return scm_from_double (result
);
4230 else if (SCM_COMPLEXP (y
))
4232 double real_part
= (mpz_get_d (SCM_I_BIG_MPZ (x
))
4233 - SCM_COMPLEX_REAL (y
));
4234 scm_remember_upto_here_1 (x
);
4235 return scm_c_make_rectangular (real_part
, - SCM_COMPLEX_IMAG (y
));
4237 else if (SCM_FRACTIONP (y
))
4238 return scm_i_make_ratio (scm_difference (scm_product (x
, SCM_FRACTION_DENOMINATOR (y
)),
4239 SCM_FRACTION_NUMERATOR (y
)),
4240 SCM_FRACTION_DENOMINATOR (y
));
4241 else SCM_WTA_DISPATCH_2 (g_difference
, x
, y
, SCM_ARGn
, s_difference
);
4243 else if (SCM_REALP (x
))
4245 if (SCM_I_INUMP (y
))
4246 return scm_from_double (SCM_REAL_VALUE (x
) - SCM_I_INUM (y
));
4247 else if (SCM_BIGP (y
))
4249 double result
= SCM_REAL_VALUE (x
) - mpz_get_d (SCM_I_BIG_MPZ (y
));
4250 scm_remember_upto_here_1 (x
);
4251 return scm_from_double (result
);
4253 else if (SCM_REALP (y
))
4254 return scm_from_double (SCM_REAL_VALUE (x
) - SCM_REAL_VALUE (y
));
4255 else if (SCM_COMPLEXP (y
))
4256 return scm_c_make_rectangular (SCM_REAL_VALUE (x
) - SCM_COMPLEX_REAL (y
),
4257 -SCM_COMPLEX_IMAG (y
));
4258 else if (SCM_FRACTIONP (y
))
4259 return scm_from_double (SCM_REAL_VALUE (x
) - scm_i_fraction2double (y
));
4261 SCM_WTA_DISPATCH_2 (g_difference
, x
, y
, SCM_ARGn
, s_difference
);
4263 else if (SCM_COMPLEXP (x
))
4265 if (SCM_I_INUMP (y
))
4266 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) - SCM_I_INUM (y
),
4267 SCM_COMPLEX_IMAG (x
));
4268 else if (SCM_BIGP (y
))
4270 double real_part
= (SCM_COMPLEX_REAL (x
)
4271 - mpz_get_d (SCM_I_BIG_MPZ (y
)));
4272 scm_remember_upto_here_1 (x
);
4273 return scm_c_make_rectangular (real_part
, SCM_COMPLEX_IMAG (y
));
4275 else if (SCM_REALP (y
))
4276 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) - SCM_REAL_VALUE (y
),
4277 SCM_COMPLEX_IMAG (x
));
4278 else if (SCM_COMPLEXP (y
))
4279 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) - SCM_COMPLEX_REAL (y
),
4280 SCM_COMPLEX_IMAG (x
) - SCM_COMPLEX_IMAG (y
));
4281 else if (SCM_FRACTIONP (y
))
4282 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) - scm_i_fraction2double (y
),
4283 SCM_COMPLEX_IMAG (x
));
4285 SCM_WTA_DISPATCH_2 (g_difference
, x
, y
, SCM_ARGn
, s_difference
);
4287 else if (SCM_FRACTIONP (x
))
4289 if (SCM_I_INUMP (y
))
4290 /* a/b - c = (a - cb) / b */
4291 return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x
),
4292 scm_product(y
, SCM_FRACTION_DENOMINATOR (x
))),
4293 SCM_FRACTION_DENOMINATOR (x
));
4294 else if (SCM_BIGP (y
))
4295 return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x
),
4296 scm_product(y
, SCM_FRACTION_DENOMINATOR (x
))),
4297 SCM_FRACTION_DENOMINATOR (x
));
4298 else if (SCM_REALP (y
))
4299 return scm_from_double (scm_i_fraction2double (x
) - SCM_REAL_VALUE (y
));
4300 else if (SCM_COMPLEXP (y
))
4301 return scm_c_make_rectangular (scm_i_fraction2double (x
) - SCM_COMPLEX_REAL (y
),
4302 -SCM_COMPLEX_IMAG (y
));
4303 else if (SCM_FRACTIONP (y
))
4304 /* a/b - c/d = (ad - bc) / bd */
4305 return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x
), SCM_FRACTION_DENOMINATOR (y
)),
4306 scm_product (SCM_FRACTION_NUMERATOR (y
), SCM_FRACTION_DENOMINATOR (x
))),
4307 scm_product (SCM_FRACTION_DENOMINATOR (x
), SCM_FRACTION_DENOMINATOR (y
)));
4309 SCM_WTA_DISPATCH_2 (g_difference
, x
, y
, SCM_ARGn
, s_difference
);
4312 SCM_WTA_DISPATCH_2 (g_difference
, x
, y
, SCM_ARG1
, s_difference
);
4317 SCM_GPROC1 (s_product
, "*", scm_tc7_asubr
, scm_product
, g_product
);
4318 /* "Return the product of all arguments. If called without arguments,\n"
4322 scm_product (SCM x
, SCM y
)
4327 return SCM_I_MAKINUM (1L);
4328 else if (SCM_NUMBERP (x
))
4331 SCM_WTA_DISPATCH_1 (g_product
, x
, SCM_ARG1
, s_product
);
4334 if (SCM_I_INUMP (x
))
4339 xx
= SCM_I_INUM (x
);
4343 case 0: return x
; break;
4344 case 1: return y
; break;
4347 if (SCM_I_INUMP (y
))
4349 long yy
= SCM_I_INUM (y
);
4351 SCM k
= SCM_I_MAKINUM (kk
);
4352 if ((kk
== SCM_I_INUM (k
)) && (kk
/ xx
== yy
))
4356 SCM result
= scm_i_long2big (xx
);
4357 mpz_mul_si (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (result
), yy
);
4358 return scm_i_normbig (result
);
4361 else if (SCM_BIGP (y
))
4363 SCM result
= scm_i_mkbig ();
4364 mpz_mul_si (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (y
), xx
);
4365 scm_remember_upto_here_1 (y
);
4368 else if (SCM_REALP (y
))
4369 return scm_from_double (xx
* SCM_REAL_VALUE (y
));
4370 else if (SCM_COMPLEXP (y
))
4371 return scm_c_make_rectangular (xx
* SCM_COMPLEX_REAL (y
),
4372 xx
* SCM_COMPLEX_IMAG (y
));
4373 else if (SCM_FRACTIONP (y
))
4374 return scm_i_make_ratio (scm_product (x
, SCM_FRACTION_NUMERATOR (y
)),
4375 SCM_FRACTION_DENOMINATOR (y
));
4377 SCM_WTA_DISPATCH_2 (g_product
, x
, y
, SCM_ARGn
, s_product
);
4379 else if (SCM_BIGP (x
))
4381 if (SCM_I_INUMP (y
))
4386 else if (SCM_BIGP (y
))
4388 SCM result
= scm_i_mkbig ();
4389 mpz_mul (SCM_I_BIG_MPZ (result
),
4392 scm_remember_upto_here_2 (x
, y
);
4395 else if (SCM_REALP (y
))
4397 double result
= mpz_get_d (SCM_I_BIG_MPZ (x
)) * SCM_REAL_VALUE (y
);
4398 scm_remember_upto_here_1 (x
);
4399 return scm_from_double (result
);
4401 else if (SCM_COMPLEXP (y
))
4403 double z
= mpz_get_d (SCM_I_BIG_MPZ (x
));
4404 scm_remember_upto_here_1 (x
);
4405 return scm_c_make_rectangular (z
* SCM_COMPLEX_REAL (y
),
4406 z
* SCM_COMPLEX_IMAG (y
));
4408 else if (SCM_FRACTIONP (y
))
4409 return scm_i_make_ratio (scm_product (x
, SCM_FRACTION_NUMERATOR (y
)),
4410 SCM_FRACTION_DENOMINATOR (y
));
4412 SCM_WTA_DISPATCH_2 (g_product
, x
, y
, SCM_ARGn
, s_product
);
4414 else if (SCM_REALP (x
))
4416 if (SCM_I_INUMP (y
))
4417 return scm_from_double (SCM_I_INUM (y
) * SCM_REAL_VALUE (x
));
4418 else if (SCM_BIGP (y
))
4420 double result
= mpz_get_d (SCM_I_BIG_MPZ (y
)) * SCM_REAL_VALUE (x
);
4421 scm_remember_upto_here_1 (y
);
4422 return scm_from_double (result
);
4424 else if (SCM_REALP (y
))
4425 return scm_from_double (SCM_REAL_VALUE (x
) * SCM_REAL_VALUE (y
));
4426 else if (SCM_COMPLEXP (y
))
4427 return scm_c_make_rectangular (SCM_REAL_VALUE (x
) * SCM_COMPLEX_REAL (y
),
4428 SCM_REAL_VALUE (x
) * SCM_COMPLEX_IMAG (y
));
4429 else if (SCM_FRACTIONP (y
))
4430 return scm_from_double (SCM_REAL_VALUE (x
) * scm_i_fraction2double (y
));
4432 SCM_WTA_DISPATCH_2 (g_product
, x
, y
, SCM_ARGn
, s_product
);
4434 else if (SCM_COMPLEXP (x
))
4436 if (SCM_I_INUMP (y
))
4437 return scm_c_make_rectangular (SCM_I_INUM (y
) * SCM_COMPLEX_REAL (x
),
4438 SCM_I_INUM (y
) * SCM_COMPLEX_IMAG (x
));
4439 else if (SCM_BIGP (y
))
4441 double z
= mpz_get_d (SCM_I_BIG_MPZ (y
));
4442 scm_remember_upto_here_1 (y
);
4443 return scm_c_make_rectangular (z
* SCM_COMPLEX_REAL (x
),
4444 z
* SCM_COMPLEX_IMAG (x
));
4446 else if (SCM_REALP (y
))
4447 return scm_c_make_rectangular (SCM_REAL_VALUE (y
) * SCM_COMPLEX_REAL (x
),
4448 SCM_REAL_VALUE (y
) * SCM_COMPLEX_IMAG (x
));
4449 else if (SCM_COMPLEXP (y
))
4451 return scm_c_make_rectangular (SCM_COMPLEX_REAL (x
) * SCM_COMPLEX_REAL (y
)
4452 - SCM_COMPLEX_IMAG (x
) * SCM_COMPLEX_IMAG (y
),
4453 SCM_COMPLEX_REAL (x
) * SCM_COMPLEX_IMAG (y
)
4454 + SCM_COMPLEX_IMAG (x
) * SCM_COMPLEX_REAL (y
));
4456 else if (SCM_FRACTIONP (y
))
4458 double yy
= scm_i_fraction2double (y
);
4459 return scm_c_make_rectangular (yy
* SCM_COMPLEX_REAL (x
),
4460 yy
* SCM_COMPLEX_IMAG (x
));
4463 SCM_WTA_DISPATCH_2 (g_product
, x
, y
, SCM_ARGn
, s_product
);
4465 else if (SCM_FRACTIONP (x
))
4467 if (SCM_I_INUMP (y
))
4468 return scm_i_make_ratio (scm_product (y
, SCM_FRACTION_NUMERATOR (x
)),
4469 SCM_FRACTION_DENOMINATOR (x
));
4470 else if (SCM_BIGP (y
))
4471 return scm_i_make_ratio (scm_product (y
, SCM_FRACTION_NUMERATOR (x
)),
4472 SCM_FRACTION_DENOMINATOR (x
));
4473 else if (SCM_REALP (y
))
4474 return scm_from_double (scm_i_fraction2double (x
) * SCM_REAL_VALUE (y
));
4475 else if (SCM_COMPLEXP (y
))
4477 double xx
= scm_i_fraction2double (x
);
4478 return scm_c_make_rectangular (xx
* SCM_COMPLEX_REAL (y
),
4479 xx
* SCM_COMPLEX_IMAG (y
));
4481 else if (SCM_FRACTIONP (y
))
4482 /* a/b * c/d = ac / bd */
4483 return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x
),
4484 SCM_FRACTION_NUMERATOR (y
)),
4485 scm_product (SCM_FRACTION_DENOMINATOR (x
),
4486 SCM_FRACTION_DENOMINATOR (y
)));
4488 SCM_WTA_DISPATCH_2 (g_product
, x
, y
, SCM_ARGn
, s_product
);
4491 SCM_WTA_DISPATCH_2 (g_product
, x
, y
, SCM_ARG1
, s_product
);
4494 #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \
4495 || (defined (HAVE_FINITE) && defined (HAVE_ISNAN)))
4496 #define ALLOW_DIVIDE_BY_ZERO
4497 /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */
4500 /* The code below for complex division is adapted from the GNU
4501 libstdc++, which adapted it from f2c's libF77, and is subject to
4504 /****************************************************************
4505 Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore.
4507 Permission to use, copy, modify, and distribute this software
4508 and its documentation for any purpose and without fee is hereby
4509 granted, provided that the above copyright notice appear in all
4510 copies and that both that the copyright notice and this
4511 permission notice and warranty disclaimer appear in supporting
4512 documentation, and that the names of AT&T Bell Laboratories or
4513 Bellcore or any of their entities not be used in advertising or
4514 publicity pertaining to distribution of the software without
4515 specific, written prior permission.
4517 AT&T and Bellcore disclaim all warranties with regard to this
4518 software, including all implied warranties of merchantability
4519 and fitness. In no event shall AT&T or Bellcore be liable for
4520 any special, indirect or consequential damages or any damages
4521 whatsoever resulting from loss of use, data or profits, whether
4522 in an action of contract, negligence or other tortious action,
4523 arising out of or in connection with the use or performance of
4525 ****************************************************************/
4527 SCM_GPROC1 (s_divide
, "/", scm_tc7_asubr
, scm_divide
, g_divide
);
4528 /* Divide the first argument by the product of the remaining
4529 arguments. If called with one argument @var{z1}, 1/@var{z1} is
4531 #define FUNC_NAME s_divide
4533 scm_i_divide (SCM x
, SCM y
, int inexact
)
4540 SCM_WTA_DISPATCH_0 (g_divide
, s_divide
);
4541 else if (SCM_I_INUMP (x
))
4543 long xx
= SCM_I_INUM (x
);
4544 if (xx
== 1 || xx
== -1)
4546 #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
4548 scm_num_overflow (s_divide
);
4553 return scm_from_double (1.0 / (double) xx
);
4554 else return scm_i_make_ratio (SCM_I_MAKINUM(1), x
);
4557 else if (SCM_BIGP (x
))
4560 return scm_from_double (1.0 / scm_i_big2dbl (x
));
4561 else return scm_i_make_ratio (SCM_I_MAKINUM(1), x
);
4563 else if (SCM_REALP (x
))
4565 double xx
= SCM_REAL_VALUE (x
);
4566 #ifndef ALLOW_DIVIDE_BY_ZERO
4568 scm_num_overflow (s_divide
);
4571 return scm_from_double (1.0 / xx
);
4573 else if (SCM_COMPLEXP (x
))
4575 double r
= SCM_COMPLEX_REAL (x
);
4576 double i
= SCM_COMPLEX_IMAG (x
);
4580 double d
= i
* (1.0 + t
* t
);
4581 return scm_c_make_rectangular (t
/ d
, -1.0 / d
);
4586 double d
= r
* (1.0 + t
* t
);
4587 return scm_c_make_rectangular (1.0 / d
, -t
/ d
);
4590 else if (SCM_FRACTIONP (x
))
4591 return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x
),
4592 SCM_FRACTION_NUMERATOR (x
));
4594 SCM_WTA_DISPATCH_1 (g_divide
, x
, SCM_ARG1
, s_divide
);
4597 if (SCM_I_INUMP (x
))
4599 long xx
= SCM_I_INUM (x
);
4600 if (SCM_I_INUMP (y
))
4602 long yy
= SCM_I_INUM (y
);
4605 #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
4606 scm_num_overflow (s_divide
);
4608 return scm_from_double ((double) xx
/ (double) yy
);
4611 else if (xx
% yy
!= 0)
4614 return scm_from_double ((double) xx
/ (double) yy
);
4615 else return scm_i_make_ratio (x
, y
);
4620 if (SCM_FIXABLE (z
))
4621 return SCM_I_MAKINUM (z
);
4623 return scm_i_long2big (z
);
4626 else if (SCM_BIGP (y
))
4629 return scm_from_double ((double) xx
/ scm_i_big2dbl (y
));
4630 else return scm_i_make_ratio (x
, y
);
4632 else if (SCM_REALP (y
))
4634 double yy
= SCM_REAL_VALUE (y
);
4635 #ifndef ALLOW_DIVIDE_BY_ZERO
4637 scm_num_overflow (s_divide
);
4640 return scm_from_double ((double) xx
/ yy
);
4642 else if (SCM_COMPLEXP (y
))
4645 complex_div
: /* y _must_ be a complex number */
4647 double r
= SCM_COMPLEX_REAL (y
);
4648 double i
= SCM_COMPLEX_IMAG (y
);
4652 double d
= i
* (1.0 + t
* t
);
4653 return scm_c_make_rectangular ((a
* t
) / d
, -a
/ d
);
4658 double d
= r
* (1.0 + t
* t
);
4659 return scm_c_make_rectangular (a
/ d
, -(a
* t
) / d
);
4663 else if (SCM_FRACTIONP (y
))
4664 /* a / b/c = ac / b */
4665 return scm_i_make_ratio (scm_product (x
, SCM_FRACTION_DENOMINATOR (y
)),
4666 SCM_FRACTION_NUMERATOR (y
));
4668 SCM_WTA_DISPATCH_2 (g_divide
, x
, y
, SCM_ARGn
, s_divide
);
4670 else if (SCM_BIGP (x
))
4672 if (SCM_I_INUMP (y
))
4674 long int yy
= SCM_I_INUM (y
);
4677 #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
4678 scm_num_overflow (s_divide
);
4680 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
4681 scm_remember_upto_here_1 (x
);
4682 return (sgn
== 0) ? scm_nan () : scm_inf ();
4689 /* FIXME: HMM, what are the relative performance issues here?
4690 We need to test. Is it faster on average to test
4691 divisible_p, then perform whichever operation, or is it
4692 faster to perform the integer div opportunistically and
4693 switch to real if there's a remainder? For now we take the
4694 middle ground: test, then if divisible, use the faster div
4697 long abs_yy
= yy
< 0 ? -yy
: yy
;
4698 int divisible_p
= mpz_divisible_ui_p (SCM_I_BIG_MPZ (x
), abs_yy
);
4702 SCM result
= scm_i_mkbig ();
4703 mpz_divexact_ui (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (x
), abs_yy
);
4704 scm_remember_upto_here_1 (x
);
4706 mpz_neg (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (result
));
4707 return scm_i_normbig (result
);
4712 return scm_from_double (scm_i_big2dbl (x
) / (double) yy
);
4713 else return scm_i_make_ratio (x
, y
);
4717 else if (SCM_BIGP (y
))
4719 int y_is_zero
= (mpz_sgn (SCM_I_BIG_MPZ (y
)) == 0);
4722 #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
4723 scm_num_overflow (s_divide
);
4725 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (x
));
4726 scm_remember_upto_here_1 (x
);
4727 return (sgn
== 0) ? scm_nan () : scm_inf ();
4733 int divisible_p
= mpz_divisible_p (SCM_I_BIG_MPZ (x
),
4737 SCM result
= scm_i_mkbig ();
4738 mpz_divexact (SCM_I_BIG_MPZ (result
),
4741 scm_remember_upto_here_2 (x
, y
);
4742 return scm_i_normbig (result
);
4748 double dbx
= mpz_get_d (SCM_I_BIG_MPZ (x
));
4749 double dby
= mpz_get_d (SCM_I_BIG_MPZ (y
));
4750 scm_remember_upto_here_2 (x
, y
);
4751 return scm_from_double (dbx
/ dby
);
4753 else return scm_i_make_ratio (x
, y
);
4757 else if (SCM_REALP (y
))
4759 double yy
= SCM_REAL_VALUE (y
);
4760 #ifndef ALLOW_DIVIDE_BY_ZERO
4762 scm_num_overflow (s_divide
);
4765 return scm_from_double (scm_i_big2dbl (x
) / yy
);
4767 else if (SCM_COMPLEXP (y
))
4769 a
= scm_i_big2dbl (x
);
4772 else if (SCM_FRACTIONP (y
))
4773 return scm_i_make_ratio (scm_product (x
, SCM_FRACTION_DENOMINATOR (y
)),
4774 SCM_FRACTION_NUMERATOR (y
));
4776 SCM_WTA_DISPATCH_2 (g_divide
, x
, y
, SCM_ARGn
, s_divide
);
4778 else if (SCM_REALP (x
))
4780 double rx
= SCM_REAL_VALUE (x
);
4781 if (SCM_I_INUMP (y
))
4783 long int yy
= SCM_I_INUM (y
);
4784 #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
4786 scm_num_overflow (s_divide
);
4789 return scm_from_double (rx
/ (double) yy
);
4791 else if (SCM_BIGP (y
))
4793 double dby
= mpz_get_d (SCM_I_BIG_MPZ (y
));
4794 scm_remember_upto_here_1 (y
);
4795 return scm_from_double (rx
/ dby
);
4797 else if (SCM_REALP (y
))
4799 double yy
= SCM_REAL_VALUE (y
);
4800 #ifndef ALLOW_DIVIDE_BY_ZERO
4802 scm_num_overflow (s_divide
);
4805 return scm_from_double (rx
/ yy
);
4807 else if (SCM_COMPLEXP (y
))
4812 else if (SCM_FRACTIONP (y
))
4813 return scm_from_double (rx
/ scm_i_fraction2double (y
));
4815 SCM_WTA_DISPATCH_2 (g_divide
, x
, y
, SCM_ARGn
, s_divide
);
4817 else if (SCM_COMPLEXP (x
))
4819 double rx
= SCM_COMPLEX_REAL (x
);
4820 double ix
= SCM_COMPLEX_IMAG (x
);
4821 if (SCM_I_INUMP (y
))
4823 long int yy
= SCM_I_INUM (y
);
4824 #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
4826 scm_num_overflow (s_divide
);
4831 return scm_c_make_rectangular (rx
/ d
, ix
/ d
);
4834 else if (SCM_BIGP (y
))
4836 double dby
= mpz_get_d (SCM_I_BIG_MPZ (y
));
4837 scm_remember_upto_here_1 (y
);
4838 return scm_c_make_rectangular (rx
/ dby
, ix
/ dby
);
4840 else if (SCM_REALP (y
))
4842 double yy
= SCM_REAL_VALUE (y
);
4843 #ifndef ALLOW_DIVIDE_BY_ZERO
4845 scm_num_overflow (s_divide
);
4848 return scm_c_make_rectangular (rx
/ yy
, ix
/ yy
);
4850 else if (SCM_COMPLEXP (y
))
4852 double ry
= SCM_COMPLEX_REAL (y
);
4853 double iy
= SCM_COMPLEX_IMAG (y
);
4857 double d
= iy
* (1.0 + t
* t
);
4858 return scm_c_make_rectangular ((rx
* t
+ ix
) / d
, (ix
* t
- rx
) / d
);
4863 double d
= ry
* (1.0 + t
* t
);
4864 return scm_c_make_rectangular ((rx
+ ix
* t
) / d
, (ix
- rx
* t
) / d
);
4867 else if (SCM_FRACTIONP (y
))
4869 double yy
= scm_i_fraction2double (y
);
4870 return scm_c_make_rectangular (rx
/ yy
, ix
/ yy
);
4873 SCM_WTA_DISPATCH_2 (g_divide
, x
, y
, SCM_ARGn
, s_divide
);
4875 else if (SCM_FRACTIONP (x
))
4877 if (SCM_I_INUMP (y
))
4879 long int yy
= SCM_I_INUM (y
);
4880 #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
4882 scm_num_overflow (s_divide
);
4885 return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x
),
4886 scm_product (SCM_FRACTION_DENOMINATOR (x
), y
));
4888 else if (SCM_BIGP (y
))
4890 return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x
),
4891 scm_product (SCM_FRACTION_DENOMINATOR (x
), y
));
4893 else if (SCM_REALP (y
))
4895 double yy
= SCM_REAL_VALUE (y
);
4896 #ifndef ALLOW_DIVIDE_BY_ZERO
4898 scm_num_overflow (s_divide
);
4901 return scm_from_double (scm_i_fraction2double (x
) / yy
);
4903 else if (SCM_COMPLEXP (y
))
4905 a
= scm_i_fraction2double (x
);
4908 else if (SCM_FRACTIONP (y
))
4909 return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x
), SCM_FRACTION_DENOMINATOR (y
)),
4910 scm_product (SCM_FRACTION_NUMERATOR (y
), SCM_FRACTION_DENOMINATOR (x
)));
4912 SCM_WTA_DISPATCH_2 (g_divide
, x
, y
, SCM_ARGn
, s_divide
);
4915 SCM_WTA_DISPATCH_2 (g_divide
, x
, y
, SCM_ARG1
, s_divide
);
4919 scm_divide (SCM x
, SCM y
)
4921 return scm_i_divide (x
, y
, 0);
4924 static SCM
scm_divide2real (SCM x
, SCM y
)
4926 return scm_i_divide (x
, y
, 1);
4932 scm_asinh (double x
)
4937 #define asinh scm_asinh
4938 return log (x
+ sqrt (x
* x
+ 1));
4941 SCM_GPROC1 (s_asinh
, "$asinh", scm_tc7_dsubr
, (SCM (*)()) asinh
, g_asinh
);
4942 /* "Return the inverse hyperbolic sine of @var{x}."
4947 scm_acosh (double x
)
4952 #define acosh scm_acosh
4953 return log (x
+ sqrt (x
* x
- 1));
4956 SCM_GPROC1 (s_acosh
, "$acosh", scm_tc7_dsubr
, (SCM (*)()) acosh
, g_acosh
);
4957 /* "Return the inverse hyperbolic cosine of @var{x}."
4962 scm_atanh (double x
)
4967 #define atanh scm_atanh
4968 return 0.5 * log ((1 + x
) / (1 - x
));
4971 SCM_GPROC1 (s_atanh
, "$atanh", scm_tc7_dsubr
, (SCM (*)()) atanh
, g_atanh
);
4972 /* "Return the inverse hyperbolic tangent of @var{x}."
4977 scm_c_truncate (double x
)
4988 /* scm_c_round is done using floor(x+0.5) to round to nearest and with
4989 half-way case (ie. when x is an integer plus 0.5) going upwards.
4990 Then half-way cases are identified and adjusted down if the
4991 round-upwards didn't give the desired even integer.
4993 "plus_half == result" identifies a half-way case. If plus_half, which is
4994 x + 0.5, is an integer then x must be an integer plus 0.5.
4996 An odd "result" value is identified with result/2 != floor(result/2).
4997 This is done with plus_half, since that value is ready for use sooner in
4998 a pipelined cpu, and we're already requiring plus_half == result.
5000 Note however that we need to be careful when x is big and already an
5001 integer. In that case "x+0.5" may round to an adjacent integer, causing
5002 us to return such a value, incorrectly. For instance if the hardware is
5003 in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF
5004 (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value
5005 returned. Or if the hardware is in round-upwards mode, then other bigger
5006 values like say x == 2^128 will see x+0.5 rounding up to the next higher
5007 representable value, 2^128+2^76 (or whatever), again incorrect.
5009 These bad roundings of x+0.5 are avoided by testing at the start whether
5010 x is already an integer. If it is then clearly that's the desired result
5011 already. And if it's not then the exponent must be small enough to allow
5012 an 0.5 to be represented, and hence added without a bad rounding. */
5015 scm_c_round (double x
)
5017 double plus_half
, result
;
5022 plus_half
= x
+ 0.5;
5023 result
= floor (plus_half
);
5024 /* Adjust so that the rounding is towards even. */
5025 return ((plus_half
== result
&& plus_half
/ 2 != floor (plus_half
/ 2))
5030 SCM_DEFINE (scm_truncate_number
, "truncate", 1, 0, 0,
5032 "Round the number @var{x} towards zero.")
5033 #define FUNC_NAME s_scm_truncate_number
5035 if (scm_is_false (scm_negative_p (x
)))
5036 return scm_floor (x
);
5038 return scm_ceiling (x
);
5042 static SCM exactly_one_half
;
5044 SCM_DEFINE (scm_round_number
, "round", 1, 0, 0,
5046 "Round the number @var{x} towards the nearest integer. "
5047 "When it is exactly halfway between two integers, "
5048 "round towards the even one.")
5049 #define FUNC_NAME s_scm_round_number
5051 if (SCM_I_INUMP (x
) || SCM_BIGP (x
))
5053 else if (SCM_REALP (x
))
5054 return scm_from_double (scm_c_round (SCM_REAL_VALUE (x
)));
5057 /* OPTIMIZE-ME: Fraction case could be done more efficiently by a
5058 single quotient+remainder division then examining to see which way
5059 the rounding should go. */
5060 SCM plus_half
= scm_sum (x
, exactly_one_half
);
5061 SCM result
= scm_floor (plus_half
);
5062 /* Adjust so that the rounding is towards even. */
5063 if (scm_is_true (scm_num_eq_p (plus_half
, result
))
5064 && scm_is_true (scm_odd_p (result
)))
5065 return scm_difference (result
, SCM_I_MAKINUM (1));
5072 SCM_PRIMITIVE_GENERIC (scm_floor
, "floor", 1, 0, 0,
5074 "Round the number @var{x} towards minus infinity.")
5075 #define FUNC_NAME s_scm_floor
5077 if (SCM_I_INUMP (x
) || SCM_BIGP (x
))
5079 else if (SCM_REALP (x
))
5080 return scm_from_double (floor (SCM_REAL_VALUE (x
)));
5081 else if (SCM_FRACTIONP (x
))
5083 SCM q
= scm_quotient (SCM_FRACTION_NUMERATOR (x
),
5084 SCM_FRACTION_DENOMINATOR (x
));
5085 if (scm_is_false (scm_negative_p (x
)))
5087 /* For positive x, rounding towards zero is correct. */
5092 /* For negative x, we need to return q-1 unless x is an
5093 integer. But fractions are never integer, per our
5095 return scm_difference (q
, SCM_I_MAKINUM (1));
5099 SCM_WTA_DISPATCH_1 (g_scm_floor
, x
, 1, s_scm_floor
);
5103 SCM_PRIMITIVE_GENERIC (scm_ceiling
, "ceiling", 1, 0, 0,
5105 "Round the number @var{x} towards infinity.")
5106 #define FUNC_NAME s_scm_ceiling
5108 if (SCM_I_INUMP (x
) || SCM_BIGP (x
))
5110 else if (SCM_REALP (x
))
5111 return scm_from_double (ceil (SCM_REAL_VALUE (x
)));
5112 else if (SCM_FRACTIONP (x
))
5114 SCM q
= scm_quotient (SCM_FRACTION_NUMERATOR (x
),
5115 SCM_FRACTION_DENOMINATOR (x
));
5116 if (scm_is_false (scm_positive_p (x
)))
5118 /* For negative x, rounding towards zero is correct. */
5123 /* For positive x, we need to return q+1 unless x is an
5124 integer. But fractions are never integer, per our
5126 return scm_sum (q
, SCM_I_MAKINUM (1));
5130 SCM_WTA_DISPATCH_1 (g_scm_ceiling
, x
, 1, s_scm_ceiling
);
5134 SCM_GPROC1 (s_i_sqrt
, "$sqrt", scm_tc7_dsubr
, (SCM (*)()) sqrt
, g_i_sqrt
);
5135 /* "Return the square root of the real number @var{x}."
5137 SCM_GPROC1 (s_i_abs
, "$abs", scm_tc7_dsubr
, (SCM (*)()) fabs
, g_i_abs
);
5138 /* "Return the absolute value of the real number @var{x}."
5140 SCM_GPROC1 (s_i_exp
, "$exp", scm_tc7_dsubr
, (SCM (*)()) exp
, g_i_exp
);
5141 /* "Return the @var{x}th power of e."
5143 SCM_GPROC1 (s_i_log
, "$log", scm_tc7_dsubr
, (SCM (*)()) log
, g_i_log
);
5144 /* "Return the natural logarithm of the real number @var{x}."
5146 SCM_GPROC1 (s_i_sin
, "$sin", scm_tc7_dsubr
, (SCM (*)()) sin
, g_i_sin
);
5147 /* "Return the sine of the real number @var{x}."
5149 SCM_GPROC1 (s_i_cos
, "$cos", scm_tc7_dsubr
, (SCM (*)()) cos
, g_i_cos
);
5150 /* "Return the cosine of the real number @var{x}."
5152 SCM_GPROC1 (s_i_tan
, "$tan", scm_tc7_dsubr
, (SCM (*)()) tan
, g_i_tan
);
5153 /* "Return the tangent of the real number @var{x}."
5155 SCM_GPROC1 (s_i_asin
, "$asin", scm_tc7_dsubr
, (SCM (*)()) asin
, g_i_asin
);
5156 /* "Return the arc sine of the real number @var{x}."
5158 SCM_GPROC1 (s_i_acos
, "$acos", scm_tc7_dsubr
, (SCM (*)()) acos
, g_i_acos
);
5159 /* "Return the arc cosine of the real number @var{x}."
5161 SCM_GPROC1 (s_i_atan
, "$atan", scm_tc7_dsubr
, (SCM (*)()) atan
, g_i_atan
);
5162 /* "Return the arc tangent of the real number @var{x}."
5164 SCM_GPROC1 (s_i_sinh
, "$sinh", scm_tc7_dsubr
, (SCM (*)()) sinh
, g_i_sinh
);
5165 /* "Return the hyperbolic sine of the real number @var{x}."
5167 SCM_GPROC1 (s_i_cosh
, "$cosh", scm_tc7_dsubr
, (SCM (*)()) cosh
, g_i_cosh
);
5168 /* "Return the hyperbolic cosine of the real number @var{x}."
5170 SCM_GPROC1 (s_i_tanh
, "$tanh", scm_tc7_dsubr
, (SCM (*)()) tanh
, g_i_tanh
);
5171 /* "Return the hyperbolic tangent of the real number @var{x}."
5179 static void scm_two_doubles (SCM x
,
5181 const char *sstring
,
5185 scm_two_doubles (SCM x
, SCM y
, const char *sstring
, struct dpair
*xy
)
5187 if (SCM_I_INUMP (x
))
5188 xy
->x
= SCM_I_INUM (x
);
5189 else if (SCM_BIGP (x
))
5190 xy
->x
= scm_i_big2dbl (x
);
5191 else if (SCM_REALP (x
))
5192 xy
->x
= SCM_REAL_VALUE (x
);
5193 else if (SCM_FRACTIONP (x
))
5194 xy
->x
= scm_i_fraction2double (x
);
5196 scm_wrong_type_arg (sstring
, SCM_ARG1
, x
);
5198 if (SCM_I_INUMP (y
))
5199 xy
->y
= SCM_I_INUM (y
);
5200 else if (SCM_BIGP (y
))
5201 xy
->y
= scm_i_big2dbl (y
);
5202 else if (SCM_REALP (y
))
5203 xy
->y
= SCM_REAL_VALUE (y
);
5204 else if (SCM_FRACTIONP (y
))
5205 xy
->y
= scm_i_fraction2double (y
);
5207 scm_wrong_type_arg (sstring
, SCM_ARG2
, y
);
5211 SCM_DEFINE (scm_sys_expt
, "$expt", 2, 0, 0,
5213 "Return @var{x} raised to the power of @var{y}. This\n"
5214 "procedure does not accept complex arguments.")
5215 #define FUNC_NAME s_scm_sys_expt
5218 scm_two_doubles (x
, y
, FUNC_NAME
, &xy
);
5219 return scm_from_double (pow (xy
.x
, xy
.y
));
5224 SCM_DEFINE (scm_sys_atan2
, "$atan2", 2, 0, 0,
5226 "Return the arc tangent of the two arguments @var{x} and\n"
5227 "@var{y}. This is similar to calculating the arc tangent of\n"
5228 "@var{x} / @var{y}, except that the signs of both arguments\n"
5229 "are used to determine the quadrant of the result. This\n"
5230 "procedure does not accept complex arguments.")
5231 #define FUNC_NAME s_scm_sys_atan2
5234 scm_two_doubles (x
, y
, FUNC_NAME
, &xy
);
5235 return scm_from_double (atan2 (xy
.x
, xy
.y
));
5240 scm_c_make_rectangular (double re
, double im
)
5243 return scm_from_double (re
);
5247 SCM_NEWSMOB (z
, scm_tc16_complex
, scm_gc_malloc (sizeof (scm_t_complex
),
5249 SCM_COMPLEX_REAL (z
) = re
;
5250 SCM_COMPLEX_IMAG (z
) = im
;
5255 SCM_DEFINE (scm_make_rectangular
, "make-rectangular", 2, 0, 0,
5256 (SCM real
, SCM imaginary
),
5257 "Return a complex number constructed of the given @var{real} and\n"
5258 "@var{imaginary} parts.")
5259 #define FUNC_NAME s_scm_make_rectangular
5262 scm_two_doubles (real
, imaginary
, FUNC_NAME
, &xy
);
5263 return scm_c_make_rectangular (xy
.x
, xy
.y
);
5268 scm_c_make_polar (double mag
, double ang
)
5272 sincos (ang
, &s
, &c
);
5277 return scm_c_make_rectangular (mag
* c
, mag
* s
);
5280 SCM_DEFINE (scm_make_polar
, "make-polar", 2, 0, 0,
5282 "Return the complex number @var{x} * e^(i * @var{y}).")
5283 #define FUNC_NAME s_scm_make_polar
5286 scm_two_doubles (x
, y
, FUNC_NAME
, &xy
);
5287 return scm_c_make_polar (xy
.x
, xy
.y
);
5292 SCM_GPROC (s_real_part
, "real-part", 1, 0, 0, scm_real_part
, g_real_part
);
5293 /* "Return the real part of the number @var{z}."
5296 scm_real_part (SCM z
)
5298 if (SCM_I_INUMP (z
))
5300 else if (SCM_BIGP (z
))
5302 else if (SCM_REALP (z
))
5304 else if (SCM_COMPLEXP (z
))
5305 return scm_from_double (SCM_COMPLEX_REAL (z
));
5306 else if (SCM_FRACTIONP (z
))
5309 SCM_WTA_DISPATCH_1 (g_real_part
, z
, SCM_ARG1
, s_real_part
);
5313 SCM_GPROC (s_imag_part
, "imag-part", 1, 0, 0, scm_imag_part
, g_imag_part
);
5314 /* "Return the imaginary part of the number @var{z}."
5317 scm_imag_part (SCM z
)
5319 if (SCM_I_INUMP (z
))
5321 else if (SCM_BIGP (z
))
5323 else if (SCM_REALP (z
))
5325 else if (SCM_COMPLEXP (z
))
5326 return scm_from_double (SCM_COMPLEX_IMAG (z
));
5327 else if (SCM_FRACTIONP (z
))
5330 SCM_WTA_DISPATCH_1 (g_imag_part
, z
, SCM_ARG1
, s_imag_part
);
5333 SCM_GPROC (s_numerator
, "numerator", 1, 0, 0, scm_numerator
, g_numerator
);
5334 /* "Return the numerator of the number @var{z}."
5337 scm_numerator (SCM z
)
5339 if (SCM_I_INUMP (z
))
5341 else if (SCM_BIGP (z
))
5343 else if (SCM_FRACTIONP (z
))
5345 scm_i_fraction_reduce (z
);
5346 return SCM_FRACTION_NUMERATOR (z
);
5348 else if (SCM_REALP (z
))
5349 return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z
)));
5351 SCM_WTA_DISPATCH_1 (g_numerator
, z
, SCM_ARG1
, s_numerator
);
5355 SCM_GPROC (s_denominator
, "denominator", 1, 0, 0, scm_denominator
, g_denominator
);
5356 /* "Return the denominator of the number @var{z}."
5359 scm_denominator (SCM z
)
5361 if (SCM_I_INUMP (z
))
5362 return SCM_I_MAKINUM (1);
5363 else if (SCM_BIGP (z
))
5364 return SCM_I_MAKINUM (1);
5365 else if (SCM_FRACTIONP (z
))
5367 scm_i_fraction_reduce (z
);
5368 return SCM_FRACTION_DENOMINATOR (z
);
5370 else if (SCM_REALP (z
))
5371 return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z
)));
5373 SCM_WTA_DISPATCH_1 (g_denominator
, z
, SCM_ARG1
, s_denominator
);
5376 SCM_GPROC (s_magnitude
, "magnitude", 1, 0, 0, scm_magnitude
, g_magnitude
);
5377 /* "Return the magnitude of the number @var{z}. This is the same as\n"
5378 * "@code{abs} for real arguments, but also allows complex numbers."
5381 scm_magnitude (SCM z
)
5383 if (SCM_I_INUMP (z
))
5385 long int zz
= SCM_I_INUM (z
);
5388 else if (SCM_POSFIXABLE (-zz
))
5389 return SCM_I_MAKINUM (-zz
);
5391 return scm_i_long2big (-zz
);
5393 else if (SCM_BIGP (z
))
5395 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (z
));
5396 scm_remember_upto_here_1 (z
);
5398 return scm_i_clonebig (z
, 0);
5402 else if (SCM_REALP (z
))
5403 return scm_from_double (fabs (SCM_REAL_VALUE (z
)));
5404 else if (SCM_COMPLEXP (z
))
5405 return scm_from_double (hypot (SCM_COMPLEX_REAL (z
), SCM_COMPLEX_IMAG (z
)));
5406 else if (SCM_FRACTIONP (z
))
5408 if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z
))))
5410 return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z
), SCM_UNDEFINED
),
5411 SCM_FRACTION_DENOMINATOR (z
));
5414 SCM_WTA_DISPATCH_1 (g_magnitude
, z
, SCM_ARG1
, s_magnitude
);
5418 SCM_GPROC (s_angle
, "angle", 1, 0, 0, scm_angle
, g_angle
);
5419 /* "Return the angle of the complex number @var{z}."
5424 /* atan(0,-1) is pi and it'd be possible to have that as a constant like
5425 scm_flo0 to save allocating a new flonum with scm_from_double each time.
5426 But if atan2 follows the floating point rounding mode, then the value
5427 is not a constant. Maybe it'd be close enough though. */
5428 if (SCM_I_INUMP (z
))
5430 if (SCM_I_INUM (z
) >= 0)
5433 return scm_from_double (atan2 (0.0, -1.0));
5435 else if (SCM_BIGP (z
))
5437 int sgn
= mpz_sgn (SCM_I_BIG_MPZ (z
));
5438 scm_remember_upto_here_1 (z
);
5440 return scm_from_double (atan2 (0.0, -1.0));
5444 else if (SCM_REALP (z
))
5446 if (SCM_REAL_VALUE (z
) >= 0)
5449 return scm_from_double (atan2 (0.0, -1.0));
5451 else if (SCM_COMPLEXP (z
))
5452 return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z
), SCM_COMPLEX_REAL (z
)));
5453 else if (SCM_FRACTIONP (z
))
5455 if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z
))))
5457 else return scm_from_double (atan2 (0.0, -1.0));
5460 SCM_WTA_DISPATCH_1 (g_angle
, z
, SCM_ARG1
, s_angle
);
5464 SCM_GPROC (s_exact_to_inexact
, "exact->inexact", 1, 0, 0, scm_exact_to_inexact
, g_exact_to_inexact
);
5465 /* Convert the number @var{x} to its inexact representation.\n"
5468 scm_exact_to_inexact (SCM z
)
5470 if (SCM_I_INUMP (z
))
5471 return scm_from_double ((double) SCM_I_INUM (z
));
5472 else if (SCM_BIGP (z
))
5473 return scm_from_double (scm_i_big2dbl (z
));
5474 else if (SCM_FRACTIONP (z
))
5475 return scm_from_double (scm_i_fraction2double (z
));
5476 else if (SCM_INEXACTP (z
))
5479 SCM_WTA_DISPATCH_1 (g_exact_to_inexact
, z
, 1, s_exact_to_inexact
);
5483 SCM_DEFINE (scm_inexact_to_exact
, "inexact->exact", 1, 0, 0,
5485 "Return an exact number that is numerically closest to @var{z}.")
5486 #define FUNC_NAME s_scm_inexact_to_exact
5488 if (SCM_I_INUMP (z
))
5490 else if (SCM_BIGP (z
))
5492 else if (SCM_REALP (z
))
5494 if (xisinf (SCM_REAL_VALUE (z
)) || xisnan (SCM_REAL_VALUE (z
)))
5495 SCM_OUT_OF_RANGE (1, z
);
5502 mpq_set_d (frac
, SCM_REAL_VALUE (z
));
5503 q
= scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac
)),
5504 scm_i_mpz2num (mpq_denref (frac
)));
5506 /* When scm_i_make_ratio throws, we leak the memory allocated
5513 else if (SCM_FRACTIONP (z
))
5516 SCM_WRONG_TYPE_ARG (1, z
);
5520 SCM_DEFINE (scm_rationalize
, "rationalize", 2, 0, 0,
5522 "Return an exact number that is within @var{err} of @var{x}.")
5523 #define FUNC_NAME s_scm_rationalize
5525 if (SCM_I_INUMP (x
))
5527 else if (SCM_BIGP (x
))
5529 else if ((SCM_REALP (x
)) || SCM_FRACTIONP (x
))
5531 /* Use continued fractions to find closest ratio. All
5532 arithmetic is done with exact numbers.
5535 SCM ex
= scm_inexact_to_exact (x
);
5536 SCM int_part
= scm_floor (ex
);
5537 SCM tt
= SCM_I_MAKINUM (1);
5538 SCM a1
= SCM_I_MAKINUM (0), a2
= SCM_I_MAKINUM (1), a
= SCM_I_MAKINUM (0);
5539 SCM b1
= SCM_I_MAKINUM (1), b2
= SCM_I_MAKINUM (0), b
= SCM_I_MAKINUM (0);
5543 if (scm_is_true (scm_num_eq_p (ex
, int_part
)))
5546 ex
= scm_difference (ex
, int_part
); /* x = x-int_part */
5547 rx
= scm_divide (ex
, SCM_UNDEFINED
); /* rx = 1/x */
5549 /* We stop after a million iterations just to be absolutely sure
5550 that we don't go into an infinite loop. The process normally
5551 converges after less than a dozen iterations.
5554 err
= scm_abs (err
);
5555 while (++i
< 1000000)
5557 a
= scm_sum (scm_product (a1
, tt
), a2
); /* a = a1*tt + a2 */
5558 b
= scm_sum (scm_product (b1
, tt
), b2
); /* b = b1*tt + b2 */
5559 if (scm_is_false (scm_zero_p (b
)) && /* b != 0 */
5561 (scm_gr_p (scm_abs (scm_difference (ex
, scm_divide (a
, b
))),
5562 err
))) /* abs(x-a/b) <= err */
5564 SCM res
= scm_sum (int_part
, scm_divide (a
, b
));
5565 if (scm_is_false (scm_exact_p (x
))
5566 || scm_is_false (scm_exact_p (err
)))
5567 return scm_exact_to_inexact (res
);
5571 rx
= scm_divide (scm_difference (rx
, tt
), /* rx = 1/(rx - tt) */
5573 tt
= scm_floor (rx
); /* tt = floor (rx) */
5579 scm_num_overflow (s_scm_rationalize
);
5582 SCM_WRONG_TYPE_ARG (1, x
);
5586 /* conversion functions */
5589 scm_is_integer (SCM val
)
5591 return scm_is_true (scm_integer_p (val
));
5595 scm_is_signed_integer (SCM val
, scm_t_intmax min
, scm_t_intmax max
)
5597 if (SCM_I_INUMP (val
))
5599 scm_t_signed_bits n
= SCM_I_INUM (val
);
5600 return n
>= min
&& n
<= max
;
5602 else if (SCM_BIGP (val
))
5604 if (min
>= SCM_MOST_NEGATIVE_FIXNUM
&& max
<= SCM_MOST_POSITIVE_FIXNUM
)
5606 else if (min
>= LONG_MIN
&& max
<= LONG_MAX
)
5608 if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val
)))
5610 long n
= mpz_get_si (SCM_I_BIG_MPZ (val
));
5611 return n
>= min
&& n
<= max
;
5621 if (mpz_sizeinbase (SCM_I_BIG_MPZ (val
), 2)
5622 > CHAR_BIT
*sizeof (scm_t_uintmax
))
5625 mpz_export (&n
, &count
, 1, sizeof (scm_t_uintmax
), 0, 0,
5626 SCM_I_BIG_MPZ (val
));
5628 if (mpz_sgn (SCM_I_BIG_MPZ (val
)) >= 0)
5640 return n
>= min
&& n
<= max
;
5648 scm_is_unsigned_integer (SCM val
, scm_t_uintmax min
, scm_t_uintmax max
)
5650 if (SCM_I_INUMP (val
))
5652 scm_t_signed_bits n
= SCM_I_INUM (val
);
5653 return n
>= 0 && ((scm_t_uintmax
)n
) >= min
&& ((scm_t_uintmax
)n
) <= max
;
5655 else if (SCM_BIGP (val
))
5657 if (max
<= SCM_MOST_POSITIVE_FIXNUM
)
5659 else if (max
<= ULONG_MAX
)
5661 if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val
)))
5663 unsigned long n
= mpz_get_ui (SCM_I_BIG_MPZ (val
));
5664 return n
>= min
&& n
<= max
;
5674 if (mpz_sgn (SCM_I_BIG_MPZ (val
)) < 0)
5677 if (mpz_sizeinbase (SCM_I_BIG_MPZ (val
), 2)
5678 > CHAR_BIT
*sizeof (scm_t_uintmax
))
5681 mpz_export (&n
, &count
, 1, sizeof (scm_t_uintmax
), 0, 0,
5682 SCM_I_BIG_MPZ (val
));
5684 return n
>= min
&& n
<= max
;
5692 scm_i_range_error (SCM bad_val
, SCM min
, SCM max
)
5694 scm_error (scm_out_of_range_key
,
5696 "Value out of range ~S to ~S: ~S",
5697 scm_list_3 (min
, max
, bad_val
),
5698 scm_list_1 (bad_val
));
5701 #define TYPE scm_t_intmax
5702 #define TYPE_MIN min
5703 #define TYPE_MAX max
5704 #define SIZEOF_TYPE 0
5705 #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max)
5706 #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg)
5707 #include "libguile/conv-integer.i.c"
5709 #define TYPE scm_t_uintmax
5710 #define TYPE_MIN min
5711 #define TYPE_MAX max
5712 #define SIZEOF_TYPE 0
5713 #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max)
5714 #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg)
5715 #include "libguile/conv-uinteger.i.c"
5717 #define TYPE scm_t_int8
5718 #define TYPE_MIN SCM_T_INT8_MIN
5719 #define TYPE_MAX SCM_T_INT8_MAX
5720 #define SIZEOF_TYPE 1
5721 #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg)
5722 #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg)
5723 #include "libguile/conv-integer.i.c"
5725 #define TYPE scm_t_uint8
5727 #define TYPE_MAX SCM_T_UINT8_MAX
5728 #define SIZEOF_TYPE 1
5729 #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg)
5730 #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg)
5731 #include "libguile/conv-uinteger.i.c"
5733 #define TYPE scm_t_int16
5734 #define TYPE_MIN SCM_T_INT16_MIN
5735 #define TYPE_MAX SCM_T_INT16_MAX
5736 #define SIZEOF_TYPE 2
5737 #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg)
5738 #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg)
5739 #include "libguile/conv-integer.i.c"
5741 #define TYPE scm_t_uint16
5743 #define TYPE_MAX SCM_T_UINT16_MAX
5744 #define SIZEOF_TYPE 2
5745 #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg)
5746 #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg)
5747 #include "libguile/conv-uinteger.i.c"
5749 #define TYPE scm_t_int32
5750 #define TYPE_MIN SCM_T_INT32_MIN
5751 #define TYPE_MAX SCM_T_INT32_MAX
5752 #define SIZEOF_TYPE 4
5753 #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg)
5754 #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg)
5755 #include "libguile/conv-integer.i.c"
5757 #define TYPE scm_t_uint32
5759 #define TYPE_MAX SCM_T_UINT32_MAX
5760 #define SIZEOF_TYPE 4
5761 #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg)
5762 #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg)
5763 #include "libguile/conv-uinteger.i.c"
5765 #if SCM_HAVE_T_INT64
5767 #define TYPE scm_t_int64
5768 #define TYPE_MIN SCM_T_INT64_MIN
5769 #define TYPE_MAX SCM_T_INT64_MAX
5770 #define SIZEOF_TYPE 8
5771 #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg)
5772 #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg)
5773 #include "libguile/conv-integer.i.c"
5775 #define TYPE scm_t_uint64
5777 #define TYPE_MAX SCM_T_UINT64_MAX
5778 #define SIZEOF_TYPE 8
5779 #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg)
5780 #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg)
5781 #include "libguile/conv-uinteger.i.c"
5786 scm_to_mpz (SCM val
, mpz_t rop
)
5788 if (SCM_I_INUMP (val
))
5789 mpz_set_si (rop
, SCM_I_INUM (val
));
5790 else if (SCM_BIGP (val
))
5791 mpz_set (rop
, SCM_I_BIG_MPZ (val
));
5793 scm_wrong_type_arg_msg (NULL
, 0, val
, "exact integer");
5797 scm_from_mpz (mpz_t val
)
5799 return scm_i_mpz2num (val
);
5803 scm_is_real (SCM val
)
5805 return scm_is_true (scm_real_p (val
));
5809 scm_is_rational (SCM val
)
5811 return scm_is_true (scm_rational_p (val
));
5815 scm_to_double (SCM val
)
5817 if (SCM_I_INUMP (val
))
5818 return SCM_I_INUM (val
);
5819 else if (SCM_BIGP (val
))
5820 return scm_i_big2dbl (val
);
5821 else if (SCM_FRACTIONP (val
))
5822 return scm_i_fraction2double (val
);
5823 else if (SCM_REALP (val
))
5824 return SCM_REAL_VALUE (val
);
5826 scm_wrong_type_arg_msg (NULL
, 0, val
, "real number");
5830 scm_from_double (double val
)
5832 SCM z
= scm_double_cell (scm_tc16_real
, 0, 0, 0);
5833 SCM_REAL_VALUE (z
) = val
;
5837 #if SCM_ENABLE_DISCOURAGED == 1
5840 scm_num2float (SCM num
, unsigned long int pos
, const char *s_caller
)
5844 float res
= mpz_get_d (SCM_I_BIG_MPZ (num
));
5848 scm_out_of_range (NULL
, num
);
5851 return scm_to_double (num
);
5855 scm_num2double (SCM num
, unsigned long int pos
, const char *s_caller
)
5859 double res
= mpz_get_d (SCM_I_BIG_MPZ (num
));
5863 scm_out_of_range (NULL
, num
);
5866 return scm_to_double (num
);
5872 scm_is_complex (SCM val
)
5874 return scm_is_true (scm_complex_p (val
));
5878 scm_c_real_part (SCM z
)
5880 if (SCM_COMPLEXP (z
))
5881 return SCM_COMPLEX_REAL (z
);
5884 /* Use the scm_real_part to get proper error checking and
5887 return scm_to_double (scm_real_part (z
));
5892 scm_c_imag_part (SCM z
)
5894 if (SCM_COMPLEXP (z
))
5895 return SCM_COMPLEX_IMAG (z
);
5898 /* Use the scm_imag_part to get proper error checking and
5899 dispatching. The result will almost always be 0.0, but not
5902 return scm_to_double (scm_imag_part (z
));
5907 scm_c_magnitude (SCM z
)
5909 return scm_to_double (scm_magnitude (z
));
5915 return scm_to_double (scm_angle (z
));
5919 scm_is_number (SCM z
)
5921 return scm_is_true (scm_number_p (z
));
5929 mpz_init_set_si (z_negative_one
, -1);
5931 /* It may be possible to tune the performance of some algorithms by using
5932 * the following constants to avoid the creation of bignums. Please, before
5933 * using these values, remember the two rules of program optimization:
5934 * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */
5935 scm_c_define ("most-positive-fixnum",
5936 SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM
));
5937 scm_c_define ("most-negative-fixnum",
5938 SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM
));
5940 scm_add_feature ("complex");
5941 scm_add_feature ("inexact");
5942 scm_flo0
= scm_from_double (0.0);
5944 /* determine floating point precision */
5945 for (i
=2; i
<= SCM_MAX_DBL_RADIX
; ++i
)
5947 init_dblprec(&scm_dblprec
[i
-2],i
);
5948 init_fx_radix(fx_per_radix
[i
-2],i
);
5951 /* hard code precision for base 10 if the preprocessor tells us to... */
5952 scm_dblprec
[10-2] = (DBL_DIG
> 20) ? 20 : DBL_DIG
;
5955 exactly_one_half
= scm_permanent_object (scm_divide (SCM_I_MAKINUM (1),
5956 SCM_I_MAKINUM (2)));
5957 #include "libguile/numbers.x"