-/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002, 2003 Free Software Foundation, Inc.
+/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004 Free Software Foundation, Inc.
*
* Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories
* and Bellcore. See scm_divide.
* All objects satisfying SCM_BIGP() are too large to fit in a fixnum.
* If an object satisfies integer?, it's either an inum, a bignum, or a real.
* If floor (r) == r, r is an int, and mpz_set_d will DTRT.
+ * All objects satisfying SCM_FRACTIONP are never an integer.
*/
/* TODO:
*/
+/* tell glibc (2.3) to give prototype for C99 trunc() */
+#define _GNU_SOURCE
+
#if HAVE_CONFIG_H
# include <config.h>
#endif
#include <ctype.h>
#include <string.h>
#include <gmp.h>
+
#include "libguile/_scm.h"
#include "libguile/feature.h"
#include "libguile/ports.h"
#include "libguile/numbers.h"
#include "libguile/deprecation.h"
+#include "libguile/eq.h"
+
\f
/*
#define SCM_I_NUMTAG(x) \
(SCM_INUMP(x) ? SCM_I_NUMTAG_INUM \
: (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \
- : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_smob) ? SCM_TYP16(x) \
+ : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \
: SCM_I_NUMTAG_NOTNUM)))
*/
+/* the macro above will not work as is with fractions */
#define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0)
#define xmpz_cmp_d(z, d) mpz_cmp_d (z, d)
#endif
-\f
+static int
+xisinf (double x)
+{
+#if defined (HAVE_ISINF)
+ return isinf (x);
+#elif defined (HAVE_FINITE) && defined (HAVE_ISNAN)
+ return (! (finite (x) || isnan (x)));
+#else
+ return 0;
+#endif
+}
-static SCM abs_most_negative_fixnum;
+static int
+xisnan (double x)
+{
+#if defined (HAVE_ISNAN)
+ return isnan (x);
+#else
+ return 0;
+#endif
+}
\f
-static const char s_bignum[] = "bignum";
+static mpz_t z_negative_one;
-SCM_C_INLINE SCM
+\f
+
+SCM_C_INLINE_KEYWORD SCM
scm_i_mkbig ()
{
/* Return a newly created bignum. */
return z;
}
-SCM_C_INLINE static SCM
+SCM_C_INLINE_KEYWORD static SCM
scm_i_clonebig (SCM src_big, int same_sign_p)
{
/* Copy src_big's value, negate it if same_sign_p is false, and return. */
SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0);
mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big));
- if (!same_sign_p) mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z));
+ if (!same_sign_p)
+ mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z));
return z;
}
-SCM_C_INLINE int
+SCM_C_INLINE_KEYWORD int
scm_i_bigcmp (SCM x, SCM y)
{
/* Return neg if x < y, pos if x > y, and 0 if x == y */
return result;
}
-SCM_C_INLINE SCM
+SCM_C_INLINE_KEYWORD SCM
scm_i_dbl2big (double d)
{
/* results are only defined if d is an integer */
return z;
}
-SCM_C_INLINE double
+/* Convert a integer in double representation to a SCM number. */
+
+SCM_C_INLINE_KEYWORD SCM
+scm_i_dbl2num (double u)
+{
+ /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both
+ powers of 2, so there's no rounding when making "double" values
+ from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could
+ get rounded on a 64-bit machine, hence the "+1".
+
+ The use of floor() to force to an integer value ensures we get a
+ "numerically closest" value without depending on how a
+ double->long cast or how mpz_set_d will round. For reference,
+ double->long probably follows the hardware rounding mode,
+ mpz_set_d truncates towards zero. */
+
+ /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not
+ representable as a double? */
+
+ if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1)
+ && u >= (double) SCM_MOST_NEGATIVE_FIXNUM)
+ return SCM_MAKINUM ((long) u);
+ else
+ return scm_i_dbl2big (u);
+}
+
+/* scm_i_big2dbl() rounds to the closest representable double, in accordance
+ with R5RS exact->inexact.
+
+ The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits
+ (ie. it truncates towards zero), then adjust to get the closest double by
+ examining the next lower bit and adding 1 if necessary.
+
+ Note that bignums exactly half way between representable doubles are
+ rounded to the next higher absolute value (ie. away from zero). This
+ seems like an adequate interpretation of R5RS "numerically closest", and
+ it's easier and faster than a full "nearest-even" style.
+
+ The bit test is done on the absolute value of the mpz_t, which means we
+ must use mpz_getlimbn. mpz_tstbit is not right, it treats negatives as
+ twos complement.
+
+ Prior to GMP 4.2, the rounding done by mpz_get_d was unspecified. It
+ happened to follow the hardware rounding mode, but on the absolute value
+ of its operand. This is not what we want, so we put the high
+ DBL_MANT_DIG bits into a temporary. This extra init/clear is a slowdown,
+ but doesn't matter too much since it's only for older GMP. */
+
+double
scm_i_big2dbl (SCM b)
{
- double result = mpz_get_d (SCM_I_BIG_MPZ (b));
+ double result;
+ size_t bits;
+
+ bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2);
+
+#if __GNU_MP_VERSION < 4 \
+ || (__GNU_MP_VERSION == 4 && __GNU_MP_VERSION_MINOR < 2)
+ {
+ /* GMP prior to 4.2, force truncate towards zero */
+ mpz_t tmp;
+ if (bits > DBL_MANT_DIG)
+ {
+ size_t shift = bits - DBL_MANT_DIG;
+ mpz_init2 (tmp, DBL_MANT_DIG);
+ mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift);
+ result = ldexp (mpz_get_d (tmp), shift);
+ mpz_clear (tmp);
+ }
+ else
+ {
+ result = mpz_get_d (SCM_I_BIG_MPZ (b));
+ }
+ }
+#else
+ /* GMP 4.2 and up */
+ result = mpz_get_d (SCM_I_BIG_MPZ (b));
+#endif
+
+ if (bits > DBL_MANT_DIG)
+ {
+ unsigned long pos = bits - DBL_MANT_DIG - 1;
+ /* test bit number "pos" in absolute value */
+ if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS)
+ & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS)))
+ {
+ result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1);
+ }
+ }
+
scm_remember_upto_here_1 (b);
return result;
}
-SCM_C_INLINE SCM
+SCM_C_INLINE_KEYWORD SCM
scm_i_normbig (SCM b)
{
/* convert a big back to a fixnum if it'll fit */
return b;
}
+static SCM_C_INLINE_KEYWORD SCM
+scm_i_mpz2num (mpz_t b)
+{
+ /* convert a mpz number to a SCM number. */
+ if (mpz_fits_slong_p (b))
+ {
+ long val = mpz_get_si (b);
+ if (SCM_FIXABLE (val))
+ return SCM_MAKINUM (val);
+ }
+
+ {
+ SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0);
+ mpz_init_set (SCM_I_BIG_MPZ (z), b);
+ return z;
+ }
+}
+
+/* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */
+static SCM scm_divide2real (SCM x, SCM y);
+
+SCM
+scm_make_ratio (SCM numerator, SCM denominator)
+#define FUNC_NAME "make-ratio"
+{
+ /* First make sure the arguments are proper.
+ */
+ if (SCM_INUMP (denominator))
+ {
+ if (SCM_EQ_P (denominator, SCM_INUM0))
+ scm_num_overflow ("make-ratio");
+ if (SCM_EQ_P (denominator, SCM_MAKINUM(1)))
+ return numerator;
+ }
+ else
+ {
+ if (!(SCM_BIGP(denominator)))
+ SCM_WRONG_TYPE_ARG (2, denominator);
+ }
+ if (!SCM_INUMP (numerator) && !SCM_BIGP (numerator))
+ SCM_WRONG_TYPE_ARG (1, numerator);
+
+ /* Then flip signs so that the denominator is positive.
+ */
+ if (SCM_NFALSEP (scm_negative_p (denominator)))
+ {
+ numerator = scm_difference (numerator, SCM_UNDEFINED);
+ denominator = scm_difference (denominator, SCM_UNDEFINED);
+ }
+
+ /* Now consider for each of the four fixnum/bignum combinations
+ whether the rational number is really an integer.
+ */
+ if (SCM_INUMP (numerator))
+ {
+ long x = SCM_INUM (numerator);
+ if (SCM_EQ_P (numerator, SCM_INUM0))
+ return SCM_INUM0;
+ if (SCM_INUMP (denominator))
+ {
+ long y;
+ y = SCM_INUM (denominator);
+ if (x == y)
+ return SCM_MAKINUM(1);
+ if ((x % y) == 0)
+ return SCM_MAKINUM (x / y);
+ }
+ else
+ {
+ /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative
+ of that value for the denominator, as a bignum. Apart from
+ that case, abs(bignum) > abs(inum) so inum/bignum is not an
+ integer. */
+ if (x == SCM_MOST_NEGATIVE_FIXNUM
+ && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator),
+ - SCM_MOST_NEGATIVE_FIXNUM) == 0)
+ return SCM_MAKINUM(-1);
+ }
+ }
+ else if (SCM_BIGP (numerator))
+ {
+ if (SCM_INUMP (denominator))
+ {
+ long yy = SCM_INUM (denominator);
+ if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy))
+ return scm_divide (numerator, denominator);
+ }
+ else
+ {
+ if (SCM_EQ_P (numerator, denominator))
+ return SCM_MAKINUM(1);
+ if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator),
+ SCM_I_BIG_MPZ (denominator)))
+ return scm_divide(numerator, denominator);
+ }
+ }
+
+ /* No, it's a proper fraction.
+ */
+ return scm_double_cell (scm_tc16_fraction,
+ SCM_UNPACK (numerator),
+ SCM_UNPACK (denominator), 0);
+}
+#undef FUNC_NAME
+
+static void scm_i_fraction_reduce (SCM z)
+{
+ if (!(SCM_FRACTION_REDUCED (z)))
+ {
+ SCM divisor;
+ divisor = scm_gcd (SCM_FRACTION_NUMERATOR (z), SCM_FRACTION_DENOMINATOR (z));
+ if (!(SCM_EQ_P (divisor, SCM_MAKINUM(1))))
+ {
+ /* is this safe? */
+ SCM_FRACTION_SET_NUMERATOR (z, scm_divide (SCM_FRACTION_NUMERATOR (z), divisor));
+ SCM_FRACTION_SET_DENOMINATOR (z, scm_divide (SCM_FRACTION_DENOMINATOR (z), divisor));
+ }
+ SCM_FRACTION_REDUCED_SET (z);
+ }
+}
+
+double
+scm_i_fraction2double (SCM z)
+{
+ return scm_num2dbl (scm_divide2real (SCM_FRACTION_NUMERATOR (z),
+ SCM_FRACTION_DENOMINATOR (z)),
+ "fraction2real");
+}
+
SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0,
(SCM x),
"Return @code{#t} if @var{x} is an exact number, @code{#f}\n"
"otherwise.")
#define FUNC_NAME s_scm_exact_p
{
- if (SCM_INUMP (x)) return SCM_BOOL_T;
- if (SCM_BIGP (x)) return SCM_BOOL_T;
- return SCM_BOOL_F;
+ if (SCM_INUMP (x))
+ return SCM_BOOL_T;
+ if (SCM_BIGP (x))
+ return SCM_BOOL_T;
+ if (SCM_FRACTIONP (x))
+ return SCM_BOOL_T;
+ if (SCM_NUMBERP (x))
+ return SCM_BOOL_F;
+ SCM_WRONG_TYPE_ARG (1, x);
}
#undef FUNC_NAME
"otherwise.")
#define FUNC_NAME s_scm_odd_p
{
- if (SCM_INUMP (n)) {
- long val = SCM_INUM (n);
- return SCM_BOOL ((val & 1L) != 0);
- } else if (SCM_BIGP (n)) {
- int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n));
- scm_remember_upto_here_1 (n);
- return SCM_BOOL (odd_p);
- } else if (scm_inf_p (n)) {
+ if (SCM_INUMP (n))
+ {
+ long val = SCM_INUM (n);
+ return SCM_BOOL ((val & 1L) != 0);
+ }
+ else if (SCM_BIGP (n))
+ {
+ int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n));
+ scm_remember_upto_here_1 (n);
+ return SCM_BOOL (odd_p);
+ }
+ else if (!SCM_FALSEP (scm_inf_p (n)))
return SCM_BOOL_T;
- } else {
+ else if (SCM_REALP (n))
+ {
+ double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0));
+ if (rem == 1.0)
+ return SCM_BOOL_T;
+ else if (rem == 0.0)
+ return SCM_BOOL_F;
+ else
+ SCM_WRONG_TYPE_ARG (1, n);
+ }
+ else
SCM_WRONG_TYPE_ARG (1, n);
- }
}
#undef FUNC_NAME
"otherwise.")
#define FUNC_NAME s_scm_even_p
{
- if (SCM_INUMP (n)) {
- long val = SCM_INUM (n);
- return SCM_BOOL ((val & 1L) == 0);
- } else if (SCM_BIGP (n)) {
- int even_p = mpz_even_p (SCM_I_BIG_MPZ (n));
- scm_remember_upto_here_1 (n);
- return SCM_BOOL (even_p);
- } else if (scm_inf_p (n)) {
+ if (SCM_INUMP (n))
+ {
+ long val = SCM_INUM (n);
+ return SCM_BOOL ((val & 1L) == 0);
+ }
+ else if (SCM_BIGP (n))
+ {
+ int even_p = mpz_even_p (SCM_I_BIG_MPZ (n));
+ scm_remember_upto_here_1 (n);
+ return SCM_BOOL (even_p);
+ }
+ else if (!SCM_FALSEP (scm_inf_p (n)))
return SCM_BOOL_T;
- } else {
+ else if (SCM_REALP (n))
+ {
+ double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0));
+ if (rem == 1.0)
+ return SCM_BOOL_F;
+ else if (rem == 0.0)
+ return SCM_BOOL_T;
+ else
+ SCM_WRONG_TYPE_ARG (1, n);
+ }
+ else
SCM_WRONG_TYPE_ARG (1, n);
- }
}
#undef FUNC_NAME
-static int
-xisinf (double x)
-{
-#if defined (HAVE_ISINF)
- return isinf (x);
-#elif defined (HAVE_FINITE) && defined (HAVE_ISNAN)
- return (! (finite (x) || isnan (x)));
-#else
- return 0;
-#endif
-}
-
-static int
-xisnan (double x)
-{
-#if defined (HAVE_ISNAN)
- return isnan (x);
-#else
- return 0;
-#endif
-}
-
-#define isfinite(x) (! xisinf (x))
-
SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0,
(SCM n),
"Return @code{#t} if @var{n} is infinite, @code{#f}\n"
"otherwise.")
#define FUNC_NAME s_scm_inf_p
{
- if (SCM_REALP (n)) {
+ if (SCM_REALP (n))
return SCM_BOOL (xisinf (SCM_REAL_VALUE (n)));
- } else if (SCM_COMPLEXP (n)) {
+ else if (SCM_COMPLEXP (n))
return SCM_BOOL (xisinf (SCM_COMPLEX_REAL (n))
|| xisinf (SCM_COMPLEX_IMAG (n)));
- } else {
+ else
return SCM_BOOL_F;
- }
}
#undef FUNC_NAME
"otherwise.")
#define FUNC_NAME s_scm_nan_p
{
- if (SCM_REALP (n)) {
+ if (SCM_REALP (n))
return SCM_BOOL (xisnan (SCM_REAL_VALUE (n)));
- } else if (SCM_COMPLEXP (n)) {
+ else if (SCM_COMPLEXP (n))
return SCM_BOOL (xisnan (SCM_COMPLEX_REAL (n))
|| xisnan (SCM_COMPLEX_IMAG (n)));
- } else {
+ else
return SCM_BOOL_F;
- }
}
#undef FUNC_NAME
/* Some version of gcc on some old version of Linux used to crash when
trying to make Inf and NaN. */
-#if defined (SCO)
- double tmp = 1.0;
- guile_Inf = 1.0 / (tmp - tmp);
-#elif defined (__alpha__) && ! defined (linux)
+#ifdef INFINITY
+ /* C99 INFINITY, when available.
+ FIXME: The standard allows for INFINITY to be something that overflows
+ at compile time. We ought to have a configure test to check for that
+ before trying to use it. (But in practice we believe this is not a
+ problem on any system guile is likely to target.) */
+ guile_Inf = INFINITY;
+#elif HAVE_DINFINITY
+ /* OSF */
extern unsigned int DINFINITY[2];
guile_Inf = (*(X_CAST(double *, DINFINITY)));
#else
#if defined (HAVE_ISNAN)
-#if defined (__alpha__) && ! defined (linux)
+#ifdef NAN
+ /* C99 NAN, when available */
+ guile_NaN = NAN;
+#elif HAVE_DQNAN
+ /* OSF */
extern unsigned int DQNAN[2];
guile_NaN = (*(X_CAST(double *, DQNAN)));
#else
#define FUNC_NAME s_scm_nan
{
static int initialized = 0;
- if (! initialized)
+ if (!initialized)
{
guile_ieee_init ();
initialized = 1;
"Return the absolute value of @var{x}.")
#define FUNC_NAME
{
- if (SCM_INUMP (x)) {
- long int xx = SCM_INUM (x);
- if (xx >= 0) {
- return x;
- } else if (SCM_POSFIXABLE (-xx)) {
- return SCM_MAKINUM (-xx);
- } else {
- return scm_i_long2big (-xx);
- }
- } else if (SCM_BIGP (x)) {
- const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- if (sgn < 0) {
- return scm_i_clonebig (x, 0);
- } else {
- return x;
- }
- } else if (SCM_REALP (x)) {
- return scm_make_real (fabs (SCM_REAL_VALUE (x)));
- } else {
+ if (SCM_INUMP (x))
+ {
+ long int xx = SCM_INUM (x);
+ if (xx >= 0)
+ return x;
+ else if (SCM_POSFIXABLE (-xx))
+ return SCM_MAKINUM (-xx);
+ else
+ return scm_i_long2big (-xx);
+ }
+ else if (SCM_BIGP (x))
+ {
+ const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ if (sgn < 0)
+ return scm_i_clonebig (x, 0);
+ else
+ return x;
+ }
+ else if (SCM_REALP (x))
+ {
+ /* note that if x is a NaN then xx<0 is false so we return x unchanged */
+ double xx = SCM_REAL_VALUE (x);
+ if (xx < 0.0)
+ return scm_make_real (-xx);
+ else
+ return x;
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (x))))
+ return x;
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED),
+ SCM_FRACTION_DENOMINATOR (x));
+ }
+ else
SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs);
- }
}
#undef FUNC_NAME
SCM
scm_quotient (SCM x, SCM y)
{
- if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- if (yy == 0) {
- scm_num_overflow (s_quotient);
- } else {
- long z = xx / yy;
- if (SCM_FIXABLE (z)) {
- return SCM_MAKINUM (z);
- } else {
- return scm_i_long2big (z);
+ if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_quotient);
+ else
+ {
+ long z = xx / yy;
+ if (SCM_FIXABLE (z))
+ return SCM_MAKINUM (z);
+ else
+ return scm_i_long2big (z);
+ }
}
- }
- } else if (SCM_BIGP (y)) {
- if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM)
- && (scm_i_bigcmp (abs_most_negative_fixnum, y) == 0))
+ else if (SCM_BIGP (y))
{
- /* Special case: x == fixnum-min && y == abs (fixnum-min) */
- return SCM_MAKINUM (-1);
+ if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM)
+ && (mpz_cmp_ui (SCM_I_BIG_MPZ (y),
+ - SCM_MOST_NEGATIVE_FIXNUM) == 0))
+ {
+ /* Special case: x == fixnum-min && y == abs (fixnum-min) */
+ scm_remember_upto_here_1 (y);
+ return SCM_MAKINUM (-1);
+ }
+ else
+ return SCM_MAKINUM (0);
}
else
- return SCM_MAKINUM (0);
- } else {
- SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
- }
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- if (yy == 0) {
- scm_num_overflow (s_quotient);
- } else if (yy == 1) {
- return x;
- } else {
- SCM result = scm_i_mkbig ();
- if (yy < 0) {
- mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - yy);
- mpz_neg(SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result));
- } else {
- mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy);
- }
- scm_remember_upto_here_1 (x);
- return scm_i_normbig (result);
- }
- } else if (SCM_BIGP (y)) {
- SCM result = scm_i_mkbig ();
- mpz_tdiv_q(SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return scm_i_normbig (result);
- } else {
- SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
+ SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
}
- } else {
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_quotient);
+ else if (yy == 1)
+ return x;
+ else
+ {
+ SCM result = scm_i_mkbig ();
+ if (yy < 0)
+ {
+ mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ - yy);
+ mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result));
+ }
+ else
+ mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy);
+ scm_remember_upto_here_1 (x);
+ return scm_i_normbig (result);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_tdiv_q (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return scm_i_normbig (result);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
+ }
+ else
SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient);
- }
}
SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder);
SCM
scm_remainder (SCM x, SCM y)
{
- if (SCM_INUMP (x)) {
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- if (yy == 0) {
- scm_num_overflow (s_remainder);
- } else {
- long z = SCM_INUM (x) % yy;
- return SCM_MAKINUM (z);
- }
- } else if (SCM_BIGP (y)) {
- if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM)
- && (scm_i_bigcmp (abs_most_negative_fixnum, y) == 0))
+ if (SCM_INUMP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_remainder);
+ else
+ {
+ long z = SCM_INUM (x) % yy;
+ return SCM_MAKINUM (z);
+ }
+ }
+ else if (SCM_BIGP (y))
{
- /* Special case: x == fixnum-min && y == abs (fixnum-min) */
- return SCM_MAKINUM (0);
+ if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM)
+ && (mpz_cmp_ui (SCM_I_BIG_MPZ (y),
+ - SCM_MOST_NEGATIVE_FIXNUM) == 0))
+ {
+ /* Special case: x == fixnum-min && y == abs (fixnum-min) */
+ scm_remember_upto_here_1 (y);
+ return SCM_MAKINUM (0);
+ }
+ else
+ return x;
}
else
- return x;
- } else {
- SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
- }
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- if (yy == 0) {
- scm_num_overflow (s_remainder);
- } else {
- SCM result = scm_i_mkbig ();
- if (yy < 0) yy = - yy;
- mpz_tdiv_r_ui(SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy);
- scm_remember_upto_here_1(x);
- return scm_i_normbig (result);
- }
- } else if (SCM_BIGP (y)) {
- SCM result = scm_i_mkbig ();
- mpz_tdiv_r (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2(x, y);
- return scm_i_normbig (result);
- } else {
- SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
+ SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
}
- } else {
- SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder);
- }
-}
-
-
-SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo);
-/* "Return the modulo of the numbers @var{x} and @var{y}.\n"
- * "@lisp\n"
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_remainder);
+ else
+ {
+ SCM result = scm_i_mkbig ();
+ if (yy < 0)
+ yy = - yy;
+ mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy);
+ scm_remember_upto_here_1 (x);
+ return scm_i_normbig (result);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_tdiv_r (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return scm_i_normbig (result);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder);
+}
+
+
+SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo);
+/* "Return the modulo of the numbers @var{x} and @var{y}.\n"
+ * "@lisp\n"
* "(modulo 13 4) @result{} 1\n"
* "(modulo -13 4) @result{} 3\n"
* "@end lisp"
SCM
scm_modulo (SCM x, SCM y)
{
- if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- if (yy == 0) {
- scm_num_overflow (s_modulo);
- } else {
- /* FIXME: I think this may be a bug on some arches -- results
- of % with negative second arg are undefined... */
- long z = xx % yy;
- long result;
-
- if (yy < 0) {
- if (z > 0) result = z + yy;
- else result = z;
- } else {
- if (z < 0) result = z + yy;
- else result = z;
- }
- return SCM_MAKINUM (result);
- }
- } else if (SCM_BIGP (y)) {
- int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
-
- if (sgn_y == 0) {
- scm_num_overflow (s_modulo);
- } else {
- mpz_t z_x;
- SCM result;
-
- if (sgn_y < 0) {
- SCM pos_y = scm_i_clonebig (y, 0);
- /* do this after the last scm_op */
- mpz_init_set_si (z_x, xx);
- result = pos_y; /* re-use this bignum */
- mpz_mod (SCM_I_BIG_MPZ (result), z_x, SCM_I_BIG_MPZ (pos_y));
- scm_remember_upto_here_1 (pos_y);
- } else {
- result = scm_i_mkbig ();
- /* do this after the last scm_op */
- mpz_init_set_si (z_x, xx);
- mpz_mod (SCM_I_BIG_MPZ (result), z_x, SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (y);
- }
+ if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_modulo);
+ else
+ {
+ /* FIXME: I think this may be a bug on some arches -- results
+ of % with negative second arg are undefined... */
+ long z = xx % yy;
+ long result;
+
+ if (yy < 0)
+ {
+ if (z > 0)
+ result = z + yy;
+ else
+ result = z;
+ }
+ else
+ {
+ if (z < 0)
+ result = z + yy;
+ else
+ result = z;
+ }
+ return SCM_MAKINUM (result);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
+ {
+ mpz_t z_x;
+ SCM result;
+
+ if (sgn_y < 0)
+ {
+ SCM pos_y = scm_i_clonebig (y, 0);
+ /* do this after the last scm_op */
+ mpz_init_set_si (z_x, xx);
+ result = pos_y; /* re-use this bignum */
+ mpz_mod (SCM_I_BIG_MPZ (result),
+ z_x,
+ SCM_I_BIG_MPZ (pos_y));
+ scm_remember_upto_here_1 (pos_y);
+ }
+ else
+ {
+ result = scm_i_mkbig ();
+ /* do this after the last scm_op */
+ mpz_init_set_si (z_x, xx);
+ mpz_mod (SCM_I_BIG_MPZ (result),
+ z_x,
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (y);
+ }
- if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) {
- mpz_add (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (y),
- SCM_I_BIG_MPZ (result));
- }
- scm_remember_upto_here_1 (y);
- /* and do this before the next one */
- mpz_clear (z_x);
- return scm_i_normbig (result);
- }
- } else {
- SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo);
- }
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- if (yy == 0) {
- scm_num_overflow (s_modulo);
- } else {
- SCM result = scm_i_mkbig ();
- mpz_mod_ui (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (x),
- (yy < 0) ? - yy : yy);
- scm_remember_upto_here_1 (x);
- if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) {
- mpz_sub_ui (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (result),
- - yy);
- }
- return scm_i_normbig (result);
- }
- } else if (SCM_BIGP (y)) {
- int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
- if (sgn_y == 0) {
- scm_num_overflow (s_modulo);
- } else {
- SCM result = scm_i_mkbig ();
- int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
- SCM pos_y = scm_i_clonebig (y, y_sgn >= 0);
- mpz_mod (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (pos_y));
+ if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)
+ mpz_add (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (y),
+ SCM_I_BIG_MPZ (result));
+ scm_remember_upto_here_1 (y);
+ /* and do this before the next one */
+ mpz_clear (z_x);
+ return scm_i_normbig (result);
+ }
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo);
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_modulo);
+ else
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_mod_ui (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ (yy < 0) ? - yy : yy);
+ scm_remember_upto_here_1 (x);
+ if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0))
+ mpz_sub_ui (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (result),
+ - yy);
+ return scm_i_normbig (result);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ {
+ SCM result = scm_i_mkbig ();
+ int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
+ SCM pos_y = scm_i_clonebig (y, y_sgn >= 0);
+ mpz_mod (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (pos_y));
- scm_remember_upto_here_1 (x);
- if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) {
- mpz_add (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (y),
- SCM_I_BIG_MPZ (result));
- }
- scm_remember_upto_here_2 (y, pos_y);
- return scm_i_normbig (result);
- }
- } else {
- SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo);
+ scm_remember_upto_here_1 (x);
+ if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0))
+ mpz_add (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (y),
+ SCM_I_BIG_MPZ (result));
+ scm_remember_upto_here_2 (y, pos_y);
+ return scm_i_normbig (result);
+ }
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo);
}
- } else {
+ else
SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo);
- }
}
SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd);
scm_gcd (SCM x, SCM y)
{
if (SCM_UNBNDP (y))
- return (SCM_UNBNDP (x)) ? SCM_INUM0 : x;
+ return SCM_UNBNDP (x) ? SCM_INUM0 : x;
if (SCM_INUMP (x))
{
long u = xx < 0 ? -xx : xx;
long v = yy < 0 ? -yy : yy;
long result;
- if (xx == 0) {
- result = v;
- } else if (yy == 0) {
- result = u;
- } else {
- long k = 1;
- long t;
- /* Determine a common factor 2^k */
- while (!(1 & (u | v)))
- {
- k <<= 1;
- u >>= 1;
- v >>= 1;
- }
- /* Now, any factor 2^n can be eliminated */
- if (u & 1)
- t = -v;
- else
- {
- t = u;
- b3:
- t = SCM_SRS (t, 1);
- }
- if (!(1 & t))
- goto b3;
- if (t > 0)
- u = t;
- else
- v = -t;
- t = u - v;
- if (t != 0)
- goto b3;
- result = u * k;
- }
- return SCM_POSFIXABLE (result) \
- ? SCM_MAKINUM (result) : scm_i_long2big (result);
+ if (xx == 0)
+ result = v;
+ else if (yy == 0)
+ result = u;
+ else
+ {
+ long k = 1;
+ long t;
+ /* Determine a common factor 2^k */
+ while (!(1 & (u | v)))
+ {
+ k <<= 1;
+ u >>= 1;
+ v >>= 1;
+ }
+ /* Now, any factor 2^n can be eliminated */
+ if (u & 1)
+ t = -v;
+ else
+ {
+ t = u;
+ b3:
+ t = SCM_SRS (t, 1);
+ }
+ if (!(1 & t))
+ goto b3;
+ if (t > 0)
+ u = t;
+ else
+ v = -t;
+ t = u - v;
+ if (t != 0)
+ goto b3;
+ result = u * k;
+ }
+ return (SCM_POSFIXABLE (result)
+ ? SCM_MAKINUM (result)
+ : scm_i_long2big (result));
}
else if (SCM_BIGP (y))
{
SCM result = scm_i_mkbig ();
SCM mx = scm_i_mkbig ();
- mpz_set_si(SCM_I_BIG_MPZ (mx), SCM_INUM (x));
+ mpz_set_si (SCM_I_BIG_MPZ (mx), SCM_INUM (x));
scm_remember_upto_here_1 (x);
- mpz_gcd(SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (mx), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2(mx, y);
+ mpz_gcd (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (mx),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (mx, y);
return scm_i_normbig (result);
}
else
long yy = SCM_INUM (y);
if (yy == 0)
return scm_abs (x);
- if (yy < 0) yy = -yy;
+ if (yy < 0)
+ yy = -yy;
result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy);
scm_remember_upto_here_1 (x);
- return SCM_POSFIXABLE (result) \
- ? SCM_MAKINUM (result) : scm_ulong2num (result);
+ return (SCM_POSFIXABLE (result)
+ ? SCM_MAKINUM (result)
+ : scm_ulong2num (result));
}
else if (SCM_BIGP (y))
{
SCM result = scm_i_mkbig ();
- mpz_gcd(SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2(x, y);
+ mpz_gcd (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
return scm_i_normbig (result);
}
else
"@lisp\n"
"(logand) @result{} -1\n"
"(logand 7) @result{} 7\n"
- "(logand #b111 #b011 #\b001) @result{} 1\n"
+ "(logand #b111 #b011 #b001) @result{} 1\n"
"@end lisp")
#define FUNC_NAME s_scm_logand
{
long int nn1;
- if (SCM_UNBNDP (n2)) {
- if (SCM_UNBNDP (n1)) {
- return SCM_MAKINUM (-1);
- } else if (!SCM_NUMBERP (n1)) {
- SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
- } else if (SCM_NUMBERP (n1)) {
- return n1;
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
+ if (SCM_UNBNDP (n2))
+ {
+ if (SCM_UNBNDP (n1))
+ return SCM_MAKINUM (-1);
+ else if (!SCM_NUMBERP (n1))
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
+ else if (SCM_NUMBERP (n1))
+ return n1;
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
}
- }
- if (SCM_INUMP (n1)) {
- nn1 = SCM_INUM (n1);
- if (SCM_INUMP (n2)) {
- long nn2 = SCM_INUM (n2);
- return SCM_MAKINUM (nn1 & nn2);
- } else if SCM_BIGP (n2) {
- intbig:
- if (n1 == 0) return SCM_INUM0;
- {
- SCM result_z = scm_i_mkbig ();
- mpz_t nn1_z;
- mpz_init_set_si (nn1_z, nn1);
- mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2));
- scm_remember_upto_here_1 (n2);
- mpz_clear (nn1_z);
- return scm_i_normbig (result_z);
- }
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
- }
- } else if (SCM_BIGP (n1)) {
- if (SCM_INUMP (n2)) {
- SCM_SWAP (n1, n2);
+ if (SCM_INUMP (n1))
+ {
nn1 = SCM_INUM (n1);
- goto intbig;
- } else if (SCM_BIGP (n2)) {
- SCM result_z = scm_i_mkbig ();
- mpz_and (SCM_I_BIG_MPZ (result_z),
- SCM_I_BIG_MPZ (n1),
- SCM_I_BIG_MPZ (n2));
- scm_remember_upto_here_2 (n1, n2);
- return scm_i_normbig (result_z);
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ if (SCM_INUMP (n2))
+ {
+ long nn2 = SCM_INUM (n2);
+ return SCM_MAKINUM (nn1 & nn2);
+ }
+ else if SCM_BIGP (n2)
+ {
+ intbig:
+ if (n1 == 0)
+ return SCM_INUM0;
+ {
+ SCM result_z = scm_i_mkbig ();
+ mpz_t nn1_z;
+ mpz_init_set_si (nn1_z, nn1);
+ mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2));
+ scm_remember_upto_here_1 (n2);
+ mpz_clear (nn1_z);
+ return scm_i_normbig (result_z);
+ }
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
}
- } else {
+ else if (SCM_BIGP (n1))
+ {
+ if (SCM_INUMP (n2))
+ {
+ SCM_SWAP (n1, n2);
+ nn1 = SCM_INUM (n1);
+ goto intbig;
+ }
+ else if (SCM_BIGP (n2))
+ {
+ SCM result_z = scm_i_mkbig ();
+ mpz_and (SCM_I_BIG_MPZ (result_z),
+ SCM_I_BIG_MPZ (n1),
+ SCM_I_BIG_MPZ (n2));
+ scm_remember_upto_here_2 (n1, n2);
+ return scm_i_normbig (result_z);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ }
+ else
SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
- }
}
#undef FUNC_NAME
{
long int nn1;
- if (SCM_UNBNDP (n2)) {
- if (SCM_UNBNDP (n1)) {
- return SCM_INUM0;
- } else if (SCM_NUMBERP (n1)) {
- return n1;
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
+ if (SCM_UNBNDP (n2))
+ {
+ if (SCM_UNBNDP (n1))
+ return SCM_INUM0;
+ else if (SCM_NUMBERP (n1))
+ return n1;
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
}
- }
- if (SCM_INUMP (n1)) {
- nn1 = SCM_INUM (n1);
- if (SCM_INUMP (n2)) {
- long nn2 = SCM_INUM (n2);
- return SCM_MAKINUM (nn1 | nn2);
- } else if (SCM_BIGP (n2)) {
- intbig:
- if (nn1 == 0) return n2;
- {
- SCM result_z = scm_i_mkbig ();
- mpz_t nn1_z;
- mpz_init_set_si (nn1_z, nn1);
- mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2));
- scm_remember_upto_here_1 (n2);
- mpz_clear (nn1_z);
- return result_z;
- }
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
- }
- } else if (SCM_BIGP (n1)) {
- if (SCM_INUMP (n2)) {
- SCM_SWAP (n1, n2);
+ if (SCM_INUMP (n1))
+ {
nn1 = SCM_INUM (n1);
- goto intbig;
- } else if (SCM_BIGP (n2)) {
- SCM result_z = scm_i_mkbig ();
- mpz_ior (SCM_I_BIG_MPZ (result_z),
- SCM_I_BIG_MPZ (n1),
- SCM_I_BIG_MPZ (n2));
- scm_remember_upto_here_2 (n1, n2);
- return result_z;
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ if (SCM_INUMP (n2))
+ {
+ long nn2 = SCM_INUM (n2);
+ return SCM_MAKINUM (nn1 | nn2);
+ }
+ else if (SCM_BIGP (n2))
+ {
+ intbig:
+ if (nn1 == 0)
+ return n2;
+ {
+ SCM result_z = scm_i_mkbig ();
+ mpz_t nn1_z;
+ mpz_init_set_si (nn1_z, nn1);
+ mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2));
+ scm_remember_upto_here_1 (n2);
+ mpz_clear (nn1_z);
+ return result_z;
+ }
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
}
- } else {
+ else if (SCM_BIGP (n1))
+ {
+ if (SCM_INUMP (n2))
+ {
+ SCM_SWAP (n1, n2);
+ nn1 = SCM_INUM (n1);
+ goto intbig;
+ }
+ else if (SCM_BIGP (n2))
+ {
+ SCM result_z = scm_i_mkbig ();
+ mpz_ior (SCM_I_BIG_MPZ (result_z),
+ SCM_I_BIG_MPZ (n1),
+ SCM_I_BIG_MPZ (n2));
+ scm_remember_upto_here_2 (n1, n2);
+ return result_z;
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ }
+ else
SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
- }
}
#undef FUNC_NAME
{
long int nn1;
- if (SCM_UNBNDP (n2)) {
- if (SCM_UNBNDP (n1)) {
- return SCM_INUM0;
- } else if (SCM_NUMBERP (n1)) {
- return n1;
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
+ if (SCM_UNBNDP (n2))
+ {
+ if (SCM_UNBNDP (n1))
+ return SCM_INUM0;
+ else if (SCM_NUMBERP (n1))
+ return n1;
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
}
- }
- if (SCM_INUMP (n1)) {
- nn1 = SCM_INUM (n1);
- if (SCM_INUMP (n2)) {
- long nn2 = SCM_INUM (n2);
- return SCM_MAKINUM (nn1 ^ nn2);
- } else if (SCM_BIGP (n2)) {
- intbig:
- {
- SCM result_z = scm_i_mkbig ();
- mpz_t nn1_z;
- mpz_init_set_si (nn1_z, nn1);
- mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2));
- scm_remember_upto_here_1 (n2);
- mpz_clear (nn1_z);
- return scm_i_normbig (result_z);
- }
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
- }
- } else if (SCM_BIGP (n1)) {
- if (SCM_INUMP (n2)) {
- SCM_SWAP (n1, n2);
+ if (SCM_INUMP (n1))
+ {
nn1 = SCM_INUM (n1);
- goto intbig;
- } else if (SCM_BIGP (n2)) {
- SCM result_z = scm_i_mkbig ();
- mpz_xor (SCM_I_BIG_MPZ (result_z),
- SCM_I_BIG_MPZ (n1),
- SCM_I_BIG_MPZ (n2));
- scm_remember_upto_here_2 (n1, n2);
- return scm_i_normbig (result_z);
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ if (SCM_INUMP (n2))
+ {
+ long nn2 = SCM_INUM (n2);
+ return SCM_MAKINUM (nn1 ^ nn2);
+ }
+ else if (SCM_BIGP (n2))
+ {
+ intbig:
+ {
+ SCM result_z = scm_i_mkbig ();
+ mpz_t nn1_z;
+ mpz_init_set_si (nn1_z, nn1);
+ mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2));
+ scm_remember_upto_here_1 (n2);
+ mpz_clear (nn1_z);
+ return scm_i_normbig (result_z);
+ }
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
}
- } else {
+ else if (SCM_BIGP (n1))
+ {
+ if (SCM_INUMP (n2))
+ {
+ SCM_SWAP (n1, n2);
+ nn1 = SCM_INUM (n1);
+ goto intbig;
+ }
+ else if (SCM_BIGP (n2))
+ {
+ SCM result_z = scm_i_mkbig ();
+ mpz_xor (SCM_I_BIG_MPZ (result_z),
+ SCM_I_BIG_MPZ (n1),
+ SCM_I_BIG_MPZ (n2));
+ scm_remember_upto_here_2 (n1, n2);
+ return scm_i_normbig (result_z);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ }
+ else
SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
- }
}
#undef FUNC_NAME
{
long int nj;
- if (SCM_INUMP (j)) {
- nj = SCM_INUM (j);
- if (SCM_INUMP (k)) {
- long nk = SCM_INUM (k);
- return SCM_BOOL (nj & nk);
- } else if (SCM_BIGP (k)) {
- intbig:
- if (nj == 0) return SCM_BOOL_F;
- {
- SCM result;
- mpz_t nj_z;
- mpz_init_set_si (nj_z, nj);
- mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k));
- scm_remember_upto_here_1 (k);
- result = SCM_BOOL (mpz_sgn (nj_z) != 0);
- mpz_clear (nj_z);
- return result;
- }
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, k);
- }
- } else if (SCM_BIGP (j)) {
- if (SCM_INUMP (k)) {
- SCM_SWAP (j, k);
+ if (SCM_INUMP (j))
+ {
nj = SCM_INUM (j);
- goto intbig;
- } else if (SCM_BIGP (k)) {
- SCM result;
- mpz_t result_z;
- mpz_init (result_z);
- mpz_and (result_z,
- SCM_I_BIG_MPZ (j),
- SCM_I_BIG_MPZ (k));
- scm_remember_upto_here_2 (j, k);
- result = SCM_BOOL (mpz_sgn (result_z) != 0);
- mpz_clear (result_z);
- return result;
- } else {
- SCM_WRONG_TYPE_ARG (SCM_ARG2, k);
+ if (SCM_INUMP (k))
+ {
+ long nk = SCM_INUM (k);
+ return SCM_BOOL (nj & nk);
+ }
+ else if (SCM_BIGP (k))
+ {
+ intbig:
+ if (nj == 0)
+ return SCM_BOOL_F;
+ {
+ SCM result;
+ mpz_t nj_z;
+ mpz_init_set_si (nj_z, nj);
+ mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k));
+ scm_remember_upto_here_1 (k);
+ result = SCM_BOOL (mpz_sgn (nj_z) != 0);
+ mpz_clear (nj_z);
+ return result;
+ }
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, k);
}
- } else {
+ else if (SCM_BIGP (j))
+ {
+ if (SCM_INUMP (k))
+ {
+ SCM_SWAP (j, k);
+ nj = SCM_INUM (j);
+ goto intbig;
+ }
+ else if (SCM_BIGP (k))
+ {
+ SCM result;
+ mpz_t result_z;
+ mpz_init (result_z);
+ mpz_and (result_z,
+ SCM_I_BIG_MPZ (j),
+ SCM_I_BIG_MPZ (k));
+ scm_remember_upto_here_2 (j, k);
+ result = SCM_BOOL (mpz_sgn (result_z) != 0);
+ mpz_clear (result_z);
+ return result;
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, k);
+ }
+ else
SCM_WRONG_TYPE_ARG (SCM_ARG1, j);
- }
}
#undef FUNC_NAME
SCM_VALIDATE_INUM_MIN (SCM_ARG1, index, 0);
iindex = (unsigned long int) SCM_INUM (index);
- if (SCM_INUMP (j)) {
+ if (SCM_INUMP (j))
return SCM_BOOL ((1L << iindex) & SCM_INUM (j));
- } else if (SCM_BIGP (j)) {
- int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex);
- scm_remember_upto_here_1 (j);
- return SCM_BOOL (val);
- } else {
+ else if (SCM_BIGP (j))
+ {
+ int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex);
+ scm_remember_upto_here_1 (j);
+ return SCM_BOOL (val);
+ }
+ else
SCM_WRONG_TYPE_ARG (SCM_ARG2, j);
- }
}
#undef FUNC_NAME
SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0,
(SCM n),
- "Return the integer which is the 2s-complement of the integer\n"
+ "Return the integer which is the ones-complement of the integer\n"
"argument.\n"
"\n"
"@lisp\n"
"@end lisp")
#define FUNC_NAME s_scm_lognot
{
- return scm_difference (SCM_MAKINUM (-1L), n);
+ if (SCM_INUMP (n)) {
+ /* No overflow here, just need to toggle all the bits making up the inum.
+ Enhancement: No need to strip the tag and add it back, could just xor
+ a block of 1 bits, if that worked with the various debug versions of
+ the SCM typedef. */
+ return SCM_MAKINUM (~ SCM_INUM (n));
+
+ } else if (SCM_BIGP (n)) {
+ SCM result = scm_i_mkbig ();
+ mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n));
+ scm_remember_upto_here_1 (n);
+ return result;
+
+ } else {
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
+ }
+}
+#undef FUNC_NAME
+
+/* returns 0 if IN is not an integer. OUT must already be
+ initialized. */
+static int
+coerce_to_big (SCM in, mpz_t out)
+{
+ if (SCM_BIGP (in))
+ mpz_set (out, SCM_I_BIG_MPZ (in));
+ else if (SCM_INUMP (in))
+ mpz_set_si (out, SCM_INUM (in));
+ else
+ return 0;
+
+ return 1;
+}
+
+SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0,
+ (SCM n, SCM k, SCM m),
+ "Return @var{n} raised to the integer exponent\n"
+ "@var{k}, modulo @var{m}.\n"
+ "\n"
+ "@lisp\n"
+ "(modulo-expt 2 3 5)\n"
+ " @result{} 3\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_modulo_expt
+{
+ mpz_t n_tmp;
+ mpz_t k_tmp;
+ mpz_t m_tmp;
+
+ /* There are two classes of error we might encounter --
+ 1) Math errors, which we'll report by calling scm_num_overflow,
+ and
+ 2) wrong-type errors, which of course we'll report by calling
+ SCM_WRONG_TYPE_ARG.
+ We don't report those errors immediately, however; instead we do
+ some cleanup first. These variables tell us which error (if
+ any) we should report after cleaning up.
+ */
+ int report_overflow = 0;
+
+ int position_of_wrong_type = 0;
+ SCM value_of_wrong_type = SCM_INUM0;
+
+ SCM result = SCM_UNDEFINED;
+
+ mpz_init (n_tmp);
+ mpz_init (k_tmp);
+ mpz_init (m_tmp);
+
+ if (SCM_EQ_P (m, SCM_INUM0))
+ {
+ report_overflow = 1;
+ goto cleanup;
+ }
+
+ if (!coerce_to_big (n, n_tmp))
+ {
+ value_of_wrong_type = n;
+ position_of_wrong_type = 1;
+ goto cleanup;
+ }
+
+ if (!coerce_to_big (k, k_tmp))
+ {
+ value_of_wrong_type = k;
+ position_of_wrong_type = 2;
+ goto cleanup;
+ }
+
+ if (!coerce_to_big (m, m_tmp))
+ {
+ value_of_wrong_type = m;
+ position_of_wrong_type = 3;
+ goto cleanup;
+ }
+
+ /* if the exponent K is negative, and we simply call mpz_powm, we
+ will get a divide-by-zero exception when an inverse 1/n mod m
+ doesn't exist (or is not unique). Since exceptions are hard to
+ handle, we'll attempt the inversion "by hand" -- that way, we get
+ a simple failure code, which is easy to handle. */
+
+ if (-1 == mpz_sgn (k_tmp))
+ {
+ if (!mpz_invert (n_tmp, n_tmp, m_tmp))
+ {
+ report_overflow = 1;
+ goto cleanup;
+ }
+ mpz_neg (k_tmp, k_tmp);
+ }
+
+ result = scm_i_mkbig ();
+ mpz_powm (SCM_I_BIG_MPZ (result),
+ n_tmp,
+ k_tmp,
+ m_tmp);
+
+ if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)
+ mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp);
+
+ cleanup:
+ mpz_clear (m_tmp);
+ mpz_clear (k_tmp);
+ mpz_clear (n_tmp);
+
+ if (report_overflow)
+ scm_num_overflow (FUNC_NAME);
+
+ if (position_of_wrong_type)
+ SCM_WRONG_TYPE_ARG (position_of_wrong_type,
+ value_of_wrong_type);
+
+ return scm_i_normbig (result);
}
#undef FUNC_NAME
else if (SCM_BIGP (k))
{
z_i2 = scm_i_clonebig (k, 1);
- mpz_init_set (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (k));
scm_remember_upto_here_1 (k);
i2_is_big = 1;
}
if ((r > SCM_MOST_POSITIVE_FIXNUM) || (r < SCM_MOST_NEGATIVE_FIXNUM))
{
z_i2 = scm_i_mkbig ();
- mpz_init_set_d (SCM_I_BIG_MPZ (z_i2), r);
+ mpz_set_d (SCM_I_BIG_MPZ (z_i2), r);
i2_is_big = 1;
}
else
{
if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0)
{
- mpz_clear (SCM_I_BIG_MPZ (z_i2));
return acc;
}
if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0)
{
- mpz_clear (SCM_I_BIG_MPZ (z_i2));
return scm_product (acc, n);
}
if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0))
SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
(SCM n, SCM cnt),
- "The function ash performs an arithmetic shift left by @var{cnt}\n"
- "bits (or shift right, if @var{cnt} is negative). 'Arithmetic'\n"
- "means, that the function does not guarantee to keep the bit\n"
- "structure of @var{n}, but rather guarantees that the result\n"
- "will always be rounded towards minus infinity. Therefore, the\n"
- "results of ash and a corresponding bitwise shift will differ if\n"
- "@var{n} is negative.\n"
+ "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n"
+ "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n"
+ "\n"
+ "This is effectively a multiplication by 2^@var{cnt}}, and when\n"
+ "@var{cnt} is negative it's a division, rounded towards negative\n"
+ "infinity. (Note that this is not the same rounding as\n"
+ "@code{quotient} does.)\n"
"\n"
- "Formally, the function returns an integer equivalent to\n"
- "@code{(inexact->exact (floor (* @var{n} (expt 2 @var{cnt}))))}.\n"
+ "With @var{n} viewed as an infinite precision twos complement,\n"
+ "@code{ash} means a left shift introducing zero bits, or a right\n"
+ "shift dropping bits.\n"
"\n"
"@lisp\n"
"(number->string (ash #b1 3) 2) @result{} \"1000\"\n"
"(number->string (ash #b1010 -1) 2) @result{} \"101\"\n"
+ "\n"
+ ";; -23 is bits ...11101001, -6 is bits ...111010\n"
+ "(ash -23 -2) @result{} -6\n"
"@end lisp")
#define FUNC_NAME s_scm_ash
{
*/
SCM div = scm_integer_expt (SCM_MAKINUM (2),
SCM_MAKINUM (-bits_to_shift));
+
+ /* scm_quotient assumes its arguments are integers, but it's legal to (ash 1/2 -1) */
if (SCM_FALSEP (scm_negative_p (n)))
return scm_quotient (n, div);
else
#undef FUNC_NAME
+#define MIN(x,y) ((x) < (y) ? (x) : (y))
+
SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0,
(SCM n, SCM start, SCM end),
"Return the integer composed of the @var{start} (inclusive)\n"
"@end lisp")
#define FUNC_NAME s_scm_bit_extract
{
- unsigned long int istart, iend;
+ unsigned long int istart, iend, bits;
SCM_VALIDATE_INUM_MIN_COPY (2, start,0, istart);
SCM_VALIDATE_INUM_MIN_COPY (3, end, 0, iend);
SCM_ASSERT_RANGE (3, end, (iend >= istart));
- if (SCM_INUMP (n)) {
- long int in = SCM_INUM (n);
- unsigned long int bits = iend - istart;
+ /* how many bits to keep */
+ bits = iend - istart;
- if (in < 0 && bits >= SCM_I_FIXNUM_BIT)
- {
- /* Since we emulate two's complement encoded numbers, this special
- * case requires us to produce a result that has more bits than can be
- * stored in a fixnum. Thus, we fall back to the more general
- * algorithm that is used for bignums.
- */
- goto generalcase;
- }
+ if (SCM_INUMP (n))
+ {
+ long int in = SCM_INUM (n);
- if (istart < SCM_I_FIXNUM_BIT)
- {
- in = in >> istart;
- if (bits < SCM_I_FIXNUM_BIT)
- return SCM_MAKINUM (in & ((1L << bits) - 1));
- else /* we know: in >= 0 */
- return SCM_MAKINUM (in);
- }
- else if (in < 0)
- {
- return SCM_MAKINUM (-1L & ((1L << bits) - 1));
- }
- else
- {
- return SCM_MAKINUM (0);
- }
- } else if (SCM_BIGP (n)) {
- generalcase:
+ /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to
+ SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in".
+ FIXME: This shift relies on signed right shifts being arithmetic,
+ which is not guaranteed by C99. */
+ in >>= MIN (istart, SCM_I_FIXNUM_BIT-1);
+
+ if (in < 0 && bits >= SCM_I_FIXNUM_BIT)
+ {
+ /* Since we emulate two's complement encoded numbers, this
+ * special case requires us to produce a result that has
+ * more bits than can be stored in a fixnum.
+ */
+ SCM result = scm_i_long2big (in);
+ mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result),
+ bits);
+ return result;
+ }
+
+ /* mask down to requisite bits */
+ bits = MIN (bits, SCM_I_FIXNUM_BIT);
+ return SCM_MAKINUM (in & ((1L << bits) - 1));
+ }
+ else if (SCM_BIGP (n))
{
- SCM num1 = SCM_MAKINUM (1L);
- SCM num2 = SCM_MAKINUM (2L);
- SCM bits = SCM_MAKINUM (iend - istart);
- SCM mask = scm_difference (scm_integer_expt (num2, bits), num1);
- return scm_logand (mask, scm_ash (n, SCM_MAKINUM (-istart)));
+ SCM result;
+ if (bits == 1)
+ {
+ result = SCM_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart));
+ }
+ else
+ {
+ /* ENHANCE-ME: It'd be nice not to allocate a new bignum when
+ bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get
+ such bits into a ulong. */
+ result = scm_i_mkbig ();
+ mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart);
+ mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits);
+ result = scm_i_normbig (result);
+ }
+ scm_remember_upto_here_1 (n);
+ return result;
}
- } else {
+ else
SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
- }
}
#undef FUNC_NAME
+
static const char scm_logtab[] = {
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
};
else if (SCM_BIGP (n))
{
unsigned long count;
- if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0)
- {
- mpz_t z_n;
- mpz_init (z_n);
- mpz_com (z_n, SCM_I_BIG_MPZ (n));
- scm_remember_upto_here_1 (n);
- count = mpz_popcount (z_n);
- mpz_clear (z_n);
- }
+ if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0)
+ count = mpz_popcount (SCM_I_BIG_MPZ (n));
else
- {
- count = mpz_popcount (SCM_I_BIG_MPZ (n));
- scm_remember_upto_here_1 (n);
- }
+ count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one);
+ scm_remember_upto_here_1 (n);
return SCM_MAKINUM (count);
}
else
"@end lisp")
#define FUNC_NAME s_scm_integer_length
{
- if (SCM_INUMP (n)) {
- unsigned long int c = 0;
- unsigned int l = 4;
- long int nn = SCM_INUM (n);
- if (nn < 0) {
- nn = -1 - nn;
- };
- while (nn) {
- c += 4;
- l = scm_ilentab [15 & nn];
- nn >>= 4;
- };
- return SCM_MAKINUM (c - 4 + l);
- } else if (SCM_BIGP (n)) {
- /* mpz_sizeinbase looks at the absolute value of negatives, whereas we
- want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is
- 1 too big, so check for that and adjust. */
- size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2);
- if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0
- && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */
- mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX)
- size--;
- scm_remember_upto_here_1 (n);
- return SCM_MAKINUM (size);
- } else {
+ if (SCM_INUMP (n))
+ {
+ unsigned long int c = 0;
+ unsigned int l = 4;
+ long int nn = SCM_INUM (n);
+ if (nn < 0)
+ nn = -1 - nn;
+ while (nn)
+ {
+ c += 4;
+ l = scm_ilentab [15 & nn];
+ nn >>= 4;
+ }
+ return SCM_MAKINUM (c - 4 + l);
+ }
+ else if (SCM_BIGP (n))
+ {
+ /* mpz_sizeinbase looks at the absolute value of negatives, whereas we
+ want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is
+ 1 too big, so check for that and adjust. */
+ size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2);
+ if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0
+ && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */
+ mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX)
+ size--;
+ scm_remember_upto_here_1 (n);
+ return SCM_MAKINUM (size);
+ }
+ else
SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
- }
}
#undef FUNC_NAME
return j;
}
-
SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0,
(SCM n, SCM radix),
"Return a string holding the external representation of the\n"
{
int base;
- if (SCM_UNBNDP (radix)) {
+ if (SCM_UNBNDP (radix))
base = 10;
- } else {
- SCM_VALIDATE_INUM (2, radix);
- base = SCM_INUM (radix);
- /* FIXME: ask if range limit was OK, and if so, document */
- SCM_ASSERT_RANGE (2, radix, (base >= 2) && (base <= 36));
- }
+ else
+ {
+ SCM_VALIDATE_INUM (2, radix);
+ base = SCM_INUM (radix);
+ /* FIXME: ask if range limit was OK, and if so, document */
+ SCM_ASSERT_RANGE (2, radix, (base >= 2) && (base <= 36));
+ }
- if (SCM_INUMP (n)) {
- char num_buf [SCM_INTBUFLEN];
- size_t length = scm_iint2str (SCM_INUM (n), base, num_buf);
- return scm_mem2string (num_buf, length);
- } else if (SCM_BIGP (n)) {
- char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n));
- scm_remember_upto_here_1 (n);
- return scm_take0str (str);
- } else if (SCM_INEXACTP (n)) {
- char num_buf [FLOBUFLEN];
- return scm_mem2string (num_buf, iflo2str (n, num_buf));
- } else {
+ if (SCM_INUMP (n))
+ {
+ char num_buf [SCM_INTBUFLEN];
+ size_t length = scm_iint2str (SCM_INUM (n), base, num_buf);
+ return scm_mem2string (num_buf, length);
+ }
+ else if (SCM_BIGP (n))
+ {
+ char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n));
+ scm_remember_upto_here_1 (n);
+ return scm_take0str (str);
+ }
+ else if (SCM_FRACTIONP (n))
+ {
+ scm_i_fraction_reduce (n);
+ return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix),
+ scm_mem2string ("/", 1),
+ scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix)));
+ }
+ else if (SCM_INEXACTP (n))
+ {
+ char num_buf [FLOBUFLEN];
+ return scm_mem2string (num_buf, iflo2str (n, num_buf));
+ }
+ else
SCM_WRONG_TYPE_ARG (1, n);
- }
}
#undef FUNC_NAME
int
scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
+
{
char num_buf[FLOBUFLEN];
scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port);
return !0;
}
+int
+scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
+{
+ SCM str;
+ scm_i_fraction_reduce (sexp);
+ str = scm_number_to_string (sexp, SCM_UNDEFINED);
+ scm_lfwrite (SCM_STRING_CHARS (str), SCM_STRING_LENGTH (str), port);
+ scm_remember_upto_here_1 (str);
+ return !0;
+}
+
int
scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED)
{
if (sign == 1)
result = scm_product (result, e);
else
- result = scm_divide (result, e);
+ result = scm_divide2real (result, e);
/* We've seen an exponent, thus the value is implicitly inexact. */
x = INEXACT;
{
enum t_exactness x = EXACT;
- /* Cobble up the fraction. We might want to set the NaN's
- mantissa from it. */
+ /* Cobble up the fractional part. We might want to set the
+ NaN's mantissa from it. */
idx += 4;
mem2uinteger (mem, len, &idx, 10, &x);
*p_idx = idx;
if (SCM_FALSEP (divisor))
return SCM_BOOL_F;
- result = scm_divide (uinteger, divisor);
+ /* both are int/big here, I assume */
+ result = scm_make_ratio (uinteger, divisor);
}
else if (radix == 10)
{
{
case EXACT:
if (SCM_INEXACTP (result))
- /* FIXME: This may change the value. */
return scm_inexact_to_exact (result);
else
return result;
SCM_VALIDATE_STRING (1, string);
SCM_VALIDATE_INUM_MIN_DEF_COPY (2, radix,2,10, base);
answer = scm_i_mem2number (SCM_STRING_CHARS (string),
- SCM_STRING_LENGTH (string),
- base);
+ SCM_STRING_LENGTH (string),
+ base);
return scm_return_first (answer, string);
}
#undef FUNC_NAME
SCM
scm_make_complex (double x, double y)
{
- if (y == 0.0) {
+ if (y == 0.0)
return scm_make_real (x);
- } else {
- SCM z;
- SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (2*sizeof (double),
- "complex"));
- SCM_COMPLEX_REAL (z) = x;
- SCM_COMPLEX_IMAG (z) = y;
- return z;
- }
+ else
+ {
+ SCM z;
+ SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex),
+ "complex"));
+ SCM_COMPLEX_REAL (z) = x;
+ SCM_COMPLEX_IMAG (z) = y;
+ return z;
+ }
}
SCM
scm_bigequal (SCM x, SCM y)
{
- int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (x));
+ int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
scm_remember_upto_here_2 (x, y);
return SCM_BOOL (0 == result);
}
&& SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y));
}
+SCM
+scm_i_fraction_equalp (SCM x, SCM y)
+{
+ scm_i_fraction_reduce (x);
+ scm_i_fraction_reduce (y);
+ if (SCM_FALSEP (scm_equal_p (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_NUMERATOR (y)))
+ || SCM_FALSEP (scm_equal_p (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_DENOMINATOR (y))))
+ return SCM_BOOL_F;
+ else
+ return SCM_BOOL_T;
+}
SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p);
#undef FUNC_NAME
-SCM_REGISTER_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p);
-/* "Return @code{#t} if @var{x} is a real number, @code{#f} else.\n"
- * "Note that the sets of integer and rational values form a subset\n"
- * "of the set of real numbers, i. e. the predicate will also\n"
- * "be fulfilled if @var{x} is an integer or a rational number."
- */
-SCM_DEFINE (scm_real_p, "rational?", 1, 0, 0,
+SCM_DEFINE (scm_real_p, "real?", 1, 0, 0,
+ (SCM x),
+ "Return @code{#t} if @var{x} is a real number, @code{#f}\n"
+ "otherwise. Note that the set of integer values forms a subset of\n"
+ "the set of real numbers, i. e. the predicate will also be\n"
+ "fulfilled if @var{x} is an integer number.")
+#define FUNC_NAME s_scm_real_p
+{
+ /* we can't represent irrational numbers. */
+ return scm_rational_p (x);
+}
+#undef FUNC_NAME
+
+SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0,
(SCM x),
"Return @code{#t} if @var{x} is a rational number, @code{#f}\n"
"otherwise. Note that the set of integer values forms a subset of\n"
"the set of rational numbers, i. e. the predicate will also be\n"
- "fulfilled if @var{x} is an integer number. Real numbers\n"
- "will also satisfy this predicate, because of their limited\n"
- "precision.")
-#define FUNC_NAME s_scm_real_p
+ "fulfilled if @var{x} is an integer number.")
+#define FUNC_NAME s_scm_rational_p
{
- if (SCM_INUMP (x)) {
+ if (SCM_INUMP (x))
return SCM_BOOL_T;
- } else if (SCM_IMP (x)) {
+ else if (SCM_IMP (x))
return SCM_BOOL_F;
- } else if (SCM_REALP (x)) {
+ else if (SCM_BIGP (x))
return SCM_BOOL_T;
- } else if (SCM_BIGP (x)) {
+ else if (SCM_FRACTIONP (x))
return SCM_BOOL_T;
- } else {
+ else if (SCM_REALP (x))
+ /* due to their limited precision, all floating point numbers are
+ rational as well. */
+ return SCM_BOOL_T;
+ else
return SCM_BOOL_F;
- }
}
#undef FUNC_NAME
"else.")
#define FUNC_NAME s_scm_inexact_p
{
- return SCM_BOOL (SCM_INEXACTP (x));
+ if (SCM_INEXACTP (x))
+ return SCM_BOOL_T;
+ if (SCM_NUMBERP (x))
+ return SCM_BOOL_F;
+ SCM_WRONG_TYPE_ARG (1, x);
}
#undef FUNC_NAME
SCM
scm_num_eq_p (SCM x, SCM y)
{
- if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- return SCM_BOOL (xx == yy);
- } else if (SCM_BIGP (y)) {
- return SCM_BOOL_F;
- } else if (SCM_REALP (y)) {
- return SCM_BOOL ((double) xx == SCM_REAL_VALUE (y));
- } else if (SCM_COMPLEXP (y)) {
- return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y))
- && (0.0 == SCM_COMPLEX_IMAG (y)));
- } else {
- SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
- }
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- return SCM_BOOL_F;
- } else if (SCM_BIGP (y)) {
- int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return SCM_BOOL (0 == cmp);
- } else if (SCM_REALP (y)) {
- int cmp;
- if (xisnan (SCM_REAL_VALUE (y))) return SCM_BOOL_F;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y));
- scm_remember_upto_here_1 (x);
- return SCM_BOOL (0 == cmp);
- } else if (SCM_COMPLEXP (y)) {
- int cmp;
- if (0.0 != SCM_COMPLEX_IMAG (y)) return SCM_BOOL_F;
- if (xisnan (SCM_COMPLEX_REAL (y))) return SCM_BOOL_F;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y));
- scm_remember_upto_here_1 (x);
- return SCM_BOOL (0 == cmp);
- } else {
- SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
- }
- } else if (SCM_REALP (x)) {
- if (SCM_INUMP (y)) {
- return SCM_BOOL (SCM_REAL_VALUE (x) == (double) SCM_INUM (y));
- } else if (SCM_BIGP (y)) {
- int cmp;
- if (xisnan (SCM_REAL_VALUE (x))) return SCM_BOOL_F;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x));
- scm_remember_upto_here_1 (y);
- return SCM_BOOL (0 == cmp);
- } else if (SCM_REALP (y)) {
- return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y));
- } else if (SCM_COMPLEXP (y)) {
- return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y))
- && (0.0 == SCM_COMPLEX_IMAG (y)));
- } else {
- SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
- }
- } else if (SCM_COMPLEXP (x)) {
- if (SCM_INUMP (y)) {
- return SCM_BOOL ((SCM_COMPLEX_REAL (x) == (double) SCM_INUM (y))
- && (SCM_COMPLEX_IMAG (x) == 0.0));
- } else if (SCM_BIGP (y)) {
- int cmp;
- if (0.0 != SCM_COMPLEX_IMAG (x)) return SCM_BOOL_F;
- if (xisnan (SCM_COMPLEX_REAL (x))) return SCM_BOOL_F;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x));
- scm_remember_upto_here_1 (y);
- return SCM_BOOL (0 == cmp);
- } else if (SCM_REALP (y)) {
- return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y))
- && (SCM_COMPLEX_IMAG (x) == 0.0));
- } else if (SCM_COMPLEXP (y)) {
- return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y))
- && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)));
- } else {
- SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
+ again:
+ if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ return SCM_BOOL (xx == yy);
+ }
+ else if (SCM_BIGP (y))
+ return SCM_BOOL_F;
+ else if (SCM_REALP (y))
+ return SCM_BOOL ((double) xx == SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y))
+ && (0.0 == SCM_COMPLEX_IMAG (y)));
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL_F;
+ else
+ SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
- } else {
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ return SCM_BOOL_F;
+ else if (SCM_BIGP (y))
+ {
+ int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return SCM_BOOL (0 == cmp);
+ }
+ else if (SCM_REALP (y))
+ {
+ int cmp;
+ if (xisnan (SCM_REAL_VALUE (y)))
+ return SCM_BOOL_F;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y));
+ scm_remember_upto_here_1 (x);
+ return SCM_BOOL (0 == cmp);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ int cmp;
+ if (0.0 != SCM_COMPLEX_IMAG (y))
+ return SCM_BOOL_F;
+ if (xisnan (SCM_COMPLEX_REAL (y)))
+ return SCM_BOOL_F;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y));
+ scm_remember_upto_here_1 (x);
+ return SCM_BOOL (0 == cmp);
+ }
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL_F;
+ else
+ SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
+ }
+ else if (SCM_REALP (x))
+ {
+ if (SCM_INUMP (y))
+ return SCM_BOOL (SCM_REAL_VALUE (x) == (double) SCM_INUM (y));
+ else if (SCM_BIGP (y))
+ {
+ int cmp;
+ if (xisnan (SCM_REAL_VALUE (x)))
+ return SCM_BOOL_F;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x));
+ scm_remember_upto_here_1 (y);
+ return SCM_BOOL (0 == cmp);
+ }
+ else if (SCM_REALP (y))
+ return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y))
+ && (0.0 == SCM_COMPLEX_IMAG (y)));
+ else if (SCM_FRACTIONP (y))
+ {
+ double xx = SCM_REAL_VALUE (x);
+ if (xisnan (xx))
+ return SCM_BOOL_F;
+ if (xisinf (xx))
+ return SCM_BOOL (xx < 0.0);
+ x = scm_inexact_to_exact (x); /* with x as frac or int */
+ goto again;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
+ }
+ else if (SCM_COMPLEXP (x))
+ {
+ if (SCM_INUMP (y))
+ return SCM_BOOL ((SCM_COMPLEX_REAL (x) == (double) SCM_INUM (y))
+ && (SCM_COMPLEX_IMAG (x) == 0.0));
+ else if (SCM_BIGP (y))
+ {
+ int cmp;
+ if (0.0 != SCM_COMPLEX_IMAG (x))
+ return SCM_BOOL_F;
+ if (xisnan (SCM_COMPLEX_REAL (x)))
+ return SCM_BOOL_F;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x));
+ scm_remember_upto_here_1 (y);
+ return SCM_BOOL (0 == cmp);
+ }
+ else if (SCM_REALP (y))
+ return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y))
+ && (SCM_COMPLEX_IMAG (x) == 0.0));
+ else if (SCM_COMPLEXP (y))
+ return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y))
+ && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)));
+ else if (SCM_FRACTIONP (y))
+ {
+ double xx;
+ if (SCM_COMPLEX_IMAG (x) != 0.0)
+ return SCM_BOOL_F;
+ xx = SCM_COMPLEX_REAL (x);
+ if (xisnan (xx))
+ return SCM_BOOL_F;
+ if (xisinf (xx))
+ return SCM_BOOL (xx < 0.0);
+ x = scm_inexact_to_exact (x); /* with x as frac or int */
+ goto again;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return SCM_BOOL_F;
+ else if (SCM_BIGP (y))
+ return SCM_BOOL_F;
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
+ if (xisnan (yy))
+ return SCM_BOOL_F;
+ if (xisinf (yy))
+ return SCM_BOOL (0.0 < yy);
+ y = scm_inexact_to_exact (y); /* with y as frac or int */
+ goto again;
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double yy;
+ if (SCM_COMPLEX_IMAG (y) != 0.0)
+ return SCM_BOOL_F;
+ yy = SCM_COMPLEX_REAL (y);
+ if (xisnan (yy))
+ return SCM_BOOL_F;
+ if (xisinf (yy))
+ return SCM_BOOL (0.0 < yy);
+ y = scm_inexact_to_exact (y); /* with y as frac or int */
+ goto again;
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_i_fraction_equalp (x, y);
+ else
+ SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
+ }
+ else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p);
- }
}
+/* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications
+ done are good for inums, but for bignums an answer can almost always be
+ had by just examining a few high bits of the operands, as done by GMP in
+ mpq_cmp. flonum/frac compares likewise, but with the slight complication
+ of the float exponent to take into account. */
+
SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p);
/* "Return @code{#t} if the list of parameters is monotonically\n"
* "increasing."
SCM
scm_less_p (SCM x, SCM y)
{
- if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- return SCM_BOOL (xx < yy);
- } else if (SCM_BIGP (y)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (y);
- return SCM_BOOL (sgn > 0);
- } else if (SCM_REALP (y)) {
- return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
+ again:
+ if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ return SCM_BOOL (xx < yy);
+ }
+ else if (SCM_BIGP (y))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (y);
+ return SCM_BOOL (sgn > 0);
+ }
+ else if (SCM_REALP (y))
+ return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y));
+ else if (SCM_FRACTIONP (y))
+ {
+ /* "x < a/b" becomes "x*b < a" */
+ int_frac:
+ x = scm_product (x, SCM_FRACTION_DENOMINATOR (y));
+ y = SCM_FRACTION_NUMERATOR (y);
+ goto again;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return SCM_BOOL (sgn < 0);
- } else if (SCM_BIGP (y)) {
- int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return SCM_BOOL (cmp < 0);
- } else if (SCM_REALP (y)) {
- int cmp;
- if (xisnan (SCM_REAL_VALUE (y))) return SCM_BOOL_F;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y));
- scm_remember_upto_here_1 (x);
- return SCM_BOOL (cmp < 0);
- } else {
- SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
- }
- } else if (SCM_REALP (x)) {
- if (SCM_INUMP (y)) {
- return SCM_BOOL (SCM_REAL_VALUE (x) < (double) SCM_INUM (y));
- } else if (SCM_BIGP (y)) {
- int cmp;
- if (xisnan (SCM_REAL_VALUE (x))) return SCM_BOOL_F;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x));
- scm_remember_upto_here_1 (y);
- return SCM_BOOL (cmp > 0);
- } else if (SCM_REALP (y)) {
- return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return SCM_BOOL (sgn < 0);
+ }
+ else if (SCM_BIGP (y))
+ {
+ int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return SCM_BOOL (cmp < 0);
+ }
+ else if (SCM_REALP (y))
+ {
+ int cmp;
+ if (xisnan (SCM_REAL_VALUE (y)))
+ return SCM_BOOL_F;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y));
+ scm_remember_upto_here_1 (x);
+ return SCM_BOOL (cmp < 0);
+ }
+ else if (SCM_FRACTIONP (y))
+ goto int_frac;
+ else
+ SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
- } else {
+ else if (SCM_REALP (x))
+ {
+ if (SCM_INUMP (y))
+ return SCM_BOOL (SCM_REAL_VALUE (x) < (double) SCM_INUM (y));
+ else if (SCM_BIGP (y))
+ {
+ int cmp;
+ if (xisnan (SCM_REAL_VALUE (x)))
+ return SCM_BOOL_F;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x));
+ scm_remember_upto_here_1 (y);
+ return SCM_BOOL (cmp > 0);
+ }
+ else if (SCM_REALP (y))
+ return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y));
+ else if (SCM_FRACTIONP (y))
+ {
+ double xx = SCM_REAL_VALUE (x);
+ if (xisnan (xx))
+ return SCM_BOOL_F;
+ if (xisinf (xx))
+ return SCM_BOOL (xx < 0.0);
+ x = scm_inexact_to_exact (x); /* with x as frac or int */
+ goto again;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y) || SCM_BIGP (y))
+ {
+ /* "a/b < y" becomes "a < y*b" */
+ y = scm_product (y, SCM_FRACTION_DENOMINATOR (x));
+ x = SCM_FRACTION_NUMERATOR (x);
+ goto again;
+ }
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
+ if (xisnan (yy))
+ return SCM_BOOL_F;
+ if (xisinf (yy))
+ return SCM_BOOL (0.0 < yy);
+ y = scm_inexact_to_exact (y); /* with y as frac or int */
+ goto again;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ /* "a/b < c/d" becomes "a*d < c*b" */
+ SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (y));
+ SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y),
+ SCM_FRACTION_DENOMINATOR (x));
+ x = new_x;
+ y = new_y;
+ goto again;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
+ }
+ else
SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p);
- }
}
SCM
scm_zero_p (SCM z)
{
- if (SCM_INUMP (z)) {
+ if (SCM_INUMP (z))
return SCM_BOOL (SCM_EQ_P (z, SCM_INUM0));
- } else if (SCM_BIGP (z)) {
+ else if (SCM_BIGP (z))
return SCM_BOOL_F;
- } else if (SCM_REALP (z)) {
+ else if (SCM_REALP (z))
return SCM_BOOL (SCM_REAL_VALUE (z) == 0.0);
- } else if (SCM_COMPLEXP (z)) {
+ else if (SCM_COMPLEXP (z))
return SCM_BOOL (SCM_COMPLEX_REAL (z) == 0.0
&& SCM_COMPLEX_IMAG (z) == 0.0);
- } else {
+ else if (SCM_FRACTIONP (z))
+ return SCM_BOOL_F;
+ else
SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p);
- }
}
SCM
scm_positive_p (SCM x)
{
- if (SCM_INUMP (x)) {
+ if (SCM_INUMP (x))
return SCM_BOOL (SCM_INUM (x) > 0);
- } else if (SCM_BIGP (x)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return SCM_BOOL (sgn > 0);
- } else if (SCM_REALP (x)) {
- return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0);
- } else {
- SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p);
- }
+ else if (SCM_BIGP (x))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return SCM_BOOL (sgn > 0);
+ }
+ else if (SCM_REALP (x))
+ return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0);
+ else if (SCM_FRACTIONP (x))
+ return scm_positive_p (SCM_FRACTION_NUMERATOR (x));
+ else
+ SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p);
}
SCM
scm_negative_p (SCM x)
{
- if (SCM_INUMP (x)) {
+ if (SCM_INUMP (x))
return SCM_BOOL (SCM_INUM (x) < 0);
- } else if (SCM_BIGP (x)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return SCM_BOOL (sgn < 0);
- } else if (SCM_REALP (x)) {
+ else if (SCM_BIGP (x))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return SCM_BOOL (sgn < 0);
+ }
+ else if (SCM_REALP (x))
return SCM_BOOL(SCM_REAL_VALUE (x) < 0.0);
- } else {
+ else if (SCM_FRACTIONP (x))
+ return scm_negative_p (SCM_FRACTION_NUMERATOR (x));
+ else
SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p);
- }
}
+/* scm_min and scm_max return an inexact when either argument is inexact, as
+ required by r5rs. On that basis, for exact/inexact combinations the
+ exact is converted to inexact to compare and possibly return. This is
+ unlike scm_less_p above which takes some trouble to preserve all bits in
+ its test, such trouble is not required for min and max. */
+
SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max);
/* "Return the maximum of all parameter values."
*/
SCM
scm_max (SCM x, SCM y)
{
- if (SCM_UNBNDP (y)) {
- if (SCM_UNBNDP (x)) {
- SCM_WTA_DISPATCH_0 (g_max, s_max);
- } else if (SCM_NUMBERP (x)) {
- return x;
- } else {
- SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max);
+ if (SCM_UNBNDP (y))
+ {
+ if (SCM_UNBNDP (x))
+ SCM_WTA_DISPATCH_0 (g_max, s_max);
+ else if (SCM_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x))
+ return x;
+ else
+ SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max);
}
- }
- if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- return (xx < yy) ? y : x;
- } else if (SCM_BIGP (y)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (y);
- return (sgn < 0) ? x : y;
- } else if (SCM_REALP (y)) {
- double z = xx;
- return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z);
- } else {
- SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
- }
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return (sgn < 0) ? y : x;
- } else if (SCM_BIGP (y)) {
- int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return (cmp > 0) ? x : y;
- } else if (SCM_REALP (y)) {
- int cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y));
- scm_remember_upto_here_1 (x);
- return (cmp > 0) ? x : y;
- } else {
- SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
- }
- } else if (SCM_REALP (x)) {
- if (SCM_INUMP (y)) {
- double z = SCM_INUM (y);
- return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x;
- } else if (SCM_BIGP (y)) {
- int cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x));
- scm_remember_upto_here_1 (y);
- return (cmp < 0) ? x : y;
- } else if (SCM_REALP (y)) {
- return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? y : x;
- } else {
- SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ return (xx < yy) ? y : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (y);
+ return (sgn < 0) ? x : y;
+ }
+ else if (SCM_REALP (y))
+ {
+ double z = xx;
+ /* if y==NaN then ">" is false and we return NaN */
+ return (z > SCM_REAL_VALUE (y)) ? scm_make_real (z) : y;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double z = xx;
+ return (z > scm_i_fraction2double (y)) ? x : y;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
}
- } else {
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return (sgn < 0) ? y : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return (cmp > 0) ? x : y;
+ }
+ else if (SCM_REALP (y))
+ {
+ /* if y==NaN then xx>yy is false, so we return the NaN y */
+ double xx, yy;
+ big_real:
+ xx = scm_i_big2dbl (x);
+ yy = SCM_REAL_VALUE (y);
+ return (xx > yy ? scm_make_real (xx) : y);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy);
+ scm_remember_upto_here_1 (x);
+ return (cmp > 0) ? x : y;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else if (SCM_REALP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ double z = SCM_INUM (y);
+ /* if x==NaN then "<" is false and we return NaN */
+ return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM t = x; x = y; y = t;
+ goto big_real;
+ }
+ else if (SCM_REALP (y))
+ {
+ /* if x==NaN then our explicit check means we return NaN
+ if y==NaN then ">" is false and we return NaN
+ calling isnan is unavoidable, since it's the only way to know
+ which of x or y causes any compares to be false */
+ double xx = SCM_REAL_VALUE (x);
+ return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = SCM_REAL_VALUE (x);
+ return (xx < yy) ? scm_make_real (yy) : x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ double z = SCM_INUM (y);
+ return (scm_i_fraction2double (x) < z) ? y : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx);
+ scm_remember_upto_here_1 (y);
+ return (cmp < 0) ? x : y;
+ }
+ else if (SCM_REALP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return (xx < SCM_REAL_VALUE (y)) ? y : scm_make_real (xx);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = scm_i_fraction2double (x);
+ return (xx < yy) ? y : x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else
SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max);
- }
}
SCM
scm_min (SCM x, SCM y)
{
- if (SCM_UNBNDP (y)) {
- if (SCM_UNBNDP (x)) {
- SCM_WTA_DISPATCH_0 (g_min, s_min);
- } else if (SCM_NUMBERP (x)) {
- return x;
- } else {
- SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min);
+ if (SCM_UNBNDP (y))
+ {
+ if (SCM_UNBNDP (x))
+ SCM_WTA_DISPATCH_0 (g_min, s_min);
+ else if (SCM_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x))
+ return x;
+ else
+ SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min);
}
- }
- if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- return (xx < yy) ? x : y;
- } else if (SCM_BIGP (y)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (y);
- return (sgn < 0) ? y : x;
- } else if (SCM_REALP (y)) {
- double z = xx;
- return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y;
- } else {
- SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
- }
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return (sgn < 0) ? x : y;
- } else if (SCM_BIGP (y)) {
- int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return (cmp > 0) ? y : x;
- } else if (SCM_REALP (y)) {
- int cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y));
- scm_remember_upto_here_1 (x);
- return (cmp > 0) ? y : x;
- } else {
- SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
- }
- } else if (SCM_REALP (x)) {
- if (SCM_INUMP (y)) {
- double z = SCM_INUM (y);
- return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z);
- } else if (SCM_BIGP (y)) {
- int cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x));
- scm_remember_upto_here_1 (y);
- return (cmp < 0) ? y : x;
- } else if (SCM_REALP (y)) {
- return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? x : y;
- } else {
- SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
+ if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ return (xx < yy) ? x : y;
+ }
+ else if (SCM_BIGP (y))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (y);
+ return (sgn < 0) ? y : x;
+ }
+ else if (SCM_REALP (y))
+ {
+ double z = xx;
+ /* if y==NaN then "<" is false and we return NaN */
+ return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double z = xx;
+ return (z < scm_i_fraction2double (y)) ? x : y;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
}
- } else {
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return (sgn < 0) ? x : y;
+ }
+ else if (SCM_BIGP (y))
+ {
+ int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return (cmp > 0) ? y : x;
+ }
+ else if (SCM_REALP (y))
+ {
+ /* if y==NaN then xx<yy is false, so we return the NaN y */
+ double xx, yy;
+ big_real:
+ xx = scm_i_big2dbl (x);
+ yy = SCM_REAL_VALUE (y);
+ return (xx < yy ? scm_make_real (xx) : y);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy);
+ scm_remember_upto_here_1 (x);
+ return (cmp > 0) ? y : x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
+ }
+ else if (SCM_REALP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ double z = SCM_INUM (y);
+ /* if x==NaN then "<" is false and we return NaN */
+ return (z < SCM_REAL_VALUE (x)) ? scm_make_real (z) : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM t = x; x = y; y = t;
+ goto big_real;
+ }
+ else if (SCM_REALP (y))
+ {
+ /* if x==NaN then our explicit check means we return NaN
+ if y==NaN then "<" is false and we return NaN
+ calling isnan is unavoidable, since it's the only way to know
+ which of x or y causes any compares to be false */
+ double xx = SCM_REAL_VALUE (x);
+ return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = SCM_REAL_VALUE (x);
+ return (yy < xx) ? scm_make_real (yy) : x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ double z = SCM_INUM (y);
+ return (scm_i_fraction2double (x) < z) ? x : y;
+ }
+ else if (SCM_BIGP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx);
+ scm_remember_upto_here_1 (y);
+ return (cmp < 0) ? y : x;
+ }
+ else if (SCM_REALP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return (SCM_REAL_VALUE (y) < xx) ? y : scm_make_real (xx);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = scm_i_fraction2double (x);
+ return (xx < yy) ? x : y;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else
SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min);
- }
}
return scm_make_complex (xx + SCM_COMPLEX_REAL (y),
SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y),
+ scm_product (x, SCM_FRACTION_DENOMINATOR (y))),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- long int inum;
- int bigsgn;
- add_big_inum:
- inum = SCM_INUM (y);
- if (inum == 0) return x;
- bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- if (inum < 0) {
- SCM result = scm_i_mkbig ();
- mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum);
- scm_remember_upto_here_1 (x);
- /* we know the result will have to be a bignum */
- if (bigsgn == -1) return result;
- return scm_i_normbig (result);
- } else {
- SCM result = scm_i_mkbig ();
- mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum);
- scm_remember_upto_here_1 (x);
- /* we know the result will have to be a bignum */
- if (bigsgn == 1) return result;
- return result;
- return scm_i_normbig (result);
+ } else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long int inum;
+ int bigsgn;
+ add_big_inum:
+ inum = SCM_INUM (y);
+ if (inum == 0)
+ return x;
+ bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ if (inum < 0)
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum);
+ scm_remember_upto_here_1 (x);
+ /* we know the result will have to be a bignum */
+ if (bigsgn == -1)
+ return result;
+ return scm_i_normbig (result);
+ }
+ else
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum);
+ scm_remember_upto_here_1 (x);
+ /* we know the result will have to be a bignum */
+ if (bigsgn == 1)
+ return result;
+ return scm_i_normbig (result);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM result = scm_i_mkbig ();
+ int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x));
+ int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
+ mpz_add (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ /* we know the result will have to be a bignum */
+ if (sgn_x == sgn_y)
+ return result;
+ return scm_i_normbig (result);
+ }
+ else if (SCM_REALP (y))
+ {
+ double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y);
+ scm_remember_upto_here_1 (x);
+ return scm_make_real (result);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x))
+ + SCM_COMPLEX_REAL (y));
+ scm_remember_upto_here_1 (x);
+ return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y),
+ scm_product (x, SCM_FRACTION_DENOMINATOR (y))),
+ SCM_FRACTION_DENOMINATOR (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
+ else if (SCM_REALP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) + SCM_INUM (y));
+ else if (SCM_BIGP (y))
+ {
+ double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x);
+ scm_remember_upto_here_1 (y);
+ return scm_make_real (result);
+ }
+ else if (SCM_REALP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y),
+ SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) + scm_i_fraction2double (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
- else if (SCM_BIGP (y)) {
- SCM result = scm_i_mkbig ();
- int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x));
- int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
- mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- /* we know the result will have to be a bignum */
- if (sgn_x == sgn_y) return result;
- return scm_i_normbig (result);
- }
- else if (SCM_REALP (y)) {
- double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y);
- scm_remember_upto_here_1 (x);
- return scm_make_real (result);
+ else if (SCM_COMPLEXP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_INUM (y),
+ SCM_COMPLEX_IMAG (x));
+ else if (SCM_BIGP (y))
+ {
+ double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y))
+ + SCM_COMPLEX_REAL (x));
+ scm_remember_upto_here_1 (y);
+ return scm_make_complex (real_part, SCM_COMPLEX_IMAG (x));
+ }
+ else if (SCM_REALP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y),
+ SCM_COMPLEX_IMAG (x));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y),
+ SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y),
+ SCM_COMPLEX_IMAG (x));
+ else
+ SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
- else if (SCM_COMPLEXP (y)) {
- double real_part = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_COMPLEX_REAL (y);
- scm_remember_upto_here_1 (x);
- return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y));
- }
- else SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
- } else if (SCM_REALP (x)) {
- if (SCM_INUMP (y)) {
- return scm_make_real (SCM_REAL_VALUE (x) + SCM_INUM (y));
- } else if (SCM_BIGP (y)) {
- double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x);
- scm_remember_upto_here_1 (y);
- return scm_make_real (result);
- } else if (SCM_REALP (y)) {
- return scm_make_real (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y));
- } else if (SCM_COMPLEXP (y)) {
- return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y),
- SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
- }
- } else if (SCM_COMPLEXP (x)) {
- if (SCM_INUMP (y)) {
- return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_INUM (y),
- SCM_COMPLEX_IMAG (x));
- } else if (SCM_BIGP (y)) {
- double real_part = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_COMPLEX_REAL (x);
- scm_remember_upto_here_1 (y);
- return scm_make_complex (real_part, SCM_COMPLEX_IMAG (x));
- } else if (SCM_REALP (y)) {
- return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y),
- SCM_COMPLEX_IMAG (x));
- } else if (SCM_COMPLEXP (y)) {
- return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y),
- SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x),
+ scm_product (y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x),
+ scm_product (y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_make_real (SCM_REAL_VALUE (y) + scm_i_fraction2double (x));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x),
+ SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ /* a/b + c/d = (ad + bc) / bd */
+ return scm_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)),
+ scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y)));
+ else
+ SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
- } else {
+ else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum);
- }
}
else if (SCM_COMPLEXP (x))
return scm_make_complex (-SCM_COMPLEX_REAL (x),
-SCM_COMPLEX_IMAG (x));
+ else if (SCM_FRACTIONP (x))
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED),
+ SCM_FRACTION_DENOMINATOR (x));
else
SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference);
}
- if (SCM_INUMP (x)) {
- if (SCM_INUMP (y)) {
- long int xx = SCM_INUM (x);
- long int yy = SCM_INUM (y);
- long int z = xx - yy;
- if (SCM_FIXABLE (z)) {
- return SCM_MAKINUM (z);
- } else {
- return scm_i_long2big (z);
- }
- } else if (SCM_BIGP (y)) {
- /* inum-x - big-y */
- long xx = SCM_INUM (x);
+ if (SCM_INUMP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long int xx = SCM_INUM (x);
+ long int yy = SCM_INUM (y);
+ long int z = xx - yy;
+ if (SCM_FIXABLE (z))
+ return SCM_MAKINUM (z);
+ else
+ return scm_i_long2big (z);
+ }
+ else if (SCM_BIGP (y))
+ {
+ /* inum-x - big-y */
+ long xx = SCM_INUM (x);
- if (xx == 0)
- return scm_i_clonebig (y, 0);
- else
- {
- int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
- SCM result = scm_i_mkbig ();
+ if (xx == 0)
+ return scm_i_clonebig (y, 0);
+ else
+ {
+ int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
+ SCM result = scm_i_mkbig ();
- if (xx >= 0)
- mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y));
- else
- {
- /* x - y == -(y + -x) */
- mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx);
- mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result));
- }
- scm_remember_upto_here_1 (y);
+ if (xx >= 0)
+ mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y));
+ else
+ {
+ /* x - y == -(y + -x) */
+ mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx);
+ mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result));
+ }
+ scm_remember_upto_here_1 (y);
- if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0))
- /* we know the result will have to be a bignum */
- return result;
- else
- return scm_i_normbig (result);
- }
- } else if (SCM_REALP (y)) {
- long int xx = SCM_INUM (x);
- return scm_make_real (xx - SCM_REAL_VALUE (y));
- } else if (SCM_COMPLEXP (y)) {
- long int xx = SCM_INUM (x);
- return scm_make_complex (xx - SCM_COMPLEX_REAL (y),
- -SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
+ if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0))
+ /* we know the result will have to be a bignum */
+ return result;
+ else
+ return scm_i_normbig (result);
+ }
+ }
+ else if (SCM_REALP (y))
+ {
+ long int xx = SCM_INUM (x);
+ return scm_make_real (xx - SCM_REAL_VALUE (y));
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ long int xx = SCM_INUM (x);
+ return scm_make_complex (xx - SCM_COMPLEX_REAL (y),
+ - SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a - b/c = (ac - b) / c */
+ return scm_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- /* big-x - inum-y */
- long yy = SCM_INUM (y);
- int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x));
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ /* big-x - inum-y */
+ long yy = SCM_INUM (y);
+ int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- if (sgn_x == 0)
- return SCM_FIXABLE (-yy) ? SCM_MAKINUM (-yy) : scm_long2num (-yy);
- else
- {
- SCM result = scm_i_mkbig ();
+ scm_remember_upto_here_1 (x);
+ if (sgn_x == 0)
+ return SCM_FIXABLE (-yy) ? SCM_MAKINUM (-yy) : scm_long2num (-yy);
+ else
+ {
+ SCM result = scm_i_mkbig ();
- mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy);
- scm_remember_upto_here_1 (x);
+ if (yy >= 0)
+ mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy);
+ else
+ mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy);
+ scm_remember_upto_here_1 (x);
- if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0))
- /* we know the result will have to be a bignum */
- return result;
- else
- return scm_i_normbig (result);
- }
+ if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0))
+ /* we know the result will have to be a bignum */
+ return result;
+ else
+ return scm_i_normbig (result);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x));
+ int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
+ SCM result = scm_i_mkbig ();
+ mpz_sub (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ /* we know the result will have to be a bignum */
+ if ((sgn_x == 1) && (sgn_y == -1))
+ return result;
+ if ((sgn_x == -1) && (sgn_y == 1))
+ return result;
+ return scm_i_normbig (result);
+ }
+ else if (SCM_REALP (y))
+ {
+ double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y);
+ scm_remember_upto_here_1 (x);
+ return scm_make_real (result);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x))
+ - SCM_COMPLEX_REAL (y));
+ scm_remember_upto_here_1 (x);
+ return scm_make_complex (real_part, - SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
+ else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
- else if (SCM_BIGP (y))
- {
- int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x));
- int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
- SCM result = scm_i_mkbig ();
- mpz_sub (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- /* we know the result will have to be a bignum */
- if ((sgn_x == 1) && (sgn_y == -1)) return result;
- if ((sgn_x == -1) && (sgn_y == 1)) return result;
- return scm_i_normbig (result);
- }
- else if (SCM_REALP (y)) {
- double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y);
- scm_remember_upto_here_1 (x);
- return scm_make_real (result);
+ else if (SCM_REALP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) - SCM_INUM (y));
+ else if (SCM_BIGP (y))
+ {
+ double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (x);
+ return scm_make_real (result);
+ }
+ else if (SCM_REALP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y),
+ -SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) - scm_i_fraction2double (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
- else if (SCM_COMPLEXP (y)) {
- double real_part = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_COMPLEX_REAL (y);
- scm_remember_upto_here_1 (x);
- return scm_make_complex (real_part, - SCM_COMPLEX_IMAG (y));
- }
- else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
- } else if (SCM_REALP (x)) {
- if (SCM_INUMP (y)) {
- return scm_make_real (SCM_REAL_VALUE (x) - SCM_INUM (y));
- } else if (SCM_BIGP (y)) {
- double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (x);
- return scm_make_real (result);
- } else if (SCM_REALP (y)) {
- return scm_make_real (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y));
- } else if (SCM_COMPLEXP (y)) {
- return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y),
- -SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
- }
- } else if (SCM_COMPLEXP (x)) {
- if (SCM_INUMP (y)) {
- return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_INUM (y),
- SCM_COMPLEX_IMAG (x));
- } else if (SCM_BIGP (y)) {
- double real_part = SCM_COMPLEX_REAL (x) - mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (x);
- return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y));
- } else if (SCM_REALP (y)) {
- return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y),
- SCM_COMPLEX_IMAG (x));
- } else if (SCM_COMPLEXP (y)) {
- return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y),
- SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
+ else if (SCM_COMPLEXP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_INUM (y),
+ SCM_COMPLEX_IMAG (x));
+ else if (SCM_BIGP (y))
+ {
+ double real_part = (SCM_COMPLEX_REAL (x)
+ - mpz_get_d (SCM_I_BIG_MPZ (y)));
+ scm_remember_upto_here_1 (x);
+ return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_REALP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y),
+ SCM_COMPLEX_IMAG (x));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y),
+ SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y),
+ SCM_COMPLEX_IMAG (x));
+ else
+ SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
- } else {
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ /* a/b - c = (a - cb) / b */
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x),
+ scm_product(y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x),
+ scm_product(y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_make_real (scm_i_fraction2double (x) - SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y),
+ -SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ /* a/b - c/d = (ad - bc) / bd */
+ return scm_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)),
+ scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y)));
+ else
+ SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
+ }
+ else
SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference);
- }
}
#undef FUNC_NAME
SCM
scm_product (SCM x, SCM y)
{
- if (SCM_UNBNDP (y)) {
- if (SCM_UNBNDP (x)) {
- return SCM_MAKINUM (1L);
- } else if (SCM_NUMBERP (x)) {
- return x;
- } else {
- SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product);
+ if (SCM_UNBNDP (y))
+ {
+ if (SCM_UNBNDP (x))
+ return SCM_MAKINUM (1L);
+ else if (SCM_NUMBERP (x))
+ return x;
+ else
+ SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product);
}
- }
- if (SCM_INUMP (x)) {
- long xx;
+ if (SCM_INUMP (x))
+ {
+ long xx;
- intbig:
- xx = SCM_INUM (x);
+ intbig:
+ xx = SCM_INUM (x);
- switch (xx)
- {
+ switch (xx)
+ {
case 0: return x; break;
case 1: return y; break;
- }
+ }
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- long kk = xx * yy;
- SCM k = SCM_MAKINUM (kk);
- if ((kk == SCM_INUM (k)) && (kk / xx == yy)) {
- return k;
- } else {
- SCM result = scm_i_long2big (xx);
- mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy);
- return scm_i_normbig (result);
- }
- } else if (SCM_BIGP (y)) {
- SCM result = scm_i_mkbig ();
- mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx);
- scm_remember_upto_here_1 (y);
- return result;
- } else if (SCM_REALP (y)) {
- return scm_make_real (xx * SCM_REAL_VALUE (y));
- } else if (SCM_COMPLEXP (y)) {
- return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
- xx * SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
- }
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- SCM_SWAP (x, y);
- goto intbig;
- } else if (SCM_BIGP (y)) {
- SCM result = scm_i_mkbig ();
- mpz_mul (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return result;
- } else if (SCM_REALP (y)) {
- double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y);
- scm_remember_upto_here_1 (x);
- return scm_make_real (result);
- } else if (SCM_COMPLEXP (y)) {
- double z = mpz_get_d (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return scm_make_complex (z * SCM_COMPLEX_REAL (y),
- z * SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
- }
- } else if (SCM_REALP (x)) {
- if (SCM_INUMP (y)) {
- return scm_make_real (SCM_INUM (y) * SCM_REAL_VALUE (x));
- } else if (SCM_BIGP (y)) {
- double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x);
- scm_remember_upto_here_1 (y);
- return scm_make_real (result);
- } else if (SCM_REALP (y)) {
- return scm_make_real (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y));
- } else if (SCM_COMPLEXP (y)) {
- return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y),
- SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
- }
- } else if (SCM_COMPLEXP (x)) {
- if (SCM_INUMP (y)) {
- return scm_make_complex (SCM_INUM (y) * SCM_COMPLEX_REAL (x),
- SCM_INUM (y) * SCM_COMPLEX_IMAG (x));
- } else if (SCM_BIGP (y)) {
- double z = mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (y);
- return scm_make_complex (z * SCM_COMPLEX_REAL (y),
- z * SCM_COMPLEX_IMAG (y));
- } else if (SCM_REALP (y)) {
- return scm_make_complex (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x),
- SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x));
- } else if (SCM_COMPLEXP (y)) {
- return scm_make_complex (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y)
- - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y),
- SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y)
- + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y));
- } else {
- SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ long kk = xx * yy;
+ SCM k = SCM_MAKINUM (kk);
+ if ((kk == SCM_INUM (k)) && (kk / xx == yy))
+ return k;
+ else
+ {
+ SCM result = scm_i_long2big (xx);
+ mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy);
+ return scm_i_normbig (result);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx);
+ scm_remember_upto_here_1 (y);
+ return result;
+ }
+ else if (SCM_REALP (y))
+ return scm_make_real (xx * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
+ xx * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
- } else {
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ SCM_SWAP (x, y);
+ goto intbig;
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_mul (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return result;
+ }
+ else if (SCM_REALP (y))
+ {
+ double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y);
+ scm_remember_upto_here_1 (x);
+ return scm_make_real (result);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double z = mpz_get_d (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return scm_make_complex (z * SCM_COMPLEX_REAL (y),
+ z * SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
+ }
+ else if (SCM_REALP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_real (SCM_INUM (y) * SCM_REAL_VALUE (x));
+ else if (SCM_BIGP (y))
+ {
+ double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x);
+ scm_remember_upto_here_1 (y);
+ return scm_make_real (result);
+ }
+ else if (SCM_REALP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y),
+ SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) * scm_i_fraction2double (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
+ }
+ else if (SCM_COMPLEXP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_complex (SCM_INUM (y) * SCM_COMPLEX_REAL (x),
+ SCM_INUM (y) * SCM_COMPLEX_IMAG (x));
+ else if (SCM_BIGP (y))
+ {
+ double z = mpz_get_d (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (y);
+ return scm_make_complex (z * SCM_COMPLEX_REAL (x),
+ z * SCM_COMPLEX_IMAG (x));
+ }
+ else if (SCM_REALP (y))
+ return scm_make_complex (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x),
+ SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x));
+ else if (SCM_COMPLEXP (y))
+ {
+ return scm_make_complex (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y)
+ - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y),
+ SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y)
+ + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ return scm_make_complex (yy * SCM_COMPLEX_REAL (x),
+ yy * SCM_COMPLEX_IMAG (x));
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_make_real (scm_i_fraction2double (x) * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
+ xx * SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a/b * c/d = ac / bd */
+ return scm_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_NUMERATOR (y)),
+ scm_product (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_DENOMINATOR (y)));
+ else
+ SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
+ }
+ else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product);
- }
}
double
scm_num2dbl (SCM a, const char *why)
#define FUNC_NAME why
{
- if (SCM_INUMP (a)) {
+ if (SCM_INUMP (a))
return (double) SCM_INUM (a);
- } else if (SCM_BIGP (a)) {
- double result = mpz_get_d (SCM_I_BIG_MPZ (a));
- scm_remember_upto_here_1 (a);
- return result;
- } else if (SCM_REALP (a)) {
+ else if (SCM_BIGP (a))
+ {
+ double result = mpz_get_d (SCM_I_BIG_MPZ (a));
+ scm_remember_upto_here_1 (a);
+ return result;
+ }
+ else if (SCM_REALP (a))
return (SCM_REAL_VALUE (a));
- } else {
+ else if (SCM_FRACTIONP (a))
+ return scm_i_fraction2double (a);
+ else
SCM_WRONG_TYPE_ARG (SCM_ARGn, a);
- }
}
#undef FUNC_NAME
arguments. If called with one argument @var{z1}, 1/@var{z1} is
returned. */
#define FUNC_NAME s_divide
-SCM
-scm_divide (SCM x, SCM y)
+static SCM
+scm_i_divide (SCM x, SCM y, int inexact)
{
double a;
- if (SCM_UNBNDP (y)) {
- if (SCM_UNBNDP (x)) {
- SCM_WTA_DISPATCH_0 (g_divide, s_divide);
- } else if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (xx == 1 || xx == -1) {
- return x;
+ if (SCM_UNBNDP (y))
+ {
+ if (SCM_UNBNDP (x))
+ SCM_WTA_DISPATCH_0 (g_divide, s_divide);
+ else if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (xx == 1 || xx == -1)
+ return x;
#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
- } else if (xx == 0) {
- scm_num_overflow (s_divide);
+ else if (xx == 0)
+ scm_num_overflow (s_divide);
#endif
- } else {
- return scm_make_real (1.0 / (double) xx);
- }
- } else if (SCM_BIGP (x)) {
- return scm_make_real (1.0 / scm_i_big2dbl (x));
- } else if (SCM_REALP (x)) {
- double xx = SCM_REAL_VALUE (x);
+ else
+ {
+ if (inexact)
+ return scm_make_real (1.0 / (double) xx);
+ else return scm_make_ratio (SCM_MAKINUM(1), x);
+ }
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (inexact)
+ return scm_make_real (1.0 / scm_i_big2dbl (x));
+ else return scm_make_ratio (SCM_MAKINUM(1), x);
+ }
+ else if (SCM_REALP (x))
+ {
+ double xx = SCM_REAL_VALUE (x);
#ifndef ALLOW_DIVIDE_BY_ZERO
- if (xx == 0.0)
- scm_num_overflow (s_divide);
- else
+ if (xx == 0.0)
+ scm_num_overflow (s_divide);
+ else
#endif
- return scm_make_real (1.0 / xx);
- } else if (SCM_COMPLEXP (x)) {
- double r = SCM_COMPLEX_REAL (x);
- double i = SCM_COMPLEX_IMAG (x);
- if (r <= i) {
- double t = r / i;
- double d = i * (1.0 + t * t);
- return scm_make_complex (t / d, -1.0 / d);
- } else {
- double t = i / r;
- double d = r * (1.0 + t * t);
- return scm_make_complex (1.0 / d, -t / d);
- }
- } else {
- SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide);
+ return scm_make_real (1.0 / xx);
+ }
+ else if (SCM_COMPLEXP (x))
+ {
+ double r = SCM_COMPLEX_REAL (x);
+ double i = SCM_COMPLEX_IMAG (x);
+ if (r <= i)
+ {
+ double t = r / i;
+ double d = i * (1.0 + t * t);
+ return scm_make_complex (t / d, -1.0 / d);
+ }
+ else
+ {
+ double t = i / r;
+ double d = r * (1.0 + t * t);
+ return scm_make_complex (1.0 / d, -t / d);
+ }
+ }
+ else if (SCM_FRACTIONP (x))
+ return scm_make_ratio (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_NUMERATOR (x));
+ else
+ SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide);
}
- }
- if (SCM_INUMP (x)) {
- long xx = SCM_INUM (x);
- if (SCM_INUMP (y)) {
- long yy = SCM_INUM (y);
- if (yy == 0) {
+ if (SCM_INUMP (x))
+ {
+ long xx = SCM_INUM (x);
+ if (SCM_INUMP (y))
+ {
+ long yy = SCM_INUM (y);
+ if (yy == 0)
+ {
#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
- scm_num_overflow (s_divide);
+ scm_num_overflow (s_divide);
#else
- return scm_make_real ((double) xx / (double) yy);
+ return scm_make_real ((double) xx / (double) yy);
#endif
- } else if (xx % yy != 0) {
- return scm_make_real ((double) xx / (double) yy);
- } else {
- long z = xx / yy;
- if (SCM_FIXABLE (z)) {
- return SCM_MAKINUM (z);
- } else {
- return scm_i_long2big (z);
+ }
+ else if (xx % yy != 0)
+ {
+ if (inexact)
+ return scm_make_real ((double) xx / (double) yy);
+ else return scm_make_ratio (x, y);
+ }
+ else
+ {
+ long z = xx / yy;
+ if (SCM_FIXABLE (z))
+ return SCM_MAKINUM (z);
+ else
+ return scm_i_long2big (z);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ if (inexact)
+ return scm_make_real ((double) xx / scm_i_big2dbl (y));
+ else return scm_make_ratio (x, y);
+ }
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
+#ifndef ALLOW_DIVIDE_BY_ZERO
+ if (yy == 0.0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ return scm_make_real ((double) xx / yy);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ a = xx;
+ complex_div: /* y _must_ be a complex number */
+ {
+ double r = SCM_COMPLEX_REAL (y);
+ double i = SCM_COMPLEX_IMAG (y);
+ if (r <= i)
+ {
+ double t = r / i;
+ double d = i * (1.0 + t * t);
+ return scm_make_complex ((a * t) / d, -a / d);
+ }
+ else
+ {
+ double t = i / r;
+ double d = r * (1.0 + t * t);
+ return scm_make_complex (a / d, -(a * t) / d);
+ }
+ }
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a / b/c = ac / b */
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long int yy = SCM_INUM (y);
+ if (yy == 0)
+ {
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ scm_num_overflow (s_divide);
+#else
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return (sgn == 0) ? scm_nan () : scm_inf ();
+#endif
+ }
+ else if (yy == 1)
+ return x;
+ else
+ {
+ /* FIXME: HMM, what are the relative performance issues here?
+ We need to test. Is it faster on average to test
+ divisible_p, then perform whichever operation, or is it
+ faster to perform the integer div opportunistically and
+ switch to real if there's a remainder? For now we take the
+ middle ground: test, then if divisible, use the faster div
+ func. */
+
+ long abs_yy = yy < 0 ? -yy : yy;
+ int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy);
+
+ if (divisible_p)
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy);
+ scm_remember_upto_here_1 (x);
+ if (yy < 0)
+ mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result));
+ return scm_i_normbig (result);
+ }
+ else
+ {
+ if (inexact)
+ return scm_make_real (scm_i_big2dbl (x) / (double) yy);
+ else return scm_make_ratio (x, y);
+ }
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0);
+ if (y_is_zero)
+ {
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ scm_num_overflow (s_divide);
+#else
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return (sgn == 0) ? scm_nan () : scm_inf ();
+#endif
+ }
+ else
+ {
+ /* big_x / big_y */
+ int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ if (divisible_p)
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_divexact (SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (x),
+ SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return scm_i_normbig (result);
+ }
+ else
+ {
+ if (inexact)
+ {
+ double dbx = mpz_get_d (SCM_I_BIG_MPZ (x));
+ double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return scm_make_real (dbx / dby);
+ }
+ else return scm_make_ratio (x, y);
+ }
+ }
+ }
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
+#ifndef ALLOW_DIVIDE_BY_ZERO
+ if (yy == 0.0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ return scm_make_real (scm_i_big2dbl (x) / yy);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ a = scm_i_big2dbl (x);
+ goto complex_div;
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
+ }
+ else if (SCM_REALP (x))
+ {
+ double rx = SCM_REAL_VALUE (x);
+ if (SCM_INUMP (y))
+ {
+ long int yy = SCM_INUM (y);
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ if (yy == 0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ return scm_make_real (rx / (double) yy);
+ }
+ else if (SCM_BIGP (y))
+ {
+ double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (y);
+ return scm_make_real (rx / dby);
}
- }
- } else if (SCM_BIGP (y)) {
- return scm_make_real ((double) xx / scm_i_big2dbl (y));
- } else if (SCM_REALP (y)) {
- double yy = SCM_REAL_VALUE (y);
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
#ifndef ALLOW_DIVIDE_BY_ZERO
- if (yy == 0.0)
- scm_num_overflow (s_divide);
- else
+ if (yy == 0.0)
+ scm_num_overflow (s_divide);
+ else
#endif
- return scm_make_real ((double) xx / yy);
- } else if (SCM_COMPLEXP (y)) {
- a = xx;
- complex_div: /* y _must_ be a complex number */
- {
- double r = SCM_COMPLEX_REAL (y);
- double i = SCM_COMPLEX_IMAG (y);
- if (r <= i) {
- double t = r / i;
- double d = i * (1.0 + t * t);
- return scm_make_complex ((a * t) / d, -a / d);
- } else {
- double t = i / r;
- double d = r * (1.0 + t * t);
- return scm_make_complex (a / d, -(a * t) / d);
+ return scm_make_real (rx / yy);
}
- }
- } else {
- SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
+ else if (SCM_COMPLEXP (y))
+ {
+ a = rx;
+ goto complex_div;
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (rx / scm_i_fraction2double (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
}
- } else if (SCM_BIGP (x)) {
- if (SCM_INUMP (y)) {
- long int yy = SCM_INUM (y);
- if (yy == 0) {
-#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
- scm_num_overflow (s_divide);
-#else
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return (sgn == 0) ? scm_nan () : scm_inf ();
-#endif
- } else if (yy == 1) {
- return x;
- } else {
- /* FIXME: HMM, what are the relative performance issues here?
- We need to test. Is it faster on average to test
- divisible_p, then perform whichever operation, or is it
- faster to perform the integer div opportunistically and
- switch to real if there's a remainder? For now we take the
- middle ground: test, then if divisible, use the faster div
- func. */
-
- long abs_yy = yy < 0 ? -yy : yy;
- int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy);
-
- if (divisible_p) {
- SCM result = scm_i_mkbig ();
- mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy);
- scm_remember_upto_here_1 (x);
- if (yy < 0)
- mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result));
- return scm_i_normbig (result);
- }
- else {
- return scm_make_real (scm_i_big2dbl (x) / (double) yy);
- }
- }
- } else if (SCM_BIGP (y)) {
- int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0);
- if (y_is_zero) {
+ else if (SCM_COMPLEXP (x))
+ {
+ double rx = SCM_COMPLEX_REAL (x);
+ double ix = SCM_COMPLEX_IMAG (x);
+ if (SCM_INUMP (y))
+ {
+ long int yy = SCM_INUM (y);
#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
- scm_num_overflow (s_divide);
-#else
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
- scm_remember_upto_here_1 (x);
- return (sgn == 0) ? scm_nan () : scm_inf ();
+ if (yy == 0)
+ scm_num_overflow (s_divide);
+ else
#endif
- } else {
- /* big_x / big_y */
- int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (y));
- if (divisible_p) {
- SCM result = scm_i_mkbig ();
- mpz_divexact (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return scm_i_normbig (result);
- }
- else {
- double dbx = mpz_get_d (SCM_I_BIG_MPZ (x));
- double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return scm_make_real (dbx / dby);
- }
- }
- } else if (SCM_REALP (y)) {
- double yy = SCM_REAL_VALUE (y);
+ {
+ double d = yy;
+ return scm_make_complex (rx / d, ix / d);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_1 (y);
+ return scm_make_complex (rx / dby, ix / dby);
+ }
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
#ifndef ALLOW_DIVIDE_BY_ZERO
- if (yy == 0.0)
- scm_num_overflow (s_divide);
- else
-#endif
- return scm_make_real (scm_i_big2dbl (x) / yy);
- } else if (SCM_COMPLEXP (y)) {
- a = scm_i_big2dbl (x);
- goto complex_div;
- } else {
- SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
- }
- } else if (SCM_REALP (x)) {
- double rx = SCM_REAL_VALUE (x);
- if (SCM_INUMP (y)) {
- long int yy = SCM_INUM (y);
-#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
- if (yy == 0)
- scm_num_overflow (s_divide);
- else
+ if (yy == 0.0)
+ scm_num_overflow (s_divide);
+ else
#endif
- return scm_make_real (rx / (double) yy);
- } else if (SCM_BIGP (y)) {
- double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (y);
- return scm_make_real (rx / dby);
- } else if (SCM_REALP (y)) {
- double yy = SCM_REAL_VALUE (y);
-#ifndef ALLOW_DIVIDE_BY_ZERO
- if (yy == 0.0)
- scm_num_overflow (s_divide);
+ return scm_make_complex (rx / yy, ix / yy);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double ry = SCM_COMPLEX_REAL (y);
+ double iy = SCM_COMPLEX_IMAG (y);
+ if (ry <= iy)
+ {
+ double t = ry / iy;
+ double d = iy * (1.0 + t * t);
+ return scm_make_complex ((rx * t + ix) / d, (ix * t - rx) / d);
+ }
+ else
+ {
+ double t = iy / ry;
+ double d = ry * (1.0 + t * t);
+ return scm_make_complex ((rx + ix * t) / d, (ix - rx * t) / d);
+ }
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ return scm_make_complex (rx / yy, ix / yy);
+ }
else
-#endif
- return scm_make_real (rx / yy);
- } else if (SCM_COMPLEXP (y)) {
- a = rx;
- goto complex_div;
- } else {
- SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
- }
- } else if (SCM_COMPLEXP (x)) {
- double rx = SCM_COMPLEX_REAL (x);
- double ix = SCM_COMPLEX_IMAG (x);
- if (SCM_INUMP (y)) {
- long int yy = SCM_INUM (y);
+ SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long int yy = SCM_INUM (y);
#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
- if (yy == 0)
- scm_num_overflow (s_divide);
- else
+ if (yy == 0)
+ scm_num_overflow (s_divide);
+ else
#endif
- {
- double d = yy;
- return scm_make_complex (rx / d, ix / d);
- }
- } else if (SCM_BIGP (y)) {
- double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_1 (y);
- return scm_make_complex (rx / dby, ix / dby);
- } else if (SCM_REALP (y)) {
- double yy = SCM_REAL_VALUE (y);
+ return scm_make_ratio (SCM_FRACTION_NUMERATOR (x),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), y));
+ }
+ else if (SCM_BIGP (y))
+ {
+ return scm_make_ratio (SCM_FRACTION_NUMERATOR (x),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), y));
+ }
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
#ifndef ALLOW_DIVIDE_BY_ZERO
- if (yy == 0.0)
- scm_num_overflow (s_divide);
- else
+ if (yy == 0.0)
+ scm_num_overflow (s_divide);
+ else
#endif
- return scm_make_complex (rx / yy, ix / yy);
- } else if (SCM_COMPLEXP (y)) {
- double ry = SCM_COMPLEX_REAL (y);
- double iy = SCM_COMPLEX_IMAG (y);
- if (ry <= iy) {
- double t = ry / iy;
- double d = iy * (1.0 + t * t);
- return scm_make_complex ((rx * t + ix) / d, (ix * t - rx) / d);
- } else {
- double t = iy / ry;
- double d = ry * (1.0 + t * t);
- return scm_make_complex ((rx + ix * t) / d, (ix - rx * t) / d);
- }
- } else {
- SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
+ return scm_make_real (scm_i_fraction2double (x) / yy);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ a = scm_i_fraction2double (x);
+ goto complex_div;
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)),
+ scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x)));
+ else
+ SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
}
- } else {
+ else
SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide);
- }
+}
+
+SCM
+scm_divide (SCM x, SCM y)
+{
+ return scm_i_divide (x, y, 0);
+}
+
+static SCM scm_divide2real (SCM x, SCM y)
+{
+ return scm_i_divide (x, y, 1);
}
#undef FUNC_NAME
-SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_cxr, (SCM (*)()) scm_asinh, g_asinh);
-/* "Return the inverse hyperbolic sine of @var{x}."
- */
+
double
scm_asinh (double x)
{
+#if HAVE_ASINH
+ return asinh (x);
+#else
+#define asinh scm_asinh
return log (x + sqrt (x * x + 1));
+#endif
}
+SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh);
+/* "Return the inverse hyperbolic sine of @var{x}."
+ */
-SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_cxr, (SCM (*)()) scm_acosh, g_acosh);
-/* "Return the inverse hyperbolic cosine of @var{x}."
- */
double
scm_acosh (double x)
{
+#if HAVE_ACOSH
+ return acosh (x);
+#else
+#define acosh scm_acosh
return log (x + sqrt (x * x - 1));
+#endif
}
+SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh);
+/* "Return the inverse hyperbolic cosine of @var{x}."
+ */
-SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_cxr, (SCM (*)()) scm_atanh, g_atanh);
-/* "Return the inverse hyperbolic tangent of @var{x}."
- */
double
scm_atanh (double x)
{
+#if HAVE_ATANH
+ return atanh (x);
+#else
+#define atanh scm_atanh
return 0.5 * log ((1 + x) / (1 - x));
+#endif
}
+SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh);
+/* "Return the inverse hyperbolic tangent of @var{x}."
+ */
-SCM_GPROC1 (s_truncate, "truncate", scm_tc7_cxr, (SCM (*)()) scm_truncate, g_truncate);
-/* "Round the inexact number @var{x} towards zero."
+/* XXX - eventually, we should remove this definition of scm_round and
+ rename scm_round_number to scm_round. Likewise for scm_truncate
+ and scm_truncate_number.
*/
+
double
scm_truncate (double x)
{
+#if HAVE_TRUNC
+ return trunc (x);
+#else
+#define trunc scm_truncate
if (x < 0.0)
return -floor (-x);
return floor (x);
+#endif
}
-
-SCM_GPROC1 (s_round, "round", scm_tc7_cxr, (SCM (*)()) scm_round, g_round);
-/* "Round the inexact number @var{x}. If @var{x} is halfway between two\n"
- * "numbers, round towards even."
- */
double
scm_round (double x)
{
double plus_half = x + 0.5;
double result = floor (plus_half);
/* Adjust so that the scm_round is towards even. */
- return (plus_half == result && plus_half / 2 != floor (plus_half / 2))
- ? result - 1 : result;
+ return ((plus_half == result && plus_half / 2 != floor (plus_half / 2))
+ ? result - 1
+ : result);
+}
+
+SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards zero.")
+#define FUNC_NAME s_scm_truncate_number
+{
+ if (SCM_FALSEP (scm_negative_p (x)))
+ return scm_floor (x);
+ else
+ return scm_ceiling (x);
}
+#undef FUNC_NAME
+static SCM exactly_one_half;
-SCM_GPROC1 (s_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor);
-/* "Round the number @var{x} towards minus infinity."
- */
-SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil);
-/* "Round the number @var{x} towards infinity."
- */
-SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_cxr, (SCM (*)()) sqrt, g_i_sqrt);
+SCM_DEFINE (scm_round_number, "round", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards the nearest integer. "
+ "When it is exactly halfway between two integers, "
+ "round towards the even one.")
+#define FUNC_NAME s_scm_round_number
+{
+ SCM plus_half = scm_sum (x, exactly_one_half);
+ SCM result = scm_floor (plus_half);
+ /* Adjust so that the scm_round is towards even. */
+ if (!SCM_FALSEP (scm_num_eq_p (plus_half, result))
+ && !SCM_FALSEP (scm_odd_p (result)))
+ return scm_difference (result, SCM_MAKINUM (1));
+ else
+ return result;
+}
+#undef FUNC_NAME
+
+SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards minus infinity.")
+#define FUNC_NAME s_scm_floor
+{
+ if (SCM_INUMP (x) || SCM_BIGP (x))
+ return x;
+ else if (SCM_REALP (x))
+ return scm_make_real (floor (SCM_REAL_VALUE (x)));
+ else if (SCM_FRACTIONP (x))
+ {
+ SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (x));
+ if (SCM_FALSEP (scm_negative_p (x)))
+ {
+ /* For positive x, rounding towards zero is correct. */
+ return q;
+ }
+ else
+ {
+ /* For negative x, we need to return q-1 unless x is an
+ integer. But fractions are never integer, per our
+ assumptions. */
+ return scm_difference (q, SCM_MAKINUM (1));
+ }
+ }
+ else
+ SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor);
+}
+#undef FUNC_NAME
+
+SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards infinity.")
+#define FUNC_NAME s_scm_ceiling
+{
+ if (SCM_INUMP (x) || SCM_BIGP (x))
+ return x;
+ else if (SCM_REALP (x))
+ return scm_make_real (ceil (SCM_REAL_VALUE (x)));
+ else if (SCM_FRACTIONP (x))
+ {
+ SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (x));
+ if (SCM_FALSEP (scm_positive_p (x)))
+ {
+ /* For negative x, rounding towards zero is correct. */
+ return q;
+ }
+ else
+ {
+ /* For positive x, we need to return q+1 unless x is an
+ integer. But fractions are never integer, per our
+ assumptions. */
+ return scm_sum (q, SCM_MAKINUM (1));
+ }
+ }
+ else
+ SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling);
+}
+#undef FUNC_NAME
+
+SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt);
/* "Return the square root of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_cxr, (SCM (*)()) fabs, g_i_abs);
+SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs);
/* "Return the absolute value of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_cxr, (SCM (*)()) exp, g_i_exp);
+SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp);
/* "Return the @var{x}th power of e."
*/
-SCM_GPROC1 (s_i_log, "$log", scm_tc7_cxr, (SCM (*)()) log, g_i_log);
+SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log);
/* "Return the natural logarithm of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_cxr, (SCM (*)()) sin, g_i_sin);
+SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin);
/* "Return the sine of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_cxr, (SCM (*)()) cos, g_i_cos);
+SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos);
/* "Return the cosine of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_cxr, (SCM (*)()) tan, g_i_tan);
+SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan);
/* "Return the tangent of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_cxr, (SCM (*)()) asin, g_i_asin);
+SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin);
/* "Return the arc sine of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_cxr, (SCM (*)()) acos, g_i_acos);
+SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos);
/* "Return the arc cosine of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_cxr, (SCM (*)()) atan, g_i_atan);
+SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan);
/* "Return the arc tangent of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_cxr, (SCM (*)()) sinh, g_i_sinh);
+SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh);
/* "Return the hyperbolic sine of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_cxr, (SCM (*)()) cosh, g_i_cosh);
+SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh);
/* "Return the hyperbolic cosine of the real number @var{x}."
*/
-SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_cxr, (SCM (*)()) tanh, g_i_tanh);
+SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh);
/* "Return the hyperbolic tangent of the real number @var{x}."
*/
static void
scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy)
{
- if (SCM_INUMP (x)) {
+ if (SCM_INUMP (x))
xy->x = SCM_INUM (x);
- } else if (SCM_BIGP (x)) {
+ else if (SCM_BIGP (x))
xy->x = scm_i_big2dbl (x);
- } else if (SCM_REALP (x)) {
+ else if (SCM_REALP (x))
xy->x = SCM_REAL_VALUE (x);
- } else {
+ else if (SCM_FRACTIONP (x))
+ xy->x = scm_i_fraction2double (x);
+ else
scm_wrong_type_arg (sstring, SCM_ARG1, x);
- }
- if (SCM_INUMP (y)) {
+ if (SCM_INUMP (y))
xy->y = SCM_INUM (y);
- } else if (SCM_BIGP (y)) {
+ else if (SCM_BIGP (y))
xy->y = scm_i_big2dbl (y);
- } else if (SCM_REALP (y)) {
+ else if (SCM_REALP (y))
xy->y = SCM_REAL_VALUE (y);
- } else {
+ else if (SCM_FRACTIONP (y))
+ xy->y = scm_i_fraction2double (y);
+ else
scm_wrong_type_arg (sstring, SCM_ARG2, y);
- }
}
#define FUNC_NAME s_scm_make_polar
{
struct dpair xy;
+ double s, c;
scm_two_doubles (x, y, FUNC_NAME, &xy);
- return scm_make_complex (xy.x * cos (xy.y), xy.x * sin (xy.y));
+#if HAVE_SINCOS
+ sincos (xy.y, &s, &c);
+#else
+ s = sin (xy.y);
+ c = cos (xy.y);
+#endif
+ return scm_make_complex (xy.x * c, xy.x * s);
}
#undef FUNC_NAME
SCM
scm_real_part (SCM z)
{
- if (SCM_INUMP (z)) {
+ if (SCM_INUMP (z))
return z;
- } else if (SCM_BIGP (z)) {
+ else if (SCM_BIGP (z))
return z;
- } else if (SCM_REALP (z)) {
+ else if (SCM_REALP (z))
return z;
- } else if (SCM_COMPLEXP (z)) {
+ else if (SCM_COMPLEXP (z))
return scm_make_real (SCM_COMPLEX_REAL (z));
- } else {
+ else if (SCM_FRACTIONP (z))
+ return z;
+ else
SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part);
- }
}
SCM
scm_imag_part (SCM z)
{
- if (SCM_INUMP (z)) {
+ if (SCM_INUMP (z))
return SCM_INUM0;
- } else if (SCM_BIGP (z)) {
+ else if (SCM_BIGP (z))
return SCM_INUM0;
- } else if (SCM_REALP (z)) {
+ else if (SCM_REALP (z))
return scm_flo0;
- } else if (SCM_COMPLEXP (z)) {
+ else if (SCM_COMPLEXP (z))
return scm_make_real (SCM_COMPLEX_IMAG (z));
- } else {
+ else if (SCM_FRACTIONP (z))
+ return SCM_INUM0;
+ else
SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part);
- }
}
+SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator);
+/* "Return the numerator of the number @var{z}."
+ */
+SCM
+scm_numerator (SCM z)
+{
+ if (SCM_INUMP (z))
+ return z;
+ else if (SCM_BIGP (z))
+ return z;
+ else if (SCM_FRACTIONP (z))
+ {
+ scm_i_fraction_reduce (z);
+ return SCM_FRACTION_NUMERATOR (z);
+ }
+ else if (SCM_REALP (z))
+ return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z)));
+ else
+ SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator);
+}
+
+
+SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator);
+/* "Return the denominator of the number @var{z}."
+ */
+SCM
+scm_denominator (SCM z)
+{
+ if (SCM_INUMP (z))
+ return SCM_MAKINUM (1);
+ else if (SCM_BIGP (z))
+ return SCM_MAKINUM (1);
+ else if (SCM_FRACTIONP (z))
+ {
+ scm_i_fraction_reduce (z);
+ return SCM_FRACTION_DENOMINATOR (z);
+ }
+ else if (SCM_REALP (z))
+ return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z)));
+ else
+ SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator);
+}
SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude);
/* "Return the magnitude of the number @var{z}. This is the same as\n"
SCM
scm_magnitude (SCM z)
{
- if (SCM_INUMP (z)) {
- long int zz = SCM_INUM (z);
- if (zz >= 0) {
- return z;
- } else if (SCM_POSFIXABLE (-zz)) {
- return SCM_MAKINUM (-zz);
- } else {
- return scm_i_long2big (-zz);
- }
- } else if (SCM_BIGP (z)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (z));
- scm_remember_upto_here_1 (z);
- if (sgn < 0) {
- return scm_i_clonebig (z, 0);
- } else {
- return z;
+ if (SCM_INUMP (z))
+ {
+ long int zz = SCM_INUM (z);
+ if (zz >= 0)
+ return z;
+ else if (SCM_POSFIXABLE (-zz))
+ return SCM_MAKINUM (-zz);
+ else
+ return scm_i_long2big (-zz);
+ }
+ else if (SCM_BIGP (z))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (z));
+ scm_remember_upto_here_1 (z);
+ if (sgn < 0)
+ return scm_i_clonebig (z, 0);
+ else
+ return z;
}
- } else if (SCM_REALP (z)) {
+ else if (SCM_REALP (z))
return scm_make_real (fabs (SCM_REAL_VALUE (z)));
- } else if (SCM_COMPLEXP (z)) {
- double r = SCM_COMPLEX_REAL (z);
- double i = SCM_COMPLEX_IMAG (z);
- return scm_make_real (sqrt (i * i + r * r));
- } else {
+ else if (SCM_COMPLEXP (z))
+ return scm_make_real (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z)));
+ else if (SCM_FRACTIONP (z))
+ {
+ if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (z))))
+ return z;
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED),
+ SCM_FRACTION_DENOMINATOR (z));
+ }
+ else
SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude);
- }
}
SCM
scm_angle (SCM z)
{
- if (SCM_INUMP (z)) {
- if (SCM_INUM (z) >= 0) {
- return scm_make_real (atan2 (0.0, 1.0));
- } else {
- return scm_make_real (atan2 (0.0, -1.0));
- }
- } else if (SCM_BIGP (z)) {
- int sgn = mpz_sgn (SCM_I_BIG_MPZ (z));
- scm_remember_upto_here_1 (z);
- if (sgn < 0) {
- return scm_make_real (atan2 (0.0, -1.0));
- } else {
- return scm_make_real (atan2 (0.0, 1.0));
- }
- } else if (SCM_REALP (z)) {
- return scm_make_real (atan2 (0.0, SCM_REAL_VALUE (z)));
- } else if (SCM_COMPLEXP (z)) {
+ /* atan(0,-1) is pi and it'd be possible to have that as a constant like
+ scm_flo0 to save allocating a new flonum with scm_make_real each time.
+ But if atan2 follows the floating point rounding mode, then the value
+ is not a constant. Maybe it'd be close enough though. */
+ if (SCM_INUMP (z))
+ {
+ if (SCM_INUM (z) >= 0)
+ return scm_flo0;
+ else
+ return scm_make_real (atan2 (0.0, -1.0));
+ }
+ else if (SCM_BIGP (z))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (z));
+ scm_remember_upto_here_1 (z);
+ if (sgn < 0)
+ return scm_make_real (atan2 (0.0, -1.0));
+ else
+ return scm_flo0;
+ }
+ else if (SCM_REALP (z))
+ {
+ if (SCM_REAL_VALUE (z) >= 0)
+ return scm_flo0;
+ else
+ return scm_make_real (atan2 (0.0, -1.0));
+ }
+ else if (SCM_COMPLEXP (z))
return scm_make_real (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z)));
- } else {
+ else if (SCM_FRACTIONP (z))
+ {
+ if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (z))))
+ return scm_flo0;
+ else return scm_make_real (atan2 (0.0, -1.0));
+ }
+ else
SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle);
- }
}
return scm_make_real ((double) SCM_INUM (z));
else if (SCM_BIGP (z))
return scm_make_real (scm_i_big2dbl (z));
+ else if (SCM_FRACTIONP (z))
+ return scm_make_real (scm_i_fraction2double (z));
else if (SCM_INEXACTP (z))
return z;
else
"Return an exact number that is numerically closest to @var{z}.")
#define FUNC_NAME s_scm_inexact_to_exact
{
- if (SCM_INUMP (z)) {
+ if (SCM_INUMP (z))
return z;
- } else if (SCM_BIGP (z)) {
+ else if (SCM_BIGP (z))
return z;
- } else if (SCM_REALP (z)) {
- double u = floor (SCM_REAL_VALUE (z) + 0.5);
- long lu = (long) u;
- if (SCM_FIXABLE (lu)) {
- return SCM_MAKINUM (lu);
- } else if (isfinite (u) && !xisnan (u)) {
- return scm_i_dbl2big (u);
- } else {
- scm_num_overflow (s_scm_inexact_to_exact);
+ else if (SCM_REALP (z))
+ {
+ if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z)))
+ SCM_OUT_OF_RANGE (1, z);
+ else
+ {
+ mpq_t frac;
+ SCM q;
+
+ mpq_init (frac);
+ mpq_set_d (frac, SCM_REAL_VALUE (z));
+ q = scm_make_ratio (scm_i_mpz2num (mpq_numref (frac)),
+ scm_i_mpz2num (mpq_denref (frac)));
+
+ /* When scm_make_ratio throws, we leak the memory allocated
+ for frac...
+ */
+ mpq_clear (frac);
+ return q;
+ }
}
- } else {
+ else if (SCM_FRACTIONP (z))
+ return z;
+ else
SCM_WRONG_TYPE_ARG (1, z);
- }
+}
+#undef FUNC_NAME
+
+SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0,
+ (SCM x, SCM err),
+ "Return an exact number that is within @var{err} of @var{x}.")
+#define FUNC_NAME s_scm_rationalize
+{
+ if (SCM_INUMP (x))
+ return x;
+ else if (SCM_BIGP (x))
+ return x;
+ else if ((SCM_REALP (x)) || SCM_FRACTIONP (x))
+ {
+ /* Use continued fractions to find closest ratio. All
+ arithmetic is done with exact numbers.
+ */
+
+ SCM ex = scm_inexact_to_exact (x);
+ SCM int_part = scm_floor (ex);
+ SCM tt = SCM_MAKINUM (1);
+ SCM a1 = SCM_MAKINUM (0), a2 = SCM_MAKINUM (1), a = SCM_MAKINUM (0);
+ SCM b1 = SCM_MAKINUM (1), b2 = SCM_MAKINUM (0), b = SCM_MAKINUM (0);
+ SCM rx;
+ int i = 0;
+
+ if (!SCM_FALSEP (scm_num_eq_p (ex, int_part)))
+ return ex;
+
+ ex = scm_difference (ex, int_part); /* x = x-int_part */
+ rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */
+
+ /* We stop after a million iterations just to be absolutely sure
+ that we don't go into an infinite loop. The process normally
+ converges after less than a dozen iterations.
+ */
+
+ err = scm_abs (err);
+ while (++i < 1000000)
+ {
+ a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */
+ b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */
+ if (SCM_FALSEP (scm_zero_p (b)) && /* b != 0 */
+ SCM_FALSEP
+ (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))),
+ err))) /* abs(x-a/b) <= err */
+ {
+ SCM res = scm_sum (int_part, scm_divide (a, b));
+ if (SCM_FALSEP (scm_exact_p (x))
+ || SCM_FALSEP (scm_exact_p (err)))
+ return scm_exact_to_inexact (res);
+ else
+ return res;
+ }
+ rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */
+ SCM_UNDEFINED);
+ tt = scm_floor (rx); /* tt = floor (rx) */
+ a2 = a1;
+ b2 = b1;
+ a1 = a;
+ b1 = b;
+ }
+ scm_num_overflow (s_scm_rationalize);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (1, x);
}
#undef FUNC_NAME
#define PTRDIFF_MAX (~ PTRDIFF_MIN)
#endif
-#define CHECK(type, v) \
- do { \
- if ((v) != scm_num2##type (scm_##type##2num (v), 1, "check_sanity")) \
- abort (); \
- } while (0);
+#define CHECK(type, v) \
+ do \
+ { \
+ if ((v) != scm_num2##type (scm_##type##2num (v), 1, "check_sanity")) \
+ abort (); \
+ } \
+ while (0)
static void
check_sanity ()
void
scm_init_numbers ()
{
- abs_most_negative_fixnum = scm_i_long2big (- SCM_MOST_NEGATIVE_FIXNUM);
- scm_permanent_object (abs_most_negative_fixnum);
+ mpz_init_set_si (z_negative_one, -1);
/* It may be possible to tune the performance of some algorithms by using
* the following constants to avoid the creation of bignums. Please, before
{ /* determine floating point precision */
double f = 0.1;
double fsum = 1.0 + f;
- while (fsum != 1.0) {
- if (++scm_dblprec > 20) {
- fsum = 1.0;
- } else {
- f /= 10.0;
- fsum = f + 1.0;
+ while (fsum != 1.0)
+ {
+ if (++scm_dblprec > 20)
+ fsum = 1.0;
+ else
+ {
+ f /= 10.0;
+ fsum = f + 1.0;
+ }
}
- }
scm_dblprec = scm_dblprec - 1;
}
#endif /* DBL_DIG */
#ifdef GUILE_DEBUG
check_sanity ();
#endif
-
+
+ exactly_one_half = scm_permanent_object (scm_divide (SCM_MAKINUM (1),
+ SCM_MAKINUM (2)));
#include "libguile/numbers.x"
}
HCoop / bpt / guile.git / blobdiff