--- /dev/null
+/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
+ *
+ * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories
+ * and Bellcore. See scm_divide.
+ *
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+ */
+
+\f
+/* General assumptions:
+ * All objects satisfying SCM_COMPLEXP() have a non-zero complex component.
+ * 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:
+
+ - see if special casing bignums and reals in integer-exponent when
+ possible (to use mpz_pow and mpf_pow_ui) is faster.
+
+ - look in to better short-circuiting of common cases in
+ integer-expt and elsewhere.
+
+ - see if direct mpz operations can help in ash and elsewhere.
+
+ */
+
+#ifdef HAVE_CONFIG_H
+# include <config.h>
+#endif
+
+#include <math.h>
+#include <ctype.h>
+#include <string.h>
+
+#if HAVE_COMPLEX_H
+#include <complex.h>
+#endif
+
+#include "libguile/_scm.h"
+#include "libguile/feature.h"
+#include "libguile/ports.h"
+#include "libguile/root.h"
+#include "libguile/smob.h"
+#include "libguile/strings.h"
+
+#include "libguile/validate.h"
+#include "libguile/numbers.h"
+#include "libguile/deprecation.h"
+
+#include "libguile/eq.h"
+
+#include "libguile/discouraged.h"
+
+/* values per glibc, if not already defined */
+#ifndef M_LOG10E
+#define M_LOG10E 0.43429448190325182765
+#endif
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+\f
+
+/*
+ Wonder if this might be faster for some of our code? A switch on
+ the numtag would jump directly to the right case, and the
+ SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests...
+
+ #define SCM_I_NUMTAG_NOTNUM 0
+ #define SCM_I_NUMTAG_INUM 1
+ #define SCM_I_NUMTAG_BIG scm_tc16_big
+ #define SCM_I_NUMTAG_REAL scm_tc16_real
+ #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex
+ #define SCM_I_NUMTAG(x) \
+ (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \
+ : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \
+ : (((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)
+
+/* FLOBUFLEN is the maximum number of characters neccessary for the
+ * printed or scm_string representation of an inexact number.
+ */
+#define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10)
+
+#if defined (SCO)
+#if ! defined (HAVE_ISNAN)
+#define HAVE_ISNAN
+static int
+isnan (double x)
+{
+ return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0;
+}
+#endif
+#if ! defined (HAVE_ISINF)
+#define HAVE_ISINF
+static int
+isinf (double x)
+{
+ return (IsNANorINF (x) && IsINF (x)) ? 1 : 0;
+}
+
+#endif
+#endif
+
+
+/* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses
+ an explicit check. In some future gmp (don't know what version number),
+ mpz_cmp_d is supposed to do this itself. */
+#if 1
+#define xmpz_cmp_d(z, d) \
+ (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d))
+#else
+#define xmpz_cmp_d(z, d) mpz_cmp_d (z, d)
+#endif
+
+/* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have
+ isinf. It does have finite and isnan though, hence the use of those.
+ fpclass would be a possibility on that system too. */
+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
+}
+
+#if defined (GUILE_I)
+#if HAVE_COMPLEX_DOUBLE
+
+/* For an SCM object Z which is a complex number (ie. satisfies
+ SCM_COMPLEXP), return its value as a C level "complex double". */
+#define SCM_COMPLEX_VALUE(z) \
+ (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z))
+
+static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED;
+
+/* Convert a C "complex double" to an SCM value. */
+static inline SCM
+scm_from_complex_double (complex double z)
+{
+ return scm_c_make_rectangular (creal (z), cimag (z));
+}
+
+#endif /* HAVE_COMPLEX_DOUBLE */
+#endif /* GUILE_I */
+
+\f
+
+static mpz_t z_negative_one;
+
+\f
+
+SCM
+scm_i_mkbig ()
+{
+ /* Return a newly created bignum. */
+ SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0);
+ mpz_init (SCM_I_BIG_MPZ (z));
+ return z;
+}
+
+SCM
+scm_i_long2big (long x)
+{
+ /* Return a newly created bignum initialized to X. */
+ SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0);
+ mpz_init_set_si (SCM_I_BIG_MPZ (z), x);
+ return z;
+}
+
+SCM
+scm_i_ulong2big (unsigned long x)
+{
+ /* Return a newly created bignum initialized to X. */
+ SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0);
+ mpz_init_set_ui (SCM_I_BIG_MPZ (z), x);
+ return z;
+}
+
+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));
+ return z;
+}
+
+int
+scm_i_bigcmp (SCM x, SCM y)
+{
+ /* Return neg if x < y, pos if x > y, and 0 if x == y */
+ /* presume we already know x and y are bignums */
+ int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return result;
+}
+
+SCM
+scm_i_dbl2big (double d)
+{
+ /* results are only defined if d is an integer */
+ SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0);
+ mpz_init_set_d (SCM_I_BIG_MPZ (z), d);
+ return z;
+}
+
+/* Convert a integer in double representation to a SCM number. */
+
+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_I_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. truncate towards zero), then adjust to get the closest double by
+ examining the next lower bit and adding 1 (to the absolute value) if
+ necessary.
+
+ 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 must be done on the absolute value of the mpz_t, which means
+ we need to use mpz_getlimbn. mpz_tstbit is not right, it treats
+ negatives as twos complement.
+
+ In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up
+ following the hardware rounding mode, but applied to the absolute value
+ of the mpz_t operand. This is not what we want so we put the high
+ DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when,
+ mpz_get_d is supposed to always truncate towards zero.
+
+ ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3
+ is a slowdown. It'd be faster to pick out the relevant high bits with
+ mpz_getlimbn if we could be bothered coding that, and if the new
+ truncating gmp doesn't come out. */
+
+double
+scm_i_big2dbl (SCM b)
+{
+ double result;
+ size_t bits;
+
+ bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2);
+
+#if 1
+ {
+ /* Current GMP, eg. 4.1.3, force truncation 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
+ /* Future GMP */
+ 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
+scm_i_normbig (SCM b)
+{
+ /* convert a big back to a fixnum if it'll fit */
+ /* presume b is a bignum */
+ if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b)))
+ {
+ long val = mpz_get_si (SCM_I_BIG_MPZ (b));
+ if (SCM_FIXABLE (val))
+ b = SCM_I_MAKINUM (val);
+ }
+ 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_I_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);
+
+static SCM
+scm_i_make_ratio (SCM numerator, SCM denominator)
+#define FUNC_NAME "make-ratio"
+{
+ /* First make sure the arguments are proper.
+ */
+ if (SCM_I_INUMP (denominator))
+ {
+ if (scm_is_eq (denominator, SCM_INUM0))
+ scm_num_overflow ("make-ratio");
+ if (scm_is_eq (denominator, SCM_I_MAKINUM(1)))
+ return numerator;
+ }
+ else
+ {
+ if (!(SCM_BIGP(denominator)))
+ SCM_WRONG_TYPE_ARG (2, denominator);
+ }
+ if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator))
+ SCM_WRONG_TYPE_ARG (1, numerator);
+
+ /* Then flip signs so that the denominator is positive.
+ */
+ if (scm_is_true (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_I_INUMP (numerator))
+ {
+ long x = SCM_I_INUM (numerator);
+ if (scm_is_eq (numerator, SCM_INUM0))
+ return SCM_INUM0;
+ if (SCM_I_INUMP (denominator))
+ {
+ long y;
+ y = SCM_I_INUM (denominator);
+ if (x == y)
+ return SCM_I_MAKINUM(1);
+ if ((x % y) == 0)
+ return SCM_I_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_I_MAKINUM(-1);
+ }
+ }
+ else if (SCM_BIGP (numerator))
+ {
+ if (SCM_I_INUMP (denominator))
+ {
+ long yy = SCM_I_INUM (denominator);
+ if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy))
+ return scm_divide (numerator, denominator);
+ }
+ else
+ {
+ if (scm_is_eq (numerator, denominator))
+ return SCM_I_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.
+ */
+ {
+ SCM divisor = scm_gcd (numerator, denominator);
+ if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1))))
+ {
+ numerator = scm_divide (numerator, divisor);
+ denominator = scm_divide (denominator, divisor);
+ }
+
+ return scm_double_cell (scm_tc16_fraction,
+ SCM_UNPACK (numerator),
+ SCM_UNPACK (denominator), 0);
+ }
+}
+#undef FUNC_NAME
+
+double
+scm_i_fraction2double (SCM z)
+{
+ return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z),
+ SCM_FRACTION_DENOMINATOR (z)));
+}
+
+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_I_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
+
+
+SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0,
+ (SCM n),
+ "Return @code{#t} if @var{n} is an odd number, @code{#f}\n"
+ "otherwise.")
+#define FUNC_NAME s_scm_odd_p
+{
+ if (SCM_I_INUMP (n))
+ {
+ long val = SCM_I_INUM (n);
+ return scm_from_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_from_bool (odd_p);
+ }
+ else if (scm_is_true (scm_inf_p (n)))
+ return SCM_BOOL_T;
+ 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
+
+
+SCM_DEFINE (scm_even_p, "even?", 1, 0, 0,
+ (SCM n),
+ "Return @code{#t} if @var{n} is an even number, @code{#f}\n"
+ "otherwise.")
+#define FUNC_NAME s_scm_even_p
+{
+ if (SCM_I_INUMP (n))
+ {
+ long val = SCM_I_INUM (n);
+ return scm_from_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_from_bool (even_p);
+ }
+ else if (scm_is_true (scm_inf_p (n)))
+ return SCM_BOOL_T;
+ 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
+
+SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0,
+ (SCM x),
+ "Return @code{#t} if @var{x} is either @samp{+inf.0}\n"
+ "or @samp{-inf.0}, @code{#f} otherwise.")
+#define FUNC_NAME s_scm_inf_p
+{
+ if (SCM_REALP (x))
+ return scm_from_bool (xisinf (SCM_REAL_VALUE (x)));
+ else if (SCM_COMPLEXP (x))
+ return scm_from_bool (xisinf (SCM_COMPLEX_REAL (x))
+ || xisinf (SCM_COMPLEX_IMAG (x)));
+ else
+ return SCM_BOOL_F;
+}
+#undef FUNC_NAME
+
+SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0,
+ (SCM n),
+ "Return @code{#t} if @var{n} is a NaN, @code{#f}\n"
+ "otherwise.")
+#define FUNC_NAME s_scm_nan_p
+{
+ if (SCM_REALP (n))
+ return scm_from_bool (xisnan (SCM_REAL_VALUE (n)));
+ else if (SCM_COMPLEXP (n))
+ return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n))
+ || xisnan (SCM_COMPLEX_IMAG (n)));
+ else
+ return SCM_BOOL_F;
+}
+#undef FUNC_NAME
+
+/* Guile's idea of infinity. */
+static double guile_Inf;
+
+/* Guile's idea of not a number. */
+static double guile_NaN;
+
+static void
+guile_ieee_init (void)
+{
+#if defined (HAVE_ISINF) || defined (HAVE_FINITE)
+
+/* Some version of gcc on some old version of Linux used to crash when
+ trying to make Inf and NaN. */
+
+#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];
+ union
+ {
+ double d;
+ int i[2];
+ } alias;
+ alias.i[0] = DINFINITY[0];
+ alias.i[1] = DINFINITY[1];
+ guile_Inf = alias.d;
+#else
+ double tmp = 1e+10;
+ guile_Inf = tmp;
+ for (;;)
+ {
+ guile_Inf *= 1e+10;
+ if (guile_Inf == tmp)
+ break;
+ tmp = guile_Inf;
+ }
+#endif
+
+#endif
+
+#if defined (HAVE_ISNAN)
+
+#if defined __GNUC__ && defined __alpha__ && !defined _IEEE_FP
+ /* On Alpha GCC must be passed `-mieee' to provide proper NaN handling.
+ See http://lists.gnu.org/archive/html/bug-gnulib/2009-05/msg00010.html
+ for more details. */
+# error NaN handling will not work when compiling without -mieee
+#endif
+
+#ifdef NAN
+ /* C99 NAN, when available */
+ guile_NaN = NAN;
+#elif HAVE_DQNAN
+ {
+ /* OSF */
+ extern unsigned int DQNAN[2];
+ union
+ {
+ double d;
+ int i[2];
+ } alias;
+ alias.i[0] = DQNAN[0];
+ alias.i[1] = DQNAN[1];
+ guile_NaN = alias.d;
+ }
+#else
+ guile_NaN = guile_Inf / guile_Inf;
+#endif
+
+#endif
+}
+
+SCM_DEFINE (scm_inf, "inf", 0, 0, 0,
+ (void),
+ "Return Inf.")
+#define FUNC_NAME s_scm_inf
+{
+ static int initialized = 0;
+ if (! initialized)
+ {
+ guile_ieee_init ();
+ initialized = 1;
+ }
+ return scm_from_double (guile_Inf);
+}
+#undef FUNC_NAME
+
+SCM_DEFINE (scm_nan, "nan", 0, 0, 0,
+ (void),
+ "Return NaN.")
+#define FUNC_NAME s_scm_nan
+{
+ static int initialized = 0;
+ if (!initialized)
+ {
+ guile_ieee_init ();
+ initialized = 1;
+ }
+ return scm_from_double (guile_NaN);
+}
+#undef FUNC_NAME
+
+
+SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0,
+ (SCM x),
+ "Return the absolute value of @var{x}.")
+#define FUNC_NAME
+{
+ if (SCM_I_INUMP (x))
+ {
+ long int xx = SCM_I_INUM (x);
+ if (xx >= 0)
+ return x;
+ else if (SCM_POSFIXABLE (-xx))
+ return SCM_I_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_from_double (-xx);
+ else
+ return x;
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x))))
+ return x;
+ return scm_i_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_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient);
+/* "Return the quotient of the numbers @var{x} and @var{y}."
+ */
+SCM
+scm_quotient (SCM x, SCM y)
+{
+ if (SCM_I_INUMP (x))
+ {
+ long xx = SCM_I_INUM (x);
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_quotient);
+ else
+ {
+ long z = xx / yy;
+ if (SCM_FIXABLE (z))
+ return SCM_I_MAKINUM (z);
+ else
+ return scm_i_long2big (z);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ if ((SCM_I_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_I_MAKINUM (-1);
+ }
+ else
+ return SCM_I_MAKINUM (0);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient);
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_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);
+/* "Return the remainder of the numbers @var{x} and @var{y}.\n"
+ * "@lisp\n"
+ * "(remainder 13 4) @result{} 1\n"
+ * "(remainder -13 4) @result{} -1\n"
+ * "@end lisp"
+ */
+SCM
+scm_remainder (SCM x, SCM y)
+{
+ if (SCM_I_INUMP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_remainder);
+ else
+ {
+ long z = SCM_I_INUM (x) % yy;
+ return SCM_I_MAKINUM (z);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ if ((SCM_I_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_I_MAKINUM (0);
+ }
+ else
+ return x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder);
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_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_I_INUMP (x))
+ {
+ long xx = SCM_I_INUM (x);
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_INUM (y);
+ if (yy == 0)
+ scm_num_overflow (s_modulo);
+ else
+ {
+ /* C99 specifies that "%" is the remainder corresponding to a
+ quotient rounded towards zero, and that's also traditional
+ for machine division, so z here should be well defined. */
+ 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_I_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_I_INUMP (y))
+ {
+ long yy = SCM_I_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);
+ }
+ 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);
+/* "Return the greatest common divisor of all arguments.\n"
+ * "If called without arguments, 0 is returned."
+ */
+SCM
+scm_gcd (SCM x, SCM y)
+{
+ if (SCM_UNBNDP (y))
+ return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x);
+
+ if (SCM_I_INUMP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ long xx = SCM_I_INUM (x);
+ long yy = SCM_I_INUM (y);
+ 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_I_MAKINUM (result)
+ : scm_i_long2big (result));
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM_SWAP (x, y);
+ goto big_inum;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd);
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ unsigned long result;
+ long yy;
+ big_inum:
+ yy = SCM_I_INUM (y);
+ if (yy == 0)
+ return scm_abs (x);
+ 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_I_MAKINUM (result)
+ : scm_from_ulong (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);
+ return scm_i_normbig (result);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd);
+}
+
+SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm);
+/* "Return the least common multiple of the arguments.\n"
+ * "If called without arguments, 1 is returned."
+ */
+SCM
+scm_lcm (SCM n1, SCM n2)
+{
+ if (SCM_UNBNDP (n2))
+ {
+ if (SCM_UNBNDP (n1))
+ return SCM_I_MAKINUM (1L);
+ n2 = SCM_I_MAKINUM (1L);
+ }
+
+ SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1),
+ g_lcm, n1, n2, SCM_ARG1, s_lcm);
+ SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2),
+ g_lcm, n1, n2, SCM_ARGn, s_lcm);
+
+ if (SCM_I_INUMP (n1))
+ {
+ if (SCM_I_INUMP (n2))
+ {
+ SCM d = scm_gcd (n1, n2);
+ if (scm_is_eq (d, SCM_INUM0))
+ return d;
+ else
+ return scm_abs (scm_product (n1, scm_quotient (n2, d)));
+ }
+ else
+ {
+ /* inum n1, big n2 */
+ inumbig:
+ {
+ SCM result = scm_i_mkbig ();
+ long nn1 = SCM_I_INUM (n1);
+ if (nn1 == 0) return SCM_INUM0;
+ if (nn1 < 0) nn1 = - nn1;
+ mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1);
+ scm_remember_upto_here_1 (n2);
+ return result;
+ }
+ }
+ }
+ else
+ {
+ /* big n1 */
+ if (SCM_I_INUMP (n2))
+ {
+ SCM_SWAP (n1, n2);
+ goto inumbig;
+ }
+ else
+ {
+ SCM result = scm_i_mkbig ();
+ mpz_lcm(SCM_I_BIG_MPZ (result),
+ SCM_I_BIG_MPZ (n1),
+ SCM_I_BIG_MPZ (n2));
+ scm_remember_upto_here_2(n1, n2);
+ /* shouldn't need to normalize b/c lcm of 2 bigs should be big */
+ return result;
+ }
+ }
+}
+
+/* Emulating 2's complement bignums with sign magnitude arithmetic:
+
+ Logand:
+ X Y Result Method:
+ (len)
+ + + + x (map digit:logand X Y)
+ + - + x (map digit:logand X (lognot (+ -1 Y)))
+ - + + y (map digit:logand (lognot (+ -1 X)) Y)
+ - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y)))
+
+ Logior:
+ X Y Result Method:
+
+ + + + (map digit:logior X Y)
+ + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y)))
+ - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y)))
+ - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y)))
+
+ Logxor:
+ X Y Result Method:
+
+ + + + (map digit:logxor X Y)
+ + - - (+ 1 (map digit:logxor X (+ -1 Y)))
+ - + - (+ 1 (map digit:logxor (+ -1 X) Y))
+ - - + (map digit:logxor (+ -1 X) (+ -1 Y))
+
+ Logtest:
+ X Y Result
+
+ + + (any digit:logand X Y)
+ + - (any digit:logand X (lognot (+ -1 Y)))
+ - + (any digit:logand (lognot (+ -1 X)) Y)
+ - - #t
+
+*/
+
+SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr,
+ (SCM n1, SCM n2),
+ "Return the bitwise AND of the integer arguments.\n\n"
+ "@lisp\n"
+ "(logand) @result{} -1\n"
+ "(logand 7) @result{} 7\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_I_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_I_INUMP (n1))
+ {
+ nn1 = SCM_I_INUM (n1);
+ if (SCM_I_INUMP (n2))
+ {
+ long nn2 = SCM_I_INUM (n2);
+ return SCM_I_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_I_INUMP (n2))
+ {
+ SCM_SWAP (n1, n2);
+ nn1 = SCM_I_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
+
+
+SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr,
+ (SCM n1, SCM n2),
+ "Return the bitwise OR of the integer arguments.\n\n"
+ "@lisp\n"
+ "(logior) @result{} 0\n"
+ "(logior 7) @result{} 7\n"
+ "(logior #b000 #b001 #b011) @result{} 3\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_logior
+{
+ 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_I_INUMP (n1))
+ {
+ nn1 = SCM_I_INUM (n1);
+ if (SCM_I_INUMP (n2))
+ {
+ long nn2 = SCM_I_INUM (n2);
+ return SCM_I_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 scm_i_normbig (result_z);
+ }
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ }
+ else if (SCM_BIGP (n1))
+ {
+ if (SCM_I_INUMP (n2))
+ {
+ SCM_SWAP (n1, n2);
+ nn1 = SCM_I_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 scm_i_normbig (result_z);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n1);
+}
+#undef FUNC_NAME
+
+
+SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr,
+ (SCM n1, SCM n2),
+ "Return the bitwise XOR of the integer arguments. A bit is\n"
+ "set in the result if it is set in an odd number of arguments.\n"
+ "@lisp\n"
+ "(logxor) @result{} 0\n"
+ "(logxor 7) @result{} 7\n"
+ "(logxor #b000 #b001 #b011) @result{} 2\n"
+ "(logxor #b000 #b001 #b011 #b011) @result{} 1\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_logxor
+{
+ 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_I_INUMP (n1))
+ {
+ nn1 = SCM_I_INUM (n1);
+ if (SCM_I_INUMP (n2))
+ {
+ long nn2 = SCM_I_INUM (n2);
+ return SCM_I_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_I_INUMP (n2))
+ {
+ SCM_SWAP (n1, n2);
+ nn1 = SCM_I_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
+
+
+SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0,
+ (SCM j, SCM k),
+ "Test whether @var{j} and @var{k} have any 1 bits in common.\n"
+ "This is equivalent to @code{(not (zero? (logand j k)))}, but\n"
+ "without actually calculating the @code{logand}, just testing\n"
+ "for non-zero.\n"
+ "\n"
+ "@lisp\n"
+ "(logtest #b0100 #b1011) @result{} #f\n"
+ "(logtest #b0100 #b0111) @result{} #t\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_logtest
+{
+ long int nj;
+
+ if (SCM_I_INUMP (j))
+ {
+ nj = SCM_I_INUM (j);
+ if (SCM_I_INUMP (k))
+ {
+ long nk = SCM_I_INUM (k);
+ return scm_from_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_from_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_I_INUMP (k))
+ {
+ SCM_SWAP (j, k);
+ nj = SCM_I_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_from_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_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0,
+ (SCM index, SCM j),
+ "Test whether bit number @var{index} in @var{j} is set.\n"
+ "@var{index} starts from 0 for the least significant bit.\n"
+ "\n"
+ "@lisp\n"
+ "(logbit? 0 #b1101) @result{} #t\n"
+ "(logbit? 1 #b1101) @result{} #f\n"
+ "(logbit? 2 #b1101) @result{} #t\n"
+ "(logbit? 3 #b1101) @result{} #t\n"
+ "(logbit? 4 #b1101) @result{} #f\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_logbit_p
+{
+ unsigned long int iindex;
+ iindex = scm_to_ulong (index);
+
+ if (SCM_I_INUMP (j))
+ {
+ /* bits above what's in an inum follow the sign bit */
+ iindex = min (iindex, SCM_LONG_BIT - 1);
+ return scm_from_bool ((1L << iindex) & SCM_I_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_from_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 ones-complement of the integer\n"
+ "argument.\n"
+ "\n"
+ "@lisp\n"
+ "(number->string (lognot #b10000000) 2)\n"
+ " @result{} \"-10000001\"\n"
+ "(number->string (lognot #b0) 2)\n"
+ " @result{} \"-1\"\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_lognot
+{
+ if (SCM_I_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_I_MAKINUM (~ SCM_I_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_I_INUMP (in))
+ mpz_set_si (out, SCM_I_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_is_eq (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
+
+SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0,
+ (SCM n, SCM k),
+ "Return @var{n} raised to the power @var{k}. @var{k} must be an\n"
+ "exact integer, @var{n} can be any number.\n"
+ "\n"
+ "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n"
+ "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n"
+ "includes @math{0^0} is 1.\n"
+ "\n"
+ "@lisp\n"
+ "(integer-expt 2 5) @result{} 32\n"
+ "(integer-expt -3 3) @result{} -27\n"
+ "(integer-expt 5 -3) @result{} 1/125\n"
+ "(integer-expt 0 0) @result{} 1\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_integer_expt
+{
+ long i2 = 0;
+ SCM z_i2 = SCM_BOOL_F;
+ int i2_is_big = 0;
+ SCM acc = SCM_I_MAKINUM (1L);
+
+ /* 0^0 == 1 according to R5RS */
+ if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc))
+ return scm_is_false (scm_zero_p(k)) ? n : acc;
+ else if (scm_is_eq (n, SCM_I_MAKINUM (-1L)))
+ return scm_is_false (scm_even_p (k)) ? n : acc;
+
+ if (SCM_I_INUMP (k))
+ i2 = SCM_I_INUM (k);
+ else if (SCM_BIGP (k))
+ {
+ z_i2 = scm_i_clonebig (k, 1);
+ scm_remember_upto_here_1 (k);
+ i2_is_big = 1;
+ }
+ else
+ SCM_WRONG_TYPE_ARG (2, k);
+
+ if (i2_is_big)
+ {
+ if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1)
+ {
+ mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2));
+ n = scm_divide (n, SCM_UNDEFINED);
+ }
+ while (1)
+ {
+ if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0)
+ {
+ return acc;
+ }
+ if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0)
+ {
+ return scm_product (acc, n);
+ }
+ if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0))
+ acc = scm_product (acc, n);
+ n = scm_product (n, n);
+ mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1);
+ }
+ }
+ else
+ {
+ if (i2 < 0)
+ {
+ i2 = -i2;
+ n = scm_divide (n, SCM_UNDEFINED);
+ }
+ while (1)
+ {
+ if (0 == i2)
+ return acc;
+ if (1 == i2)
+ return scm_product (acc, n);
+ if (i2 & 1)
+ acc = scm_product (acc, n);
+ n = scm_product (n, n);
+ i2 >>= 1;
+ }
+ }
+}
+#undef FUNC_NAME
+
+SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
+ (SCM n, SCM cnt),
+ "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"
+ "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
+{
+ long bits_to_shift;
+ bits_to_shift = scm_to_long (cnt);
+
+ if (SCM_I_INUMP (n))
+ {
+ long nn = SCM_I_INUM (n);
+
+ if (bits_to_shift > 0)
+ {
+ /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always
+ overflow a non-zero fixnum. For smaller shifts we check the
+ bits going into positions above SCM_I_FIXNUM_BIT-1. If they're
+ all 0s for nn>=0, or all 1s for nn<0 then there's no overflow.
+ Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 -
+ bits_to_shift)". */
+
+ if (nn == 0)
+ return n;
+
+ if (bits_to_shift < SCM_I_FIXNUM_BIT-1
+ && ((unsigned long)
+ (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1)
+ <= 1))
+ {
+ return SCM_I_MAKINUM (nn << bits_to_shift);
+ }
+ else
+ {
+ SCM result = scm_i_long2big (nn);
+ mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result),
+ bits_to_shift);
+ return result;
+ }
+ }
+ else
+ {
+ bits_to_shift = -bits_to_shift;
+ if (bits_to_shift >= SCM_LONG_BIT)
+ return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1));
+ else
+ return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift));
+ }
+
+ }
+ else if (SCM_BIGP (n))
+ {
+ SCM result;
+
+ if (bits_to_shift == 0)
+ return n;
+
+ result = scm_i_mkbig ();
+ if (bits_to_shift >= 0)
+ {
+ mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n),
+ bits_to_shift);
+ return result;
+ }
+ else
+ {
+ /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so
+ we have to allocate a bignum even if the result is going to be a
+ fixnum. */
+ mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n),
+ -bits_to_shift);
+ return scm_i_normbig (result);
+ }
+
+ }
+ else
+ {
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
+ }
+}
+#undef FUNC_NAME
+
+
+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"
+ "through @var{end} (exclusive) bits of @var{n}. The\n"
+ "@var{start}th bit becomes the 0-th bit in the result.\n"
+ "\n"
+ "@lisp\n"
+ "(number->string (bit-extract #b1101101010 0 4) 2)\n"
+ " @result{} \"1010\"\n"
+ "(number->string (bit-extract #b1101101010 4 9) 2)\n"
+ " @result{} \"10110\"\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_bit_extract
+{
+ unsigned long int istart, iend, bits;
+ istart = scm_to_ulong (start);
+ iend = scm_to_ulong (end);
+ SCM_ASSERT_RANGE (3, end, (iend >= istart));
+
+ /* how many bits to keep */
+ bits = iend - istart;
+
+ if (SCM_I_INUMP (n))
+ {
+ long int in = SCM_I_INUM (n);
+
+ /* 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". */
+ in = SCM_SRS (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_I_MAKINUM (in & ((1L << bits) - 1));
+ }
+ else if (SCM_BIGP (n))
+ {
+ SCM result;
+ if (bits == 1)
+ {
+ result = SCM_I_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
+ 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
+};
+
+SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0,
+ (SCM n),
+ "Return the number of bits in integer @var{n}. If integer is\n"
+ "positive, the 1-bits in its binary representation are counted.\n"
+ "If negative, the 0-bits in its two's-complement binary\n"
+ "representation are counted. If 0, 0 is returned.\n"
+ "\n"
+ "@lisp\n"
+ "(logcount #b10101010)\n"
+ " @result{} 4\n"
+ "(logcount 0)\n"
+ " @result{} 0\n"
+ "(logcount -2)\n"
+ " @result{} 1\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_logcount
+{
+ if (SCM_I_INUMP (n))
+ {
+ unsigned long int c = 0;
+ long int nn = SCM_I_INUM (n);
+ if (nn < 0)
+ nn = -1 - nn;
+ while (nn)
+ {
+ c += scm_logtab[15 & nn];
+ nn >>= 4;
+ }
+ return SCM_I_MAKINUM (c);
+ }
+ else if (SCM_BIGP (n))
+ {
+ unsigned long count;
+ if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0)
+ count = mpz_popcount (SCM_I_BIG_MPZ (n));
+ else
+ count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one);
+ scm_remember_upto_here_1 (n);
+ return SCM_I_MAKINUM (count);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
+}
+#undef FUNC_NAME
+
+
+static const char scm_ilentab[] = {
+ 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4
+};
+
+
+SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0,
+ (SCM n),
+ "Return the number of bits necessary to represent @var{n}.\n"
+ "\n"
+ "@lisp\n"
+ "(integer-length #b10101010)\n"
+ " @result{} 8\n"
+ "(integer-length 0)\n"
+ " @result{} 0\n"
+ "(integer-length #b1111)\n"
+ " @result{} 4\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_integer_length
+{
+ if (SCM_I_INUMP (n))
+ {
+ unsigned long int c = 0;
+ unsigned int l = 4;
+ long int nn = SCM_I_INUM (n);
+ if (nn < 0)
+ nn = -1 - nn;
+ while (nn)
+ {
+ c += 4;
+ l = scm_ilentab [15 & nn];
+ nn >>= 4;
+ }
+ return SCM_I_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_I_MAKINUM (size);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
+}
+#undef FUNC_NAME
+
+/*** NUMBERS -> STRINGS ***/
+#define SCM_MAX_DBL_PREC 60
+#define SCM_MAX_DBL_RADIX 36
+
+/* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */
+static int scm_dblprec[SCM_MAX_DBL_RADIX - 1];
+static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC];
+
+static
+void init_dblprec(int *prec, int radix) {
+ /* determine floating point precision by adding successively
+ smaller increments to 1.0 until it is considered == 1.0 */
+ double f = ((double)1.0)/radix;
+ double fsum = 1.0 + f;
+
+ *prec = 0;
+ while (fsum != 1.0)
+ {
+ if (++(*prec) > SCM_MAX_DBL_PREC)
+ fsum = 1.0;
+ else
+ {
+ f /= radix;
+ fsum = f + 1.0;
+ }
+ }
+ (*prec) -= 1;
+}
+
+static
+void init_fx_radix(double *fx_list, int radix)
+{
+ /* initialize a per-radix list of tolerances. When added
+ to a number < 1.0, we can determine if we should raund
+ up and quit converting a number to a string. */
+ int i;
+ fx_list[0] = 0.0;
+ fx_list[1] = 0.5;
+ for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i )
+ fx_list[i] = (fx_list[i-1] / radix);
+}
+
+/* use this array as a way to generate a single digit */
+static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
+
+static size_t
+idbl2str (double f, char *a, int radix)
+{
+ int efmt, dpt, d, i, wp;
+ double *fx;
+#ifdef DBL_MIN_10_EXP
+ double f_cpy;
+ int exp_cpy;
+#endif /* DBL_MIN_10_EXP */
+ size_t ch = 0;
+ int exp = 0;
+
+ if(radix < 2 ||
+ radix > SCM_MAX_DBL_RADIX)
+ {
+ /* revert to existing behavior */
+ radix = 10;
+ }
+
+ wp = scm_dblprec[radix-2];
+ fx = fx_per_radix[radix-2];
+
+ if (f == 0.0)
+ {
+#ifdef HAVE_COPYSIGN
+ double sgn = copysign (1.0, f);
+
+ if (sgn < 0.0)
+ a[ch++] = '-';
+#endif
+ goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */
+ }
+
+ if (xisinf (f))
+ {
+ if (f < 0)
+ strcpy (a, "-inf.0");
+ else
+ strcpy (a, "+inf.0");
+ return ch+6;
+ }
+ else if (xisnan (f))
+ {
+ strcpy (a, "+nan.0");
+ return ch+6;
+ }
+
+ if (f < 0.0)
+ {
+ f = -f;
+ a[ch++] = '-';
+ }
+
+#ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from
+ make-uniform-vector, from causing infinite loops. */
+ /* just do the checking...if it passes, we do the conversion for our
+ radix again below */
+ f_cpy = f;
+ exp_cpy = exp;
+
+ while (f_cpy < 1.0)
+ {
+ f_cpy *= 10.0;
+ if (exp_cpy-- < DBL_MIN_10_EXP)
+ {
+ a[ch++] = '#';
+ a[ch++] = '.';
+ a[ch++] = '#';
+ return ch;
+ }
+ }
+ while (f_cpy > 10.0)
+ {
+ f_cpy *= 0.10;
+ if (exp_cpy++ > DBL_MAX_10_EXP)
+ {
+ a[ch++] = '#';
+ a[ch++] = '.';
+ a[ch++] = '#';
+ return ch;
+ }
+ }
+#endif
+
+ while (f < 1.0)
+ {
+ f *= radix;
+ exp--;
+ }
+ while (f > radix)
+ {
+ f /= radix;
+ exp++;
+ }
+
+ if (f + fx[wp] >= radix)
+ {
+ f = 1.0;
+ exp++;
+ }
+ zero:
+#ifdef ENGNOT
+ /* adding 9999 makes this equivalent to abs(x) % 3 */
+ dpt = (exp + 9999) % 3;
+ exp -= dpt++;
+ efmt = 1;
+#else
+ efmt = (exp < -3) || (exp > wp + 2);
+ if (!efmt)
+ {
+ if (exp < 0)
+ {
+ a[ch++] = '0';
+ a[ch++] = '.';
+ dpt = exp;
+ while (++dpt)
+ a[ch++] = '0';
+ }
+ else
+ dpt = exp + 1;
+ }
+ else
+ dpt = 1;
+#endif
+
+ do
+ {
+ d = f;
+ f -= d;
+ a[ch++] = number_chars[d];
+ if (f < fx[wp])
+ break;
+ if (f + fx[wp] >= 1.0)
+ {
+ a[ch - 1] = number_chars[d+1];
+ break;
+ }
+ f *= radix;
+ if (!(--dpt))
+ a[ch++] = '.';
+ }
+ while (wp--);
+
+ if (dpt > 0)
+ {
+#ifndef ENGNOT
+ if ((dpt > 4) && (exp > 6))
+ {
+ d = (a[0] == '-' ? 2 : 1);
+ for (i = ch++; i > d; i--)
+ a[i] = a[i - 1];
+ a[d] = '.';
+ efmt = 1;
+ }
+ else
+#endif
+ {
+ while (--dpt)
+ a[ch++] = '0';
+ a[ch++] = '.';
+ }
+ }
+ if (a[ch - 1] == '.')
+ a[ch++] = '0'; /* trailing zero */
+ if (efmt && exp)
+ {
+ a[ch++] = 'e';
+ if (exp < 0)
+ {
+ exp = -exp;
+ a[ch++] = '-';
+ }
+ for (i = radix; i <= exp; i *= radix);
+ for (i /= radix; i; i /= radix)
+ {
+ a[ch++] = number_chars[exp / i];
+ exp %= i;
+ }
+ }
+ return ch;
+}
+
+
+static size_t
+icmplx2str (double real, double imag, char *str, int radix)
+{
+ size_t i;
+
+ i = idbl2str (real, str, radix);
+ if (imag != 0.0)
+ {
+ /* Don't output a '+' for negative numbers or for Inf and
+ NaN. They will provide their own sign. */
+ if (0 <= imag && !xisinf (imag) && !xisnan (imag))
+ str[i++] = '+';
+ i += idbl2str (imag, &str[i], radix);
+ str[i++] = 'i';
+ }
+ return i;
+}
+
+static size_t
+iflo2str (SCM flt, char *str, int radix)
+{
+ size_t i;
+ if (SCM_REALP (flt))
+ i = idbl2str (SCM_REAL_VALUE (flt), str, radix);
+ else
+ i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt),
+ str, radix);
+ return i;
+}
+
+/* convert a scm_t_intmax to a string (unterminated). returns the number of
+ characters in the result.
+ rad is output base
+ p is destination: worst case (base 2) is SCM_INTBUFLEN */
+size_t
+scm_iint2str (scm_t_intmax num, int rad, char *p)
+{
+ if (num < 0)
+ {
+ *p++ = '-';
+ return scm_iuint2str (-num, rad, p) + 1;
+ }
+ else
+ return scm_iuint2str (num, rad, p);
+}
+
+/* convert a scm_t_intmax to a string (unterminated). returns the number of
+ characters in the result.
+ rad is output base
+ p is destination: worst case (base 2) is SCM_INTBUFLEN */
+size_t
+scm_iuint2str (scm_t_uintmax num, int rad, char *p)
+{
+ size_t j = 1;
+ size_t i;
+ scm_t_uintmax n = num;
+
+ for (n /= rad; n > 0; n /= rad)
+ j++;
+
+ i = j;
+ n = num;
+ while (i--)
+ {
+ int d = n % rad;
+
+ n /= rad;
+ p[i] = d + ((d < 10) ? '0' : 'a' - 10);
+ }
+ 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"
+ "number @var{n} in the given @var{radix}. If @var{n} is\n"
+ "inexact, a radix of 10 will be used.")
+#define FUNC_NAME s_scm_number_to_string
+{
+ int base;
+
+ if (SCM_UNBNDP (radix))
+ base = 10;
+ else
+ base = scm_to_signed_integer (radix, 2, 36);
+
+ if (SCM_I_INUMP (n))
+ {
+ char num_buf [SCM_INTBUFLEN];
+ size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf);
+ return scm_from_locale_stringn (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_take_locale_string (str);
+ }
+ else if (SCM_FRACTIONP (n))
+ {
+ return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix),
+ scm_from_locale_string ("/"),
+ scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix)));
+ }
+ else if (SCM_INEXACTP (n))
+ {
+ char num_buf [FLOBUFLEN];
+ return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base));
+ }
+ else
+ SCM_WRONG_TYPE_ARG (1, n);
+}
+#undef FUNC_NAME
+
+
+/* These print routines used to be stubbed here so that scm_repl.c
+ wouldn't need SCM_BIGDIG conditionals (pre GMP) */
+
+int
+scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
+{
+ char num_buf[FLOBUFLEN];
+ scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port);
+ return !0;
+}
+
+void
+scm_i_print_double (double val, SCM port)
+{
+ char num_buf[FLOBUFLEN];
+ scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port);
+}
+
+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, 10), port);
+ return !0;
+}
+
+void
+scm_i_print_complex (double real, double imag, SCM port)
+{
+ char num_buf[FLOBUFLEN];
+ scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port);
+}
+
+int
+scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
+{
+ SCM str;
+ str = scm_number_to_string (sexp, SCM_UNDEFINED);
+ scm_lfwrite (scm_i_string_chars (str), scm_i_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)
+{
+ char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp));
+ scm_remember_upto_here_1 (exp);
+ scm_lfwrite (str, (size_t) strlen (str), port);
+ free (str);
+ return !0;
+}
+/*** END nums->strs ***/
+
+
+/*** STRINGS -> NUMBERS ***/
+
+/* The following functions implement the conversion from strings to numbers.
+ * The implementation somehow follows the grammar for numbers as it is given
+ * in R5RS. Thus, the functions resemble syntactic units (<ureal R>,
+ * <uinteger R>, ...) that are used to build up numbers in the grammar. Some
+ * points should be noted about the implementation:
+ * * Each function keeps a local index variable 'idx' that points at the
+ * current position within the parsed string. The global index is only
+ * updated if the function could parse the corresponding syntactic unit
+ * successfully.
+ * * Similarly, the functions keep track of indicators of inexactness ('#',
+ * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the
+ * global exactness information is only updated after each part has been
+ * successfully parsed.
+ * * Sequences of digits are parsed into temporary variables holding fixnums.
+ * Only if these fixnums would overflow, the result variables are updated
+ * using the standard functions scm_add, scm_product, scm_divide etc. Then,
+ * the temporary variables holding the fixnums are cleared, and the process
+ * starts over again. If for example fixnums were able to store five decimal
+ * digits, a number 1234567890 would be parsed in two parts 12345 and 67890,
+ * and the result was computed as 12345 * 100000 + 67890. In other words,
+ * only every five digits two bignum operations were performed.
+ */
+
+enum t_exactness {NO_EXACTNESS, INEXACT, EXACT};
+
+/* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */
+
+/* In non ASCII-style encodings the following macro might not work. */
+#define XDIGIT2UINT(d) \
+ (isdigit ((int) (unsigned char) d) \
+ ? (d) - '0' \
+ : tolower ((int) (unsigned char) d) - 'a' + 10)
+
+static SCM
+mem2uinteger (const char* mem, size_t len, unsigned int *p_idx,
+ unsigned int radix, enum t_exactness *p_exactness)
+{
+ unsigned int idx = *p_idx;
+ unsigned int hash_seen = 0;
+ scm_t_bits shift = 1;
+ scm_t_bits add = 0;
+ unsigned int digit_value;
+ SCM result;
+ char c;
+
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ c = mem[idx];
+ if (!isxdigit ((int) (unsigned char) c))
+ return SCM_BOOL_F;
+ digit_value = XDIGIT2UINT (c);
+ if (digit_value >= radix)
+ return SCM_BOOL_F;
+
+ idx++;
+ result = SCM_I_MAKINUM (digit_value);
+ while (idx != len)
+ {
+ char c = mem[idx];
+ if (isxdigit ((int) (unsigned char) c))
+ {
+ if (hash_seen)
+ break;
+ digit_value = XDIGIT2UINT (c);
+ if (digit_value >= radix)
+ break;
+ }
+ else if (c == '#')
+ {
+ hash_seen = 1;
+ digit_value = 0;
+ }
+ else
+ break;
+
+ idx++;
+ if (SCM_MOST_POSITIVE_FIXNUM / radix < shift)
+ {
+ result = scm_product (result, SCM_I_MAKINUM (shift));
+ if (add > 0)
+ result = scm_sum (result, SCM_I_MAKINUM (add));
+
+ shift = radix;
+ add = digit_value;
+ }
+ else
+ {
+ shift = shift * radix;
+ add = add * radix + digit_value;
+ }
+ };
+
+ if (shift > 1)
+ result = scm_product (result, SCM_I_MAKINUM (shift));
+ if (add > 0)
+ result = scm_sum (result, SCM_I_MAKINUM (add));
+
+ *p_idx = idx;
+ if (hash_seen)
+ *p_exactness = INEXACT;
+
+ return result;
+}
+
+
+/* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only
+ * covers the parts of the rules that start at a potential point. The value
+ * of the digits up to the point have been parsed by the caller and are given
+ * in variable result. The content of *p_exactness indicates, whether a hash
+ * has already been seen in the digits before the point.
+ */
+
+/* In non ASCII-style encodings the following macro might not work. */
+#define DIGIT2UINT(d) ((d) - '0')
+
+static SCM
+mem2decimal_from_point (SCM result, const char* mem, size_t len,
+ unsigned int *p_idx, enum t_exactness *p_exactness)
+{
+ unsigned int idx = *p_idx;
+ enum t_exactness x = *p_exactness;
+
+ if (idx == len)
+ return result;
+
+ if (mem[idx] == '.')
+ {
+ scm_t_bits shift = 1;
+ scm_t_bits add = 0;
+ unsigned int digit_value;
+ SCM big_shift = SCM_I_MAKINUM (1);
+
+ idx++;
+ while (idx != len)
+ {
+ char c = mem[idx];
+ if (isdigit ((int) (unsigned char) c))
+ {
+ if (x == INEXACT)
+ return SCM_BOOL_F;
+ else
+ digit_value = DIGIT2UINT (c);
+ }
+ else if (c == '#')
+ {
+ x = INEXACT;
+ digit_value = 0;
+ }
+ else
+ break;
+
+ idx++;
+ if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift)
+ {
+ big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift));
+ result = scm_product (result, SCM_I_MAKINUM (shift));
+ if (add > 0)
+ result = scm_sum (result, SCM_I_MAKINUM (add));
+
+ shift = 10;
+ add = digit_value;
+ }
+ else
+ {
+ shift = shift * 10;
+ add = add * 10 + digit_value;
+ }
+ };
+
+ if (add > 0)
+ {
+ big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift));
+ result = scm_product (result, SCM_I_MAKINUM (shift));
+ result = scm_sum (result, SCM_I_MAKINUM (add));
+ }
+
+ result = scm_divide (result, big_shift);
+
+ /* We've seen a decimal point, thus the value is implicitly inexact. */
+ x = INEXACT;
+ }
+
+ if (idx != len)
+ {
+ int sign = 1;
+ unsigned int start;
+ char c;
+ int exponent;
+ SCM e;
+
+ /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */
+
+ switch (mem[idx])
+ {
+ case 'd': case 'D':
+ case 'e': case 'E':
+ case 'f': case 'F':
+ case 'l': case 'L':
+ case 's': case 'S':
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ start = idx;
+ c = mem[idx];
+ if (c == '-')
+ {
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ sign = -1;
+ c = mem[idx];
+ }
+ else if (c == '+')
+ {
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ sign = 1;
+ c = mem[idx];
+ }
+ else
+ sign = 1;
+
+ if (!isdigit ((int) (unsigned char) c))
+ return SCM_BOOL_F;
+
+ idx++;
+ exponent = DIGIT2UINT (c);
+ while (idx != len)
+ {
+ char c = mem[idx];
+ if (isdigit ((int) (unsigned char) c))
+ {
+ idx++;
+ if (exponent <= SCM_MAXEXP)
+ exponent = exponent * 10 + DIGIT2UINT (c);
+ }
+ else
+ break;
+ }
+
+ if (exponent > SCM_MAXEXP)
+ {
+ size_t exp_len = idx - start;
+ SCM exp_string = scm_from_locale_stringn (&mem[start], exp_len);
+ SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED);
+ scm_out_of_range ("string->number", exp_num);
+ }
+
+ e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent));
+ if (sign == 1)
+ result = scm_product (result, e);
+ else
+ result = scm_divide2real (result, e);
+
+ /* We've seen an exponent, thus the value is implicitly inexact. */
+ x = INEXACT;
+
+ break;
+
+ default:
+ break;
+ }
+ }
+
+ *p_idx = idx;
+ if (x == INEXACT)
+ *p_exactness = x;
+
+ return result;
+}
+
+
+/* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */
+
+static SCM
+mem2ureal (const char* mem, size_t len, unsigned int *p_idx,
+ unsigned int radix, enum t_exactness *p_exactness)
+{
+ unsigned int idx = *p_idx;
+ SCM result;
+
+ /* Start off believing that the number will be exact. This changes
+ to INEXACT if we see a decimal point or a hash. */
+ enum t_exactness x = EXACT;
+
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5))
+ {
+ *p_idx = idx+5;
+ return scm_inf ();
+ }
+
+ if (idx+4 < len && !strncmp (mem+idx, "nan.", 4))
+ {
+ /* 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;
+ return scm_nan ();
+ }
+
+ if (mem[idx] == '.')
+ {
+ if (radix != 10)
+ return SCM_BOOL_F;
+ else if (idx + 1 == len)
+ return SCM_BOOL_F;
+ else if (!isdigit ((int) (unsigned char) mem[idx + 1]))
+ return SCM_BOOL_F;
+ else
+ result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len,
+ p_idx, &x);
+ }
+ else
+ {
+ SCM uinteger;
+
+ uinteger = mem2uinteger (mem, len, &idx, radix, &x);
+ if (scm_is_false (uinteger))
+ return SCM_BOOL_F;
+
+ if (idx == len)
+ result = uinteger;
+ else if (mem[idx] == '/')
+ {
+ SCM divisor;
+
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ divisor = mem2uinteger (mem, len, &idx, radix, &x);
+ if (scm_is_false (divisor))
+ return SCM_BOOL_F;
+
+ /* both are int/big here, I assume */
+ result = scm_i_make_ratio (uinteger, divisor);
+ }
+ else if (radix == 10)
+ {
+ result = mem2decimal_from_point (uinteger, mem, len, &idx, &x);
+ if (scm_is_false (result))
+ return SCM_BOOL_F;
+ }
+ else
+ result = uinteger;
+
+ *p_idx = idx;
+ }
+
+ /* Update *p_exactness if the number just read was inexact. This is
+ important for complex numbers, so that a complex number is
+ treated as inexact overall if either its real or imaginary part
+ is inexact.
+ */
+ if (x == INEXACT)
+ *p_exactness = x;
+
+ /* When returning an inexact zero, make sure it is represented as a
+ floating point value so that we can change its sign.
+ */
+ if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT)
+ result = scm_from_double (0.0);
+
+ return result;
+}
+
+
+/* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */
+
+static SCM
+mem2complex (const char* mem, size_t len, unsigned int idx,
+ unsigned int radix, enum t_exactness *p_exactness)
+{
+ char c;
+ int sign = 0;
+ SCM ureal;
+
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ c = mem[idx];
+ if (c == '+')
+ {
+ idx++;
+ sign = 1;
+ }
+ else if (c == '-')
+ {
+ idx++;
+ sign = -1;
+ }
+
+ if (idx == len)
+ return SCM_BOOL_F;
+
+ ureal = mem2ureal (mem, len, &idx, radix, p_exactness);
+ if (scm_is_false (ureal))
+ {
+ /* input must be either +i or -i */
+
+ if (sign == 0)
+ return SCM_BOOL_F;
+
+ if (mem[idx] == 'i' || mem[idx] == 'I')
+ {
+ idx++;
+ if (idx != len)
+ return SCM_BOOL_F;
+
+ return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign));
+ }
+ else
+ return SCM_BOOL_F;
+ }
+ else
+ {
+ if (sign == -1 && scm_is_false (scm_nan_p (ureal)))
+ ureal = scm_difference (ureal, SCM_UNDEFINED);
+
+ if (idx == len)
+ return ureal;
+
+ c = mem[idx];
+ switch (c)
+ {
+ case 'i': case 'I':
+ /* either +<ureal>i or -<ureal>i */
+
+ idx++;
+ if (sign == 0)
+ return SCM_BOOL_F;
+ if (idx != len)
+ return SCM_BOOL_F;
+ return scm_make_rectangular (SCM_I_MAKINUM (0), ureal);
+
+ case '@':
+ /* polar input: <real>@<real>. */
+
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+ else
+ {
+ int sign;
+ SCM angle;
+ SCM result;
+
+ c = mem[idx];
+ if (c == '+')
+ {
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+ sign = 1;
+ }
+ else if (c == '-')
+ {
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+ sign = -1;
+ }
+ else
+ sign = 1;
+
+ angle = mem2ureal (mem, len, &idx, radix, p_exactness);
+ if (scm_is_false (angle))
+ return SCM_BOOL_F;
+ if (idx != len)
+ return SCM_BOOL_F;
+
+ if (sign == -1 && scm_is_false (scm_nan_p (ureal)))
+ angle = scm_difference (angle, SCM_UNDEFINED);
+
+ result = scm_make_polar (ureal, angle);
+ return result;
+ }
+ case '+':
+ case '-':
+ /* expecting input matching <real>[+-]<ureal>?i */
+
+ idx++;
+ if (idx == len)
+ return SCM_BOOL_F;
+ else
+ {
+ int sign = (c == '+') ? 1 : -1;
+ SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness);
+
+ if (scm_is_false (imag))
+ imag = SCM_I_MAKINUM (sign);
+ else if (sign == -1 && scm_is_false (scm_nan_p (ureal)))
+ imag = scm_difference (imag, SCM_UNDEFINED);
+
+ if (idx == len)
+ return SCM_BOOL_F;
+ if (mem[idx] != 'i' && mem[idx] != 'I')
+ return SCM_BOOL_F;
+
+ idx++;
+ if (idx != len)
+ return SCM_BOOL_F;
+
+ return scm_make_rectangular (ureal, imag);
+ }
+ default:
+ return SCM_BOOL_F;
+ }
+ }
+}
+
+
+/* R5RS, section 7.1.1, lexical structure of numbers: <number> */
+
+enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16};
+
+SCM
+scm_c_locale_stringn_to_number (const char* mem, size_t len,
+ unsigned int default_radix)
+{
+ unsigned int idx = 0;
+ unsigned int radix = NO_RADIX;
+ enum t_exactness forced_x = NO_EXACTNESS;
+ enum t_exactness implicit_x = EXACT;
+ SCM result;
+
+ /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */
+ while (idx + 2 < len && mem[idx] == '#')
+ {
+ switch (mem[idx + 1])
+ {
+ case 'b': case 'B':
+ if (radix != NO_RADIX)
+ return SCM_BOOL_F;
+ radix = DUAL;
+ break;
+ case 'd': case 'D':
+ if (radix != NO_RADIX)
+ return SCM_BOOL_F;
+ radix = DEC;
+ break;
+ case 'i': case 'I':
+ if (forced_x != NO_EXACTNESS)
+ return SCM_BOOL_F;
+ forced_x = INEXACT;
+ break;
+ case 'e': case 'E':
+ if (forced_x != NO_EXACTNESS)
+ return SCM_BOOL_F;
+ forced_x = EXACT;
+ break;
+ case 'o': case 'O':
+ if (radix != NO_RADIX)
+ return SCM_BOOL_F;
+ radix = OCT;
+ break;
+ case 'x': case 'X':
+ if (radix != NO_RADIX)
+ return SCM_BOOL_F;
+ radix = HEX;
+ break;
+ default:
+ return SCM_BOOL_F;
+ }
+ idx += 2;
+ }
+
+ /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */
+ if (radix == NO_RADIX)
+ result = mem2complex (mem, len, idx, default_radix, &implicit_x);
+ else
+ result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x);
+
+ if (scm_is_false (result))
+ return SCM_BOOL_F;
+
+ switch (forced_x)
+ {
+ case EXACT:
+ if (SCM_INEXACTP (result))
+ return scm_inexact_to_exact (result);
+ else
+ return result;
+ case INEXACT:
+ if (SCM_INEXACTP (result))
+ return result;
+ else
+ return scm_exact_to_inexact (result);
+ case NO_EXACTNESS:
+ default:
+ if (implicit_x == INEXACT)
+ {
+ if (SCM_INEXACTP (result))
+ return result;
+ else
+ return scm_exact_to_inexact (result);
+ }
+ else
+ return result;
+ }
+}
+
+
+SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0,
+ (SCM string, SCM radix),
+ "Return a number of the maximally precise representation\n"
+ "expressed by the given @var{string}. @var{radix} must be an\n"
+ "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n"
+ "is a default radix that may be overridden by an explicit radix\n"
+ "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n"
+ "supplied, then the default radix is 10. If string is not a\n"
+ "syntactically valid notation for a number, then\n"
+ "@code{string->number} returns @code{#f}.")
+#define FUNC_NAME s_scm_string_to_number
+{
+ SCM answer;
+ unsigned int base;
+ SCM_VALIDATE_STRING (1, string);
+
+ if (SCM_UNBNDP (radix))
+ base = 10;
+ else
+ base = scm_to_unsigned_integer (radix, 2, INT_MAX);
+
+ answer = scm_c_locale_stringn_to_number (scm_i_string_chars (string),
+ scm_i_string_length (string),
+ base);
+ scm_remember_upto_here_1 (string);
+ return answer;
+}
+#undef FUNC_NAME
+
+
+/*** END strs->nums ***/
+
+
+SCM
+scm_bigequal (SCM x, SCM y)
+{
+ int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return scm_from_bool (0 == result);
+}
+
+SCM
+scm_real_equalp (SCM x, SCM y)
+{
+ return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y));
+}
+
+SCM
+scm_complex_equalp (SCM x, SCM y)
+{
+ return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)
+ && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y));
+}
+
+SCM
+scm_i_fraction_equalp (SCM x, SCM y)
+{
+ if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_NUMERATOR (y)))
+ || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_DENOMINATOR (y))))
+ return SCM_BOOL_F;
+ else
+ return SCM_BOOL_T;
+}
+
+
+SCM_DEFINE (scm_number_p, "number?", 1, 0, 0,
+ (SCM x),
+ "Return @code{#t} if @var{x} is a number, @code{#f}\n"
+ "otherwise.")
+#define FUNC_NAME s_scm_number_p
+{
+ return scm_from_bool (SCM_NUMBERP (x));
+}
+#undef FUNC_NAME
+
+SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0,
+ (SCM x),
+ "Return @code{#t} if @var{x} is a complex number, @code{#f}\n"
+ "otherwise. Note that the sets of real, rational and integer\n"
+ "values form subsets of the set of complex numbers, i. e. the\n"
+ "predicate will also be fulfilled if @var{x} is a real,\n"
+ "rational or integer number.")
+#define FUNC_NAME s_scm_complex_p
+{
+ /* all numbers are complex. */
+ return scm_number_p (x);
+}
+#undef FUNC_NAME
+
+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.")
+#define FUNC_NAME s_scm_rational_p
+{
+ if (SCM_I_INUMP (x))
+ return SCM_BOOL_T;
+ else if (SCM_IMP (x))
+ return SCM_BOOL_F;
+ else if (SCM_BIGP (x))
+ return SCM_BOOL_T;
+ else if (SCM_FRACTIONP (x))
+ return SCM_BOOL_T;
+ 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
+
+SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0,
+ (SCM x),
+ "Return @code{#t} if @var{x} is an integer number, @code{#f}\n"
+ "else.")
+#define FUNC_NAME s_scm_integer_p
+{
+ double r;
+ if (SCM_I_INUMP (x))
+ return SCM_BOOL_T;
+ if (SCM_IMP (x))
+ return SCM_BOOL_F;
+ if (SCM_BIGP (x))
+ return SCM_BOOL_T;
+ if (!SCM_INEXACTP (x))
+ return SCM_BOOL_F;
+ if (SCM_COMPLEXP (x))
+ return SCM_BOOL_F;
+ r = SCM_REAL_VALUE (x);
+ /* +/-inf passes r==floor(r), making those #t */
+ if (r == floor (r))
+ return SCM_BOOL_T;
+ return SCM_BOOL_F;
+}
+#undef FUNC_NAME
+
+
+SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0,
+ (SCM x),
+ "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n"
+ "else.")
+#define FUNC_NAME s_scm_inexact_p
+{
+ 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_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p);
+/* "Return @code{#t} if all parameters are numerically equal." */
+SCM
+scm_num_eq_p (SCM x, SCM y)
+{
+ again:
+ if (SCM_I_INUMP (x))
+ {
+ long xx = SCM_I_INUM (x);
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_INUM (y);
+ return scm_from_bool (xx == yy);
+ }
+ else if (SCM_BIGP (y))
+ return SCM_BOOL_F;
+ else if (SCM_REALP (y))
+ {
+ /* On a 32-bit system an inum fits a double, we can cast the inum
+ to a double and compare.
+
+ But on a 64-bit system an inum is bigger than a double and
+ casting it to a double (call that dxx) will round. dxx is at
+ worst 1 bigger or smaller than xx, so if dxx==yy we know yy is
+ an integer and fits a long. So we cast yy to a long and
+ compare with plain xx.
+
+ An alternative (for any size system actually) would be to check
+ yy is an integer (with floor) and is in range of an inum
+ (compare against appropriate powers of 2) then test
+ xx==(long)yy. It's just a matter of which casts/comparisons
+ might be fastest or easiest for the cpu. */
+
+ double yy = SCM_REAL_VALUE (y);
+ return scm_from_bool ((double) xx == yy
+ && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1
+ || xx == (long) yy));
+ }
+ else if (SCM_COMPLEXP (y))
+ return scm_from_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 if (SCM_BIGP (x))
+ {
+ if (SCM_I_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_from_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_from_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_from_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))
+ {
+ double xx = SCM_REAL_VALUE (x);
+ if (SCM_I_INUMP (y))
+ {
+ /* see comments with inum/real above */
+ long yy = SCM_I_INUM (y);
+ return scm_from_bool (xx == (double) yy
+ && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1
+ || (long) xx == yy));
+ }
+ 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_from_bool (0 == cmp);
+ }
+ else if (SCM_REALP (y))
+ return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_from_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_from_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_I_INUMP (y))
+ return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_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_from_bool (0 == cmp);
+ }
+ else if (SCM_REALP (y))
+ return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y))
+ && (SCM_COMPLEX_IMAG (x) == 0.0));
+ else if (SCM_COMPLEXP (y))
+ return scm_from_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_from_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_I_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_from_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_from_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)
+{
+ again:
+ if (SCM_I_INUMP (x))
+ {
+ long xx = SCM_I_INUM (x);
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_INUM (y);
+ return scm_from_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_from_bool (sgn > 0);
+ }
+ else if (SCM_REALP (y))
+ return scm_from_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_I_INUMP (y))
+ {
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return scm_from_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_from_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_from_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 if (SCM_REALP (x))
+ {
+ if (SCM_I_INUMP (y))
+ return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_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_from_bool (cmp > 0);
+ }
+ else if (SCM_REALP (y))
+ return scm_from_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_from_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_I_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_from_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_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p);
+/* "Return @code{#t} if the list of parameters is monotonically\n"
+ * "decreasing."
+ */
+#define FUNC_NAME s_scm_gr_p
+SCM
+scm_gr_p (SCM x, SCM y)
+{
+ if (!SCM_NUMBERP (x))
+ SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME);
+ else if (!SCM_NUMBERP (y))
+ SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME);
+ else
+ return scm_less_p (y, x);
+}
+#undef FUNC_NAME
+
+
+SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p);
+/* "Return @code{#t} if the list of parameters is monotonically\n"
+ * "non-decreasing."
+ */
+#define FUNC_NAME s_scm_leq_p
+SCM
+scm_leq_p (SCM x, SCM y)
+{
+ if (!SCM_NUMBERP (x))
+ SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME);
+ else if (!SCM_NUMBERP (y))
+ SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME);
+ else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y)))
+ return SCM_BOOL_F;
+ else
+ return scm_not (scm_less_p (y, x));
+}
+#undef FUNC_NAME
+
+
+SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p);
+/* "Return @code{#t} if the list of parameters is monotonically\n"
+ * "non-increasing."
+ */
+#define FUNC_NAME s_scm_geq_p
+SCM
+scm_geq_p (SCM x, SCM y)
+{
+ if (!SCM_NUMBERP (x))
+ SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME);
+ else if (!SCM_NUMBERP (y))
+ SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME);
+ else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y)))
+ return SCM_BOOL_F;
+ else
+ return scm_not (scm_less_p (x, y));
+}
+#undef FUNC_NAME
+
+
+SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p);
+/* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n"
+ * "zero."
+ */
+SCM
+scm_zero_p (SCM z)
+{
+ if (SCM_I_INUMP (z))
+ return scm_from_bool (scm_is_eq (z, SCM_INUM0));
+ else if (SCM_BIGP (z))
+ return SCM_BOOL_F;
+ else if (SCM_REALP (z))
+ return scm_from_bool (SCM_REAL_VALUE (z) == 0.0);
+ else if (SCM_COMPLEXP (z))
+ return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0
+ && SCM_COMPLEX_IMAG (z) == 0.0);
+ else if (SCM_FRACTIONP (z))
+ return SCM_BOOL_F;
+ else
+ SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p);
+}
+
+
+SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p);
+/* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n"
+ * "zero."
+ */
+SCM
+scm_positive_p (SCM x)
+{
+ if (SCM_I_INUMP (x))
+ return scm_from_bool (SCM_I_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_from_bool (sgn > 0);
+ }
+ else if (SCM_REALP (x))
+ return scm_from_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_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p);
+/* "Return @code{#t} if @var{x} is an exact or inexact number less than\n"
+ * "zero."
+ */
+SCM
+scm_negative_p (SCM x)
+{
+ if (SCM_I_INUMP (x))
+ return scm_from_bool (SCM_I_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_from_bool (sgn < 0);
+ }
+ else if (SCM_REALP (x))
+ return scm_from_bool(SCM_REAL_VALUE (x) < 0.0);
+ 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_I_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_I_INUMP (x))
+ {
+ long xx = SCM_I_INUM (x);
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_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_from_double (z) : y;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ use_less:
+ return (scm_is_false (scm_less_p (x, y)) ? x : y);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_I_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_from_double (xx) : y);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ goto use_less;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else if (SCM_REALP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ double z = SCM_I_INUM (y);
+ /* if x==NaN then "<" is false and we return NaN */
+ return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM_SWAP (x, y);
+ 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_from_double (yy) : x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ goto use_less;
+ }
+ else if (SCM_BIGP (y))
+ {
+ goto use_less;
+ }
+ else if (SCM_REALP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ goto use_less;
+ }
+ 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_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min);
+/* "Return the minium of all parameter values."
+ */
+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_I_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_I_INUMP (x))
+ {
+ long xx = SCM_I_INUM (x);
+ if (SCM_I_INUMP (y))
+ {
+ long yy = SCM_I_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_from_double (z) : y;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ use_less:
+ return (scm_is_false (scm_less_p (x, y)) ? y : x);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (SCM_I_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_from_double (xx) : y);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ goto use_less;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
+ }
+ else if (SCM_REALP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ double z = SCM_I_INUM (y);
+ /* if x==NaN then "<" is false and we return NaN */
+ return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM_SWAP (x, y);
+ 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_from_double (yy) : x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ goto use_less;
+ }
+ else if (SCM_BIGP (y))
+ {
+ goto use_less;
+ }
+ else if (SCM_REALP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ goto use_less;
+ }
+ 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);
+}
+
+
+SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum);
+/* "Return the sum of all parameter values. Return 0 if called without\n"
+ * "any parameters."
+ */
+SCM
+scm_sum (SCM x, SCM y)
+{
+ if (SCM_UNLIKELY (SCM_UNBNDP (y)))
+ {
+ if (SCM_NUMBERP (x)) return x;
+ if (SCM_UNBNDP (x)) return SCM_INUM0;
+ SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum);
+ }
+
+ if (SCM_LIKELY (SCM_I_INUMP (x)))
+ {
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
+ {
+ long xx = SCM_I_INUM (x);
+ long yy = SCM_I_INUM (y);
+ long int z = xx + yy;
+ return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z);
+ }
+ else if (SCM_BIGP (y))
+ {
+ SCM_SWAP (x, y);
+ goto add_big_inum;
+ }
+ else if (SCM_REALP (y))
+ {
+ long int xx = SCM_I_INUM (x);
+ return scm_from_double (xx + SCM_REAL_VALUE (y));
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ long int xx = SCM_I_INUM (x);
+ return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y),
+ SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_i_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_I_INUMP (y))
+ {
+ long int inum;
+ int bigsgn;
+ add_big_inum:
+ inum = SCM_I_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_from_double (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_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_i_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_I_INUMP (y))
+ return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_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_from_double (result);
+ }
+ else if (SCM_REALP (y))
+ return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y),
+ SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
+ }
+ else if (SCM_COMPLEXP (x))
+ {
+ if (SCM_I_INUMP (y))
+ return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_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_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x));
+ }
+ else if (SCM_REALP (y))
+ return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y),
+ SCM_COMPLEX_IMAG (x));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y),
+ SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_c_make_rectangular (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_FRACTIONP (x))
+ {
+ if (SCM_I_INUMP (y))
+ return scm_i_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_i_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_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (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_i_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
+ SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum);
+}
+
+
+SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0,
+ (SCM x),
+ "Return @math{@var{x}+1}.")
+#define FUNC_NAME s_scm_oneplus
+{
+ return scm_sum (x, SCM_I_MAKINUM (1));
+}
+#undef FUNC_NAME
+
+
+SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference);
+/* If called with one argument @var{z1}, -@var{z1} returned. Otherwise
+ * the sum of all but the first argument are subtracted from the first
+ * argument. */
+#define FUNC_NAME s_difference
+SCM
+scm_difference (SCM x, SCM y)
+{
+ if (SCM_UNLIKELY (SCM_UNBNDP (y)))
+ {
+ if (SCM_UNBNDP (x))
+ SCM_WTA_DISPATCH_0 (g_difference, s_difference);
+ else
+ if (SCM_I_INUMP (x))
+ {
+ long xx = -SCM_I_INUM (x);
+ if (SCM_FIXABLE (xx))
+ return SCM_I_MAKINUM (xx);
+ else
+ return scm_i_long2big (xx);
+ }
+ else if (SCM_BIGP (x))
+ /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a
+ bignum, but negating that gives a fixnum. */
+ return scm_i_normbig (scm_i_clonebig (x, 0));
+ else if (SCM_REALP (x))
+ return scm_from_double (-SCM_REAL_VALUE (x));
+ else if (SCM_COMPLEXP (x))
+ return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x),
+ -SCM_COMPLEX_IMAG (x));
+ else if (SCM_FRACTIONP (x))
+ return scm_i_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_LIKELY (SCM_I_INUMP (x)))
+ {
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
+ {
+ long int xx = SCM_I_INUM (x);
+ long int yy = SCM_I_INUM (y);
+ long int z = xx - yy;
+ if (SCM_FIXABLE (z))
+ return SCM_I_MAKINUM (z);
+ else
+ return scm_i_long2big (z);
+ }
+ else if (SCM_BIGP (y))
+ {
+ /* inum-x - big-y */
+ long xx = SCM_I_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)
+ 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_I_INUM (x);
+ return scm_from_double (xx - SCM_REAL_VALUE (y));
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ long int xx = SCM_I_INUM (x);
+ return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y),
+ - SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a - b/c = (ac - b) / c */
+ return scm_i_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_I_INUMP (y))
+ {
+ /* big-x - inum-y */
+ long yy = SCM_I_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_I_MAKINUM (-yy) : scm_from_long (-yy));
+ else
+ {
+ SCM result = scm_i_mkbig ();
+
+ 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);
+ }
+ }
+ 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_from_double (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_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_i_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_REALP (x))
+ {
+ if (SCM_I_INUMP (y))
+ return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_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_from_double (result);
+ }
+ else if (SCM_REALP (y))
+ return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y),
+ -SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_from_double (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 (x))
+ {
+ if (SCM_I_INUMP (y))
+ return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_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_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_REALP (y))
+ return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y),
+ SCM_COMPLEX_IMAG (x));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y),
+ SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_c_make_rectangular (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 if (SCM_FRACTIONP (x))
+ {
+ if (SCM_I_INUMP (y))
+ /* a/b - c = (a - cb) / b */
+ return scm_i_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_i_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_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (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_i_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_DEFINE (scm_oneminus, "1-", 1, 0, 0,
+ (SCM x),
+ "Return @math{@var{x}-1}.")
+#define FUNC_NAME s_scm_oneminus
+{
+ return scm_difference (x, SCM_I_MAKINUM (1));
+}
+#undef FUNC_NAME
+
+
+SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product);
+/* "Return the product of all arguments. If called without arguments,\n"
+ * "1 is returned."
+ */
+SCM
+scm_product (SCM x, SCM y)
+{
+ if (SCM_UNLIKELY (SCM_UNBNDP (y)))
+ {
+ if (SCM_UNBNDP (x))
+ return SCM_I_MAKINUM (1L);
+ else if (SCM_NUMBERP (x))
+ return x;
+ else
+ SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product);
+ }
+
+ if (SCM_LIKELY (SCM_I_INUMP (x)))
+ {
+ long xx;
+
+ intbig:
+ xx = SCM_I_INUM (x);
+
+ switch (xx)
+ {
+ case 0: return x; break;
+ case 1: return y; break;
+ }
+
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
+ {
+ long yy = SCM_I_INUM (y);
+ long kk = xx * yy;
+ SCM k = SCM_I_MAKINUM (kk);
+ if ((kk == SCM_I_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_from_double (xx * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y),
+ xx * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_i_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_BIGP (x))
+ {
+ if (SCM_I_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_from_double (result);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double z = mpz_get_d (SCM_I_BIG_MPZ (x));
+ scm_remember_upto_here_1 (x);
+ return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y),
+ z * SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_i_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_I_INUMP (y))
+ {
+ /* inexact*exact0 => exact 0, per R5RS "Exactness" section */
+ if (scm_is_eq (y, SCM_INUM0))
+ return y;
+ return scm_from_double (SCM_I_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_from_double (result);
+ }
+ else if (SCM_REALP (y))
+ return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y),
+ SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_from_double (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_I_INUMP (y))
+ {
+ /* inexact*exact0 => exact 0, per R5RS "Exactness" section */
+ if (scm_is_eq (y, SCM_INUM0))
+ return y;
+ return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x),
+ SCM_I_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_c_make_rectangular (z * SCM_COMPLEX_REAL (x),
+ z * SCM_COMPLEX_IMAG (x));
+ }
+ else if (SCM_REALP (y))
+ return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x),
+ SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x));
+ else if (SCM_COMPLEXP (y))
+ {
+ return scm_c_make_rectangular (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_c_make_rectangular (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_I_INUMP (y))
+ return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y),
+ xx * SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a/b * c/d = ac / bd */
+ return scm_i_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);
+}
+
+#if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \
+ || (defined (HAVE_FINITE) && defined (HAVE_ISNAN)))
+#define ALLOW_DIVIDE_BY_ZERO
+/* #define ALLOW_DIVIDE_BY_EXACT_ZERO */
+#endif
+
+/* The code below for complex division is adapted from the GNU
+ libstdc++, which adapted it from f2c's libF77, and is subject to
+ this copyright: */
+
+/****************************************************************
+Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore.
+
+Permission to use, copy, modify, and distribute this software
+and its documentation for any purpose and without fee is hereby
+granted, provided that the above copyright notice appear in all
+copies and that both that the copyright notice and this
+permission notice and warranty disclaimer appear in supporting
+documentation, and that the names of AT&T Bell Laboratories or
+Bellcore or any of their entities not be used in advertising or
+publicity pertaining to distribution of the software without
+specific, written prior permission.
+
+AT&T and Bellcore disclaim all warranties with regard to this
+software, including all implied warranties of merchantability
+and fitness. In no event shall AT&T or Bellcore be liable for
+any special, indirect or consequential damages or any damages
+whatsoever resulting from loss of use, data or profits, whether
+in an action of contract, negligence or other tortious action,
+arising out of or in connection with the use or performance of
+this software.
+****************************************************************/
+
+SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide);
+/* Divide the first argument by the product of the remaining
+ arguments. If called with one argument @var{z1}, 1/@var{z1} is
+ returned. */
+#define FUNC_NAME s_divide
+static SCM
+scm_i_divide (SCM x, SCM y, int inexact)
+{
+ double a;
+
+ if (SCM_UNLIKELY (SCM_UNBNDP (y)))
+ {
+ if (SCM_UNBNDP (x))
+ SCM_WTA_DISPATCH_0 (g_divide, s_divide);
+ else if (SCM_I_INUMP (x))
+ {
+ long xx = SCM_I_INUM (x);
+ if (xx == 1 || xx == -1)
+ return x;
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ else if (xx == 0)
+ scm_num_overflow (s_divide);
+#endif
+ else
+ {
+ if (inexact)
+ return scm_from_double (1.0 / (double) xx);
+ else return scm_i_make_ratio (SCM_I_MAKINUM(1), x);
+ }
+ }
+ else if (SCM_BIGP (x))
+ {
+ if (inexact)
+ return scm_from_double (1.0 / scm_i_big2dbl (x));
+ else return scm_i_make_ratio (SCM_I_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
+#endif
+ return scm_from_double (1.0 / xx);
+ }
+ else if (SCM_COMPLEXP (x))
+ {
+ double r = SCM_COMPLEX_REAL (x);
+ double i = SCM_COMPLEX_IMAG (x);
+ if (fabs(r) <= fabs(i))
+ {
+ double t = r / i;
+ double d = i * (1.0 + t * t);
+ return scm_c_make_rectangular (t / d, -1.0 / d);
+ }
+ else
+ {
+ double t = i / r;
+ double d = r * (1.0 + t * t);
+ return scm_c_make_rectangular (1.0 / d, -t / d);
+ }
+ }
+ else if (SCM_FRACTIONP (x))
+ return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_NUMERATOR (x));
+ else
+ SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide);
+ }
+
+ if (SCM_LIKELY (SCM_I_INUMP (x)))
+ {
+ long xx = SCM_I_INUM (x);
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
+ {
+ long yy = SCM_I_INUM (y);
+ if (yy == 0)
+ {
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ scm_num_overflow (s_divide);
+#else
+ return scm_from_double ((double) xx / (double) yy);
+#endif
+ }
+ else if (xx % yy != 0)
+ {
+ if (inexact)
+ return scm_from_double ((double) xx / (double) yy);
+ else return scm_i_make_ratio (x, y);
+ }
+ else
+ {
+ long z = xx / yy;
+ if (SCM_FIXABLE (z))
+ return SCM_I_MAKINUM (z);
+ else
+ return scm_i_long2big (z);
+ }
+ }
+ else if (SCM_BIGP (y))
+ {
+ if (inexact)
+ return scm_from_double ((double) xx / scm_i_big2dbl (y));
+ else return scm_i_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_from_double ((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 (fabs(r) <= fabs(i))
+ {
+ double t = r / i;
+ double d = i * (1.0 + t * t);
+ return scm_c_make_rectangular ((a * t) / d, -a / d);
+ }
+ else
+ {
+ double t = i / r;
+ double d = r * (1.0 + t * t);
+ return scm_c_make_rectangular (a / d, -(a * t) / d);
+ }
+ }
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a / b/c = ac / b */
+ return scm_i_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_I_INUMP (y))
+ {
+ long int yy = SCM_I_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_from_double (scm_i_big2dbl (x) / (double) yy);
+ else return scm_i_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 */
+ if (inexact)
+ {
+ /* It's easily possible for the ratio x/y to fit a double
+ but one or both x and y be too big to fit a double,
+ hence the use of mpq_get_d rather than converting and
+ dividing. */
+ mpq_t q;
+ *mpq_numref(q) = *SCM_I_BIG_MPZ (x);
+ *mpq_denref(q) = *SCM_I_BIG_MPZ (y);
+ return scm_from_double (mpq_get_d (q));
+ }
+ else
+ {
+ 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
+ return scm_i_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_from_double (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_i_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_I_INUMP (y))
+ {
+ long int yy = SCM_I_INUM (y);
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ if (yy == 0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ return scm_from_double (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_from_double (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);
+ else
+#endif
+ return scm_from_double (rx / yy);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ a = rx;
+ goto complex_div;
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_from_double (rx / scm_i_fraction2double (y));
+ 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_I_INUMP (y))
+ {
+ long int yy = SCM_I_INUM (y);
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ if (yy == 0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ {
+ double d = yy;
+ return scm_c_make_rectangular (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_c_make_rectangular (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_c_make_rectangular (rx / yy, ix / yy);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double ry = SCM_COMPLEX_REAL (y);
+ double iy = SCM_COMPLEX_IMAG (y);
+ if (fabs(ry) <= fabs(iy))
+ {
+ double t = ry / iy;
+ double d = iy * (1.0 + t * t);
+ return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d);
+ }
+ else
+ {
+ double t = iy / ry;
+ double d = ry * (1.0 + t * t);
+ return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d);
+ }
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ return scm_c_make_rectangular (rx / yy, ix / yy);
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_I_INUMP (y))
+ {
+ long int yy = SCM_I_INUM (y);
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ if (yy == 0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), y));
+ }
+ else if (SCM_BIGP (y))
+ {
+ return scm_i_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
+#endif
+ return scm_from_double (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_i_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
+ 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
+
+
+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, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh);
+/* "Return the inverse hyperbolic sine of @var{x}."
+ */
+
+
+double
+scm_acosh (double x)
+{
+#if HAVE_ACOSH
+ return acosh (x);
+#else
+#define acosh scm_acosh
+ return log (x + sqrt (x * x - 1));
+#endif
+}
+SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh);
+/* "Return the inverse hyperbolic cosine of @var{x}."
+ */
+
+
+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}."
+ */
+
+
+double
+scm_c_truncate (double x)
+{
+#if HAVE_TRUNC
+ return trunc (x);
+#else
+ if (x < 0.0)
+ return -floor (-x);
+ return floor (x);
+#endif
+}
+
+/* scm_c_round is done using floor(x+0.5) to round to nearest and with
+ half-way case (ie. when x is an integer plus 0.5) going upwards.
+ Then half-way cases are identified and adjusted down if the
+ round-upwards didn't give the desired even integer.
+
+ "plus_half == result" identifies a half-way case. If plus_half, which is
+ x + 0.5, is an integer then x must be an integer plus 0.5.
+
+ An odd "result" value is identified with result/2 != floor(result/2).
+ This is done with plus_half, since that value is ready for use sooner in
+ a pipelined cpu, and we're already requiring plus_half == result.
+
+ Note however that we need to be careful when x is big and already an
+ integer. In that case "x+0.5" may round to an adjacent integer, causing
+ us to return such a value, incorrectly. For instance if the hardware is
+ in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF
+ (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value
+ returned. Or if the hardware is in round-upwards mode, then other bigger
+ values like say x == 2^128 will see x+0.5 rounding up to the next higher
+ representable value, 2^128+2^76 (or whatever), again incorrect.
+
+ These bad roundings of x+0.5 are avoided by testing at the start whether
+ x is already an integer. If it is then clearly that's the desired result
+ already. And if it's not then the exponent must be small enough to allow
+ an 0.5 to be represented, and hence added without a bad rounding. */
+
+double
+scm_c_round (double x)
+{
+ double plus_half, result;
+
+ if (x == floor (x))
+ return x;
+
+ plus_half = x + 0.5;
+ result = floor (plus_half);
+ /* Adjust so that the rounding is towards even. */
+ 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_is_false (scm_negative_p (x)))
+ return scm_floor (x);
+ else
+ return scm_ceiling (x);
+}
+#undef FUNC_NAME
+
+static SCM exactly_one_half;
+
+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
+{
+ if (SCM_I_INUMP (x) || SCM_BIGP (x))
+ return x;
+ else if (SCM_REALP (x))
+ return scm_from_double (scm_c_round (SCM_REAL_VALUE (x)));
+ else
+ {
+ /* OPTIMIZE-ME: Fraction case could be done more efficiently by a
+ single quotient+remainder division then examining to see which way
+ the rounding should go. */
+ SCM plus_half = scm_sum (x, exactly_one_half);
+ SCM result = scm_floor (plus_half);
+ /* Adjust so that the rounding is towards even. */
+ if (scm_is_true (scm_num_eq_p (plus_half, result))
+ && scm_is_true (scm_odd_p (result)))
+ return scm_difference (result, SCM_I_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_I_INUMP (x) || SCM_BIGP (x))
+ return x;
+ else if (SCM_REALP (x))
+ return scm_from_double (floor (SCM_REAL_VALUE (x)));
+ else if (SCM_FRACTIONP (x))
+ {
+ SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (x));
+ if (scm_is_false (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_I_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_I_INUMP (x) || SCM_BIGP (x))
+ return x;
+ else if (SCM_REALP (x))
+ return scm_from_double (ceil (SCM_REAL_VALUE (x)));
+ else if (SCM_FRACTIONP (x))
+ {
+ SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (x));
+ if (scm_is_false (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_I_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, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs);
+/* "Return the absolute value of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp);
+/* "Return the @var{x}th power of e."
+ */
+SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log);
+/* "Return the natural logarithm of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin);
+/* "Return the sine of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos);
+/* "Return the cosine of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan);
+/* "Return the tangent of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin);
+/* "Return the arc sine of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos);
+/* "Return the arc cosine of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan);
+/* "Return the arc tangent of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh);
+/* "Return the hyperbolic sine of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh);
+/* "Return the hyperbolic cosine of the real number @var{x}."
+ */
+SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh);
+/* "Return the hyperbolic tangent of the real number @var{x}."
+ */
+
+struct dpair
+{
+ double x, y;
+};
+
+static void scm_two_doubles (SCM x,
+ SCM y,
+ const char *sstring,
+ struct dpair * xy);
+
+static void
+scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy)
+{
+ if (SCM_I_INUMP (x))
+ xy->x = SCM_I_INUM (x);
+ else if (SCM_BIGP (x))
+ xy->x = scm_i_big2dbl (x);
+ else if (SCM_REALP (x))
+ xy->x = SCM_REAL_VALUE (x);
+ else if (SCM_FRACTIONP (x))
+ xy->x = scm_i_fraction2double (x);
+ else
+ scm_wrong_type_arg (sstring, SCM_ARG1, x);
+
+ if (SCM_I_INUMP (y))
+ xy->y = SCM_I_INUM (y);
+ else if (SCM_BIGP (y))
+ xy->y = scm_i_big2dbl (y);
+ else if (SCM_REALP (y))
+ xy->y = SCM_REAL_VALUE (y);
+ else if (SCM_FRACTIONP (y))
+ xy->y = scm_i_fraction2double (y);
+ else
+ scm_wrong_type_arg (sstring, SCM_ARG2, y);
+}
+
+
+SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0,
+ (SCM x, SCM y),
+ "Return @var{x} raised to the power of @var{y}. This\n"
+ "procedure does not accept complex arguments.")
+#define FUNC_NAME s_scm_sys_expt
+{
+ struct dpair xy;
+ scm_two_doubles (x, y, FUNC_NAME, &xy);
+ return scm_from_double (pow (xy.x, xy.y));
+}
+#undef FUNC_NAME
+
+
+SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0,
+ (SCM x, SCM y),
+ "Return the arc tangent of the two arguments @var{x} and\n"
+ "@var{y}. This is similar to calculating the arc tangent of\n"
+ "@var{x} / @var{y}, except that the signs of both arguments\n"
+ "are used to determine the quadrant of the result. This\n"
+ "procedure does not accept complex arguments.")
+#define FUNC_NAME s_scm_sys_atan2
+{
+ struct dpair xy;
+ scm_two_doubles (x, y, FUNC_NAME, &xy);
+ return scm_from_double (atan2 (xy.x, xy.y));
+}
+#undef FUNC_NAME
+
+SCM
+scm_c_make_rectangular (double re, double im)
+{
+ if (im == 0.0)
+ return scm_from_double (re);
+ else
+ {
+ SCM z;
+ SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex),
+ "complex"));
+ SCM_COMPLEX_REAL (z) = re;
+ SCM_COMPLEX_IMAG (z) = im;
+ return z;
+ }
+}
+
+SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0,
+ (SCM real_part, SCM imaginary_part),
+ "Return a complex number constructed of the given @var{real-part} "
+ "and @var{imaginary-part} parts.")
+#define FUNC_NAME s_scm_make_rectangular
+{
+ struct dpair xy;
+ scm_two_doubles (real_part, imaginary_part, FUNC_NAME, &xy);
+ return scm_c_make_rectangular (xy.x, xy.y);
+}
+#undef FUNC_NAME
+
+SCM
+scm_c_make_polar (double mag, double ang)
+{
+ double s, c;
+
+ /* The sincos(3) function is undocumented an broken on Tru64. Thus we only
+ use it on Glibc-based systems that have it (it's a GNU extension). See
+ http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for
+ details. */
+#if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE)
+ sincos (ang, &s, &c);
+#else
+ s = sin (ang);
+ c = cos (ang);
+#endif
+ return scm_c_make_rectangular (mag * c, mag * s);
+}
+
+SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0,
+ (SCM x, SCM y),
+ "Return the complex number @var{x} * e^(i * @var{y}).")
+#define FUNC_NAME s_scm_make_polar
+{
+ struct dpair xy;
+ scm_two_doubles (x, y, FUNC_NAME, &xy);
+ return scm_c_make_polar (xy.x, xy.y);
+}
+#undef FUNC_NAME
+
+
+SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part);
+/* "Return the real part of the number @var{z}."
+ */
+SCM
+scm_real_part (SCM z)
+{
+ if (SCM_I_INUMP (z))
+ return z;
+ else if (SCM_BIGP (z))
+ return z;
+ else if (SCM_REALP (z))
+ return z;
+ else if (SCM_COMPLEXP (z))
+ return scm_from_double (SCM_COMPLEX_REAL (z));
+ else if (SCM_FRACTIONP (z))
+ return z;
+ else
+ SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part);
+}
+
+
+SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part);
+/* "Return the imaginary part of the number @var{z}."
+ */
+SCM
+scm_imag_part (SCM z)
+{
+ if (SCM_I_INUMP (z))
+ return SCM_INUM0;
+ else if (SCM_BIGP (z))
+ return SCM_INUM0;
+ else if (SCM_REALP (z))
+ return scm_flo0;
+ else if (SCM_COMPLEXP (z))
+ return scm_from_double (SCM_COMPLEX_IMAG (z));
+ 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_I_INUMP (z))
+ return z;
+ else if (SCM_BIGP (z))
+ return z;
+ else if (SCM_FRACTIONP (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_I_INUMP (z))
+ return SCM_I_MAKINUM (1);
+ else if (SCM_BIGP (z))
+ return SCM_I_MAKINUM (1);
+ else if (SCM_FRACTIONP (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"
+ * "@code{abs} for real arguments, but also allows complex numbers."
+ */
+SCM
+scm_magnitude (SCM z)
+{
+ if (SCM_I_INUMP (z))
+ {
+ long int zz = SCM_I_INUM (z);
+ if (zz >= 0)
+ return z;
+ else if (SCM_POSFIXABLE (-zz))
+ return SCM_I_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))
+ return scm_from_double (fabs (SCM_REAL_VALUE (z)));
+ else if (SCM_COMPLEXP (z))
+ return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z)));
+ else if (SCM_FRACTIONP (z))
+ {
+ if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z))))
+ return z;
+ return scm_i_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_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle);
+/* "Return the angle of the complex number @var{z}."
+ */
+SCM
+scm_angle (SCM 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_from_double 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_I_INUMP (z))
+ {
+ if (SCM_I_INUM (z) >= 0)
+ return scm_flo0;
+ else
+ return scm_from_double (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_from_double (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_from_double (atan2 (0.0, -1.0));
+ }
+ else if (SCM_COMPLEXP (z))
+ return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z)));
+ else if (SCM_FRACTIONP (z))
+ {
+ if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z))))
+ return scm_flo0;
+ else return scm_from_double (atan2 (0.0, -1.0));
+ }
+ else
+ SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle);
+}
+
+
+SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact);
+/* Convert the number @var{x} to its inexact representation.\n"
+ */
+SCM
+scm_exact_to_inexact (SCM z)
+{
+ if (SCM_I_INUMP (z))
+ return scm_from_double ((double) SCM_I_INUM (z));
+ else if (SCM_BIGP (z))
+ return scm_from_double (scm_i_big2dbl (z));
+ else if (SCM_FRACTIONP (z))
+ return scm_from_double (scm_i_fraction2double (z));
+ else if (SCM_INEXACTP (z))
+ return z;
+ else
+ SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact);
+}
+
+
+SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0,
+ (SCM z),
+ "Return an exact number that is numerically closest to @var{z}.")
+#define FUNC_NAME s_scm_inexact_to_exact
+{
+ if (SCM_I_INUMP (z))
+ return z;
+ else if (SCM_BIGP (z))
+ return z;
+ 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_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)),
+ scm_i_mpz2num (mpq_denref (frac)));
+
+ /* When scm_i_make_ratio throws, we leak the memory allocated
+ for frac...
+ */
+ mpq_clear (frac);
+ return q;
+ }
+ }
+ 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 eps),
+ "Returns the @emph{simplest} rational number differing\n"
+ "from @var{x} by no more than @var{eps}.\n"
+ "\n"
+ "As required by @acronym{R5RS}, @code{rationalize} only returns an\n"
+ "exact result when both its arguments are exact. Thus, you might need\n"
+ "to use @code{inexact->exact} on the arguments.\n"
+ "\n"
+ "@lisp\n"
+ "(rationalize (inexact->exact 1.2) 1/100)\n"
+ "@result{} 6/5\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_rationalize
+{
+ if (SCM_I_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_I_MAKINUM (1);
+ SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0);
+ SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0);
+ SCM rx;
+ int i = 0;
+
+ if (scm_is_true (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.
+ */
+
+ eps = scm_abs (eps);
+ 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_is_false (scm_zero_p (b)) && /* b != 0 */
+ scm_is_false
+ (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))),
+ eps))) /* abs(x-a/b) <= eps */
+ {
+ SCM res = scm_sum (int_part, scm_divide (a, b));
+ if (scm_is_false (scm_exact_p (x))
+ || scm_is_false (scm_exact_p (eps)))
+ 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
+
+/* conversion functions */
+
+int
+scm_is_integer (SCM val)
+{
+ return scm_is_true (scm_integer_p (val));
+}
+
+int
+scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max)
+{
+ if (SCM_I_INUMP (val))
+ {
+ scm_t_signed_bits n = SCM_I_INUM (val);
+ return n >= min && n <= max;
+ }
+ else if (SCM_BIGP (val))
+ {
+ if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM)
+ return 0;
+ else if (min >= LONG_MIN && max <= LONG_MAX)
+ {
+ if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val)))
+ {
+ long n = mpz_get_si (SCM_I_BIG_MPZ (val));
+ return n >= min && n <= max;
+ }
+ else
+ return 0;
+ }
+ else
+ {
+ scm_t_intmax n;
+ size_t count;
+
+ if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2)
+ > CHAR_BIT*sizeof (scm_t_uintmax))
+ return 0;
+
+ mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0,
+ SCM_I_BIG_MPZ (val));
+
+ if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0)
+ {
+ if (n < 0)
+ return 0;
+ }
+ else
+ {
+ n = -n;
+ if (n >= 0)
+ return 0;
+ }
+
+ return n >= min && n <= max;
+ }
+ }
+ else
+ return 0;
+}
+
+int
+scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max)
+{
+ if (SCM_I_INUMP (val))
+ {
+ scm_t_signed_bits n = SCM_I_INUM (val);
+ return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max;
+ }
+ else if (SCM_BIGP (val))
+ {
+ if (max <= SCM_MOST_POSITIVE_FIXNUM)
+ return 0;
+ else if (max <= ULONG_MAX)
+ {
+ if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val)))
+ {
+ unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val));
+ return n >= min && n <= max;
+ }
+ else
+ return 0;
+ }
+ else
+ {
+ scm_t_uintmax n;
+ size_t count;
+
+ if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0)
+ return 0;
+
+ if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2)
+ > CHAR_BIT*sizeof (scm_t_uintmax))
+ return 0;
+
+ mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0,
+ SCM_I_BIG_MPZ (val));
+
+ return n >= min && n <= max;
+ }
+ }
+ else
+ return 0;
+}
+
+static void
+scm_i_range_error (SCM bad_val, SCM min, SCM max)
+{
+ scm_error (scm_out_of_range_key,
+ NULL,
+ "Value out of range ~S to ~S: ~S",
+ scm_list_3 (min, max, bad_val),
+ scm_list_1 (bad_val));
+}
+
+#define TYPE scm_t_intmax
+#define TYPE_MIN min
+#define TYPE_MAX max
+#define SIZEOF_TYPE 0
+#define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg)
+#include "libguile/conv-integer.i.c"
+
+#define TYPE scm_t_uintmax
+#define TYPE_MIN min
+#define TYPE_MAX max
+#define SIZEOF_TYPE 0
+#define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg)
+#include "libguile/conv-uinteger.i.c"
+
+#define TYPE scm_t_int8
+#define TYPE_MIN SCM_T_INT8_MIN
+#define TYPE_MAX SCM_T_INT8_MAX
+#define SIZEOF_TYPE 1
+#define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg)
+#include "libguile/conv-integer.i.c"
+
+#define TYPE scm_t_uint8
+#define TYPE_MIN 0
+#define TYPE_MAX SCM_T_UINT8_MAX
+#define SIZEOF_TYPE 1
+#define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg)
+#include "libguile/conv-uinteger.i.c"
+
+#define TYPE scm_t_int16
+#define TYPE_MIN SCM_T_INT16_MIN
+#define TYPE_MAX SCM_T_INT16_MAX
+#define SIZEOF_TYPE 2
+#define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg)
+#include "libguile/conv-integer.i.c"
+
+#define TYPE scm_t_uint16
+#define TYPE_MIN 0
+#define TYPE_MAX SCM_T_UINT16_MAX
+#define SIZEOF_TYPE 2
+#define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg)
+#include "libguile/conv-uinteger.i.c"
+
+#define TYPE scm_t_int32
+#define TYPE_MIN SCM_T_INT32_MIN
+#define TYPE_MAX SCM_T_INT32_MAX
+#define SIZEOF_TYPE 4
+#define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg)
+#include "libguile/conv-integer.i.c"
+
+#define TYPE scm_t_uint32
+#define TYPE_MIN 0
+#define TYPE_MAX SCM_T_UINT32_MAX
+#define SIZEOF_TYPE 4
+#define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg)
+#include "libguile/conv-uinteger.i.c"
+
+#define TYPE scm_t_int64
+#define TYPE_MIN SCM_T_INT64_MIN
+#define TYPE_MAX SCM_T_INT64_MAX
+#define SIZEOF_TYPE 8
+#define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg)
+#include "libguile/conv-integer.i.c"
+
+#define TYPE scm_t_uint64
+#define TYPE_MIN 0
+#define TYPE_MAX SCM_T_UINT64_MAX
+#define SIZEOF_TYPE 8
+#define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg)
+#define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg)
+#include "libguile/conv-uinteger.i.c"
+
+void
+scm_to_mpz (SCM val, mpz_t rop)
+{
+ if (SCM_I_INUMP (val))
+ mpz_set_si (rop, SCM_I_INUM (val));
+ else if (SCM_BIGP (val))
+ mpz_set (rop, SCM_I_BIG_MPZ (val));
+ else
+ scm_wrong_type_arg_msg (NULL, 0, val, "exact integer");
+}
+
+SCM
+scm_from_mpz (mpz_t val)
+{
+ return scm_i_mpz2num (val);
+}
+
+int
+scm_is_real (SCM val)
+{
+ return scm_is_true (scm_real_p (val));
+}
+
+int
+scm_is_rational (SCM val)
+{
+ return scm_is_true (scm_rational_p (val));
+}
+
+double
+scm_to_double (SCM val)
+{
+ if (SCM_I_INUMP (val))
+ return SCM_I_INUM (val);
+ else if (SCM_BIGP (val))
+ return scm_i_big2dbl (val);
+ else if (SCM_FRACTIONP (val))
+ return scm_i_fraction2double (val);
+ else if (SCM_REALP (val))
+ return SCM_REAL_VALUE (val);
+ else
+ scm_wrong_type_arg_msg (NULL, 0, val, "real number");
+}
+
+SCM
+scm_from_double (double val)
+{
+ SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0);
+ SCM_REAL_VALUE (z) = val;
+ return z;
+}
+
+#if SCM_ENABLE_DISCOURAGED == 1
+
+float
+scm_num2float (SCM num, unsigned long int pos, const char *s_caller)
+{
+ if (SCM_BIGP (num))
+ {
+ float res = mpz_get_d (SCM_I_BIG_MPZ (num));
+ if (!xisinf (res))
+ return res;
+ else
+ scm_out_of_range (NULL, num);
+ }
+ else
+ return scm_to_double (num);
+}
+
+double
+scm_num2double (SCM num, unsigned long int pos, const char *s_caller)
+{
+ if (SCM_BIGP (num))
+ {
+ double res = mpz_get_d (SCM_I_BIG_MPZ (num));
+ if (!xisinf (res))
+ return res;
+ else
+ scm_out_of_range (NULL, num);
+ }
+ else
+ return scm_to_double (num);
+}
+
+#endif
+
+int
+scm_is_complex (SCM val)
+{
+ return scm_is_true (scm_complex_p (val));
+}
+
+double
+scm_c_real_part (SCM z)
+{
+ if (SCM_COMPLEXP (z))
+ return SCM_COMPLEX_REAL (z);
+ else
+ {
+ /* Use the scm_real_part to get proper error checking and
+ dispatching.
+ */
+ return scm_to_double (scm_real_part (z));
+ }
+}
+
+double
+scm_c_imag_part (SCM z)
+{
+ if (SCM_COMPLEXP (z))
+ return SCM_COMPLEX_IMAG (z);
+ else
+ {
+ /* Use the scm_imag_part to get proper error checking and
+ dispatching. The result will almost always be 0.0, but not
+ always.
+ */
+ return scm_to_double (scm_imag_part (z));
+ }
+}
+
+double
+scm_c_magnitude (SCM z)
+{
+ return scm_to_double (scm_magnitude (z));
+}
+
+double
+scm_c_angle (SCM z)
+{
+ return scm_to_double (scm_angle (z));
+}
+
+int
+scm_is_number (SCM z)
+{
+ return scm_is_true (scm_number_p (z));
+}
+
+
+/* In the following functions we dispatch to the real-arg funcs like log()
+ when we know the arg is real, instead of just handing everything to
+ clog() for instance. This is in case clog() doesn't optimize for a
+ real-only case, and because we have to test SCM_COMPLEXP anyway so may as
+ well use it to go straight to the applicable C func. */
+
+SCM_DEFINE (scm_log, "log", 1, 0, 0,
+ (SCM z),
+ "Return the natural logarithm of @var{z}.")
+#define FUNC_NAME s_scm_log
+{
+ if (SCM_COMPLEXP (z))
+ {
+#if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE)
+ return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z)));
+#else
+ double re = SCM_COMPLEX_REAL (z);
+ double im = SCM_COMPLEX_IMAG (z);
+ return scm_c_make_rectangular (log (hypot (re, im)),
+ atan2 (im, re));
+#endif
+ }
+ else
+ {
+ /* ENHANCE-ME: When z is a bignum the logarithm will fit a double
+ although the value itself overflows. */
+ double re = scm_to_double (z);
+ double l = log (fabs (re));
+ if (re >= 0.0)
+ return scm_from_double (l);
+ else
+ return scm_c_make_rectangular (l, M_PI);
+ }
+}
+#undef FUNC_NAME
+
+
+SCM_DEFINE (scm_log10, "log10", 1, 0, 0,
+ (SCM z),
+ "Return the base 10 logarithm of @var{z}.")
+#define FUNC_NAME s_scm_log10
+{
+ if (SCM_COMPLEXP (z))
+ {
+ /* Mingw has clog() but not clog10(). (Maybe it'd be worth using
+ clog() and a multiply by M_LOG10E, rather than the fallback
+ log10+hypot+atan2.) */
+#if HAVE_COMPLEX_DOUBLE && HAVE_CLOG10 && defined (SCM_COMPLEX_VALUE)
+ return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z)));
+#else
+ double re = SCM_COMPLEX_REAL (z);
+ double im = SCM_COMPLEX_IMAG (z);
+ return scm_c_make_rectangular (log10 (hypot (re, im)),
+ M_LOG10E * atan2 (im, re));
+#endif
+ }
+ else
+ {
+ /* ENHANCE-ME: When z is a bignum the logarithm will fit a double
+ although the value itself overflows. */
+ double re = scm_to_double (z);
+ double l = log10 (fabs (re));
+ if (re >= 0.0)
+ return scm_from_double (l);
+ else
+ return scm_c_make_rectangular (l, M_LOG10E * M_PI);
+ }
+}
+#undef FUNC_NAME
+
+
+SCM_DEFINE (scm_exp, "exp", 1, 0, 0,
+ (SCM z),
+ "Return @math{e} to the power of @var{z}, where @math{e} is the\n"
+ "base of natural logarithms (2.71828@dots{}).")
+#define FUNC_NAME s_scm_exp
+{
+ if (SCM_COMPLEXP (z))
+ {
+#if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE)
+ return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z)));
+#else
+ return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)),
+ SCM_COMPLEX_IMAG (z));
+#endif
+ }
+ else
+ {
+ /* When z is a negative bignum the conversion to double overflows,
+ giving -infinity, but that's ok, the exp is still 0.0. */
+ return scm_from_double (exp (scm_to_double (z)));
+ }
+}
+#undef FUNC_NAME
+
+
+SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0,
+ (SCM x),
+ "Return the square root of @var{z}. Of the two possible roots\n"
+ "(positive and negative), the one with the a positive real part\n"
+ "is returned, or if that's zero then a positive imaginary part.\n"
+ "Thus,\n"
+ "\n"
+ "@example\n"
+ "(sqrt 9.0) @result{} 3.0\n"
+ "(sqrt -9.0) @result{} 0.0+3.0i\n"
+ "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n"
+ "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n"
+ "@end example")
+#define FUNC_NAME s_scm_sqrt
+{
+ if (SCM_COMPLEXP (x))
+ {
+#if HAVE_COMPLEX_DOUBLE && HAVE_USABLE_CSQRT && defined (SCM_COMPLEX_VALUE)
+ return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x)));
+#else
+ double re = SCM_COMPLEX_REAL (x);
+ double im = SCM_COMPLEX_IMAG (x);
+ return scm_c_make_polar (sqrt (hypot (re, im)),
+ 0.5 * atan2 (im, re));
+#endif
+ }
+ else
+ {
+ double xx = scm_to_double (x);
+ if (xx < 0)
+ return scm_c_make_rectangular (0.0, sqrt (-xx));
+ else
+ return scm_from_double (sqrt (xx));
+ }
+}
+#undef FUNC_NAME
+
+
+
+void
+scm_init_numbers ()
+{
+ int i;
+
+ 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
+ * using these values, remember the two rules of program optimization:
+ * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */
+ scm_c_define ("most-positive-fixnum",
+ SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM));
+ scm_c_define ("most-negative-fixnum",
+ SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM));
+
+ scm_add_feature ("complex");
+ scm_add_feature ("inexact");
+ scm_flo0 = scm_from_double (0.0);
+
+ /* determine floating point precision */
+ for (i=2; i <= SCM_MAX_DBL_RADIX; ++i)
+ {
+ init_dblprec(&scm_dblprec[i-2],i);
+ init_fx_radix(fx_per_radix[i-2],i);
+ }
+#ifdef DBL_DIG
+ /* hard code precision for base 10 if the preprocessor tells us to... */
+ scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG;
+#endif
+
+ exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1),
+ SCM_I_MAKINUM (2)));
+#include "libguile/numbers.x"
+}
+
+/*
+ Local Variables:
+ c-file-style: "gnu"
+ End:
+*/
projects / lilypond.git / blobdiff