-/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004 Free Software Foundation, Inc.
+/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008 Free Software Foundation, Inc.
*
* Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories
* and Bellcore. See scm_divide.
*
* 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
\f
*/
-/* tell glibc (2.3) to give prototype for C99 trunc() */
-#define _GNU_SOURCE
-
-#if HAVE_CONFIG_H
+#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include <math.h>
#include <ctype.h>
#include <string.h>
-#include <gmp.h>
+
+#if HAVE_COMPLEX_H
+#include <complex.h>
+#endif
#include "libguile/_scm.h"
#include "libguile/feature.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
/*
#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_C_INLINE_KEYWORD SCM
+SCM
scm_i_mkbig ()
{
/* Return a newly created bignum. */
return z;
}
-SCM_C_INLINE_KEYWORD SCM
+SCM
scm_i_long2big (long x)
{
/* Return a newly created bignum initialized to X. */
return z;
}
-SCM_C_INLINE_KEYWORD SCM
+SCM
scm_i_ulong2big (unsigned long x)
{
/* Return a newly created bignum initialized to X. */
return z;
}
-SCM_C_INLINE_KEYWORD static SCM
+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. */
return z;
}
-SCM_C_INLINE_KEYWORD int
+int
scm_i_bigcmp (SCM x, SCM y)
{
/* Return neg if x < y, pos if x > y, and 0 if x == y */
return result;
}
-SCM_C_INLINE_KEYWORD SCM
+SCM
scm_i_dbl2big (double d)
{
/* results are only defined if d is an integer */
/* Convert a integer in double representation to a SCM number. */
-SCM_C_INLINE_KEYWORD SCM
+SCM
scm_i_dbl2num (double u)
{
/* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both
return result;
}
-SCM_C_INLINE_KEYWORD SCM
+SCM
scm_i_normbig (SCM b)
{
/* convert a big back to a fixnum if it'll fit */
/* No, it's a proper fraction.
*/
- return scm_double_cell (scm_tc16_fraction,
- SCM_UNPACK (numerator),
- SCM_UNPACK (denominator), 0);
+ {
+ 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
-static void scm_i_fraction_reduce (SCM z)
-{
- if (!(SCM_FRACTION_REDUCED (z)))
- {
- SCM divisor;
- divisor = scm_gcd (SCM_FRACTION_NUMERATOR (z), SCM_FRACTION_DENOMINATOR (z));
- if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1))))
- {
- /* is this safe? */
- SCM_FRACTION_SET_NUMERATOR (z, scm_divide (SCM_FRACTION_NUMERATOR (z), divisor));
- SCM_FRACTION_SET_DENOMINATOR (z, scm_divide (SCM_FRACTION_DENOMINATOR (z), divisor));
- }
- SCM_FRACTION_REDUCED_SET (z);
- }
-}
-
double
scm_i_fraction2double (SCM z)
{
#elif HAVE_DINFINITY
/* OSF */
extern unsigned int DINFINITY[2];
- guile_Inf = (*(X_CAST(double *, DINFINITY)));
+ guile_Inf = (*((double *) (DINFINITY)));
#else
double tmp = 1e+10;
guile_Inf = tmp;
/* C99 NAN, when available */
guile_NaN = NAN;
#elif HAVE_DQNAN
- /* OSF */
- extern unsigned int DQNAN[2];
- guile_NaN = (*(X_CAST(double *, DQNAN)));
+ {
+ /* OSF */
+ extern unsigned int DQNAN[2];
+ guile_NaN = (*((double *)(DQNAN)));
+ }
#else
guile_NaN = guile_Inf / guile_Inf;
#endif
scm_num_overflow (s_modulo);
else
{
- /* FIXME: I think this may be a bug on some arches -- results
- of % with negative second arg are undefined... */
+ /* 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;
mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2));
scm_remember_upto_here_1 (n2);
mpz_clear (nn1_z);
- return result_z;
+ return scm_i_normbig (result_z);
}
}
else
SCM_I_BIG_MPZ (n1),
SCM_I_BIG_MPZ (n2));
scm_remember_upto_here_2 (n1, n2);
- return result_z;
+ return scm_i_normbig (result_z);
}
else
SCM_WRONG_TYPE_ARG (SCM_ARG2, n2);
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 j k) @equiv{} (not (zero? (logand j k)))\n\n"
"(logtest #b0100 #b1011) @result{} #f\n"
"(logtest #b0100 #b0111) @result{} #t\n"
"@end lisp")
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? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n"
"(logbit? 0 #b1101) @result{} #t\n"
"(logbit? 1 #b1101) @result{} #f\n"
"(logbit? 2 #b1101) @result{} #t\n"
SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0,
(SCM n, SCM k),
- "Return @var{n} raised to the non-negative integer exponent\n"
- "@var{k}.\n"
+ "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)\n"
- " @result{} 32\n"
- "(integer-expt -3 3)\n"
- " @result{} -27\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
{
scm_remember_upto_here_1 (k);
i2_is_big = 1;
}
- else if (SCM_REALP (k))
- {
- double r = SCM_REAL_VALUE (k);
- if (floor (r) != r || xisinf (r))
- SCM_WRONG_TYPE_ARG (2, k);
- if ((r > SCM_MOST_POSITIVE_FIXNUM) || (r < SCM_MOST_NEGATIVE_FIXNUM))
- {
- z_i2 = scm_i_mkbig ();
- mpz_set_d (SCM_I_BIG_MPZ (z_i2), r);
- i2_is_big = 1;
- }
- else
- {
- i2 = r;
- }
- }
else
SCM_WRONG_TYPE_ARG (2, k);
long bits_to_shift;
bits_to_shift = scm_to_long (cnt);
- if (bits_to_shift < 0)
+ if (SCM_I_INUMP (n))
{
- /* Shift right by abs(cnt) bits. This is realized as a division
- by div:=2^abs(cnt). However, to guarantee the floor
- rounding, negative values require some special treatment.
- */
- SCM div = scm_integer_expt (SCM_I_MAKINUM (2),
- scm_from_long (-bits_to_shift));
+ 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;
- /* scm_quotient assumes its arguments are integers, but it's legal to (ash 1/2 -1) */
- if (scm_is_false (scm_negative_p (n)))
- return scm_quotient (n, div);
+ 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
- return scm_sum (SCM_I_MAKINUM (-1L),
- scm_quotient (scm_sum (SCM_I_MAKINUM (1L), n), div));
+ {
+ /* 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
- /* Shift left is done by multiplication with 2^CNT */
- return scm_product (n, scm_integer_expt (SCM_I_MAKINUM (2), cnt));
+ {
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
+ }
}
#undef FUNC_NAME
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)
{
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)
{
- i = idbl2str (SCM_COMPLEX_REAL (flt), str, radix);
- if (SCM_COMPLEX_IMAG (flt) != 0.0)
- {
- double imag = SCM_COMPLEX_IMAG (flt);
- /* 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';
- }
+ *p++ = '-';
+ return scm_iuint2str (-num, rad, p) + 1;
}
- return i;
+ else
+ return scm_iuint2str (num, rad, p);
}
-/* convert a long to a string (unterminated). returns the number of
+/* 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 (long num, int rad, char *p)
+scm_iuint2str (scm_t_uintmax num, int rad, char *p)
{
size_t j = 1;
size_t i;
- unsigned long n = (num < 0) ? -num : num;
+ scm_t_uintmax n = num;
for (n /= rad; n > 0; n /= rad)
j++;
i = j;
- if (num < 0)
- {
- *p++ = '-';
- j++;
- n = -num;
- }
- else
- n = num;
+ n = num;
while (i--)
{
int d = n % rad;
}
else if (SCM_FRACTIONP (n))
{
- scm_i_fraction_reduce (n);
return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix),
scm_from_locale_string ("/"),
scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix)));
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)
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;
- scm_i_fraction_reduce (sexp);
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);
enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16};
SCM
-scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix)
+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;
else
base = scm_to_unsigned_integer (radix, 2, INT_MAX);
- answer = scm_i_mem2number (scm_i_string_chars (string),
- scm_i_string_length (string),
- base);
+ 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;
}
SCM
scm_i_fraction_equalp (SCM x, SCM y)
{
- scm_i_fraction_reduce (x);
- scm_i_fraction_reduce (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),
if (SCM_COMPLEXP (x))
return SCM_BOOL_F;
r = SCM_REAL_VALUE (x);
- if (xisinf (r))
- return SCM_BOOL_F;
+ /* +/-inf passes r==floor(r), making those #t */
if (r == floor (r))
return SCM_BOOL_T;
return SCM_BOOL_F;
else if (SCM_BIGP (y))
return SCM_BOOL_F;
else if (SCM_REALP (y))
- return scm_from_bool ((double) xx == SCM_REAL_VALUE (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_REALP (x))
{
+ double xx = SCM_REAL_VALUE (x);
if (SCM_I_INUMP (y))
- return scm_from_bool (SCM_REAL_VALUE (x) == (double) SCM_I_INUM (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;
SCM
scm_sum (SCM x, SCM y)
{
- if (SCM_UNBNDP (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_I_INUMP (x))
+ if (SCM_LIKELY (SCM_I_INUMP (x)))
{
- if (SCM_I_INUMP (y))
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
{
long xx = SCM_I_INUM (x);
long yy = SCM_I_INUM (y);
}
+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
SCM
scm_difference (SCM x, SCM y)
{
- if (SCM_UNBNDP (y))
+ if (SCM_UNLIKELY (SCM_UNBNDP (y)))
{
if (SCM_UNBNDP (x))
SCM_WTA_DISPATCH_0 (g_difference, s_difference);
return scm_i_long2big (xx);
}
else if (SCM_BIGP (x))
- /* FIXME: do we really need to normalize here? */
+ /* 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));
SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference);
}
- if (SCM_I_INUMP (x))
+ if (SCM_LIKELY (SCM_I_INUMP (x)))
{
- if (SCM_I_INUMP (y))
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
{
long int xx = SCM_I_INUM (x);
long int yy = SCM_I_INUM (y);
#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_UNBNDP (y))
+ if (SCM_UNLIKELY (SCM_UNBNDP (y)))
{
if (SCM_UNBNDP (x))
return SCM_I_MAKINUM (1L);
SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product);
}
- if (SCM_I_INUMP (x))
+ if (SCM_LIKELY (SCM_I_INUMP (x)))
{
long xx;
case 1: return y; break;
}
- if (SCM_I_INUMP (y))
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
{
long yy = SCM_I_INUM (y);
long kk = xx * yy;
else if (SCM_REALP (x))
{
if (SCM_I_INUMP (y))
- return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x));
+ {
+ /* 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);
else if (SCM_COMPLEXP (x))
{
if (SCM_I_INUMP (y))
- return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x),
- SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x));
+ {
+ /* 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));
{
double a;
- if (SCM_UNBNDP (y))
+ if (SCM_UNLIKELY (SCM_UNBNDP (y)))
{
if (SCM_UNBNDP (x))
SCM_WTA_DISPATCH_0 (g_divide, s_divide);
{
double r = SCM_COMPLEX_REAL (x);
double i = SCM_COMPLEX_IMAG (x);
- if (r <= i)
+ if (fabs(r) <= fabs(i))
{
double t = r / i;
double d = i * (1.0 + t * t);
SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide);
}
- if (SCM_I_INUMP (x))
+ if (SCM_LIKELY (SCM_I_INUMP (x)))
{
long xx = SCM_I_INUM (x);
- if (SCM_I_INUMP (y))
+ if (SCM_LIKELY (SCM_I_INUMP (y)))
{
long yy = SCM_I_INUM (y);
if (yy == 0)
{
double r = SCM_COMPLEX_REAL (y);
double i = SCM_COMPLEX_IMAG (y);
- if (r <= i)
+ if (fabs(r) <= fabs(i))
{
double t = r / i;
double d = i * (1.0 + t * t);
else
{
/* big_x / big_y */
- int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (y));
- if (divisible_p)
- {
- SCM result = scm_i_mkbig ();
- mpz_divexact (SCM_I_BIG_MPZ (result),
- SCM_I_BIG_MPZ (x),
- SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return scm_i_normbig (result);
- }
- else
- {
- if (inexact)
- {
- double dbx = mpz_get_d (SCM_I_BIG_MPZ (x));
- double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return scm_from_double (dbx / dby);
- }
- else return scm_i_make_ratio (x, 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 ry = SCM_COMPLEX_REAL (y);
double iy = SCM_COMPLEX_IMAG (y);
- if (ry <= iy)
+ if (fabs(ry) <= fabs(iy))
{
double t = ry / iy;
double d = iy * (1.0 + t * t);
else
{
SCM z;
- SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex),
- "complex"));
+ SCM_NEWSMOB (z, scm_tc16_complex,
+ scm_gc_malloc_pointerless (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, SCM imaginary),
- "Return a complex number constructed of the given @var{real} and\n"
- "@var{imaginary} parts.")
+ (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, imaginary, FUNC_NAME, &xy);
+ scm_two_doubles (real_part, imaginary_part, FUNC_NAME, &xy);
return scm_c_make_rectangular (xy.x, xy.y);
}
#undef FUNC_NAME
else if (SCM_BIGP (z))
return z;
else if (SCM_FRACTIONP (z))
- {
- scm_i_fraction_reduce (z);
- return SCM_FRACTION_NUMERATOR (z);
- }
+ return SCM_FRACTION_NUMERATOR (z);
else if (SCM_REALP (z))
return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z)));
else
else if (SCM_BIGP (z))
return SCM_I_MAKINUM (1);
else if (SCM_FRACTIONP (z))
- {
- scm_i_fraction_reduce (z);
- return SCM_FRACTION_DENOMINATOR (z);
- }
+ return SCM_FRACTION_DENOMINATOR (z);
else if (SCM_REALP (z))
return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z)));
else
#undef FUNC_NAME
SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0,
- (SCM x, SCM err),
- "Return an exact number that is within @var{err} of @var{x}.")
+ (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))
converges after less than a dozen iterations.
*/
- err = scm_abs (err);
+ eps = scm_abs (eps);
while (++i < 1000000)
{
a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */
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))),
- err))) /* abs(x-a/b) <= err */
+ 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 (err)))
+ || scm_is_false (scm_exact_p (eps)))
return scm_exact_to_inexact (res);
else
return res;
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
#endif
+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)
{
else if (SCM_REALP (val))
return SCM_REAL_VALUE (val);
else
- scm_wrong_type_arg (NULL, 0, val);
+ scm_wrong_type_arg_msg (NULL, 0, val, "real number");
}
SCM
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 ()
{
HCoop / bpt / guile.git / blobdiff