-/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003 Free Software Foundation, Inc.
+/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004 Free Software Foundation, Inc.
*
* Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories
* and Bellcore. See scm_divide.
* All objects satisfying SCM_BIGP() are too large to fit in a fixnum.
* If an object satisfies integer?, it's either an inum, a bignum, or a real.
* If floor (r) == r, r is an int, and mpz_set_d will DTRT.
+ * All objects satisfying SCM_FRACTIONP are never an integer.
*/
/* TODO:
#include <ctype.h>
#include <string.h>
#include <gmp.h>
+
#include "libguile/_scm.h"
#include "libguile/feature.h"
#include "libguile/ports.h"
#include "libguile/numbers.h"
#include "libguile/deprecation.h"
+#include "libguile/eq.h"
+
\f
/*
#define SCM_I_NUMTAG(x) \
(SCM_INUMP(x) ? SCM_I_NUMTAG_INUM \
: (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \
- : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_smob) ? SCM_TYP16(x) \
+ : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \
: SCM_I_NUMTAG_NOTNUM)))
*/
+/* the macro above will not work as is with fractions */
#define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0)
#define xmpz_cmp_d(z, d) mpz_cmp_d (z, d)
#endif
+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
+}
+
\f
-static SCM abs_most_negative_fixnum;
static mpz_t z_negative_one;
\f
-static const char s_bignum[] = "bignum";
-
-SCM_C_INLINE SCM
+SCM_C_INLINE_KEYWORD SCM
scm_i_mkbig ()
{
/* Return a newly created bignum. */
return z;
}
-SCM_C_INLINE static SCM
+SCM_C_INLINE_KEYWORD static SCM
scm_i_clonebig (SCM src_big, int same_sign_p)
{
/* Copy src_big's value, negate it if same_sign_p is false, and return. */
return z;
}
-SCM_C_INLINE int
+SCM_C_INLINE_KEYWORD int
scm_i_bigcmp (SCM x, SCM y)
{
/* Return neg if x < y, pos if x > y, and 0 if x == y */
return result;
}
-SCM_C_INLINE SCM
+SCM_C_INLINE_KEYWORD SCM
scm_i_dbl2big (double d)
{
/* results are only defined if d is an integer */
return z;
}
-SCM_C_INLINE double
+/* Convert a integer in double representation to a SCM number. */
+
+SCM_C_INLINE_KEYWORD SCM
+scm_i_dbl2num (double u)
+{
+ /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both
+ powers of 2, so there's no rounding when making "double" values
+ from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could
+ get rounded on a 64-bit machine, hence the "+1".
+
+ The use of floor() to force to an integer value ensures we get a
+ "numerically closest" value without depending on how a
+ double->long cast or how mpz_set_d will round. For reference,
+ double->long probably follows the hardware rounding mode,
+ mpz_set_d truncates towards zero. */
+
+ /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not
+ representable as a double? */
+
+ if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1)
+ && u >= (double) SCM_MOST_NEGATIVE_FIXNUM)
+ return SCM_MAKINUM ((long) u);
+ else
+ return scm_i_dbl2big (u);
+}
+
+/* scm_i_big2dbl() rounds to the closest representable double, in accordance
+ with R5RS exact->inexact.
+
+ The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits
+ (ie. it truncates towards zero), then adjust to get the closest double by
+ examining the next lower bit and adding 1 if necessary.
+
+ Note that bignums exactly half way between representable doubles are
+ rounded to the next higher absolute value (ie. away from zero). This
+ seems like an adequate interpretation of R5RS "numerically closest", and
+ it's easier and faster than a full "nearest-even" style.
+
+ The bit test is done on the absolute value of the mpz_t, which means we
+ must use mpz_getlimbn. mpz_tstbit is not right, it treats negatives as
+ twos complement.
+
+ Prior to GMP 4.2, the rounding done by mpz_get_d was unspecified. It
+ happened to follow the hardware rounding mode, but on the absolute value
+ of its operand. This is not what we want, so we put the high
+ DBL_MANT_DIG bits into a temporary. This extra init/clear is a slowdown,
+ but doesn't matter too much since it's only for older GMP. */
+
+double
scm_i_big2dbl (SCM b)
{
- double result = mpz_get_d (SCM_I_BIG_MPZ (b));
+ double result;
+ size_t bits;
+
+ bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2);
+
+#if __GNU_MP_VERSION < 4 \
+ || (__GNU_MP_VERSION == 4 && __GNU_MP_VERSION_MINOR < 2)
+ {
+ /* GMP prior to 4.2, force truncate towards zero */
+ mpz_t tmp;
+ if (bits > DBL_MANT_DIG)
+ {
+ size_t shift = bits - DBL_MANT_DIG;
+ mpz_init2 (tmp, DBL_MANT_DIG);
+ mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift);
+ result = ldexp (mpz_get_d (tmp), shift);
+ mpz_clear (tmp);
+ }
+ else
+ {
+ result = mpz_get_d (SCM_I_BIG_MPZ (b));
+ }
+ }
+#else
+ /* GMP 4.2 and up */
+ result = mpz_get_d (SCM_I_BIG_MPZ (b));
+#endif
+
+ if (bits > DBL_MANT_DIG)
+ {
+ unsigned long pos = bits - DBL_MANT_DIG - 1;
+ /* test bit number "pos" in absolute value */
+ if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS)
+ & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS)))
+ {
+ result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1);
+ }
+ }
+
scm_remember_upto_here_1 (b);
return result;
}
-SCM_C_INLINE SCM
+SCM_C_INLINE_KEYWORD SCM
scm_i_normbig (SCM b)
{
/* convert a big back to a fixnum if it'll fit */
return b;
}
+static SCM_C_INLINE_KEYWORD SCM
+scm_i_mpz2num (mpz_t b)
+{
+ /* convert a mpz number to a SCM number. */
+ if (mpz_fits_slong_p (b))
+ {
+ long val = mpz_get_si (b);
+ if (SCM_FIXABLE (val))
+ return SCM_MAKINUM (val);
+ }
+
+ {
+ SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0);
+ mpz_init_set (SCM_I_BIG_MPZ (z), b);
+ return z;
+ }
+}
+
+/* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */
+static SCM scm_divide2real (SCM x, SCM y);
+
+SCM
+scm_make_ratio (SCM numerator, SCM denominator)
+#define FUNC_NAME "make-ratio"
+{
+ /* First make sure the arguments are proper.
+ */
+ if (SCM_INUMP (denominator))
+ {
+ if (SCM_EQ_P (denominator, SCM_INUM0))
+ scm_num_overflow ("make-ratio");
+ if (SCM_EQ_P (denominator, SCM_MAKINUM(1)))
+ return numerator;
+ }
+ else
+ {
+ if (!(SCM_BIGP(denominator)))
+ SCM_WRONG_TYPE_ARG (2, denominator);
+ }
+ if (!SCM_INUMP (numerator) && !SCM_BIGP (numerator))
+ SCM_WRONG_TYPE_ARG (1, numerator);
+
+ /* Then flip signs so that the denominator is positive.
+ */
+ if (SCM_NFALSEP (scm_negative_p (denominator)))
+ {
+ numerator = scm_difference (numerator, SCM_UNDEFINED);
+ denominator = scm_difference (denominator, SCM_UNDEFINED);
+ }
+
+ /* Now consider for each of the four fixnum/bignum combinations
+ whether the rational number is really an integer.
+ */
+ if (SCM_INUMP (numerator))
+ {
+ long x = SCM_INUM (numerator);
+ if (SCM_EQ_P (numerator, SCM_INUM0))
+ return SCM_INUM0;
+ if (SCM_INUMP (denominator))
+ {
+ long y;
+ y = SCM_INUM (denominator);
+ if (x == y)
+ return SCM_MAKINUM(1);
+ if ((x % y) == 0)
+ return SCM_MAKINUM (x / y);
+ }
+ else
+ {
+ /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative
+ of that value for the denominator, as a bignum. Apart from
+ that case, abs(bignum) > abs(inum) so inum/bignum is not an
+ integer. */
+ if (x == SCM_MOST_NEGATIVE_FIXNUM
+ && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator),
+ - SCM_MOST_NEGATIVE_FIXNUM) == 0)
+ return SCM_MAKINUM(-1);
+ }
+ }
+ else if (SCM_BIGP (numerator))
+ {
+ if (SCM_INUMP (denominator))
+ {
+ long yy = SCM_INUM (denominator);
+ if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy))
+ return scm_divide (numerator, denominator);
+ }
+ else
+ {
+ if (SCM_EQ_P (numerator, denominator))
+ return SCM_MAKINUM(1);
+ if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator),
+ SCM_I_BIG_MPZ (denominator)))
+ return scm_divide(numerator, denominator);
+ }
+ }
+
+ /* No, it's a proper fraction.
+ */
+ return scm_double_cell (scm_tc16_fraction,
+ SCM_UNPACK (numerator),
+ SCM_UNPACK (denominator), 0);
+}
+#undef FUNC_NAME
+
+static void scm_i_fraction_reduce (SCM z)
+{
+ if (!(SCM_FRACTION_REDUCED (z)))
+ {
+ SCM divisor;
+ divisor = scm_gcd (SCM_FRACTION_NUMERATOR (z), SCM_FRACTION_DENOMINATOR (z));
+ if (!(SCM_EQ_P (divisor, SCM_MAKINUM(1))))
+ {
+ /* is this safe? */
+ SCM_FRACTION_SET_NUMERATOR (z, scm_divide (SCM_FRACTION_NUMERATOR (z), divisor));
+ SCM_FRACTION_SET_DENOMINATOR (z, scm_divide (SCM_FRACTION_DENOMINATOR (z), divisor));
+ }
+ SCM_FRACTION_REDUCED_SET (z);
+ }
+}
+
+double
+scm_i_fraction2double (SCM z)
+{
+ return scm_num2dbl (scm_divide2real (SCM_FRACTION_NUMERATOR (z),
+ SCM_FRACTION_DENOMINATOR (z)),
+ "fraction2real");
+}
+
SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0,
(SCM x),
"Return @code{#t} if @var{x} is an exact number, @code{#f}\n"
return SCM_BOOL_T;
if (SCM_BIGP (x))
return SCM_BOOL_T;
- return SCM_BOOL_F;
+ 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
}
else if (!SCM_FALSEP (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);
}
}
else if (!SCM_FALSEP (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
-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
-}
-
SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0,
(SCM n),
"Return @code{#t} if @var{n} is infinite, @code{#f}\n"
/* Some version of gcc on some old version of Linux used to crash when
trying to make Inf and NaN. */
-#if defined (SCO)
- double tmp = 1.0;
- guile_Inf = 1.0 / (tmp - tmp);
-#elif defined (__alpha__) && ! defined (linux)
+#ifdef INFINITY
+ /* C99 INFINITY, when available.
+ FIXME: The standard allows for INFINITY to be something that overflows
+ at compile time. We ought to have a configure test to check for that
+ before trying to use it. (But in practice we believe this is not a
+ problem on any system guile is likely to target.) */
+ guile_Inf = INFINITY;
+#elif HAVE_DINFINITY
+ /* OSF */
extern unsigned int DINFINITY[2];
guile_Inf = (*(X_CAST(double *, DINFINITY)));
#else
#if defined (HAVE_ISNAN)
-#if defined (__alpha__) && ! defined (linux)
+#ifdef NAN
+ /* C99 NAN, when available */
+ guile_NaN = NAN;
+#elif HAVE_DQNAN
+ /* OSF */
extern unsigned int DQNAN[2];
guile_NaN = (*(X_CAST(double *, DQNAN)));
#else
return x;
}
else if (SCM_REALP (x))
- return scm_make_real (fabs (SCM_REAL_VALUE (x)));
+ {
+ /* note that if x is a NaN then xx<0 is false so we return x unchanged */
+ double xx = SCM_REAL_VALUE (x);
+ if (xx < 0.0)
+ return scm_make_real (-xx);
+ else
+ return x;
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (x))))
+ return x;
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED),
+ SCM_FRACTION_DENOMINATOR (x));
+ }
else
SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs);
}
else if (SCM_BIGP (y))
{
if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM)
- && (scm_i_bigcmp (abs_most_negative_fixnum, y) == 0))
- /* Special case: x == fixnum-min && y == abs (fixnum-min) */
- return SCM_MAKINUM (-1);
+ && (mpz_cmp_ui (SCM_I_BIG_MPZ (y),
+ - SCM_MOST_NEGATIVE_FIXNUM) == 0))
+ {
+ /* Special case: x == fixnum-min && y == abs (fixnum-min) */
+ scm_remember_upto_here_1 (y);
+ return SCM_MAKINUM (-1);
+ }
else
return SCM_MAKINUM (0);
}
else if (SCM_BIGP (y))
{
if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM)
- && (scm_i_bigcmp (abs_most_negative_fixnum, y) == 0))
- /* Special case: x == fixnum-min && y == abs (fixnum-min) */
- return SCM_MAKINUM (0);
+ && (mpz_cmp_ui (SCM_I_BIG_MPZ (y),
+ - SCM_MOST_NEGATIVE_FIXNUM) == 0))
+ {
+ /* Special case: x == fixnum-min && y == abs (fixnum-min) */
+ scm_remember_upto_here_1 (y);
+ return SCM_MAKINUM (0);
+ }
else
return x;
}
else if (SCM_BIGP (y))
{
int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
-
- if (sgn_y == 0)
- scm_num_overflow (s_modulo);
- else
{
mpz_t z_x;
SCM result;
}
else if (SCM_BIGP (y))
{
- int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y));
- if (sgn_y == 0)
- scm_num_overflow (s_modulo);
- else
{
SCM result = scm_i_mkbig ();
int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y));
"@lisp\n"
"(logand) @result{} -1\n"
"(logand 7) @result{} 7\n"
- "(logand #b111 #b011 #\b001) @result{} 1\n"
+ "(logand #b111 #b011 #b001) @result{} 1\n"
"@end lisp")
#define FUNC_NAME s_scm_logand
{
SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0,
(SCM n),
- "Return the integer which is the 2s-complement of the integer\n"
+ "Return the integer which is the ones-complement of the integer\n"
"argument.\n"
"\n"
"@lisp\n"
"@end lisp")
#define FUNC_NAME s_scm_lognot
{
- return scm_difference (SCM_MAKINUM (-1L), n);
+ if (SCM_INUMP (n)) {
+ /* No overflow here, just need to toggle all the bits making up the inum.
+ Enhancement: No need to strip the tag and add it back, could just xor
+ a block of 1 bits, if that worked with the various debug versions of
+ the SCM typedef. */
+ return SCM_MAKINUM (~ SCM_INUM (n));
+
+ } else if (SCM_BIGP (n)) {
+ SCM result = scm_i_mkbig ();
+ mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n));
+ scm_remember_upto_here_1 (n);
+ return result;
+
+ } else {
+ SCM_WRONG_TYPE_ARG (SCM_ARG1, n);
+ }
+}
+#undef FUNC_NAME
+
+/* returns 0 if IN is not an integer. OUT must already be
+ initialized. */
+static int
+coerce_to_big (SCM in, mpz_t out)
+{
+ if (SCM_BIGP (in))
+ mpz_set (out, SCM_I_BIG_MPZ (in));
+ else if (SCM_INUMP (in))
+ mpz_set_si (out, SCM_INUM (in));
+ else
+ return 0;
+
+ return 1;
+}
+
+SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0,
+ (SCM n, SCM k, SCM m),
+ "Return @var{n} raised to the integer exponent\n"
+ "@var{k}, modulo @var{m}.\n"
+ "\n"
+ "@lisp\n"
+ "(modulo-expt 2 3 5)\n"
+ " @result{} 3\n"
+ "@end lisp")
+#define FUNC_NAME s_scm_modulo_expt
+{
+ mpz_t n_tmp;
+ mpz_t k_tmp;
+ mpz_t m_tmp;
+
+ /* There are two classes of error we might encounter --
+ 1) Math errors, which we'll report by calling scm_num_overflow,
+ and
+ 2) wrong-type errors, which of course we'll report by calling
+ SCM_WRONG_TYPE_ARG.
+ We don't report those errors immediately, however; instead we do
+ some cleanup first. These variables tell us which error (if
+ any) we should report after cleaning up.
+ */
+ int report_overflow = 0;
+
+ int position_of_wrong_type = 0;
+ SCM value_of_wrong_type = SCM_INUM0;
+
+ SCM result = SCM_UNDEFINED;
+
+ mpz_init (n_tmp);
+ mpz_init (k_tmp);
+ mpz_init (m_tmp);
+
+ if (SCM_EQ_P (m, SCM_INUM0))
+ {
+ report_overflow = 1;
+ goto cleanup;
+ }
+
+ if (!coerce_to_big (n, n_tmp))
+ {
+ value_of_wrong_type = n;
+ position_of_wrong_type = 1;
+ goto cleanup;
+ }
+
+ if (!coerce_to_big (k, k_tmp))
+ {
+ value_of_wrong_type = k;
+ position_of_wrong_type = 2;
+ goto cleanup;
+ }
+
+ if (!coerce_to_big (m, m_tmp))
+ {
+ value_of_wrong_type = m;
+ position_of_wrong_type = 3;
+ goto cleanup;
+ }
+
+ /* if the exponent K is negative, and we simply call mpz_powm, we
+ will get a divide-by-zero exception when an inverse 1/n mod m
+ doesn't exist (or is not unique). Since exceptions are hard to
+ handle, we'll attempt the inversion "by hand" -- that way, we get
+ a simple failure code, which is easy to handle. */
+
+ if (-1 == mpz_sgn (k_tmp))
+ {
+ if (!mpz_invert (n_tmp, n_tmp, m_tmp))
+ {
+ report_overflow = 1;
+ goto cleanup;
+ }
+ mpz_neg (k_tmp, k_tmp);
+ }
+
+ result = scm_i_mkbig ();
+ mpz_powm (SCM_I_BIG_MPZ (result),
+ n_tmp,
+ k_tmp,
+ m_tmp);
+
+ if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)
+ mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp);
+
+ cleanup:
+ mpz_clear (m_tmp);
+ mpz_clear (k_tmp);
+ mpz_clear (n_tmp);
+
+ if (report_overflow)
+ scm_num_overflow (FUNC_NAME);
+
+ if (position_of_wrong_type)
+ SCM_WRONG_TYPE_ARG (position_of_wrong_type,
+ value_of_wrong_type);
+
+ return scm_i_normbig (result);
}
#undef FUNC_NAME
else if (SCM_BIGP (k))
{
z_i2 = scm_i_clonebig (k, 1);
- mpz_init_set (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (k));
scm_remember_upto_here_1 (k);
i2_is_big = 1;
}
if ((r > SCM_MOST_POSITIVE_FIXNUM) || (r < SCM_MOST_NEGATIVE_FIXNUM))
{
z_i2 = scm_i_mkbig ();
- mpz_init_set_d (SCM_I_BIG_MPZ (z_i2), r);
+ mpz_set_d (SCM_I_BIG_MPZ (z_i2), r);
i2_is_big = 1;
}
else
{
if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0)
{
- mpz_clear (SCM_I_BIG_MPZ (z_i2));
return acc;
}
if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0)
{
- mpz_clear (SCM_I_BIG_MPZ (z_i2));
return scm_product (acc, n);
}
if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0))
SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
(SCM n, SCM cnt),
- "The function ash performs an arithmetic shift left by @var{cnt}\n"
- "bits (or shift right, if @var{cnt} is negative). 'Arithmetic'\n"
- "means, that the function does not guarantee to keep the bit\n"
- "structure of @var{n}, but rather guarantees that the result\n"
- "will always be rounded towards minus infinity. Therefore, the\n"
- "results of ash and a corresponding bitwise shift will differ if\n"
- "@var{n} is negative.\n"
+ "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n"
+ "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n"
+ "\n"
+ "This is effectively a multiplication by 2^@var{cnt}}, and when\n"
+ "@var{cnt} is negative it's a division, rounded towards negative\n"
+ "infinity. (Note that this is not the same rounding as\n"
+ "@code{quotient} does.)\n"
"\n"
- "Formally, the function returns an integer equivalent to\n"
- "@code{(inexact->exact (floor (* @var{n} (expt 2 @var{cnt}))))}.\n"
+ "With @var{n} viewed as an infinite precision twos complement,\n"
+ "@code{ash} means a left shift introducing zero bits, or a right\n"
+ "shift dropping bits.\n"
"\n"
"@lisp\n"
"(number->string (ash #b1 3) 2) @result{} \"1000\"\n"
"(number->string (ash #b1010 -1) 2) @result{} \"101\"\n"
+ "\n"
+ ";; -23 is bits ...11101001, -6 is bits ...111010\n"
+ "(ash -23 -2) @result{} -6\n"
"@end lisp")
#define FUNC_NAME s_scm_ash
{
*/
SCM div = scm_integer_expt (SCM_MAKINUM (2),
SCM_MAKINUM (-bits_to_shift));
+
+ /* scm_quotient assumes its arguments are integers, but it's legal to (ash 1/2 -1) */
if (SCM_FALSEP (scm_negative_p (n)))
return scm_quotient (n, div);
else
#undef FUNC_NAME
+#define MIN(x,y) ((x) < (y) ? (x) : (y))
+
SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0,
(SCM n, SCM start, SCM end),
"Return the integer composed of the @var{start} (inclusive)\n"
"@end lisp")
#define FUNC_NAME s_scm_bit_extract
{
- unsigned long int istart, iend;
+ unsigned long int istart, iend, bits;
SCM_VALIDATE_INUM_MIN_COPY (2, start,0, istart);
SCM_VALIDATE_INUM_MIN_COPY (3, end, 0, iend);
SCM_ASSERT_RANGE (3, end, (iend >= istart));
+ /* how many bits to keep */
+ bits = iend - istart;
+
if (SCM_INUMP (n))
{
long int in = SCM_INUM (n);
- unsigned long int bits = iend - istart;
+
+ /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to
+ SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in".
+ FIXME: This shift relies on signed right shifts being arithmetic,
+ which is not guaranteed by C99. */
+ in >>= MIN (istart, SCM_I_FIXNUM_BIT-1);
if (in < 0 && bits >= SCM_I_FIXNUM_BIT)
{
/* Since we emulate two's complement encoded numbers, this
* special case requires us to produce a result that has
- * more bits than can be stored in a fixnum. Thus, we fall
- * back to the more general algorithm that is used for
- * bignums.
+ * more bits than can be stored in a fixnum.
*/
- goto generalcase;
+ SCM result = scm_i_long2big (in);
+ mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result),
+ bits);
+ return result;
}
- if (istart < SCM_I_FIXNUM_BIT)
- {
- in = in >> istart;
- if (bits < SCM_I_FIXNUM_BIT)
- return SCM_MAKINUM (in & ((1L << bits) - 1));
- else /* we know: in >= 0 */
- return SCM_MAKINUM (in);
- }
- else if (in < 0)
- return SCM_MAKINUM (-1L & ((1L << bits) - 1));
- else
- return SCM_MAKINUM (0);
+ /* mask down to requisite bits */
+ bits = MIN (bits, SCM_I_FIXNUM_BIT);
+ return SCM_MAKINUM (in & ((1L << bits) - 1));
}
else if (SCM_BIGP (n))
{
- generalcase:
- {
- SCM num1 = SCM_MAKINUM (1L);
- SCM num2 = SCM_MAKINUM (2L);
- SCM bits = SCM_MAKINUM (iend - istart);
- SCM mask = scm_difference (scm_integer_expt (num2, bits), num1);
- return scm_logand (mask, scm_ash (n, SCM_MAKINUM (-istart)));
- }
+ SCM result;
+ if (bits == 1)
+ {
+ result = SCM_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart));
+ }
+ else
+ {
+ /* ENHANCE-ME: It'd be nice not to allocate a new bignum when
+ bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get
+ such bits into a ulong. */
+ result = scm_i_mkbig ();
+ mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart);
+ mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits);
+ result = scm_i_normbig (result);
+ }
+ scm_remember_upto_here_1 (n);
+ return result;
}
else
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
};
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"
scm_remember_upto_here_1 (n);
return scm_take0str (str);
}
+ else if (SCM_FRACTIONP (n))
+ {
+ scm_i_fraction_reduce (n);
+ return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix),
+ scm_mem2string ("/", 1),
+ scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix)));
+ }
else if (SCM_INEXACTP (n))
{
char num_buf [FLOBUFLEN];
int
scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
+
{
char num_buf[FLOBUFLEN];
scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port);
return !0;
}
+int
+scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
+{
+ SCM str;
+ scm_i_fraction_reduce (sexp);
+ str = scm_number_to_string (sexp, SCM_UNDEFINED);
+ scm_lfwrite (SCM_STRING_CHARS (str), SCM_STRING_LENGTH (str), port);
+ scm_remember_upto_here_1 (str);
+ return !0;
+}
+
int
scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED)
{
if (sign == 1)
result = scm_product (result, e);
else
- result = scm_divide (result, e);
+ result = scm_divide2real (result, e);
/* We've seen an exponent, thus the value is implicitly inexact. */
x = INEXACT;
{
enum t_exactness x = EXACT;
- /* Cobble up the fraction. We might want to set the NaN's
- mantissa from it. */
+ /* Cobble up the fractional part. We might want to set the
+ NaN's mantissa from it. */
idx += 4;
mem2uinteger (mem, len, &idx, 10, &x);
*p_idx = idx;
if (SCM_FALSEP (divisor))
return SCM_BOOL_F;
- result = scm_divide (uinteger, divisor);
+ /* both are int/big here, I assume */
+ result = scm_make_ratio (uinteger, divisor);
}
else if (radix == 10)
{
{
case EXACT:
if (SCM_INEXACTP (result))
- /* FIXME: This may change the value. */
return scm_inexact_to_exact (result);
else
return result;
SCM_VALIDATE_STRING (1, string);
SCM_VALIDATE_INUM_MIN_DEF_COPY (2, radix,2,10, base);
answer = scm_i_mem2number (SCM_STRING_CHARS (string),
- SCM_STRING_LENGTH (string),
- base);
+ SCM_STRING_LENGTH (string),
+ base);
return scm_return_first (answer, string);
}
#undef FUNC_NAME
else
{
SCM z;
- SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (2*sizeof (double),
+ SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex),
"complex"));
SCM_COMPLEX_REAL (z) = x;
SCM_COMPLEX_IMAG (z) = y;
SCM
scm_bigequal (SCM x, SCM y)
{
- int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (x));
+ int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y));
scm_remember_upto_here_2 (x, y);
return SCM_BOOL (0 == result);
}
&& SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y));
}
+SCM
+scm_i_fraction_equalp (SCM x, SCM y)
+{
+ scm_i_fraction_reduce (x);
+ scm_i_fraction_reduce (y);
+ if (SCM_FALSEP (scm_equal_p (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_NUMERATOR (y)))
+ || SCM_FALSEP (scm_equal_p (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_DENOMINATOR (y))))
+ return SCM_BOOL_F;
+ else
+ return SCM_BOOL_T;
+}
SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p);
#undef FUNC_NAME
-SCM_REGISTER_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p);
-/* "Return @code{#t} if @var{x} is a real number, @code{#f} else.\n"
- * "Note that the sets of integer and rational values form a subset\n"
- * "of the set of real numbers, i. e. the predicate will also\n"
- * "be fulfilled if @var{x} is an integer or a rational number."
- */
-SCM_DEFINE (scm_real_p, "rational?", 1, 0, 0,
+SCM_DEFINE (scm_real_p, "real?", 1, 0, 0,
+ (SCM x),
+ "Return @code{#t} if @var{x} is a real number, @code{#f}\n"
+ "otherwise. Note that the set of integer values forms a subset of\n"
+ "the set of real numbers, i. e. the predicate will also be\n"
+ "fulfilled if @var{x} is an integer number.")
+#define FUNC_NAME s_scm_real_p
+{
+ /* we can't represent irrational numbers. */
+ return scm_rational_p (x);
+}
+#undef FUNC_NAME
+
+SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0,
(SCM x),
"Return @code{#t} if @var{x} is a rational number, @code{#f}\n"
"otherwise. Note that the set of integer values forms a subset of\n"
"the set of rational numbers, i. e. the predicate will also be\n"
- "fulfilled if @var{x} is an integer number. Real numbers\n"
- "will also satisfy this predicate, because of their limited\n"
- "precision.")
-#define FUNC_NAME s_scm_real_p
+ "fulfilled if @var{x} is an integer number.")
+#define FUNC_NAME s_scm_rational_p
{
if (SCM_INUMP (x))
return SCM_BOOL_T;
else if (SCM_IMP (x))
return SCM_BOOL_F;
- else if (SCM_REALP (x))
- return SCM_BOOL_T;
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;
}
"else.")
#define FUNC_NAME s_scm_inexact_p
{
- return SCM_BOOL (SCM_INEXACTP (x));
+ if (SCM_INEXACTP (x))
+ return SCM_BOOL_T;
+ if (SCM_NUMBERP (x))
+ return SCM_BOOL_F;
+ SCM_WRONG_TYPE_ARG (1, x);
}
#undef FUNC_NAME
SCM
scm_num_eq_p (SCM x, SCM y)
{
+ again:
if (SCM_INUMP (x))
{
long xx = SCM_INUM (x);
else if (SCM_COMPLEXP (y))
return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y))
&& (0.0 == SCM_COMPLEX_IMAG (y)));
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL_F;
else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
scm_remember_upto_here_1 (x);
return SCM_BOOL (0 == cmp);
}
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL_F;
else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
else if (SCM_COMPLEXP (y))
return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y))
&& (0.0 == SCM_COMPLEX_IMAG (y)));
- else
+ else if (SCM_FRACTIONP (y))
+ {
+ double xx = SCM_REAL_VALUE (x);
+ if (xisnan (xx))
+ return SCM_BOOL_F;
+ if (xisinf (xx))
+ return SCM_BOOL (xx < 0.0);
+ x = scm_inexact_to_exact (x); /* with x as frac or int */
+ goto again;
+ }
+ else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
else if (SCM_COMPLEXP (x))
else if (SCM_COMPLEXP (y))
return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y))
&& (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)));
+ else if (SCM_FRACTIONP (y))
+ {
+ double xx;
+ if (SCM_COMPLEX_IMAG (x) != 0.0)
+ return SCM_BOOL_F;
+ xx = SCM_COMPLEX_REAL (x);
+ if (xisnan (xx))
+ return SCM_BOOL_F;
+ if (xisinf (xx))
+ return SCM_BOOL (xx < 0.0);
+ x = scm_inexact_to_exact (x); /* with x as frac or int */
+ goto again;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return SCM_BOOL_F;
+ else if (SCM_BIGP (y))
+ return SCM_BOOL_F;
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
+ if (xisnan (yy))
+ return SCM_BOOL_F;
+ if (xisinf (yy))
+ return SCM_BOOL (0.0 < yy);
+ y = scm_inexact_to_exact (y); /* with y as frac or int */
+ goto again;
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ double yy;
+ if (SCM_COMPLEX_IMAG (y) != 0.0)
+ return SCM_BOOL_F;
+ yy = SCM_COMPLEX_REAL (y);
+ if (xisnan (yy))
+ return SCM_BOOL_F;
+ if (xisinf (yy))
+ return SCM_BOOL (0.0 < yy);
+ y = scm_inexact_to_exact (y); /* with y as frac or int */
+ goto again;
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_i_fraction_equalp (x, y);
else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
}
+/* 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_INUMP (x))
{
long xx = SCM_INUM (x);
}
else if (SCM_REALP (y))
return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y));
+ else if (SCM_FRACTIONP (y))
+ {
+ /* "x < a/b" becomes "x*b < a" */
+ int_frac:
+ x = scm_product (x, SCM_FRACTION_DENOMINATOR (y));
+ y = SCM_FRACTION_NUMERATOR (y);
+ goto again;
+ }
else
SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
scm_remember_upto_here_1 (x);
return SCM_BOOL (cmp < 0);
}
+ else if (SCM_FRACTIONP (y))
+ goto int_frac;
else
SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
}
else if (SCM_REALP (y))
return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y));
+ else if (SCM_FRACTIONP (y))
+ {
+ double xx = SCM_REAL_VALUE (x);
+ if (xisnan (xx))
+ return SCM_BOOL_F;
+ if (xisinf (xx))
+ return SCM_BOOL (xx < 0.0);
+ x = scm_inexact_to_exact (x); /* with x as frac or int */
+ goto again;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y) || SCM_BIGP (y))
+ {
+ /* "a/b < y" becomes "a < y*b" */
+ y = scm_product (y, SCM_FRACTION_DENOMINATOR (x));
+ x = SCM_FRACTION_NUMERATOR (x);
+ goto again;
+ }
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
+ if (xisnan (yy))
+ return SCM_BOOL_F;
+ if (xisinf (yy))
+ return SCM_BOOL (0.0 < yy);
+ y = scm_inexact_to_exact (y); /* with y as frac or int */
+ goto again;
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ /* "a/b < c/d" becomes "a*d < c*b" */
+ SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (y));
+ SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y),
+ SCM_FRACTION_DENOMINATOR (x));
+ x = new_x;
+ y = new_y;
+ goto again;
+ }
else
SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
else if (SCM_COMPLEXP (z))
return SCM_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);
}
}
else if (SCM_REALP (x))
return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0);
+ else if (SCM_FRACTIONP (x))
+ return scm_positive_p (SCM_FRACTION_NUMERATOR (x));
else
SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p);
}
}
else if (SCM_REALP (x))
return SCM_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."
*/
{
if (SCM_UNBNDP (x))
SCM_WTA_DISPATCH_0 (g_max, s_max);
- else if (SCM_NUMBERP (x))
+ else if (SCM_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x))
return x;
else
SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max);
/* if y==NaN then ">" is false and we return NaN */
return (z > SCM_REAL_VALUE (y)) ? scm_make_real (z) : y;
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double z = xx;
+ return (z > scm_i_fraction2double (y)) ? x : y;
+ }
else
SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
}
}
else if (SCM_REALP (y))
{
- double yy = SCM_REAL_VALUE (y);
+ /* if y==NaN then xx>yy is false, so we return the NaN y */
+ double xx, yy;
+ big_real:
+ xx = scm_i_big2dbl (x);
+ yy = SCM_REAL_VALUE (y);
+ return (xx > yy ? scm_make_real (xx) : y);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
int cmp;
- if (xisnan (yy))
- return y;
cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy);
scm_remember_upto_here_1 (x);
return (cmp > 0) ? x : y;
}
else if (SCM_BIGP (y))
{
- double xx = SCM_REAL_VALUE (x);
- int cmp;
- if (xisnan (xx))
- return x;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx);
- scm_remember_upto_here_1 (y);
- return (cmp < 0) ? x : y;
+ SCM t = x; x = y; y = t;
+ goto big_real;
}
else if (SCM_REALP (y))
{
double xx = SCM_REAL_VALUE (x);
return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y;
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = SCM_REAL_VALUE (x);
+ return (xx < yy) ? scm_make_real (yy) : x;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ double z = SCM_INUM (y);
+ return (scm_i_fraction2double (x) < z) ? y : x;
+ }
+ else if (SCM_BIGP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx);
+ scm_remember_upto_here_1 (y);
+ return (cmp < 0) ? x : y;
+ }
+ else if (SCM_REALP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return (xx < SCM_REAL_VALUE (y)) ? y : scm_make_real (xx);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = scm_i_fraction2double (x);
+ return (xx < yy) ? y : x;
+ }
else
SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
}
{
if (SCM_UNBNDP (x))
SCM_WTA_DISPATCH_0 (g_min, s_min);
- else if (SCM_NUMBERP (x))
+ else if (SCM_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x))
return x;
else
SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min);
/* if y==NaN then "<" is false and we return NaN */
return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y;
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double z = xx;
+ return (z < scm_i_fraction2double (y)) ? x : y;
+ }
else
SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
}
}
else if (SCM_REALP (y))
{
- double yy = SCM_REAL_VALUE (y);
+ /* if y==NaN then xx<yy is false, so we return the NaN y */
+ double xx, yy;
+ big_real:
+ xx = scm_i_big2dbl (x);
+ yy = SCM_REAL_VALUE (y);
+ return (xx < yy ? scm_make_real (xx) : y);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
int cmp;
- if (xisnan (yy))
- return y;
cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy);
scm_remember_upto_here_1 (x);
return (cmp > 0) ? y : x;
}
else if (SCM_BIGP (y))
{
- double xx = SCM_REAL_VALUE (x);
- int cmp;
- if (xisnan (xx))
- return x;
- cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx);
- scm_remember_upto_here_1 (y);
- return (cmp < 0) ? y : x;
+ SCM t = x; x = y; y = t;
+ goto big_real;
}
else if (SCM_REALP (y))
{
double xx = SCM_REAL_VALUE (x);
return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y;
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = SCM_REAL_VALUE (x);
+ return (yy < xx) ? scm_make_real (yy) : x;
+ }
else
SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
}
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ double z = SCM_INUM (y);
+ return (scm_i_fraction2double (x) < z) ? x : y;
+ }
+ else if (SCM_BIGP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx);
+ scm_remember_upto_here_1 (y);
+ return (cmp < 0) ? y : x;
+ }
+ else if (SCM_REALP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return (SCM_REAL_VALUE (y) < xx) ? y : scm_make_real (xx);
+ }
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ double xx = scm_i_fraction2double (x);
+ return (xx < yy) ? x : y;
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
+ }
else
SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min);
}
return scm_make_complex (xx + SCM_COMPLEX_REAL (y),
SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y),
+ scm_product (x, SCM_FRACTION_DENOMINATOR (y))),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
} else if (SCM_BIGP (x))
scm_remember_upto_here_1 (x);
return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y),
+ scm_product (x, SCM_FRACTION_DENOMINATOR (y))),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y),
SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) + scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y),
SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y),
+ SCM_COMPLEX_IMAG (x));
+ else
+ SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x),
+ scm_product (y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x),
+ scm_product (y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_make_real (SCM_REAL_VALUE (y) + scm_i_fraction2double (x));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x),
+ SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ /* a/b + c/d = (ad + bc) / bd */
+ return scm_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)),
+ scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y)));
else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
else if (SCM_COMPLEXP (x))
return scm_make_complex (-SCM_COMPLEX_REAL (x),
-SCM_COMPLEX_IMAG (x));
+ else if (SCM_FRACTIONP (x))
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED),
+ SCM_FRACTION_DENOMINATOR (x));
else
SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference);
}
return scm_make_complex (xx - SCM_COMPLEX_REAL (y),
- SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ /* a - b/c = (ac - b) / c */
+ return scm_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
{
SCM result = scm_i_mkbig ();
- mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy);
+ 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))
scm_remember_upto_here_1 (x);
return scm_make_complex (real_part, - SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
else if (SCM_REALP (x))
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y),
-SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) - scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y),
SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_complex (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y),
+ SCM_COMPLEX_IMAG (x));
+ else
+ SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ /* a/b - c = (a - cb) / b */
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x),
+ scm_product(y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x),
+ scm_product(y, SCM_FRACTION_DENOMINATOR (x))),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_make_real (scm_i_fraction2double (x) - SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return scm_make_complex (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y),
+ -SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ /* a/b - c/d = (ad - bc) / bd */
+ return scm_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)),
+ scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y)));
else
SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
else if (SCM_COMPLEXP (y))
return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
xx * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
return scm_make_complex (z * SCM_COMPLEX_REAL (y),
z * SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y),
SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) * scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y)
+ SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y));
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ return scm_make_complex (yy * SCM_COMPLEX_REAL (x),
+ yy * SCM_COMPLEX_IMAG (x));
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_make_real (scm_i_fraction2double (x) * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
+ xx * SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a/b * c/d = ac / bd */
+ return scm_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_NUMERATOR (y)),
+ scm_product (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_DENOMINATOR (y)));
else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
}
else if (SCM_REALP (a))
return (SCM_REAL_VALUE (a));
+ else if (SCM_FRACTIONP (a))
+ return scm_i_fraction2double (a);
else
SCM_WRONG_TYPE_ARG (SCM_ARGn, a);
}
arguments. If called with one argument @var{z1}, 1/@var{z1} is
returned. */
#define FUNC_NAME s_divide
-SCM
-scm_divide (SCM x, SCM y)
+static SCM
+scm_i_divide (SCM x, SCM y, int inexact)
{
double a;
scm_num_overflow (s_divide);
#endif
else
- return scm_make_real (1.0 / (double) xx);
+ {
+ if (inexact)
+ return scm_make_real (1.0 / (double) xx);
+ else return scm_make_ratio (SCM_MAKINUM(1), x);
+ }
}
else if (SCM_BIGP (x))
- return scm_make_real (1.0 / scm_i_big2dbl (x));
+ {
+ if (inexact)
+ return scm_make_real (1.0 / scm_i_big2dbl (x));
+ else return scm_make_ratio (SCM_MAKINUM(1), x);
+ }
else if (SCM_REALP (x))
{
double xx = SCM_REAL_VALUE (x);
return scm_make_complex (1.0 / d, -t / d);
}
}
+ else if (SCM_FRACTIONP (x))
+ return scm_make_ratio (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_NUMERATOR (x));
else
SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide);
}
#endif
}
else if (xx % yy != 0)
- return scm_make_real ((double) xx / (double) yy);
+ {
+ if (inexact)
+ return scm_make_real ((double) xx / (double) yy);
+ else return scm_make_ratio (x, y);
+ }
else
{
long z = xx / yy;
}
}
else if (SCM_BIGP (y))
- return scm_make_real ((double) xx / scm_i_big2dbl (y));
+ {
+ if (inexact)
+ return scm_make_real ((double) xx / scm_i_big2dbl (y));
+ else return scm_make_ratio (x, y);
+ }
else if (SCM_REALP (y))
{
double yy = SCM_REAL_VALUE (y);
}
}
}
+ else if (SCM_FRACTIONP (y))
+ /* a / b/c = ac / b */
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y));
else
SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
}
return scm_i_normbig (result);
}
else
- return scm_make_real (scm_i_big2dbl (x) / (double) yy);
+ {
+ if (inexact)
+ return scm_make_real (scm_i_big2dbl (x) / (double) yy);
+ else return scm_make_ratio (x, y);
+ }
}
}
else if (SCM_BIGP (y))
}
else
{
- double dbx = mpz_get_d (SCM_I_BIG_MPZ (x));
- double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
- scm_remember_upto_here_2 (x, y);
- return scm_make_real (dbx / dby);
+ if (inexact)
+ {
+ double dbx = mpz_get_d (SCM_I_BIG_MPZ (x));
+ double dby = mpz_get_d (SCM_I_BIG_MPZ (y));
+ scm_remember_upto_here_2 (x, y);
+ return scm_make_real (dbx / dby);
+ }
+ else return scm_make_ratio (x, y);
}
}
}
a = scm_i_big2dbl (x);
goto complex_div;
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y));
else
SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
}
a = rx;
goto complex_div;
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (rx / scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
}
return scm_make_complex ((rx + ix * t) / d, (ix - rx * t) / d);
}
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ return scm_make_complex (rx / yy, ix / yy);
+ }
else
SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
}
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ {
+ long int yy = SCM_INUM (y);
+#ifndef ALLOW_DIVIDE_BY_EXACT_ZERO
+ if (yy == 0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ return scm_make_ratio (SCM_FRACTION_NUMERATOR (x),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), y));
+ }
+ else if (SCM_BIGP (y))
+ {
+ return scm_make_ratio (SCM_FRACTION_NUMERATOR (x),
+ scm_product (SCM_FRACTION_DENOMINATOR (x), y));
+ }
+ else if (SCM_REALP (y))
+ {
+ double yy = SCM_REAL_VALUE (y);
+#ifndef ALLOW_DIVIDE_BY_ZERO
+ if (yy == 0.0)
+ scm_num_overflow (s_divide);
+ else
+#endif
+ return scm_make_real (scm_i_fraction2double (x) / yy);
+ }
+ else if (SCM_COMPLEXP (y))
+ {
+ a = scm_i_fraction2double (x);
+ goto complex_div;
+ }
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)),
+ scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x)));
+ else
+ SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
+ }
else
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
*/
+/* XXX - eventually, we should remove this definition of scm_round and
+ rename scm_round_number to scm_round. Likewise for scm_truncate
+ and scm_truncate_number.
+ */
+
double
scm_truncate (double x)
{
return floor (x);
#endif
}
-SCM_GPROC1 (s_truncate, "truncate", scm_tc7_dsubr, (SCM (*)()) trunc, g_truncate);
-/* "Round the inexact number @var{x} towards zero."
- */
-
-SCM_GPROC1 (s_round, "round", scm_tc7_dsubr, (SCM (*)()) scm_round, g_round);
-/* "Round the inexact number @var{x}. If @var{x} is halfway between two\n"
- * "numbers, round towards even."
- */
double
scm_round (double x)
{
: result);
}
+SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards zero.")
+#define FUNC_NAME s_scm_truncate_number
+{
+ if (SCM_FALSEP (scm_negative_p (x)))
+ return scm_floor (x);
+ else
+ return scm_ceiling (x);
+}
+#undef FUNC_NAME
+
+static SCM exactly_one_half;
+
+SCM_DEFINE (scm_round_number, "round", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards the nearest integer. "
+ "When it is exactly halfway between two integers, "
+ "round towards the even one.")
+#define FUNC_NAME s_scm_round_number
+{
+ SCM plus_half = scm_sum (x, exactly_one_half);
+ SCM result = scm_floor (plus_half);
+ /* Adjust so that the scm_round is towards even. */
+ if (!SCM_FALSEP (scm_num_eq_p (plus_half, result))
+ && !SCM_FALSEP (scm_odd_p (result)))
+ return scm_difference (result, SCM_MAKINUM (1));
+ else
+ return result;
+}
+#undef FUNC_NAME
+
+SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards minus infinity.")
+#define FUNC_NAME s_scm_floor
+{
+ if (SCM_INUMP (x) || SCM_BIGP (x))
+ return x;
+ else if (SCM_REALP (x))
+ return scm_make_real (floor (SCM_REAL_VALUE (x)));
+ else if (SCM_FRACTIONP (x))
+ {
+ SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (x));
+ if (SCM_FALSEP (scm_negative_p (x)))
+ {
+ /* For positive x, rounding towards zero is correct. */
+ return q;
+ }
+ else
+ {
+ /* For negative x, we need to return q-1 unless x is an
+ integer. But fractions are never integer, per our
+ assumptions. */
+ return scm_difference (q, SCM_MAKINUM (1));
+ }
+ }
+ else
+ SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor);
+}
+#undef FUNC_NAME
+
+SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0,
+ (SCM x),
+ "Round the number @var{x} towards infinity.")
+#define FUNC_NAME s_scm_ceiling
+{
+ if (SCM_INUMP (x) || SCM_BIGP (x))
+ return x;
+ else if (SCM_REALP (x))
+ return scm_make_real (ceil (SCM_REAL_VALUE (x)));
+ else if (SCM_FRACTIONP (x))
+ {
+ SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_DENOMINATOR (x));
+ if (SCM_FALSEP (scm_positive_p (x)))
+ {
+ /* For negative x, rounding towards zero is correct. */
+ return q;
+ }
+ else
+ {
+ /* For positive x, we need to return q+1 unless x is an
+ integer. But fractions are never integer, per our
+ assumptions. */
+ return scm_sum (q, SCM_MAKINUM (1));
+ }
+ }
+ else
+ SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling);
+}
+#undef FUNC_NAME
-SCM_GPROC1 (s_i_floor, "floor", scm_tc7_dsubr, (SCM (*)()) floor, g_i_floor);
-/* "Round the number @var{x} towards minus infinity."
- */
-SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_dsubr, (SCM (*)()) ceil, g_i_ceil);
-/* "Round the number @var{x} towards infinity."
- */
SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt);
/* "Return the square root of the real number @var{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);
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);
}
return z;
else if (SCM_COMPLEXP (z))
return scm_make_real (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);
}
return scm_flo0;
else if (SCM_COMPLEXP (z))
return scm_make_real (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_INUMP (z))
+ return z;
+ else if (SCM_BIGP (z))
+ return z;
+ else if (SCM_FRACTIONP (z))
+ {
+ scm_i_fraction_reduce (z);
+ return SCM_FRACTION_NUMERATOR (z);
+ }
+ else if (SCM_REALP (z))
+ return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z)));
+ else
+ SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator);
+}
+
+
+SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator);
+/* "Return the denominator of the number @var{z}."
+ */
+SCM
+scm_denominator (SCM z)
+{
+ if (SCM_INUMP (z))
+ return SCM_MAKINUM (1);
+ else if (SCM_BIGP (z))
+ return SCM_MAKINUM (1);
+ else if (SCM_FRACTIONP (z))
+ {
+ scm_i_fraction_reduce (z);
+ return SCM_FRACTION_DENOMINATOR (z);
+ }
+ else if (SCM_REALP (z))
+ return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z)));
+ else
+ SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator);
+}
SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude);
/* "Return the magnitude of the number @var{z}. This is the same as\n"
return scm_make_real (fabs (SCM_REAL_VALUE (z)));
else if (SCM_COMPLEXP (z))
return scm_make_real (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z)));
+ else if (SCM_FRACTIONP (z))
+ {
+ if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (z))))
+ return z;
+ return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED),
+ SCM_FRACTION_DENOMINATOR (z));
+ }
else
SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude);
}
}
else if (SCM_COMPLEXP (z))
return scm_make_real (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z)));
+ else if (SCM_FRACTIONP (z))
+ {
+ if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (z))))
+ return scm_flo0;
+ else return scm_make_real (atan2 (0.0, -1.0));
+ }
else
SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle);
}
return scm_make_real ((double) SCM_INUM (z));
else if (SCM_BIGP (z))
return scm_make_real (scm_i_big2dbl (z));
+ else if (SCM_FRACTIONP (z))
+ return scm_make_real (scm_i_fraction2double (z));
else if (SCM_INEXACTP (z))
return z;
else
return z;
else if (SCM_REALP (z))
{
- double u = floor (SCM_REAL_VALUE (z) + 0.5);
- long lu = (long) u;
- if (SCM_FIXABLE (lu))
- return SCM_MAKINUM (lu);
- else if (!xisinf (u) && !xisnan (u))
- return scm_i_dbl2big (u);
+ if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z)))
+ SCM_OUT_OF_RANGE (1, z);
else
- scm_num_overflow (s_scm_inexact_to_exact);
+ {
+ mpq_t frac;
+ SCM q;
+
+ mpq_init (frac);
+ mpq_set_d (frac, SCM_REAL_VALUE (z));
+ q = scm_make_ratio (scm_i_mpz2num (mpq_numref (frac)),
+ scm_i_mpz2num (mpq_denref (frac)));
+
+ /* When scm_make_ratio throws, we leak the memory allocated
+ for frac...
+ */
+ mpq_clear (frac);
+ return q;
+ }
}
+ else if (SCM_FRACTIONP (z))
+ return z;
else
SCM_WRONG_TYPE_ARG (1, z);
}
#undef FUNC_NAME
+SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0,
+ (SCM x, SCM err),
+ "Return an exact number that is within @var{err} of @var{x}.")
+#define FUNC_NAME s_scm_rationalize
+{
+ if (SCM_INUMP (x))
+ return x;
+ else if (SCM_BIGP (x))
+ return x;
+ else if ((SCM_REALP (x)) || SCM_FRACTIONP (x))
+ {
+ /* Use continued fractions to find closest ratio. All
+ arithmetic is done with exact numbers.
+ */
+
+ SCM ex = scm_inexact_to_exact (x);
+ SCM int_part = scm_floor (ex);
+ SCM tt = SCM_MAKINUM (1);
+ SCM a1 = SCM_MAKINUM (0), a2 = SCM_MAKINUM (1), a = SCM_MAKINUM (0);
+ SCM b1 = SCM_MAKINUM (1), b2 = SCM_MAKINUM (0), b = SCM_MAKINUM (0);
+ SCM rx;
+ int i = 0;
+
+ if (!SCM_FALSEP (scm_num_eq_p (ex, int_part)))
+ return ex;
+
+ ex = scm_difference (ex, int_part); /* x = x-int_part */
+ rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */
+
+ /* We stop after a million iterations just to be absolutely sure
+ that we don't go into an infinite loop. The process normally
+ converges after less than a dozen iterations.
+ */
+
+ err = scm_abs (err);
+ while (++i < 1000000)
+ {
+ a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */
+ b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */
+ if (SCM_FALSEP (scm_zero_p (b)) && /* b != 0 */
+ SCM_FALSEP
+ (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))),
+ err))) /* abs(x-a/b) <= err */
+ {
+ SCM res = scm_sum (int_part, scm_divide (a, b));
+ if (SCM_FALSEP (scm_exact_p (x))
+ || SCM_FALSEP (scm_exact_p (err)))
+ return scm_exact_to_inexact (res);
+ else
+ return res;
+ }
+ rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */
+ SCM_UNDEFINED);
+ tt = scm_floor (rx); /* tt = floor (rx) */
+ a2 = a1;
+ b2 = b1;
+ a1 = a;
+ b1 = b;
+ }
+ scm_num_overflow (s_scm_rationalize);
+ }
+ else
+ SCM_WRONG_TYPE_ARG (1, x);
+}
+#undef FUNC_NAME
+
/* if you need to change this, change test-num2integral.c as well */
#if SCM_SIZEOF_LONG_LONG != 0
# ifndef LLONG_MAX
void
scm_init_numbers ()
{
- abs_most_negative_fixnum = scm_i_long2big (- SCM_MOST_NEGATIVE_FIXNUM);
- scm_permanent_object (abs_most_negative_fixnum);
-
mpz_init_set_si (z_negative_one, -1);
/* It may be possible to tune the performance of some algorithms by using
#ifdef GUILE_DEBUG
check_sanity ();
#endif
-
+
+ exactly_one_half = scm_permanent_object (scm_divide (SCM_MAKINUM (1),
+ SCM_MAKINUM (2)));
#include "libguile/numbers.x"
}
HCoop / bpt / guile.git / blobdiff