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authorMarius Vollmer <mvo@zagadka.de>2003-11-18 19:59:53 +0000
committerMarius Vollmer <mvo@zagadka.de>2003-11-18 19:59:53 +0000
commitf92e85f7352174c9fe0ac0e67e6c38cfce923300 (patch)
treebc52293ad0d0d1770d35bd58a118744a80e86957
parent9dd9857f77451a706052cae009d2fe7150373c5a (diff)
downloadguile-f92e85f7352174c9fe0ac0e67e6c38cfce923300.tar.gz
* print.c (scm_iprin1): Handle fractions.
* objects.h (scm_class_fraction): New. * objects.c (scm_class_fraction): New. (scm_class_of): Handle fractions. * hash.c (scm_hasher): Handle fractions. * numbers.c: New code for handling fraction all over the place. (scm_odd_p, scm_even_p): Handle inexact integers. (scm_rational_p): New function, same as scm_real_p. (scm_round_number, scm_truncate_number, scm_ceiling, scm_floor): New exact functions that replace the inexact 'dsubr' implementations. (scm_numerator, scm_denominator): New. * numbers.h (SCM_NUMP): Recognize fractions. (SCM_FRACTIONP, SCM_SLOPPY_FRACTIONP, SCM_FRACTION_NUMERATOR, SCM_FRACTION_DENOMINATOR, SCM_FRACTION_SET_NUMERATOR, SCM_FRACTION_SET_DENOMINATOR, SCM_FRACTION_REDUCED_BIT, SCM_FRACTION_REDUCED_SET, SCM_FRACTION_REDUCED_CLEAR, SCM_FRACTION_REDUCED): New. (scm_floor, scm_ceiling, scm_truncate_number, scm_round_number): New prototypes. (scm_make_ratio, scm_rationalize, scm_numerator, scm_denominator, scm_rational_p): New prototypes. (scm_i_dbl2num, scm_i_fraction2double, scm_i_fraction_equalp, scm_i_print_fraction): New prototypes. * goops.c (create_standard_classes): Create "<fraction>" class. * gc-mark.c (scm_gc_mark_dependencies): Handle fractions. * gc-card.c (scm_i_sweep_card): Include scm_tc16_fraction as a case in the switch, but do nothing for now. * eval.c (SCM_CEVAL, SCM_APPLY, call_dsubr_1): Convert fractions to doubles when calling 'dsubr' functions. * eq.c (scm_eqv_p, scm_equal_p): Handle fractions.
-rw-r--r--libguile/eq.c35
-rw-r--r--libguile/eval.c22
-rw-r--r--libguile/gc-card.c4
-rw-r--r--libguile/gc-mark.c6
-rw-r--r--libguile/goops.c2
-rw-r--r--libguile/hash.c1
-rw-r--r--libguile/numbers.c971
-rw-r--r--libguile/numbers.h34
-rw-r--r--libguile/objects.c4
-rw-r--r--libguile/objects.h1
-rw-r--r--libguile/print.c3
11 files changed, 993 insertions, 90 deletions
diff --git a/libguile/eq.c b/libguile/eq.c
index 06467c486..40d5d86ec 100644
--- a/libguile/eq.c
+++ b/libguile/eq.c
@@ -61,6 +61,7 @@ real_eqv (double x, double y)
return !memcmp (&x, &y, sizeof(double));
}
+#include <stdio.h>
SCM_PRIMITIVE_GENERIC_1 (scm_eqv_p, "eqv?", scm_tc7_rpsubr,
(SCM x, SCM y),
"The @code{eqv?} procedure defines a useful equivalence relation on objects.\n"
@@ -77,8 +78,14 @@ SCM_PRIMITIVE_GENERIC_1 (scm_eqv_p, "eqv?", scm_tc7_rpsubr,
if (SCM_IMP (y))
return SCM_BOOL_F;
/* this ensures that types and scm_length are the same. */
+
if (SCM_CELL_TYPE (x) != SCM_CELL_TYPE (y))
{
+ /* fractions use 0x10000 as a flag (at the suggestion of Marius Vollmer),
+ but this checks the entire type word, so fractions may be accidentally
+ flagged here as unequal. Perhaps I should use the 4th double_cell word?
+ */
+
/* treat mixes of real and complex types specially */
if (SCM_INEXACTP (x))
{
@@ -93,6 +100,9 @@ SCM_PRIMITIVE_GENERIC_1 (scm_eqv_p, "eqv?", scm_tc7_rpsubr,
SCM_REAL_VALUE (y))
&& SCM_COMPLEX_IMAG (x) == 0.0);
}
+
+ if (SCM_FRACTIONP (x) && SCM_FRACTIONP (y))
+ return scm_i_fraction_equalp (x, y);
return SCM_BOOL_F;
}
if (SCM_NUMP (x))
@@ -101,6 +111,8 @@ SCM_PRIMITIVE_GENERIC_1 (scm_eqv_p, "eqv?", scm_tc7_rpsubr,
return SCM_BOOL (scm_i_bigcmp (x, y) == 0);
} else if (SCM_REALP (x)) {
return SCM_BOOL (real_eqv (SCM_REAL_VALUE (x), SCM_REAL_VALUE (y)));
+ } else if (SCM_FRACTIONP (x)) {
+ return scm_i_fraction_equalp (x, y);
} else { /* complex */
return SCM_BOOL (real_eqv (SCM_COMPLEX_REAL (x),
SCM_COMPLEX_REAL (y))
@@ -149,7 +161,7 @@ SCM_PRIMITIVE_GENERIC_1 (scm_equal_p, "equal?", scm_tc7_rpsubr,
if (SCM_CELL_TYPE (x) != SCM_CELL_TYPE (y))
{
/* treat mixes of real and complex types specially */
- if (SCM_INEXACTP (x))
+ if (SCM_INEXACTP (x) && SCM_INEXACTP (y))
{
if (SCM_REALP (x))
return SCM_BOOL (SCM_COMPLEXP (y)
@@ -160,6 +172,25 @@ SCM_PRIMITIVE_GENERIC_1 (scm_equal_p, "equal?", scm_tc7_rpsubr,
&& SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)
&& SCM_COMPLEX_IMAG (x) == 0.0);
}
+
+ /* should we handle fractions here also? */
+ else if ((SCM_FRACTIONP (x)) && (SCM_INEXACTP (y)))
+ {
+ if (SCM_REALP (y))
+ return SCM_BOOL (scm_i_fraction2double (x) == SCM_REAL_VALUE (y));
+ else
+ return SCM_BOOL (SCM_COMPLEX_REAL (y) == scm_i_fraction2double (x)
+ && SCM_COMPLEX_IMAG (y) == 0.0);
+ }
+ else if ((SCM_FRACTIONP (y)) && (SCM_INEXACTP (x)))
+ {
+ if (SCM_REALP (x))
+ return SCM_BOOL (scm_i_fraction2double (y) == SCM_REAL_VALUE (x));
+ else
+ return SCM_BOOL (SCM_COMPLEX_REAL (x) == scm_i_fraction2double (y)
+ && SCM_COMPLEX_IMAG (x) == 0.0);
+ }
+
return SCM_BOOL_F;
}
switch (SCM_TYP7 (x))
@@ -175,6 +206,8 @@ SCM_PRIMITIVE_GENERIC_1 (scm_equal_p, "equal?", scm_tc7_rpsubr,
return scm_real_equalp (x, y);
case scm_tc16_complex:
return scm_complex_equalp (x, y);
+ case scm_tc16_fraction:
+ return scm_i_fraction_equalp (x, y);
}
case scm_tc7_vector:
case scm_tc7_wvect:
diff --git a/libguile/eval.c b/libguile/eval.c
index d6135b407..913fe6243 100644
--- a/libguile/eval.c
+++ b/libguile/eval.c
@@ -3856,7 +3856,11 @@ evapply: /* inputs: x, proc */
{
RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_big2dbl (arg1))));
}
- SCM_WTA_DISPATCH_1 (*SCM_SUBR_GENERIC (proc), arg1,
+ else if (SCM_FRACTIONP (arg1))
+ {
+ RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_fraction2double (arg1))));
+ }
+ SCM_WTA_DISPATCH_1 (*SCM_SUBR_GENERIC (proc), arg1,
SCM_ARG1, SCM_SYMBOL_CHARS (SCM_SNAME (proc)));
case scm_tc7_cxr:
{
@@ -4536,7 +4540,13 @@ tail:
RETURN (scm_make_real (SCM_DSUBRF (proc) (SCM_REAL_VALUE (arg1))));
}
else if (SCM_BIGP (arg1))
- RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_big2dbl (arg1))));
+ {
+ RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_big2dbl (arg1))));
+ }
+ else if (SCM_FRACTIONP (arg1))
+ {
+ RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_fraction2double (arg1))));
+ }
SCM_WTA_DISPATCH_1 (*SCM_SUBR_GENERIC (proc), arg1,
SCM_ARG1, SCM_SYMBOL_CHARS (SCM_SNAME (proc)));
case scm_tc7_cxr:
@@ -4882,7 +4892,13 @@ call_dsubr_1 (SCM proc, SCM arg1)
RETURN (scm_make_real (SCM_DSUBRF (proc) (SCM_REAL_VALUE (arg1))));
}
else if (SCM_BIGP (arg1))
- RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_big2dbl (arg1))));
+ {
+ RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_big2dbl (arg1))));
+ }
+ else if (SCM_FRACTIONP (arg1))
+ {
+ RETURN (scm_make_real (SCM_DSUBRF (proc) (scm_i_fraction2double (arg1))));
+ }
SCM_WTA_DISPATCH_1 (*SCM_SUBR_GENERIC (proc), arg1,
SCM_ARG1, SCM_SYMBOL_CHARS (SCM_SNAME (proc)));
}
diff --git a/libguile/gc-card.c b/libguile/gc-card.c
index 432ead5a9..7189927ec 100644
--- a/libguile/gc-card.c
+++ b/libguile/gc-card.c
@@ -186,6 +186,10 @@ scm_i_sweep_card (scm_t_cell * p, SCM *free_list, scm_t_heap_segment*seg)
scm_gc_free (SCM_COMPLEX_MEM (scmptr), sizeof (scm_t_complex),
"complex");
break;
+ case scm_tc16_fraction:
+ /* nothing to do here since the num/denum of a fraction
+ are proper SCM objects themselves. */
+ break;
}
break;
case scm_tc7_string:
diff --git a/libguile/gc-mark.c b/libguile/gc-mark.c
index 994d3aa88..10f1522e0 100644
--- a/libguile/gc-mark.c
+++ b/libguile/gc-mark.c
@@ -281,6 +281,12 @@ scm_gc_mark_dependencies (SCM p)
break;
case scm_tc7_number:
+ if (SCM_TYP16 (ptr) == scm_tc16_fraction)
+ {
+ scm_gc_mark (SCM_CELL_OBJECT_1 (ptr));
+ ptr = SCM_CELL_OBJECT_2 (ptr);
+ goto gc_mark_loop;
+ }
break;
case scm_tc7_wvect:
diff --git a/libguile/goops.c b/libguile/goops.c
index cccdf205a..ea09366ad 100644
--- a/libguile/goops.c
+++ b/libguile/goops.c
@@ -2406,6 +2406,8 @@ create_standard_classes (void)
scm_class_class, scm_class_complex, SCM_EOL);
make_stdcls (&scm_class_integer, "<integer>",
scm_class_class, scm_class_real, SCM_EOL);
+ make_stdcls (&scm_class_fraction, "<fraction>",
+ scm_class_class, scm_class_real, SCM_EOL);
make_stdcls (&scm_class_keyword, "<keyword>",
scm_class_class, scm_class_top, SCM_EOL);
make_stdcls (&scm_class_unknown, "<unknown>",
diff --git a/libguile/hash.c b/libguile/hash.c
index 37ff07797..4294556ba 100644
--- a/libguile/hash.c
+++ b/libguile/hash.c
@@ -103,6 +103,7 @@ scm_hasher(SCM obj, unsigned long n, size_t d)
}
/* Fall through */
case scm_tc16_complex:
+ case scm_tc16_fraction:
obj = scm_number_to_string (obj, SCM_MAKINUM (10));
/* Fall through */
}
diff --git a/libguile/numbers.c b/libguile/numbers.c
index d36194f9e..311caf791 100644
--- a/libguile/numbers.c
+++ b/libguile/numbers.c
@@ -25,6 +25,7 @@
* 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:
@@ -50,6 +51,7 @@
#include <ctype.h>
#include <string.h>
#include <gmp.h>
+
#include "libguile/_scm.h"
#include "libguile/feature.h"
#include "libguile/ports.h"
@@ -61,6 +63,8 @@
#include "libguile/numbers.h"
#include "libguile/deprecation.h"
+#include "libguile/eq.h"
+
/*
@@ -79,6 +83,7 @@
: (((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)
@@ -119,6 +124,28 @@ isinf (double x)
#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
+}
+
static SCM abs_most_negative_fixnum;
@@ -167,6 +194,32 @@ scm_i_dbl2big (double d)
return z;
}
+/* 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.
@@ -249,6 +302,134 @@ scm_i_normbig (SCM b)
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)
+{
+#if 0
+ return scm_divide2real(numerator, denominator);
+#else
+ #define FUNC_NAME "make-ratio"
+ 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))
+ {
+ if (SCM_EQ_P (numerator, SCM_INUM0))
+ return SCM_INUM0;
+ if (SCM_INUMP (denominator))
+ {
+ long x, y;
+ x = SCM_INUM (numerator);
+ y = SCM_INUM (denominator);
+ if (x == y)
+ return SCM_MAKINUM(1);
+ if ((x % y) == 0)
+ return SCM_MAKINUM (x / y);
+ if (y < 0)
+ return scm_double_cell (scm_tc16_fraction, (scm_t_bits)SCM_MAKINUM(-x), (scm_t_bits)SCM_MAKINUM(-y), 0);
+ else return scm_double_cell (scm_tc16_fraction, (scm_t_bits)numerator, (scm_t_bits)denominator, 0);
+ }
+ else
+ {
+ /* I assume bignums are actually big, so here there's no point in looking for a integer */
+ int sgn = mpz_sgn (SCM_I_BIG_MPZ (denominator));
+ if (sgn < 0) /* if denominator negative, flip signs */
+ return scm_double_cell (scm_tc16_fraction,
+ (scm_t_bits)scm_difference (numerator, SCM_UNDEFINED),
+ (scm_t_bits)scm_difference (denominator, SCM_UNDEFINED),
+ 0);
+ else return scm_double_cell (scm_tc16_fraction, (scm_t_bits)numerator, (scm_t_bits)denominator, 0);
+
+ /* should this use SCM_UNPACK for the bignums? */
+ }
+ }
+ else
+ {
+ if (SCM_BIGP (numerator))
+ {
+ /* can't use scm_divide to find integer here */
+ if (SCM_INUMP (denominator))
+ {
+ long yy = SCM_INUM (denominator);
+ long abs_yy = yy < 0 ? -yy : yy;
+ int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), abs_yy);
+ if (divisible_p)
+ return scm_divide(numerator, denominator);
+ else return scm_double_cell (scm_tc16_fraction, (scm_t_bits)numerator, (scm_t_bits)denominator, 0);
+ }
+ else
+ {
+ /* both are bignums */
+ if (SCM_EQ_P (numerator, denominator))
+ return SCM_MAKINUM(1);
+ int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (numerator),
+ SCM_I_BIG_MPZ (denominator));
+ if (divisible_p)
+ return scm_divide(numerator, denominator);
+ else return scm_double_cell (scm_tc16_fraction, (scm_t_bits)numerator, (scm_t_bits)denominator, 0);
+ }
+ }
+ else SCM_WRONG_TYPE_ARG (1, numerator);
+ }
+ return SCM_BOOL_F; /* won't happen */
+ #undef FUNC_NAME
+#endif
+}
+
+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"
@@ -259,6 +440,8 @@ SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0,
return SCM_BOOL_T;
if (SCM_BIGP (x))
return SCM_BOOL_T;
+ if (SCM_FRACTIONP (x))
+ return SCM_BOOL_T;
return SCM_BOOL_F;
}
#undef FUNC_NAME
@@ -283,6 +466,16 @@ SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0,
}
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);
}
@@ -308,33 +501,21 @@ SCM_DEFINE (scm_even_p, "even?", 1, 0, 0,
}
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"
@@ -469,6 +650,13 @@ SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0,
}
else if (SCM_REALP (x))
return scm_make_real (fabs (SCM_REAL_VALUE (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);
}
@@ -1462,6 +1650,8 @@ SCM_DEFINE (scm_ash, "ash", 2, 0, 0,
*/
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
@@ -1867,7 +2057,6 @@ scm_iint2str (long num, int rad, char *p)
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"
@@ -1899,6 +2088,13 @@ SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0,
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];
@@ -1923,6 +2119,7 @@ scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
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);
@@ -1930,6 +2127,17 @@ scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED)
}
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)
{
char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp));
@@ -2117,7 +2325,7 @@ mem2decimal_from_point (SCM result, const char* mem, size_t len,
result = scm_sum (result, SCM_MAKINUM (add));
}
- result = scm_divide (result, big_shift);
+ result = scm_divide2real (result, big_shift);
/* We've seen a decimal point, thus the value is implicitly inexact. */
x = INEXACT;
@@ -2188,7 +2396,7 @@ mem2decimal_from_point (SCM result, const char* mem, size_t len,
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;
@@ -2271,7 +2479,8 @@ mem2ureal (const char* mem, size_t len, unsigned int *p_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)
{
@@ -2604,6 +2813,14 @@ scm_complex_equalp (SCM x, SCM y)
&& 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);
+ return SCM_BOOL (scm_equal_p (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_NUMERATOR (y))
+ && scm_equal_p (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y)));
+}
SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p);
@@ -2626,30 +2843,39 @@ SCM_DEFINE (scm_number_p, "complex?", 1, 0, 0,
#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;
}
@@ -2712,6 +2938,8 @@ scm_num_eq_p (SCM x, SCM y)
else if (SCM_COMPLEXP (y))
return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y))
&& (0.0 == SCM_COMPLEX_IMAG (y)));
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL_F;
else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
@@ -2745,6 +2973,8 @@ scm_num_eq_p (SCM x, SCM y)
scm_remember_upto_here_1 (x);
return SCM_BOOL (0 == cmp);
}
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL_F;
else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
@@ -2766,6 +2996,8 @@ scm_num_eq_p (SCM x, SCM y)
else if (SCM_COMPLEXP (y))
return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y))
&& (0.0 == SCM_COMPLEX_IMAG (y)));
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL (SCM_REAL_VALUE (x) == scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p);
}
@@ -2791,6 +3023,25 @@ scm_num_eq_p (SCM x, SCM y)
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))
+ return SCM_BOOL ((SCM_COMPLEX_REAL (x) == scm_i_fraction2double (y))
+ && (SCM_COMPLEX_IMAG (x) == 0.0));
+ 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))
+ return SCM_BOOL (scm_i_fraction2double (x) == SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ return SCM_BOOL ((scm_i_fraction2double (x) == SCM_COMPLEX_REAL (y))
+ && (0.0 == SCM_COMPLEX_IMAG (y)));
+ 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);
}
@@ -2822,6 +3073,8 @@ scm_less_p (SCM x, SCM y)
}
else if (SCM_REALP (y))
return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y));
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL ((double) xx < scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
@@ -2848,6 +3101,13 @@ scm_less_p (SCM x, SCM y)
scm_remember_upto_here_1 (x);
return SCM_BOOL (cmp < 0);
}
+ else if (SCM_FRACTIONP (y))
+ {
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), scm_i_fraction2double (y));
+ scm_remember_upto_here_1 (x);
+ return SCM_BOOL (cmp < 0);
+ }
else
SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
@@ -2866,6 +3126,28 @@ scm_less_p (SCM x, SCM y)
}
else if (SCM_REALP (y))
return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y));
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL (SCM_REAL_VALUE (x) < scm_i_fraction2double (y));
+ else
+ SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return SCM_BOOL (scm_i_fraction2double (x) < (double) SCM_INUM (y));
+ else if (SCM_BIGP (y))
+ {
+ int cmp;
+ if (xisnan (SCM_REAL_VALUE (x)))
+ return SCM_BOOL_F;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), scm_i_fraction2double (x));
+ scm_remember_upto_here_1 (y);
+ return SCM_BOOL (cmp > 0);
+ }
+ else if (SCM_REALP (y))
+ return SCM_BOOL (scm_i_fraction2double (x) < SCM_REAL_VALUE (y));
+ else if (SCM_FRACTIONP (y))
+ return SCM_BOOL (scm_i_fraction2double (x) < scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p);
}
@@ -2948,6 +3230,8 @@ scm_zero_p (SCM z)
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);
}
@@ -2970,6 +3254,8 @@ scm_positive_p (SCM x)
}
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);
}
@@ -2992,6 +3278,8 @@ scm_negative_p (SCM x)
}
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);
}
@@ -3033,6 +3321,11 @@ scm_max (SCM x, SCM y)
/* 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);
}
@@ -3060,6 +3353,14 @@ scm_max (SCM x, SCM y)
scm_remember_upto_here_1 (x);
return (cmp > 0) ? x : y;
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy);
+ scm_remember_upto_here_1 (x);
+ return (cmp > 0) ? x : y;
+ }
else
SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max);
}
@@ -3090,6 +3391,41 @@ scm_max (SCM x, SCM 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);
}
@@ -3134,6 +3470,11 @@ scm_min (SCM x, SCM y)
/* 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);
}
@@ -3161,6 +3502,14 @@ scm_min (SCM x, SCM y)
scm_remember_upto_here_1 (x);
return (cmp > 0) ? y : x;
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ int cmp;
+ cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy);
+ scm_remember_upto_here_1 (x);
+ return (cmp > 0) ? y : x;
+ }
else
SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min);
}
@@ -3191,9 +3540,44 @@ scm_min (SCM x, SCM 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);
}
@@ -3238,6 +3622,10 @@ scm_sum (SCM x, SCM y)
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))
@@ -3299,6 +3687,10 @@ scm_sum (SCM x, SCM y)
scm_remember_upto_here_1 (x);
return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y),
+ scm_product (x, SCM_FRACTION_DENOMINATOR (y))),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
@@ -3317,6 +3709,8 @@ scm_sum (SCM x, SCM y)
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y),
SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) + scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum);
}
@@ -3338,6 +3732,32 @@ scm_sum (SCM x, SCM y)
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);
}
@@ -3375,6 +3795,9 @@ scm_difference (SCM x, SCM y)
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);
}
@@ -3431,6 +3854,11 @@ scm_difference (SCM x, SCM y)
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);
}
@@ -3491,6 +3919,10 @@ scm_difference (SCM x, SCM y)
scm_remember_upto_here_1 (x);
return scm_make_complex (real_part, - SCM_COMPLEX_IMAG (y));
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)),
+ SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
else if (SCM_REALP (x))
@@ -3508,6 +3940,8 @@ scm_difference (SCM x, SCM y)
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y),
-SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) - scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference);
}
@@ -3529,6 +3963,33 @@ scm_difference (SCM x, SCM y)
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);
}
@@ -3594,6 +4055,9 @@ scm_product (SCM x, SCM y)
else if (SCM_COMPLEXP (y))
return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
xx * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)),
+ SCM_FRACTION_DENOMINATOR (y));
else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
@@ -3626,6 +4090,9 @@ scm_product (SCM x, SCM y)
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);
}
@@ -3644,6 +4111,8 @@ scm_product (SCM x, SCM y)
else if (SCM_COMPLEXP (y))
return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y),
SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y));
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (SCM_REAL_VALUE (x) * scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
@@ -3669,6 +4138,37 @@ scm_product (SCM x, SCM y)
SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y)
+ SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y));
}
+ else if (SCM_FRACTIONP (y))
+ {
+ double yy = scm_i_fraction2double (y);
+ return scm_make_complex (yy * SCM_COMPLEX_REAL (x),
+ yy * SCM_COMPLEX_IMAG (x));
+ }
+ else
+ SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
+ }
+ else if (SCM_FRACTIONP (x))
+ {
+ if (SCM_INUMP (y))
+ return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_BIGP (y))
+ return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)),
+ SCM_FRACTION_DENOMINATOR (x));
+ else if (SCM_REALP (y))
+ return scm_make_real (scm_i_fraction2double (x) * SCM_REAL_VALUE (y));
+ else if (SCM_COMPLEXP (y))
+ {
+ double xx = scm_i_fraction2double (x);
+ return scm_make_complex (xx * SCM_COMPLEX_REAL (y),
+ xx * SCM_COMPLEX_IMAG (y));
+ }
+ else if (SCM_FRACTIONP (y))
+ /* a/b * c/d = ac / bd */
+ return scm_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x),
+ SCM_FRACTION_NUMERATOR (y)),
+ scm_product (SCM_FRACTION_DENOMINATOR (x),
+ SCM_FRACTION_DENOMINATOR (y)));
else
SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product);
}
@@ -3690,6 +4190,8 @@ scm_num2dbl (SCM a, const char *why)
}
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);
}
@@ -3733,8 +4235,8 @@ SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide);
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;
@@ -3752,10 +4254,18 @@ scm_divide (SCM x, SCM y)
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);
@@ -3783,6 +4293,9 @@ scm_divide (SCM x, SCM y)
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);
}
@@ -3802,7 +4315,11 @@ scm_divide (SCM x, SCM y)
#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;
@@ -3813,7 +4330,11 @@ scm_divide (SCM x, SCM y)
}
}
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);
@@ -3845,6 +4366,10 @@ scm_divide (SCM x, SCM 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);
}
@@ -3888,7 +4413,11 @@ scm_divide (SCM x, SCM y)
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))
@@ -3920,10 +4449,14 @@ scm_divide (SCM x, SCM 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);
}
}
}
@@ -3942,6 +4475,9 @@ scm_divide (SCM x, SCM 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);
}
@@ -3979,6 +4515,8 @@ scm_divide (SCM x, SCM y)
a = rx;
goto complex_div;
}
+ else if (SCM_FRACTIONP (y))
+ return scm_make_real (rx / scm_i_fraction2double (y));
else
SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide);
}
@@ -4032,12 +4570,67 @@ scm_divide (SCM x, SCM y)
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
@@ -4086,6 +4679,11 @@ SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh);
*/
+/* 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)
{
@@ -4098,15 +4696,7 @@ 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)
{
@@ -4118,13 +4708,100 @@ 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}."
*/
@@ -4184,6 +4861,8 @@ scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy)
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);
@@ -4193,6 +4872,8 @@ scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy)
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);
}
@@ -4274,6 +4955,8 @@ scm_real_part (SCM z)
return z;
else if (SCM_COMPLEXP (z))
return scm_make_real (SCM_COMPLEX_REAL (z));
+ else if (SCM_FRACTIONP (z))
+ return scm_make_real (scm_i_fraction2double (z));
else
SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part);
}
@@ -4293,10 +4976,54 @@ scm_imag_part (SCM z)
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"
@@ -4328,6 +5055,13 @@ scm_magnitude (SCM z)
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);
}
@@ -4368,6 +5102,12 @@ scm_angle (SCM z)
}
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);
}
@@ -4383,6 +5123,8 @@ scm_exact_to_inexact (SCM z)
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
@@ -4401,32 +5143,91 @@ SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0,
return z;
else if (SCM_REALP (z))
{
- /* 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. */
-
- double u = SCM_REAL_VALUE (z);
- if (xisinf (u) || xisnan (u))
- scm_num_overflow (s_scm_inexact_to_exact);
- u = floor (u + 0.5);
- if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1)
- && u >= (double) SCM_MOST_NEGATIVE_FIXNUM)
- return SCM_MAKINUM ((long) u);
+ if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z)))
+ SCM_OUT_OF_RANGE (1, z);
else
- return scm_i_dbl2big (u);
+ {
+ 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 */
+ return scm_sum (int_part, scm_divide (a, b)); /* int_part+a/b */
+ 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
@@ -4721,7 +5522,9 @@ scm_init_numbers ()
#ifdef GUILE_DEBUG
check_sanity ();
#endif
-
+
+ exactly_one_half = scm_permanent_object (scm_divide (SCM_MAKINUM (1),
+ SCM_MAKINUM (2)));
#include "libguile/numbers.x"
}
diff --git a/libguile/numbers.h b/libguile/numbers.h
index 8bf211d6f..772a0ebe5 100644
--- a/libguile/numbers.h
+++ b/libguile/numbers.h
@@ -131,6 +131,7 @@
#define scm_tc16_big (scm_tc7_number + 1 * 256L)
#define scm_tc16_real (scm_tc7_number + 2 * 256L)
#define scm_tc16_complex (scm_tc7_number + 3 * 256L)
+#define scm_tc16_fraction (scm_tc7_number + 4 * 256L)
#define SCM_INEXACTP(x) \
(!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
@@ -148,7 +149,21 @@
#define SCM_NUMBERP(x) (SCM_INUMP(x) || SCM_NUMP(x))
#define SCM_NUMP(x) (!SCM_IMP(x) \
- && (0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number)
+ && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
+ || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
+/* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
+
+#define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
+#define SCM_SLOPPY_FRACTIONP(x) (SCM_TYP16 (x) == scm_tc16_fraction)
+#define SCM_FRACTION_NUMERATOR(x) ((SCM) (SCM_CELL_WORD_1 (x)))
+#define SCM_FRACTION_DENOMINATOR(x) ((SCM) (SCM_CELL_WORD_2 (x)))
+#define SCM_FRACTION_SET_NUMERATOR(x, v) ((SCM) (SCM_SET_CELL_WORD_1 ((x), (v))))
+#define SCM_FRACTION_SET_DENOMINATOR(x, v) ((SCM) (SCM_SET_CELL_WORD_2 ((x), (v))))
+ /* I think the left half word is free in the type, so I'll use bit 17 */
+#define SCM_FRACTION_REDUCED_BIT 0x10000
+#define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
+#define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
+#define SCM_FRACTION_REDUCED(x) (0x10000 & SCM_CELL_TYPE (x))
@@ -223,11 +238,15 @@ SCM_API SCM scm_difference (SCM x, SCM y);
SCM_API SCM scm_product (SCM x, SCM y);
SCM_API double scm_num2dbl (SCM a, const char * why);
SCM_API SCM scm_divide (SCM x, SCM y);
+SCM_API SCM scm_floor (SCM x);
+SCM_API SCM scm_ceiling (SCM x);
SCM_API double scm_asinh (double x);
SCM_API double scm_acosh (double x);
SCM_API double scm_atanh (double x);
SCM_API double scm_truncate (double x);
SCM_API double scm_round (double x);
+SCM_API SCM scm_truncate_number (SCM x);
+SCM_API SCM scm_round_number (SCM x);
SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
@@ -286,6 +305,7 @@ SCM_API SCM scm_i_mkbig (void);
SCM_API SCM scm_i_normbig (SCM x);
SCM_API int scm_i_bigcmp (SCM a, SCM b);
SCM_API SCM scm_i_dbl2big (double d);
+SCM_API SCM scm_i_dbl2num (double d);
SCM_API double scm_i_big2dbl (SCM b);
SCM_API SCM scm_i_short2big (short n);
SCM_API SCM scm_i_ushort2big (unsigned short n);
@@ -302,6 +322,18 @@ SCM_API SCM scm_i_ulong_long2big (unsigned long long n);
#endif
+/* ratio functions */
+SCM_API SCM scm_make_ratio (SCM num, SCM den);
+SCM_API SCM scm_rationalize (SCM x, SCM err);
+SCM_API SCM scm_numerator (SCM z);
+SCM_API SCM scm_denominator (SCM z);
+SCM_API SCM scm_rational_p (SCM z);
+
+/* fraction internal functions */
+SCM_API double scm_i_fraction2double (SCM z);
+SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
+SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
+
#ifdef GUILE_DEBUG
SCM_API SCM scm_sys_check_number_conversions (void);
diff --git a/libguile/objects.c b/libguile/objects.c
index 12ee5a9c0..f655470da 100644
--- a/libguile/objects.c
+++ b/libguile/objects.c
@@ -48,7 +48,7 @@ SCM scm_class_boolean, scm_class_char, scm_class_pair;
SCM scm_class_procedure, scm_class_string, scm_class_symbol;
SCM scm_class_procedure_with_setter, scm_class_primitive_generic;
SCM scm_class_vector, scm_class_null;
-SCM scm_class_integer, scm_class_real, scm_class_complex;
+SCM scm_class_integer, scm_class_real, scm_class_complex, scm_class_fraction;
SCM scm_class_unknown;
SCM *scm_port_class = 0;
@@ -110,6 +110,8 @@ SCM_DEFINE (scm_class_of, "class-of", 1, 0, 0,
return scm_class_real;
case scm_tc16_complex:
return scm_class_complex;
+ case scm_tc16_fraction:
+ return scm_class_fraction;
}
case scm_tc7_asubr:
case scm_tc7_subr_0:
diff --git a/libguile/objects.h b/libguile/objects.h
index 3217df025..11ab78b5f 100644
--- a/libguile/objects.h
+++ b/libguile/objects.h
@@ -190,6 +190,7 @@ SCM_API SCM scm_class_vector, scm_class_null;
SCM_API SCM scm_class_real;
SCM_API SCM scm_class_complex;
SCM_API SCM scm_class_integer;
+SCM_API SCM scm_class_fraction;
SCM_API SCM scm_class_unknown;
SCM_API SCM *scm_port_class;
SCM_API SCM *scm_smob_class;
diff --git a/libguile/print.c b/libguile/print.c
index 4ff0aeb3e..9e7fe1c06 100644
--- a/libguile/print.c
+++ b/libguile/print.c
@@ -529,6 +529,9 @@ scm_iprin1 (SCM exp, SCM port, scm_print_state *pstate)
case scm_tc16_complex:
scm_print_complex (exp, port, pstate);
break;
+ case scm_tc16_fraction:
+ scm_i_print_fraction (exp, port, pstate);
+ break;
}
break;
case scm_tc7_string: