* 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
/*
: (((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;
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.
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"
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
}
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"
}
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);
}
*/
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
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)
{
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;
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;
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)
{
&& 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);
#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 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 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);
}
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);
}
}
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);
}
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);
}
}
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);
}
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);
}
/* 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);
}
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);
}
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 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);
}
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);
}
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_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 scm_make_real (scm_i_fraction2double (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))
{
- /* 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
#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