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-rw-r--r--ruby_1_9_3/rational.c2409
1 files changed, 0 insertions, 2409 deletions
diff --git a/ruby_1_9_3/rational.c b/ruby_1_9_3/rational.c
deleted file mode 100644
index 8aced2aee8..0000000000
--- a/ruby_1_9_3/rational.c
+++ /dev/null
@@ -1,2409 +0,0 @@
-/*
- rational.c: Coded by Tadayoshi Funaba 2008-2011
-
- This implementation is based on Keiju Ishitsuka's Rational library
- which is written in ruby.
-*/
-
-#include "ruby.h"
-#include "internal.h"
-#include <math.h>
-#include <float.h>
-
-#ifdef HAVE_IEEEFP_H
-#include <ieeefp.h>
-#endif
-
-#define NDEBUG
-#include <assert.h>
-
-#define ZERO INT2FIX(0)
-#define ONE INT2FIX(1)
-#define TWO INT2FIX(2)
-
-VALUE rb_cRational;
-
-static ID id_abs, id_cmp, id_convert, id_eqeq_p, id_expt, id_fdiv,
- id_floor, id_idiv, id_inspect, id_integer_p, id_negate, id_to_f,
- id_to_i, id_to_s, id_truncate;
-
-#define f_boolcast(x) ((x) ? Qtrue : Qfalse)
-
-#define binop(n,op) \
-inline static VALUE \
-f_##n(VALUE x, VALUE y)\
-{\
- return rb_funcall(x, (op), 1, y);\
-}
-
-#define fun1(n) \
-inline static VALUE \
-f_##n(VALUE x)\
-{\
- return rb_funcall(x, id_##n, 0);\
-}
-
-#define fun2(n) \
-inline static VALUE \
-f_##n(VALUE x, VALUE y)\
-{\
- return rb_funcall(x, id_##n, 1, y);\
-}
-
-inline static VALUE
-f_add(VALUE x, VALUE y)
-{
- if (FIXNUM_P(y) && FIX2LONG(y) == 0)
- return x;
- else if (FIXNUM_P(x) && FIX2LONG(x) == 0)
- return y;
- return rb_funcall(x, '+', 1, y);
-}
-
-inline static VALUE
-f_cmp(VALUE x, VALUE y)
-{
- if (FIXNUM_P(x) && FIXNUM_P(y)) {
- long c = FIX2LONG(x) - FIX2LONG(y);
- if (c > 0)
- c = 1;
- else if (c < 0)
- c = -1;
- return INT2FIX(c);
- }
- return rb_funcall(x, id_cmp, 1, y);
-}
-
-inline static VALUE
-f_div(VALUE x, VALUE y)
-{
- if (FIXNUM_P(y) && FIX2LONG(y) == 1)
- return x;
- return rb_funcall(x, '/', 1, y);
-}
-
-inline static VALUE
-f_gt_p(VALUE x, VALUE y)
-{
- if (FIXNUM_P(x) && FIXNUM_P(y))
- return f_boolcast(FIX2LONG(x) > FIX2LONG(y));
- return rb_funcall(x, '>', 1, y);
-}
-
-inline static VALUE
-f_lt_p(VALUE x, VALUE y)
-{
- if (FIXNUM_P(x) && FIXNUM_P(y))
- return f_boolcast(FIX2LONG(x) < FIX2LONG(y));
- return rb_funcall(x, '<', 1, y);
-}
-
-binop(mod, '%')
-
-inline static VALUE
-f_mul(VALUE x, VALUE y)
-{
- if (FIXNUM_P(y)) {
- long iy = FIX2LONG(y);
- if (iy == 0) {
- if (FIXNUM_P(x) || TYPE(x) == T_BIGNUM)
- return ZERO;
- }
- else if (iy == 1)
- return x;
- }
- else if (FIXNUM_P(x)) {
- long ix = FIX2LONG(x);
- if (ix == 0) {
- if (FIXNUM_P(y) || TYPE(y) == T_BIGNUM)
- return ZERO;
- }
- else if (ix == 1)
- return y;
- }
- return rb_funcall(x, '*', 1, y);
-}
-
-inline static VALUE
-f_sub(VALUE x, VALUE y)
-{
- if (FIXNUM_P(y) && FIX2LONG(y) == 0)
- return x;
- return rb_funcall(x, '-', 1, y);
-}
-
-fun1(abs)
-fun1(floor)
-fun1(inspect)
-fun1(integer_p)
-fun1(negate)
-
-inline static VALUE
-f_to_i(VALUE x)
-{
- if (TYPE(x) == T_STRING)
- return rb_str_to_inum(x, 10, 0);
- return rb_funcall(x, id_to_i, 0);
-}
-inline static VALUE
-f_to_f(VALUE x)
-{
- if (TYPE(x) == T_STRING)
- return DBL2NUM(rb_str_to_dbl(x, 0));
- return rb_funcall(x, id_to_f, 0);
-}
-
-fun1(to_s)
-fun1(truncate)
-
-inline static VALUE
-f_eqeq_p(VALUE x, VALUE y)
-{
- if (FIXNUM_P(x) && FIXNUM_P(y))
- return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
- return rb_funcall(x, id_eqeq_p, 1, y);
-}
-
-fun2(expt)
-fun2(fdiv)
-fun2(idiv)
-
-#define f_expt10(x) f_expt(INT2FIX(10), x)
-
-inline static VALUE
-f_negative_p(VALUE x)
-{
- if (FIXNUM_P(x))
- return f_boolcast(FIX2LONG(x) < 0);
- return rb_funcall(x, '<', 1, ZERO);
-}
-
-#define f_positive_p(x) (!f_negative_p(x))
-
-inline static VALUE
-f_zero_p(VALUE x)
-{
- switch (TYPE(x)) {
- case T_FIXNUM:
- return f_boolcast(FIX2LONG(x) == 0);
- case T_BIGNUM:
- return Qfalse;
- case T_RATIONAL:
- {
- VALUE num = RRATIONAL(x)->num;
-
- return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 0);
- }
- }
- return rb_funcall(x, id_eqeq_p, 1, ZERO);
-}
-
-#define f_nonzero_p(x) (!f_zero_p(x))
-
-inline static VALUE
-f_one_p(VALUE x)
-{
- switch (TYPE(x)) {
- case T_FIXNUM:
- return f_boolcast(FIX2LONG(x) == 1);
- case T_BIGNUM:
- return Qfalse;
- case T_RATIONAL:
- {
- VALUE num = RRATIONAL(x)->num;
- VALUE den = RRATIONAL(x)->den;
-
- return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 1 &&
- FIXNUM_P(den) && FIX2LONG(den) == 1);
- }
- }
- return rb_funcall(x, id_eqeq_p, 1, ONE);
-}
-
-inline static VALUE
-f_kind_of_p(VALUE x, VALUE c)
-{
- return rb_obj_is_kind_of(x, c);
-}
-
-inline static VALUE
-k_numeric_p(VALUE x)
-{
- return f_kind_of_p(x, rb_cNumeric);
-}
-
-inline static VALUE
-k_integer_p(VALUE x)
-{
- return f_kind_of_p(x, rb_cInteger);
-}
-
-inline static VALUE
-k_float_p(VALUE x)
-{
- return f_kind_of_p(x, rb_cFloat);
-}
-
-inline static VALUE
-k_rational_p(VALUE x)
-{
- return f_kind_of_p(x, rb_cRational);
-}
-
-#define k_exact_p(x) (!k_float_p(x))
-#define k_inexact_p(x) k_float_p(x)
-
-#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x))
-#define k_exact_one_p(x) (k_exact_p(x) && f_one_p(x))
-
-#ifndef NDEBUG
-#define f_gcd f_gcd_orig
-#endif
-
-inline static long
-i_gcd(long x, long y)
-{
- if (x < 0)
- x = -x;
- if (y < 0)
- y = -y;
-
- if (x == 0)
- return y;
- if (y == 0)
- return x;
-
- while (x > 0) {
- long t = x;
- x = y % x;
- y = t;
- }
- return y;
-}
-
-inline static VALUE
-f_gcd(VALUE x, VALUE y)
-{
- VALUE z;
-
- if (FIXNUM_P(x) && FIXNUM_P(y))
- return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y)));
-
- if (f_negative_p(x))
- x = f_negate(x);
- if (f_negative_p(y))
- y = f_negate(y);
-
- if (f_zero_p(x))
- return y;
- if (f_zero_p(y))
- return x;
-
- for (;;) {
- if (FIXNUM_P(x)) {
- if (FIX2LONG(x) == 0)
- return y;
- if (FIXNUM_P(y))
- return LONG2NUM(i_gcd(FIX2LONG(x), FIX2LONG(y)));
- }
- z = x;
- x = f_mod(y, x);
- y = z;
- }
- /* NOTREACHED */
-}
-
-#ifndef NDEBUG
-#undef f_gcd
-
-inline static VALUE
-f_gcd(VALUE x, VALUE y)
-{
- VALUE r = f_gcd_orig(x, y);
- if (f_nonzero_p(r)) {
- assert(f_zero_p(f_mod(x, r)));
- assert(f_zero_p(f_mod(y, r)));
- }
- return r;
-}
-#endif
-
-inline static VALUE
-f_lcm(VALUE x, VALUE y)
-{
- if (f_zero_p(x) || f_zero_p(y))
- return ZERO;
- return f_abs(f_mul(f_div(x, f_gcd(x, y)), y));
-}
-
-#define get_dat1(x) \
- struct RRational *dat;\
- dat = ((struct RRational *)(x))
-
-#define get_dat2(x,y) \
- struct RRational *adat, *bdat;\
- adat = ((struct RRational *)(x));\
- bdat = ((struct RRational *)(y))
-
-inline static VALUE
-nurat_s_new_internal(VALUE klass, VALUE num, VALUE den)
-{
- NEWOBJ(obj, struct RRational);
- OBJSETUP(obj, klass, T_RATIONAL);
-
- obj->num = num;
- obj->den = den;
-
- return (VALUE)obj;
-}
-
-static VALUE
-nurat_s_alloc(VALUE klass)
-{
- return nurat_s_new_internal(klass, ZERO, ONE);
-}
-
-#define rb_raise_zerodiv() rb_raise(rb_eZeroDivError, "divided by 0")
-
-#if 0
-static VALUE
-nurat_s_new_bang(int argc, VALUE *argv, VALUE klass)
-{
- VALUE num, den;
-
- switch (rb_scan_args(argc, argv, "11", &num, &den)) {
- case 1:
- if (!k_integer_p(num))
- num = f_to_i(num);
- den = ONE;
- break;
- default:
- if (!k_integer_p(num))
- num = f_to_i(num);
- if (!k_integer_p(den))
- den = f_to_i(den);
-
- switch (FIX2INT(f_cmp(den, ZERO))) {
- case -1:
- num = f_negate(num);
- den = f_negate(den);
- break;
- case 0:
- rb_raise_zerodiv();
- break;
- }
- break;
- }
-
- return nurat_s_new_internal(klass, num, den);
-}
-#endif
-
-inline static VALUE
-f_rational_new_bang1(VALUE klass, VALUE x)
-{
- return nurat_s_new_internal(klass, x, ONE);
-}
-
-inline static VALUE
-f_rational_new_bang2(VALUE klass, VALUE x, VALUE y)
-{
- assert(f_positive_p(y));
- assert(f_nonzero_p(y));
- return nurat_s_new_internal(klass, x, y);
-}
-
-#ifdef CANONICALIZATION_FOR_MATHN
-#define CANON
-#endif
-
-#ifdef CANON
-static int canonicalization = 0;
-
-RUBY_FUNC_EXPORTED void
-nurat_canonicalization(int f)
-{
- canonicalization = f;
-}
-#endif
-
-inline static void
-nurat_int_check(VALUE num)
-{
- switch (TYPE(num)) {
- case T_FIXNUM:
- case T_BIGNUM:
- break;
- default:
- if (!k_numeric_p(num) || !f_integer_p(num))
- rb_raise(rb_eTypeError, "not an integer");
- }
-}
-
-inline static VALUE
-nurat_int_value(VALUE num)
-{
- nurat_int_check(num);
- if (!k_integer_p(num))
- num = f_to_i(num);
- return num;
-}
-
-inline static VALUE
-nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den)
-{
- VALUE gcd;
-
- switch (FIX2INT(f_cmp(den, ZERO))) {
- case -1:
- num = f_negate(num);
- den = f_negate(den);
- break;
- case 0:
- rb_raise_zerodiv();
- break;
- }
-
- gcd = f_gcd(num, den);
- num = f_idiv(num, gcd);
- den = f_idiv(den, gcd);
-
-#ifdef CANON
- if (f_one_p(den) && canonicalization)
- return num;
-#endif
- return nurat_s_new_internal(klass, num, den);
-}
-
-inline static VALUE
-nurat_s_canonicalize_internal_no_reduce(VALUE klass, VALUE num, VALUE den)
-{
- switch (FIX2INT(f_cmp(den, ZERO))) {
- case -1:
- num = f_negate(num);
- den = f_negate(den);
- break;
- case 0:
- rb_raise_zerodiv();
- break;
- }
-
-#ifdef CANON
- if (f_one_p(den) && canonicalization)
- return num;
-#endif
- return nurat_s_new_internal(klass, num, den);
-}
-
-static VALUE
-nurat_s_new(int argc, VALUE *argv, VALUE klass)
-{
- VALUE num, den;
-
- switch (rb_scan_args(argc, argv, "11", &num, &den)) {
- case 1:
- num = nurat_int_value(num);
- den = ONE;
- break;
- default:
- num = nurat_int_value(num);
- den = nurat_int_value(den);
- break;
- }
-
- return nurat_s_canonicalize_internal(klass, num, den);
-}
-
-inline static VALUE
-f_rational_new1(VALUE klass, VALUE x)
-{
- assert(!k_rational_p(x));
- return nurat_s_canonicalize_internal(klass, x, ONE);
-}
-
-inline static VALUE
-f_rational_new2(VALUE klass, VALUE x, VALUE y)
-{
- assert(!k_rational_p(x));
- assert(!k_rational_p(y));
- return nurat_s_canonicalize_internal(klass, x, y);
-}
-
-inline static VALUE
-f_rational_new_no_reduce1(VALUE klass, VALUE x)
-{
- assert(!k_rational_p(x));
- return nurat_s_canonicalize_internal_no_reduce(klass, x, ONE);
-}
-
-inline static VALUE
-f_rational_new_no_reduce2(VALUE klass, VALUE x, VALUE y)
-{
- assert(!k_rational_p(x));
- assert(!k_rational_p(y));
- return nurat_s_canonicalize_internal_no_reduce(klass, x, y);
-}
-
-/*
- * call-seq:
- * Rational(x[, y]) -> numeric
- *
- * Returns x/y;
- */
-static VALUE
-nurat_f_rational(int argc, VALUE *argv, VALUE klass)
-{
- return rb_funcall2(rb_cRational, id_convert, argc, argv);
-}
-
-/*
- * call-seq:
- * rat.numerator -> integer
- *
- * Returns the numerator.
- *
- * For example:
- *
- * Rational(7).numerator #=> 7
- * Rational(7, 1).numerator #=> 7
- * Rational(9, -4).numerator #=> -9
- * Rational(-2, -10).numerator #=> 1
- */
-static VALUE
-nurat_numerator(VALUE self)
-{
- get_dat1(self);
- return dat->num;
-}
-
-/*
- * call-seq:
- * rat.denominator -> integer
- *
- * Returns the denominator (always positive).
- *
- * For example:
- *
- * Rational(7).denominator #=> 1
- * Rational(7, 1).denominator #=> 1
- * Rational(9, -4).denominator #=> 4
- * Rational(-2, -10).denominator #=> 5
- * rat.numerator.gcd(rat.denominator) #=> 1
- */
-static VALUE
-nurat_denominator(VALUE self)
-{
- get_dat1(self);
- return dat->den;
-}
-
-#ifndef NDEBUG
-#define f_imul f_imul_orig
-#endif
-
-inline static VALUE
-f_imul(long a, long b)
-{
- VALUE r;
- volatile long c;
-
- if (a == 0 || b == 0)
- return ZERO;
- else if (a == 1)
- return LONG2NUM(b);
- else if (b == 1)
- return LONG2NUM(a);
-
- c = a * b;
- r = LONG2NUM(c);
- if (NUM2LONG(r) != c || (c / a) != b)
- r = rb_big_mul(rb_int2big(a), rb_int2big(b));
- return r;
-}
-
-#ifndef NDEBUG
-#undef f_imul
-
-inline static VALUE
-f_imul(long x, long y)
-{
- VALUE r = f_imul_orig(x, y);
- assert(f_eqeq_p(r, f_mul(LONG2NUM(x), LONG2NUM(y))));
- return r;
-}
-#endif
-
-inline static VALUE
-f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
-{
- VALUE num, den;
-
- if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
- FIXNUM_P(bnum) && FIXNUM_P(bden)) {
- long an = FIX2LONG(anum);
- long ad = FIX2LONG(aden);
- long bn = FIX2LONG(bnum);
- long bd = FIX2LONG(bden);
- long ig = i_gcd(ad, bd);
-
- VALUE g = LONG2NUM(ig);
- VALUE a = f_imul(an, bd / ig);
- VALUE b = f_imul(bn, ad / ig);
- VALUE c;
-
- if (k == '+')
- c = f_add(a, b);
- else
- c = f_sub(a, b);
-
- b = f_idiv(aden, g);
- g = f_gcd(c, g);
- num = f_idiv(c, g);
- a = f_idiv(bden, g);
- den = f_mul(a, b);
- }
- else {
- VALUE g = f_gcd(aden, bden);
- VALUE a = f_mul(anum, f_idiv(bden, g));
- VALUE b = f_mul(bnum, f_idiv(aden, g));
- VALUE c;
-
- if (k == '+')
- c = f_add(a, b);
- else
- c = f_sub(a, b);
-
- b = f_idiv(aden, g);
- g = f_gcd(c, g);
- num = f_idiv(c, g);
- a = f_idiv(bden, g);
- den = f_mul(a, b);
- }
- return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
-}
-
-/*
- * call-seq:
- * rat + numeric -> numeric
- *
- * Performs addition.
- *
- * For example:
- *
- * Rational(2, 3) + Rational(2, 3) #=> (4/3)
- * Rational(900) + Rational(1) #=> (900/1)
- * Rational(-2, 9) + Rational(-9, 2) #=> (-85/18)
- * Rational(9, 8) + 4 #=> (41/8)
- * Rational(20, 9) + 9.8 #=> 12.022222222222222
- */
-static VALUE
-nurat_add(VALUE self, VALUE other)
-{
- switch (TYPE(other)) {
- case T_FIXNUM:
- case T_BIGNUM:
- {
- get_dat1(self);
-
- return f_addsub(self,
- dat->num, dat->den,
- other, ONE, '+');
- }
- case T_FLOAT:
- return f_add(f_to_f(self), other);
- case T_RATIONAL:
- {
- get_dat2(self, other);
-
- return f_addsub(self,
- adat->num, adat->den,
- bdat->num, bdat->den, '+');
- }
- default:
- return rb_num_coerce_bin(self, other, '+');
- }
-}
-
-/*
- * call-seq:
- * rat - numeric -> numeric
- *
- * Performs subtraction.
- *
- * For example:
- *
- * Rational(2, 3) - Rational(2, 3) #=> (0/1)
- * Rational(900) - Rational(1) #=> (899/1)
- * Rational(-2, 9) - Rational(-9, 2) #=> (77/18)
- * Rational(9, 8) - 4 #=> (23/8)
- * Rational(20, 9) - 9.8 #=> -7.577777777777778
- */
-static VALUE
-nurat_sub(VALUE self, VALUE other)
-{
- switch (TYPE(other)) {
- case T_FIXNUM:
- case T_BIGNUM:
- {
- get_dat1(self);
-
- return f_addsub(self,
- dat->num, dat->den,
- other, ONE, '-');
- }
- case T_FLOAT:
- return f_sub(f_to_f(self), other);
- case T_RATIONAL:
- {
- get_dat2(self, other);
-
- return f_addsub(self,
- adat->num, adat->den,
- bdat->num, bdat->den, '-');
- }
- default:
- return rb_num_coerce_bin(self, other, '-');
- }
-}
-
-inline static VALUE
-f_muldiv(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
-{
- VALUE num, den;
-
- if (k == '/') {
- VALUE t;
-
- if (f_negative_p(bnum)) {
- anum = f_negate(anum);
- bnum = f_negate(bnum);
- }
- t = bnum;
- bnum = bden;
- bden = t;
- }
-
- if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
- FIXNUM_P(bnum) && FIXNUM_P(bden)) {
- long an = FIX2LONG(anum);
- long ad = FIX2LONG(aden);
- long bn = FIX2LONG(bnum);
- long bd = FIX2LONG(bden);
- long g1 = i_gcd(an, bd);
- long g2 = i_gcd(ad, bn);
-
- num = f_imul(an / g1, bn / g2);
- den = f_imul(ad / g2, bd / g1);
- }
- else {
- VALUE g1 = f_gcd(anum, bden);
- VALUE g2 = f_gcd(aden, bnum);
-
- num = f_mul(f_idiv(anum, g1), f_idiv(bnum, g2));
- den = f_mul(f_idiv(aden, g2), f_idiv(bden, g1));
- }
- return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
-}
-
-/*
- * call-seq:
- * rat * numeric -> numeric
- *
- * Performs multiplication.
- *
- * For example:
- *
- * Rational(2, 3) * Rational(2, 3) #=> (4/9)
- * Rational(900) * Rational(1) #=> (900/1)
- * Rational(-2, 9) * Rational(-9, 2) #=> (1/1)
- * Rational(9, 8) * 4 #=> (9/2)
- * Rational(20, 9) * 9.8 #=> 21.77777777777778
- */
-static VALUE
-nurat_mul(VALUE self, VALUE other)
-{
- switch (TYPE(other)) {
- case T_FIXNUM:
- case T_BIGNUM:
- {
- get_dat1(self);
-
- return f_muldiv(self,
- dat->num, dat->den,
- other, ONE, '*');
- }
- case T_FLOAT:
- return f_mul(f_to_f(self), other);
- case T_RATIONAL:
- {
- get_dat2(self, other);
-
- return f_muldiv(self,
- adat->num, adat->den,
- bdat->num, bdat->den, '*');
- }
- default:
- return rb_num_coerce_bin(self, other, '*');
- }
-}
-
-/*
- * call-seq:
- * rat / numeric -> numeric
- * rat.quo(numeric) -> numeric
- *
- * Performs division.
- *
- * For example:
- *
- * Rational(2, 3) / Rational(2, 3) #=> (1/1)
- * Rational(900) / Rational(1) #=> (900/1)
- * Rational(-2, 9) / Rational(-9, 2) #=> (4/81)
- * Rational(9, 8) / 4 #=> (9/32)
- * Rational(20, 9) / 9.8 #=> 0.22675736961451246
- */
-static VALUE
-nurat_div(VALUE self, VALUE other)
-{
- switch (TYPE(other)) {
- case T_FIXNUM:
- case T_BIGNUM:
- if (f_zero_p(other))
- rb_raise_zerodiv();
- {
- get_dat1(self);
-
- return f_muldiv(self,
- dat->num, dat->den,
- other, ONE, '/');
- }
- case T_FLOAT:
- {
- double x = RFLOAT_VALUE(other), den;
- get_dat1(self);
-
- if (isnan(x)) return DBL2NUM(NAN);
- if (isinf(x)) return INT2FIX(0);
- if (x != 0.0 && modf(x, &den) == 0.0) {
- return rb_rational_raw2(dat->num, f_mul(rb_dbl2big(den), dat->den));
- }
- }
- return rb_funcall(f_to_f(self), '/', 1, other);
- case T_RATIONAL:
- if (f_zero_p(other))
- rb_raise_zerodiv();
- {
- get_dat2(self, other);
-
- if (f_one_p(self))
- return f_rational_new_no_reduce2(CLASS_OF(self),
- bdat->den, bdat->num);
-
- return f_muldiv(self,
- adat->num, adat->den,
- bdat->num, bdat->den, '/');
- }
- default:
- return rb_num_coerce_bin(self, other, '/');
- }
-}
-
-/*
- * call-seq:
- * rat.fdiv(numeric) -> float
- *
- * Performs division and returns the value as a float.
- *
- * For example:
- *
- * Rational(2, 3).fdiv(1) #=> 0.6666666666666666
- * Rational(2, 3).fdiv(0.5) #=> 1.3333333333333333
- * Rational(2).fdiv(3) #=> 0.6666666666666666
- */
-static VALUE
-nurat_fdiv(VALUE self, VALUE other)
-{
- if (f_zero_p(other))
- return f_div(self, f_to_f(other));
- return f_to_f(f_div(self, other));
-}
-
-/*
- * call-seq:
- * rat ** numeric -> numeric
- *
- * Performs exponentiation.
- *
- * For example:
- *
- * Rational(2) ** Rational(3) #=> (8/1)
- * Rational(10) ** -2 #=> (1/100)
- * Rational(10) ** -2.0 #=> 0.01
- * Rational(-4) ** Rational(1,2) #=> (1.2246063538223773e-16+2.0i)
- * Rational(1, 2) ** 0 #=> (1/1)
- * Rational(1, 2) ** 0.0 #=> 1.0
- */
-static VALUE
-nurat_expt(VALUE self, VALUE other)
-{
- if (k_numeric_p(other) && k_exact_zero_p(other))
- return f_rational_new_bang1(CLASS_OF(self), ONE);
-
- if (k_rational_p(other)) {
- get_dat1(other);
-
- if (f_one_p(dat->den))
- other = dat->num; /* c14n */
- }
-
- switch (TYPE(other)) {
- case T_FIXNUM:
- {
- VALUE num, den;
-
- get_dat1(self);
-
- switch (FIX2INT(f_cmp(other, ZERO))) {
- case 1:
- num = f_expt(dat->num, other);
- den = f_expt(dat->den, other);
- break;
- case -1:
- num = f_expt(dat->den, f_negate(other));
- den = f_expt(dat->num, f_negate(other));
- break;
- default:
- num = ONE;
- den = ONE;
- break;
- }
- return f_rational_new2(CLASS_OF(self), num, den);
- }
- case T_BIGNUM:
- rb_warn("in a**b, b may be too big");
- /* fall through */
- case T_FLOAT:
- case T_RATIONAL:
- return f_expt(f_to_f(self), other);
- default:
- return rb_num_coerce_bin(self, other, id_expt);
- }
-}
-
-/*
- * call-seq:
- * rat <=> numeric -> -1, 0, +1 or nil
- *
- * Performs comparison and returns -1, 0, or +1.
- *
- * For example:
- *
- * Rational(2, 3) <=> Rational(2, 3) #=> 0
- * Rational(5) <=> 5 #=> 0
- * Rational(2,3) <=> Rational(1,3) #=> 1
- * Rational(1,3) <=> 1 #=> -1
- * Rational(1,3) <=> 0.3 #=> 1
- */
-static VALUE
-nurat_cmp(VALUE self, VALUE other)
-{
- switch (TYPE(other)) {
- case T_FIXNUM:
- case T_BIGNUM:
- {
- get_dat1(self);
-
- if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1)
- return f_cmp(dat->num, other); /* c14n */
- return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other));
- }
- case T_FLOAT:
- return f_cmp(f_to_f(self), other);
- case T_RATIONAL:
- {
- VALUE num1, num2;
-
- get_dat2(self, other);
-
- if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) &&
- FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) {
- num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den));
- num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den));
- }
- else {
- num1 = f_mul(adat->num, bdat->den);
- num2 = f_mul(bdat->num, adat->den);
- }
- return f_cmp(f_sub(num1, num2), ZERO);
- }
- default:
- return rb_num_coerce_cmp(self, other, id_cmp);
- }
-}
-
-/*
- * call-seq:
- * rat == object -> true or false
- *
- * Returns true if rat equals object numerically.
- *
- * For example:
- *
- * Rational(2, 3) == Rational(2, 3) #=> true
- * Rational(5) == 5 #=> true
- * Rational(0) == 0.0 #=> true
- * Rational('1/3') == 0.33 #=> false
- * Rational('1/2') == '1/2' #=> false
- */
-static VALUE
-nurat_eqeq_p(VALUE self, VALUE other)
-{
- switch (TYPE(other)) {
- case T_FIXNUM:
- case T_BIGNUM:
- {
- get_dat1(self);
-
- if (f_zero_p(dat->num) && f_zero_p(other))
- return Qtrue;
-
- if (!FIXNUM_P(dat->den))
- return Qfalse;
- if (FIX2LONG(dat->den) != 1)
- return Qfalse;
- if (f_eqeq_p(dat->num, other))
- return Qtrue;
- return Qfalse;
- }
- case T_FLOAT:
- return f_eqeq_p(f_to_f(self), other);
- case T_RATIONAL:
- {
- get_dat2(self, other);
-
- if (f_zero_p(adat->num) && f_zero_p(bdat->num))
- return Qtrue;
-
- return f_boolcast(f_eqeq_p(adat->num, bdat->num) &&
- f_eqeq_p(adat->den, bdat->den));
- }
- default:
- return f_eqeq_p(other, self);
- }
-}
-
-/* :nodoc: */
-static VALUE
-nurat_coerce(VALUE self, VALUE other)
-{
- switch (TYPE(other)) {
- case T_FIXNUM:
- case T_BIGNUM:
- return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self);
- case T_FLOAT:
- return rb_assoc_new(other, f_to_f(self));
- case T_RATIONAL:
- return rb_assoc_new(other, self);
- case T_COMPLEX:
- if (k_exact_zero_p(RCOMPLEX(other)->imag))
- return rb_assoc_new(f_rational_new_bang1
- (CLASS_OF(self), RCOMPLEX(other)->real), self);
- else
- return rb_assoc_new(other, rb_Complex(self, INT2FIX(0)));
- }
-
- rb_raise(rb_eTypeError, "%s can't be coerced into %s",
- rb_obj_classname(other), rb_obj_classname(self));
- return Qnil;
-}
-
-#if 0
-/* :nodoc: */
-static VALUE
-nurat_idiv(VALUE self, VALUE other)
-{
- return f_idiv(self, other);
-}
-
-/* :nodoc: */
-static VALUE
-nurat_quot(VALUE self, VALUE other)
-{
- return f_truncate(f_div(self, other));
-}
-
-/* :nodoc: */
-static VALUE
-nurat_quotrem(VALUE self, VALUE other)
-{
- VALUE val = f_truncate(f_div(self, other));
- return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
-}
-#endif
-
-#if 0
-/* :nodoc: */
-static VALUE
-nurat_true(VALUE self)
-{
- return Qtrue;
-}
-#endif
-
-static VALUE
-nurat_floor(VALUE self)
-{
- get_dat1(self);
- return f_idiv(dat->num, dat->den);
-}
-
-static VALUE
-nurat_ceil(VALUE self)
-{
- get_dat1(self);
- return f_negate(f_idiv(f_negate(dat->num), dat->den));
-}
-
-/*
- * call-seq:
- * rat.to_i -> integer
- *
- * Returns the truncated value as an integer.
- *
- * Equivalent to
- * rat.truncate.
- *
- * For example:
- *
- * Rational(2, 3).to_i #=> 0
- * Rational(3).to_i #=> 3
- * Rational(300.6).to_i #=> 300
- * Rational(98,71).to_i #=> 1
- * Rational(-30,2).to_i #=> -15
- */
-static VALUE
-nurat_truncate(VALUE self)
-{
- get_dat1(self);
- if (f_negative_p(dat->num))
- return f_negate(f_idiv(f_negate(dat->num), dat->den));
- return f_idiv(dat->num, dat->den);
-}
-
-static VALUE
-nurat_round(VALUE self)
-{
- VALUE num, den, neg;
-
- get_dat1(self);
-
- num = dat->num;
- den = dat->den;
- neg = f_negative_p(num);
-
- if (neg)
- num = f_negate(num);
-
- num = f_add(f_mul(num, TWO), den);
- den = f_mul(den, TWO);
- num = f_idiv(num, den);
-
- if (neg)
- num = f_negate(num);
-
- return num;
-}
-
-static VALUE
-f_round_common(int argc, VALUE *argv, VALUE self, VALUE (*func)(VALUE))
-{
- VALUE n, b, s;
-
- if (argc == 0)
- return (*func)(self);
-
- rb_scan_args(argc, argv, "01", &n);
-
- if (!k_integer_p(n))
- rb_raise(rb_eTypeError, "not an integer");
-
- b = f_expt10(n);
- s = f_mul(self, b);
-
- s = (*func)(s);
-
- s = f_div(f_rational_new_bang1(CLASS_OF(self), s), b);
-
- if (f_lt_p(n, ONE))
- s = f_to_i(s);
-
- return s;
-}
-
-/*
- * call-seq:
- * rat.floor -> integer
- * rat.floor(precision=0) -> rational
- *
- * Returns the truncated value (toward negative infinity).
- *
- * For example:
- *
- * Rational(3).floor #=> 3
- * Rational(2, 3).floor #=> 0
- * Rational(-3, 2).floor #=> -1
- *
- * decimal - 1 2 3 . 4 5 6
- * ^ ^ ^ ^ ^ ^
- * precision -3 -2 -1 0 +1 +2
- *
- * '%f' % Rational('-123.456').floor(+1) #=> "-123.500000"
- * '%f' % Rational('-123.456').floor(-1) #=> "-130.000000"
- */
-static VALUE
-nurat_floor_n(int argc, VALUE *argv, VALUE self)
-{
- return f_round_common(argc, argv, self, nurat_floor);
-}
-
-/*
- * call-seq:
- * rat.ceil -> integer
- * rat.ceil(precision=0) -> rational
- *
- * Returns the truncated value (toward positive infinity).
- *
- * For example:
- *
- * Rational(3).ceil #=> 3
- * Rational(2, 3).ceil #=> 1
- * Rational(-3, 2).ceil #=> -1
- *
- * decimal - 1 2 3 . 4 5 6
- * ^ ^ ^ ^ ^ ^
- * precision -3 -2 -1 0 +1 +2
- *
- * '%f' % Rational('-123.456').ceil(+1) #=> "-123.400000"
- * '%f' % Rational('-123.456').ceil(-1) #=> "-120.000000"
- */
-static VALUE
-nurat_ceil_n(int argc, VALUE *argv, VALUE self)
-{
- return f_round_common(argc, argv, self, nurat_ceil);
-}
-
-/*
- * call-seq:
- * rat.truncate -> integer
- * rat.truncate(precision=0) -> rational
- *
- * Returns the truncated value (toward zero).
- *
- * For example:
- *
- * Rational(3).truncate #=> 3
- * Rational(2, 3).truncate #=> 0
- * Rational(-3, 2).truncate #=> -1
- *
- * decimal - 1 2 3 . 4 5 6
- * ^ ^ ^ ^ ^ ^
- * precision -3 -2 -1 0 +1 +2
- *
- * '%f' % Rational('-123.456').truncate(+1) #=> "-123.400000"
- * '%f' % Rational('-123.456').truncate(-1) #=> "-120.000000"
- */
-static VALUE
-nurat_truncate_n(int argc, VALUE *argv, VALUE self)
-{
- return f_round_common(argc, argv, self, nurat_truncate);
-}
-
-/*
- * call-seq:
- * rat.round -> integer
- * rat.round(precision=0) -> rational
- *
- * Returns the truncated value (toward the nearest integer;
- * 0.5 => 1; -0.5 => -1).
- *
- * For example:
- *
- * Rational(3).round #=> 3
- * Rational(2, 3).round #=> 1
- * Rational(-3, 2).round #=> -2
- *
- * decimal - 1 2 3 . 4 5 6
- * ^ ^ ^ ^ ^ ^
- * precision -3 -2 -1 0 +1 +2
- *
- * '%f' % Rational('-123.456').round(+1) #=> "-123.500000"
- * '%f' % Rational('-123.456').round(-1) #=> "-120.000000"
- */
-static VALUE
-nurat_round_n(int argc, VALUE *argv, VALUE self)
-{
- return f_round_common(argc, argv, self, nurat_round);
-}
-
-/*
- * call-seq:
- * rat.to_f -> float
- *
- * Return the value as a float.
- *
- * For example:
- *
- * Rational(2).to_f #=> 2.0
- * Rational(9, 4).to_f #=> 2.25
- * Rational(-3, 4).to_f #=> -0.75
- * Rational(20, 3).to_f #=> 6.666666666666667
- */
-static VALUE
-nurat_to_f(VALUE self)
-{
- get_dat1(self);
- return f_fdiv(dat->num, dat->den);
-}
-
-/*
- * call-seq:
- * rat.to_r -> self
- *
- * Returns self.
- *
- * For example:
- *
- * Rational(2).to_r #=> (2/1)
- * Rational(-8, 6).to_r #=> (-4/3)
- */
-static VALUE
-nurat_to_r(VALUE self)
-{
- return self;
-}
-
-#define id_ceil rb_intern("ceil")
-#define f_ceil(x) rb_funcall((x), id_ceil, 0)
-
-#define id_quo rb_intern("quo")
-#define f_quo(x,y) rb_funcall((x), id_quo, 1, (y))
-
-#define f_reciprocal(x) f_quo(ONE, (x))
-
-/*
- The algorithm here is the method described in CLISP. Bruno Haible has
- graciously given permission to use this algorithm. He says, "You can use
- it, if you present the following explanation of the algorithm."
-
- Algorithm (recursively presented):
- If x is a rational number, return x.
- If x = 0.0, return 0.
- If x < 0.0, return (- (rationalize (- x))).
- If x > 0.0:
- Call (integer-decode-float x). It returns a m,e,s=1 (mantissa,
- exponent, sign).
- If m = 0 or e >= 0: return x = m*2^e.
- Search a rational number between a = (m-1/2)*2^e and b = (m+1/2)*2^e
- with smallest possible numerator and denominator.
- Note 1: If m is a power of 2, we ought to take a = (m-1/4)*2^e.
- But in this case the result will be x itself anyway, regardless of
- the choice of a. Therefore we can simply ignore this case.
- Note 2: At first, we need to consider the closed interval [a,b].
- but since a and b have the denominator 2^(|e|+1) whereas x itself
- has a denominator <= 2^|e|, we can restrict the search to the open
- interval (a,b).
- So, for given a and b (0 < a < b) we are searching a rational number
- y with a <= y <= b.
- Recursive algorithm fraction_between(a,b):
- c := (ceiling a)
- if c < b
- then return c ; because a <= c < b, c integer
- else
- ; a is not integer (otherwise we would have had c = a < b)
- k := c-1 ; k = floor(a), k < a < b <= k+1
- return y = k + 1/fraction_between(1/(b-k), 1/(a-k))
- ; note 1 <= 1/(b-k) < 1/(a-k)
-
- You can see that we are actually computing a continued fraction expansion.
-
- Algorithm (iterative):
- If x is rational, return x.
- Call (integer-decode-float x). It returns a m,e,s (mantissa,
- exponent, sign).
- If m = 0 or e >= 0, return m*2^e*s. (This includes the case x = 0.0.)
- Create rational numbers a := (2*m-1)*2^(e-1) and b := (2*m+1)*2^(e-1)
- (positive and already in lowest terms because the denominator is a
- power of two and the numerator is odd).
- Start a continued fraction expansion
- p[-1] := 0, p[0] := 1, q[-1] := 1, q[0] := 0, i := 0.
- Loop
- c := (ceiling a)
- if c >= b
- then k := c-1, partial_quotient(k), (a,b) := (1/(b-k),1/(a-k)),
- goto Loop
- finally partial_quotient(c).
- Here partial_quotient(c) denotes the iteration
- i := i+1, p[i] := c*p[i-1]+p[i-2], q[i] := c*q[i-1]+q[i-2].
- At the end, return s * (p[i]/q[i]).
- This rational number is already in lowest terms because
- p[i]*q[i-1]-p[i-1]*q[i] = (-1)^i.
-*/
-
-static void
-nurat_rationalize_internal(VALUE a, VALUE b, VALUE *p, VALUE *q)
-{
- VALUE c, k, t, p0, p1, p2, q0, q1, q2;
-
- p0 = ZERO;
- p1 = ONE;
- q0 = ONE;
- q1 = ZERO;
-
- while (1) {
- c = f_ceil(a);
- if (f_lt_p(c, b))
- break;
- k = f_sub(c, ONE);
- p2 = f_add(f_mul(k, p1), p0);
- q2 = f_add(f_mul(k, q1), q0);
- t = f_reciprocal(f_sub(b, k));
- b = f_reciprocal(f_sub(a, k));
- a = t;
- p0 = p1;
- q0 = q1;
- p1 = p2;
- q1 = q2;
- }
- *p = f_add(f_mul(c, p1), p0);
- *q = f_add(f_mul(c, q1), q0);
-}
-
-/*
- * call-seq:
- * rat.rationalize -> self
- * rat.rationalize(eps) -> rational
- *
- * Returns a simpler approximation of the value if an optional
- * argument eps is given (rat-|eps| <= result <= rat+|eps|), self
- * otherwise.
- *
- * For example:
- *
- * r = Rational(5033165, 16777216)
- * r.rationalize #=> (5033165/16777216)
- * r.rationalize(Rational('0.01')) #=> (3/10)
- * r.rationalize(Rational('0.1')) #=> (1/3)
- */
-static VALUE
-nurat_rationalize(int argc, VALUE *argv, VALUE self)
-{
- VALUE e, a, b, p, q;
-
- if (argc == 0)
- return self;
-
- if (f_negative_p(self))
- return f_negate(nurat_rationalize(argc, argv, f_abs(self)));
-
- rb_scan_args(argc, argv, "01", &e);
- e = f_abs(e);
- a = f_sub(self, e);
- b = f_add(self, e);
-
- if (f_eqeq_p(a, b))
- return self;
-
- nurat_rationalize_internal(a, b, &p, &q);
- return f_rational_new2(CLASS_OF(self), p, q);
-}
-
-/* :nodoc: */
-static VALUE
-nurat_hash(VALUE self)
-{
- st_index_t v, h[2];
- VALUE n;
-
- get_dat1(self);
- n = rb_hash(dat->num);
- h[0] = NUM2LONG(n);
- n = rb_hash(dat->den);
- h[1] = NUM2LONG(n);
- v = rb_memhash(h, sizeof(h));
- return LONG2FIX(v);
-}
-
-static VALUE
-f_format(VALUE self, VALUE (*func)(VALUE))
-{
- VALUE s;
- get_dat1(self);
-
- s = (*func)(dat->num);
- rb_str_cat2(s, "/");
- rb_str_concat(s, (*func)(dat->den));
-
- return s;
-}
-
-/*
- * call-seq:
- * rat.to_s -> string
- *
- * Returns the value as a string.
- *
- * For example:
- *
- * Rational(2).to_s #=> "2/1"
- * Rational(-8, 6).to_s #=> "-4/3"
- * Rational('0.5').to_s #=> "1/2"
- */
-static VALUE
-nurat_to_s(VALUE self)
-{
- return f_format(self, f_to_s);
-}
-
-/*
- * call-seq:
- * rat.inspect -> string
- *
- * Returns the value as a string for inspection.
- *
- * For example:
- *
- * Rational(2).inspect #=> "(2/1)"
- * Rational(-8, 6).inspect #=> "(-4/3)"
- * Rational('0.5').inspect #=> "(1/2)"
- */
-static VALUE
-nurat_inspect(VALUE self)
-{
- VALUE s;
-
- s = rb_usascii_str_new2("(");
- rb_str_concat(s, f_format(self, f_inspect));
- rb_str_cat2(s, ")");
-
- return s;
-}
-
-/* :nodoc: */
-static VALUE
-nurat_marshal_dump(VALUE self)
-{
- VALUE a;
- get_dat1(self);
-
- a = rb_assoc_new(dat->num, dat->den);
- rb_copy_generic_ivar(a, self);
- return a;
-}
-
-/* :nodoc: */
-static VALUE
-nurat_marshal_load(VALUE self, VALUE a)
-{
- get_dat1(self);
- Check_Type(a, T_ARRAY);
- if (RARRAY_LEN(a) != 2)
- rb_raise(rb_eArgError, "marshaled rational must have an array whose length is 2 but %ld", RARRAY_LEN(a));
- dat->num = RARRAY_PTR(a)[0];
- dat->den = RARRAY_PTR(a)[1];
- rb_copy_generic_ivar(self, a);
-
- if (f_zero_p(dat->den))
- rb_raise_zerodiv();
-
- return self;
-}
-
-/* --- */
-
-VALUE
-rb_rational_reciprocal(VALUE x)
-{
- get_dat1(x);
- return f_rational_new_no_reduce2(CLASS_OF(x), dat->den, dat->num);
-}
-
-/*
- * call-seq:
- * int.gcd(int2) -> integer
- *
- * Returns the greatest common divisor (always positive). 0.gcd(x)
- * and x.gcd(0) return abs(x).
- *
- * For example:
- *
- * 2.gcd(2) #=> 2
- * 3.gcd(-7) #=> 1
- * ((1<<31)-1).gcd((1<<61)-1) #=> 1
- */
-VALUE
-rb_gcd(VALUE self, VALUE other)
-{
- other = nurat_int_value(other);
- return f_gcd(self, other);
-}
-
-/*
- * call-seq:
- * int.lcm(int2) -> integer
- *
- * Returns the least common multiple (always positive). 0.lcm(x) and
- * x.lcm(0) return zero.
- *
- * For example:
- *
- * 2.lcm(2) #=> 2
- * 3.lcm(-7) #=> 21
- * ((1<<31)-1).lcm((1<<61)-1) #=> 4951760154835678088235319297
- */
-VALUE
-rb_lcm(VALUE self, VALUE other)
-{
- other = nurat_int_value(other);
- return f_lcm(self, other);
-}
-
-/*
- * call-seq:
- * int.gcdlcm(int2) -> array
- *
- * Returns an array; [int.gcd(int2), int.lcm(int2)].
- *
- * For example:
- *
- * 2.gcdlcm(2) #=> [2, 2]
- * 3.gcdlcm(-7) #=> [1, 21]
- * ((1<<31)-1).gcdlcm((1<<61)-1) #=> [1, 4951760154835678088235319297]
- */
-VALUE
-rb_gcdlcm(VALUE self, VALUE other)
-{
- other = nurat_int_value(other);
- return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
-}
-
-VALUE
-rb_rational_raw(VALUE x, VALUE y)
-{
- return nurat_s_new_internal(rb_cRational, x, y);
-}
-
-VALUE
-rb_rational_new(VALUE x, VALUE y)
-{
- return nurat_s_canonicalize_internal(rb_cRational, x, y);
-}
-
-static VALUE nurat_s_convert(int argc, VALUE *argv, VALUE klass);
-
-VALUE
-rb_Rational(VALUE x, VALUE y)
-{
- VALUE a[2];
- a[0] = x;
- a[1] = y;
- return nurat_s_convert(2, a, rb_cRational);
-}
-
-#define id_numerator rb_intern("numerator")
-#define f_numerator(x) rb_funcall((x), id_numerator, 0)
-
-#define id_denominator rb_intern("denominator")
-#define f_denominator(x) rb_funcall((x), id_denominator, 0)
-
-#define id_to_r rb_intern("to_r")
-#define f_to_r(x) rb_funcall((x), id_to_r, 0)
-
-/*
- * call-seq:
- * num.numerator -> integer
- *
- * Returns the numerator.
- */
-static VALUE
-numeric_numerator(VALUE self)
-{
- return f_numerator(f_to_r(self));
-}
-
-/*
- * call-seq:
- * num.denominator -> integer
- *
- * Returns the denominator (always positive).
- */
-static VALUE
-numeric_denominator(VALUE self)
-{
- return f_denominator(f_to_r(self));
-}
-
-/*
- * call-seq:
- * int.numerator -> self
- *
- * Returns self.
- */
-static VALUE
-integer_numerator(VALUE self)
-{
- return self;
-}
-
-/*
- * call-seq:
- * int.denominator -> 1
- *
- * Returns 1.
- */
-static VALUE
-integer_denominator(VALUE self)
-{
- return INT2FIX(1);
-}
-
-/*
- * call-seq:
- * flo.numerator -> integer
- *
- * Returns the numerator. The result is machine dependent.
- *
- * For example:
- *
- * n = 0.3.numerator #=> 5404319552844595
- * d = 0.3.denominator #=> 18014398509481984
- * n.fdiv(d) #=> 0.3
- */
-static VALUE
-float_numerator(VALUE self)
-{
- double d = RFLOAT_VALUE(self);
- if (isinf(d) || isnan(d))
- return self;
- return rb_call_super(0, 0);
-}
-
-/*
- * call-seq:
- * flo.denominator -> integer
- *
- * Returns the denominator (always positive). The result is machine
- * dependent.
- *
- * See numerator.
- */
-static VALUE
-float_denominator(VALUE self)
-{
- double d = RFLOAT_VALUE(self);
- if (isinf(d) || isnan(d))
- return INT2FIX(1);
- return rb_call_super(0, 0);
-}
-
-/*
- * call-seq:
- * nil.to_r -> (0/1)
- *
- * Returns zero as a rational.
- */
-static VALUE
-nilclass_to_r(VALUE self)
-{
- return rb_rational_new1(INT2FIX(0));
-}
-
-/*
- * call-seq:
- * nil.rationalize([eps]) -> (0/1)
- *
- * Returns zero as a rational. An optional argument eps is always
- * ignored.
- */
-static VALUE
-nilclass_rationalize(int argc, VALUE *argv, VALUE self)
-{
- rb_scan_args(argc, argv, "01", NULL);
- return nilclass_to_r(self);
-}
-
-/*
- * call-seq:
- * int.to_r -> rational
- *
- * Returns the value as a rational.
- *
- * For example:
- *
- * 1.to_r #=> (1/1)
- * (1<<64).to_r #=> (18446744073709551616/1)
- */
-static VALUE
-integer_to_r(VALUE self)
-{
- return rb_rational_new1(self);
-}
-
-/*
- * call-seq:
- * int.rationalize([eps]) -> rational
- *
- * Returns the value as a rational. An optional argument eps is
- * always ignored.
- */
-static VALUE
-integer_rationalize(int argc, VALUE *argv, VALUE self)
-{
- rb_scan_args(argc, argv, "01", NULL);
- return integer_to_r(self);
-}
-
-static void
-float_decode_internal(VALUE self, VALUE *rf, VALUE *rn)
-{
- double f;
- int n;
-
- f = frexp(RFLOAT_VALUE(self), &n);
- f = ldexp(f, DBL_MANT_DIG);
- n -= DBL_MANT_DIG;
- *rf = rb_dbl2big(f);
- *rn = INT2FIX(n);
-}
-
-#if 0
-static VALUE
-float_decode(VALUE self)
-{
- VALUE f, n;
-
- float_decode_internal(self, &f, &n);
- return rb_assoc_new(f, n);
-}
-#endif
-
-#define id_lshift rb_intern("<<")
-#define f_lshift(x,n) rb_funcall((x), id_lshift, 1, (n))
-
-/*
- * call-seq:
- * flt.to_r -> rational
- *
- * Returns the value as a rational.
- *
- * NOTE: 0.3.to_r isn't the same as '0.3'.to_r. The latter is
- * equivalent to '3/10'.to_r, but the former isn't so.
- *
- * For example:
- *
- * 2.0.to_r #=> (2/1)
- * 2.5.to_r #=> (5/2)
- * -0.75.to_r #=> (-3/4)
- * 0.0.to_r #=> (0/1)
- */
-static VALUE
-float_to_r(VALUE self)
-{
- VALUE f, n;
-
- float_decode_internal(self, &f, &n);
-#if FLT_RADIX == 2
- {
- long ln = FIX2LONG(n);
-
- if (ln == 0)
- return f_to_r(f);
- if (ln > 0)
- return f_to_r(f_lshift(f, n));
- ln = -ln;
- return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln)));
- }
-#else
- return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n)));
-#endif
-}
-
-/*
- * call-seq:
- * flt.rationalize([eps]) -> rational
- *
- * Returns a simpler approximation of the value (flt-|eps| <= result
- * <= flt+|eps|). if eps is not given, it will be chosen
- * automatically.
- *
- * For example:
- *
- * 0.3.rationalize #=> (3/10)
- * 1.333.rationalize #=> (1333/1000)
- * 1.333.rationalize(0.01) #=> (4/3)
- */
-static VALUE
-float_rationalize(int argc, VALUE *argv, VALUE self)
-{
- VALUE e, a, b, p, q;
-
- if (f_negative_p(self))
- return f_negate(float_rationalize(argc, argv, f_abs(self)));
-
- rb_scan_args(argc, argv, "01", &e);
-
- if (argc != 0) {
- e = f_abs(e);
- a = f_sub(self, e);
- b = f_add(self, e);
- }
- else {
- VALUE f, n;
-
- float_decode_internal(self, &f, &n);
- if (f_zero_p(f) || f_positive_p(n))
- return rb_rational_new1(f_lshift(f, n));
-
-#if FLT_RADIX == 2
- a = rb_rational_new2(f_sub(f_mul(TWO, f), ONE),
- f_lshift(ONE, f_sub(ONE, n)));
- b = rb_rational_new2(f_add(f_mul(TWO, f), ONE),
- f_lshift(ONE, f_sub(ONE, n)));
-#else
- a = rb_rational_new2(f_sub(f_mul(INT2FIX(FLT_RADIX), f),
- INT2FIX(FLT_RADIX - 1)),
- f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n)));
- b = rb_rational_new2(f_add(f_mul(INT2FIX(FLT_RADIX), f),
- INT2FIX(FLT_RADIX - 1)),
- f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n)));
-#endif
- }
-
- if (f_eqeq_p(a, b))
- return f_to_r(self);
-
- nurat_rationalize_internal(a, b, &p, &q);
- return rb_rational_new2(p, q);
-}
-
-static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore;
-
-#define WS "\\s*"
-#define DIGITS "(?:[0-9](?:_[0-9]|[0-9])*)"
-#define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
-#define DENOMINATOR DIGITS
-#define PATTERN "\\A" WS "([-+])?(" NUMERATOR ")(?:\\/(" DENOMINATOR "))?" WS
-
-static void
-make_patterns(void)
-{
- static const char rat_pat_source[] = PATTERN;
- static const char an_e_pat_source[] = "[eE]";
- static const char a_dot_pat_source[] = "\\.";
- static const char underscores_pat_source[] = "_+";
-
- if (rat_pat) return;
-
- rat_pat = rb_reg_new(rat_pat_source, sizeof rat_pat_source - 1, 0);
- rb_gc_register_mark_object(rat_pat);
-
- an_e_pat = rb_reg_new(an_e_pat_source, sizeof an_e_pat_source - 1, 0);
- rb_gc_register_mark_object(an_e_pat);
-
- a_dot_pat = rb_reg_new(a_dot_pat_source, sizeof a_dot_pat_source - 1, 0);
- rb_gc_register_mark_object(a_dot_pat);
-
- underscores_pat = rb_reg_new(underscores_pat_source,
- sizeof underscores_pat_source - 1, 0);
- rb_gc_register_mark_object(underscores_pat);
-
- an_underscore = rb_usascii_str_new2("_");
- rb_gc_register_mark_object(an_underscore);
-}
-
-#define id_match rb_intern("match")
-#define f_match(x,y) rb_funcall((x), id_match, 1, (y))
-
-#define id_split rb_intern("split")
-#define f_split(x,y) rb_funcall((x), id_split, 1, (y))
-
-#include <ctype.h>
-
-static VALUE
-string_to_r_internal(VALUE self)
-{
- VALUE s, m;
-
- s = self;
-
- if (RSTRING_LEN(s) == 0)
- return rb_assoc_new(Qnil, self);
-
- m = f_match(rat_pat, s);
-
- if (!NIL_P(m)) {
- VALUE v, ifp, exp, ip, fp;
- VALUE si = rb_reg_nth_match(1, m);
- VALUE nu = rb_reg_nth_match(2, m);
- VALUE de = rb_reg_nth_match(3, m);
- VALUE re = rb_reg_match_post(m);
-
- {
- VALUE a;
-
- if (!strpbrk(RSTRING_PTR(nu), "eE")) {
- ifp = nu; /* not a copy */
- exp = Qnil;
- }
- else {
- a = f_split(nu, an_e_pat);
- ifp = RARRAY_PTR(a)[0];
- if (RARRAY_LEN(a) != 2)
- exp = Qnil;
- else
- exp = RARRAY_PTR(a)[1];
- }
-
- if (!strchr(RSTRING_PTR(ifp), '.')) {
- ip = ifp; /* not a copy */
- fp = Qnil;
- }
- else {
- a = f_split(ifp, a_dot_pat);
- ip = RARRAY_PTR(a)[0];
- if (RARRAY_LEN(a) != 2)
- fp = Qnil;
- else
- fp = RARRAY_PTR(a)[1];
- }
- }
-
- v = rb_rational_new1(f_to_i(ip));
-
- if (!NIL_P(fp)) {
- char *p = RSTRING_PTR(fp);
- long count = 0;
- VALUE l;
-
- while (*p) {
- if (rb_isdigit(*p))
- count++;
- p++;
- }
- l = f_expt10(LONG2NUM(count));
- v = f_mul(v, l);
- v = f_add(v, f_to_i(fp));
- v = f_div(v, l);
- }
- if (!NIL_P(si) && *RSTRING_PTR(si) == '-')
- v = f_negate(v);
- if (!NIL_P(exp))
- v = f_mul(v, f_expt10(f_to_i(exp)));
-#if 0
- if (!NIL_P(de) && (!NIL_P(fp) || !NIL_P(exp)))
- return rb_assoc_new(v, rb_usascii_str_new2("dummy"));
-#endif
- if (!NIL_P(de))
- v = f_div(v, f_to_i(de));
-
- return rb_assoc_new(v, re);
- }
- return rb_assoc_new(Qnil, self);
-}
-
-static VALUE
-string_to_r_strict(VALUE self)
-{
- VALUE a = string_to_r_internal(self);
- if (NIL_P(RARRAY_PTR(a)[0]) || RSTRING_LEN(RARRAY_PTR(a)[1]) > 0) {
- VALUE s = f_inspect(self);
- rb_raise(rb_eArgError, "invalid value for convert(): %s",
- StringValuePtr(s));
- }
- return RARRAY_PTR(a)[0];
-}
-
-#define id_gsub rb_intern("gsub")
-#define f_gsub(x,y,z) rb_funcall((x), id_gsub, 2, (y), (z))
-
-/*
- * call-seq:
- * str.to_r -> rational
- *
- * Returns a rational which denotes the string form. The parser
- * ignores leading whitespaces and trailing garbage. Any digit
- * sequences can be separated by an underscore. Returns zero for null
- * or garbage string.
- *
- * NOTE: '0.3'.to_r isn't the same as 0.3.to_r. The former is
- * equivalent to '3/10'.to_r, but the latter isn't so.
- *
- * For example:
- *
- * ' 2 '.to_r #=> (2/1)
- * '300/2'.to_r #=> (150/1)
- * '-9.2'.to_r #=> (-46/5)
- * '-9.2e2'.to_r #=> (-920/1)
- * '1_234_567'.to_r #=> (1234567/1)
- * '21 june 09'.to_r #=> (21/1)
- * '21/06/09'.to_r #=> (7/2)
- * 'bwv 1079'.to_r #=> (0/1)
- */
-static VALUE
-string_to_r(VALUE self)
-{
- VALUE s, a, a1, backref;
-
- backref = rb_backref_get();
- rb_match_busy(backref);
-
- s = f_gsub(self, underscores_pat, an_underscore);
- a = string_to_r_internal(s);
-
- rb_backref_set(backref);
-
- a1 = RARRAY_PTR(a)[0];
- if (!NIL_P(a1)) {
- if (TYPE(a1) == T_FLOAT)
- rb_raise(rb_eFloatDomainError, "Infinity");
- return a1;
- }
- return rb_rational_new1(INT2FIX(0));
-}
-
-#define id_to_r rb_intern("to_r")
-#define f_to_r(x) rb_funcall((x), id_to_r, 0)
-
-static VALUE
-nurat_s_convert(int argc, VALUE *argv, VALUE klass)
-{
- VALUE a1, a2, backref;
-
- rb_scan_args(argc, argv, "11", &a1, &a2);
-
- if (NIL_P(a1) || (argc == 2 && NIL_P(a2)))
- rb_raise(rb_eTypeError, "can't convert nil into Rational");
-
- switch (TYPE(a1)) {
- case T_COMPLEX:
- if (k_exact_zero_p(RCOMPLEX(a1)->imag))
- a1 = RCOMPLEX(a1)->real;
- }
-
- switch (TYPE(a2)) {
- case T_COMPLEX:
- if (k_exact_zero_p(RCOMPLEX(a2)->imag))
- a2 = RCOMPLEX(a2)->real;
- }
-
- backref = rb_backref_get();
- rb_match_busy(backref);
-
- switch (TYPE(a1)) {
- case T_FIXNUM:
- case T_BIGNUM:
- break;
- case T_FLOAT:
- a1 = f_to_r(a1);
- break;
- case T_STRING:
- a1 = string_to_r_strict(a1);
- break;
- }
-
- switch (TYPE(a2)) {
- case T_FIXNUM:
- case T_BIGNUM:
- break;
- case T_FLOAT:
- a2 = f_to_r(a2);
- break;
- case T_STRING:
- a2 = string_to_r_strict(a2);
- break;
- }
-
- rb_backref_set(backref);
-
- switch (TYPE(a1)) {
- case T_RATIONAL:
- if (argc == 1 || (k_exact_one_p(a2)))
- return a1;
- }
-
- if (argc == 1) {
- if (!(k_numeric_p(a1) && k_integer_p(a1)))
- return rb_convert_type(a1, T_RATIONAL, "Rational", "to_r");
- }
- else {
- if ((k_numeric_p(a1) && k_numeric_p(a2)) &&
- (!f_integer_p(a1) || !f_integer_p(a2)))
- return f_div(a1, a2);
- }
-
- {
- VALUE argv2[2];
- argv2[0] = a1;
- argv2[1] = a2;
- return nurat_s_new(argc, argv2, klass);
- }
-}
-
-/*
- * A rational number can be represented as a paired integer number;
- * a/b (b>0). Where a is numerator and b is denominator. Integer a
- * equals rational a/1 mathematically.
- *
- * In ruby, you can create rational object with Rational, to_r or
- * rationalize method. The return values will be irreducible.
- *
- * Rational(1) #=> (1/1)
- * Rational(2, 3) #=> (2/3)
- * Rational(4, -6) #=> (-2/3)
- * 3.to_r #=> (3/1)
- *
- * You can also create rational object from floating-point numbers or
- * strings.
- *
- * Rational(0.3) #=> (5404319552844595/18014398509481984)
- * Rational('0.3') #=> (3/10)
- * Rational('2/3') #=> (2/3)
- *
- * 0.3.to_r #=> (5404319552844595/18014398509481984)
- * '0.3'.to_r #=> (3/10)
- * '2/3'.to_r #=> (2/3)
- * 0.3.rationalize #=> (3/10)
- *
- * A rational object is an exact number, which helps you to write
- * program without any rounding errors.
- *
- * 10.times.inject(0){|t,| t + 0.1} #=> 0.9999999999999999
- * 10.times.inject(0){|t,| t + Rational('0.1')} #=> (1/1)
- *
- * However, when an expression has inexact factor (numerical value or
- * operation), will produce an inexact result.
- *
- * Rational(10) / 3 #=> (10/3)
- * Rational(10) / 3.0 #=> 3.3333333333333335
- *
- * Rational(-8) ** Rational(1, 3)
- * #=> (1.0000000000000002+1.7320508075688772i)
- */
-void
-Init_Rational(void)
-{
-#undef rb_intern
-#define rb_intern(str) rb_intern_const(str)
-
- assert(fprintf(stderr, "assert() is now active\n"));
-
- id_abs = rb_intern("abs");
- id_cmp = rb_intern("<=>");
- id_convert = rb_intern("convert");
- id_eqeq_p = rb_intern("==");
- id_expt = rb_intern("**");
- id_fdiv = rb_intern("fdiv");
- id_floor = rb_intern("floor");
- id_idiv = rb_intern("div");
- id_inspect = rb_intern("inspect");
- id_integer_p = rb_intern("integer?");
- id_negate = rb_intern("-@");
- id_to_f = rb_intern("to_f");
- id_to_i = rb_intern("to_i");
- id_to_s = rb_intern("to_s");
- id_truncate = rb_intern("truncate");
-
- rb_cRational = rb_define_class("Rational", rb_cNumeric);
-
- rb_define_alloc_func(rb_cRational, nurat_s_alloc);
- rb_undef_method(CLASS_OF(rb_cRational), "allocate");
-
-#if 0
- rb_define_private_method(CLASS_OF(rb_cRational), "new!", nurat_s_new_bang, -1);
- rb_define_private_method(CLASS_OF(rb_cRational), "new", nurat_s_new, -1);
-#else
- rb_undef_method(CLASS_OF(rb_cRational), "new");
-#endif
-
- rb_define_global_function("Rational", nurat_f_rational, -1);
-
- rb_define_method(rb_cRational, "numerator", nurat_numerator, 0);
- rb_define_method(rb_cRational, "denominator", nurat_denominator, 0);
-
- rb_define_method(rb_cRational, "+", nurat_add, 1);
- rb_define_method(rb_cRational, "-", nurat_sub, 1);
- rb_define_method(rb_cRational, "*", nurat_mul, 1);
- rb_define_method(rb_cRational, "/", nurat_div, 1);
- rb_define_method(rb_cRational, "quo", nurat_div, 1);
- rb_define_method(rb_cRational, "fdiv", nurat_fdiv, 1);
- rb_define_method(rb_cRational, "**", nurat_expt, 1);
-
- rb_define_method(rb_cRational, "<=>", nurat_cmp, 1);
- rb_define_method(rb_cRational, "==", nurat_eqeq_p, 1);
- rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
-
-#if 0 /* NUBY */
- rb_define_method(rb_cRational, "//", nurat_idiv, 1);
-#endif
-
-#if 0
- rb_define_method(rb_cRational, "quot", nurat_quot, 1);
- rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
-#endif
-
-#if 0
- rb_define_method(rb_cRational, "rational?", nurat_true, 0);
- rb_define_method(rb_cRational, "exact?", nurat_true, 0);
-#endif
-
- rb_define_method(rb_cRational, "floor", nurat_floor_n, -1);
- rb_define_method(rb_cRational, "ceil", nurat_ceil_n, -1);
- rb_define_method(rb_cRational, "truncate", nurat_truncate_n, -1);
- rb_define_method(rb_cRational, "round", nurat_round_n, -1);
-
- rb_define_method(rb_cRational, "to_i", nurat_truncate, 0);
- rb_define_method(rb_cRational, "to_f", nurat_to_f, 0);
- rb_define_method(rb_cRational, "to_r", nurat_to_r, 0);
- rb_define_method(rb_cRational, "rationalize", nurat_rationalize, -1);
-
- rb_define_method(rb_cRational, "hash", nurat_hash, 0);
-
- rb_define_method(rb_cRational, "to_s", nurat_to_s, 0);
- rb_define_method(rb_cRational, "inspect", nurat_inspect, 0);
-
- rb_define_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
- rb_define_method(rb_cRational, "marshal_load", nurat_marshal_load, 1);
-
- /* --- */
-
- rb_define_method(rb_cInteger, "gcd", rb_gcd, 1);
- rb_define_method(rb_cInteger, "lcm", rb_lcm, 1);
- rb_define_method(rb_cInteger, "gcdlcm", rb_gcdlcm, 1);
-
- rb_define_method(rb_cNumeric, "numerator", numeric_numerator, 0);
- rb_define_method(rb_cNumeric, "denominator", numeric_denominator, 0);
-
- rb_define_method(rb_cInteger, "numerator", integer_numerator, 0);
- rb_define_method(rb_cInteger, "denominator", integer_denominator, 0);
-
- rb_define_method(rb_cFloat, "numerator", float_numerator, 0);
- rb_define_method(rb_cFloat, "denominator", float_denominator, 0);
-
- rb_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
- rb_define_method(rb_cNilClass, "rationalize", nilclass_rationalize, -1);
- rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
- rb_define_method(rb_cInteger, "rationalize", integer_rationalize, -1);
- rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
- rb_define_method(rb_cFloat, "rationalize", float_rationalize, -1);
-
- make_patterns();
-
- rb_define_method(rb_cString, "to_r", string_to_r, 0);
-
- rb_define_private_method(CLASS_OF(rb_cRational), "convert", nurat_s_convert, -1);
-}
-
-/*
-Local variables:
-c-file-style: "ruby"
-End:
-*/