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-rw-r--r--ext/mathn/rational/extconf.rb5
-rw-r--r--ext/mathn/rational/rational.c1593
2 files changed, 1598 insertions, 0 deletions
diff --git a/ext/mathn/rational/extconf.rb b/ext/mathn/rational/extconf.rb
new file mode 100644
index 0000000..23cff7a
--- /dev/null
+++ b/ext/mathn/rational/extconf.rb
@@ -0,0 +1,5 @@
+require "mkmf"
+
+$CPPFLAGS = "-DEXT_MATHN -DCANON -DCLCANON"
+
+create_makefile "mathn/rational"
diff --git a/ext/mathn/rational/rational.c b/ext/mathn/rational/rational.c
new file mode 100644
index 0000000..ebbaa9b
--- /dev/null
+++ b/ext/mathn/rational/rational.c
@@ -0,0 +1,1593 @@
+/*
+
+ rational.c of mathn version
+
+ Original file is built-in rational.c:
+ --
+ rational.c: Coded by Tadayoshi Funaba 2008
+
+ This implementation is based on Keiju Ishitsuka's Rational library
+ which is written in ruby.
+ --
+*/
+
+#include "ruby.h"
+#include <math.h>
+#include <float.h>
+
+#ifdef HAVE_IEEEFP_H
+#include <ieeefp.h>
+#endif
+
+#define NDEBUG
+#include <assert.h>
+
+#ifndef RATIONAL_NAME
+#define RATIONAL_NAME "Rational"
+#endif
+
+#define ZERO INT2FIX(0)
+#define ONE INT2FIX(1)
+#define TWO INT2FIX(2)
+
+VALUE rb_cRational;
+
+static ID id_abs, id_cmp, id_convert, id_equal_p, id_expt, id_floor,
+ id_format, id_hash, 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);
+}
+
+binop(xor, '^')
+
+fun1(abs)
+fun1(floor)
+fun1(hash)
+fun1(inspect)
+fun1(integer_p)
+fun1(negate)
+fun1(to_f)
+fun1(to_i)
+fun1(to_s)
+fun1(truncate)
+
+inline static VALUE
+f_equal_p(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(x) && FIXNUM_P(y))
+ return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
+ return rb_funcall(x, id_equal_p, 1, y);
+}
+
+fun2(expt)
+fun2(idiv)
+
+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)
+{
+ if (FIXNUM_P(x))
+ return f_boolcast(FIX2LONG(x) == 0);
+ return rb_funcall(x, id_equal_p, 1, ZERO);
+}
+
+#define f_nonzero_p(x) (!f_zero_p(x))
+
+inline static VALUE
+f_one_p(VALUE x)
+{
+ if (FIXNUM_P(x))
+ return f_boolcast(FIX2LONG(x) == 1);
+ return rb_funcall(x, id_equal_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)
+
+#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 zero")
+
+#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);
+}
+
+#ifndef EXT_MATHN
+#define f_unify_p(klass) rb_const_defined(klass, id_Unify)
+#else
+#define f_unify_p(klass) 1
+#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_eArgError, "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) && f_unify_p(klass))
+ 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) && f_unify_p(klass))
+ 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);
+}
+
+static VALUE
+nurat_f_rational(int argc, VALUE *argv, VALUE klass)
+{
+ return rb_funcall2(rb_cRational, id_convert, argc, argv);
+}
+
+static VALUE
+nurat_numerator(VALUE self)
+{
+ get_dat1(self);
+ return dat->num;
+}
+
+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;
+ 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_equal_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);
+}
+
+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, '+');
+ }
+}
+
+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);
+}
+
+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, '*');
+ }
+}
+
+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:
+ return rb_funcall(f_to_f(self), '/', 1, other);
+ case T_RATIONAL:
+ if (f_zero_p(other))
+ rb_raise_zerodiv();
+ {
+ get_dat2(self, other);
+
+ return f_muldiv(self,
+ adat->num, adat->den,
+ bdat->num, bdat->den, '/');
+ }
+ default:
+ return rb_num_coerce_bin(self, other, '/');
+ }
+}
+
+static VALUE
+nurat_fdiv(VALUE self, VALUE other)
+{
+ return f_div(f_to_f(self), other);
+}
+
+static VALUE
+nurat_expt(VALUE self, VALUE other)
+{
+ if (k_exact_p(other) && f_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; /* good? */
+ }
+
+ switch (TYPE(other)) {
+ case T_FIXNUM:
+ case T_BIGNUM:
+ {
+ 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_FLOAT:
+ case T_RATIONAL:
+ return f_expt(f_to_f(self), other);
+ default:
+ return rb_num_coerce_bin(self, other, id_expt);
+ }
+}
+
+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);
+ 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_bin(self, other, id_cmp);
+ }
+}
+
+static VALUE
+nurat_equal_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_equal_p(dat->num, other))
+ return Qtrue;
+ return Qfalse;
+ }
+ case T_FLOAT:
+ return f_equal_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_equal_p(adat->num, bdat->num) &&
+ f_equal_p(adat->den, bdat->den));
+ }
+ default:
+ return f_equal_p(other, self);
+ }
+}
+
+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));
+ }
+
+ rb_raise(rb_eTypeError, "%s can't be coerced into %s",
+ rb_obj_classname(other), rb_obj_classname(self));
+ return Qnil;
+}
+
+static VALUE
+nurat_idiv(VALUE self, VALUE other)
+{
+ return f_floor(f_div(self, other));
+}
+
+static VALUE
+nurat_mod(VALUE self, VALUE other)
+{
+ VALUE val = f_floor(f_div(self, other));
+ return f_sub(self, f_mul(other, val));
+}
+
+static VALUE
+nurat_divmod(VALUE self, VALUE other)
+{
+ VALUE val = f_floor(f_div(self, other));
+ return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
+}
+
+#if 0
+static VALUE
+nurat_quot(VALUE self, VALUE other)
+{
+ return f_truncate(f_div(self, other));
+}
+#endif
+
+static VALUE
+nurat_rem(VALUE self, VALUE other)
+{
+ VALUE val = f_truncate(f_div(self, other));
+ return f_sub(self, f_mul(other, val));
+}
+
+#if 0
+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
+
+static VALUE
+nurat_abs(VALUE self)
+{
+ if (f_positive_p(self))
+ return self;
+ return f_negate(self);
+}
+
+#if 0
+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));
+}
+
+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)
+{
+ get_dat1(self);
+
+ if (f_negative_p(dat->num)) {
+ VALUE num, den;
+
+ num = f_negate(dat->num);
+ num = f_add(f_mul(num, TWO), dat->den);
+ den = f_mul(dat->den, TWO);
+ return f_negate(f_idiv(num, den));
+ }
+ else {
+ VALUE num = f_add(f_mul(dat->num, TWO), dat->den);
+ VALUE den = f_mul(dat->den, TWO);
+ return f_idiv(num, den);
+ }
+}
+
+#define f_size(x) rb_funcall(x, rb_intern("size"), 0)
+#define f_rshift(x,y) rb_funcall(x, rb_intern(">>"), 1, y)
+
+inline static long
+i_ilog2(VALUE x)
+{
+ long q, r, fx;
+
+ assert(!f_lt_p(x, ONE));
+
+ q = (NUM2LONG(f_size(x)) - sizeof(long)) * 8 + 1;
+
+ if (q > 0)
+ x = f_rshift(x, LONG2NUM(q));
+
+ fx = NUM2LONG(x);
+
+ r = -1;
+ while (fx) {
+ fx >>= 1;
+ r += 1;
+ }
+
+ return q + r;
+}
+
+static long ml;
+
+static VALUE
+nurat_to_f(VALUE self)
+{
+ VALUE num, den;
+ int minus = 0;
+ long nl, dl, ne, de;
+ int e;
+ double f;
+
+ {
+ get_dat1(self);
+
+ if (f_zero_p(dat->num))
+ return rb_float_new(0.0);
+
+ num = dat->num;
+ den = dat->den;
+ }
+
+ if (f_negative_p(num)) {
+ num = f_negate(num);
+ minus = 1;
+ }
+
+ nl = i_ilog2(num);
+ dl = i_ilog2(den);
+
+ ne = 0;
+ if (nl > ml) {
+ ne = nl - ml;
+ num = f_rshift(num, LONG2NUM(ne));
+ }
+
+ de = 0;
+ if (dl > ml) {
+ de = dl - ml;
+ den = f_rshift(den, LONG2NUM(de));
+ }
+
+ e = (int)(ne - de);
+
+ if ((e > DBL_MAX_EXP) || (e < DBL_MIN_EXP)) {
+ rb_warning("%s out of Float range", rb_obj_classname(self));
+ return rb_float_new(e > 0 ? HUGE_VAL : 0.0);
+ }
+
+ f = NUM2DBL(num) / NUM2DBL(den);
+ if (minus)
+ f = -f;
+ f = ldexp(f, e);
+
+ if (isinf(f) || isnan(f))
+ rb_warning("%s out of Float range", rb_obj_classname(self));
+
+ return rb_float_new(f);
+}
+
+static VALUE
+nurat_to_r(VALUE self)
+{
+ return self;
+}
+
+static VALUE
+nurat_hash(VALUE self)
+{
+ get_dat1(self);
+ return f_xor(f_hash(dat->num), f_hash(dat->den));
+}
+
+static VALUE
+nurat_to_s(VALUE self)
+{
+ get_dat1(self);
+ return rb_funcall(rb_mKernel, id_format, 3,
+ rb_str_new2("%d/%d"), dat->num, dat->den);
+}
+
+static VALUE
+nurat_inspect(VALUE self)
+{
+ get_dat1(self);
+ return rb_funcall(rb_mKernel, id_format, 3,
+ rb_str_new2("(%d/%d)"), dat->num, dat->den);
+}
+
+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;
+}
+
+static VALUE
+nurat_marshal_load(VALUE self, VALUE a)
+{
+ get_dat1(self);
+ 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_gcd(VALUE self, VALUE other)
+{
+ other = nurat_int_value(other);
+ return f_gcd(self, other);
+}
+
+VALUE
+rb_lcm(VALUE self, VALUE other)
+{
+ other = nurat_int_value(other);
+ return f_lcm(self, other);
+}
+
+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);
+}
+
+static VALUE
+nilclass_to_r(VALUE self)
+{
+ return rb_rational_new1(INT2FIX(0));
+}
+
+static VALUE
+integer_to_r(VALUE self)
+{
+ return rb_rational_new1(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
+
+static VALUE
+float_to_r(VALUE self)
+{
+ VALUE f, n;
+
+ float_decode_internal(self, &f, &n);
+ return f_mul(f, f_expt(INT2FIX(FLT_RADIX), n));
+}
+
+static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore;
+
+#define WS "\\s*"
+#define DIGITS "(?:\\d(?:_\\d|\\d)*)"
+#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_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_aref rb_intern("[]")
+#define f_aref(x,y) rb_funcall(x, id_aref, 1, y)
+
+#define id_post_match rb_intern("post_match")
+#define f_post_match(x) rb_funcall(x, id_post_match, 0)
+
+#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 = f_aref(m, INT2FIX(1));
+ VALUE nu = f_aref(m, INT2FIX(2));
+ VALUE de = f_aref(m, INT2FIX(3));
+ VALUE re = f_post_match(m);
+
+ {
+ VALUE a;
+
+ 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];
+
+ 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 = StringValuePtr(fp);
+ long count = 0;
+ VALUE l;
+
+ while (*p) {
+ if (rb_isdigit(*p))
+ count++;
+ p++;
+ }
+
+ l = f_expt(INT2FIX(10), LONG2NUM(count));
+ v = f_mul(v, l);
+ v = f_add(v, f_to_i(fp));
+ v = f_div(v, l);
+ }
+ if (!NIL_P(si) && *StringValuePtr(si) == '-')
+ v = f_negate(v);
+ if (!NIL_P(exp))
+ v = f_mul(v, f_expt(INT2FIX(10), f_to_i(exp)));
+#if 0
+ if (!NIL_P(de) && (!NIL_P(fp) || !NIL_P(exp)))
+ return rb_assoc_new(v, rb_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 Rational: %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)
+
+static VALUE
+string_to_r(VALUE self)
+{
+ VALUE s, a, 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);
+
+ if (!NIL_P(RARRAY_PTR(a)[0]))
+ return RARRAY_PTR(a)[0];
+ 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);
+
+ switch (TYPE(a1)) {
+ case T_COMPLEX:
+ if (k_exact_p(RCOMPLEX(a1)->imag) && f_zero_p(RCOMPLEX(a1)->imag))
+ a1 = RCOMPLEX(a1)->real;
+ }
+
+ switch (TYPE(a2)) {
+ case T_COMPLEX:
+ if (k_exact_p(RCOMPLEX(a2)->imag) && f_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_p(a2) && f_one_p(a2)))
+ return a1;
+ }
+
+ if (argc == 1) {
+ if (k_numeric_p(a1) && !f_integer_p(a1))
+ return a1;
+ }
+ 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);
+ }
+}
+
+#ifndef EXT_MATHN
+void
+Init_Rational(void)
+#else
+void
+Init_rational(void)
+#endif
+{
+#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_equal_p = rb_intern("==");
+ id_expt = rb_intern("**");
+ id_floor = rb_intern("floor");
+ id_format = rb_intern("format");
+ id_hash = rb_intern("hash");
+ 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");
+
+ ml = (long)(log(DBL_MAX) / log(2.0) - 1);
+
+ rb_cRational = rb_define_class(RATIONAL_NAME, 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_NAME, 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_equal_p, 1);
+ rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
+
+ rb_define_method(rb_cRational, "div", nurat_idiv, 1);
+#if NUBY
+ rb_define_method(rb_cRational, "//", nurat_idiv, 1);
+#endif
+ rb_define_method(rb_cRational, "modulo", nurat_mod, 1);
+ rb_define_method(rb_cRational, "%", nurat_mod, 1);
+ rb_define_method(rb_cRational, "divmod", nurat_divmod, 1);
+
+#if 0
+ rb_define_method(rb_cRational, "quot", nurat_quot, 1);
+#endif
+ rb_define_method(rb_cRational, "remainder", nurat_rem, 1);
+#if 0
+ rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
+#endif
+
+ rb_define_method(rb_cRational, "abs", nurat_abs, 0);
+
+#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, 0);
+ rb_define_method(rb_cRational, "ceil", nurat_ceil, 0);
+ rb_define_method(rb_cRational, "truncate", nurat_truncate, 0);
+ rb_define_method(rb_cRational, "round", nurat_round, 0);
+
+ 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, "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_cNilClass, "to_r", nilclass_to_r, 0);
+ rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
+ rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
+
+ 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:
+*/