* lib/mathn.rb: moved into ext/mathn/rational/rational.c and

   ext/mathn/complex/complex.c.
 * ext/mathn: new mathn ext-libralies.



git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@19911 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

1 files changed, 1593 insertions, 0 deletions

diff --git a/ext/mathn/rational/rational.c b/ext/mathn/rational/rational.c
new file mode 100644
index 0000000000..ebbaa9b9ee
--- /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:
+*/