* complex.c: continues to support canonicalization *unofficially*

	  for an odd library mathn for the time being (only 1.9.x).
	  since grand mathn is must be very very special library for us.

	* rational.c: ditto.

	* ext/mathn/*/*: follow the above changes.



git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@20001 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

1 files changed, 2 insertions, 1618 deletions

diff --git a/ext/mathn/rational/rational.c b/ext/mathn/rational/rational.c
index 68f471260c..fe6797454d 100644
--- a/ext/mathn/rational/rational.c
+++ b/ext/mathn/rational/rational.c
@@ -1,1623 +1,7 @@
-/*
+extern void nurat_canonicalize(int);
 
-  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)
-
-#if 0
-VALUE rb_cRational;
-#endif
-
-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;
-}
-
-/* --- */
-
-#ifdef EXT_MATHN
-static
-#endif
-VALUE
-rb_gcd(VALUE self, VALUE other)
-{
-    other = nurat_int_value(other);
-    return f_gcd(self, other);
-}
-
-#ifdef EXT_MATHN
-static
-#endif
-VALUE
-rb_lcm(VALUE self, VALUE other)
-{
-    other = nurat_int_value(other);
-    return f_lcm(self, other);
-}
-
-#ifdef EXT_MATHN
-static
-#endif
-VALUE
-rb_gcdlcm(VALUE self, VALUE other)
-{
-    other = nurat_int_value(other);
-    return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
-}
-
-#ifdef EXT_MATHN
-VALUE
-rb_rational_raw(VALUE x, VALUE y)
-{
-    return nurat_s_new_internal(rb_cRational, x, y);
-}
-#endif
-
-#ifdef EXT_MATHN
-
-#undef rb_rational_new1
-#undef rb_rational_new2
-#define rb_rational_new1(x) rb_rational_new_mathn(x, INT2FIX(1))
-#define rb_rational_new2(x,y) rb_rational_new_mathn(x, y)
-
-static VALUE
-rb_rational_new_mathn(VALUE x, VALUE y)
-{
-    return nurat_s_canonicalize_internal(rb_cRational, x, y);
-}
-#else
-VALUE
-rb_rational_new(VALUE x, VALUE y)
-{
-    return nurat_s_canonicalize_internal(rb_cRational, x, y);
-}
-#endif
-
-static VALUE nurat_s_convert(int argc, VALUE *argv, VALUE klass);
-
-#ifdef EXT_MATHN
-VALUE
-rb_Rational(VALUE x, VALUE y)
-{
-    VALUE a[2];
-    a[0] = x;
-    a[1] = y;
-    return nurat_s_convert(2, a, rb_cRational);
-}
-#endif
-
-
-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);
+    nurat_canonicalize(1);
 }
-
-/*
-Local variables:
-c-file-style: "ruby"
-End:
-*/