Fresh start

1 files changed, 2625 insertions, 0 deletions

diff --git a/jni/ruby/rational.c b/jni/ruby/rational.c
new file mode 100644
index 0000000..134db64
--- /dev/null
+++ b/jni/ruby/rational.c
@@ -0,0 +1,2625 @@
+/*
+  rational.c: Coded by Tadayoshi Funaba 2008-2012
+
+  This implementation is based on Keiju Ishitsuka's Rational library
+  which is written in ruby.
+*/
+
+#include "internal.h"
+#include <math.h>
+#include <float.h>
+
+#ifdef HAVE_IEEEFP_H
+#include <ieeefp.h>
+#endif
+
+#define NDEBUG
+#include <assert.h>
+
+#if defined(HAVE_LIBGMP) && defined(HAVE_GMP_H)
+#define USE_GMP
+#include <gmp.h>
+#endif
+
+#define ZERO INT2FIX(0)
+#define ONE INT2FIX(1)
+#define TWO INT2FIX(2)
+
+#define GMP_GCD_DIGITS 1
+
+VALUE rb_cRational;
+
+static ID id_abs, id_cmp, id_convert, id_eqeq_p, id_expt, id_fdiv,
+    id_idiv, id_integer_p, id_negate, id_to_f,
+    id_to_i, id_truncate, id_i_num, id_i_den;
+
+#define f_boolcast(x) ((x) ? Qtrue : Qfalse)
+#define f_inspect rb_inspect
+#define f_to_s rb_obj_as_string
+
+#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_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) || RB_TYPE_P(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) || RB_TYPE_P(y, T_BIGNUM))
+		return ZERO;
+	}
+	else if (ix == 1)
+	    return y;
+    }
+    return rb_funcall(x, '*', 1, y);
+}
+
+inline static VALUE
+f_sub(VALUE x, VALUE y)
+{
+    if (FIXNUM_P(y) && FIX2LONG(y) == 0)
+	return x;
+    return rb_funcall(x, '-', 1, y);
+}
+
+fun1(abs)
+fun1(integer_p)
+fun1(negate)
+
+inline static VALUE
+f_to_i(VALUE x)
+{
+    if (RB_TYPE_P(x, T_STRING))
+	return rb_str_to_inum(x, 10, 0);
+    return rb_funcall(x, id_to_i, 0);
+}
+inline static VALUE
+f_to_f(VALUE x)
+{
+    if (RB_TYPE_P(x, T_STRING))
+	return DBL2NUM(rb_str_to_dbl(x, 0));
+    return rb_funcall(x, id_to_f, 0);
+}
+
+inline static VALUE
+f_eqeq_p(VALUE x, VALUE y)
+{
+    if (FIXNUM_P(x) && FIXNUM_P(y))
+	return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
+    return rb_funcall(x, id_eqeq_p, 1, y);
+}
+
+fun2(expt)
+fun2(fdiv)
+fun2(idiv)
+
+#define f_expt10(x) f_expt(INT2FIX(10), x)
+
+inline static VALUE
+f_negative_p(VALUE x)
+{
+    if (FIXNUM_P(x))
+	return f_boolcast(FIX2LONG(x) < 0);
+    return rb_funcall(x, '<', 1, ZERO);
+}
+
+#define f_positive_p(x) (!f_negative_p(x))
+
+inline static VALUE
+f_zero_p(VALUE x)
+{
+    if (RB_TYPE_P(x, T_FIXNUM)) {
+	return f_boolcast(FIX2LONG(x) == 0);
+    }
+    else if (RB_TYPE_P(x, T_BIGNUM)) {
+	return Qfalse;
+    }
+    else if (RB_TYPE_P(x, T_RATIONAL)) {
+	VALUE num = RRATIONAL(x)->num;
+
+	return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 0);
+    }
+    return rb_funcall(x, id_eqeq_p, 1, ZERO);
+}
+
+#define f_nonzero_p(x) (!f_zero_p(x))
+
+inline static VALUE
+f_one_p(VALUE x)
+{
+    if (RB_TYPE_P(x, T_FIXNUM)) {
+	return f_boolcast(FIX2LONG(x) == 1);
+    }
+    else if (RB_TYPE_P(x, T_BIGNUM)) {
+	return Qfalse;
+    }
+    else if (RB_TYPE_P(x, T_RATIONAL)) {
+	VALUE num = RRATIONAL(x)->num;
+	VALUE den = RRATIONAL(x)->den;
+
+	return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == 1 &&
+			  FIXNUM_P(den) && FIX2LONG(den) == 1);
+    }
+    return rb_funcall(x, id_eqeq_p, 1, ONE);
+}
+
+inline static VALUE
+f_minus_one_p(VALUE x)
+{
+    if (RB_TYPE_P(x, T_FIXNUM)) {
+	return f_boolcast(FIX2LONG(x) == -1);
+    }
+    else if (RB_TYPE_P(x, T_BIGNUM)) {
+	return Qfalse;
+    }
+    else if (RB_TYPE_P(x, T_RATIONAL)) {
+	VALUE num = RRATIONAL(x)->num;
+	VALUE den = RRATIONAL(x)->den;
+
+	return f_boolcast(FIXNUM_P(num) && FIX2LONG(num) == -1 &&
+			  FIXNUM_P(den) && FIX2LONG(den) == 1);
+    }
+    return rb_funcall(x, id_eqeq_p, 1, INT2FIX(-1));
+}
+
+inline static VALUE
+f_kind_of_p(VALUE x, VALUE c)
+{
+    return rb_obj_is_kind_of(x, c);
+}
+
+inline static VALUE
+k_numeric_p(VALUE x)
+{
+    return f_kind_of_p(x, rb_cNumeric);
+}
+
+inline static VALUE
+k_integer_p(VALUE x)
+{
+    return f_kind_of_p(x, rb_cInteger);
+}
+
+inline static VALUE
+k_float_p(VALUE x)
+{
+    return f_kind_of_p(x, rb_cFloat);
+}
+
+inline static VALUE
+k_rational_p(VALUE x)
+{
+    return f_kind_of_p(x, rb_cRational);
+}
+
+#define k_exact_p(x) (!k_float_p(x))
+#define k_inexact_p(x) k_float_p(x)
+
+#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x))
+#define k_exact_one_p(x) (k_exact_p(x) && f_one_p(x))
+
+#ifdef USE_GMP
+VALUE
+rb_gcd_gmp(VALUE x, VALUE y)
+{
+    const size_t nails = (sizeof(BDIGIT)-SIZEOF_BDIGIT)*CHAR_BIT;
+    mpz_t mx, my, mz;
+    size_t count;
+    VALUE z;
+    long zn;
+
+    mpz_init(mx);
+    mpz_init(my);
+    mpz_init(mz);
+    mpz_import(mx, BIGNUM_LEN(x), -1, sizeof(BDIGIT), 0, nails, BIGNUM_DIGITS(x));
+    mpz_import(my, BIGNUM_LEN(y), -1, sizeof(BDIGIT), 0, nails, BIGNUM_DIGITS(y));
+
+    mpz_gcd(mz, mx, my);
+
+    zn = (mpz_sizeinbase(mz, 16) + SIZEOF_BDIGIT*2 - 1) / (SIZEOF_BDIGIT*2);
+    z = rb_big_new(zn, 1);
+    mpz_export(BIGNUM_DIGITS(z), &count, -1, sizeof(BDIGIT), 0, nails, mz);
+
+    return rb_big_norm(z);
+}
+#endif
+
+#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_normal(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 */
+}
+
+VALUE
+rb_gcd_normal(VALUE x, VALUE y)
+{
+    return f_gcd_normal(x, y);
+}
+
+inline static VALUE
+f_gcd(VALUE x, VALUE y)
+{
+#ifdef USE_GMP
+    if (RB_TYPE_P(x, T_BIGNUM) && RB_TYPE_P(y, T_BIGNUM)) {
+        size_t xn = BIGNUM_LEN(x);
+        size_t yn = BIGNUM_LEN(y);
+        if (GMP_GCD_DIGITS <= xn || GMP_GCD_DIGITS <= yn)
+            return rb_gcd_gmp(x, y);
+    }
+#endif
+    return f_gcd_normal(x, y);
+}
+
+#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))
+
+#define RRATIONAL_SET_NUM(rat, n) RB_OBJ_WRITE((rat), &((struct RRational *)(rat))->num,(n))
+#define RRATIONAL_SET_DEN(rat, d) RB_OBJ_WRITE((rat), &((struct RRational *)(rat))->den,(d))
+
+inline static VALUE
+nurat_s_new_internal(VALUE klass, VALUE num, VALUE den)
+{
+    NEWOBJ_OF(obj, struct RRational, klass, T_RATIONAL | (RGENGC_WB_PROTECTED_RATIONAL ? FL_WB_PROTECTED : 0));
+
+    RRATIONAL_SET_NUM(obj, num);
+    RRATIONAL_SET_DEN(obj, den);
+
+    return (VALUE)obj;
+}
+
+static VALUE
+nurat_s_alloc(VALUE klass)
+{
+    return nurat_s_new_internal(klass, ZERO, ONE);
+}
+
+#define rb_raise_zerodiv() rb_raise(rb_eZeroDivError, "divided by 0")
+
+#if 0
+static VALUE
+nurat_s_new_bang(int argc, VALUE *argv, VALUE klass)
+{
+    VALUE num, den;
+
+    switch (rb_scan_args(argc, argv, "11", &num, &den)) {
+      case 1:
+	if (!k_integer_p(num))
+	    num = f_to_i(num);
+	den = ONE;
+	break;
+      default:
+	if (!k_integer_p(num))
+	    num = f_to_i(num);
+	if (!k_integer_p(den))
+	    den = f_to_i(den);
+
+	switch (FIX2INT(f_cmp(den, ZERO))) {
+	  case -1:
+	    num = f_negate(num);
+	    den = f_negate(den);
+	    break;
+	  case 0:
+	    rb_raise_zerodiv();
+	    break;
+	}
+	break;
+    }
+
+    return nurat_s_new_internal(klass, num, den);
+}
+#endif
+
+inline static VALUE
+f_rational_new_bang1(VALUE klass, VALUE x)
+{
+    return nurat_s_new_internal(klass, x, ONE);
+}
+
+#ifdef CANONICALIZATION_FOR_MATHN
+#define CANON
+#endif
+
+#ifdef CANON
+static int canonicalization = 0;
+
+RUBY_FUNC_EXPORTED void
+nurat_canonicalization(int f)
+{
+    canonicalization = f;
+}
+#endif
+
+inline static void
+nurat_int_check(VALUE num)
+{
+    if (!(RB_TYPE_P(num, T_FIXNUM) || RB_TYPE_P(num, T_BIGNUM))) {
+	if (!k_numeric_p(num) || !f_integer_p(num))
+	    rb_raise(rb_eTypeError, "not an integer");
+    }
+}
+
+inline static VALUE
+nurat_int_value(VALUE num)
+{
+    nurat_int_check(num);
+    if (!k_integer_p(num))
+	num = f_to_i(num);
+    return num;
+}
+
+inline static VALUE
+nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den)
+{
+    VALUE gcd;
+
+    switch (FIX2INT(f_cmp(den, ZERO))) {
+      case -1:
+	num = f_negate(num);
+	den = f_negate(den);
+	break;
+      case 0:
+	rb_raise_zerodiv();
+	break;
+    }
+
+    gcd = f_gcd(num, den);
+    num = f_idiv(num, gcd);
+    den = f_idiv(den, gcd);
+
+#ifdef CANON
+    if (f_one_p(den) && canonicalization)
+	return num;
+#endif
+    return nurat_s_new_internal(klass, num, den);
+}
+
+inline static VALUE
+nurat_s_canonicalize_internal_no_reduce(VALUE klass, VALUE num, VALUE den)
+{
+    switch (FIX2INT(f_cmp(den, ZERO))) {
+      case -1:
+	num = f_negate(num);
+	den = f_negate(den);
+	break;
+      case 0:
+	rb_raise_zerodiv();
+	break;
+    }
+
+#ifdef CANON
+    if (f_one_p(den) && canonicalization)
+	return num;
+#endif
+    return nurat_s_new_internal(klass, num, den);
+}
+
+static VALUE
+nurat_s_new(int argc, VALUE *argv, VALUE klass)
+{
+    VALUE num, den;
+
+    switch (rb_scan_args(argc, argv, "11", &num, &den)) {
+      case 1:
+	num = nurat_int_value(num);
+	den = ONE;
+	break;
+      default:
+	num = nurat_int_value(num);
+	den = nurat_int_value(den);
+	break;
+    }
+
+    return nurat_s_canonicalize_internal(klass, num, den);
+}
+
+inline static VALUE
+f_rational_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_reduce2(VALUE klass, VALUE x, VALUE y)
+{
+    assert(!k_rational_p(x));
+    assert(!k_rational_p(y));
+    return nurat_s_canonicalize_internal_no_reduce(klass, x, y);
+}
+
+/*
+ * call-seq:
+ *    Rational(x[, y])  ->  numeric
+ *
+ * Returns x/y;
+ *
+ *    Rational(1, 2)   #=> (1/2)
+ *    Rational('1/2')  #=> (1/2)
+ *    Rational(nil)    #=> TypeError
+ *    Rational(1, nil) #=> TypeError
+ *
+ * Syntax of string form:
+ *
+ *   string form = extra spaces , rational , extra spaces ;
+ *   rational = [ sign ] , unsigned rational ;
+ *   unsigned rational = numerator | numerator , "/" , denominator ;
+ *   numerator = integer part | fractional part | integer part , fractional part ;
+ *   denominator = digits ;
+ *   integer part = digits ;
+ *   fractional part = "." , digits , [ ( "e" | "E" ) , [ sign ] , digits ] ;
+ *   sign = "-" | "+" ;
+ *   digits = digit , { digit | "_" , digit } ;
+ *   digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
+ *   extra spaces = ? \s* ? ;
+ *
+ * See String#to_r.
+ */
+static VALUE
+nurat_f_rational(int argc, VALUE *argv, VALUE klass)
+{
+    return rb_funcall2(rb_cRational, id_convert, argc, argv);
+}
+
+/*
+ * call-seq:
+ *    rat.numerator  ->  integer
+ *
+ * Returns the numerator.
+ *
+ *    Rational(7).numerator        #=> 7
+ *    Rational(7, 1).numerator     #=> 7
+ *    Rational(9, -4).numerator    #=> -9
+ *    Rational(-2, -10).numerator  #=> 1
+ */
+static VALUE
+nurat_numerator(VALUE self)
+{
+    get_dat1(self);
+    return dat->num;
+}
+
+/*
+ * call-seq:
+ *    rat.denominator  ->  integer
+ *
+ * Returns the denominator (always positive).
+ *
+ *    Rational(7).denominator             #=> 1
+ *    Rational(7, 1).denominator          #=> 1
+ *    Rational(9, -4).denominator         #=> 4
+ *    Rational(-2, -10).denominator       #=> 5
+ *    rat.numerator.gcd(rat.denominator)  #=> 1
+ */
+static VALUE
+nurat_denominator(VALUE self)
+{
+    get_dat1(self);
+    return dat->den;
+}
+
+#ifndef NDEBUG
+#define f_imul f_imul_orig
+#endif
+
+inline static VALUE
+f_imul(long a, long b)
+{
+    VALUE r;
+
+    if (a == 0 || b == 0)
+	return ZERO;
+    else if (a == 1)
+	return LONG2NUM(b);
+    else if (b == 1)
+	return LONG2NUM(a);
+
+    if (MUL_OVERFLOW_LONG_P(a, b))
+	r = rb_big_mul(rb_int2big(a), rb_int2big(b));
+    else
+        r = LONG2NUM(a * b);
+    return r;
+}
+
+#ifndef NDEBUG
+#undef f_imul
+
+inline static VALUE
+f_imul(long x, long y)
+{
+    VALUE r = f_imul_orig(x, y);
+    assert(f_eqeq_p(r, f_mul(LONG2NUM(x), LONG2NUM(y))));
+    return r;
+}
+#endif
+
+inline static VALUE
+f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
+{
+    VALUE num, den;
+
+    if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
+	FIXNUM_P(bnum) && FIXNUM_P(bden)) {
+	long an = FIX2LONG(anum);
+	long ad = FIX2LONG(aden);
+	long bn = FIX2LONG(bnum);
+	long bd = FIX2LONG(bden);
+	long ig = i_gcd(ad, bd);
+
+	VALUE g = LONG2NUM(ig);
+	VALUE a = f_imul(an, bd / ig);
+	VALUE b = f_imul(bn, ad / ig);
+	VALUE c;
+
+	if (k == '+')
+	    c = f_add(a, b);
+	else
+	    c = f_sub(a, b);
+
+	b = f_idiv(aden, g);
+	g = f_gcd(c, g);
+	num = f_idiv(c, g);
+	a = f_idiv(bden, g);
+	den = f_mul(a, b);
+    }
+    else {
+	VALUE g = f_gcd(aden, bden);
+	VALUE a = f_mul(anum, f_idiv(bden, g));
+	VALUE b = f_mul(bnum, f_idiv(aden, g));
+	VALUE c;
+
+	if (k == '+')
+	    c = f_add(a, b);
+	else
+	    c = f_sub(a, b);
+
+	b = f_idiv(aden, g);
+	g = f_gcd(c, g);
+	num = f_idiv(c, g);
+	a = f_idiv(bden, g);
+	den = f_mul(a, b);
+    }
+    return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
+}
+
+/*
+ * call-seq:
+ *    rat + numeric  ->  numeric
+ *
+ * Performs addition.
+ *
+ *    Rational(2, 3)  + Rational(2, 3)   #=> (4/3)
+ *    Rational(900)   + Rational(1)      #=> (900/1)
+ *    Rational(-2, 9) + Rational(-9, 2)  #=> (-85/18)
+ *    Rational(9, 8)  + 4                #=> (41/8)
+ *    Rational(20, 9) + 9.8              #=> 12.022222222222222
+ */
+static VALUE
+nurat_add(VALUE self, VALUE other)
+{
+    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
+	{
+	    get_dat1(self);
+
+	    return f_addsub(self,
+			    dat->num, dat->den,
+			    other, ONE, '+');
+	}
+    }
+    else if (RB_TYPE_P(other, T_FLOAT)) {
+	return f_add(f_to_f(self), other);
+    }
+    else if (RB_TYPE_P(other, T_RATIONAL)) {
+	{
+	    get_dat2(self, other);
+
+	    return f_addsub(self,
+			    adat->num, adat->den,
+			    bdat->num, bdat->den, '+');
+	}
+    }
+    else {
+	return rb_num_coerce_bin(self, other, '+');
+    }
+}
+
+/*
+ * call-seq:
+ *    rat - numeric  ->  numeric
+ *
+ * Performs subtraction.
+ *
+ *    Rational(2, 3)  - Rational(2, 3)   #=> (0/1)
+ *    Rational(900)   - Rational(1)      #=> (899/1)
+ *    Rational(-2, 9) - Rational(-9, 2)  #=> (77/18)
+ *    Rational(9, 8)  - 4                #=> (23/8)
+ *    Rational(20, 9) - 9.8              #=> -7.577777777777778
+ */
+static VALUE
+nurat_sub(VALUE self, VALUE other)
+{
+    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
+	{
+	    get_dat1(self);
+
+	    return f_addsub(self,
+			    dat->num, dat->den,
+			    other, ONE, '-');
+	}
+    }
+    else if (RB_TYPE_P(other, T_FLOAT)) {
+	return f_sub(f_to_f(self), other);
+    }
+    else if (RB_TYPE_P(other, T_RATIONAL)) {
+	{
+	    get_dat2(self, other);
+
+	    return f_addsub(self,
+			    adat->num, adat->den,
+			    bdat->num, bdat->den, '-');
+	}
+    }
+    else {
+	return rb_num_coerce_bin(self, other, '-');
+    }
+}
+
+inline static VALUE
+f_muldiv(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
+{
+    VALUE num, den;
+
+    if (k == '/') {
+	VALUE t;
+
+	if (f_negative_p(bnum)) {
+	    anum = f_negate(anum);
+	    bnum = f_negate(bnum);
+	}
+	t = bnum;
+	bnum = bden;
+	bden = t;
+    }
+
+    if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
+	FIXNUM_P(bnum) && FIXNUM_P(bden)) {
+	long an = FIX2LONG(anum);
+	long ad = FIX2LONG(aden);
+	long bn = FIX2LONG(bnum);
+	long bd = FIX2LONG(bden);
+	long g1 = i_gcd(an, bd);
+	long g2 = i_gcd(ad, bn);
+
+	num = f_imul(an / g1, bn / g2);
+	den = f_imul(ad / g2, bd / g1);
+    }
+    else {
+	VALUE g1 = f_gcd(anum, bden);
+	VALUE g2 = f_gcd(aden, bnum);
+
+	num = f_mul(f_idiv(anum, g1), f_idiv(bnum, g2));
+	den = f_mul(f_idiv(aden, g2), f_idiv(bden, g1));
+    }
+    return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
+}
+
+/*
+ * call-seq:
+ *    rat * numeric  ->  numeric
+ *
+ * Performs multiplication.
+ *
+ *    Rational(2, 3)  * Rational(2, 3)   #=> (4/9)
+ *    Rational(900)   * Rational(1)      #=> (900/1)
+ *    Rational(-2, 9) * Rational(-9, 2)  #=> (1/1)
+ *    Rational(9, 8)  * 4                #=> (9/2)
+ *    Rational(20, 9) * 9.8              #=> 21.77777777777778
+ */
+static VALUE
+nurat_mul(VALUE self, VALUE other)
+{
+    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
+	{
+	    get_dat1(self);
+
+	    return f_muldiv(self,
+			    dat->num, dat->den,
+			    other, ONE, '*');
+	}
+    }
+    else if (RB_TYPE_P(other, T_FLOAT)) {
+	return f_mul(f_to_f(self), other);
+    }
+    else if (RB_TYPE_P(other, T_RATIONAL)) {
+	{
+	    get_dat2(self, other);
+
+	    return f_muldiv(self,
+			    adat->num, adat->den,
+			    bdat->num, bdat->den, '*');
+	}
+    }
+    else {
+	return rb_num_coerce_bin(self, other, '*');
+    }
+}
+
+/*
+ * call-seq:
+ *    rat / numeric     ->  numeric
+ *    rat.quo(numeric)  ->  numeric
+ *
+ * Performs division.
+ *
+ *    Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
+ *    Rational(900)   / Rational(1)      #=> (900/1)
+ *    Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
+ *    Rational(9, 8)  / 4                #=> (9/32)
+ *    Rational(20, 9) / 9.8              #=> 0.22675736961451246
+ */
+static VALUE
+nurat_div(VALUE self, VALUE other)
+{
+    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
+	if (f_zero_p(other))
+	    rb_raise_zerodiv();
+	{
+	    get_dat1(self);
+
+	    return f_muldiv(self,
+			    dat->num, dat->den,
+			    other, ONE, '/');
+	}
+    }
+    else if (RB_TYPE_P(other, T_FLOAT))
+	return rb_funcall(f_to_f(self), '/', 1, other);
+    else if (RB_TYPE_P(other, T_RATIONAL)) {
+	if (f_zero_p(other))
+	    rb_raise_zerodiv();
+	{
+	    get_dat2(self, other);
+
+	    if (f_one_p(self))
+		return f_rational_new_no_reduce2(CLASS_OF(self),
+						 bdat->den, bdat->num);
+
+	    return f_muldiv(self,
+			    adat->num, adat->den,
+			    bdat->num, bdat->den, '/');
+	}
+    }
+    else {
+	return rb_num_coerce_bin(self, other, '/');
+    }
+}
+
+/*
+ * call-seq:
+ *    rat.fdiv(numeric)  ->  float
+ *
+ * Performs division and returns the value as a float.
+ *
+ *    Rational(2, 3).fdiv(1)       #=> 0.6666666666666666
+ *    Rational(2, 3).fdiv(0.5)     #=> 1.3333333333333333
+ *    Rational(2).fdiv(3)          #=> 0.6666666666666666
+ */
+static VALUE
+nurat_fdiv(VALUE self, VALUE other)
+{
+    if (f_zero_p(other))
+	return f_div(self, f_to_f(other));
+    return f_to_f(f_div(self, other));
+}
+
+inline static VALUE
+f_odd_p(VALUE integer)
+{
+    if (rb_funcall(integer, '%', 1, INT2FIX(2)) != INT2FIX(0)) {
+	return Qtrue;
+    }
+    return Qfalse;
+}
+
+/*
+ * call-seq:
+ *    rat ** numeric  ->  numeric
+ *
+ * Performs exponentiation.
+ *
+ *    Rational(2)    ** Rational(3)    #=> (8/1)
+ *    Rational(10)   ** -2             #=> (1/100)
+ *    Rational(10)   ** -2.0           #=> 0.01
+ *    Rational(-4)   ** Rational(1,2)  #=> (1.2246063538223773e-16+2.0i)
+ *    Rational(1, 2) ** 0              #=> (1/1)
+ *    Rational(1, 2) ** 0.0            #=> 1.0
+ */
+static VALUE
+nurat_expt(VALUE self, VALUE other)
+{
+    if (k_numeric_p(other) && k_exact_zero_p(other))
+	return f_rational_new_bang1(CLASS_OF(self), ONE);
+
+    if (k_rational_p(other)) {
+	get_dat1(other);
+
+	if (f_one_p(dat->den))
+	    other = dat->num; /* c14n */
+    }
+
+    /* Deal with special cases of 0**n and 1**n */
+    if (k_numeric_p(other) && k_exact_p(other)) {
+	get_dat1(self);
+	if (f_one_p(dat->den)) {
+	    if (f_one_p(dat->num)) {
+		return f_rational_new_bang1(CLASS_OF(self), ONE);
+	    }
+	    else if (f_minus_one_p(dat->num) && k_integer_p(other)) {
+		return f_rational_new_bang1(CLASS_OF(self), INT2FIX(f_odd_p(other) ? -1 : 1));
+	    }
+	    else if (f_zero_p(dat->num)) {
+		if (FIX2INT(f_cmp(other, ZERO)) == -1) {
+		    rb_raise_zerodiv();
+		}
+		else {
+		    return f_rational_new_bang1(CLASS_OF(self), ZERO);
+		}
+	    }
+	}
+    }
+
+    /* General case */
+    if (RB_TYPE_P(other, T_FIXNUM)) {
+	{
+	    VALUE num, den;
+
+	    get_dat1(self);
+
+	    switch (FIX2INT(f_cmp(other, ZERO))) {
+	      case 1:
+		num = f_expt(dat->num, other);
+		den = f_expt(dat->den, other);
+		break;
+	      case -1:
+		num = f_expt(dat->den, f_negate(other));
+		den = f_expt(dat->num, f_negate(other));
+		break;
+	      default:
+		num = ONE;
+		den = ONE;
+		break;
+	    }
+	    return f_rational_new2(CLASS_OF(self), num, den);
+	}
+    }
+    else if (RB_TYPE_P(other, T_BIGNUM)) {
+	rb_warn("in a**b, b may be too big");
+	return f_expt(f_to_f(self), other);
+    }
+    else if (RB_TYPE_P(other, T_FLOAT) || RB_TYPE_P(other, T_RATIONAL)) {
+	return f_expt(f_to_f(self), other);
+    }
+    else {
+	return rb_num_coerce_bin(self, other, id_expt);
+    }
+}
+
+/*
+ * call-seq:
+ *    rational <=> numeric  ->  -1, 0, +1 or nil
+ *
+ * Performs comparison and returns -1, 0, or +1.
+ *
+ * +nil+ is returned if the two values are incomparable.
+ *
+ *    Rational(2, 3)  <=> Rational(2, 3)  #=> 0
+ *    Rational(5)     <=> 5               #=> 0
+ *    Rational(2,3)   <=> Rational(1,3)   #=> 1
+ *    Rational(1,3)   <=> 1               #=> -1
+ *    Rational(1,3)   <=> 0.3             #=> 1
+ */
+static VALUE
+nurat_cmp(VALUE self, VALUE other)
+{
+    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
+	{
+	    get_dat1(self);
+
+	    if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1)
+		return f_cmp(dat->num, other); /* c14n */
+	    return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other));
+	}
+    }
+    else if (RB_TYPE_P(other, T_FLOAT)) {
+	return f_cmp(f_to_f(self), other);
+    }
+    else if (RB_TYPE_P(other, 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);
+	}
+    }
+    else {
+	return rb_num_coerce_cmp(self, other, id_cmp);
+    }
+}
+
+/*
+ * call-seq:
+ *    rat == object  ->  true or false
+ *
+ * Returns true if rat equals object numerically.
+ *
+ *    Rational(2, 3)  == Rational(2, 3)   #=> true
+ *    Rational(5)     == 5                #=> true
+ *    Rational(0)     == 0.0              #=> true
+ *    Rational('1/3') == 0.33             #=> false
+ *    Rational('1/2') == '1/2'            #=> false
+ */
+static VALUE
+nurat_eqeq_p(VALUE self, VALUE other)
+{
+    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
+	{
+	    get_dat1(self);
+
+	    if (f_zero_p(dat->num) && f_zero_p(other))
+		return Qtrue;
+
+	    if (!FIXNUM_P(dat->den))
+		return Qfalse;
+	    if (FIX2LONG(dat->den) != 1)
+		return Qfalse;
+	    if (f_eqeq_p(dat->num, other))
+		return Qtrue;
+	    return Qfalse;
+	}
+    }
+    else if (RB_TYPE_P(other, T_FLOAT)) {
+	return f_eqeq_p(f_to_f(self), other);
+    }
+    else if (RB_TYPE_P(other, T_RATIONAL)) {
+	{
+	    get_dat2(self, other);
+
+	    if (f_zero_p(adat->num) && f_zero_p(bdat->num))
+		return Qtrue;
+
+	    return f_boolcast(f_eqeq_p(adat->num, bdat->num) &&
+			      f_eqeq_p(adat->den, bdat->den));
+	}
+    }
+    else {
+	return f_eqeq_p(other, self);
+    }
+}
+
+/* :nodoc: */
+static VALUE
+nurat_coerce(VALUE self, VALUE other)
+{
+    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
+	return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self);
+    }
+    else if (RB_TYPE_P(other, T_FLOAT)) {
+	return rb_assoc_new(other, f_to_f(self));
+    }
+    else if (RB_TYPE_P(other, T_RATIONAL)) {
+	return rb_assoc_new(other, self);
+    }
+    else if (RB_TYPE_P(other, T_COMPLEX)) {
+	if (k_exact_zero_p(RCOMPLEX(other)->imag))
+	    return rb_assoc_new(f_rational_new_bang1
+				(CLASS_OF(self), RCOMPLEX(other)->real), self);
+	else
+	    return rb_assoc_new(other, rb_Complex(self, INT2FIX(0)));
+    }
+
+    rb_raise(rb_eTypeError, "%s can't be coerced into %s",
+	     rb_obj_classname(other), rb_obj_classname(self));
+    return Qnil;
+}
+
+#if 0
+/* :nodoc: */
+static VALUE
+nurat_idiv(VALUE self, VALUE other)
+{
+    return f_idiv(self, other);
+}
+
+/* :nodoc: */
+static VALUE
+nurat_quot(VALUE self, VALUE other)
+{
+    return f_truncate(f_div(self, other));
+}
+
+/* :nodoc: */
+static VALUE
+nurat_quotrem(VALUE self, VALUE other)
+{
+    VALUE val = f_truncate(f_div(self, other));
+    return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
+}
+#endif
+
+#if 0
+/* :nodoc: */
+static VALUE
+nurat_true(VALUE self)
+{
+    return Qtrue;
+}
+#endif
+
+static VALUE
+nurat_floor(VALUE self)
+{
+    get_dat1(self);
+    return f_idiv(dat->num, dat->den);
+}
+
+static VALUE
+nurat_ceil(VALUE self)
+{
+    get_dat1(self);
+    return f_negate(f_idiv(f_negate(dat->num), dat->den));
+}
+
+/*
+ * call-seq:
+ *    rat.to_i  ->  integer
+ *
+ * Returns the truncated value as an integer.
+ *
+ * Equivalent to
+ *    rat.truncate.
+ *
+ *    Rational(2, 3).to_i   #=> 0
+ *    Rational(3).to_i      #=> 3
+ *    Rational(300.6).to_i  #=> 300
+ *    Rational(98,71).to_i  #=> 1
+ *    Rational(-30,2).to_i  #=> -15
+ */
+static VALUE
+nurat_truncate(VALUE self)
+{
+    get_dat1(self);
+    if (f_negative_p(dat->num))
+	return f_negate(f_idiv(f_negate(dat->num), dat->den));
+    return f_idiv(dat->num, dat->den);
+}
+
+static VALUE
+nurat_round(VALUE self)
+{
+    VALUE num, den, neg;
+
+    get_dat1(self);
+
+    num = dat->num;
+    den = dat->den;
+    neg = f_negative_p(num);
+
+    if (neg)
+	num = f_negate(num);
+
+    num = f_add(f_mul(num, TWO), den);
+    den = f_mul(den, TWO);
+    num = f_idiv(num, den);
+
+    if (neg)
+	num = f_negate(num);
+
+    return num;
+}
+
+static VALUE
+f_round_common(int argc, VALUE *argv, VALUE self, VALUE (*func)(VALUE))
+{
+    VALUE n, b, s;
+
+    if (argc == 0)
+	return (*func)(self);
+
+    rb_scan_args(argc, argv, "01", &n);
+
+    if (!k_integer_p(n))
+	rb_raise(rb_eTypeError, "not an integer");
+
+    b = f_expt10(n);
+    s = f_mul(self, b);
+
+    if (k_float_p(s)) {
+	if (f_lt_p(n, ZERO))
+	    return ZERO;
+	return self;
+    }
+
+    if (!k_rational_p(s)) {
+	s = f_rational_new_bang1(CLASS_OF(self), s);
+    }
+
+    s = (*func)(s);
+
+    s = f_div(f_rational_new_bang1(CLASS_OF(self), s), b);
+
+    if (f_lt_p(n, ONE))
+	s = f_to_i(s);
+
+    return s;
+}
+
+/*
+ * call-seq:
+ *    rat.floor               ->  integer
+ *    rat.floor(precision=0)  ->  rational
+ *
+ * Returns the truncated value (toward negative infinity).
+ *
+ *    Rational(3).floor      #=> 3
+ *    Rational(2, 3).floor   #=> 0
+ *    Rational(-3, 2).floor  #=> -1
+ *
+ *           decimal      -  1  2  3 . 4  5  6
+ *                          ^  ^  ^  ^   ^  ^
+ *          precision      -3 -2 -1  0  +1 +2
+ *
+ *    '%f' % Rational('-123.456').floor(+1)  #=> "-123.500000"
+ *    '%f' % Rational('-123.456').floor(-1)  #=> "-130.000000"
+ */
+static VALUE
+nurat_floor_n(int argc, VALUE *argv, VALUE self)
+{
+    return f_round_common(argc, argv, self, nurat_floor);
+}
+
+/*
+ * call-seq:
+ *    rat.ceil               ->  integer
+ *    rat.ceil(precision=0)  ->  rational
+ *
+ * Returns the truncated value (toward positive infinity).
+ *
+ *    Rational(3).ceil      #=> 3
+ *    Rational(2, 3).ceil   #=> 1
+ *    Rational(-3, 2).ceil  #=> -1
+ *
+ *           decimal      -  1  2  3 . 4  5  6
+ *                          ^  ^  ^  ^   ^  ^
+ *          precision      -3 -2 -1  0  +1 +2
+ *
+ *    '%f' % Rational('-123.456').ceil(+1)  #=> "-123.400000"
+ *    '%f' % Rational('-123.456').ceil(-1)  #=> "-120.000000"
+ */
+static VALUE
+nurat_ceil_n(int argc, VALUE *argv, VALUE self)
+{
+    return f_round_common(argc, argv, self, nurat_ceil);
+}
+
+/*
+ * call-seq:
+ *    rat.truncate               ->  integer
+ *    rat.truncate(precision=0)  ->  rational
+ *
+ * Returns the truncated value (toward zero).
+ *
+ *    Rational(3).truncate      #=> 3
+ *    Rational(2, 3).truncate   #=> 0
+ *    Rational(-3, 2).truncate  #=> -1
+ *
+ *           decimal      -  1  2  3 . 4  5  6
+ *                          ^  ^  ^  ^   ^  ^
+ *          precision      -3 -2 -1  0  +1 +2
+ *
+ *    '%f' % Rational('-123.456').truncate(+1)  #=>  "-123.400000"
+ *    '%f' % Rational('-123.456').truncate(-1)  #=>  "-120.000000"
+ */
+static VALUE
+nurat_truncate_n(int argc, VALUE *argv, VALUE self)
+{
+    return f_round_common(argc, argv, self, nurat_truncate);
+}
+
+/*
+ * call-seq:
+ *    rat.round               ->  integer
+ *    rat.round(precision=0)  ->  rational
+ *
+ * Returns the truncated value (toward the nearest integer;
+ * 0.5 => 1; -0.5 => -1).
+ *
+ *    Rational(3).round      #=> 3
+ *    Rational(2, 3).round   #=> 1
+ *    Rational(-3, 2).round  #=> -2
+ *
+ *           decimal      -  1  2  3 . 4  5  6
+ *                          ^  ^  ^  ^   ^  ^
+ *          precision      -3 -2 -1  0  +1 +2
+ *
+ *    '%f' % Rational('-123.456').round(+1)  #=> "-123.500000"
+ *    '%f' % Rational('-123.456').round(-1)  #=> "-120.000000"
+ */
+static VALUE
+nurat_round_n(int argc, VALUE *argv, VALUE self)
+{
+    return f_round_common(argc, argv, self, nurat_round);
+}
+
+/*
+ * call-seq:
+ *    rat.to_f  ->  float
+ *
+ * Return the value as a float.
+ *
+ *    Rational(2).to_f      #=> 2.0
+ *    Rational(9, 4).to_f   #=> 2.25
+ *    Rational(-3, 4).to_f  #=> -0.75
+ *    Rational(20, 3).to_f  #=> 6.666666666666667
+ */
+static VALUE
+nurat_to_f(VALUE self)
+{
+    get_dat1(self);
+    return f_fdiv(dat->num, dat->den);
+}
+
+/*
+ * call-seq:
+ *    rat.to_r  ->  self
+ *
+ * Returns self.
+ *
+ *    Rational(2).to_r      #=> (2/1)
+ *    Rational(-8, 6).to_r  #=> (-4/3)
+ */
+static VALUE
+nurat_to_r(VALUE self)
+{
+    return self;
+}
+
+#define id_ceil rb_intern("ceil")
+#define f_ceil(x) rb_funcall((x), id_ceil, 0)
+
+#define id_quo rb_intern("quo")
+#define f_quo(x,y) rb_funcall((x), id_quo, 1, (y))
+
+#define f_reciprocal(x) f_quo(ONE, (x))
+
+/*
+  The algorithm here is the method described in CLISP.  Bruno Haible has
+  graciously given permission to use this algorithm.  He says, "You can use
+  it, if you present the following explanation of the algorithm."
+
+  Algorithm (recursively presented):
+    If x is a rational number, return x.
+    If x = 0.0, return 0.
+    If x < 0.0, return (- (rationalize (- x))).
+    If x > 0.0:
+      Call (integer-decode-float x). It returns a m,e,s=1 (mantissa,
+      exponent, sign).
+      If m = 0 or e >= 0: return x = m*2^e.
+      Search a rational number between a = (m-1/2)*2^e and b = (m+1/2)*2^e
+      with smallest possible numerator and denominator.
+      Note 1: If m is a power of 2, we ought to take a = (m-1/4)*2^e.
+        But in this case the result will be x itself anyway, regardless of
+        the choice of a. Therefore we can simply ignore this case.
+      Note 2: At first, we need to consider the closed interval [a,b].
+        but since a and b have the denominator 2^(|e|+1) whereas x itself
+        has a denominator <= 2^|e|, we can restrict the search to the open
+        interval (a,b).
+      So, for given a and b (0 < a < b) we are searching a rational number
+      y with a <= y <= b.
+      Recursive algorithm fraction_between(a,b):
+        c := (ceiling a)
+        if c < b
+          then return c       ; because a <= c < b, c integer
+          else
+            ; a is not integer (otherwise we would have had c = a < b)
+            k := c-1          ; k = floor(a), k < a < b <= k+1
+            return y = k + 1/fraction_between(1/(b-k), 1/(a-k))
+                              ; note 1 <= 1/(b-k) < 1/(a-k)
+
+  You can see that we are actually computing a continued fraction expansion.
+
+  Algorithm (iterative):
+    If x is rational, return x.
+    Call (integer-decode-float x). It returns a m,e,s (mantissa,
+      exponent, sign).
+    If m = 0 or e >= 0, return m*2^e*s. (This includes the case x = 0.0.)
+    Create rational numbers a := (2*m-1)*2^(e-1) and b := (2*m+1)*2^(e-1)
+    (positive and already in lowest terms because the denominator is a
+    power of two and the numerator is odd).
+    Start a continued fraction expansion
+      p[-1] := 0, p[0] := 1, q[-1] := 1, q[0] := 0, i := 0.
+    Loop
+      c := (ceiling a)
+      if c >= b
+        then k := c-1, partial_quotient(k), (a,b) := (1/(b-k),1/(a-k)),
+             goto Loop
+    finally partial_quotient(c).
+    Here partial_quotient(c) denotes the iteration
+      i := i+1, p[i] := c*p[i-1]+p[i-2], q[i] := c*q[i-1]+q[i-2].
+    At the end, return s * (p[i]/q[i]).
+    This rational number is already in lowest terms because
+    p[i]*q[i-1]-p[i-1]*q[i] = (-1)^i.
+*/
+
+static void
+nurat_rationalize_internal(VALUE a, VALUE b, VALUE *p, VALUE *q)
+{
+    VALUE c, k, t, p0, p1, p2, q0, q1, q2;
+
+    p0 = ZERO;
+    p1 = ONE;
+    q0 = ONE;
+    q1 = ZERO;
+
+    while (1) {
+	c = f_ceil(a);
+	if (f_lt_p(c, b))
+	    break;
+	k = f_sub(c, ONE);
+	p2 = f_add(f_mul(k, p1), p0);
+	q2 = f_add(f_mul(k, q1), q0);
+	t = f_reciprocal(f_sub(b, k));
+	b = f_reciprocal(f_sub(a, k));
+	a = t;
+	p0 = p1;
+	q0 = q1;
+	p1 = p2;
+	q1 = q2;
+    }
+    *p = f_add(f_mul(c, p1), p0);
+    *q = f_add(f_mul(c, q1), q0);
+}
+
+/*
+ * call-seq:
+ *    rat.rationalize       ->  self
+ *    rat.rationalize(eps)  ->  rational
+ *
+ * Returns a simpler approximation of the value if the optional
+ * argument eps is given (rat-|eps| <= result <= rat+|eps|), self
+ * otherwise.
+ *
+ *    r = Rational(5033165, 16777216)
+ *    r.rationalize                    #=> (5033165/16777216)
+ *    r.rationalize(Rational('0.01'))  #=> (3/10)
+ *    r.rationalize(Rational('0.1'))   #=> (1/3)
+ */
+static VALUE
+nurat_rationalize(int argc, VALUE *argv, VALUE self)
+{
+    VALUE e, a, b, p, q;
+
+    if (argc == 0)
+	return self;
+
+    if (f_negative_p(self))
+	return f_negate(nurat_rationalize(argc, argv, f_abs(self)));
+
+    rb_scan_args(argc, argv, "01", &e);
+    e = f_abs(e);
+    a = f_sub(self, e);
+    b = f_add(self, e);
+
+    if (f_eqeq_p(a, b))
+	return self;
+
+    nurat_rationalize_internal(a, b, &p, &q);
+    return f_rational_new2(CLASS_OF(self), p, q);
+}
+
+/* :nodoc: */
+static VALUE
+nurat_hash(VALUE self)
+{
+    st_index_t v, h[2];
+    VALUE n;
+
+    get_dat1(self);
+    n = rb_hash(dat->num);
+    h[0] = NUM2LONG(n);
+    n = rb_hash(dat->den);
+    h[1] = NUM2LONG(n);
+    v = rb_memhash(h, sizeof(h));
+    return LONG2FIX(v);
+}
+
+static VALUE
+f_format(VALUE self, VALUE (*func)(VALUE))
+{
+    VALUE s;
+    get_dat1(self);
+
+    s = (*func)(dat->num);
+    rb_str_cat2(s, "/");
+    rb_str_concat(s, (*func)(dat->den));
+
+    return s;
+}
+
+/*
+ * call-seq:
+ *    rat.to_s  ->  string
+ *
+ * Returns the value as a string.
+ *
+ *    Rational(2).to_s      #=> "2/1"
+ *    Rational(-8, 6).to_s  #=> "-4/3"
+ *    Rational('1/2').to_s  #=> "1/2"
+ */
+static VALUE
+nurat_to_s(VALUE self)
+{
+    return f_format(self, f_to_s);
+}
+
+/*
+ * call-seq:
+ *    rat.inspect  ->  string
+ *
+ * Returns the value as a string for inspection.
+ *
+ *    Rational(2).inspect      #=> "(2/1)"
+ *    Rational(-8, 6).inspect  #=> "(-4/3)"
+ *    Rational('1/2').inspect  #=> "(1/2)"
+ */
+static VALUE
+nurat_inspect(VALUE self)
+{
+    VALUE s;
+
+    s = rb_usascii_str_new2("(");
+    rb_str_concat(s, f_format(self, f_inspect));
+    rb_str_cat2(s, ")");
+
+    return s;
+}
+
+/* :nodoc: */
+static VALUE
+nurat_dumper(VALUE self)
+{
+    return self;
+}
+
+/* :nodoc: */
+static VALUE
+nurat_loader(VALUE self, VALUE a)
+{
+    get_dat1(self);
+
+    RRATIONAL_SET_NUM(dat, rb_ivar_get(a, id_i_num));
+    RRATIONAL_SET_DEN(dat, rb_ivar_get(a, id_i_den));
+
+    return self;
+}
+
+/* :nodoc: */
+static VALUE
+nurat_marshal_dump(VALUE self)
+{
+    VALUE a;
+    get_dat1(self);
+
+    a = rb_assoc_new(dat->num, dat->den);
+    rb_copy_generic_ivar(a, self);
+    return a;
+}
+
+/* :nodoc: */
+static VALUE
+nurat_marshal_load(VALUE self, VALUE a)
+{
+    rb_check_frozen(self);
+    rb_check_trusted(self);
+
+    Check_Type(a, T_ARRAY);
+    if (RARRAY_LEN(a) != 2)
+	rb_raise(rb_eArgError, "marshaled rational must have an array whose length is 2 but %ld", RARRAY_LEN(a));
+    if (f_zero_p(RARRAY_AREF(a, 1)))
+	rb_raise_zerodiv();
+
+    rb_ivar_set(self, id_i_num, RARRAY_AREF(a, 0));
+    rb_ivar_set(self, id_i_den, RARRAY_AREF(a, 1));
+
+    return self;
+}
+
+/* --- */
+
+VALUE
+rb_rational_reciprocal(VALUE x)
+{
+    get_dat1(x);
+    return f_rational_new_no_reduce2(CLASS_OF(x), dat->den, dat->num);
+}
+
+/*
+ * call-seq:
+ *    int.gcd(int2)  ->  integer
+ *
+ * Returns the greatest common divisor (always positive).  0.gcd(x)
+ * and x.gcd(0) return abs(x).
+ *
+ *    2.gcd(2)                    #=> 2
+ *    3.gcd(-7)                   #=> 1
+ *    ((1<<31)-1).gcd((1<<61)-1)  #=> 1
+ */
+VALUE
+rb_gcd(VALUE self, VALUE other)
+{
+    other = nurat_int_value(other);
+    return f_gcd(self, other);
+}
+
+/*
+ * call-seq:
+ *    int.lcm(int2)  ->  integer
+ *
+ * Returns the least common multiple (always positive).  0.lcm(x) and
+ * x.lcm(0) return zero.
+ *
+ *    2.lcm(2)                    #=> 2
+ *    3.lcm(-7)                   #=> 21
+ *    ((1<<31)-1).lcm((1<<61)-1)  #=> 4951760154835678088235319297
+ */
+VALUE
+rb_lcm(VALUE self, VALUE other)
+{
+    other = nurat_int_value(other);
+    return f_lcm(self, other);
+}
+
+/*
+ * call-seq:
+ *    int.gcdlcm(int2)  ->  array
+ *
+ * Returns an array; [int.gcd(int2), int.lcm(int2)].
+ *
+ *    2.gcdlcm(2)                    #=> [2, 2]
+ *    3.gcdlcm(-7)                   #=> [1, 21]
+ *    ((1<<31)-1).gcdlcm((1<<61)-1)  #=> [1, 4951760154835678088235319297]
+ */
+VALUE
+rb_gcdlcm(VALUE self, VALUE other)
+{
+    other = nurat_int_value(other);
+    return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
+}
+
+VALUE
+rb_rational_raw(VALUE x, VALUE y)
+{
+    return nurat_s_new_internal(rb_cRational, x, y);
+}
+
+VALUE
+rb_rational_new(VALUE x, VALUE y)
+{
+    return nurat_s_canonicalize_internal(rb_cRational, x, y);
+}
+
+static VALUE nurat_s_convert(int argc, VALUE *argv, VALUE klass);
+
+VALUE
+rb_Rational(VALUE x, VALUE y)
+{
+    VALUE a[2];
+    a[0] = x;
+    a[1] = y;
+    return nurat_s_convert(2, a, rb_cRational);
+}
+
+VALUE
+rb_rational_num(VALUE rat)
+{
+    return nurat_numerator(rat);
+}
+
+VALUE
+rb_rational_den(VALUE rat)
+{
+    return nurat_denominator(rat);
+}
+
+#define id_numerator rb_intern("numerator")
+#define f_numerator(x) rb_funcall((x), id_numerator, 0)
+
+#define id_denominator rb_intern("denominator")
+#define f_denominator(x) rb_funcall((x), id_denominator, 0)
+
+#define id_to_r rb_intern("to_r")
+#define f_to_r(x) rb_funcall((x), id_to_r, 0)
+
+/*
+ * call-seq:
+ *    num.numerator  ->  integer
+ *
+ * Returns the numerator.
+ */
+static VALUE
+numeric_numerator(VALUE self)
+{
+    return f_numerator(f_to_r(self));
+}
+
+/*
+ * call-seq:
+ *    num.denominator  ->  integer
+ *
+ * Returns the denominator (always positive).
+ */
+static VALUE
+numeric_denominator(VALUE self)
+{
+    return f_denominator(f_to_r(self));
+}
+
+
+/*
+ *  call-seq:
+ *     num.quo(int_or_rat)   ->  rat
+ *     num.quo(flo)          ->  flo
+ *
+ *  Returns most exact division (rational for integers, float for floats).
+ */
+
+static VALUE
+numeric_quo(VALUE x, VALUE y)
+{
+    if (RB_TYPE_P(y, T_FLOAT)) {
+        return f_fdiv(x, y);
+    }
+
+#ifdef CANON
+    if (canonicalization) {
+        x = rb_rational_raw1(x);
+    }
+    else
+#endif
+    {
+        x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r");
+    }
+    return rb_funcall(x, '/', 1, y);
+}
+
+
+/*
+ * call-seq:
+ *    int.numerator  ->  self
+ *
+ * Returns self.
+ */
+static VALUE
+integer_numerator(VALUE self)
+{
+    return self;
+}
+
+/*
+ * call-seq:
+ *    int.denominator  ->  1
+ *
+ * Returns 1.
+ */
+static VALUE
+integer_denominator(VALUE self)
+{
+    return INT2FIX(1);
+}
+
+/*
+ * call-seq:
+ *    flo.numerator  ->  integer
+ *
+ * Returns the numerator.  The result is machine dependent.
+ *
+ *    n = 0.3.numerator    #=> 5404319552844595
+ *    d = 0.3.denominator  #=> 18014398509481984
+ *    n.fdiv(d)            #=> 0.3
+ */
+static VALUE
+float_numerator(VALUE self)
+{
+    double d = RFLOAT_VALUE(self);
+    if (isinf(d) || isnan(d))
+	return self;
+    return rb_call_super(0, 0);
+}
+
+/*
+ * call-seq:
+ *    flo.denominator  ->  integer
+ *
+ * Returns the denominator (always positive).  The result is machine
+ * dependent.
+ *
+ * See numerator.
+ */
+static VALUE
+float_denominator(VALUE self)
+{
+    double d = RFLOAT_VALUE(self);
+    if (isinf(d) || isnan(d))
+	return INT2FIX(1);
+    return rb_call_super(0, 0);
+}
+
+/*
+ * call-seq:
+ *    nil.to_r  ->  (0/1)
+ *
+ * Returns zero as a rational.
+ */
+static VALUE
+nilclass_to_r(VALUE self)
+{
+    return rb_rational_new1(INT2FIX(0));
+}
+
+/*
+ * call-seq:
+ *    nil.rationalize([eps])  ->  (0/1)
+ *
+ * Returns zero as a rational.  The optional argument eps is always
+ * ignored.
+ */
+static VALUE
+nilclass_rationalize(int argc, VALUE *argv, VALUE self)
+{
+    rb_scan_args(argc, argv, "01", NULL);
+    return nilclass_to_r(self);
+}
+
+/*
+ * call-seq:
+ *    int.to_r  ->  rational
+ *
+ * Returns the value as a rational.
+ *
+ *    1.to_r        #=> (1/1)
+ *    (1<<64).to_r  #=> (18446744073709551616/1)
+ */
+static VALUE
+integer_to_r(VALUE self)
+{
+    return rb_rational_new1(self);
+}
+
+/*
+ * call-seq:
+ *    int.rationalize([eps])  ->  rational
+ *
+ * Returns the value as a rational.  The optional argument eps is
+ * always ignored.
+ */
+static VALUE
+integer_rationalize(int argc, VALUE *argv, VALUE self)
+{
+    rb_scan_args(argc, argv, "01", NULL);
+    return integer_to_r(self);
+}
+
+static void
+float_decode_internal(VALUE self, VALUE *rf, VALUE *rn)
+{
+    double f;
+    int n;
+
+    f = frexp(RFLOAT_VALUE(self), &n);
+    f = ldexp(f, DBL_MANT_DIG);
+    n -= DBL_MANT_DIG;
+    *rf = rb_dbl2big(f);
+    *rn = INT2FIX(n);
+}
+
+#if 0
+static VALUE
+float_decode(VALUE self)
+{
+    VALUE f, n;
+
+    float_decode_internal(self, &f, &n);
+    return rb_assoc_new(f, n);
+}
+#endif
+
+#define id_lshift rb_intern("<<")
+#define f_lshift(x,n) rb_funcall((x), id_lshift, 1, (n))
+
+/*
+ * call-seq:
+ *    flt.to_r  ->  rational
+ *
+ * Returns the value as a rational.
+ *
+ * NOTE: 0.3.to_r isn't the same as '0.3'.to_r.  The latter is
+ * equivalent to '3/10'.to_r, but the former isn't so.
+ *
+ *    2.0.to_r    #=> (2/1)
+ *    2.5.to_r    #=> (5/2)
+ *    -0.75.to_r  #=> (-3/4)
+ *    0.0.to_r    #=> (0/1)
+ *
+ * See rationalize.
+ */
+static VALUE
+float_to_r(VALUE self)
+{
+    VALUE f, n;
+
+    float_decode_internal(self, &f, &n);
+#if FLT_RADIX == 2
+    {
+	long ln = FIX2LONG(n);
+
+	if (ln == 0)
+	    return f_to_r(f);
+	if (ln > 0)
+	    return f_to_r(f_lshift(f, n));
+	ln = -ln;
+	return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln)));
+    }
+#else
+    return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n)));
+#endif
+}
+
+VALUE
+rb_flt_rationalize_with_prec(VALUE flt, VALUE prec)
+{
+    VALUE e, a, b, p, q;
+
+    e = f_abs(prec);
+    a = f_sub(flt, e);
+    b = f_add(flt, e);
+
+    if (f_eqeq_p(a, b))
+        return f_to_r(flt);
+
+    nurat_rationalize_internal(a, b, &p, &q);
+    return rb_rational_new2(p, q);
+}
+
+VALUE
+rb_flt_rationalize(VALUE flt)
+{
+    VALUE a, b, f, n, p, q;
+
+    float_decode_internal(flt, &f, &n);
+    if (f_zero_p(f) || f_positive_p(n))
+        return rb_rational_new1(f_lshift(f, n));
+
+#if FLT_RADIX == 2
+    {
+        VALUE two_times_f, den;
+
+        two_times_f = f_mul(TWO, f);
+        den = f_lshift(ONE, f_sub(ONE, n));
+
+        a = rb_rational_new2(f_sub(two_times_f, ONE), den);
+        b = rb_rational_new2(f_add(two_times_f, ONE), den);
+    }
+#else
+    {
+        VALUE radix_times_f, den;
+
+        radix_times_f = f_mul(INT2FIX(FLT_RADIX), f);
+        den = f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n));
+
+        a = rb_rational_new2(f_sub(radix_times_f, INT2FIX(FLT_RADIX - 1)), den);
+        b = rb_rational_new2(f_add(radix_times_f, INT2FIX(FLT_RADIX - 1)), den);
+    }
+#endif
+
+    if (f_eqeq_p(a, b))
+        return f_to_r(flt);
+
+    nurat_rationalize_internal(a, b, &p, &q);
+    return rb_rational_new2(p, q);
+}
+
+/*
+ * call-seq:
+ *    flt.rationalize([eps])  ->  rational
+ *
+ * Returns a simpler approximation of the value (flt-|eps| <= result
+ * <= flt+|eps|).  if the optional eps is not given, it will be chosen
+ * automatically.
+ *
+ *    0.3.rationalize          #=> (3/10)
+ *    1.333.rationalize        #=> (1333/1000)
+ *    1.333.rationalize(0.01)  #=> (4/3)
+ *
+ * See to_r.
+ */
+static VALUE
+float_rationalize(int argc, VALUE *argv, VALUE self)
+{
+    VALUE e;
+
+    if (f_negative_p(self))
+        return f_negate(float_rationalize(argc, argv, f_abs(self)));
+
+    rb_scan_args(argc, argv, "01", &e);
+
+    if (argc != 0) {
+        return rb_flt_rationalize_with_prec(self, e);
+    }
+    else {
+        return rb_flt_rationalize(self);
+    }
+}
+
+#include <ctype.h>
+
+inline static int
+issign(int c)
+{
+    return (c == '-' || c == '+');
+}
+
+static int
+read_sign(const char **s)
+{
+    int sign = '?';
+
+    if (issign(**s)) {
+	sign = **s;
+	(*s)++;
+    }
+    return sign;
+}
+
+inline static int
+isdecimal(int c)
+{
+    return isdigit((unsigned char)c);
+}
+
+static int
+read_digits(const char **s, int strict,
+	    VALUE *num, int *count)
+{
+    char *b, *bb;
+    int us = 1, ret = 1;
+    VALUE tmp;
+
+    if (!isdecimal(**s)) {
+	*num = ZERO;
+	return 0;
+    }
+
+    bb = b = ALLOCV_N(char, tmp, strlen(*s) + 1);
+
+    while (isdecimal(**s) || **s == '_') {
+	if (**s == '_') {
+	    if (strict) {
+		if (us) {
+		    ret = 0;
+		    goto conv;
+		}
+	    }
+	    us = 1;
+	}
+	else {
+	    if (count)
+		(*count)++;
+	    *b++ = **s;
+	    us = 0;
+	}
+	(*s)++;
+    }
+    if (us)
+	do {
+	    (*s)--;
+	} while (**s == '_');
+  conv:
+    *b = '\0';
+    *num = rb_cstr_to_inum(bb, 10, 0);
+    ALLOCV_END(tmp);
+    return ret;
+}
+
+inline static int
+islettere(int c)
+{
+    return (c == 'e' || c == 'E');
+}
+
+static int
+read_num(const char **s, int numsign, int strict,
+	 VALUE *num)
+{
+    VALUE ip, fp, exp;
+
+    *num = rb_rational_new2(ZERO, ONE);
+    exp = Qnil;
+
+    if (**s != '.') {
+	if (!read_digits(s, strict, &ip, NULL))
+	    return 0;
+	*num = rb_rational_new2(ip, ONE);
+    }
+
+    if (**s == '.') {
+	int count = 0;
+
+	(*s)++;
+	if (!read_digits(s, strict, &fp, &count))
+	    return 0;
+	{
+	    VALUE l = f_expt10(INT2NUM(count));
+	    *num = f_mul(*num, l);
+	    *num = f_add(*num, fp);
+	    *num = f_div(*num, l);
+	}
+    }
+
+    if (islettere(**s)) {
+	int expsign;
+
+	(*s)++;
+	expsign = read_sign(s);
+	if (!read_digits(s, strict, &exp, NULL))
+	    return 0;
+	if (expsign == '-')
+	    exp = f_negate(exp);
+    }
+
+    if (numsign == '-')
+	*num = f_negate(*num);
+    if (!NIL_P(exp)) {
+	VALUE l = f_expt10(exp);
+	*num = f_mul(*num, l);
+    }
+    return 1;
+}
+
+inline static int
+read_den(const char **s, int strict,
+	 VALUE *num)
+{
+    if (!read_digits(s, strict, num, NULL))
+	return 0;
+    return 1;
+}
+
+static int
+read_rat_nos(const char **s, int sign, int strict,
+	     VALUE *num)
+{
+    VALUE den;
+
+    if (!read_num(s, sign, strict, num))
+	return 0;
+    if (**s == '/') {
+	(*s)++;
+	if (!read_den(s, strict, &den))
+	    return 0;
+	if (!(FIXNUM_P(den) && FIX2LONG(den) == 1))
+	    *num = f_div(*num, den);
+    }
+    return 1;
+}
+
+static int
+read_rat(const char **s, int strict,
+	 VALUE *num)
+{
+    int sign;
+
+    sign = read_sign(s);
+    if (!read_rat_nos(s, sign, strict, num))
+	return 0;
+    return 1;
+}
+
+inline static void
+skip_ws(const char **s)
+{
+    while (isspace((unsigned char)**s))
+	(*s)++;
+}
+
+static int
+parse_rat(const char *s, int strict,
+	  VALUE *num)
+{
+    skip_ws(&s);
+    if (!read_rat(&s, strict, num))
+	return 0;
+    skip_ws(&s);
+
+    if (strict)
+	if (*s != '\0')
+	    return 0;
+    return 1;
+}
+
+static VALUE
+string_to_r_strict(VALUE self)
+{
+    char *s;
+    VALUE num;
+
+    rb_must_asciicompat(self);
+
+    s = RSTRING_PTR(self);
+
+    if (!s || memchr(s, '\0', RSTRING_LEN(self)))
+	rb_raise(rb_eArgError, "string contains null byte");
+
+    if (s && s[RSTRING_LEN(self)]) {
+	rb_str_modify(self);
+	s = RSTRING_PTR(self);
+	s[RSTRING_LEN(self)] = '\0';
+    }
+
+    if (!s)
+	s = (char *)"";
+
+    if (!parse_rat(s, 1, &num)) {
+	VALUE ins = f_inspect(self);
+	rb_raise(rb_eArgError, "invalid value for convert(): %s",
+		 StringValuePtr(ins));
+    }
+
+    if (RB_TYPE_P(num, T_FLOAT))
+	rb_raise(rb_eFloatDomainError, "Infinity");
+    return num;
+}
+
+/*
+ * call-seq:
+ *    str.to_r  ->  rational
+ *
+ * Returns a rational which denotes the string form.  The parser
+ * ignores leading whitespaces and trailing garbage.  Any digit
+ * sequences can be separated by an underscore.  Returns zero for null
+ * or garbage string.
+ *
+ * NOTE: '0.3'.to_r isn't the same as 0.3.to_r.  The former is
+ * equivalent to '3/10'.to_r, but the latter isn't so.
+ *
+ *    '  2  '.to_r       #=> (2/1)
+ *    '300/2'.to_r       #=> (150/1)
+ *    '-9.2'.to_r        #=> (-46/5)
+ *    '-9.2e2'.to_r      #=> (-920/1)
+ *    '1_234_567'.to_r   #=> (1234567/1)
+ *    '21 june 09'.to_r  #=> (21/1)
+ *    '21/06/09'.to_r    #=> (7/2)
+ *    'bwv 1079'.to_r    #=> (0/1)
+ *
+ * See Kernel.Rational.
+ */
+static VALUE
+string_to_r(VALUE self)
+{
+    char *s;
+    VALUE num;
+
+    rb_must_asciicompat(self);
+
+    s = RSTRING_PTR(self);
+
+    if (s && s[RSTRING_LEN(self)]) {
+	rb_str_modify(self);
+	s = RSTRING_PTR(self);
+	s[RSTRING_LEN(self)] = '\0';
+    }
+
+    if (!s)
+	s = (char *)"";
+
+    (void)parse_rat(s, 0, &num);
+
+    if (RB_TYPE_P(num, T_FLOAT))
+	rb_raise(rb_eFloatDomainError, "Infinity");
+    return num;
+}
+
+VALUE
+rb_cstr_to_rat(const char *s, int strict) /* for complex's internal */
+{
+    VALUE num;
+
+    (void)parse_rat(s, strict, &num);
+
+    if (RB_TYPE_P(num, T_FLOAT))
+	rb_raise(rb_eFloatDomainError, "Infinity");
+    return num;
+}
+
+static VALUE
+nurat_s_convert(int argc, VALUE *argv, VALUE klass)
+{
+    VALUE a1, a2, backref;
+
+    rb_scan_args(argc, argv, "11", &a1, &a2);
+
+    if (NIL_P(a1) || (argc == 2 && NIL_P(a2)))
+	rb_raise(rb_eTypeError, "can't convert nil into Rational");
+
+    if (RB_TYPE_P(a1, T_COMPLEX)) {
+	if (k_exact_zero_p(RCOMPLEX(a1)->imag))
+	    a1 = RCOMPLEX(a1)->real;
+    }
+
+    if (RB_TYPE_P(a2, T_COMPLEX)) {
+	if (k_exact_zero_p(RCOMPLEX(a2)->imag))
+	    a2 = RCOMPLEX(a2)->real;
+    }
+
+    backref = rb_backref_get();
+    rb_match_busy(backref);
+
+    if (RB_TYPE_P(a1, T_FLOAT)) {
+	a1 = f_to_r(a1);
+    }
+    else if (RB_TYPE_P(a1, T_STRING)) {
+	a1 = string_to_r_strict(a1);
+    }
+
+    if (RB_TYPE_P(a2, T_FLOAT)) {
+	a2 = f_to_r(a2);
+    }
+    else if (RB_TYPE_P(a2, T_STRING)) {
+	a2 = string_to_r_strict(a2);
+    }
+
+    rb_backref_set(backref);
+
+    if (RB_TYPE_P(a1, T_RATIONAL)) {
+	if (argc == 1 || (k_exact_one_p(a2)))
+	    return a1;
+    }
+
+    if (argc == 1) {
+	if (!(k_numeric_p(a1) && k_integer_p(a1)))
+	    return rb_convert_type(a1, T_RATIONAL, "Rational", "to_r");
+    }
+    else {
+	if ((k_numeric_p(a1) && k_numeric_p(a2)) &&
+	    (!f_integer_p(a1) || !f_integer_p(a2)))
+	    return f_div(a1, a2);
+    }
+
+    {
+	VALUE argv2[2];
+	argv2[0] = a1;
+	argv2[1] = a2;
+	return nurat_s_new(argc, argv2, klass);
+    }
+}
+
+/*
+ * A rational number can be represented as a paired integer number;
+ * a/b (b>0).  Where a is numerator and b is denominator.  Integer a
+ * equals rational a/1 mathematically.
+ *
+ * In ruby, you can create rational object with Rational, to_r,
+ * rationalize method or suffixing r to a literal.  The return values will be irreducible.
+ *
+ *    Rational(1)      #=> (1/1)
+ *    Rational(2, 3)   #=> (2/3)
+ *    Rational(4, -6)  #=> (-2/3)
+ *    3.to_r           #=> (3/1)
+ *    2/3r             #=> (2/3)
+ *
+ * You can also create rational object from floating-point numbers or
+ * strings.
+ *
+ *    Rational(0.3)    #=> (5404319552844595/18014398509481984)
+ *    Rational('0.3')  #=> (3/10)
+ *    Rational('2/3')  #=> (2/3)
+ *
+ *    0.3.to_r         #=> (5404319552844595/18014398509481984)
+ *    '0.3'.to_r       #=> (3/10)
+ *    '2/3'.to_r       #=> (2/3)
+ *    0.3.rationalize  #=> (3/10)
+ *
+ * A rational object is an exact number, which helps you to write
+ * program without any rounding errors.
+ *
+ *    10.times.inject(0){|t,| t + 0.1}              #=> 0.9999999999999999
+ *    10.times.inject(0){|t,| t + Rational('0.1')}  #=> (1/1)
+ *
+ * However, when an expression has inexact factor (numerical value or
+ * operation), will produce an inexact result.
+ *
+ *    Rational(10) / 3   #=> (10/3)
+ *    Rational(10) / 3.0 #=> 3.3333333333333335
+ *
+ *    Rational(-8) ** Rational(1, 3)
+ *                       #=> (1.0000000000000002+1.7320508075688772i)
+ */
+void
+Init_Rational(void)
+{
+    VALUE compat;
+#undef rb_intern
+#define rb_intern(str) rb_intern_const(str)
+
+    assert(fprintf(stderr, "assert() is now active\n"));
+
+    id_abs = rb_intern("abs");
+    id_cmp = rb_intern("<=>");
+    id_convert = rb_intern("convert");
+    id_eqeq_p = rb_intern("==");
+    id_expt = rb_intern("**");
+    id_fdiv = rb_intern("fdiv");
+    id_idiv = rb_intern("div");
+    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_truncate = rb_intern("truncate");
+    id_i_num = rb_intern("@numerator");
+    id_i_den = rb_intern("@denominator");
+
+    rb_cRational = rb_define_class("Rational", rb_cNumeric);
+
+    rb_define_alloc_func(rb_cRational, nurat_s_alloc);
+    rb_undef_method(CLASS_OF(rb_cRational), "allocate");
+
+#if 0
+    rb_define_private_method(CLASS_OF(rb_cRational), "new!", nurat_s_new_bang, -1);
+    rb_define_private_method(CLASS_OF(rb_cRational), "new", nurat_s_new, -1);
+#else
+    rb_undef_method(CLASS_OF(rb_cRational), "new");
+#endif
+
+    rb_define_global_function("Rational", nurat_f_rational, -1);
+
+    rb_define_method(rb_cRational, "numerator", nurat_numerator, 0);
+    rb_define_method(rb_cRational, "denominator", nurat_denominator, 0);
+
+    rb_define_method(rb_cRational, "+", nurat_add, 1);
+    rb_define_method(rb_cRational, "-", nurat_sub, 1);
+    rb_define_method(rb_cRational, "*", nurat_mul, 1);
+    rb_define_method(rb_cRational, "/", nurat_div, 1);
+    rb_define_method(rb_cRational, "quo", nurat_div, 1);
+    rb_define_method(rb_cRational, "fdiv", nurat_fdiv, 1);
+    rb_define_method(rb_cRational, "**", nurat_expt, 1);
+
+    rb_define_method(rb_cRational, "<=>", nurat_cmp, 1);
+    rb_define_method(rb_cRational, "==", nurat_eqeq_p, 1);
+    rb_define_method(rb_cRational, "coerce", nurat_coerce, 1);
+
+#if 0 /* NUBY */
+    rb_define_method(rb_cRational, "//", nurat_idiv, 1);
+#endif
+
+#if 0
+    rb_define_method(rb_cRational, "quot", nurat_quot, 1);
+    rb_define_method(rb_cRational, "quotrem", nurat_quotrem, 1);
+#endif
+
+#if 0
+    rb_define_method(rb_cRational, "rational?", nurat_true, 0);
+    rb_define_method(rb_cRational, "exact?", nurat_true, 0);
+#endif
+
+    rb_define_method(rb_cRational, "floor", nurat_floor_n, -1);
+    rb_define_method(rb_cRational, "ceil", nurat_ceil_n, -1);
+    rb_define_method(rb_cRational, "truncate", nurat_truncate_n, -1);
+    rb_define_method(rb_cRational, "round", nurat_round_n, -1);
+
+    rb_define_method(rb_cRational, "to_i", nurat_truncate, 0);
+    rb_define_method(rb_cRational, "to_f", nurat_to_f, 0);
+    rb_define_method(rb_cRational, "to_r", nurat_to_r, 0);
+    rb_define_method(rb_cRational, "rationalize", nurat_rationalize, -1);
+
+    rb_define_method(rb_cRational, "hash", nurat_hash, 0);
+
+    rb_define_method(rb_cRational, "to_s", nurat_to_s, 0);
+    rb_define_method(rb_cRational, "inspect", nurat_inspect, 0);
+
+    rb_define_private_method(rb_cRational, "marshal_dump", nurat_marshal_dump, 0);
+    compat = rb_define_class_under(rb_cRational, "compatible", rb_cObject);
+    rb_define_private_method(compat, "marshal_load", nurat_marshal_load, 1);
+    rb_marshal_define_compat(rb_cRational, compat, nurat_dumper, nurat_loader);
+
+    /* --- */
+
+    rb_define_method(rb_cInteger, "gcd", rb_gcd, 1);
+    rb_define_method(rb_cInteger, "lcm", rb_lcm, 1);
+    rb_define_method(rb_cInteger, "gcdlcm", rb_gcdlcm, 1);
+
+    rb_define_method(rb_cNumeric, "numerator", numeric_numerator, 0);
+    rb_define_method(rb_cNumeric, "denominator", numeric_denominator, 0);
+    rb_define_method(rb_cNumeric, "quo", numeric_quo, 1);
+
+    rb_define_method(rb_cInteger, "numerator", integer_numerator, 0);
+    rb_define_method(rb_cInteger, "denominator", integer_denominator, 0);
+
+    rb_define_method(rb_cFloat, "numerator", float_numerator, 0);
+    rb_define_method(rb_cFloat, "denominator", float_denominator, 0);
+
+    rb_define_method(rb_cNilClass, "to_r", nilclass_to_r, 0);
+    rb_define_method(rb_cNilClass, "rationalize", nilclass_rationalize, -1);
+    rb_define_method(rb_cInteger, "to_r", integer_to_r, 0);
+    rb_define_method(rb_cInteger, "rationalize", integer_rationalize, -1);
+    rb_define_method(rb_cFloat, "to_r", float_to_r, 0);
+    rb_define_method(rb_cFloat, "rationalize", float_rationalize, -1);
+
+    rb_define_method(rb_cString, "to_r", string_to_r, 0);
+
+    rb_define_private_method(CLASS_OF(rb_cRational), "convert", nurat_s_convert, -1);
+
+    rb_provide("rational.so");	/* for backward compatibility */
+}
+
+/*
+Local variables:
+c-file-style: "ruby"
+End:
+*/