both complex and rational are now builtin classes.

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@15783 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

1 files changed, 1111 insertions, 0 deletions

diff --git a/rational.c b/rational.c
new file mode 100644
index 0000000000..ba8583b310
--- /dev/null
+++ b/rational.c
@@ -0,0 +1,1111 @@
+/*
+  nurat_core.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>
+
+#define NDEBUG
+#include <assert.h>
+
+#ifndef RATIONAL_NAME
+#define RATIONAL_NAME "Rational"
+#endif
+
+#define ZERO INT2FIX(0)
+#define ONE INT2FIX(1)
+#define TWO INT2FIX(2)
+
+VALUE rb_cRational;
+
+static ID id_Unify, id_cmp, id_coerce, id_convert, id_equal_p, id_expt,
+  id_floor, id_format,id_idiv, id_inspect, id_negate, id_new, id_new_bang,
+  id_to_f, id_to_i, id_to_s, id_truncate;
+
+#define f_add(x,y) rb_funcall(x, '+', 1, y)
+#define f_div(x,y) rb_funcall(x, '/', 1, y)
+#define f_gt_p(x,y) rb_funcall(x, '>', 1, y)
+#define f_lt_p(x,y) rb_funcall(x, '<', 1, y)
+#define f_mod(x,y) rb_funcall(x, '%', 1, y)
+#define f_mul(x,y) rb_funcall(x, '*', 1, y)
+#define f_sub(x,y) rb_funcall(x, '-', 1, y)
+#define f_xor(x,y) rb_funcall(x, '^', 1, y)
+
+#define f_floor(x) rb_funcall(x, id_floor, 0)
+#define f_inspect(x) rb_funcall(x, id_inspect, 0)
+#define f_to_f(x) rb_funcall(x, id_to_f, 0)
+#define f_to_i(x) rb_funcall(x, id_to_i, 0)
+#define f_to_s(x) rb_funcall(x, id_to_s, 0)
+#define f_truncate(x) rb_funcall(x, id_truncate, 0)
+#define f_cmp(x,y) rb_funcall(x, id_cmp, 1, y)
+#define f_coerce(x,y) rb_funcall(x, id_coerce, 1, y)
+#define f_equal_p(x,y) rb_funcall(x, id_equal_p, 1, y)
+#define f_expt(x,y) rb_funcall(x, id_expt, 1, y)
+#define f_idiv(x,y) rb_funcall(x, id_idiv, 1, y)
+#define f_negate(x) rb_funcall(x, id_negate, 0)
+
+#define f_negative_p(x) f_lt_p(x, ZERO)
+#define f_zero_p(x) f_equal_p(x, ZERO)
+#define f_one_p(x) f_equal_p(x, ONE)
+#define f_kind_of_p(x,c) rb_obj_is_kind_of(x, c)
+#define k_numeric_p(x) f_kind_of_p(x, rb_cNumeric)
+#define k_integer_p(x) f_kind_of_p(x, rb_cInteger)
+#define k_float_p(x) f_kind_of_p(x, rb_cFloat)
+#define k_rational_p(x) f_kind_of_p(x, rb_cRational)
+
+#define f_boolcast(x) ((x) ? Qtrue : Qfalse)
+
+inline static long
+i_gcd(long x, long y)
+{
+  long b;
+
+  if (x < 0)
+    x = -x;
+  if (y < 0)
+    y = -y;
+
+  if (x == 0)
+    return y;
+  if (y == 0)
+    return x;
+
+  b = 0;
+  while ((x & 1) == 0 && (y & 1) == 0) {
+    b += 1;
+    x >>= 1;
+    y >>= 1;
+  }
+
+  while ((x & 1) == 0)
+    x >>= 1;
+
+  while ((y & 1) == 0)
+    y >>= 1;
+
+  while (x != y) {
+    if (y > x) {
+      long t;
+      t = x;
+      x = y;
+      y = t;
+    }
+    x -= y;
+    while ((x & 1) == 0)
+      x >>= 1;
+  }
+
+  return x << b;
+}
+
+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 (FIX2INT(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 */
+}
+
+#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);
+}
+
+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);
+
+    if (f_negative_p(den)) {
+      num = f_negate(num);
+      den = f_negate(den);
+    }
+    break;
+  }
+
+  return nurat_s_new_internal(klass, num, den);
+}
+
+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_negative_p(y));
+  assert(!f_zero_p(y));
+  return nurat_s_new_internal(klass, x, y);
+}
+
+#define f_unify_p(klass) rb_const_defined(klass, id_Unify)
+
+inline static VALUE
+nurat_s_canonicalize_internal(VALUE klass, VALUE num, VALUE den)
+{
+  VALUE gcd;
+
+  switch (FIX2INT(f_cmp(den, ZERO))) {
+  case -1:
+    if (f_negative_p(den)) {
+      num = f_negate(num);
+      den = f_negate(den);
+    }
+    break;
+  case 0:
+    rb_raise(rb_eZeroDivError, "devided by zero");
+    break;
+  }
+
+  gcd = f_gcd(num, den);
+  num = f_idiv(num, gcd);
+  den = f_idiv(den, gcd);
+
+  if (f_one_p(den) && f_unify_p(klass))
+    return num;
+  else
+    return nurat_s_new_internal(klass, num, den);
+}
+
+static VALUE
+nurat_s_canonicalize(int argc, VALUE *argv, VALUE klass)
+{
+  VALUE num, den;
+
+  switch (rb_scan_args(argc, argv, "11", &num, &den)) {
+  case 1:
+    den = ONE;
+    break;
+  }
+
+  switch (TYPE(num)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    break;
+  default:
+    rb_raise(rb_eArgError, "not an integer");
+  }
+
+  switch (TYPE(den)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    break;
+  default:
+    rb_raise(rb_eArgError, "not an integer");
+  }
+
+  return nurat_s_canonicalize_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:
+    den = ONE;
+    break;
+  }
+
+  switch (TYPE(num)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    break;
+  default:
+    rb_raise(rb_eArgError, "not an integer");
+  }
+
+  switch (TYPE(den)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    break;
+  default:
+    rb_raise(rb_eArgError, "not an integer");
+  }
+
+  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);
+}
+
+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;
+}
+
+static VALUE
+nurat_add(VALUE self, VALUE other)
+{
+  switch (TYPE(other)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    return f_add(self, f_rational_new_bang1(CLASS_OF(self), other));
+  case T_FLOAT:
+    return f_add(f_to_f(self), other);
+  case T_RATIONAL:
+    {
+      VALUE num1, num2;
+
+      get_dat2(self, other);
+
+      num1 = f_mul(adat->num, bdat->den);
+      num2 = f_mul(bdat->num, adat->den);
+
+      return f_rational_new2(CLASS_OF(self),
+			     f_add(num1, num2),
+			     f_mul(adat->den, bdat->den));
+    }
+  default:
+    {
+      VALUE a = f_coerce(other, self);
+      return f_add(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
+    }
+  }
+}
+
+static VALUE
+nurat_sub(VALUE self, VALUE other)
+{
+  switch (TYPE(other)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    return f_sub(self, f_rational_new_bang1(CLASS_OF(self), other));
+  case T_FLOAT:
+    return f_sub(f_to_f(self), other);
+  case T_RATIONAL:
+    {
+      VALUE num1, num2;
+
+      get_dat2(self, other);
+
+      num1 = f_mul(adat->num, bdat->den);
+      num2 = f_mul(bdat->num, adat->den);
+
+      return f_rational_new2(CLASS_OF(self),
+			     f_sub(num1, num2),
+			     f_mul(adat->den, bdat->den));
+    }
+  default:
+    {
+      VALUE a = f_coerce(other, self);
+      return f_sub(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
+    }
+  }
+}
+
+static VALUE
+nurat_mul(VALUE self, VALUE other)
+{
+  switch (TYPE(other)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    return f_mul(self, f_rational_new_bang1(CLASS_OF(self), other));
+  case T_FLOAT:
+    return f_mul(f_to_f(self), other);
+  case T_RATIONAL:
+    {
+      VALUE num, den;
+
+      get_dat2(self, other);
+
+      num = f_mul(adat->num, bdat->num);
+      den = f_mul(adat->den, bdat->den);
+
+      return f_rational_new2(CLASS_OF(self), num, den);
+    }
+  default:
+    {
+      VALUE a = f_coerce(other, self);
+      return f_mul(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
+    }
+  }
+}
+
+static VALUE
+nurat_div(VALUE self, VALUE other)
+{
+  switch (TYPE(other)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    if (f_zero_p(other))
+      rb_raise(rb_eZeroDivError, "devided by zero");
+    return f_div(self, f_rational_new_bang1(CLASS_OF(self), other));
+  case T_FLOAT:
+    return f_div(f_to_f(self), other);
+  case T_RATIONAL:
+    {
+      VALUE num, den;
+
+      get_dat2(self, other);
+
+      num = f_mul(adat->num, bdat->den);
+      den = f_mul(adat->den, bdat->num);
+
+      return f_rational_new2(CLASS_OF(self), num, den);
+    }
+  default:
+    {
+      VALUE a = f_coerce(other, self);
+      return f_div(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
+    }
+  }
+}
+
+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 (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;
+      }
+      if (f_negative_p(den)) { /* or use normal new */
+	num = f_negate(num);
+	den = f_negate(den);
+      }
+      return f_rational_new_bang2(CLASS_OF(self), num, den);
+    }
+  case T_FLOAT:
+  case T_RATIONAL:
+    return f_expt(f_to_f(self), other);
+  default:
+    {
+      VALUE a = f_coerce(other, self);
+      return f_expt(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
+    }
+  }
+}
+
+static VALUE
+nurat_cmp(VALUE self, VALUE other)
+{
+  switch (TYPE(other)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    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);
+
+      num1 = f_mul(adat->num, bdat->den);
+      num2 = f_mul(bdat->num, adat->den);
+      return f_cmp(f_sub(num1, num2), ZERO);
+    }
+  default:
+    {
+      VALUE a = f_coerce(other, self);
+      return f_cmp(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
+    }
+  }
+}
+
+static VALUE
+nurat_equal_p(VALUE self, VALUE other)
+{
+  switch (TYPE(other)) {
+  case T_FIXNUM:
+  case T_BIGNUM:
+    return f_equal_p(self, f_rational_new_bang1(CLASS_OF(self), other));
+  case T_FLOAT:
+    return f_equal_p(f_to_f(self), other);
+  case T_RATIONAL:
+    {
+      get_dat2(self, other);
+
+      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)));
+}
+
+static VALUE
+nurat_quot(VALUE self, VALUE other)
+{
+  return f_truncate(f_div(self, other));
+}
+static VALUE
+nurat_rem(VALUE self, VALUE other)
+{
+  VALUE val = f_truncate(f_div(self, other));
+  return f_sub(self, f_mul(other, val));
+}
+
+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)));
+}
+
+static VALUE
+nurat_abs(VALUE self)
+{
+  if (!f_negative_p(self))
+    return self;
+  else
+    return f_negate(self);
+}
+
+static VALUE
+nurat_true(VALUE self)
+{
+  return Qtrue;
+}
+
+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);
+  }
+}
+
+static VALUE
+nurat_to_f(VALUE self)
+{
+  get_dat1(self);
+  return f_div(f_to_f(dat->num), dat->den); /* enough? */
+}
+
+static VALUE
+nurat_to_r(VALUE self)
+{
+  return self;
+}
+
+static VALUE
+nurat_hash(VALUE self)
+{
+  get_dat1(self);
+  return f_xor(dat->num, dat->den);
+}
+
+static VALUE
+nurat_to_s(VALUE self)
+{
+  get_dat1(self);
+
+  if (f_one_p(dat->den))
+    return f_to_s(dat->num);
+  else
+    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("Rational(%d, %d)"), dat->num, dat->den);
+}
+
+static VALUE
+nurat_marshal_dump(VALUE self)
+{
+  get_dat1(self);
+  return rb_assoc_new(dat->num, dat->den);
+}
+
+static VALUE
+nurat_marshal_load(VALUE self, VALUE a)
+{
+  get_dat1(self);
+  dat->num = RARRAY_PTR(a)[0];
+  dat->den = RARRAY_PTR(a)[1];
+  return self;
+}
+
+/* --- */
+
+VALUE
+rb_rational_raw(VALUE x, VALUE y)
+{
+  return nurat_s_new_internal(rb_cRational, x, y);
+}
+
+VALUE
+rb_rational_new(VALUE x, VALUE y)
+{
+  return nurat_s_canonicalize_internal(rb_cRational, x, y);
+}
+
+static VALUE nurat_s_convert(int argc, VALUE *argv, VALUE klass);
+
+VALUE
+rb_Rational(VALUE x, VALUE y)
+{
+  VALUE a[2];
+  a[0] = x;
+  a[1] = y;
+  return nurat_s_convert(2, a, rb_cRational);
+}
+
+static VALUE
+nilclass_to_r(VALUE self)
+{
+  return rb_rational_new1(INT2FIX(0));
+}
+
+static VALUE
+integer_to_r(VALUE self)
+{
+  return rb_rational_new1(self);
+}
+
+#include <float.h>
+
+static VALUE
+float_decode(VALUE self)
+{
+  double f;
+  int n;
+
+  f = frexp(RFLOAT_VALUE(self), &n);
+  f = ldexp(f, DBL_MANT_DIG);
+  n -= DBL_MANT_DIG;
+  return rb_assoc_new(f_to_i(rb_float_new(f)), INT2FIX(n));
+}
+
+static VALUE
+float_to_r(VALUE self)
+{
+  VALUE a = float_decode(self);
+  return f_mul(RARRAY_PTR(a)[0], f_expt(INT2FIX(FLT_RADIX), RARRAY_PTR(a)[1]));
+}
+
+static VALUE rat_pat, an_e_pat, a_dot_pat, underscores_pat, an_underscore;
+
+#define DIGITS "(?:\\d(?:_\\d|\\d)*)"
+#define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
+#define DENOMINATOR "[-+]?" DIGITS
+#define PATTERN "\\A([-+])?(" NUMERATOR ")(?:\\/(" DENOMINATOR "))?"
+
+static void
+make_patterns(void)
+{
+  static char *rat_pat_source = PATTERN;
+  static char *an_e_pat_source = "[eE]";
+  static char *a_dot_pat_source = "\\.";
+  static char *underscores_pat_source = "_+";
+
+  rat_pat = rb_reg_new(rat_pat_source, strlen(rat_pat_source), 0);
+  rb_global_variable(&rat_pat);
+
+  an_e_pat = rb_reg_new(an_e_pat_source, strlen(an_e_pat_source), 0);
+  rb_global_variable(&an_e_pat);
+
+  a_dot_pat = rb_reg_new(a_dot_pat_source, strlen(a_dot_pat_source), 0);
+  rb_global_variable(&a_dot_pat);
+
+  underscores_pat = rb_reg_new(underscores_pat_source,
+			       strlen(underscores_pat_source), 0);
+  rb_global_variable(&underscores_pat);
+
+  an_underscore = rb_str_new2("_");
+  rb_global_variable(&an_underscore);
+}
+
+#define id_strip rb_intern("strip")
+#define f_strip(x) rb_funcall(x, id_strip, 0)
+
+#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 = f_strip(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 (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(exp))
+      v = f_mul(v, f_expt(INT2FIX(10), f_to_i(exp)));
+    if (!NIL_P(si) && *StringValuePtr(si) == '-')
+      v = f_negate(v);
+    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 = f_gsub(self, underscores_pat, an_underscore);
+  VALUE a = string_to_r_internal(s);
+  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;
+
+  a1 = Qnil;
+  a2 = Qnil;
+  rb_scan_args(argc, argv, "02", &a1, &a2);
+
+  switch (TYPE(a1)) {
+  case T_COMPLEX:
+    if (k_float_p(RCOMPLEX(a1)->image) || !f_zero_p(RCOMPLEX(a1)->image)) {
+      VALUE s = f_to_s(a1);
+      rb_raise(rb_eRangeError, "can't accept %s",
+	       StringValuePtr(s));
+    }
+    a1 = RCOMPLEX(a1)->real;
+  }
+
+  switch (TYPE(a2)) {
+  case T_COMPLEX:
+    if (k_float_p(RCOMPLEX(a2)->image) || !f_zero_p(RCOMPLEX(a2)->image)) {
+      VALUE s = f_to_s(a2);
+      rb_raise(rb_eRangeError, "can't accept %s",
+	       StringValuePtr(s));
+    }
+    a2 = RCOMPLEX(a2)->real;
+  }
+
+  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;
+  }
+
+  switch (TYPE(a1)) {
+  case T_RATIONAL:
+    if (NIL_P(a2) || f_zero_p(a2))
+      return a1;
+    else
+      return f_div(a1, a2);
+  }
+
+  switch (TYPE(a2)) {
+  case T_RATIONAL:
+    return f_div(a1, a2);
+  }
+
+  {
+    VALUE argv2[2];
+    argv2[0] = a1;
+    argv2[1] = a2;
+    return nurat_s_new(argc, argv2, klass);
+  }
+}
+
+static VALUE
+nurat_s_induced_from(VALUE klass, VALUE n)
+{
+  return f_to_r(n);
+}
+
+void
+Init_Rational(void)
+{
+  assert(fprintf(stderr, "assert() is now active\n"));
+
+  id_Unify = rb_intern("Unify");
+  id_cmp = rb_intern("<=>");
+  id_coerce = rb_intern("coerce");
+  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_idiv = rb_intern("div");
+  id_inspect = rb_intern("inspect");
+  id_negate = rb_intern("-@");
+  id_new = rb_intern("new");
+  id_new_bang = rb_intern("new!");
+  id_to_f = rb_intern("to_f");
+  id_to_i = rb_intern("to_i");
+  id_to_s = rb_intern("to_s");
+  id_truncate = rb_intern("truncate");
+
+  rb_cRational = rb_define_class(RATIONAL_NAME, rb_cNumeric);
+
+  rb_define_alloc_func(rb_cRational, nurat_s_alloc);
+  rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
+	     ID2SYM(rb_intern("allocate")));
+
+  rb_define_singleton_method(rb_cRational, "new!", nurat_s_new_bang, -1);
+  rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
+	     ID2SYM(rb_intern("new!")));
+
+  rb_define_singleton_method(rb_cRational, "new", nurat_s_new, -1);
+  rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
+	     ID2SYM(rb_intern("new")));
+
+  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, "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_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_singleton_method(rb_cRational, "convert", nurat_s_convert, -1);
+  rb_funcall(rb_cRational, rb_intern("private_class_method"), 1,
+	     ID2SYM(rb_intern("convert")));
+
+  rb_include_module(rb_cRational, rb_mPrecision);
+  rb_define_singleton_method(rb_cRational, "induced_from",
+			     nurat_s_induced_from, 1);
+}