path: root/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>

#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);
}

#if 0
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);
}
#endif

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)));
}

#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_negative_p(self))
    return self;
  else
    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);
  }
}

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;

#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 const char rat_pat_source[] = PATTERN;
  static const char an_e_pat_source[] = "[eE]";
  static const char a_dot_pat_source[] = "\\.";
#define REG_NEW(s) rb_reg_new(s, sizeof(s) - 1, 0)

  rat_pat = REG_NEW(rat_pat_source);
  rb_global_variable(&rat_pat);

  an_e_pat = REG_NEW(an_e_pat_source);
  rb_global_variable(&an_e_pat);

  a_dot_pat = REG_NEW(a_dot_pat_source);
  rb_global_variable(&a_dot_pat);

#undef REG_NEW
}

#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 a = string_to_r_internal(self);
  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);
}