ruby--ruby/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_boolcast(x) ((x) ? Qtrue : Qfalse)

#define binop(n,op) \
inline static VALUE \
f_##n(VALUE x, VALUE y)\
{\
  return rb_funcall(x, op, 1, y);\
}

#define fun1(n) \
inline static VALUE \
f_##n(VALUE x)\
{\
  return rb_funcall(x, id_##n, 0);\
}

#define fun2(n) \
inline static VALUE \
f_##n(VALUE x, VALUE y)\
{\
  return rb_funcall(x, id_##n, 1, y);\
}

inline static VALUE
f_add(VALUE x, VALUE y)
{
   VALUE _r;
   if (FIXNUM_P(y)) {
     if (FIX2INT(y) == 0)
       _r = x;
     else
       _r = rb_funcall(x, '+', 1, y);
   } else if (FIXNUM_P(x)) {
     if (FIX2INT(x) == 0)
       _r = y;
     else
       _r = rb_funcall(x, '+', 1, y);
   } else
     _r = rb_funcall(x, '+', 1, y);
   return _r;
}

inline static VALUE
f_div(x, y)
{
  VALUE _r;
  if (FIXNUM_P(y) && FIX2INT(y) == 1)
    _r = x;
   else
     _r = rb_funcall(x, '/', 1, y);
  return _r;
}

inline static VALUE
f_gt_p(VALUE x, VALUE y)
{
   VALUE _r;
  if (FIXNUM_P(x) && FIXNUM_P(y))
    _r = f_boolcast(FIX2INT(x) > FIX2INT(y));
  else
    _r = rb_funcall(x, '>', 1, y);
  return _r;
}

inline static VALUE
f_lt_p(VALUE x, VALUE y)
{
   VALUE _r;
  if (FIXNUM_P(x) && FIXNUM_P(y))
    _r = f_boolcast(FIX2INT(x) < FIX2INT(y));
  else
    _r = rb_funcall(x, '<', 1, y);
  return _r;
}

binop(mod, '%')

inline static VALUE
f_mul(VALUE x, VALUE y)
{
   VALUE _r;
   if (FIXNUM_P(y)) {
     int _iy = FIX2INT(y);
     if (_iy == 0) {
       if (TYPE(x) == T_FLOAT)
	 _r = rb_float_new(0.0);
       else
	 _r = ZERO;
     } else if (_iy == 1)
       _r = x;
     else
       _r = rb_funcall(x, '*', 1, y);
   } else if (FIXNUM_P(x)) {
     int _ix = FIX2INT(x);
     if (_ix == 0) {
       if (TYPE(y) == T_FLOAT)
	 _r = rb_float_new(0.0);
       else
	 _r = ZERO;
     } else if (_ix == 1)
       _r = y;
     else
       _r = rb_funcall(x, '*', 1, y);
   } else
     _r = rb_funcall(x, '*', 1, y);
   return _r;
}

inline static VALUE
f_sub(VALUE x, VALUE y)
{
   VALUE _r;
   if (FIXNUM_P(y)) {
     if (FIX2INT(y) == 0)
       _r = x;
     else
       _r = rb_funcall(x, '-', 1, y);
   } else
    _r = rb_funcall(x, '-', 1, y);
   return _r;
}

binop(xor, '^')

fun1(floor)
fun1(inspect)
fun1(negate)
fun1(to_f)
fun1(to_i)
fun1(to_s)
fun1(truncate)

inline static VALUE
f_cmp(VALUE x, VALUE y)
{
   VALUE _r;
   if (FIXNUM_P(x) && FIXNUM_P(y)) {
     int c = FIX2INT(x) - FIX2INT(y);
     if (c > 0)
       c = 1;
     else if (c < 0)
       c = -1;
     _r = INT2FIX(c);
   } else
     _r = rb_funcall(x, id_cmp, 1, y);
   return _r;
}

fun2(coerce)

inline static VALUE
f_equal_p(VALUE x, VALUE y)
{
   VALUE _r;
   if (FIXNUM_P(x) && FIXNUM_P(y))
     _r = f_boolcast(FIX2INT(x) == FIX2INT(y));
   else
     _r = rb_funcall(x, id_equal_p, 1, y);
   return _r;
}

fun2(expt)
fun2(idiv)

inline static VALUE
f_negative_p(VALUE x)
{
   VALUE _r;
  if (FIXNUM_P(x))
    _r = f_boolcast(FIX2INT(x) < 0);
  else
    _r = rb_funcall(x, '<', 1, ZERO);
  return _r;
}

inline static VALUE
f_zero_p(VALUE x)
{
   VALUE _r;
   if (FIXNUM_P(x))
     _r = f_boolcast(FIX2INT(x) == 0);
   else
     _r = rb_funcall(x, id_equal_p, 1, ZERO);
   return _r;
}

inline static VALUE
f_one_p(VALUE x)
{
   VALUE _r;
   if (FIXNUM_P(x))
     _r = f_boolcast(FIX2INT(x) == 1);
   else
     _r = rb_funcall(x, id_equal_p, 1, ONE);
   return _r;
}

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);
}

#ifndef NDEBUG
#define f_gcd f_gcd_orig
#endif

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 */
}

#ifndef NDEBUG
#undef f_gcd

inline static VALUE
f_gcd(VALUE x, VALUE y)
{
  VALUE r = f_gcd_orig(x, y);
  if (!f_zero_p(r)) {
    assert(f_zero_p(f_mod(x, r)));
    assert(f_zero_p(f_mod(y, r)));
  }
  return r;
}
#endif

VALUE
rb_gcd(VALUE x, VALUE y)
{
  return f_gcd(x, y);
}

#define get_dat1(x) \
  struct RRational *dat;\
  dat = ((struct RRational *)(x))

#define get_dat2(x,y) \
  struct RRational *adat, *bdat;\
  adat = ((struct RRational *)(x));\
  bdat = ((struct RRational *)(y))

inline static VALUE
nurat_s_new_internal(VALUE klass, VALUE num, VALUE den)
{
  NEWOBJ(obj, struct RRational);
  OBJSETUP(obj, klass, T_RATIONAL);

  obj->num = num;
  obj->den = den;

  return (VALUE)obj;
}

static VALUE
nurat_s_alloc(VALUE klass)
{
  return nurat_s_new_internal(klass, ZERO, ONE);
}

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);
}

inline static VALUE
nurat_s_canonicalize_internal_no_reduce(VALUE klass, VALUE num, VALUE den)
{
  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;
  }

  if (f_equal_p(den, ONE) && 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);
}

inline static VALUE
f_rational_new_no_reduce1(VALUE klass, VALUE x)
{
  assert(!k_rational_p(x));
  return nurat_s_canonicalize_internal_no_reduce(klass, x, ONE);
}

inline static VALUE
f_rational_new_no_reduce2(VALUE klass, VALUE x, VALUE y)
{
  assert(!k_rational_p(x));
  assert(!k_rational_p(y));
  return nurat_s_canonicalize_internal_no_reduce(klass, x, y);
}

static VALUE
nurat_f_rational(int argc, VALUE *argv, VALUE klass)
{
  return rb_funcall2(rb_cRational, id_convert, argc, argv);
}

static VALUE
nurat_numerator(VALUE self)
{
  get_dat1(self);
  return dat->num;
}

static VALUE
nurat_denominator(VALUE self)
{
  get_dat1(self);
  return dat->den;
}

#ifndef NDEBUG
#define f_imul f_imul_orig
#endif

inline static VALUE
f_imul(long a, long b)
{
  VALUE r;
  long c;

  if (a == 0 || b == 0)
    return ZERO;
  else if (a == 1)
    return LONG2NUM(b);
  else if (b == 1)
    return LONG2NUM(a);

  c = a * b;
  r = LONG2NUM(c);
  if (NUM2LONG(r) != c || (c / a) != b)
    r = rb_big_mul(rb_int2big(a), rb_int2big(b));
  return r;
}

#ifndef NDEBUG
#undef f_imul

inline static VALUE
f_imul(long x, long y)
{
  VALUE r = f_imul_orig(x, y);
  assert(f_equal_p(r, f_mul(LONG2NUM(x), LONG2NUM(y))));
  return r;
}
#endif

inline static VALUE
f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
{
  VALUE num, den;

  if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
      FIXNUM_P(bnum) && FIXNUM_P(bden)) {
    long an = FIX2LONG(anum);
    long ad = FIX2LONG(aden);
    long bn = FIX2LONG(bnum);
    long bd = FIX2LONG(bden);
    long ig = i_gcd(ad, bd);

    VALUE g = LONG2NUM(ig);
    VALUE a = f_imul(an, bd / ig);
    VALUE b = f_imul(bn, ad / ig);
    VALUE c;

    if (k == '+')
      c = f_add(a, b);
    else
      c = f_sub(a, b);

    b = f_idiv(aden, g);
    g = f_gcd(c, g);
    num = f_idiv(c, g);
    a = f_idiv(bden, g);
    den = f_mul(a, b);
  } else {
    VALUE g = f_gcd(aden, bden);
    VALUE a = f_mul(anum, f_idiv(bden, g));
    VALUE b = f_mul(bnum, f_idiv(aden, g));
    VALUE c;

    if (k == '+')
      c = f_add(a, b);
    else
      c = f_sub(a, b);

    b = f_idiv(aden, g);
    g = f_gcd(c, g);
    num = f_idiv(c, g);
    a = f_idiv(bden, g);
    den = f_mul(a, b);
  }
  return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
}

static VALUE
nurat_add(VALUE self, VALUE other)
{
  switch (TYPE(other)) {
  case T_FIXNUM:
  case T_BIGNUM:
    {
      get_dat1(self);

      return f_addsub(self,
		      dat->num, dat->den,
		      other, ONE, '+');
    }
  case T_FLOAT:
    return f_add(f_to_f(self), other);
  case T_RATIONAL:
    {
      get_dat2(self, other);

      return f_addsub(self,
		      adat->num, adat->den,
		      bdat->num, bdat->den, '+');
    }
  default:
    {
      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:
    {
      get_dat1(self);

      return f_addsub(self,
		      dat->num, dat->den,
		      other, ONE, '-');
    }
  case T_FLOAT:
    return f_sub(f_to_f(self), other);
  case T_RATIONAL:
    {
      get_dat2(self, other);

      return f_addsub(self,
		      adat->num, adat->den,
		      bdat->num, bdat->den, '-');
    }
  default:
    {
      VALUE a = f_coerce(other, self);
      return f_sub(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
    }
  }
}

inline static VALUE
f_muldiv(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
{
  VALUE num, den;

  if (k == '/') {
    VALUE t;

    if (f_negative_p(bnum)) {
      anum = f_negate(anum);
      bnum = f_negate(bnum);
    }
    t = bnum;
    bnum = bden;
    bden = t;
  }

  if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
      FIXNUM_P(bnum) && FIXNUM_P(bden)) {
    long an = FIX2LONG(anum);
    long ad = FIX2LONG(aden);
    long bn = FIX2LONG(bnum);
    long bd = FIX2LONG(bden);
    long g1 = i_gcd(an, bd);
    long g2 = i_gcd(ad, bn);

    num = f_imul(an / g1, bn / g2);
    den = f_imul(ad / g2, bd / g1);
  } else {
    VALUE g1 = f_gcd(anum, bden);
    VALUE g2 = f_gcd(aden, bnum);

    num = f_mul(f_idiv(anum, g1), f_idiv(bnum, g2));
    den = f_mul(f_idiv(aden, g2), f_idiv(bden, g1));
  }
  return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
}

static VALUE
nurat_mul(VALUE self, VALUE other)
{
  switch (TYPE(other)) {
  case T_FIXNUM:
  case T_BIGNUM:
    {
      get_dat1(self);

      return f_muldiv(self,
		      dat->num, dat->den,
		      other, ONE, '*');
    }
  case T_FLOAT:
    return f_mul(f_to_f(self), other);
  case T_RATIONAL:
    {
      get_dat2(self, other);

      return f_muldiv(self,
		      adat->num, adat->den,
		      bdat->num, bdat->den, '*');
    }
  default:
    {
      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");
    {
      get_dat1(self);

      return f_muldiv(self,
		      dat->num, dat->den,
		      other, ONE, '/');
    }
  case T_FLOAT:
    return f_div(f_to_f(self), other);
  case T_RATIONAL:
    if (f_zero_p(other))
      rb_raise(rb_eZeroDivError, "devided by zero");
    {
      get_dat2(self, other);

      return f_muldiv(self,
		      adat->num, adat->den,
		      bdat->num, bdat->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:
    {
      get_dat1(self);

      if (FIXNUM_P(dat->den) && FIX2INT(dat->den) == 1)
	return f_cmp(dat->num, other);
      else
	return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other));
    }
  case T_FLOAT:
    return f_cmp(f_to_f(self), other);
  case T_RATIONAL:
    {
      VALUE num1, num2;

      get_dat2(self, other);

      if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) &&
	  FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) {
	num1 = f_imul(FIX2INT(adat->num), FIX2INT(bdat->den));
	num2 = f_imul(FIX2INT(bdat->num), FIX2INT(adat->den));
      } else {
	num1 = f_mul(adat->num, bdat->den);
	num2 = f_mul(bdat->num, adat->den);
      }
      return f_cmp(f_sub(num1, num2), ZERO);
    }
  default:
    {
      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:
    {
      get_dat1(self);

      if (!FIXNUM_P(dat->den))
	return Qfalse;
      if (FIX2INT(dat->den) != 1)
	return Qfalse;
      if (f_equal_p(dat->num, other))
	return Qtrue;
      else
	return Qfalse;
    }
  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);
  }
}

#define f_size(x) rb_funcall(x, rb_intern("size"), 0)
#define f_rshift(x,y) rb_funcall(x, rb_intern(">>"), 1, y)

inline static long
i_ilog2(VALUE x)
{
  long q, r, fx;

  assert(!f_lt_p(x, ONE));

  q = (NUM2LONG(f_size(x)) - sizeof(long)) * 8 + 1;

  if (q > 0)
    x = f_rshift(x, LONG2NUM(q));

  fx = NUM2LONG(x);

  r = -1;
  while (fx) {
    fx >>= 1;
    r += 1;
  }

  return q + r;
}

#include <float.h>

static VALUE
nurat_to_f(VALUE self)
{
  get_dat1(self);
  VALUE num, den;
  int minus = 0;
  long nl, dl, ml, ne, de;
  int e;
  double f;

  if (f_zero_p(dat->num))
    return rb_float_new(0.0);

  num = dat->num;
  den = dat->den;

  if (f_negative_p(num)) {
    num = f_negate(num);
    minus = 1;
  }

  nl = i_ilog2(num);
  dl = i_ilog2(den);
  ml = (long)(log(DBL_MAX) / log(2) - 1); /* should be a static */

  ne = 0;
  if (nl > ml) {
    ne = nl - ml;
    num = f_rshift(num, LONG2NUM(ne));
  }

  de = 0;
  if (dl > ml) {
    de = dl - ml;
    den = f_rshift(den, LONG2NUM(de));
  }

  e = (int)(ne - de);

  if ((e > DBL_MAX_EXP) || (e < DBL_MIN_EXP)) {
    rb_warn("%s out of Float range", rb_obj_classname(self));
    return rb_float_new(e > 0 ? HUGE_VAL : 0.0);
  }

  f = NUM2DBL(num) / NUM2DBL(den);
  if (minus)
    f = -f;
  f = ldexp(f, e);

  if (isinf(f) || isnan(f))
    rb_warn("%s out of Float range", rb_obj_classname(self));

  return rb_float_new(f);
}

static VALUE
nurat_to_r(VALUE self)
{
  return self;
}

static VALUE
nurat_hash(VALUE self)
{
  get_dat1(self);
  return f_xor(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);
}