ruby--ruby/complex.c

/*
  complex.c: Coded by Tadayoshi Funaba 2008

  This implementation is based on Keiju Ishitsuka's Complex library
  which is written in ruby.
*/

#include "ruby.h"
#include <math.h>

#define NDEBUG
#include <assert.h>

#ifndef COMPLEX_NAME
#define COMPLEX_NAME "Complex"
#endif

#define ZERO INT2FIX(0)
#define ONE INT2FIX(1)
#define TWO INT2FIX(2)

VALUE rb_cComplex;

static ID id_Unify, id_abs, id_abs2, id_arg, id_atan2_bang, id_cmp,
  id_coerce, id_conjugate, id_convert, id_cos, id_denominator, id_divmod,
  id_equal_p, id_exact_p, id_exp_bang, id_expt, id_floor, id_format,
  id_hypot, id_idiv, id_inspect, id_log_bang, id_negate, id_new, id_new_bang,
  id_numerator, id_polar, id_quo, id_scalar_p, id_sin, id_sqrt, id_to_f,
  id_to_i, id_to_r, 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_abs(x) rb_funcall(x, id_abs, 0)
#define f_abs2(x) rb_funcall(x, id_abs2, 0)
#define f_arg(x) rb_funcall(x, id_arg, 0)
#define f_conjugate(x) rb_funcall(x, id_conjugate, 0)
#define f_denominator(x) rb_funcall(x, id_denominator, 0)
#define f_exact_p(x) rb_funcall(x, id_exact_p, 0)
#define f_floor(x) rb_funcall(x, id_floor, 0)
#define f_negate(x) rb_funcall(x, id_negate, 0)
#define f_numerator(x) rb_funcall(x, id_numerator, 0)
#define f_polar(x) rb_funcall(x, id_polar, 0)
#define f_scalar_p(x) rb_funcall(x, id_scalar_p, 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_r(x) rb_funcall(x, id_to_r, 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_divmod(x,y) rb_funcall(x, id_divmod, 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_inspect(x) rb_funcall(x, id_inspect, 0)
#define f_quo(x,y) rb_funcall(x, id_quo, 1, y)

#if 0
#define m_cos(x) rb_funcall(rb_mMath, id_cos, 1, x)
#define m_exp_bang(x) rb_funcall(rb_mMath, id_exp_bang, 1, x)
#define m_log_bang(x) rb_funcall(rb_mMath, id_log_bang, 1, x)
#define m_sin(x) rb_funcall(rb_mMath, id_sin, 1, x)
#define m_sqrt(x) rb_funcall(rb_mMath, id_sqrt, 1, x)
#define m_atan2_bang(x,y) rb_funcall(rb_mMath, id_atan2_bang, 2, x, y)
#define m_hypot(x,y) rb_funcall(rb_mMath, id_hypot, 2, x, y)
#endif

#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 k_complex_p(x) f_kind_of_p(x, rb_cComplex)

#define f_boolcast(x) ((x) ? Qtrue : Qfalse)

inline static VALUE
f_generic_p(VALUE x)
{
  switch (TYPE(x)) {
  case T_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
  case T_RATIONAL:
    return Qtrue;
  default:
    return Qfalse;
  }
}

static VALUE
nucomp_s_generic_p(VALUE klass, VALUE x)
{
  return f_generic_p(x);
}

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

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

inline static VALUE
nucomp_s_new_internal(VALUE klass, VALUE real, VALUE image)
{
  NEWOBJ(obj, struct RComplex);
  OBJSETUP(obj, klass, T_COMPLEX);

  obj->real = real;
  obj->image = image;

  return (VALUE)obj;
}

static VALUE
nucomp_s_alloc(VALUE klass)
{
  return nucomp_s_new_internal(klass, ZERO, ZERO);
}

static VALUE
nucomp_s_new_bang(int argc, VALUE *argv, VALUE klass)
{
  VALUE real, image;

  switch (rb_scan_args(argc, argv, "11", &real, &image)) {
  case 1:
    if (!k_numeric_p(real))
      real = f_to_i(real);
    image = ZERO;
    break;
  default:
    if (!k_numeric_p(real))
      real = f_to_i(real);
    if (!k_numeric_p(image))
      image = f_to_i(image);
    break;
  }

  return nucomp_s_new_internal(klass, real, image);
}

inline static VALUE
f_complex_new_bang1(VALUE klass, VALUE x)
{
  return nucomp_s_new_internal(klass, x, ZERO);
}

inline static VALUE
f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
{
  return nucomp_s_new_internal(klass, x, y);
}

#define f_unify_p(klass) rb_const_defined(klass, id_Unify)

inline static VALUE
nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE image)
{
#define CL_CANON
#ifdef CL_CANON
  if (f_zero_p(image) && f_unify_p(klass) &&
      !k_float_p(real) && !k_float_p(image))
    return real;
#else
  if (f_zero_p(image) && f_unify_p(klass))
    return real;
#endif
  else if (f_scalar_p(real) && f_scalar_p(image))
    return nucomp_s_new_internal(klass, real, image);
  else if (f_scalar_p(real)) {
    get_dat1(image);

    return nucomp_s_new_internal(klass,
				 f_sub(real, dat->image),
				 f_add(ZERO, dat->real));
  } else if (f_scalar_p(image)) {
    get_dat1(real);

    return nucomp_s_new_internal(klass,
				 dat->real,
				 f_add(dat->image, image));
  } else {
    get_dat2(real, image);

    return nucomp_s_new_internal(klass,
				 f_sub(adat->real, bdat->image),
				 f_add(adat->image, bdat->real));
  }
}

static VALUE
nucomp_s_canonicalize(int argc, VALUE *argv, VALUE klass)
{
  VALUE real, image;

  switch (rb_scan_args(argc, argv, "11", &real, &image)) {
  case 1:
    image = ZERO;
    break;
  }

  switch (TYPE(real)) {
  case T_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
    break;
  default:
    if (!k_rational_p(real))
      rb_raise(rb_eArgError, "not a real");
  }

  switch (TYPE(image)) {
  case T_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
    break;
  default:
    if (!k_rational_p(image))
      rb_raise(rb_eArgError, "not a real");
  }

  return nucomp_s_canonicalize_internal(klass, real, image);
}

static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
{
  VALUE real, image;

  switch (rb_scan_args(argc, argv, "11", &real, &image)) {
  case 1:
    image = ZERO;
    break;
  }

  switch (TYPE(real)) {
  case T_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
    break;
  default:
    if (!k_rational_p(real))
      rb_raise(rb_eArgError, "not a real");
  }

  switch (TYPE(image)) {
  case T_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
    break;
  default:
    if (!k_rational_p(image))
      rb_raise(rb_eArgError, "not a real");
  }

  return nucomp_s_canonicalize_internal(klass, real, image);
}

inline static VALUE
f_complex_new1(VALUE klass, VALUE x)
{
  assert(!k_complex_p(x));
  return nucomp_s_canonicalize_internal(klass, x, ZERO);
}

inline static VALUE
f_complex_new2(VALUE klass, VALUE x, VALUE y)
{
  assert(!k_complex_p(x));
  return nucomp_s_canonicalize_internal(klass, x, y);
}

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

#if 1
/* the following code is copied from math.c */

#include <errno.h>

#define Need_Float(x) (x) = rb_Float(x)
#define Need_Float2(x,y) do {\
    Need_Float(x);\
    Need_Float(y);\
} while (0)

static void
domain_check(double x, char *msg)
{
  while(1) {
    if (errno) {
      rb_sys_fail(msg);
    }
    if (isnan(x)) {
#if defined(EDOM)
      errno = EDOM;
#elif defined(ERANGE)
      errno = ERANGE;
#endif
      continue;
    }
    break;
  }
}

static VALUE
m_cos_bang(VALUE x)
{
  Need_Float(x);
  return DOUBLE2NUM(cos(RFLOAT_VALUE(x)));
}

static VALUE m_cos_bang(VALUE);
static VALUE m_cosh_bang(VALUE);
static VALUE m_sin_bang(VALUE);
static VALUE m_sinh_bang(VALUE);

static VALUE
m_cos(VALUE x)
{
  get_dat1(x);

  if (f_generic_p(x))
    return m_cos_bang(x);
  else
    return f_complex_new2(rb_cComplex,
			  f_mul(m_cos_bang(dat->real),
				m_cosh_bang(dat->image)),
			  f_mul(f_negate(m_sin_bang(dat->real)),
				m_sinh_bang(dat->image)));
}

#ifndef HAVE_COSH
double
cosh(double x)
{
  return (exp(x) + exp(-x)) / 2;
}
#endif

static VALUE
m_cosh_bang(VALUE x)
{
  Need_Float(x);
  return DOUBLE2NUM(cosh(RFLOAT_VALUE(x)));
}

static VALUE
m_exp_bang(VALUE x)
{
  Need_Float(x);
  return DOUBLE2NUM(exp(RFLOAT_VALUE(x)));
}

static VALUE
m_log_bang(VALUE x)
{
  double d;

  Need_Float(x);
  errno = 0;
  d = log(RFLOAT_VALUE(x));
  domain_check(d, "log");
  return DOUBLE2NUM(d);
}

static VALUE
m_sin_bang(VALUE x)
{
  Need_Float(x);
  return DOUBLE2NUM(sin(RFLOAT_VALUE(x)));
}

static VALUE
m_sin(VALUE x)
{
  get_dat1(x);

  if (f_generic_p(x))
    return m_sin_bang(x);
  else
    return f_complex_new2(rb_cComplex,
			  f_mul(m_sin_bang(dat->real),
				m_cosh_bang(dat->image)),
			  f_mul(m_cos_bang(dat->real),
				m_sinh_bang(dat->image)));
}

#ifndef HAVE_SINH
double
sinh(double x)
{
  return (exp(x) - exp(-x)) / 2;
}
#endif

static VALUE
m_sinh_bang(VALUE x)
{
  Need_Float(x);
  return DOUBLE2NUM(sinh(RFLOAT_VALUE(x)));
}

static VALUE
m_sqrt_bang(VALUE x)
{
  double d;

  Need_Float(x);
  errno = 0;
  d = sqrt(RFLOAT_VALUE(x));
  domain_check(d, "sqrt");
  return DOUBLE2NUM(d);
}

static VALUE
m_sqrt(VALUE x)
{
  if (f_generic_p(x)) {
    if (!f_negative_p(x))
      return m_sqrt_bang(x);
    else
      return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x)));
  } else {
    get_dat1(x);

    if (f_negative_p(dat->image))
      return f_conjugate(m_sqrt(f_conjugate(x)));
    else {
      VALUE a = f_abs(x);
      return f_complex_new2(rb_cComplex,
			    m_sqrt_bang(f_div(f_add(a, dat->real), TWO)),
			    m_sqrt_bang(f_div(f_sub(a, dat->real), TWO)));
    }
  }
}

static VALUE
m_atan2_bang(VALUE y, VALUE x)
{
  Need_Float2(y, x);
  return DOUBLE2NUM(atan2(RFLOAT_VALUE(y), RFLOAT_VALUE(x)));
}

static VALUE
m_hypot(VALUE x, VALUE y)
{
  Need_Float2(x, y);
  return DOUBLE2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
}
#endif

static VALUE
nucomp_s_polar(VALUE klass, VALUE abs, VALUE arg)
{
  return f_complex_new2(klass,
			f_mul(abs, m_cos(arg)),
			f_mul(abs, m_sin(arg)));
}

static VALUE
nucomp_real(VALUE self)
{
  get_dat1(self);
  return dat->real;
}

static VALUE
nucomp_image(VALUE self)
{
  get_dat1(self);
  return dat->image;
}

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

      return f_complex_new2(CLASS_OF(self),
			    f_add(dat->real, other), dat->image);
    }
  case T_COMPLEX:
    {
      VALUE real, image;

      get_dat2(self, other);

      real = f_add(adat->real, bdat->real);
      image = f_add(adat->image, bdat->image);

      return f_complex_new2(CLASS_OF(self), real, image);
    }
  default:
    {
      VALUE a = f_coerce(other, self);
      return f_add(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
    }
  }
}

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

      return f_complex_new2(CLASS_OF(self),
			    f_sub(dat->real, other), dat->image);
    }
  case T_COMPLEX:
    {
      VALUE real, image;

      get_dat2(self, other);

      real = f_sub(adat->real, bdat->real);
      image = f_sub(adat->image, bdat->image);

      return f_complex_new2(CLASS_OF(self), real, image);
    }
  default:
    {
      VALUE a = f_coerce(other, self);
      return f_add(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
    }
  }
}

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

      return f_complex_new2(CLASS_OF(self),
			    f_mul(dat->real, other),
			    f_mul(dat->image, other));
    }
  case T_COMPLEX:
    {
      VALUE real, image;

      get_dat2(self, other);

      real = f_sub(f_mul(adat->real, bdat->real),
		   f_mul(adat->image, bdat->image));
      image = f_add(f_mul(adat->real, bdat->image),
		    f_mul(adat->image, bdat->real));

      return f_complex_new2(CLASS_OF(self), real, image);
    }
  default:
    {
      VALUE a = f_coerce(other, self);
      return f_mul(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
    }
  }
}

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

      return f_complex_new2(CLASS_OF(self),
			    f_div(dat->real, other),
			    f_div(dat->image, other));
    }
  case T_COMPLEX:
    return f_div(f_mul(self, f_conjugate(other)), f_abs2(other));
  default:
    {
      VALUE a = f_coerce(other, self);
      return f_div(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
    }
  }
}

static VALUE
nucomp_rdiv(VALUE self, VALUE other)
{
  get_dat1(self);

  return f_div(f_complex_new2(CLASS_OF(self),
			      f_to_r(dat->real),
			      f_to_r(dat->image)), other);
}

static VALUE
nucomp_fdiv(VALUE self, VALUE other)
{
  get_dat1(self);

  return f_div(f_complex_new2(CLASS_OF(self),
			      f_to_f(dat->real),
			      f_to_f(dat->image)), other);
}

static VALUE
nucomp_expt(VALUE self, VALUE other)
{
  if (f_zero_p(other))
    return f_complex_new_bang1(CLASS_OF(self), ONE);

  if (k_rational_p(other) && f_one_p(f_denominator(other)))
    other = f_numerator(other); /* good? */

  switch (TYPE(other)) {
  case T_FIXNUM:
  case T_BIGNUM:
    if (f_gt_p(other, ZERO)) {
      VALUE x, z, n;

      x = self;
      z = x;
      n = f_sub(other, ONE);

      while (!f_zero_p(n)) {
	VALUE a;

	while (a = f_divmod(n, TWO),
	       f_zero_p(RARRAY_PTR(a)[1])) {
	  get_dat1(x);

	  x = f_complex_new2(CLASS_OF(self),
			     f_sub(f_mul(dat->real, dat->real),
				   f_mul(dat->image, dat->image)),
			     f_mul(f_mul(TWO, dat->real), dat->image));
	  n = RARRAY_PTR(a)[0];
	}
	z = f_mul(z, x);
	n = f_sub(n, ONE);
      }
      return z;
    } else {
      return f_expt(f_div(f_to_r(ONE), self), f_negate(other));
    }
  case T_FLOAT:
  case T_RATIONAL:
    {
      VALUE a, r, theta;

      a = f_polar(self);
      r = RARRAY_PTR(a)[0];
      theta = RARRAY_PTR(a)[1];
      return nucomp_s_polar(CLASS_OF(self), f_expt(r, other),
			    f_mul(theta, other));
    }
  case T_COMPLEX:
    {
      VALUE a, r, theta, ore, oim, nr, ntheta;

      get_dat1(other);

      a = f_polar(self);
      r = RARRAY_PTR(a)[0];
      theta = RARRAY_PTR(a)[1];

      ore = dat->real;
      oim = dat->image;
      nr = m_exp_bang(f_sub(f_mul(ore, m_log_bang(r)),
			    f_mul(oim, theta)));
      ntheta = f_add(f_mul(theta, ore), f_mul(oim, m_log_bang(r)));
      return nucomp_s_polar(CLASS_OF(self), nr, ntheta);
    }
  default:
    {
      VALUE a = f_coerce(other, self);
      return f_div(RARRAY_PTR(a)[0], RARRAY_PTR(a)[1]);
    }
  }
}

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

      return f_boolcast(f_equal_p(dat->real, other) && f_zero_p(dat->image));
    }
  case T_COMPLEX:
    {
      get_dat2(self, other);

      return f_boolcast(f_equal_p(adat->real, bdat->real) &&
			f_equal_p(adat->image, bdat->image));
    }
  default:
    return f_equal_p(other, self);
  }
}

static VALUE
nucomp_coerce(VALUE self, VALUE other)
{
  switch (TYPE(other)) {
  case T_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
  case T_RATIONAL:
    return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
  }

  rb_raise(rb_eTypeError, "%s can't be coerced into %s",
	   rb_obj_classname(other), rb_obj_classname(self));
  return Qnil;
}

static VALUE
nucomp_abs(VALUE self)
{
  get_dat1(self);
  return m_sqrt(f_add(f_mul(dat->real, dat->real),
		      f_mul(dat->image, dat->image)));
}

static VALUE
nucomp_abs2(VALUE self)
{
  get_dat1(self);
  return f_add(f_mul(dat->real, dat->real),
	       f_mul(dat->image, dat->image));
}

static VALUE
nucomp_arg(VALUE self)
{
  get_dat1(self);
  return m_atan2_bang(dat->image, dat->real);
}

static VALUE
nucomp_polar(VALUE self)
{
  return rb_assoc_new(f_abs(self), f_arg(self));
}

static VALUE
nucomp_conjugate(VALUE self)
{
  get_dat1(self);
  return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->image));
}

static VALUE
nucomp_real_p(VALUE self)
{
  return Qfalse;
}

static VALUE
nucomp_complex_p(VALUE self)
{
  return Qtrue;
}

static VALUE
nucomp_exact_p(VALUE self)
{
  get_dat1(self);
  return f_boolcast(f_exact_p(dat->real) && f_exact_p(dat->image));
}

static VALUE
nucomp_inexact_p(VALUE self)
{
  return f_boolcast(!nucomp_exact_p(self));
}

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 */
}

static VALUE
f_lcm(VALUE x, VALUE y)
{
  if (f_zero_p(x) || f_zero_p(y))
    return ZERO;
  else
    return f_abs(f_mul(f_div(x, f_gcd(x, y)), y));
}

static VALUE
nucomp_denominator(VALUE self)
{
  get_dat1(self);
  return f_lcm(f_denominator(dat->real), f_denominator(dat->image));
}

static VALUE
nucomp_numerator(VALUE self)
{
  VALUE cd;

  get_dat1(self);

  cd = f_denominator(self);
  return f_complex_new2(CLASS_OF(self),
			f_mul(f_numerator(dat->real),
			      f_div(cd, f_denominator(dat->real))),
			f_mul(f_numerator(dat->image),
			      f_div(cd, f_denominator(dat->image))));
}

static VALUE
nucomp_hash(VALUE self)
{
  get_dat1(self);
  return f_xor(dat->real, dat->image);
}

#ifndef HAVE_SIGNBIT
#ifdef signbit
#define HAVE_SIGNBIT 1
#endif
#endif

inline static VALUE
f_signbit(VALUE x)
{
  switch (TYPE(x)) {
  case T_FLOAT:
#ifdef HAVE_SIGNBIT
    return f_boolcast(signbit(RFLOAT_VALUE(x)));
#else
    {
      char s[2];

      (void)snprintf(s, sizeof s, "%.0f", RFLOAT_VALUE(x));

      return f_boolcast(s[0] == '-');
    }
#endif
  }
  return f_negative_p(x);
}

inline static VALUE
f_tzero_p(VALUE x)
{
  return f_boolcast(f_zero_p(x) && !f_signbit(x));
}

inline static VALUE
f_tpositive_p(VALUE x)
{
  return f_boolcast(!f_signbit(x));
}

static VALUE
nucomp_to_s(VALUE self)
{
  VALUE s, rezero, impos;

  get_dat1(self);

  rezero = f_tzero_p(dat->real);
  impos = f_tpositive_p(dat->image);

  if (rezero)
    s = rb_str_new2("");
  else {
    s = f_to_s(dat->real);
    rb_str_concat(s, rb_str_new2(!impos ? "-" : "+"));
  }

  if (k_rational_p(dat->image) &&
      !f_one_p(f_denominator(dat->image))) {
    rb_str_concat(s, rb_str_new2("("));
    rb_str_concat(s, f_to_s(rezero ? dat->image : f_abs(dat->image)));
    rb_str_concat(s, rb_str_new2(")i"));
  } else {
    rb_str_concat(s, f_to_s(rezero ? dat->image : f_abs(dat->image)));
    rb_str_concat(s, rb_str_new2("i"));
  }

  return s;
}

static VALUE
nucomp_inspect(VALUE self)
{
  VALUE s;

  get_dat1(self);

  s = rb_str_new2("Complex(");
  rb_str_concat(s, f_inspect(dat->real));
  rb_str_concat(s, rb_str_new2(", "));
  rb_str_concat(s, f_inspect(dat->image));
  rb_str_concat(s, rb_str_new2(")"));

  return s;
}

static VALUE
nucomp_marshal_dump(VALUE self)
{
  get_dat1(self);
  return rb_assoc_new(dat->real, dat->image);
}

static VALUE
nucomp_marshal_load(VALUE self, VALUE a)
{
  get_dat1(self);
  dat->real = RARRAY_PTR(a)[0];
  dat->image = RARRAY_PTR(a)[1];
  return self;
}

/* --- */

VALUE
rb_complex_raw(VALUE x, VALUE y)
{
  return nucomp_s_new_internal(rb_cComplex, x, y);
}

VALUE
rb_complex_new(VALUE x, VALUE y)
{
  return nucomp_s_canonicalize_internal(rb_cComplex, x, y);
}

static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass);

VALUE
rb_Complex(VALUE x, VALUE y)
{
  VALUE a[2];
  a[0] = x;
  a[1] = y;
  return nucomp_s_convert(2, a, rb_cComplex);
}

static VALUE
nucomp_scalar_p(VALUE self)
{
  return Qfalse;
}

static VALUE
nucomp_to_i(VALUE self)
{
  get_dat1(self);

  if (k_float_p(dat->image) || !f_zero_p(dat->image)) {
    VALUE s = f_to_s(self);
    rb_raise(rb_eRangeError, "can't convert %s into Integer",
	     StringValuePtr(s));
  }
  return f_to_i(dat->real);
}

static VALUE
nucomp_to_f(VALUE self)
{
  get_dat1(self);

  if (k_float_p(dat->image) || !f_zero_p(dat->image)) {
    VALUE s = f_to_s(self);
    rb_raise(rb_eRangeError, "can't convert %s into Integer",
	     StringValuePtr(s));
  }
  return f_to_f(dat->real);
}

static VALUE
nucomp_to_r(VALUE self)
{
  get_dat1(self);

  if (k_float_p(dat->image) || !f_zero_p(dat->image)) {
    VALUE s = f_to_s(self);
    rb_raise(rb_eRangeError, "can't convert %s into Integer",
	     StringValuePtr(s));
  }
  return f_to_r(dat->real);
}

static VALUE
nilclass_to_c(VALUE self)
{
  return rb_complex_new1(INT2FIX(0));
}

static VALUE
numeric_to_c(VALUE self)
{
  return rb_complex_new1(self);
}

static VALUE comp_pat1, comp_pat2, a_slash, a_dot_and_an_e,
  image_garbages_pat, null_string, underscores_pat, an_underscore;

#define DIGITS "(?:\\d(?:_\\d|\\d)*)"
#define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
#define DENOMINATOR "[-+]?" DIGITS
#define NUMBER "[-+]?" NUMERATOR "(?:\\/" DENOMINATOR ")?"
#define NUMBERNOS NUMERATOR "(?:\\/" DENOMINATOR ")?"
#define PATTERN1 "\\A(" NUMBER "|\\(" NUMBER "\\))[iIjJ]"
#define PATTERN2 "\\A(" NUMBER ")([-+](?:" NUMBERNOS "|\\(" NUMBER "\\))[iIjJ])?"

static void
make_patterns(void)
{
  static char *comp_pat1_source = PATTERN1;
  static char *comp_pat2_source = PATTERN2;
  static char *image_garbages_pat_source = "[+\\(\\)iIjJ]";
  static char *underscores_pat_source = "_+";

  comp_pat1 = rb_reg_new(comp_pat1_source, strlen(comp_pat1_source), 0);
  rb_global_variable(&comp_pat1);

  comp_pat2 = rb_reg_new(comp_pat2_source, strlen(comp_pat2_source), 0);
  rb_global_variable(&comp_pat2);

  a_slash = rb_str_new2("/");
  rb_global_variable(&a_slash);

  a_dot_and_an_e = rb_str_new2(".eE");
  rb_global_variable(&a_dot_and_an_e);

  image_garbages_pat = rb_reg_new(image_garbages_pat_source,
				  strlen(image_garbages_pat_source), 0);
  rb_global_variable(&image_garbages_pat);

  null_string = rb_str_new2("");
  rb_global_variable(&null_string);

  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)

#define id_include_p rb_intern("include?")
#define f_include_p(x,y) rb_funcall(x, id_include_p, 1, y)

#define id_count rb_intern("count")
#define f_count(x,y) rb_funcall(x, id_count, 1, y)

#define id_gsub_bang rb_intern("gsub!")
#define f_gsub_bang(x,y,z) rb_funcall(x, id_gsub_bang, 2, y, z)

static VALUE
string_to_c_internal(VALUE self)
{
  VALUE s;

  s = f_strip(self);

  if (RSTRING_LEN(s) == 0)
    return rb_assoc_new(Qnil, self);

  {
    VALUE m, sr, si, re, r, i;

    m = f_match(comp_pat1, s);
    if (!NIL_P(m)) {
      sr = Qnil;
      si = f_aref(m, INT2FIX(1));
      re = f_post_match(m);
    }
    if (NIL_P(m)) {
      m = f_match(comp_pat2, s);
      if (NIL_P(m))
	return rb_assoc_new(Qnil, self);
      sr = f_aref(m, INT2FIX(1));
      si = f_aref(m, INT2FIX(2));
      re = f_post_match(m);
    }
    r = INT2FIX(0);
    i = INT2FIX(0);
    if (!NIL_P(sr)) {
      if (f_include_p(sr, a_slash))
	r = f_to_r(sr);
      else if (f_gt_p(f_count(sr, a_dot_and_an_e), INT2FIX(0)))
	r = f_to_f(sr);
      else
	r = f_to_i(sr);
    }
    if (!NIL_P(si)) {
      f_gsub_bang(si, image_garbages_pat, null_string);
      if (f_include_p(si, a_slash))
	i = f_to_r(si);
      else if (f_gt_p(f_count(si, a_dot_and_an_e), INT2FIX(0)))
	i = f_to_f(si);
      else
	i = f_to_i(si);
    }
    return rb_assoc_new(rb_complex_new2(r, i), re);
  }
}

static VALUE
string_to_c_strict(VALUE self)
{
  VALUE a = string_to_c_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 Complex: %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_c(VALUE self)
{
  VALUE s = f_gsub(self, underscores_pat, an_underscore);
  VALUE a = string_to_c_internal(s);
  if (!NIL_P(RARRAY_PTR(a)[0]))
    return RARRAY_PTR(a)[0];
  return rb_complex_new1(INT2FIX(0));
}

static VALUE
nucomp_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_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
    break;
  case T_STRING:
    a1 = string_to_c_strict(a1);
    break;
  }

  switch (TYPE(a2)) {
  case T_FIXNUM:
  case T_BIGNUM:
  case T_FLOAT:
    break;
  case T_STRING:
    a2 = string_to_c_strict(a2);
    break;
  }

  switch (TYPE(a1)) {
  case T_COMPLEX:
    {
      get_dat1(a1);

      if (!k_float_p(dat->image) && f_zero_p(dat->image))
	a1 = dat->real;
    }
  }

  switch (TYPE(a2)) {
  case T_COMPLEX:
    {
      get_dat1(a2);

      if (!k_float_p(dat->image) && f_zero_p(dat->image))
	a2 = dat->real;
    }
  }

  switch (TYPE(a1)) {
  case T_COMPLEX:
    if (NIL_P(a2) || f_zero_p(a2))
      return a1;
  }

  {
    VALUE argv2[2];
    argv2[0] = a1;
    argv2[1] = a2;
    return nucomp_s_new(argc, argv2, klass);
  }
}

/* --- */

#define id_Complex rb_intern("Complex")

static VALUE
numeric_re(VALUE self)
{
  return rb_Complex1(self);
}

static VALUE
numeric_im(VALUE self)
{
  return rb_Complex2(ZERO, self);
}

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

static VALUE
numeric_image(VALUE self)
{
  return INT2FIX(0);
}

#define id_PI rb_intern("PI")

static VALUE
numeric_arg(VALUE self)
{
  if (!f_negative_p(self))
    return INT2FIX(0);
  return rb_const_get(rb_mMath, id_PI);
}

static VALUE
numeric_polar(VALUE self)
{
  return rb_assoc_new(f_abs(self), f_arg(self));
}

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

void
Init_Complex(void)
{
  assert(fprintf(stderr, "assert() is now active\n"));

  id_Unify = rb_intern("Unify");
  id_abs = rb_intern("abs");
  id_abs2 = rb_intern("abs2");
  id_arg = rb_intern("arg");
  id_atan2_bang = rb_intern("atan2!");
  id_cmp = rb_intern("<=>");
  id_coerce = rb_intern("coerce");
  id_conjugate = rb_intern("conjugate");
  id_convert = rb_intern("convert");
  id_cos = rb_intern("cos");
  id_denominator = rb_intern("denominator");
  id_divmod = rb_intern("divmod");
  id_equal_p = rb_intern("==");
  id_exact_p = rb_intern("exact?");
  id_exp_bang = rb_intern("exp!");
  id_expt = rb_intern("**");
  id_floor = rb_intern("floor");
  id_format = rb_intern("format");
  id_hypot = rb_intern("hypot");
  id_idiv = rb_intern("div");
  id_inspect = rb_intern("inspect");
  id_log_bang = rb_intern("log!");
  id_negate = rb_intern("-@");
  id_new = rb_intern("new");
  id_new_bang = rb_intern("new!");
  id_numerator = rb_intern("numerator");
  id_polar = rb_intern("polar");
  id_quo = rb_intern("quo");
  id_scalar_p = rb_intern("scalar?");
  id_sin = rb_intern("sin");
  id_sqrt = rb_intern("sqrt");
  id_to_f = rb_intern("to_f");
  id_to_i = rb_intern("to_i");
  id_to_r = rb_intern("to_r");
  id_to_s = rb_intern("to_s");
  id_truncate = rb_intern("truncate");

  rb_cComplex = rb_define_class(COMPLEX_NAME, rb_cNumeric);

  rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
  rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
	     ID2SYM(rb_intern("allocate")));

  rb_define_singleton_method(rb_cComplex, "generic?", nucomp_s_generic_p, 1);

  rb_define_singleton_method(rb_cComplex, "new!", nucomp_s_new_bang, -1);
  rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
	     ID2SYM(rb_intern("new!")));

  rb_define_singleton_method(rb_cComplex, "new", nucomp_s_new, -1);
  rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
	     ID2SYM(rb_intern("new")));

#if 0
  rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1);
  rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1);
#endif
  rb_define_singleton_method(rb_cComplex, "polar", nucomp_s_polar, 2);

  rb_define_global_function(COMPLEX_NAME, nucomp_f_complex, -1);

  rb_undef_method(rb_cComplex, "<");
  rb_undef_method(rb_cComplex, "<=");
  rb_undef_method(rb_cComplex, "<=>");
  rb_undef_method(rb_cComplex, ">");
  rb_undef_method(rb_cComplex, ">=");
  rb_undef_method(rb_cComplex, "between?");
  rb_undef_method(rb_cComplex, "divmod");
  rb_undef_method(rb_cComplex, "floor");
  rb_undef_method(rb_cComplex, "ceil");
  rb_undef_method(rb_cComplex, "modulo");
  rb_undef_method(rb_cComplex, "round");
  rb_undef_method(rb_cComplex, "step");
  rb_undef_method(rb_cComplex, "truncate");

#if NUBY
  rb_undef_method(rb_cComplex, "//");
#endif

  rb_define_method(rb_cComplex, "real", nucomp_real, 0);
  rb_define_method(rb_cComplex, "image", nucomp_image, 0);
  rb_define_method(rb_cComplex, "imag", nucomp_image, 0);

  rb_define_method(rb_cComplex, "+", nucomp_add, 1);
  rb_define_method(rb_cComplex, "-", nucomp_sub, 1);
  rb_define_method(rb_cComplex, "*", nucomp_mul, 1);
  rb_define_method(rb_cComplex, "/", nucomp_div, 1);
  rb_define_method(rb_cComplex, "quo", nucomp_rdiv, 1);
  rb_define_method(rb_cComplex, "rdiv", nucomp_rdiv, 1);
  rb_define_method(rb_cComplex, "fdiv", nucomp_rdiv, 1);
  rb_define_method(rb_cComplex, "**", nucomp_expt, 1);

  rb_define_method(rb_cComplex, "==", nucomp_equal_p, 1);
  rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1);

  rb_define_method(rb_cComplex, "abs", nucomp_abs, 0);
#if 0
  rb_define_method(rb_cComplex, "magnitude", nucomp_abs, 0);
#endif
  rb_define_method(rb_cComplex, "abs2", nucomp_abs2, 0);
  rb_define_method(rb_cComplex, "arg", nucomp_arg, 0);
  rb_define_method(rb_cComplex, "angle", nucomp_arg, 0);
  rb_define_method(rb_cComplex, "polar", nucomp_polar, 0);
  rb_define_method(rb_cComplex, "conjugate", nucomp_conjugate, 0);
  rb_define_method(rb_cComplex, "conj", nucomp_conjugate, 0);
#if 0
  rb_define_method(rb_cComplex, "~", nucomp_conjugate, 0); /* gcc */
#endif

#if 0
  rb_define_method(rb_cComplex, "real?", nucomp_real_p, 0);
  rb_define_method(rb_cComplex, "complex?", nucomp_complex_p, 0);
  rb_define_method(rb_cComplex, "exact?", nucomp_exact_p, 0);
  rb_define_method(rb_cComplex, "inexact?", nucomp_inexact_p, 0);
#endif

  rb_define_method(rb_cComplex, "numerator", nucomp_numerator, 0);
  rb_define_method(rb_cComplex, "denominator", nucomp_denominator, 0);

  rb_define_method(rb_cComplex, "hash", nucomp_hash, 0);

  rb_define_method(rb_cComplex, "to_s", nucomp_to_s, 0);
  rb_define_method(rb_cComplex, "inspect", nucomp_inspect, 0);

  rb_define_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0);
  rb_define_method(rb_cComplex, "marshal_load", nucomp_marshal_load, 1);

  /* --- */

  rb_define_method(rb_cComplex, "scalar?", nucomp_scalar_p, 0);
  rb_define_method(rb_cComplex, "to_i", nucomp_to_i, 0);
  rb_define_method(rb_cComplex, "to_f", nucomp_to_f, 0);
  rb_define_method(rb_cComplex, "to_r", nucomp_to_r, 0);
  rb_define_method(rb_cNilClass, "to_c", nilclass_to_c, 0);
  rb_define_method(rb_cNumeric, "to_c", numeric_to_c, 0);

  make_patterns();

  rb_define_method(rb_cString, "to_c", string_to_c, 0);

  rb_define_singleton_method(rb_cComplex, "convert", nucomp_s_convert, -1);
  rb_funcall(rb_cComplex, rb_intern("private_class_method"), 1,
	     ID2SYM(rb_intern("convert")));

  /* --- */

  rb_define_method(rb_cNumeric, "re", numeric_re, 0);
  rb_define_method(rb_cNumeric, "im", numeric_im, 0);
  rb_define_method(rb_cNumeric, "real", numeric_real, 0);
  rb_define_method(rb_cNumeric, "image", numeric_image, 0);
  rb_define_method(rb_cNumeric, "imag", numeric_image, 0);
  rb_define_method(rb_cNumeric, "arg", numeric_arg, 0);
  rb_define_method(rb_cNumeric, "angle", numeric_arg, 0);
  rb_define_method(rb_cNumeric, "polar", numeric_polar, 0);
  rb_define_method(rb_cNumeric, "conjugate", numeric_conjugate, 0);
  rb_define_method(rb_cNumeric, "conj", numeric_conjugate, 0);

  rb_define_const(rb_cComplex, "I",
		  f_complex_new_bang2(rb_cComplex, ZERO, ONE));
}