* lib/mathn.rb: moved into ext/mathn/rational/rational.c and

   ext/mathn/complex/complex.c.
 * ext/mathn: new mathn ext-libralies.



git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@19911 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

2 files changed, 1516 insertions, 0 deletions

diff --git a/ext/mathn/complex/complex.c b/ext/mathn/complex/complex.c
new file mode 100644
index 0000000000..5a24c6a351
--- /dev/null
+++ b/ext/mathn/complex/complex.c
@@ -0,0 +1,1511 @@
+/*
+
+  complex.c of mathn version
+
+  Original file is built-in 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_abs, id_abs2, id_arg, id_cmp, id_conj, id_convert,
+    id_denominator, id_divmod, id_equal_p, id_expt, id_floor, id_hash,
+    id_idiv, id_inspect, id_negate, id_numerator, id_polar, id_quo,
+    id_real_p, id_to_f, id_to_i, id_to_r, id_to_s;
+
+#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);\
+}
+
+#define math1(n) \
+inline static VALUE \
+m_##n(VALUE x)\
+{\
+    return rb_funcall(rb_mMath, id_##n, 1, x);\
+}
+
+#define math2(n) \
+inline static VALUE \
+m_##n(VALUE x, VALUE y)\
+{\
+    return rb_funcall(rb_mMath, id_##n, 2, x, y);\
+}
+
+#define PRESERVE_SIGNEDZERO
+
+inline static VALUE
+f_add(VALUE x, VALUE y)
+{
+#ifndef PRESERVE_SIGNEDZERO
+    if (FIXNUM_P(y) && FIX2LONG(y) == 0)
+	return x;
+    else if (FIXNUM_P(x) && FIX2LONG(x) == 0)
+	return y;
+#endif
+    return rb_funcall(x, '+', 1, y);
+}
+
+inline static VALUE
+f_cmp(VALUE x, VALUE y)
+{
+    if (FIXNUM_P(x) && FIXNUM_P(y)) {
+	long c = FIX2LONG(x) - FIX2LONG(y);
+	if (c > 0)
+	    c = 1;
+	else if (c < 0)
+	    c = -1;
+	return INT2FIX(c);
+    }
+    return rb_funcall(x, id_cmp, 1, y);
+}
+
+inline static VALUE
+f_div(VALUE x, VALUE y)
+{
+    if (FIXNUM_P(y) && FIX2LONG(y) == 1)
+	return x;
+    return rb_funcall(x, '/', 1, y);
+}
+
+inline static VALUE
+f_gt_p(VALUE x, VALUE y)
+{
+    if (FIXNUM_P(x) && FIXNUM_P(y))
+	return f_boolcast(FIX2LONG(x) > FIX2LONG(y));
+    return rb_funcall(x, '>', 1, y);
+}
+
+inline static VALUE
+f_lt_p(VALUE x, VALUE y)
+{
+    if (FIXNUM_P(x) && FIXNUM_P(y))
+	return f_boolcast(FIX2LONG(x) < FIX2LONG(y));
+    return rb_funcall(x, '<', 1, y);
+}
+
+binop(mod, '%')
+
+inline static VALUE
+f_mul(VALUE x, VALUE y)
+{
+#ifndef PRESERVE_SIGNEDZERO
+    if (FIXNUM_P(y)) {
+	long iy = FIX2LONG(y);
+	if (iy == 0) {
+	    if (FIXNUM_P(x) || TYPE(x) == T_BIGNUM)
+		return ZERO;
+	}
+	else if (iy == 1)
+	    return x;
+    }
+    else if (FIXNUM_P(x)) {
+	long ix = FIX2LONG(x);
+	if (ix == 0) {
+	    if (FIXNUM_P(y) || TYPE(y) == T_BIGNUM)
+		return ZERO;
+	}
+	else if (ix == 1)
+	    return y;
+    }
+#endif
+    return rb_funcall(x, '*', 1, y);
+}
+
+inline static VALUE
+f_sub(VALUE x, VALUE y)
+{
+#ifndef PRESERVE_SIGNEDZERO
+    if (FIXNUM_P(y) && FIX2LONG(y) == 0)
+	return x;
+#endif
+    return rb_funcall(x, '-', 1, y);
+}
+
+binop(xor, '^')
+
+fun1(abs)
+fun1(abs2)
+fun1(arg)
+fun1(conj)
+fun1(denominator)
+fun1(floor)
+fun1(hash)
+fun1(inspect)
+fun1(negate)
+fun1(numerator)
+fun1(polar)
+fun1(real_p)
+
+fun1(to_f)
+fun1(to_i)
+fun1(to_r)
+fun1(to_s)
+
+fun2(divmod)
+
+inline static VALUE
+f_equal_p(VALUE x, VALUE y)
+{
+    if (FIXNUM_P(x) && FIXNUM_P(y))
+	return f_boolcast(FIX2LONG(x) == FIX2LONG(y));
+    return rb_funcall(x, id_equal_p, 1, y);
+}
+
+fun2(expt)
+fun2(idiv)
+fun2(quo)
+
+inline static VALUE
+f_negative_p(VALUE x)
+{
+    if (FIXNUM_P(x))
+	return f_boolcast(FIX2LONG(x) < 0);
+    return rb_funcall(x, '<', 1, ZERO);
+}
+
+#define f_positive_p(x) (!f_negative_p(x))
+
+inline static VALUE
+f_zero_p(VALUE x)
+{
+    if (FIXNUM_P(x))
+	return f_boolcast(FIX2LONG(x) == 0);
+    return rb_funcall(x, id_equal_p, 1, ZERO);
+}
+
+#define f_nonzero_p(x) (!f_zero_p(x))
+
+inline static VALUE
+f_one_p(VALUE x)
+{
+    if (FIXNUM_P(x))
+	return f_boolcast(FIX2LONG(x) == 1);
+    return rb_funcall(x, id_equal_p, 1, ONE);
+}
+
+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);
+}
+
+inline static VALUE
+k_complex_p(VALUE x)
+{
+    return f_kind_of_p(x, rb_cComplex);
+}
+
+#define k_exact_p(x) (!k_float_p(x))
+#define k_inexact_p(x) k_float_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 imag)
+{
+    NEWOBJ(obj, struct RComplex);
+    OBJSETUP(obj, klass, T_COMPLEX);
+
+    obj->real = real;
+    obj->imag = imag;
+
+    return (VALUE)obj;
+}
+
+static VALUE
+nucomp_s_alloc(VALUE klass)
+{
+    return nucomp_s_new_internal(klass, ZERO, ZERO);
+}
+
+#if 0
+static VALUE
+nucomp_s_new_bang(int argc, VALUE *argv, VALUE klass)
+{
+    VALUE real, imag;
+
+    switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
+      case 1:
+	if (!k_numeric_p(real))
+	    real = f_to_i(real);
+	imag = ZERO;
+	break;
+      default:
+	if (!k_numeric_p(real))
+	    real = f_to_i(real);
+	if (!k_numeric_p(imag))
+	    imag = f_to_i(imag);
+	break;
+    }
+
+    return nucomp_s_new_internal(klass, real, imag);
+}
+#endif
+
+inline static VALUE
+f_complex_new_bang1(VALUE klass, VALUE x)
+{
+    assert(!k_complex_p(x));
+    return nucomp_s_new_internal(klass, x, ZERO);
+}
+
+inline static VALUE
+f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
+{
+    assert(!k_complex_p(x));
+    assert(!k_complex_p(y));
+    return nucomp_s_new_internal(klass, x, y);
+}
+
+#ifndef EXT_MATHN
+#define f_unify_p(klass) rb_const_defined(klass, id_Unify)
+#else
+#define f_unify_p(klass) 1
+#endif
+
+inline static void
+nucomp_real_check(VALUE num)
+{
+    switch (TYPE(num)) {
+      case T_FIXNUM:
+      case T_BIGNUM:
+      case T_FLOAT:
+      case T_RATIONAL:
+	break;
+      default:
+	if (!k_numeric_p(num) || !f_real_p(num))
+	    rb_raise(rb_eArgError, "not a real");
+    }
+}
+
+inline static VALUE
+nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
+{
+#ifdef CANON
+#define CL_CANON
+#ifdef CL_CANON
+    if (f_zero_p(imag) && k_exact_p(imag) && f_unify_p(klass))
+	return real;
+#else
+    if (f_zero_p(imag) && f_unify_p(klass))
+	return real;
+#endif
+#endif
+    if (f_real_p(real) && f_real_p(imag))
+	return nucomp_s_new_internal(klass, real, imag);
+    else if (f_real_p(real)) {
+	get_dat1(imag);
+
+	return nucomp_s_new_internal(klass,
+				     f_sub(real, dat->imag),
+				     f_add(ZERO, dat->real));
+    }
+    else if (f_real_p(imag)) {
+	get_dat1(real);
+
+	return nucomp_s_new_internal(klass,
+				     dat->real,
+				     f_add(dat->imag, imag));
+    }
+    else {
+	get_dat2(real, imag);
+
+	return nucomp_s_new_internal(klass,
+				     f_sub(adat->real, bdat->imag),
+				     f_add(adat->imag, bdat->real));
+    }
+}
+
+static VALUE
+nucomp_s_new(int argc, VALUE *argv, VALUE klass)
+{
+    VALUE real, imag;
+
+    switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
+      case 1:
+	nucomp_real_check(real);
+	imag = ZERO;
+	break;
+      default:
+	nucomp_real_check(real);
+	nucomp_real_check(imag);
+	break;
+    }
+
+    return nucomp_s_canonicalize_internal(klass, real, imag);
+}
+
+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);
+}
+
+extern VALUE math_atan2(VALUE obj, VALUE x, VALUE y);
+extern VALUE math_cos(VALUE obj, VALUE x);
+extern VALUE math_cosh(VALUE obj, VALUE x);
+extern VALUE math_exp(VALUE obj, VALUE x);
+extern VALUE math_hypot(VALUE obj, VALUE x, VALUE y);
+extern VALUE math_log(int argc, VALUE *argv);
+extern VALUE math_sin(VALUE obj, VALUE x);
+extern VALUE math_sinh(VALUE obj, VALUE x);
+extern VALUE math_sqrt(VALUE obj, VALUE x);
+
+#define m_atan2_bang(x,y) math_atan2(Qnil,x,y)
+#define m_cos_bang(x) math_cos(Qnil,x)
+#define m_cosh_bang(x) math_cosh(Qnil,x)
+#define m_exp_bang(x) math_exp(Qnil,x)
+#define m_hypot(x,y) math_hypot(Qnil,x,y)
+
+static VALUE
+m_log_bang(VALUE x)
+{
+    return math_log(1, &x);
+}
+
+#define m_sin_bang(x) math_sin(Qnil,x)
+#define m_sinh_bang(x) math_sinh(Qnil,x)
+#define m_sqrt_bang(x) math_sqrt(Qnil,x)
+
+static VALUE
+m_cos(VALUE x)
+{
+    if (f_real_p(x))
+	return m_cos_bang(x);
+    {
+	get_dat1(x);
+	return f_complex_new2(rb_cComplex,
+			      f_mul(m_cos_bang(dat->real),
+				    m_cosh_bang(dat->imag)),
+			      f_mul(f_negate(m_sin_bang(dat->real)),
+				    m_sinh_bang(dat->imag)));
+    }
+}
+
+static VALUE
+m_sin(VALUE x)
+{
+    if (f_real_p(x))
+	return m_sin_bang(x);
+    {
+	get_dat1(x);
+	return f_complex_new2(rb_cComplex,
+			      f_mul(m_sin_bang(dat->real),
+				    m_cosh_bang(dat->imag)),
+			      f_mul(m_cos_bang(dat->real),
+				    m_sinh_bang(dat->imag)));
+    }
+}
+
+#if 0
+static VALUE
+m_sqrt(VALUE x)
+{
+    if (f_real_p(x)) {
+	if (f_positive_p(x))
+	    return m_sqrt_bang(x);
+	return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x)));
+    }
+    else {
+	get_dat1(x);
+
+	if (f_negative_p(dat->imag))
+	    return f_conj(m_sqrt(f_conj(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)));
+	}
+    }
+}
+#endif
+
+inline static VALUE
+f_complex_polar(VALUE klass, VALUE x, VALUE y)
+{
+    assert(!k_complex_p(x));
+    assert(!k_complex_p(y));
+    return nucomp_s_canonicalize_internal(klass,
+					  f_mul(x, m_cos(y)),
+					  f_mul(x, m_sin(y)));
+}
+
+static VALUE
+nucomp_s_polar(VALUE klass, VALUE abs, VALUE arg)
+{
+    return f_complex_polar(klass, abs, arg);
+}
+
+static VALUE
+nucomp_real(VALUE self)
+{
+    get_dat1(self);
+    return dat->real;
+}
+
+static VALUE
+nucomp_imag(VALUE self)
+{
+    get_dat1(self);
+    return dat->imag;
+}
+
+static VALUE
+nucomp_negate(VALUE self)
+{
+  get_dat1(self);
+  return f_complex_new2(CLASS_OF(self),
+			f_negate(dat->real), f_negate(dat->imag));
+}
+
+static VALUE
+nucomp_add(VALUE self, VALUE other)
+{
+    if (k_complex_p(other)) {
+	VALUE real, imag;
+
+	get_dat2(self, other);
+
+	real = f_add(adat->real, bdat->real);
+	imag = f_add(adat->imag, bdat->imag);
+
+	return f_complex_new2(CLASS_OF(self), real, imag);
+    }
+    if (k_numeric_p(other) && f_real_p(other)) {
+	get_dat1(self);
+
+	return f_complex_new2(CLASS_OF(self),
+			      f_add(dat->real, other), dat->imag);
+    }
+    return rb_num_coerce_bin(self, other, '+');
+}
+
+static VALUE
+nucomp_sub(VALUE self, VALUE other)
+{
+    if (k_complex_p(other)) {
+	VALUE real, imag;
+
+	get_dat2(self, other);
+
+	real = f_sub(adat->real, bdat->real);
+	imag = f_sub(adat->imag, bdat->imag);
+
+	return f_complex_new2(CLASS_OF(self), real, imag);
+    }
+    if (k_numeric_p(other) && f_real_p(other)) {
+	get_dat1(self);
+
+	return f_complex_new2(CLASS_OF(self),
+			      f_sub(dat->real, other), dat->imag);
+    }
+    return rb_num_coerce_bin(self, other, '-');
+}
+
+static VALUE
+nucomp_mul(VALUE self, VALUE other)
+{
+    if (k_complex_p(other)) {
+	VALUE real, imag;
+
+	get_dat2(self, other);
+
+	real = f_sub(f_mul(adat->real, bdat->real),
+		     f_mul(adat->imag, bdat->imag));
+	imag = f_add(f_mul(adat->real, bdat->imag),
+		      f_mul(adat->imag, bdat->real));
+
+	return f_complex_new2(CLASS_OF(self), real, imag);
+    }
+    if (k_numeric_p(other) && f_real_p(other)) {
+	get_dat1(self);
+
+	return f_complex_new2(CLASS_OF(self),
+			      f_mul(dat->real, other),
+			      f_mul(dat->imag, other));
+    }
+    return rb_num_coerce_bin(self, other, '*');
+}
+
+#define f_div f_quo
+
+static VALUE
+nucomp_div(VALUE self, VALUE other)
+{
+    if (k_complex_p(other)) {
+	get_dat2(self, other);
+
+	if (TYPE(adat->real)  == T_FLOAT ||
+	    TYPE(adat->imag) == T_FLOAT ||
+	    TYPE(bdat->real)  == T_FLOAT ||
+	    TYPE(bdat->imag) == T_FLOAT) {
+	    VALUE magn = m_hypot(bdat->real, bdat->imag);
+	    VALUE tmp = f_complex_new_bang2(CLASS_OF(self),
+					    f_div(bdat->real, magn),
+					    f_div(bdat->imag, magn));
+	    return f_div(f_mul(self, f_conj(tmp)), magn);
+	}
+	return f_div(f_mul(self, f_conj(other)), f_abs2(other));
+    }
+    if (k_numeric_p(other) && f_real_p(other)) {
+	get_dat1(self);
+
+	return f_complex_new2(CLASS_OF(self),
+			      f_div(dat->real, other),
+			      f_div(dat->imag, other));
+    }
+    return rb_num_coerce_bin(self, other, '/');
+}
+
+#undef f_div
+#define nucomp_quo nucomp_div
+
+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->imag)), other);
+}
+
+static VALUE
+nucomp_expt(VALUE self, VALUE other)
+{
+    if (k_exact_p(other) && 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? */
+
+    if (k_complex_p(other)) {
+	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->imag;
+	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 f_complex_polar(CLASS_OF(self), nr, ntheta);
+    }
+    if (k_integer_p(other)) {
+	if (f_gt_p(other, ZERO)) {
+	    VALUE x, z, n;
+
+	    x = self;
+	    z = x;
+	    n = f_sub(other, ONE);
+
+	    while (f_nonzero_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->imag, dat->imag)),
+				       f_mul(f_mul(TWO, dat->real), dat->imag));
+		    n = RARRAY_PTR(a)[0];
+		}
+		z = f_mul(z, x);
+		n = f_sub(n, ONE);
+	    }
+	    return z;
+	}
+	return f_expt(f_div(f_to_r(ONE), self), f_negate(other));
+    }
+    if (k_numeric_p(other) && f_real_p(other)) {
+	VALUE a, r, theta;
+
+	a = f_polar(self);
+	r = RARRAY_PTR(a)[0];
+	theta = RARRAY_PTR(a)[1];
+	return f_complex_polar(CLASS_OF(self), f_expt(r, other),
+			      f_mul(theta, other));
+    }
+    return rb_num_coerce_bin(self, other, id_expt);
+}
+
+static VALUE
+nucomp_equal_p(VALUE self, VALUE other)
+{
+    if (k_complex_p(other)) {
+	get_dat2(self, other);
+
+	return f_boolcast(f_equal_p(adat->real, bdat->real) &&
+			  f_equal_p(adat->imag, bdat->imag));
+    }
+    if (k_numeric_p(other) && f_real_p(other)) {
+	get_dat1(self);
+
+	return f_boolcast(f_equal_p(dat->real, other) && f_zero_p(dat->imag));
+    }
+    return f_equal_p(other, self);
+}
+
+static VALUE
+nucomp_coerce(VALUE self, VALUE other)
+{
+    if (k_numeric_p(other) && f_real_p(other))
+	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_hypot(dat->real, dat->imag);
+}
+
+static VALUE
+nucomp_abs2(VALUE self)
+{
+    get_dat1(self);
+    return f_add(f_mul(dat->real, dat->real),
+		 f_mul(dat->imag, dat->imag));
+}
+
+static VALUE
+nucomp_arg(VALUE self)
+{
+    get_dat1(self);
+    return m_atan2_bang(dat->imag, dat->real);
+}
+
+static VALUE
+nucomp_rect(VALUE self)
+{
+    get_dat1(self);
+    return rb_assoc_new(dat->real, dat->imag);
+}
+
+static VALUE
+nucomp_polar(VALUE self)
+{
+    return rb_assoc_new(f_abs(self), f_arg(self));
+}
+
+static VALUE
+nucomp_conj(VALUE self)
+{
+    get_dat1(self);
+    return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
+}
+
+#if 0
+static VALUE
+nucomp_true(VALUE self)
+{
+    return Qtrue;
+}
+#endif
+
+static VALUE
+nucomp_false(VALUE self)
+{
+    return Qfalse;
+}
+
+#if 0
+static VALUE
+nucomp_exact_p(VALUE self)
+{
+    get_dat1(self);
+    return f_boolcast(f_exact_p(dat->real) && f_exact_p(dat->imag));
+}
+
+static VALUE
+nucomp_inexact_p(VALUE self)
+{
+    return f_boolcast(!nucomp_exact_p(self));
+}
+#endif
+
+extern VALUE rb_lcm(VALUE x, VALUE y);
+
+static VALUE
+nucomp_denominator(VALUE self)
+{
+    get_dat1(self);
+    return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
+}
+
+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->imag),
+				f_div(cd, f_denominator(dat->imag))));
+}
+
+static VALUE
+nucomp_hash(VALUE self)
+{
+    get_dat1(self);
+    return f_xor(f_hash(dat->real), f_hash(dat->imag));
+}
+
+static VALUE
+nucomp_eql_p(VALUE self, VALUE other)
+{
+    if (k_complex_p(other)) {
+	get_dat2(self, other);
+
+	return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
+			  (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
+			  f_equal_p(self, other));
+
+    }
+    return Qfalse;
+}
+
+#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_tpositive_p(VALUE x)
+{
+    return f_boolcast(!f_signbit(x));
+}
+
+static VALUE
+nucomp_to_s(VALUE self)
+{
+    VALUE s, impos;
+
+    get_dat1(self);
+
+    impos = f_tpositive_p(dat->imag);
+
+    s = f_to_s(dat->real);
+    rb_str_cat2(s, !impos ? "-" : "+");
+
+    rb_str_concat(s, f_to_s(f_abs(dat->imag)));
+    rb_str_cat2(s, "i");
+
+    return s;
+}
+
+static VALUE
+nucomp_inspect(VALUE self)
+{
+    VALUE s, impos;
+
+    get_dat1(self);
+
+    impos = f_tpositive_p(dat->imag);
+
+    s = rb_str_new2("(");
+    rb_str_concat(s, f_inspect(dat->real));
+    rb_str_cat2(s, !impos ? "-" : "+");
+
+    rb_str_concat(s, f_inspect(f_abs(dat->imag)));
+    rb_str_cat2(s, "i)");
+
+    return s;
+}
+
+static VALUE
+nucomp_marshal_dump(VALUE self)
+{
+    VALUE a;
+    get_dat1(self);
+
+    a = rb_assoc_new(dat->real, dat->imag);
+    rb_copy_generic_ivar(a, self);
+    return a;
+}
+
+static VALUE
+nucomp_marshal_load(VALUE self, VALUE a)
+{
+    get_dat1(self);
+    dat->real = RARRAY_PTR(a)[0];
+    dat->imag = RARRAY_PTR(a)[1];
+    rb_copy_generic_ivar(self, a);
+    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);
+}
+
+VALUE
+rb_complex_polar(VALUE x, VALUE y)
+{
+    return nucomp_s_polar(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_to_i(VALUE self)
+{
+    get_dat1(self);
+
+    if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) {
+	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_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) {
+	VALUE s = f_to_s(self);
+	rb_raise(rb_eRangeError, "can't convert %s into Float",
+		 StringValuePtr(s));
+    }
+    return f_to_f(dat->real);
+}
+
+static VALUE
+nucomp_to_r(VALUE self)
+{
+    get_dat1(self);
+
+    if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) {
+	VALUE s = f_to_s(self);
+	rb_raise(rb_eRangeError, "can't convert %s into Rational",
+		 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_pat0, comp_pat1, comp_pat2, a_slash, a_dot_and_an_e,
+    null_string, underscores_pat, an_underscore;
+
+#define WS "\\s*"
+#define DIGITS "(?:\\d(?:_\\d|\\d)*)"
+#define NUMERATOR "(?:" DIGITS "?\\.)?" DIGITS "(?:[eE][-+]?" DIGITS ")?"
+#define DENOMINATOR DIGITS
+#define NUMBER "[-+]?" NUMERATOR "(?:\\/" DENOMINATOR ")?"
+#define NUMBERNOS NUMERATOR "(?:\\/" DENOMINATOR ")?"
+#define PATTERN0 "\\A" WS "(" NUMBER ")@(" NUMBER ")" WS
+#define PATTERN1 "\\A" WS "([-+])?(" NUMBER ")?[iIjJ]" WS
+#define PATTERN2 "\\A" WS "(" NUMBER ")(([-+])(" NUMBERNOS ")?[iIjJ])?" WS
+
+static void
+make_patterns(void)
+{
+    static const char comp_pat0_source[] = PATTERN0;
+    static const char comp_pat1_source[] = PATTERN1;
+    static const char comp_pat2_source[] = PATTERN2;
+    static const char underscores_pat_source[] = "_+";
+
+    if (comp_pat0) return;
+
+    comp_pat0 = rb_reg_new(comp_pat0_source, sizeof comp_pat0_source - 1, 0);
+    rb_gc_register_mark_object(comp_pat0);
+
+    comp_pat1 = rb_reg_new(comp_pat1_source, sizeof comp_pat1_source - 1, 0);
+    rb_gc_register_mark_object(comp_pat1);
+
+    comp_pat2 = rb_reg_new(comp_pat2_source, sizeof comp_pat2_source - 1, 0);
+    rb_gc_register_mark_object(comp_pat2);
+
+    a_slash = rb_str_new2("/");
+    rb_gc_register_mark_object(a_slash);
+
+    a_dot_and_an_e = rb_str_new2(".eE");
+    rb_gc_register_mark_object(a_dot_and_an_e);
+
+    null_string = rb_str_new2("");
+    rb_gc_register_mark_object(null_string);
+
+    underscores_pat = rb_reg_new(underscores_pat_source,
+				 sizeof underscores_pat_source - 1, 0);
+    rb_gc_register_mark_object(underscores_pat);
+
+    an_underscore = rb_str_new2("_");
+    rb_gc_register_mark_object(an_underscore);
+}
+
+#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 = self;
+
+    if (RSTRING_LEN(s) == 0)
+	return rb_assoc_new(Qnil, self);
+
+    {
+	VALUE m, sr, si, re, r, i;
+	int po;
+
+	m = f_match(comp_pat0, s);
+	if (!NIL_P(m)) {
+	  sr = f_aref(m, INT2FIX(1));
+	  si = f_aref(m, INT2FIX(2));
+	  re = f_post_match(m);
+	  po = 1;
+	}
+	if (NIL_P(m)) {
+	    m = f_match(comp_pat1, s);
+	    if (!NIL_P(m)) {
+		sr = Qnil;
+		si = f_aref(m, INT2FIX(1));
+		if (NIL_P(si))
+		    si = rb_str_new2("");
+		{
+		    VALUE t;
+
+		    t = f_aref(m, INT2FIX(2));
+		    if (NIL_P(t))
+			t = rb_str_new2("1");
+		    rb_str_concat(si, t);
+		}
+		re = f_post_match(m);
+		po = 0;
+	    }
+	}
+	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));
+	    if (NIL_P(f_aref(m, INT2FIX(2))))
+		si = Qnil;
+	    else {
+		VALUE t;
+
+		si = f_aref(m, INT2FIX(3));
+		t = f_aref(m, INT2FIX(4));
+		if (NIL_P(t))
+		    t = rb_str_new2("1");
+		rb_str_concat(si, t);
+	    }
+	    re = f_post_match(m);
+	    po = 0;
+	}
+	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)) {
+	    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);
+	}
+	if (po)
+	    return rb_assoc_new(rb_complex_polar(r, i), re);
+	else
+	    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, a, backref;
+
+    backref = rb_backref_get();
+    rb_match_busy(backref);
+
+    s = f_gsub(self, underscores_pat, an_underscore);
+    a = string_to_c_internal(s);
+
+    rb_backref_set(backref);
+
+    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, backref;
+
+    rb_scan_args(argc, argv, "11", &a1, &a2);
+
+    backref = rb_backref_get();
+    rb_match_busy(backref);
+
+    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;
+    }
+
+    rb_backref_set(backref);
+
+    switch (TYPE(a1)) {
+      case T_COMPLEX:
+	{
+	    get_dat1(a1);
+
+	    if (k_exact_p(dat->imag) && f_zero_p(dat->imag))
+		a1 = dat->real;
+	}
+    }
+
+    switch (TYPE(a2)) {
+      case T_COMPLEX:
+	{
+	    get_dat1(a2);
+
+	    if (k_exact_p(dat->imag) && f_zero_p(dat->imag))
+		a2 = dat->real;
+	}
+    }
+
+    switch (TYPE(a1)) {
+      case T_COMPLEX:
+	if (argc == 1 || (k_exact_p(a2) && f_zero_p(a2)))
+	    return a1;
+    }
+
+    if (argc == 1) {
+	if (k_numeric_p(a1) && !f_real_p(a1))
+	    return a1;
+    }
+    else {
+	if ((k_numeric_p(a1) && k_numeric_p(a2)) &&
+	    (!f_real_p(a1) || !f_real_p(a2)))
+	    return f_add(a1,
+			 f_mul(a2,
+			       f_complex_new_bang2(rb_cComplex, ZERO, ONE)));
+    }
+
+    {
+	VALUE argv2[2];
+	argv2[0] = a1;
+	argv2[1] = a2;
+	return nucomp_s_new(argc, argv2, klass);
+    }
+}
+
+/* --- */
+
+static VALUE
+numeric_real(VALUE self)
+{
+    return self;
+}
+
+static VALUE
+numeric_imag(VALUE self)
+{
+    return INT2FIX(0);
+}
+
+static VALUE
+numeric_abs2(VALUE self)
+{
+    return f_mul(self, self);
+}
+
+#define id_PI rb_intern("PI")
+
+static VALUE
+numeric_arg(VALUE self)
+{
+    if (f_positive_p(self))
+	return INT2FIX(0);
+    return rb_const_get(rb_mMath, id_PI);
+}
+
+static VALUE
+numeric_rect(VALUE self)
+{
+    return rb_assoc_new(self, INT2FIX(0));
+}
+
+static VALUE
+numeric_polar(VALUE self)
+{
+    return rb_assoc_new(f_abs(self), f_arg(self));
+}
+
+static VALUE
+numeric_conj(VALUE self)
+{
+    return self;
+}
+
+void
+#ifndef EXT_MATHN
+Init_Complex(void)
+#else
+Init_complex(void)
+#endif    
+{
+#undef rb_intern
+#define rb_intern(str) rb_intern_const(str)
+
+    assert(fprintf(stderr, "assert() is now active\n"));
+
+    id_abs = rb_intern("abs");
+    id_abs2 = rb_intern("abs2");
+    id_arg = rb_intern("arg");
+    id_cmp = rb_intern("<=>");
+    id_conj = rb_intern("conj");
+    id_convert = rb_intern("convert");
+    id_denominator = rb_intern("denominator");
+    id_divmod = rb_intern("divmod");
+    id_equal_p = rb_intern("==");
+    id_expt = rb_intern("**");
+    id_floor = rb_intern("floor");
+    id_hash = rb_intern("hash");
+    id_idiv = rb_intern("div");
+    id_inspect = rb_intern("inspect");
+    id_negate = rb_intern("-@");
+    id_numerator = rb_intern("numerator");
+    id_polar = rb_intern("polar");
+    id_quo = rb_intern("quo");
+    id_real_p = rb_intern("real?");
+    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");
+
+    rb_cComplex = rb_define_class(COMPLEX_NAME, rb_cNumeric);
+
+    rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
+    rb_undef_method(CLASS_OF(rb_cComplex), "allocate");
+
+#if 0
+    rb_define_private_method(CLASS_OF(rb_cComplex), "new!", nucomp_s_new_bang, -1);
+    rb_define_private_method(CLASS_OF(rb_cComplex), "new", nucomp_s_new, -1);
+#else
+    rb_undef_method(CLASS_OF(rb_cComplex), "new");
+#endif
+
+    rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1);
+    rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1);
+    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, "imaginary", nucomp_imag, 0);
+    rb_define_method(rb_cComplex, "imag", nucomp_imag, 0);
+
+    rb_define_method(rb_cComplex, "-@", nucomp_negate, 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_quo, 1);
+    rb_define_method(rb_cComplex, "fdiv", nucomp_fdiv, 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);
+    rb_define_method(rb_cComplex, "magnitude", nucomp_abs, 0);
+    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, "phase", nucomp_arg, 0);
+    rb_define_method(rb_cComplex, "rectangular", nucomp_rect, 0);
+    rb_define_method(rb_cComplex, "rect", nucomp_rect, 0);
+    rb_define_method(rb_cComplex, "polar", nucomp_polar, 0);
+    rb_define_method(rb_cComplex, "conjugate", nucomp_conj, 0);
+    rb_define_method(rb_cComplex, "conj", nucomp_conj, 0);
+#if 0
+    rb_define_method(rb_cComplex, "~", nucomp_conj, 0); /* gcc */
+#endif
+
+    rb_define_method(rb_cComplex, "real?", nucomp_false, 0);
+#if 0
+    rb_define_method(rb_cComplex, "complex?", nucomp_true, 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, "eql?", nucomp_eql_p, 1);
+
+    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, "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_private_method(CLASS_OF(rb_cComplex), "convert", nucomp_s_convert, -1);
+
+    /* --- */
+
+    rb_define_method(rb_cNumeric, "real", numeric_real, 0);
+    rb_define_method(rb_cNumeric, "imaginary", numeric_imag, 0);
+    rb_define_method(rb_cNumeric, "imag", numeric_imag, 0);
+    rb_define_method(rb_cNumeric, "abs2", numeric_abs2, 0);
+    rb_define_method(rb_cNumeric, "arg", numeric_arg, 0);
+    rb_define_method(rb_cNumeric, "angle", numeric_arg, 0);
+    rb_define_method(rb_cNumeric, "phase", numeric_arg, 0);
+    rb_define_method(rb_cNumeric, "rectangular", numeric_rect, 0);
+    rb_define_method(rb_cNumeric, "rect", numeric_rect, 0);
+    rb_define_method(rb_cNumeric, "polar", numeric_polar, 0);
+    rb_define_method(rb_cNumeric, "conjugate", numeric_conj, 0);
+    rb_define_method(rb_cNumeric, "conj", numeric_conj, 0);
+
+#ifndef EXT_MATHN    
+    rb_define_const(rb_cComplex, "I",
+		    f_complex_new_bang2(rb_cComplex, ZERO, ONE));
+#endif    
+}
+
+/*
+Local variables:
+c-file-style: "ruby"
+End:
+*/
diff --git a/ext/mathn/complex/extconf.rb b/ext/mathn/complex/extconf.rb
new file mode 100644
index 0000000000..32f181f997
--- /dev/null
+++ b/ext/mathn/complex/extconf.rb
@@ -0,0 +1,5 @@
+require "mkmf"
+
+$CPPFLAGS = "-DEXT_MATHN -DCANON -DCLCANON "
+
+create_makefile "mathn/complex"