#include "ruby/config.h"
#if defined _MSC_VER
# define _USE_MATH_DEFINES 1
#endif
#include <math.h>
#include "internal.h"
#include "id.h"
#define NDEBUG
#include "ruby_assert.h"
#define ZERO INT2FIX(0)
#define ONE INT2FIX(1)
#define TWO INT2FIX(2)
#if USE_FLONUM
#define RFLOAT_0 DBL2NUM(0)
#else
static VALUE RFLOAT_0;
#endif
#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \
!defined(signbit)
extern int signbit(double);
#endif
VALUE rb_cComplex;
static ID id_abs, id_arg,
id_denominator, id_fdiv, id_numerator, id_quo,
id_real_p, id_i_real, id_i_imag,
id_finite_p, id_infinite_p, id_rationalize,
id_PI;
#define id_to_i idTo_i
#define id_to_r idTo_r
#define id_negate idUMinus
#define id_expt idPow
#define id_to_f idTo_f
#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 PRESERVE_SIGNEDZERO
inline static VALUE
f_add(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(x) &&
LIKELY(rb_method_basic_definition_p(rb_cInteger, idPLUS))) {
if (FIXNUM_ZERO_P(x))
return y;
if (FIXNUM_ZERO_P(y))
return x;
return rb_int_plus(x, y);
}
else if (RB_FLOAT_TYPE_P(x) &&
LIKELY(rb_method_basic_definition_p(rb_cFloat, idPLUS))) {
if (FIXNUM_ZERO_P(y))
return x;
return rb_float_plus(x, y);
}
else if (RB_TYPE_P(x, T_RATIONAL) &&
LIKELY(rb_method_basic_definition_p(rb_cRational, idPLUS))) {
if (FIXNUM_ZERO_P(y))
return x;
return rb_rational_plus(x, y);
}
return rb_funcall(x, '+', 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 int
f_gt_p(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(x)) {
if (FIXNUM_P(x) && FIXNUM_P(y))
return (SIGNED_VALUE)x > (SIGNED_VALUE)y;
return RTEST(rb_int_gt(x, y));
}
else if (RB_FLOAT_TYPE_P(x))
return RTEST(rb_float_gt(x, y));
else if (RB_TYPE_P(x, T_RATIONAL)) {
int const cmp = rb_cmpint(rb_rational_cmp(x, y), x, y);
return cmp > 0;
}
return RTEST(rb_funcall(x, '>', 1, y));
}
inline static VALUE
f_mul(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(x) &&
LIKELY(rb_method_basic_definition_p(rb_cInteger, idMULT))) {
if (FIXNUM_ZERO_P(y))
return ZERO;
if (FIXNUM_ZERO_P(x) && RB_INTEGER_TYPE_P(y))
return ZERO;
if (x == ONE) return y;
if (y == ONE) return x;
return rb_int_mul(x, y);
}
else if (RB_FLOAT_TYPE_P(x) &&
LIKELY(rb_method_basic_definition_p(rb_cFloat, idMULT))) {
if (y == ONE) return x;
return rb_float_mul(x, y);
}
else if (RB_TYPE_P(x, T_RATIONAL) &&
LIKELY(rb_method_basic_definition_p(rb_cRational, idMULT))) {
if (y == ONE) return x;
return rb_rational_mul(x, y);
}
else if (LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMULT))) {
if (y == ONE) return x;
}
return rb_funcall(x, '*', 1, y);
}
inline static VALUE
f_sub(VALUE x, VALUE y)
{
if (FIXNUM_ZERO_P(y) &&
LIKELY(rb_method_basic_definition_p(CLASS_OF(x), idMINUS))) {
return x;
}
return rb_funcall(x, '-', 1, y);
}
fun1(abs)
fun1(arg)
fun1(denominator)
inline static VALUE
f_negate(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return rb_int_uminus(x);
}
else if (RB_FLOAT_TYPE_P(x)) {
return rb_float_uminus(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return rb_rational_uminus(x);
}
else if (RB_TYPE_P(x, T_COMPLEX)) {
return rb_complex_uminus(x);
}
return rb_funcall(x, id_negate, 0);
}
fun1(numerator)
fun1(real_p)
inline static VALUE
f_to_i(VALUE x)
{
if (RB_TYPE_P(x, T_STRING))
return rb_str_to_inum(x, 10, 0);
return rb_funcall(x, id_to_i, 0);
}
inline static VALUE
f_to_f(VALUE x)
{
if (RB_TYPE_P(x, T_STRING))
return DBL2NUM(rb_str_to_dbl(x, 0));
return rb_funcall(x, id_to_f, 0);
}
fun1(to_r)
inline static int
f_eqeq_p(VALUE x, VALUE y)
{
if (FIXNUM_P(x) && FIXNUM_P(y))
return x == y;
else if (RB_FLOAT_TYPE_P(x) || RB_FLOAT_TYPE_P(y))
return NUM2DBL(x) == NUM2DBL(y);
return (int)rb_equal(x, y);
}
fun2(expt)
fun2(fdiv)
fun2(quo)
inline static int
f_negative_p(VALUE x)
{
if (RB_INTEGER_TYPE_P(x))
return INT_NEGATIVE_P(x);
else if (RB_FLOAT_TYPE_P(x))
return RFLOAT_VALUE(x) < 0.0;
else if (RB_TYPE_P(x, T_RATIONAL))
return INT_NEGATIVE_P(RRATIONAL(x)->num);
return rb_num_negative_p(x);
}
#define f_positive_p(x) (!f_negative_p(x))
inline static int
f_zero_p(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return FIXNUM_ZERO_P(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
const VALUE num = RRATIONAL(x)->num;
return FIXNUM_ZERO_P(num);
}
return (int)rb_equal(x, ZERO);
}
#define f_nonzero_p(x) (!f_zero_p(x))
VALUE rb_flo_is_finite_p(VALUE num);
inline static int
f_finite_p(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return TRUE;
}
else if (RB_FLOAT_TYPE_P(x)) {
return (int)rb_flo_is_finite_p(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return TRUE;
}
return RTEST(rb_funcallv(x, id_finite_p, 0, 0));
}
VALUE rb_flo_is_infinite_p(VALUE num);
inline static VALUE
f_infinite_p(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return Qnil;
}
else if (RB_FLOAT_TYPE_P(x)) {
return rb_flo_is_infinite_p(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return Qnil;
}
return rb_funcallv(x, id_infinite_p, 0, 0);
}
inline static int
f_kind_of_p(VALUE x, VALUE c)
{
return (int)rb_obj_is_kind_of(x, c);
}
inline static int
k_numeric_p(VALUE x)
{
return f_kind_of_p(x, rb_cNumeric);
}
#define k_exact_p(x) (!RB_FLOAT_TYPE_P(x))
#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x))
#define get_dat1(x) \
struct RComplex *dat = RCOMPLEX(x)
#define get_dat2(x,y) \
struct RComplex *adat = RCOMPLEX(x), *bdat = RCOMPLEX(y)
inline static VALUE
nucomp_s_new_internal(VALUE klass, VALUE real, VALUE imag)
{
NEWOBJ_OF(obj, struct RComplex, klass, T_COMPLEX | (RGENGC_WB_PROTECTED_COMPLEX ? FL_WB_PROTECTED : 0));
RCOMPLEX_SET_REAL(obj, real);
RCOMPLEX_SET_IMAG(obj, imag);
OBJ_FREEZE_RAW(obj);
return (VALUE)obj;
}
static VALUE
nucomp_s_alloc(VALUE klass)
{
return nucomp_s_new_internal(klass, ZERO, ZERO);
}
inline static VALUE
f_complex_new_bang1(VALUE klass, VALUE x)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
return nucomp_s_new_internal(klass, x, ZERO);
}
inline static VALUE
f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
assert(!RB_TYPE_P(y, T_COMPLEX));
return nucomp_s_new_internal(klass, x, y);
}
#ifdef CANONICALIZATION_FOR_MATHN
static int canonicalization = 0;
RUBY_FUNC_EXPORTED void
nucomp_canonicalization(int f)
{
canonicalization = f;
}
#else
#define canonicalization 0
#endif
inline static void
nucomp_real_check(VALUE num)
{
if (!RB_INTEGER_TYPE_P(num) &&
!RB_FLOAT_TYPE_P(num) &&
!RB_TYPE_P(num, T_RATIONAL)) {
if (!k_numeric_p(num) || !f_real_p(num))
rb_raise(rb_eTypeError, "not a real");
}
}
inline static VALUE
nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
{
int complex_r, complex_i;
#ifdef CANONICALIZATION_FOR_MATHN
if (k_exact_zero_p(imag) && canonicalization)
return real;
#endif
complex_r = RB_TYPE_P(real, T_COMPLEX);
complex_i = RB_TYPE_P(imag, T_COMPLEX);
if (!complex_r && !complex_i) {
return nucomp_s_new_internal(klass, real, imag);
}
else if (!complex_r) {
get_dat1(imag);
return nucomp_s_new_internal(klass,
f_sub(real, dat->imag),
f_add(ZERO, dat->real));
}
else if (!complex_i) {
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_new2(VALUE klass, VALUE x, VALUE y)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
return nucomp_s_canonicalize_internal(klass, x, y);
}
static VALUE nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise);
static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass);
static VALUE
nucomp_f_complex(int argc, VALUE *argv, VALUE klass)
{
VALUE a1, a2, opts = Qnil;
int raise = TRUE;
if (rb_scan_args(argc, argv, "11:", &a1, &a2, &opts) == 1) {
a2 = Qundef;
}
if (!NIL_P(opts)) {
static ID kwds[1];
VALUE exception;
if (!kwds[0]) {
kwds[0] = idException;
}
rb_get_kwargs(opts, kwds, 0, 1, &exception);
raise = (exception != Qfalse);
}
return nucomp_convert(rb_cComplex, a1, a2, raise);
}
#define imp1(n) \
inline static VALUE \
m_##n##_bang(VALUE x)\
{\
return rb_math_##n(x);\
}
imp1(cos)
imp1(cosh)
imp1(exp)
static VALUE
m_log_bang(VALUE x)
{
return rb_math_log(1, &x);
}
imp1(sin)
imp1(sinh)
static VALUE
m_cos(VALUE x)
{
if (!RB_TYPE_P(x, T_COMPLEX))
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 (!RB_TYPE_P(x, T_COMPLEX))
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)));
}
}
static VALUE
f_complex_polar(VALUE klass, VALUE x, VALUE y)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
assert(!RB_TYPE_P(y, T_COMPLEX));
if (f_zero_p(x) || f_zero_p(y)) {
if (canonicalization) return x;
return nucomp_s_new_internal(klass, x, RFLOAT_0);
}
if (RB_FLOAT_TYPE_P(y)) {
const double arg = RFLOAT_VALUE(y);
if (arg == M_PI) {
x = f_negate(x);
if (canonicalization) return x;
y = RFLOAT_0;
}
else if (arg == M_PI_2) {
y = x;
x = RFLOAT_0;
}
else if (arg == M_PI_2+M_PI) {
y = f_negate(x);
x = RFLOAT_0;
}
else if (RB_FLOAT_TYPE_P(x)) {
const double abs = RFLOAT_VALUE(x);
const double real = abs * cos(arg), imag = abs * sin(arg);
x = DBL2NUM(real);
if (canonicalization && imag == 0.0) return x;
y = DBL2NUM(imag);
}
else {
y = f_mul(x, DBL2NUM(sin(arg)));
x = f_mul(x, DBL2NUM(cos(arg)));
if (canonicalization && f_zero_p(y)) return x;
}
return nucomp_s_new_internal(klass, x, y);
}
return nucomp_s_canonicalize_internal(klass,
f_mul(x, m_cos(y)),
f_mul(x, m_sin(y)));
}
VALUE
rb_dbl_complex_new_polar_pi(double abs, double ang)
{
double fi;
const double fr = modf(ang, &fi);
int pos = fr == +0.5;
if (pos || fr == -0.5) {
if ((modf(fi / 2.0, &fi) != fr) ^ pos) abs = -abs;
return rb_complex_new(RFLOAT_0, DBL2NUM(abs));
}
else if (fr == 0.0) {
if (modf(fi / 2.0, &fi) != 0.0) abs = -abs;
return DBL2NUM(abs);
}
else {
ang *= M_PI;
return rb_complex_new(DBL2NUM(abs * cos(ang)), DBL2NUM(abs * sin(ang)));
}
}
static VALUE
nucomp_s_polar(int argc, VALUE *argv, VALUE klass)
{
VALUE abs, arg;
switch (rb_scan_args(argc, argv, "11", &abs, &arg)) {
case 1:
nucomp_real_check(abs);
if (canonicalization) return abs;
return nucomp_s_new_internal(klass, abs, ZERO);
default:
nucomp_real_check(abs);
nucomp_real_check(arg);
break;
}
return f_complex_polar(klass, abs, arg);
}
VALUE
rb_complex_real(VALUE self)
{
get_dat1(self);
return dat->real;
}
VALUE
rb_complex_imag(VALUE self)
{
get_dat1(self);
return dat->imag;
}
VALUE
rb_complex_uminus(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_negate(dat->real), f_negate(dat->imag));
}
VALUE
rb_complex_plus(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
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, '+');
}
VALUE
rb_complex_minus(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
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
safe_mul(VALUE a, VALUE b, int az, int bz)
{
double v;
if (!az && bz && RB_FLOAT_TYPE_P(a) && (v = RFLOAT_VALUE(a), !isnan(v))) {
a = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
}
if (!bz && az && RB_FLOAT_TYPE_P(b) && (v = RFLOAT_VALUE(b), !isnan(v))) {
b = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
}
return f_mul(a, b);
}
static void
comp_mul(VALUE areal, VALUE aimag, VALUE breal, VALUE bimag, VALUE *real, VALUE *imag)
{
int arzero = f_zero_p(areal);
int aizero = f_zero_p(aimag);
int brzero = f_zero_p(breal);
int bizero = f_zero_p(bimag);
*real = f_sub(safe_mul(areal, breal, arzero, brzero),
safe_mul(aimag, bimag, aizero, bizero));
*imag = f_add(safe_mul(areal, bimag, arzero, bizero),
safe_mul(aimag, breal, aizero, brzero));
}
VALUE
rb_complex_mul(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
VALUE real, imag;
get_dat2(self, other);
comp_mul(adat->real, adat->imag, bdat->real, bdat->imag, &real, &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_mul(dat->real, other),
f_mul(dat->imag, other));
}
return rb_num_coerce_bin(self, other, '*');
}
inline static VALUE
f_divide(VALUE self, VALUE other,
VALUE (*func)(VALUE, VALUE), ID id)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
VALUE r, n, x, y;
int flo;
get_dat2(self, other);
flo = (RB_FLOAT_TYPE_P(adat->real) || RB_FLOAT_TYPE_P(adat->imag) ||
RB_FLOAT_TYPE_P(bdat->real) || RB_FLOAT_TYPE_P(bdat->imag));
if (f_gt_p(f_abs(bdat->real), f_abs(bdat->imag))) {
r = (*func)(bdat->imag, bdat->real);
n = f_mul(bdat->real, f_add(ONE, f_mul(r, r)));
if (flo)
return f_complex_new2(CLASS_OF(self),
(*func)(self, n),
(*func)(f_negate(f_mul(self, r)), n));
x = (*func)(f_add(adat->real, f_mul(adat->imag, r)), n);
y = (*func)(f_sub(adat->imag, f_mul(adat->real, r)), n);
}
else {
r = (*func)(bdat->real, bdat->imag);
n = f_mul(bdat->imag, f_add(ONE, f_mul(r, r)));
if (flo)
return f_complex_new2(CLASS_OF(self),
(*func)(f_mul(self, r), n),
(*func)(f_negate(self), n));
x = (*func)(f_add(f_mul(adat->real, r), adat->imag), n);
y = (*func)(f_sub(f_mul(adat->imag, r), adat->real), n);
}
x = rb_rational_canonicalize(x);
y = rb_rational_canonicalize(y);
return f_complex_new2(CLASS_OF(self), x, y);
}
if (k_numeric_p(other) && f_real_p(other)) {
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
(*func)(dat->real, other),
(*func)(dat->imag, other));
}
return rb_num_coerce_bin(self, other, id);
}
#define rb_raise_zerodiv() rb_raise(rb_eZeroDivError, "divided by 0")
VALUE
rb_complex_div(VALUE self, VALUE other)
{
return f_divide(self, other, f_quo, id_quo);
}
#define nucomp_quo rb_complex_div
static VALUE
nucomp_fdiv(VALUE self, VALUE other)
{
return f_divide(self, other, f_fdiv, id_fdiv);
}
inline static VALUE
f_reciprocal(VALUE x)
{
return f_quo(ONE, x);
}
VALUE
rb_complex_pow(VALUE self, VALUE other)
{
if (k_numeric_p(other) && k_exact_zero_p(other))
return f_complex_new_bang1(CLASS_OF(self), ONE);
if (RB_TYPE_P(other, T_RATIONAL) && RRATIONAL(other)->den == LONG2FIX(1))
other = RRATIONAL(other)->num;
if (RB_TYPE_P(other, T_COMPLEX)) {
get_dat1(other);
if (k_exact_zero_p(dat->imag))
other = dat->real;
}
if (RB_TYPE_P(other, T_COMPLEX)) {
VALUE r, theta, nr, ntheta;
get_dat1(other);
r = f_abs(self);
theta = f_arg(self);
nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)),
f_mul(dat->imag, theta)));
ntheta = f_add(f_mul(theta, dat->real),
f_mul(dat->imag, m_log_bang(r)));
return f_complex_polar(CLASS_OF(self), nr, ntheta);
}
if (FIXNUM_P(other)) {
long n = FIX2LONG(other);
if (n == 0) {
return nucomp_s_new_internal(CLASS_OF(self), ONE, ZERO);
}
if (n < 0) {
self = f_reciprocal(self);
other = rb_int_uminus(other);
n = -n;
}
{
get_dat1(self);
VALUE xr = dat->real, xi = dat->imag, zr = xr, zi = xi;
if (f_zero_p(xi)) {
zr = rb_num_pow(zr, other);
}
else if (f_zero_p(xr)) {
zi = rb_num_pow(zi, other);
if (n & 2) zi = f_negate(zi);
if (!(n & 1)) {
VALUE tmp = zr;
zr = zi;
zi = tmp;
}
}
else {
while (--n) {
long q, r;
for (; q = n / 2, r = n % 2, r == 0; n = q) {
VALUE tmp = f_sub(f_mul(xr, xr), f_mul(xi, xi));
xi = f_mul(f_mul(TWO, xr), xi);
xr = tmp;
}
comp_mul(zr, zi, xr, xi, &zr, &zi);
}
}
return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
}
}
if (k_numeric_p(other) && f_real_p(other)) {
VALUE r, theta;
if (RB_TYPE_P(other, T_BIGNUM))
rb_warn("in a**b, b may be too big");
r = f_abs(self);
theta = f_arg(self);
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_eqeq_p(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
get_dat2(self, other);
return f_boolcast(f_eqeq_p(adat->real, bdat->real) &&
f_eqeq_p(adat->imag, bdat->imag));
}
if (k_numeric_p(other) && f_real_p(other)) {
get_dat1(self);
return f_boolcast(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
}
return f_boolcast(f_eqeq_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);
if (RB_TYPE_P(other, T_COMPLEX))
return rb_assoc_new(other, self);
rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
rb_obj_class(other), rb_obj_class(self));
return Qnil;
}
VALUE
rb_complex_abs(VALUE self)
{
get_dat1(self);
if (f_zero_p(dat->real)) {
VALUE a = f_abs(dat->imag);
if (RB_FLOAT_TYPE_P(dat->real) && !RB_FLOAT_TYPE_P(dat->imag))
a = f_to_f(a);
return a;
}
if (f_zero_p(dat->imag)) {
VALUE a = f_abs(dat->real);
if (!RB_FLOAT_TYPE_P(dat->real) && RB_FLOAT_TYPE_P(dat->imag))
a = f_to_f(a);
return a;
}
return rb_math_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));
}
VALUE
rb_complex_arg(VALUE self)
{
get_dat1(self);
return rb_math_atan2(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));
}
VALUE
rb_complex_conjugate(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}
static VALUE
nucomp_false(VALUE self)
{
return Qfalse;
}
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)
{
st_index_t v, h[2];
VALUE n;
get_dat1(self);
n = rb_hash(dat->real);
h[0] = NUM2LONG(n);
n = rb_hash(dat->imag);
h[1] = NUM2LONG(n);
v = rb_memhash(h, sizeof(h));
return ST2FIX(v);
}
static VALUE
nucomp_eql_p(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
get_dat2(self, other);
return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
(CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
f_eqeq_p(self, other));
}
return Qfalse;
}
inline static int
f_signbit(VALUE x)
{
if (RB_FLOAT_TYPE_P(x)) {
double f = RFLOAT_VALUE(x);
return !isnan(f) && signbit(f);
}
return f_negative_p(x);
}
inline static int
f_tpositive_p(VALUE x)
{
return !f_signbit(x);
}
static VALUE
f_format(VALUE self, VALUE (*func)(VALUE))
{
VALUE s;
int impos;
get_dat1(self);
impos = f_tpositive_p(dat->imag);
s = (*func)(dat->real);
rb_str_cat2(s, !impos ? "-" : "+");
rb_str_concat(s, (*func)(f_abs(dat->imag)));
if (!rb_isdigit(RSTRING_PTR(s)[RSTRING_LEN(s) - 1]))
rb_str_cat2(s, "*");
rb_str_cat2(s, "i");
return s;
}
static VALUE
nucomp_to_s(VALUE self)
{
return f_format(self, rb_String);
}
static VALUE
nucomp_inspect(VALUE self)
{
VALUE s;
s = rb_usascii_str_new2("(");
rb_str_concat(s, f_format(self, rb_inspect));
rb_str_cat2(s, ")");
return s;
}
#define FINITE_TYPE_P(v) (RB_INTEGER_TYPE_P(v) || RB_TYPE_P(v, T_RATIONAL))
static VALUE
rb_complex_finite_p(VALUE self)
{
get_dat1(self);
if (f_finite_p(dat->real) && f_finite_p(dat->imag)) {
return Qtrue;
}
return Qfalse;
}
static VALUE
rb_complex_infinite_p(VALUE self)
{
get_dat1(self);
if (NIL_P(f_infinite_p(dat->real)) && NIL_P(f_infinite_p(dat->imag))) {
return Qnil;
}
return ONE;
}
static VALUE
nucomp_dumper(VALUE self)
{
return self;
}
static VALUE
nucomp_loader(VALUE self, VALUE a)
{
get_dat1(self);
RCOMPLEX_SET_REAL(dat, rb_ivar_get(a, id_i_real));
RCOMPLEX_SET_IMAG(dat, rb_ivar_get(a, id_i_imag));
OBJ_FREEZE_RAW(self);
return self;
}
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)
{
Check_Type(a, T_ARRAY);
if (RARRAY_LEN(a) != 2)
rb_raise(rb_eArgError, "marshaled complex must have an array whose length is 2 but %ld", RARRAY_LEN(a));
rb_ivar_set(self, id_i_real, RARRAY_AREF(a, 0));
rb_ivar_set(self, id_i_imag, RARRAY_AREF(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);
}
VALUE
rb_complex_new_polar(VALUE x, VALUE y)
{
return f_complex_polar(rb_cComplex, x, y);
}
VALUE
rb_complex_polar(VALUE x, VALUE y)
{
return rb_complex_new_polar(x, y);
}
VALUE
rb_Complex(VALUE x, VALUE y)
{
VALUE a[2];
a[0] = x;
a[1] = y;
return nucomp_s_convert(2, a, rb_cComplex);
}
VALUE
rb_dbl_complex_new(double real, double imag)
{
return rb_complex_raw(DBL2NUM(real), DBL2NUM(imag));
}
static VALUE
nucomp_to_i(VALUE self)
{
get_dat1(self);
if (!k_exact_zero_p(dat->imag)) {
rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer",
self);
}
return f_to_i(dat->real);
}
static VALUE
nucomp_to_f(VALUE self)
{
get_dat1(self);
if (!k_exact_zero_p(dat->imag)) {
rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float",
self);
}
return f_to_f(dat->real);
}
static VALUE
nucomp_to_r(VALUE self)
{
get_dat1(self);
if (!k_exact_zero_p(dat->imag)) {
rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
self);
}
return f_to_r(dat->real);
}
static VALUE
nucomp_rationalize(int argc, VALUE *argv, VALUE self)
{
get_dat1(self);
rb_check_arity(argc, 0, 1);
if (!k_exact_zero_p(dat->imag)) {
rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
self);
}
return rb_funcallv(dat->real, id_rationalize, argc, argv);
}
static VALUE
nucomp_to_c(VALUE self)
{
return self;
}
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);
}
#include <ctype.h>
inline static int
issign(int c)
{
return (c == '-' || c == '+');
}
static int
read_sign(const char **s,
char **b)
{
int sign = '?';
if (issign(**s)) {
sign = **b = **s;
(*s)++;
(*b)++;
}
return sign;
}
inline static int
isdecimal(int c)
{
return isdigit((unsigned char)c);
}
static int
read_digits(const char **s, int strict,
char **b)
{
int us = 1;
if (!isdecimal(**s))
return 0;
while (isdecimal(**s) || **s == '_') {
if (**s == '_') {
if (strict) {
if (us)
return 0;
}
us = 1;
}
else {
**b = **s;
(*b)++;
us = 0;
}
(*s)++;
}
if (us)
do {
(*s)--;
} while (**s == '_');
return 1;
}
inline static int
islettere(int c)
{
return (c == 'e' || c == 'E');
}
static int
read_num(const char **s, int strict,
char **b)
{
if (**s != '.') {
if (!read_digits(s, strict, b))
return 0;
}
if (**s == '.') {
**b = **s;
(*s)++;
(*b)++;
if (!read_digits(s, strict, b)) {
(*b)--;
return 0;
}
}
if (islettere(**s)) {
**b = **s;
(*s)++;
(*b)++;
read_sign(s, b);
if (!read_digits(s, strict, b)) {
(*b)--;
return 0;
}
}
return 1;
}
inline static int
read_den(const char **s, int strict,
char **b)
{
if (!read_digits(s, strict, b))
return 0;
return 1;
}
static int
read_rat_nos(const char **s, int strict,
char **b)
{
if (!read_num(s, strict, b))
return 0;
if (**s == '/') {
**b = **s;
(*s)++;
(*b)++;
if (!read_den(s, strict, b)) {
(*b)--;
return 0;
}
}
return 1;
}
static int
read_rat(const char **s, int strict,
char **b)
{
read_sign(s, b);
if (!read_rat_nos(s, strict, b))
return 0;
return 1;
}
inline static int
isimagunit(int c)
{
return (c == 'i' || c == 'I' ||
c == 'j' || c == 'J');
}
static VALUE
str2num(char *s)
{
if (strchr(s, '/'))
return rb_cstr_to_rat(s, 0);
if (strpbrk(s, ".eE"))
return DBL2NUM(rb_cstr_to_dbl(s, 0));
return rb_cstr_to_inum(s, 10, 0);
}
static int
read_comp(const char **s, int strict,
VALUE *ret, char **b)
{
char *bb;
int sign;
VALUE num, num2;
bb = *b;
sign = read_sign(s, b);
if (isimagunit(**s)) {
(*s)++;
num = INT2FIX((sign == '-') ? -1 : + 1);
*ret = rb_complex_new2(ZERO, num);
return 1;
}
if (!read_rat_nos(s, strict, b)) {
**b = '\0';
num = str2num(bb);
*ret = rb_complex_new2(num, ZERO);
return 0;
}
**b = '\0';
num = str2num(bb);
if (isimagunit(**s)) {
(*s)++;
*ret = rb_complex_new2(ZERO, num);
return 1;
}
if (**s == '@') {
int st;
(*s)++;
bb = *b;
st = read_rat(s, strict, b);
**b = '\0';
if (strlen(bb) < 1 ||
!isdecimal(*(bb + strlen(bb) - 1))) {
*ret = rb_complex_new2(num, ZERO);
return 0;
}
num2 = str2num(bb);
*ret = rb_complex_new_polar(num, num2);
if (!st)
return 0;
else
return 1;
}
if (issign(**s)) {
bb = *b;
sign = read_sign(s, b);
if (isimagunit(**s))
num2 = INT2FIX((sign == '-') ? -1 : + 1);
else {
if (!read_rat_nos(s, strict, b)) {
*ret = rb_complex_new2(num, ZERO);
return 0;
}
**b = '\0';
num2 = str2num(bb);
}
if (!isimagunit(**s)) {
*ret = rb_complex_new2(num, ZERO);
return 0;
}
(*s)++;
*ret = rb_complex_new2(num, num2);
return 1;
}
{
*ret = rb_complex_new2(num, ZERO);
return 1;
}
}
inline static void
skip_ws(const char **s)
{
while (isspace((unsigned char)**s))
(*s)++;
}
static int
parse_comp(const char *s, int strict, VALUE *num)
{
char *buf, *b;
VALUE tmp;
int ret = 1;
buf = ALLOCV_N(char, tmp, strlen(s) + 1);
b = buf;
skip_ws(&s);
if (!read_comp(&s, strict, num, &b)) {
ret = 0;
}
else {
skip_ws(&s);
if (strict)
if (*s != '\0')
ret = 0;
}
ALLOCV_END(tmp);
return ret;
}
static VALUE
string_to_c_strict(VALUE self, int raise)
{
char *s;
VALUE num;
rb_must_asciicompat(self);
s = RSTRING_PTR(self);
if (!s || memchr(s, '\0', RSTRING_LEN(self))) {
if (!raise) return Qnil;
rb_raise(rb_eArgError, "string contains null byte");
}
if (s && s[RSTRING_LEN(self)]) {
rb_str_modify(self);
s = RSTRING_PTR(self);
s[RSTRING_LEN(self)] = '\0';
}
if (!s)
s = (char *)"";
if (!parse_comp(s, 1, &num)) {
if (!raise) return Qnil;
rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE,
self);
}
return num;
}
static VALUE
string_to_c(VALUE self)
{
char *s;
VALUE num;
rb_must_asciicompat(self);
s = RSTRING_PTR(self);
if (s && s[RSTRING_LEN(self)]) {
rb_str_modify(self);
s = RSTRING_PTR(self);
s[RSTRING_LEN(self)] = '\0';
}
if (!s)
s = (char *)"";
(void)parse_comp(s, 0, &num);
return num;
}
static VALUE
to_complex(VALUE val)
{
return rb_convert_type(val, T_COMPLEX, "Complex", "to_c");
}
static VALUE
nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise)
{
if (NIL_P(a1) || NIL_P(a2)) {
if (!raise) return Qnil;
rb_raise(rb_eTypeError, "can't convert nil into Complex");
}
if (RB_TYPE_P(a1, T_STRING)) {
a1 = string_to_c_strict(a1, raise);
if (NIL_P(a1)) return Qnil;
}
if (RB_TYPE_P(a2, T_STRING)) {
a2 = string_to_c_strict(a2, raise);
if (NIL_P(a2)) return Qnil;
}
if (RB_TYPE_P(a1, T_COMPLEX)) {
{
get_dat1(a1);
if (k_exact_zero_p(dat->imag))
a1 = dat->real;
}
}
if (RB_TYPE_P(a2, T_COMPLEX)) {
{
get_dat1(a2);
if (k_exact_zero_p(dat->imag))
a2 = dat->real;
}
}
if (RB_TYPE_P(a1, T_COMPLEX)) {
if (a2 == Qundef || (k_exact_zero_p(a2)))
return a1;
}
if (a2 == Qundef) {
if (k_numeric_p(a1) && !f_real_p(a1))
return a1;
if (!k_numeric_p(a1)) {
if (!raise)
return rb_protect(to_complex, a1, NULL);
return to_complex(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)));
}
{
int argc;
VALUE argv2[2];
argv2[0] = a1;
if (a2 == Qundef) {
argv2[1] = Qnil;
argc = 1;
}
else {
if (!raise && !RB_INTEGER_TYPE_P(a2) && !RB_FLOAT_TYPE_P(a2) && !RB_TYPE_P(a2, T_RATIONAL))
return Qnil;
argv2[1] = a2;
argc = 2;
}
return nucomp_s_new(argc, argv2, klass);
}
}
static VALUE
nucomp_s_convert(int argc, VALUE *argv, VALUE klass)
{
VALUE a1, a2;
if (rb_scan_args(argc, argv, "11", &a1, &a2) == 1) {
a2 = Qundef;
}
return nucomp_convert(klass, a1, a2, TRUE);
}
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);
}
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return DBL2NUM(M_PI);
}
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
static VALUE float_arg(VALUE self);
static VALUE
numeric_polar(VALUE self)
{
VALUE abs, arg;
if (RB_INTEGER_TYPE_P(self)) {
abs = rb_int_abs(self);
arg = numeric_arg(self);
}
else if (RB_FLOAT_TYPE_P(self)) {
abs = rb_float_abs(self);
arg = float_arg(self);
}
else if (RB_TYPE_P(self, T_RATIONAL)) {
abs = rb_rational_abs(self);
arg = numeric_arg(self);
}
else {
abs = f_abs(self);
arg = f_arg(self);
}
return rb_assoc_new(abs, arg);
}
static VALUE
numeric_conj(VALUE self)
{
return self;
}
static VALUE
float_arg(VALUE self)
{
if (isnan(RFLOAT_VALUE(self)))
return self;
if (f_tpositive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}
void
Init_Complex(void)
{
VALUE compat;
#undef rb_intern
#define rb_intern(str) rb_intern_const(str)
id_abs = rb_intern("abs");
id_arg = rb_intern("arg");
id_denominator = rb_intern("denominator");
id_fdiv = rb_intern("fdiv");
id_numerator = rb_intern("numerator");
id_quo = rb_intern("quo");
id_real_p = rb_intern("real?");
id_i_real = rb_intern("@real");
id_i_imag = rb_intern("@image");
id_finite_p = rb_intern("finite?");
id_infinite_p = rb_intern("infinite?");
id_rationalize = rb_intern("rationalize");
id_PI = rb_intern("PI");
rb_cComplex = rb_define_class("Complex", rb_cNumeric);
rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
rb_undef_method(CLASS_OF(rb_cComplex), "allocate");
rb_undef_method(CLASS_OF(rb_cComplex), "new");
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, -1);
rb_define_global_function("Complex", nucomp_f_complex, -1);
rb_undef_methods_from(rb_cComplex, rb_mComparable);
rb_undef_method(rb_cComplex, "%");
rb_undef_method(rb_cComplex, "<=>");
rb_undef_method(rb_cComplex, "div");
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, "remainder");
rb_undef_method(rb_cComplex, "round");
rb_undef_method(rb_cComplex, "step");
rb_undef_method(rb_cComplex, "truncate");
rb_undef_method(rb_cComplex, "i");
rb_define_method(rb_cComplex, "real", rb_complex_real, 0);
rb_define_method(rb_cComplex, "imaginary", rb_complex_imag, 0);
rb_define_method(rb_cComplex, "imag", rb_complex_imag, 0);
rb_define_method(rb_cComplex, "-@", rb_complex_uminus, 0);
rb_define_method(rb_cComplex, "+", rb_complex_plus, 1);
rb_define_method(rb_cComplex, "-", rb_complex_minus, 1);
rb_define_method(rb_cComplex, "*", rb_complex_mul, 1);
rb_define_method(rb_cComplex, "/", rb_complex_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, "**", rb_complex_pow, 1);
rb_define_method(rb_cComplex, "==", nucomp_eqeq_p, 1);
rb_define_method(rb_cComplex, "coerce", nucomp_coerce, 1);
rb_define_method(rb_cComplex, "abs", rb_complex_abs, 0);
rb_define_method(rb_cComplex, "magnitude", rb_complex_abs, 0);
rb_define_method(rb_cComplex, "abs2", nucomp_abs2, 0);
rb_define_method(rb_cComplex, "arg", rb_complex_arg, 0);
rb_define_method(rb_cComplex, "angle", rb_complex_arg, 0);
rb_define_method(rb_cComplex, "phase", rb_complex_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", rb_complex_conjugate, 0);
rb_define_method(rb_cComplex, "conj", rb_complex_conjugate, 0);
rb_define_method(rb_cComplex, "real?", nucomp_false, 0);
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_undef_method(rb_cComplex, "positive?");
rb_undef_method(rb_cComplex, "negative?");
rb_define_method(rb_cComplex, "finite?", rb_complex_finite_p, 0);
rb_define_method(rb_cComplex, "infinite?", rb_complex_infinite_p, 0);
rb_define_private_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0);
compat = rb_define_class_under(rb_cComplex, "compatible", rb_cObject);
rb_define_private_method(compat, "marshal_load", nucomp_marshal_load, 1);
rb_marshal_define_compat(rb_cComplex, compat, nucomp_dumper, nucomp_loader);
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_cComplex, "rationalize", nucomp_rationalize, -1);
rb_define_method(rb_cComplex, "to_c", nucomp_to_c, 0);
rb_define_method(rb_cNilClass, "to_c", nilclass_to_c, 0);
rb_define_method(rb_cNumeric, "to_c", numeric_to_c, 0);
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);
rb_define_method(rb_cFloat, "arg", float_arg, 0);
rb_define_method(rb_cFloat, "angle", float_arg, 0);
rb_define_method(rb_cFloat, "phase", float_arg, 0);
rb_define_const(rb_cComplex, "I",
f_complex_new_bang2(rb_cComplex, ZERO, ONE));
#if !USE_FLONUM
rb_gc_register_mark_object(RFLOAT_0 = DBL2NUM(0.0));
#endif
rb_provide("complex.so");
}