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ruby/complex.c

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/*
complex.c: Coded by Tadayoshi Funaba 2008-2012
This implementation is based on Keiju Ishitsuka's Complex library
which is written in ruby.
*/
#include "ruby/internal/config.h"
#if defined _MSC_VER
/* Microsoft Visual C does not define M_PI and others by default */
# define _USE_MATH_DEFINES 1
#endif
#include <ctype.h>
#include <math.h>
#include "id.h"
#include "internal.h"
#include "internal/array.h"
#include "internal/class.h"
#include "internal/complex.h"
#include "internal/math.h"
#include "internal/numeric.h"
#include "internal/object.h"
#include "internal/rational.h"
#include "internal/string.h"
#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
VALUE rb_cComplex;
static ID id_abs, id_arg,
id_denominator, id_numerator,
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 id_quo idQuo
#define id_fdiv idFdiv
#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);
}
inline static VALUE
f_abs(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return rb_int_abs(x);
}
else if (RB_FLOAT_TYPE_P(x)) {
return rb_float_abs(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return rb_rational_abs(x);
}
else if (RB_TYPE_P(x, T_COMPLEX)) {
return rb_complex_abs(x);
}
return rb_funcall(x, id_abs, 0);
}
static VALUE numeric_arg(VALUE self);
static VALUE float_arg(VALUE self);
inline static VALUE
f_arg(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return numeric_arg(x);
}
else if (RB_FLOAT_TYPE_P(x)) {
return float_arg(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return numeric_arg(x);
}
else if (RB_TYPE_P(x, T_COMPLEX)) {
return rb_complex_arg(x);
}
return rb_funcall(x, id_arg, 0);
}
inline static VALUE
f_numerator(VALUE x)
{
if (RB_TYPE_P(x, T_RATIONAL)) {
return RRATIONAL(x)->num;
}
if (RB_FLOAT_TYPE_P(x)) {
return rb_float_numerator(x);
}
return x;
}
inline static VALUE
f_denominator(VALUE x)
{
if (RB_TYPE_P(x, T_RATIONAL)) {
return RRATIONAL(x)->den;
}
if (RB_FLOAT_TYPE_P(x)) {
return rb_float_denominator(x);
}
return INT2FIX(1);
}
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);
}
static bool nucomp_real_p(VALUE self);
static inline bool
f_real_p(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return true;
}
else if (RB_FLOAT_TYPE_P(x)) {
return true;
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return true;
}
else if (RB_TYPE_P(x, T_COMPLEX)) {
return nucomp_real_p(x);
}
return rb_funcall(x, id_real_p, 0);
}
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)
static VALUE
f_quo(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(x))
return rb_numeric_quo(x, y);
if (RB_FLOAT_TYPE_P(x))
return rb_float_div(x, y);
if (RB_TYPE_P(x, T_RATIONAL))
return rb_numeric_quo(x, y);
return rb_funcallv(x, id_quo, 1, &y);
}
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 bool
f_zero_p(VALUE x)
{
if (RB_FLOAT_TYPE_P(x)) {
return FLOAT_ZERO_P(x);
}
else 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 rb_equal(x, ZERO) != 0;
}
#define f_nonzero_p(x) (!f_zero_p(x))
static inline bool
always_finite_type_p(VALUE x)
{
if (FIXNUM_P(x)) return true;
if (FLONUM_P(x)) return true; /* Infinity can't be a flonum */
return (RB_INTEGER_TYPE_P(x) || RB_TYPE_P(x, T_RATIONAL));
}
inline static int
f_finite_p(VALUE x)
{
if (always_finite_type_p(x)) {
return TRUE;
}
else if (RB_FLOAT_TYPE_P(x)) {
return isfinite(RFLOAT_VALUE(x));
}
return RTEST(rb_funcallv(x, id_finite_p, 0, 0));
}
inline static int
f_infinite_p(VALUE x)
{
if (always_finite_type_p(x)) {
return FALSE;
}
else if (RB_FLOAT_TYPE_P(x)) {
return isinf(RFLOAT_VALUE(x));
}
return RTEST(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), sizeof(struct RComplex), 0);
RCOMPLEX_SET_REAL(obj, real);
RCOMPLEX_SET_IMAG(obj, imag);
OBJ_FREEZE((VALUE)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)
{
RUBY_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)
{
RUBY_ASSERT(!RB_TYPE_P(x, T_COMPLEX));
RUBY_ASSERT(!RB_TYPE_P(y, T_COMPLEX));
return nucomp_s_new_internal(klass, x, y);
}
WARN_UNUSED_RESULT(inline static VALUE nucomp_real_check(VALUE num));
inline static VALUE
nucomp_real_check(VALUE num)
{
if (!RB_INTEGER_TYPE_P(num) &&
!RB_FLOAT_TYPE_P(num) &&
!RB_TYPE_P(num, T_RATIONAL)) {
if (RB_TYPE_P(num, T_COMPLEX) && nucomp_real_p(num)) {
VALUE real = RCOMPLEX(num)->real;
RUBY_ASSERT(!RB_TYPE_P(real, T_COMPLEX));
return real;
}
if (!k_numeric_p(num) || !f_real_p(num))
rb_raise(rb_eTypeError, "not a real");
}
return num;
}
inline static VALUE
nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
{
int complex_r, complex_i;
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));
}
}
/*
* call-seq:
* Complex.rect(real, imag = 0) -> complex
*
* Returns a new \Complex object formed from the arguments,
* each of which must be an instance of Numeric,
* or an instance of one of its subclasses:
* \Complex, Float, Integer, Rational;
* see {Rectangular Coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]:
*
* Complex.rect(3) # => (3+0i)
* Complex.rect(3, Math::PI) # => (3+3.141592653589793i)
* Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i)
*
* \Complex.rectangular is an alias for \Complex.rect.
*/
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:
real = nucomp_real_check(real);
imag = ZERO;
break;
default:
real = nucomp_real_check(real);
imag = nucomp_real_check(imag);
break;
}
return nucomp_s_new_internal(klass, real, imag);
}
inline static VALUE
f_complex_new2(VALUE klass, VALUE x, VALUE y)
{
if (RB_TYPE_P(x, T_COMPLEX)) {
get_dat1(x);
x = dat->real;
y = f_add(dat->imag, y);
}
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);
/*
* call-seq:
* Complex(real, imag = 0, exception: true) -> complex or nil
* Complex(s, exception: true) -> complex or nil
*
* Returns a new \Complex object if the arguments are valid;
* otherwise raises an exception if +exception+ is +true+;
* otherwise returns +nil+.
*
* With Numeric arguments +real+ and +imag+,
* returns <tt>Complex.rect(real, imag)</tt> if the arguments are valid.
*
* With string argument +s+, returns a new \Complex object if the argument is valid;
* the string may have:
*
* - One or two numeric substrings,
* each of which specifies a Complex, Float, Integer, Numeric, or Rational value,
* specifying {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates]:
*
* - Sign-separated real and imaginary numeric substrings
* (with trailing character <tt>'i'</tt>):
*
* Complex('1+2i') # => (1+2i)
* Complex('+1+2i') # => (1+2i)
* Complex('+1-2i') # => (1-2i)
* Complex('-1+2i') # => (-1+2i)
* Complex('-1-2i') # => (-1-2i)
*
* - Real-only numeric string (without trailing character <tt>'i'</tt>):
*
* Complex('1') # => (1+0i)
* Complex('+1') # => (1+0i)
* Complex('-1') # => (-1+0i)
*
* - Imaginary-only numeric string (with trailing character <tt>'i'</tt>):
*
* Complex('1i') # => (0+1i)
* Complex('+1i') # => (0+1i)
* Complex('-1i') # => (0-1i)
*
* - At-sign separated real and imaginary rational substrings,
* each of which specifies a Rational value,
* specifying {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
*
* Complex('1/2@3/4') # => (0.36584443443691045+0.34081938001166706i)
* Complex('+1/2@+3/4') # => (0.36584443443691045+0.34081938001166706i)
* Complex('+1/2@-3/4') # => (0.36584443443691045-0.34081938001166706i)
* Complex('-1/2@+3/4') # => (-0.36584443443691045-0.34081938001166706i)
* Complex('-1/2@-3/4') # => (-0.36584443443691045+0.34081938001166706i)
*
*/
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)) {
raise = rb_opts_exception_p(opts, raise);
}
if (argc > 0 && CLASS_OF(a1) == rb_cComplex && UNDEF_P(a2)) {
return a1;
}
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_real(VALUE klass, VALUE x, VALUE y)
{
if (f_zero_p(x) || f_zero_p(y)) {
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);
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);
y = DBL2NUM(imag);
}
else {
const double ax = sin(arg), ay = cos(arg);
y = f_mul(x, DBL2NUM(ax));
x = f_mul(x, DBL2NUM(ay));
}
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)));
}
static VALUE
f_complex_polar(VALUE klass, VALUE x, VALUE y)
{
x = nucomp_real_check(x);
y = nucomp_real_check(y);
return f_complex_polar_real(klass, x, y);
}
#ifdef HAVE___COSPI
# define cospi(x) __cospi(x)
#else
# define cospi(x) cos((x) * M_PI)
#endif
#ifdef HAVE___SINPI
# define sinpi(x) __sinpi(x)
#else
# define sinpi(x) sin((x) * M_PI)
#endif
/* returns a Complex or Float of ang*PI-rotated abs */
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 {
const double real = abs * cospi(ang), imag = abs * sinpi(ang);
return rb_complex_new(DBL2NUM(real), DBL2NUM(imag));
}
}
/*
* call-seq:
* Complex.polar(abs, arg = 0) -> complex
*
* Returns a new \Complex object formed from the arguments,
* each of which must be an instance of Numeric,
* or an instance of one of its subclasses:
* \Complex, Float, Integer, Rational.
* Argument +arg+ is given in radians;
* see {Polar Coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
*
* Complex.polar(3) # => (3+0i)
* Complex.polar(3, 2.0) # => (-1.2484405096414273+2.727892280477045i)
* Complex.polar(-3, -2.0) # => (1.2484405096414273+2.727892280477045i)
*
*/
static VALUE
nucomp_s_polar(int argc, VALUE *argv, VALUE klass)
{
VALUE abs, arg;
argc = rb_scan_args(argc, argv, "11", &abs, &arg);
abs = nucomp_real_check(abs);
if (argc == 2) {
arg = nucomp_real_check(arg);
}
else {
arg = ZERO;
}
return f_complex_polar_real(klass, abs, arg);
}
/*
* call-seq:
* real -> numeric
*
* Returns the real value for +self+:
*
* Complex.rect(7).real # => 7
* Complex.rect(9, -4).real # => 9
*
* If +self+ was created with
* {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value
* is computed, and may be inexact:
*
* Complex.polar(1, Math::PI/4).real # => 0.7071067811865476 # Square root of 2.
*
*/
VALUE
rb_complex_real(VALUE self)
{
get_dat1(self);
return dat->real;
}
/*
* call-seq:
* imag -> numeric
*
* Returns the imaginary value for +self+:
*
* Complex.rect(7).imag # => 0
* Complex.rect(9, -4).imag # => -4
*
* If +self+ was created with
* {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value
* is computed, and may be inexact:
*
* Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2.
*
*/
VALUE
rb_complex_imag(VALUE self)
{
get_dat1(self);
return dat->imag;
}
/*
* call-seq:
* -complex -> new_complex
*
* Returns the negation of +self+, which is the negation of each of its parts:
*
* -Complex.rect(1, 2) # => (-1-2i)
* -Complex.rect(-1, -2) # => (1+2i)
*
*/
VALUE
rb_complex_uminus(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_negate(dat->real), f_negate(dat->imag));
}
/*
* call-seq:
* complex + numeric -> new_complex
*
* Returns the sum of +self+ and +numeric+:
*
* Complex.rect(2, 3) + Complex.rect(2, 3) # => (4+6i)
* Complex.rect(900) + Complex.rect(1) # => (901+0i)
* Complex.rect(-2, 9) + Complex.rect(-9, 2) # => (-11+11i)
* Complex.rect(9, 8) + 4 # => (13+8i)
* Complex.rect(20, 9) + 9.8 # => (29.8+9i)
*
*/
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, '+');
}
/*
* call-seq:
* complex - numeric -> new_complex
*
* Returns the difference of +self+ and +numeric+:
*
* Complex.rect(2, 3) - Complex.rect(2, 3) # => (0+0i)
* Complex.rect(900) - Complex.rect(1) # => (899+0i)
* Complex.rect(-2, 9) - Complex.rect(-9, 2) # => (7+7i)
* Complex.rect(9, 8) - 4 # => (5+8i)
* Complex.rect(20, 9) - 9.8 # => (10.2+9i)
*
*/
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, bool az, bool 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)
{
bool arzero = f_zero_p(areal);
bool aizero = f_zero_p(aimag);
bool brzero = f_zero_p(breal);
bool 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));
}
/*
* call-seq:
* complex * numeric -> new_complex
*
* Returns the product of +self+ and +numeric+:
*
* Complex.rect(2, 3) * Complex.rect(2, 3) # => (-5+12i)
* Complex.rect(900) * Complex.rect(1) # => (900+0i)
* Complex.rect(-2, 9) * Complex.rect(-9, 2) # => (0-85i)
* Complex.rect(9, 8) * 4 # => (36+32i)
* Complex.rect(20, 9) * 9.8 # => (196.0+88.2i)
*
*/
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)));
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)));
x = (*func)(f_add(f_mul(adat->real, r), adat->imag), n);
y = (*func)(f_sub(f_mul(adat->imag, r), adat->real), n);
}
if (!flo) {
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)) {
VALUE x, y;
get_dat1(self);
x = rb_rational_canonicalize((*func)(dat->real, other));
y = rb_rational_canonicalize((*func)(dat->imag, other));
return f_complex_new2(CLASS_OF(self), x, y);
}
return rb_num_coerce_bin(self, other, id);
}
#define rb_raise_zerodiv() rb_raise(rb_eZeroDivError, "divided by 0")
/*
* call-seq:
* complex / numeric -> new_complex
*
* Returns the quotient of +self+ and +numeric+:
*
* Complex.rect(2, 3) / Complex.rect(2, 3) # => (1+0i)
* Complex.rect(900) / Complex.rect(1) # => (900+0i)
* Complex.rect(-2, 9) / Complex.rect(-9, 2) # => ((36/85)-(77/85)*i)
* Complex.rect(9, 8) / 4 # => ((9/4)+2i)
* Complex.rect(20, 9) / 9.8 # => (2.0408163265306123+0.9183673469387754i)
*
*/
VALUE
rb_complex_div(VALUE self, VALUE other)
{
return f_divide(self, other, f_quo, id_quo);
}
#define nucomp_quo rb_complex_div
/*
* call-seq:
* fdiv(numeric) -> new_complex
*
* Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>:
*
* Complex.rect(11, 22).fdiv(3) # => (3.6666666666666665+7.333333333333333i)
*
*/
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);
}
static VALUE
zero_for(VALUE x)
{
if (RB_FLOAT_TYPE_P(x))
return DBL2NUM(0);
if (RB_TYPE_P(x, T_RATIONAL))
return rb_rational_new(INT2FIX(0), INT2FIX(1));
return INT2FIX(0);
}
static VALUE
complex_pow_for_special_angle(VALUE self, VALUE other)
{
if (!rb_integer_type_p(other)) {
return Qundef;
}
get_dat1(self);
VALUE x = Qundef;
int dir;
if (f_zero_p(dat->imag)) {
x = dat->real;
dir = 0;
}
else if (f_zero_p(dat->real)) {
x = dat->imag;
dir = 2;
}
else if (f_eqeq_p(dat->real, dat->imag)) {
x = dat->real;
dir = 1;
}
else if (f_eqeq_p(dat->real, f_negate(dat->imag))) {
x = dat->imag;
dir = 3;
} else {
dir = 0;
}
if (UNDEF_P(x)) return x;
if (f_negative_p(x)) {
x = f_negate(x);
dir += 4;
}
VALUE zx;
if (dir % 2 == 0) {
zx = rb_num_pow(x, other);
}
else {
zx = rb_num_pow(
rb_funcall(rb_int_mul(TWO, x), '*', 1, x),
rb_int_div(other, TWO)
);
if (rb_int_odd_p(other)) {
zx = rb_funcall(zx, '*', 1, x);
}
}
static const int dirs[][2] = {
{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}
};
int z_dir = FIX2INT(rb_int_modulo(rb_int_mul(INT2FIX(dir), other), INT2FIX(8)));
VALUE zr = Qfalse, zi = Qfalse;
switch (dirs[z_dir][0]) {
case 0: zr = zero_for(zx); break;
case 1: zr = zx; break;
case -1: zr = f_negate(zx); break;
}
switch (dirs[z_dir][1]) {
case 0: zi = zero_for(zx); break;
case 1: zi = zx; break;
case -1: zi = f_negate(zx); break;
}
return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
}
/*
* call-seq:
* complex ** numeric -> new_complex
*
* Returns +self+ raised to power +numeric+:
*
* Complex.rect(0, 1) ** 2 # => (-1+0i)
* Complex.rect(-8) ** Rational(1, 3) # => (1.0000000000000002+1.7320508075688772i)
*
*/
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; /* c14n */
if (RB_TYPE_P(other, T_COMPLEX)) {
get_dat1(other);
if (k_exact_zero_p(dat->imag))
other = dat->real; /* c14n */
}
if (other == ONE) {
get_dat1(self);
return nucomp_s_new_internal(CLASS_OF(self), dat->real, dat->imag);
}
VALUE result = complex_pow_for_special_angle(self, other);
if (!UNDEF_P(result)) return result;
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_BIGNUM_TYPE_P(other))
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);
}
/*
* call-seq:
* complex == object -> true or false
*
* Returns +true+ if <tt>self.real == object.real</tt>
* and <tt>self.imag == object.imag</tt>:
*
* Complex.rect(2, 3) == Complex.rect(2.0, 3.0) # => true
*
*/
static VALUE
nucomp_eqeq_p(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
get_dat2(self, other);
return RBOOL(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 RBOOL(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
}
return RBOOL(f_eqeq_p(other, self));
}
static bool
nucomp_real_p(VALUE self)
{
get_dat1(self);
return f_zero_p(dat->imag);
}
/*
* call-seq:
* complex <=> object -> -1, 0, 1, or nil
*
* Returns:
*
* - <tt>self.real <=> object.real</tt> if both of the following are true:
*
* - <tt>self.imag == 0</tt>.
* - <tt>object.imag == 0</tt>. # Always true if object is numeric but not complex.
*
* - +nil+ otherwise.
*
* Examples:
*
* Complex.rect(2) <=> 3 # => -1
* Complex.rect(2) <=> 2 # => 0
* Complex.rect(2) <=> 1 # => 1
* Complex.rect(2, 1) <=> 1 # => nil # self.imag not zero.
* Complex.rect(1) <=> Complex.rect(1, 1) # => nil # object.imag not zero.
* Complex.rect(1) <=> 'Foo' # => nil # object.imag not defined.
*
*/
static VALUE
nucomp_cmp(VALUE self, VALUE other)
{
if (!k_numeric_p(other)) {
return rb_num_coerce_cmp(self, other, idCmp);
}
if (!nucomp_real_p(self)) {
return Qnil;
}
if (RB_TYPE_P(other, T_COMPLEX)) {
if (nucomp_real_p(other)) {
get_dat2(self, other);
return rb_funcall(adat->real, idCmp, 1, bdat->real);
}
}
else {
get_dat1(self);
if (f_real_p(other)) {
return rb_funcall(dat->real, idCmp, 1, other);
}
else {
return rb_num_coerce_cmp(dat->real, other, idCmp);
}
}
return Qnil;
}
/* :nodoc: */
static VALUE
nucomp_coerce(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX))
return rb_assoc_new(other, self);
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, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
rb_obj_class(other), rb_obj_class(self));
return Qnil;
}
/*
* call-seq:
* abs -> float
*
* Returns the absolute value (magnitude) for +self+;
* see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
*
* Complex.polar(-1, 0).abs # => 1.0
*
* If +self+ was created with
* {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value
* is computed, and may be inexact:
*
* Complex.rectangular(1, 1).abs # => 1.4142135623730951 # The square root of 2.
*
*/
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);
}
/*
* call-seq:
* abs2 -> float
*
* Returns square of the absolute value (magnitude) for +self+;
* see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
*
* Complex.polar(2, 2).abs2 # => 4.0
*
* If +self+ was created with
* {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value
* is computed, and may be inexact:
*
* Complex.rectangular(1.0/3, 1.0/3).abs2 # => 0.2222222222222222
*
*/
static VALUE
nucomp_abs2(VALUE self)
{
get_dat1(self);
return f_add(f_mul(dat->real, dat->real),
f_mul(dat->imag, dat->imag));
}
/*
* call-seq:
* arg -> float
*
* Returns the argument (angle) for +self+ in radians;
* see {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates]:
*
* Complex.polar(3, Math::PI/2).arg # => 1.57079632679489660
*
* If +self+ was created with
* {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value
* is computed, and may be inexact:
*
* Complex.polar(1, 1.0/3).arg # => 0.33333333333333326
*
*/
VALUE
rb_complex_arg(VALUE self)
{
get_dat1(self);
return rb_math_atan2(dat->imag, dat->real);
}
/*
* call-seq:
* rect -> array
*
* Returns the array <tt>[self.real, self.imag]</tt>:
*
* Complex.rect(1, 2).rect # => [1, 2]
*
* See {Rectangular Coordinates}[rdoc-ref:Complex@Rectangular+Coordinates].
*
* If +self+ was created with
* {polar coordinates}[rdoc-ref:Complex@Polar+Coordinates], the returned value
* is computed, and may be inexact:
*
* Complex.polar(1.0, 1.0).rect # => [0.5403023058681398, 0.8414709848078965]
*
*
* Complex#rectangular is an alias for Complex#rect.
*/
static VALUE
nucomp_rect(VALUE self)
{
get_dat1(self);
return rb_assoc_new(dat->real, dat->imag);
}
/*
* call-seq:
* polar -> array
*
* Returns the array <tt>[self.abs, self.arg]</tt>:
*
* Complex.polar(1, 2).polar # => [1.0, 2.0]
*
* See {Polar Coordinates}[rdoc-ref:Complex@Polar+Coordinates].
*
* If +self+ was created with
* {rectangular coordinates}[rdoc-ref:Complex@Rectangular+Coordinates], the returned value
* is computed, and may be inexact:
*
* Complex.rect(1, 1).polar # => [1.4142135623730951, 0.7853981633974483]
*
*/
static VALUE
nucomp_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
/*
* call-seq:
* conj -> complex
*
* Returns the conjugate of +self+, <tt>Complex.rect(self.imag, self.real)</tt>:
*
* Complex.rect(1, 2).conj # => (1-2i)
*
*/
VALUE
rb_complex_conjugate(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}
/*
* call-seq:
* real? -> false
*
* Returns +false+; for compatibility with Numeric#real?.
*/
static VALUE
nucomp_real_p_m(VALUE self)
{
return Qfalse;
}
/*
* call-seq:
* denominator -> integer
*
* Returns the denominator of +self+, which is
* the {least common multiple}[https://en.wikipedia.org/wiki/Least_common_multiple]
* of <tt>self.real.denominator</tt> and <tt>self.imag.denominator</tt>:
*
* Complex.rect(Rational(1, 2), Rational(2, 3)).denominator # => 6
*
* Note that <tt>n.denominator</tt> of a non-rational numeric is +1+.
*
* Related: Complex#numerator.
*/
static VALUE
nucomp_denominator(VALUE self)
{
get_dat1(self);
return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
}
/*
* call-seq:
* numerator -> new_complex
*
* Returns the \Complex object created from the numerators
* of the real and imaginary parts of +self+,
* after converting each part to the
* {lowest common denominator}[https://en.wikipedia.org/wiki/Lowest_common_denominator]
* of the two:
*
* c = Complex.rect(Rational(2, 3), Rational(3, 4)) # => ((2/3)+(3/4)*i)
* c.numerator # => (8+9i)
*
* In this example, the lowest common denominator of the two parts is 12;
* the two converted parts may be thought of as \Rational(8, 12) and \Rational(9, 12),
* whose numerators, respectively, are 8 and 9;
* so the returned value of <tt>c.numerator</tt> is <tt>Complex.rect(8, 9)</tt>.
*
* Related: Complex#denominator.
*/
static VALUE
nucomp_numerator(VALUE self)
{
VALUE cd;
get_dat1(self);
cd = nucomp_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))));
}
/* :nodoc: */
st_index_t
rb_complex_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 v;
}
/*
* :call-seq:
* hash -> integer
*
* Returns the integer hash value for +self+.
*
* Two \Complex objects created from the same values will have the same hash value
* (and will compare using #eql?):
*
* Complex.rect(1, 2).hash == Complex.rect(1, 2).hash # => true
*
*/
static VALUE
nucomp_hash(VALUE self)
{
return ST2FIX(rb_complex_hash(self));
}
/* :nodoc: */
static VALUE
nucomp_eql_p(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
get_dat2(self, other);
return RBOOL((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;
}
/*
* call-seq:
* to_s -> string
*
* Returns a string representation of +self+:
*
* Complex.rect(2).to_s # => "2+0i"
* Complex.rect(-8, 6).to_s # => "-8+6i"
* Complex.rect(0, Rational(1, 2)).to_s # => "0+1/2i"
* Complex.rect(0, Float::INFINITY).to_s # => "0+Infinity*i"
* Complex.rect(Float::NAN, Float::NAN).to_s # => "NaN+NaN*i"
*
*/
static VALUE
nucomp_to_s(VALUE self)
{
return f_format(self, rb_String);
}
/*
* call-seq:
* inspect -> string
*
* Returns a string representation of +self+:
*
* Complex.rect(2).inspect # => "(2+0i)"
* Complex.rect(-8, 6).inspect # => "(-8+6i)"
* Complex.rect(0, Rational(1, 2)).inspect # => "(0+(1/2)*i)"
* Complex.rect(0, Float::INFINITY).inspect # => "(0+Infinity*i)"
* Complex.rect(Float::NAN, Float::NAN).inspect # => "(NaN+NaN*i)"
*
*/
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))
/*
* call-seq:
* finite? -> true or false
*
* Returns +true+ if both <tt>self.real.finite?</tt> and <tt>self.imag.finite?</tt>
* are true, +false+ otherwise:
*
* Complex.rect(1, 1).finite? # => true
* Complex.rect(Float::INFINITY, 0).finite? # => false
*
* Related: Numeric#finite?, Float#finite?.
*/
static VALUE
rb_complex_finite_p(VALUE self)
{
get_dat1(self);
return RBOOL(f_finite_p(dat->real) && f_finite_p(dat->imag));
}
/*
* call-seq:
* infinite? -> 1 or nil
*
* Returns +1+ if either <tt>self.real.infinite?</tt> or <tt>self.imag.infinite?</tt>
* is true, +nil+ otherwise:
*
* Complex.rect(Float::INFINITY, 0).infinite? # => 1
* Complex.rect(1, 1).infinite? # => nil
*
* Related: Numeric#infinite?, Float#infinite?.
*/
static VALUE
rb_complex_infinite_p(VALUE self)
{
get_dat1(self);
if (!f_infinite_p(dat->real) && !f_infinite_p(dat->imag)) {
return Qnil;
}
return ONE;
}
/* :nodoc: */
static VALUE
nucomp_dumper(VALUE self)
{
return self;
}
/* :nodoc: */
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(self);
return self;
}
/* :nodoc: */
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;
}
/* :nodoc: */
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));
}
/*
* call-seq:
* to_i -> integer
*
* Returns the value of <tt>self.real</tt> as an Integer, if possible:
*
* Complex.rect(1, 0).to_i # => 1
* Complex.rect(1, Rational(0, 1)).to_i # => 1
*
* Raises RangeError if <tt>self.imag</tt> is not exactly zero
* (either <tt>Integer(0)</tt> or <tt>Rational(0, _n_)</tt>).
*/
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);
}
/*
* call-seq:
* to_f -> float
*
* Returns the value of <tt>self.real</tt> as a Float, if possible:
*
* Complex.rect(1, 0).to_f # => 1.0
* Complex.rect(1, Rational(0, 1)).to_f # => 1.0
*
* Raises RangeError if <tt>self.imag</tt> is not exactly zero
* (either <tt>Integer(0)</tt> or <tt>Rational(0, _n_)</tt>).
*/
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);
}
/*
* call-seq:
* to_r -> rational
*
* Returns the value of <tt>self.real</tt> as a Rational, if possible:
*
* Complex.rect(1, 0).to_r # => (1/1)
* Complex.rect(1, Rational(0, 1)).to_r # => (1/1)
* Complex.rect(1, 0.0).to_r # => (1/1)
*
* Raises RangeError if <tt>self.imag</tt> is not exactly zero
* (either <tt>Integer(0)</tt> or <tt>Rational(0, _n_)</tt>)
* and <tt>self.imag.to_r</tt> is not exactly zero.
*
* Related: Complex#rationalize.
*/
static VALUE
nucomp_to_r(VALUE self)
{
get_dat1(self);
if (RB_FLOAT_TYPE_P(dat->imag) && FLOAT_ZERO_P(dat->imag)) {
/* Do nothing here */
}
else if (!k_exact_zero_p(dat->imag)) {
VALUE imag = rb_check_convert_type_with_id(dat->imag, T_RATIONAL, "Rational", idTo_r);
if (NIL_P(imag) || !k_exact_zero_p(imag)) {
rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
self);
}
}
return f_to_r(dat->real);
}
/*
* call-seq:
* rationalize(epsilon = nil) -> rational
*
* Returns a Rational object whose value is exactly or approximately
* equivalent to that of <tt>self.real</tt>.
*
* With no argument +epsilon+ given, returns a \Rational object
* whose value is exactly equal to that of <tt>self.real.rationalize</tt>:
*
* Complex.rect(1, 0).rationalize # => (1/1)
* Complex.rect(1, Rational(0, 1)).rationalize # => (1/1)
* Complex.rect(3.14159, 0).rationalize # => (314159/100000)
*
* With argument +epsilon+ given, returns a \Rational object
* whose value is exactly or approximately equal to that of <tt>self.real</tt>
* to the given precision:
*
* Complex.rect(3.14159, 0).rationalize(0.1) # => (16/5)
* Complex.rect(3.14159, 0).rationalize(0.01) # => (22/7)
* Complex.rect(3.14159, 0).rationalize(0.001) # => (201/64)
* Complex.rect(3.14159, 0).rationalize(0.0001) # => (333/106)
* Complex.rect(3.14159, 0).rationalize(0.00001) # => (355/113)
* Complex.rect(3.14159, 0).rationalize(0.000001) # => (7433/2366)
* Complex.rect(3.14159, 0).rationalize(0.0000001) # => (9208/2931)
* Complex.rect(3.14159, 0).rationalize(0.00000001) # => (47460/15107)
* Complex.rect(3.14159, 0).rationalize(0.000000001) # => (76149/24239)
* Complex.rect(3.14159, 0).rationalize(0.0000000001) # => (314159/100000)
* Complex.rect(3.14159, 0).rationalize(0.0) # => (3537115888337719/1125899906842624)
*
* Related: Complex#to_r.
*/
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);
}
/*
* call-seq:
* to_c -> self
*
* Returns +self+.
*/
static VALUE
nucomp_to_c(VALUE self)
{
return self;
}
/*
* call-seq:
* to_c -> (0+0i)
*
* Returns zero as a Complex:
*
* nil.to_c # => (0+0i)
*
*/
static VALUE
nilclass_to_c(VALUE self)
{
return rb_complex_new1(INT2FIX(0));
}
/*
* call-seq:
* to_c -> complex
*
* Returns +self+ as a Complex object.
*/
static VALUE
numeric_to_c(VALUE self)
{
return rb_complex_new1(self);
}
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 (us) {
if (strict) return 0;
break;
}
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; /* e.g. "i" */
}
if (!read_rat_nos(s, strict, b)) {
**b = '\0';
num = str2num(bb);
*ret = rb_complex_new2(num, ZERO);
return 0; /* e.g. "-" */
}
**b = '\0';
num = str2num(bb);
if (isimagunit(**s)) {
(*s)++;
*ret = rb_complex_new2(ZERO, num);
return 1; /* e.g. "3i" */
}
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; /* e.g. "1@-" */
}
num2 = str2num(bb);
*ret = rb_complex_new_polar(num, num2);
if (!st)
return 0; /* e.g. "1@2." */
else
return 1; /* e.g. "1@2" */
}
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; /* e.g. "1+xi" */
}
**b = '\0';
num2 = str2num(bb);
}
if (!isimagunit(**s)) {
*ret = rb_complex_new2(num, ZERO);
return 0; /* e.g. "1+3x" */
}
(*s)++;
*ret = rb_complex_new2(num, num2);
return 1; /* e.g. "1+2i" */
}
/* !(@, - or +) */
{
*ret = rb_complex_new2(num, ZERO);
return 1; /* e.g. "3" */
}
}
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);
if (raise) {
s = StringValueCStr(self);
}
else if (!(s = rb_str_to_cstr(self))) {
return Qnil;
}
if (!parse_comp(s, TRUE, &num)) {
if (!raise) return Qnil;
rb_raise(rb_eArgError, "invalid value for convert(): %+"PRIsVALUE,
self);
}
return num;
}
/*
* call-seq:
* to_c -> complex
*
* Returns +self+ interpreted as a Complex object;
* leading whitespace and trailing garbage are ignored:
*
* '9'.to_c # => (9+0i)
* '2.5'.to_c # => (2.5+0i)
* '2.5/1'.to_c # => ((5/2)+0i)
* '-3/2'.to_c # => ((-3/2)+0i)
* '-i'.to_c # => (0-1i)
* '45i'.to_c # => (0+45i)
* '3-4i'.to_c # => (3-4i)
* '-4e2-4e-2i'.to_c # => (-400.0-0.04i)
* '-0.0-0.0i'.to_c # => (-0.0-0.0i)
* '1/2+3/4i'.to_c # => ((1/2)+(3/4)*i)
* '1.0@0'.to_c # => (1+0.0i)
* "1.0@#{Math::PI/2}".to_c # => (0.0+1i)
* "1.0@#{Math::PI}".to_c # => (-1+0.0i)
*
* Returns \Complex zero if the string cannot be converted:
*
* 'ruby'.to_c # => (0+0i)
*
* See Kernel#Complex.
*/
static VALUE
string_to_c(VALUE self)
{
VALUE num;
rb_must_asciicompat(self);
(void)parse_comp(rb_str_fill_terminator(self, 1), FALSE, &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 (UNDEF_P(a2) || (k_exact_zero_p(a2)))
return a1;
}
if (UNDEF_P(a2)) {
if (k_numeric_p(a1) && !f_real_p(a1))
return a1;
/* should raise exception for consistency */
if (!k_numeric_p(a1)) {
if (!raise) {
a1 = rb_protect(to_complex, a1, NULL);
rb_set_errinfo(Qnil);
return a1;
}
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 (UNDEF_P(a2)) {
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);
}
/*
* call-seq:
* abs2 -> real
*
* Returns the square of +self+.
*/
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
/*
* call-seq:
* arg -> 0 or Math::PI
*
* Returns zero if +self+ is positive, Math::PI otherwise.
*/
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return DBL2NUM(M_PI);
}
/*
* call-seq:
* rect -> array
*
* Returns array <tt>[self, 0]</tt>.
*/
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
/*
* call-seq:
* polar -> array
*
* Returns array <tt>[self.abs, self.arg]</tt>.
*/
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);
}
/*
* call-seq:
* arg -> 0 or Math::PI
*
* Returns 0 if +self+ is positive, Math::PI otherwise.
*/
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);
}
/*
* A \Complex object houses a pair of values,
* given when the object is created as either <i>rectangular coordinates</i>
* or <i>polar coordinates</i>.
*
* == Rectangular Coordinates
*
* The rectangular coordinates of a complex number
* are called the _real_ and _imaginary_ parts;
* see {Complex number definition}[https://en.wikipedia.org/wiki/Complex_number#Definition_and_basic_operations].
*
* You can create a \Complex object from rectangular coordinates with:
*
* - A {complex literal}[rdoc-ref:doc/syntax/literals.rdoc@Complex+Literals].
* - \Method Complex.rect.
* - \Method Kernel#Complex, either with numeric arguments or with certain string arguments.
* - \Method String#to_c, for certain strings.
*
* Note that each of the stored parts may be a an instance one of the classes
* Complex, Float, Integer, or Rational;
* they may be retrieved:
*
* - Separately, with methods Complex#real and Complex#imaginary.
* - Together, with method Complex#rect.
*
* The corresponding (computed) polar values may be retrieved:
*
* - Separately, with methods Complex#abs and Complex#arg.
* - Together, with method Complex#polar.
*
* == Polar Coordinates
*
* The polar coordinates of a complex number
* are called the _absolute_ and _argument_ parts;
* see {Complex polar plane}[https://en.wikipedia.org/wiki/Complex_number#Polar_form].
*
* In this class, the argument part
* in expressed {radians}[https://en.wikipedia.org/wiki/Radian]
* (not {degrees}[https://en.wikipedia.org/wiki/Degree_(angle)]).
*
* You can create a \Complex object from polar coordinates with:
*
* - \Method Complex.polar.
* - \Method Kernel#Complex, with certain string arguments.
* - \Method String#to_c, for certain strings.
*
* Note that each of the stored parts may be a an instance one of the classes
* Complex, Float, Integer, or Rational;
* they may be retrieved:
*
* - Separately, with methods Complex#abs and Complex#arg.
* - Together, with method Complex#polar.
*
* The corresponding (computed) rectangular values may be retrieved:
*
* - Separately, with methods Complex#real and Complex#imag.
* - Together, with method Complex#rect.
*
* == What's Here
*
* First, what's elsewhere:
*
* - \Class \Complex inherits (directly or indirectly)
* from classes {Numeric}[rdoc-ref:Numeric@What-27s+Here]
* and {Object}[rdoc-ref:Object@What-27s+Here].
* - Includes (indirectly) module {Comparable}[rdoc-ref:Comparable@What-27s+Here].
*
* Here, class \Complex has methods for:
*
* === Creating \Complex Objects
*
* - ::polar: Returns a new \Complex object based on given polar coordinates.
* - ::rect (and its alias ::rectangular):
* Returns a new \Complex object based on given rectangular coordinates.
*
* === Querying
*
* - #abs (and its alias #magnitude): Returns the absolute value for +self+.
* - #arg (and its aliases #angle and #phase):
* Returns the argument (angle) for +self+ in radians.
* - #denominator: Returns the denominator of +self+.
* - #finite?: Returns whether both +self.real+ and +self.image+ are finite.
* - #hash: Returns the integer hash value for +self+.
* - #imag (and its alias #imaginary): Returns the imaginary value for +self+.
* - #infinite?: Returns whether +self.real+ or +self.image+ is infinite.
* - #numerator: Returns the numerator of +self+.
* - #polar: Returns the array <tt>[self.abs, self.arg]</tt>.
* - #inspect: Returns a string representation of +self+.
* - #real: Returns the real value for +self+.
* - #real?: Returns +false+; for compatibility with Numeric#real?.
* - #rect (and its alias #rectangular):
* Returns the array <tt>[self.real, self.imag]</tt>.
*
* === Comparing
*
* - #<=>: Returns whether +self+ is less than, equal to, or greater than the given argument.
* - #==: Returns whether +self+ is equal to the given argument.
*
* === Converting
*
* - #rationalize: Returns a Rational object whose value is exactly
* or approximately equivalent to that of <tt>self.real</tt>.
* - #to_c: Returns +self+.
* - #to_d: Returns the value as a BigDecimal object.
* - #to_f: Returns the value of <tt>self.real</tt> as a Float, if possible.
* - #to_i: Returns the value of <tt>self.real</tt> as an Integer, if possible.
* - #to_r: Returns the value of <tt>self.real</tt> as a Rational, if possible.
* - #to_s: Returns a string representation of +self+.
*
* === Performing Complex Arithmetic
*
* - #*: Returns the product of +self+ and the given numeric.
* - #**: Returns +self+ raised to power of the given numeric.
* - #+: Returns the sum of +self+ and the given numeric.
* - #-: Returns the difference of +self+ and the given numeric.
* - #-@: Returns the negation of +self+.
* - #/: Returns the quotient of +self+ and the given numeric.
* - #abs2: Returns square of the absolute value (magnitude) for +self+.
* - #conj (and its alias #conjugate): Returns the conjugate of +self+.
* - #fdiv: Returns <tt>Complex.rect(self.real/numeric, self.imag/numeric)</tt>.
*
* === Working with JSON
*
* - ::json_create: Returns a new \Complex object,
* deserialized from the given serialized hash.
* - #as_json: Returns a serialized hash constructed from +self+.
* - #to_json: Returns a JSON string representing +self+.
*
* These methods are provided by the {JSON gem}[https://github.com/flori/json]. To make these methods available:
*
* require 'json/add/complex'
*
*/
void
Init_Complex(void)
{
VALUE compat;
id_abs = rb_intern_const("abs");
id_arg = rb_intern_const("arg");
id_denominator = rb_intern_const("denominator");
id_numerator = rb_intern_const("numerator");
id_real_p = rb_intern_const("real?");
id_i_real = rb_intern_const("@real");
id_i_imag = rb_intern_const("@image"); /* @image, not @imag */
id_finite_p = rb_intern_const("finite?");
id_infinite_p = rb_intern_const("infinite?");
id_rationalize = rb_intern_const("rationalize");
id_PI = rb_intern_const("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, RCLASS_ORIGIN(rb_mComparable));
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, "<=>", nucomp_cmp, 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_real_p_m, 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);
/* :nodoc: */
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, "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_cFloat, "arg", float_arg, 0);
rb_define_method(rb_cFloat, "angle", float_arg, 0);
rb_define_method(rb_cFloat, "phase", float_arg, 0);
/*
* Equivalent
* to <tt>Complex.rect(0, 1)</tt>:
*
* Complex::I # => (0+1i)
*
*/
rb_define_const(rb_cComplex, "I",
f_complex_new_bang2(rb_cComplex, ZERO, ONE));
#if !USE_FLONUM
rb_vm_register_global_object(RFLOAT_0 = DBL2NUM(0.0));
#endif
rb_provide("complex.so"); /* for backward compatibility */
}
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