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ruby/complex.c

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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 "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_RAW((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)
{
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);
}
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;
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]) -> complex
* Complex.rectangular(real[, imag]) -> complex
*
* Returns a complex object which denotes the given rectangular form.
*
* Complex.rectangular(1, 2) #=> (1+2i)
*/
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(x[, y], exception: true) -> numeric or nil
*
* Returns x+i*y;
*
* Complex(1, 2) #=> (1+2i)
* Complex('1+2i') #=> (1+2i)
* Complex(nil) #=> TypeError
* Complex(1, nil) #=> TypeError
*
* Complex(1, nil, exception: false) #=> nil
* Complex('1+2', exception: false) #=> nil
*
* Syntax of string form:
*
* string form = extra spaces , complex , extra spaces ;
* complex = real part | [ sign ] , imaginary part
* | real part , sign , imaginary part
* | rational , "@" , rational ;
* real part = rational ;
* imaginary part = imaginary unit | unsigned rational , imaginary unit ;
* rational = [ sign ] , unsigned rational ;
* unsigned rational = numerator | numerator , "/" , denominator ;
* numerator = integer part | fractional part | integer part , fractional part ;
* denominator = digits ;
* integer part = digits ;
* fractional part = "." , digits , [ ( "e" | "E" ) , [ sign ] , digits ] ;
* imaginary unit = "i" | "I" | "j" | "J" ;
* sign = "-" | "+" ;
* digits = digit , { digit | "_" , digit };
* digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
* extra spaces = ? \s* ? ;
*
* See String#to_c.
*/
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]) -> complex
*
* Returns a complex object which denotes the given polar form.
*
* Complex.polar(3, 0) #=> (3.0+0.0i)
* Complex.polar(3, Math::PI/2) #=> (1.836909530733566e-16+3.0i)
* Complex.polar(3, Math::PI) #=> (-3.0+3.673819061467132e-16i)
* Complex.polar(3, -Math::PI/2) #=> (1.836909530733566e-16-3.0i)
*/
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:
* cmp.real -> real
*
* Returns the real part.
*
* Complex(7).real #=> 7
* Complex(9, -4).real #=> 9
*/
VALUE
rb_complex_real(VALUE self)
{
get_dat1(self);
return dat->real;
}
/*
* call-seq:
* cmp.imag -> real
* cmp.imaginary -> real
*
* Returns the imaginary part.
*
* Complex(7).imaginary #=> 0
* Complex(9, -4).imaginary #=> -4
*/
VALUE
rb_complex_imag(VALUE self)
{
get_dat1(self);
return dat->imag;
}
/*
* call-seq:
* -cmp -> complex
*
* Returns negation of the value.
*
* -Complex(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:
* cmp + numeric -> complex
*
* Performs addition.
*
* Complex(2, 3) + Complex(2, 3) #=> (4+6i)
* Complex(900) + Complex(1) #=> (901+0i)
* Complex(-2, 9) + Complex(-9, 2) #=> (-11+11i)
* Complex(9, 8) + 4 #=> (13+8i)
* Complex(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:
* cmp - numeric -> complex
*
* Performs subtraction.
*
* Complex(2, 3) - Complex(2, 3) #=> (0+0i)
* Complex(900) - Complex(1) #=> (899+0i)
* Complex(-2, 9) - Complex(-9, 2) #=> (7+7i)
* Complex(9, 8) - 4 #=> (5+8i)
* Complex(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:
* cmp * numeric -> complex
*
* Performs multiplication.
*
* Complex(2, 3) * Complex(2, 3) #=> (-5+12i)
* Complex(900) * Complex(1) #=> (900+0i)
* Complex(-2, 9) * Complex(-9, 2) #=> (0-85i)
* Complex(9, 8) * 4 #=> (36+32i)
* Complex(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:
* cmp / numeric -> complex
* cmp.quo(numeric) -> complex
*
* Performs division.
*
* Complex(2, 3) / Complex(2, 3) #=> ((1/1)+(0/1)*i)
* Complex(900) / Complex(1) #=> ((900/1)+(0/1)*i)
* Complex(-2, 9) / Complex(-9, 2) #=> ((36/85)-(77/85)*i)
* Complex(9, 8) / 4 #=> ((9/4)+(2/1)*i)
* Complex(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:
* cmp.fdiv(numeric) -> complex
*
* Performs division as each part is a float, never returns a float.
*
* Complex(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;
}
if (x == Qundef) 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:
* cmp ** numeric -> complex
*
* Performs exponentiation.
*
* Complex('i') ** 2 #=> (-1+0i)
* Complex(-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 (result != Qundef) 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:
* cmp == object -> true or false
*
* Returns true if cmp equals object numerically.
*
* Complex(2, 3) == Complex(2, 3) #=> true
* Complex(5) == 5 #=> true
* Complex(0) == 0.0 #=> true
* Complex('1/3') == 0.33 #=> false
* Complex('1/2') == '1/2' #=> false
*/
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:
* cmp <=> object -> 0, 1, -1, or nil
*
* If +cmp+'s imaginary part is zero, and +object+ is also a
* real number (or a Complex number where the imaginary part is zero),
* compare the real part of +cmp+ to object. Otherwise, return nil.
*
* Complex(2, 3) <=> Complex(2, 3) #=> nil
* Complex(2, 3) <=> 1 #=> nil
* Complex(2) <=> 1 #=> 1
* Complex(2) <=> 2 #=> 0
* Complex(2) <=> 3 #=> -1
*/
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:
* cmp.abs -> real
* cmp.magnitude -> real
*
* Returns the absolute part of its polar form.
*
* Complex(-1).abs #=> 1
* Complex(3.0, -4.0).abs #=> 5.0
*/
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:
* cmp.abs2 -> real
*
* Returns square of the absolute value.
*
* Complex(-1).abs2 #=> 1
* Complex(3.0, -4.0).abs2 #=> 25.0
*/
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:
* cmp.arg -> float
* cmp.angle -> float
* cmp.phase -> float
*
* Returns the angle part of its polar form.
*
* Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966
*/
VALUE
rb_complex_arg(VALUE self)
{
get_dat1(self);
return rb_math_atan2(dat->imag, dat->real);
}
/*
* call-seq:
* cmp.rect -> array
* cmp.rectangular -> array
*
* Returns an array; [cmp.real, cmp.imag].
*
* Complex(1, 2).rectangular #=> [1, 2]
*/
static VALUE
nucomp_rect(VALUE self)
{
get_dat1(self);
return rb_assoc_new(dat->real, dat->imag);
}
/*
* call-seq:
* cmp.polar -> array
*
* Returns an array; [cmp.abs, cmp.arg].
*
* Complex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904]
*/
static VALUE
nucomp_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
/*
* call-seq:
* cmp.conj -> complex
* cmp.conjugate -> complex
*
* Returns the complex conjugate.
*
* Complex(1, 2).conjugate #=> (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:
* Complex(1).real? -> false
* Complex(1, 2).real? -> false
*
* Returns false, even if the complex number has no imaginary part.
*/
static VALUE
nucomp_real_p_m(VALUE self)
{
return Qfalse;
}
/*
* call-seq:
* cmp.denominator -> integer
*
* Returns the denominator (lcm of both denominator - real and imag).
*
* See numerator.
*/
static VALUE
nucomp_denominator(VALUE self)
{
get_dat1(self);
return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
}
/*
* call-seq:
* cmp.numerator -> numeric
*
* Returns the numerator.
*
* 1 2 3+4i <- numerator
* - + -i -> ----
* 2 3 6 <- denominator
*
* c = Complex('1/2+2/3i') #=> ((1/2)+(2/3)*i)
* n = c.numerator #=> (3+4i)
* d = c.denominator #=> 6
* n / d #=> ((1/2)+(2/3)*i)
* Complex(Rational(n.real, d), Rational(n.imag, d))
* #=> ((1/2)+(2/3)*i)
* See 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;
}
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:
* cmp.to_s -> string
*
* Returns the value as a string.
*
* Complex(2).to_s #=> "2+0i"
* Complex('-8/6').to_s #=> "-4/3+0i"
* Complex('1/2i').to_s #=> "0+1/2i"
* Complex(0, Float::INFINITY).to_s #=> "0+Infinity*i"
* Complex(Float::NAN, Float::NAN).to_s #=> "NaN+NaN*i"
*/
static VALUE
nucomp_to_s(VALUE self)
{
return f_format(self, rb_String);
}
/*
* call-seq:
* cmp.inspect -> string
*
* Returns the value as a string for inspection.
*
* Complex(2).inspect #=> "(2+0i)"
* Complex('-8/6').inspect #=> "((-4/3)+0i)"
* Complex('1/2i').inspect #=> "(0+(1/2)*i)"
* Complex(0, Float::INFINITY).inspect #=> "(0+Infinity*i)"
* Complex(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:
* cmp.finite? -> true or false
*
* Returns +true+ if +cmp+'s real and imaginary parts are both finite numbers,
* otherwise returns +false+.
*/
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:
* cmp.infinite? -> nil or 1
*
* Returns +1+ if +cmp+'s real or imaginary part is an infinite number,
* otherwise returns +nil+.
*
* For example:
*
* (1+1i).infinite? #=> nil
* (Float::INFINITY + 1i).infinite? #=> 1
*/
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_RAW(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:
* cmp.to_i -> integer
*
* Returns the value as an integer if possible (the imaginary part
* should be exactly zero).
*
* Complex(1, 0).to_i #=> 1
* Complex(1, 0.0).to_i # RangeError
* Complex(1, 2).to_i # RangeError
*/
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:
* cmp.to_f -> float
*
* Returns the value as a float if possible (the imaginary part should
* be exactly zero).
*
* Complex(1, 0).to_f #=> 1.0
* Complex(1, 0.0).to_f # RangeError
* Complex(1, 2).to_f # RangeError
*/
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:
* cmp.to_r -> rational
*
* Returns the value as a rational if possible (the imaginary part
* should be exactly zero).
*
* Complex(1, 0).to_r #=> (1/1)
* Complex(1, 0.0).to_r # RangeError
* Complex(1, 2).to_r # RangeError
*
* See rationalize.
*/
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);
}
/*
* call-seq:
* cmp.rationalize([eps]) -> rational
*
* Returns the value as a rational if possible (the imaginary part
* should be exactly zero).
*
* Complex(1.0/3, 0).rationalize #=> (1/3)
* Complex(1, 0.0).rationalize # RangeError
* Complex(1, 2).rationalize # RangeError
*
* See 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:
* complex.to_c -> self
*
* Returns self.
*
* Complex(2).to_c #=> (2+0i)
* Complex(-8, 6).to_c #=> (-8+6i)
*/
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:
* num.to_c -> complex
*
* Returns the value as a complex.
*/
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);
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;
}
/*
* call-seq:
* str.to_c -> complex
*
* Returns a complex which denotes the string form. The parser
* ignores leading whitespaces and trailing garbage. Any digit
* sequences can be separated by an underscore. Returns zero for null
* or garbage string.
*
* '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)
* 'ruby'.to_c #=> (0+0i)
*
* Polar form:
* include Math
* "1.0@0".to_c #=> (1+0.0i)
* "1.0@#{PI/2}".to_c #=> (0.0+1i)
* "1.0@#{PI}".to_c #=> (-1+0.0i)
*
* See Kernel.Complex.
*/
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 (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)
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 (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:
* num.abs2 -> real
*
* Returns square of self.
*/
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
/*
* call-seq:
* num.arg -> 0 or float
* num.angle -> 0 or float
* num.phase -> 0 or float
*
* Returns 0 if the value is positive, pi otherwise.
*/
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return DBL2NUM(M_PI);
}
/*
* call-seq:
* num.rect -> array
* num.rectangular -> array
*
* Returns an array; [num, 0].
*/
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
/*
* call-seq:
* num.polar -> array
*
* Returns an array; [num.abs, num.arg].
*/
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:
* flo.arg -> 0 or float
* flo.angle -> 0 or float
* flo.phase -> 0 or float
*
* Returns 0 if the value is positive, 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 number can be represented as a paired real number with
* imaginary unit; a+bi. Where a is real part, b is imaginary part
* and i is imaginary unit. Real a equals complex a+0i
* mathematically.
*
* You can create a \Complex object explicitly with:
*
* - A {complex literal}[rdoc-ref:syntax/literals.rdoc@Complex+Literals].
*
* You can convert certain objects to \Complex objects with:
*
* - \Method #Complex.
*
* Complex object can be created as literal, and also by using
* Kernel#Complex, Complex::rect, Complex::polar or to_c method.
*
* 2+1i #=> (2+1i)
* Complex(1) #=> (1+0i)
* Complex(2, 3) #=> (2+3i)
* Complex.polar(2, 3) #=> (-1.9799849932008908+0.2822400161197344i)
* 3.to_c #=> (3+0i)
*
* You can also create complex object from floating-point numbers or
* strings.
*
* Complex(0.3) #=> (0.3+0i)
* Complex('0.3-0.5i') #=> (0.3-0.5i)
* Complex('2/3+3/4i') #=> ((2/3)+(3/4)*i)
* Complex('1@2') #=> (-0.4161468365471424+0.9092974268256817i)
*
* 0.3.to_c #=> (0.3+0i)
* '0.3-0.5i'.to_c #=> (0.3-0.5i)
* '2/3+3/4i'.to_c #=> ((2/3)+(3/4)*i)
* '1@2'.to_c #=> (-0.4161468365471424+0.9092974268256817i)
*
* A complex object is either an exact or an inexact number.
*
* Complex(1, 1) / 2 #=> ((1/2)+(1/2)*i)
* Complex(1, 1) / 2.0 #=> (0.5+0.5i)
*/
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);
/*
* The imaginary unit.
*/
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"); /* for backward compatibility */
}
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