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ruby--ruby/complex.c
Jeremy Evans 2e551356a7 Make Kernel#{Pathname,BigDecimal,Complex} return argument if given correct type 
This is how Kernel#{Array,String,Float,Integer,Hash,Rational} work.
BigDecimal and Complex instances are always frozen, so this should
not cause backwards compatibility issues for those.  Pathname
instances are not frozen, so potentially this could cause backwards
compatibility issues by not returning a new object.

Based on a patch from Joshua Ballanco, some minor changes by me.

Fixes [Bug #7522]
2019-09-21 16:10:37 -07:00

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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/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 <math.h>
#include "internal.h"
#include "id.h"
#define NDEBUG
#include "ruby_assert.h"
#define ZERO INT2FIX(0)
#define ONE INT2FIX(1)
#define TWO INT2FIX(2)
#if USE_FLONUM
#define RFLOAT_0 DBL2NUM(0)
#else
static VALUE RFLOAT_0;
#endif
#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \
!defined(signbit)
extern int signbit(double);
#endif
VALUE rb_cComplex;
static ID id_abs, id_arg,
id_denominator, id_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 f_boolcast(x) ((x) ? Qtrue : Qfalse)
#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 VALUE 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 int
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 (int)rb_equal(x, ZERO);
}
#define f_nonzero_p(x) (!f_zero_p(x))
VALUE rb_flo_is_finite_p(VALUE num);
inline static int
f_finite_p(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return TRUE;
}
else if (RB_FLOAT_TYPE_P(x)) {
return (int)rb_flo_is_finite_p(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return TRUE;
}
return RTEST(rb_funcallv(x, id_finite_p, 0, 0));
}
VALUE rb_flo_is_infinite_p(VALUE num);
inline static VALUE
f_infinite_p(VALUE x)
{
if (RB_INTEGER_TYPE_P(x)) {
return Qnil;
}
else if (RB_FLOAT_TYPE_P(x)) {
return rb_flo_is_infinite_p(x);
}
else if (RB_TYPE_P(x, T_RATIONAL)) {
return Qnil;
}
return rb_funcallv(x, id_infinite_p, 0, 0);
}
inline static int
f_kind_of_p(VALUE x, VALUE c)
{
return (int)rb_obj_is_kind_of(x, c);
}
inline static int
k_numeric_p(VALUE x)
{
return f_kind_of_p(x, rb_cNumeric);
}
#define k_exact_p(x) (!RB_FLOAT_TYPE_P(x))
#define k_exact_zero_p(x) (k_exact_p(x) && f_zero_p(x))
#define get_dat1(x) \
struct RComplex *dat = RCOMPLEX(x)
#define get_dat2(x,y) \
struct RComplex *adat = RCOMPLEX(x), *bdat = RCOMPLEX(y)
inline static VALUE
nucomp_s_new_internal(VALUE klass, VALUE real, VALUE imag)
{
NEWOBJ_OF(obj, struct RComplex, klass, T_COMPLEX | (RGENGC_WB_PROTECTED_COMPLEX ? FL_WB_PROTECTED : 0));
RCOMPLEX_SET_REAL(obj, real);
RCOMPLEX_SET_IMAG(obj, imag);
OBJ_FREEZE_RAW(obj);
return (VALUE)obj;
}
static VALUE
nucomp_s_alloc(VALUE klass)
{
return nucomp_s_new_internal(klass, ZERO, ZERO);
}
inline static VALUE
f_complex_new_bang1(VALUE klass, VALUE x)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
return nucomp_s_new_internal(klass, x, ZERO);
}
inline static VALUE
f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
assert(!RB_TYPE_P(y, T_COMPLEX));
return nucomp_s_new_internal(klass, x, y);
}
#ifdef CANONICALIZATION_FOR_MATHN
static int canonicalization = 0;
RUBY_FUNC_EXPORTED void
nucomp_canonicalization(int f)
{
canonicalization = f;
}
#else
#define canonicalization 0
#endif
inline static void
nucomp_real_check(VALUE num)
{
if (!RB_INTEGER_TYPE_P(num) &&
!RB_FLOAT_TYPE_P(num) &&
!RB_TYPE_P(num, T_RATIONAL)) {
if (!k_numeric_p(num) || !f_real_p(num))
rb_raise(rb_eTypeError, "not a real");
}
}
inline static VALUE
nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
{
int complex_r, complex_i;
#ifdef CANONICALIZATION_FOR_MATHN
if (k_exact_zero_p(imag) && canonicalization)
return real;
#endif
complex_r = RB_TYPE_P(real, T_COMPLEX);
complex_i = RB_TYPE_P(imag, T_COMPLEX);
if (!complex_r && !complex_i) {
return nucomp_s_new_internal(klass, real, imag);
}
else if (!complex_r) {
get_dat1(imag);
return nucomp_s_new_internal(klass,
f_sub(real, dat->imag),
f_add(ZERO, dat->real));
}
else if (!complex_i) {
get_dat1(real);
return nucomp_s_new_internal(klass,
dat->real,
f_add(dat->imag, imag));
}
else {
get_dat2(real, imag);
return nucomp_s_new_internal(klass,
f_sub(adat->real, bdat->imag),
f_add(adat->imag, bdat->real));
}
}
/*
* 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:
nucomp_real_check(real);
imag = ZERO;
break;
default:
nucomp_real_check(real);
nucomp_real_check(imag);
break;
}
return nucomp_s_canonicalize_internal(klass, real, imag);
}
inline static VALUE
f_complex_new2(VALUE klass, VALUE x, VALUE y)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
return nucomp_s_canonicalize_internal(klass, x, y);
}
static VALUE nucomp_convert(VALUE klass, VALUE a1, VALUE a2, int raise);
static VALUE nucomp_s_convert(int argc, VALUE *argv, VALUE klass);
/*
* 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 && a2 == Qundef) {
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(VALUE klass, VALUE x, VALUE y)
{
assert(!RB_TYPE_P(x, T_COMPLEX));
assert(!RB_TYPE_P(y, T_COMPLEX));
if (f_zero_p(x) || f_zero_p(y)) {
if (canonicalization) return x;
return nucomp_s_new_internal(klass, x, RFLOAT_0);
}
if (RB_FLOAT_TYPE_P(y)) {
const double arg = RFLOAT_VALUE(y);
if (arg == M_PI) {
x = f_negate(x);
if (canonicalization) return x;
y = RFLOAT_0;
}
else if (arg == M_PI_2) {
y = x;
x = RFLOAT_0;
}
else if (arg == M_PI_2+M_PI) {
y = f_negate(x);
x = RFLOAT_0;
}
else if (RB_FLOAT_TYPE_P(x)) {
const double abs = RFLOAT_VALUE(x);
const double real = abs * cos(arg), imag = abs * sin(arg);
x = DBL2NUM(real);
if (canonicalization && imag == 0.0) return x;
y = DBL2NUM(imag);
}
else {
y = f_mul(x, DBL2NUM(sin(arg)));
x = f_mul(x, DBL2NUM(cos(arg)));
if (canonicalization && f_zero_p(y)) return x;
}
return nucomp_s_new_internal(klass, x, y);
}
return nucomp_s_canonicalize_internal(klass,
f_mul(x, m_cos(y)),
f_mul(x, m_sin(y)));
}
/* 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 {
ang *= M_PI;
return rb_complex_new(DBL2NUM(abs * cos(ang)), DBL2NUM(abs * sin(ang)));
}
}
/*
* 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;
switch (rb_scan_args(argc, argv, "11", &abs, &arg)) {
case 1:
nucomp_real_check(abs);
if (canonicalization) return abs;
return nucomp_s_new_internal(klass, abs, ZERO);
default:
nucomp_real_check(abs);
nucomp_real_check(arg);
break;
}
return f_complex_polar(klass, abs, arg);
}
/*
* 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, int az, int bz)
{
double v;
if (!az && bz && RB_FLOAT_TYPE_P(a) && (v = RFLOAT_VALUE(a), !isnan(v))) {
a = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
}
if (!bz && az && RB_FLOAT_TYPE_P(b) && (v = RFLOAT_VALUE(b), !isnan(v))) {
b = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
}
return f_mul(a, b);
}
static void
comp_mul(VALUE areal, VALUE aimag, VALUE breal, VALUE bimag, VALUE *real, VALUE *imag)
{
int arzero = f_zero_p(areal);
int aizero = f_zero_p(aimag);
int brzero = f_zero_p(breal);
int bizero = f_zero_p(bimag);
*real = f_sub(safe_mul(areal, breal, arzero, brzero),
safe_mul(aimag, bimag, aizero, bizero));
*imag = f_add(safe_mul(areal, bimag, arzero, bizero),
safe_mul(aimag, breal, aizero, brzero));
}
/*
* 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);
}
/*
* 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 (RB_TYPE_P(other, T_COMPLEX)) {
VALUE r, theta, nr, ntheta;
get_dat1(other);
r = f_abs(self);
theta = f_arg(self);
nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)),
f_mul(dat->imag, theta)));
ntheta = f_add(f_mul(theta, dat->real),
f_mul(dat->imag, m_log_bang(r)));
return f_complex_polar(CLASS_OF(self), nr, ntheta);
}
if (FIXNUM_P(other)) {
long n = FIX2LONG(other);
if (n == 0) {
return nucomp_s_new_internal(CLASS_OF(self), ONE, ZERO);
}
if (n < 0) {
self = f_reciprocal(self);
other = rb_int_uminus(other);
n = -n;
}
{
get_dat1(self);
VALUE xr = dat->real, xi = dat->imag, zr = xr, zi = xi;
if (f_zero_p(xi)) {
zr = rb_num_pow(zr, other);
}
else if (f_zero_p(xr)) {
zi = rb_num_pow(zi, other);
if (n & 2) zi = f_negate(zi);
if (!(n & 1)) {
VALUE tmp = zr;
zr = zi;
zi = tmp;
}
}
else {
while (--n) {
long q, r;
for (; q = n / 2, r = n % 2, r == 0; n = q) {
VALUE tmp = f_sub(f_mul(xr, xr), f_mul(xi, xi));
xi = f_mul(f_mul(TWO, xr), xi);
xr = tmp;
}
comp_mul(zr, zi, xr, xi, &zr, &zi);
}
}
return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
}
}
if (k_numeric_p(other) && f_real_p(other)) {
VALUE r, theta;
if (RB_TYPE_P(other, T_BIGNUM))
rb_warn("in a**b, b may be too big");
r = f_abs(self);
theta = f_arg(self);
return f_complex_polar(CLASS_OF(self), f_expt(r, other),
f_mul(theta, other));
}
return rb_num_coerce_bin(self, other, id_expt);
}
/*
* 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 f_boolcast(f_eqeq_p(adat->real, bdat->real) &&
f_eqeq_p(adat->imag, bdat->imag));
}
if (k_numeric_p(other) && f_real_p(other)) {
get_dat1(self);
return f_boolcast(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
}
return f_boolcast(f_eqeq_p(other, self));
}
static VALUE
nucomp_real_p(VALUE self)
{
get_dat1(self);
return(f_zero_p(dat->imag) ? Qtrue : Qfalse);
}
/*
* 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 (nucomp_real_p(self) && k_numeric_p(other)) {
if (RB_TYPE_P(other, T_COMPLEX) && nucomp_real_p(other)) {
get_dat2(self, other);
return rb_funcall(adat->real, idCmp, 1, bdat->real);
}
else if (f_real_p(other)) {
get_dat1(self);
return rb_funcall(dat->real, idCmp, 1, other);
}
}
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_false(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: */
static VALUE
nucomp_hash(VALUE self)
{
st_index_t v, h[2];
VALUE n;
get_dat1(self);
n = rb_hash(dat->real);
h[0] = NUM2LONG(n);
n = rb_hash(dat->imag);
h[1] = NUM2LONG(n);
v = rb_memhash(h, sizeof(h));
return ST2FIX(v);
}
/* :nodoc: */
static VALUE
nucomp_eql_p(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
get_dat2(self, other);
return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
(CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
f_eqeq_p(self, other));
}
return Qfalse;
}
inline static int
f_signbit(VALUE x)
{
if (RB_FLOAT_TYPE_P(x)) {
double f = RFLOAT_VALUE(x);
return !isnan(f) && signbit(f);
}
return f_negative_p(x);
}
inline static int
f_tpositive_p(VALUE x)
{
return !f_signbit(x);
}
static VALUE
f_format(VALUE self, VALUE (*func)(VALUE))
{
VALUE s;
int impos;
get_dat1(self);
impos = f_tpositive_p(dat->imag);
s = (*func)(dat->real);
rb_str_cat2(s, !impos ? "-" : "+");
rb_str_concat(s, (*func)(f_abs(dat->imag)));
if (!rb_isdigit(RSTRING_PTR(s)[RSTRING_LEN(s) - 1]))
rb_str_cat2(s, "*");
rb_str_cat2(s, "i");
return s;
}
/*
* 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);
if (f_finite_p(dat->real) && f_finite_p(dat->imag)) {
return Qtrue;
}
return Qfalse;
}
/*
* 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 (NIL_P(f_infinite_p(dat->real)) && NIL_P(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);
}
/*!
* Creates a Complex object.
*
* \param real real part value
* \param imag imaginary part value
* \return a new Complex object
*/
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:
* nil.to_c -> (0+0i)
*
* Returns zero as a complex.
*/
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);
}
#include <ctype.h>
inline static int
issign(int c)
{
return (c == '-' || c == '+');
}
static int
read_sign(const char **s,
char **b)
{
int sign = '?';
if (issign(**s)) {
sign = **b = **s;
(*s)++;
(*b)++;
}
return sign;
}
inline static int
isdecimal(int c)
{
return isdigit((unsigned char)c);
}
static int
read_digits(const char **s, int strict,
char **b)
{
int us = 1;
if (!isdecimal(**s))
return 0;
while (isdecimal(**s) || **s == '_') {
if (**s == '_') {
if (strict) {
if (us)
return 0;
}
us = 1;
}
else {
**b = **s;
(*b)++;
us = 0;
}
(*s)++;
}
if (us)
do {
(*s)--;
} while (**s == '_');
return 1;
}
inline static int
islettere(int c)
{
return (c == 'e' || c == 'E');
}
static int
read_num(const char **s, int strict,
char **b)
{
if (**s != '.') {
if (!read_digits(s, strict, b))
return 0;
}
if (**s == '.') {
**b = **s;
(*s)++;
(*b)++;
if (!read_digits(s, strict, b)) {
(*b)--;
return 0;
}
}
if (islettere(**s)) {
**b = **s;
(*s)++;
(*b)++;
read_sign(s, b);
if (!read_digits(s, strict, b)) {
(*b)--;
return 0;
}
}
return 1;
}
inline static int
read_den(const char **s, int strict,
char **b)
{
if (!read_digits(s, strict, b))
return 0;
return 1;
}
static int
read_rat_nos(const char **s, int strict,
char **b)
{
if (!read_num(s, strict, b))
return 0;
if (**s == '/') {
**b = **s;
(*s)++;
(*b)++;
if (!read_den(s, strict, b)) {
(*b)--;
return 0;
}
}
return 1;
}
static int
read_rat(const char **s, int strict,
char **b)
{
read_sign(s, b);
if (!read_rat_nos(s, strict, b))
return 0;
return 1;
}
inline static int
isimagunit(int c)
{
return (c == 'i' || c == 'I' ||
c == 'j' || c == 'J');
}
static VALUE
str2num(char *s)
{
if (strchr(s, '/'))
return rb_cstr_to_rat(s, 0);
if (strpbrk(s, ".eE"))
return DBL2NUM(rb_cstr_to_dbl(s, 0));
return rb_cstr_to_inum(s, 10, 0);
}
static int
read_comp(const char **s, int strict,
VALUE *ret, char **b)
{
char *bb;
int sign;
VALUE num, num2;
bb = *b;
sign = read_sign(s, b);
if (isimagunit(**s)) {
(*s)++;
num = INT2FIX((sign == '-') ? -1 : + 1);
*ret = rb_complex_new2(ZERO, num);
return 1; /* 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)
*
* 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 (a2 == Qundef || (k_exact_zero_p(a2)))
return a1;
}
if (a2 == Qundef) {
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 (a2 == Qundef) {
argv2[1] = Qnil;
argc = 1;
}
else {
if (!raise && !RB_INTEGER_TYPE_P(a2) && !RB_FLOAT_TYPE_P(a2) && !RB_TYPE_P(a2, T_RATIONAL))
return Qnil;
argv2[1] = a2;
argc = 2;
}
return nucomp_s_new(argc, argv2, klass);
}
}
static VALUE
nucomp_s_convert(int argc, VALUE *argv, VALUE klass)
{
VALUE a1, a2;
if (rb_scan_args(argc, argv, "11", &a1, &a2) == 1) {
a2 = Qundef;
}
return nucomp_convert(klass, a1, a2, TRUE);
}
/* --- */
/*
* call-seq:
* num.real -> self
*
* Returns self.
*/
static VALUE
numeric_real(VALUE self)
{
return self;
}
/*
* call-seq:
* num.imag -> 0
* num.imaginary -> 0
*
* Returns zero.
*/
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
/*
* 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));
}
static VALUE float_arg(VALUE self);
/*
* 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:
* num.conj -> self
* num.conjugate -> self
*
* Returns self.
*/
static VALUE
numeric_conj(VALUE self)
{
return self;
}
/*
* 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.
*
* 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;
#undef rb_intern
#define rb_intern(str) rb_intern_const(str)
id_abs = rb_intern("abs");
id_arg = rb_intern("arg");
id_denominator = rb_intern("denominator");
id_numerator = rb_intern("numerator");
id_real_p = rb_intern("real?");
id_i_real = rb_intern("@real");
id_i_imag = rb_intern("@image"); /* @image, not @imag */
id_finite_p = rb_intern("finite?");
id_infinite_p = rb_intern("infinite?");
id_rationalize = rb_intern("rationalize");
id_PI = rb_intern("PI");
rb_cComplex = rb_define_class("Complex", rb_cNumeric);
rb_define_alloc_func(rb_cComplex, nucomp_s_alloc);
rb_undef_method(CLASS_OF(rb_cComplex), "allocate");
rb_undef_method(CLASS_OF(rb_cComplex), "new");
rb_define_singleton_method(rb_cComplex, "rectangular", nucomp_s_new, -1);
rb_define_singleton_method(rb_cComplex, "rect", nucomp_s_new, -1);
rb_define_singleton_method(rb_cComplex, "polar", nucomp_s_polar, -1);
rb_define_global_function("Complex", nucomp_f_complex, -1);
rb_undef_methods_from(rb_cComplex, rb_mComparable);
rb_undef_method(rb_cComplex, "%");
rb_undef_method(rb_cComplex, "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_false, 0);
rb_define_method(rb_cComplex, "numerator", nucomp_numerator, 0);
rb_define_method(rb_cComplex, "denominator", nucomp_denominator, 0);
rb_define_method(rb_cComplex, "hash", nucomp_hash, 0);
rb_define_method(rb_cComplex, "eql?", nucomp_eql_p, 1);
rb_define_method(rb_cComplex, "to_s", nucomp_to_s, 0);
rb_define_method(rb_cComplex, "inspect", nucomp_inspect, 0);
rb_undef_method(rb_cComplex, "positive?");
rb_undef_method(rb_cComplex, "negative?");
rb_define_method(rb_cComplex, "finite?", rb_complex_finite_p, 0);
rb_define_method(rb_cComplex, "infinite?", rb_complex_infinite_p, 0);
rb_define_private_method(rb_cComplex, "marshal_dump", nucomp_marshal_dump, 0);
/* :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, "real", numeric_real, 0);
rb_define_method(rb_cNumeric, "imaginary", numeric_imag, 0);
rb_define_method(rb_cNumeric, "imag", numeric_imag, 0);
rb_define_method(rb_cNumeric, "abs2", numeric_abs2, 0);
rb_define_method(rb_cNumeric, "arg", numeric_arg, 0);
rb_define_method(rb_cNumeric, "angle", numeric_arg, 0);
rb_define_method(rb_cNumeric, "phase", numeric_arg, 0);
rb_define_method(rb_cNumeric, "rectangular", numeric_rect, 0);
rb_define_method(rb_cNumeric, "rect", numeric_rect, 0);
rb_define_method(rb_cNumeric, "polar", numeric_polar, 0);
rb_define_method(rb_cNumeric, "conjugate", numeric_conj, 0);
rb_define_method(rb_cNumeric, "conj", numeric_conj, 0);
rb_define_method(rb_cFloat, "arg", float_arg, 0);
rb_define_method(rb_cFloat, "angle", float_arg, 0);
rb_define_method(rb_cFloat, "phase", float_arg, 0);
/*
* 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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