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complex.c
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/*
complex.c: Coded by Tadayoshi Funaba 2008
This implementation is based on Keiju Ishitsuka's Complex library
which is written in ruby.
*/
#include "ruby.h"
#include <math.h>
#define NDEBUG
#include <assert.h>
#ifndef COMPLEX_NAME
#define COMPLEX_NAME "Complex"
#endif
#define ZERO INT2FIX(0)
#define ONE INT2FIX(1)
#define TWO INT2FIX(2)
VALUE rb_cComplex;
static ID id_Unify, id_abs, id_abs2, id_arg, id_atan2_bang, id_cmp,
id_conjugate, id_convert, id_cos, id_denominator, id_divmod,
id_equal_p, id_exact_p, id_exp_bang, id_expt, id_floor, id_format,
id_hypot, id_idiv, id_inspect, id_log_bang, id_negate, id_new, id_new_bang,
id_numerator, id_polar, id_quo, id_scalar_p, id_sin, id_sqrt, id_to_f,
id_to_i, id_to_r, id_to_s, id_truncate;
#define f_boolcast(x) ((x) ? Qtrue : Qfalse)
#define binop(n,op) \
inline static VALUE \
f_##n(VALUE x, VALUE y)\
{\
return rb_funcall(x, op, 1, y);\
}
#define fun1(n) \
inline static VALUE \
f_##n(VALUE x)\
{\
return rb_funcall(x, id_##n, 0);\
}
#define fun2(n) \
inline static VALUE \
f_##n(VALUE x, VALUE y)\
{\
return rb_funcall(x, id_##n, 1, y);\
}
#define math1(n) \
inline static VALUE \
m_##n(VALUE x)\
{\
return rb_funcall(rb_mMath, id_##n, 1, x);\
}
#define math2(n) \
inline static VALUE \
m_##n(VALUE x, VALUE y)\
{\
return rb_funcall(rb_mMath, id_##n, 2, x, y);\
}
inline static VALUE
f_add(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(y)) {
if (FIX2LONG(y) == 0)
r = x;
else
r = rb_funcall(x, '+', 1, y);
} else if (FIXNUM_P(x)) {
if (FIX2LONG(x) == 0)
r = y;
else
r = rb_funcall(x, '+', 1, y);
} else
r = rb_funcall(x, '+', 1, y);
return r;
}
inline static VALUE
f_cmp(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y)) {
long c = FIX2LONG(x) - FIX2LONG(y);
if (c > 0)
c = 1;
else if (c < 0)
c = -1;
r = INT2FIX(c);
} else
r = rb_funcall(x, id_cmp, 1, y);
return r;
}
inline static VALUE
f_div(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(y) && FIX2LONG(y) == 1)
r = x;
else
r = rb_funcall(x, '/', 1, y);
return r;
}
inline static VALUE
f_gt_p(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y))
r = f_boolcast(FIX2LONG(x) > FIX2LONG(y));
else
r = rb_funcall(x, '>', 1, y);
return r;
}
inline static VALUE
f_lt_p(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y))
r = f_boolcast(FIX2LONG(x) < FIX2LONG(y));
else
r = rb_funcall(x, '<', 1, y);
return r;
}
binop(mod, '%')
inline static VALUE
f_mul(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(y)) {
long _iy = FIX2LONG(y);
if (_iy == 0) {
if (TYPE(x) == T_FLOAT)
r = rb_float_new(0.0);
else
r = ZERO;
} else if (_iy == 1)
r = x;
else
r = rb_funcall(x, '*', 1, y);
} else if (FIXNUM_P(x)) {
long _ix = FIX2LONG(x);
if (_ix == 0) {
if (TYPE(y) == T_FLOAT)
r = rb_float_new(0.0);
else
r = ZERO;
} else if (_ix == 1)
r = y;
else
r = rb_funcall(x, '*', 1, y);
} else
r = rb_funcall(x, '*', 1, y);
return r;
}
inline static VALUE
f_sub(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(y)) {
if (FIX2LONG(y) == 0)
r = x;
else
r = rb_funcall(x, '-', 1, y);
} else
r = rb_funcall(x, '-', 1, y);
return r;
}
binop(xor, '^')
fun1(abs)
fun1(abs2)
fun1(arg)
fun1(conjugate)
fun1(denominator)
fun1(exact_p)
fun1(floor)
fun1(inspect)
fun1(negate)
fun1(numerator)
fun1(polar)
fun1(scalar_p)
fun1(to_f)
fun1(to_i)
fun1(to_r)
fun1(to_s)
fun1(truncate)
fun2(divmod)
inline static VALUE
f_equal_p(VALUE x, VALUE y)
{
VALUE r;
if (FIXNUM_P(x) && FIXNUM_P(y))
r = f_boolcast(FIX2LONG(x) == FIX2LONG(y));
else
r = rb_funcall(x, id_equal_p, 1, y);
return r;
}
fun2(expt)
fun2(idiv)
fun2(quo)
inline static VALUE
f_negative_p(VALUE x)
{
VALUE r;
if (FIXNUM_P(x))
r = f_boolcast(FIX2LONG(x) < 0);
else
r = rb_funcall(x, '<', 1, ZERO);
return r;
}
inline static VALUE
f_zero_p(VALUE x)
{
VALUE r;
if (FIXNUM_P(x))
r = f_boolcast(FIX2LONG(x) == 0);
else
r = rb_funcall(x, id_equal_p, 1, ZERO);
return r;
}
inline static VALUE
f_one_p(VALUE x)
{
VALUE r;
if (FIXNUM_P(x))
r = f_boolcast(FIX2LONG(x) == 1);
else
r = rb_funcall(x, id_equal_p, 1, ONE);
return r;
}
inline static VALUE
f_kind_of_p(VALUE x, VALUE c)
{
return rb_obj_is_kind_of(x, c);
}
inline static VALUE
k_numeric_p(VALUE x)
{
return f_kind_of_p(x, rb_cNumeric);
}
inline static VALUE
k_integer_p(VALUE x)
{
return f_kind_of_p(x, rb_cInteger);
}
inline static VALUE
k_float_p(VALUE x)
{
return f_kind_of_p(x, rb_cFloat);
}
inline static VALUE
k_rational_p(VALUE x)
{
return f_kind_of_p(x, rb_cRational);
}
inline static VALUE
k_complex_p(VALUE x)
{
return f_kind_of_p(x, rb_cComplex);
}
inline static VALUE
f_generic_p(VALUE x)
{
switch (TYPE(x)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
return Qtrue;
default:
return Qfalse;
}
}
static VALUE
nucomp_s_generic_p(VALUE klass, VALUE x)
{
return f_generic_p(x);
}
#define get_dat1(x) \
struct RComplex *dat;\
dat = ((struct RComplex *)(x))
#define get_dat2(x,y) \
struct RComplex *adat, *bdat;\
adat = ((struct RComplex *)(x));\
bdat = ((struct RComplex *)(y))
inline static VALUE
nucomp_s_new_internal(VALUE klass, VALUE real, VALUE image)
{
NEWOBJ(obj, struct RComplex);
OBJSETUP(obj, klass, T_COMPLEX);
obj->real = real;
obj->image = image;
return (VALUE)obj;
}
static VALUE
nucomp_s_alloc(VALUE klass)
{
return nucomp_s_new_internal(klass, ZERO, ZERO);
}
static VALUE
nucomp_s_new_bang(int argc, VALUE *argv, VALUE klass)
{
VALUE real, image;
switch (rb_scan_args(argc, argv, "11", &real, &image)) {
case 1:
if (!k_numeric_p(real))
real = f_to_i(real);
image = ZERO;
break;
default:
if (!k_numeric_p(real))
real = f_to_i(real);
if (!k_numeric_p(image))
image = f_to_i(image);
break;
}
return nucomp_s_new_internal(klass, real, image);
}
inline static VALUE
f_complex_new_bang1(VALUE klass, VALUE x)
{
return nucomp_s_new_internal(klass, x, ZERO);
}
inline static VALUE
f_complex_new_bang2(VALUE klass, VALUE x, VALUE y)
{
return nucomp_s_new_internal(klass, x, y);
}
#define f_unify_p(klass) rb_const_defined(klass, id_Unify)
inline static void
nucomp_real_check(VALUE num)
{
switch (TYPE(num)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
break;
default:
rb_raise(rb_eArgError, "not a real");
}
}
inline static VALUE
nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE image)
{
#define CL_CANON
#ifdef CL_CANON
if (f_zero_p(image) && f_unify_p(klass) &&
!k_float_p(real) && !k_float_p(image))
return real;
#else
if (f_zero_p(image) && f_unify_p(klass))
return real;
#endif
else if (f_scalar_p(real) && f_scalar_p(image))
return nucomp_s_new_internal(klass, real, image);
else if (f_scalar_p(real)) {
get_dat1(image);
return nucomp_s_new_internal(klass,
f_sub(real, dat->image),
f_add(ZERO, dat->real));
} else if (f_scalar_p(image)) {
get_dat1(real);
return nucomp_s_new_internal(klass,
dat->real,
f_add(dat->image, image));
} else {
get_dat2(real, image);
return nucomp_s_new_internal(klass,
f_sub(adat->real, bdat->image),
f_add(adat->image, bdat->real));
}
}
#if 0
static VALUE
nucomp_s_canonicalize(int argc, VALUE *argv, VALUE klass)
{
VALUE real, image;
switch (rb_scan_args(argc, argv, "11", &real, &image)) {
case 1:
image = ZERO;
break;
}
nucomp_real_check(real);
nucomp_real_check(image);
return nucomp_s_canonicalize_internal(klass, real, image);
}
#endif
static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
{
VALUE real, image;
switch (rb_scan_args(argc, argv, "11", &real, &image)) {
case 1:
image = ZERO;
break;
}
nucomp_real_check(real);
nucomp_real_check(image);
return nucomp_s_canonicalize_internal(klass, real, image);
}
inline static VALUE
f_complex_new1(VALUE klass, VALUE x)
{
assert(!k_complex_p(x));
return nucomp_s_canonicalize_internal(klass, x, ZERO);
}
inline static VALUE
f_complex_new2(VALUE klass, VALUE x, VALUE y)
{
assert(!k_complex_p(x));
return nucomp_s_canonicalize_internal(klass, x, y);
}
static VALUE
nucomp_f_complex(int argc, VALUE *argv, VALUE klass)
{
return rb_funcall2(rb_cComplex, id_convert, argc, argv);
}
extern VALUE math_atan2(VALUE obj, VALUE x, VALUE y);
extern VALUE math_cos(VALUE obj, VALUE x);
extern VALUE math_cosh(VALUE obj, VALUE x);
extern VALUE math_exp(VALUE obj, VALUE x);
extern VALUE math_hypot(VALUE obj, VALUE x, VALUE y);
extern VALUE math_log(int argc, VALUE *argv);
extern VALUE math_sin(VALUE obj, VALUE x);
extern VALUE math_sinh(VALUE obj, VALUE x);
extern VALUE math_sqrt(VALUE obj, VALUE x);
#define m_atan2_bang(x,y) math_atan2(Qnil,x,y)
#define m_cos_bang(x) math_cos(Qnil,x)
#define m_cosh_bang(x) math_cosh(Qnil,x)
#define m_exp_bang(x) math_exp(Qnil,x)
#define m_hypot(x,y) math_hypot(Qnil,x,y)
static VALUE
m_log_bang(VALUE x)
{
return math_log(1, &x);
}
#define m_sin_bang(x) math_sin(Qnil,x)
#define m_sinh_bang(x) math_sinh(Qnil,x)
#define m_sqrt_bang(x) math_sqrt(Qnil,x)
static VALUE
m_cos(VALUE x)
{
get_dat1(x);
if (f_generic_p(x))
return m_cos_bang(x);
else
return f_complex_new2(rb_cComplex,
f_mul(m_cos_bang(dat->real),
m_cosh_bang(dat->image)),
f_mul(f_negate(m_sin_bang(dat->real)),
m_sinh_bang(dat->image)));
}
static VALUE
m_sin(VALUE x)
{
get_dat1(x);
if (f_generic_p(x))
return m_sin_bang(x);
else
return f_complex_new2(rb_cComplex,
f_mul(m_sin_bang(dat->real),
m_cosh_bang(dat->image)),
f_mul(m_cos_bang(dat->real),
m_sinh_bang(dat->image)));
}
static VALUE
m_sqrt(VALUE x)
{
if (f_generic_p(x)) {
if (!f_negative_p(x))
return m_sqrt_bang(x);
else
return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x)));
} else {
get_dat1(x);
if (f_negative_p(dat->image))
return f_conjugate(m_sqrt(f_conjugate(x)));
else {
VALUE a = f_abs(x);
return f_complex_new2(rb_cComplex,
m_sqrt_bang(f_div(f_add(a, dat->real), TWO)),
m_sqrt_bang(f_div(f_sub(a, dat->real), TWO)));
}
}
}
static VALUE
nucomp_s_polar(VALUE klass, VALUE abs, VALUE arg)
{
return f_complex_new2(klass,
f_mul(abs, m_cos(arg)),
f_mul(abs, m_sin(arg)));
}
static VALUE
nucomp_real(VALUE self)
{
get_dat1(self);
return dat->real;
}
static VALUE
nucomp_image(VALUE self)
{
get_dat1(self);
return dat->image;
}
static VALUE
nucomp_add(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_add(dat->real, other), dat->image);
}
case T_COMPLEX:
{
VALUE real, image;
get_dat2(self, other);
real = f_add(adat->real, bdat->real);
image = f_add(adat->image, bdat->image);
return f_complex_new2(CLASS_OF(self), real, image);
}
default:
return rb_num_coerce_bin(self, other, '+');
}
}
static VALUE
nucomp_sub(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_sub(dat->real, other), dat->image);
}
case T_COMPLEX:
{
VALUE real, image;
get_dat2(self, other);
real = f_sub(adat->real, bdat->real);
image = f_sub(adat->image, bdat->image);
return f_complex_new2(CLASS_OF(self), real, image);
}
default:
return rb_num_coerce_bin(self, other, '-');
}
}
static VALUE
nucomp_mul(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_mul(dat->real, other),
f_mul(dat->image, other));
}
case T_COMPLEX:
{
VALUE real, image;
get_dat2(self, other);
real = f_sub(f_mul(adat->real, bdat->real),
f_mul(adat->image, bdat->image));
image = f_add(f_mul(adat->real, bdat->image),
f_mul(adat->image, bdat->real));
return f_complex_new2(CLASS_OF(self), real, image);
}
default:
return rb_num_coerce_bin(self, other, '*');
}
}
static VALUE
nucomp_div(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_div(dat->real, other),
f_div(dat->image, other));
}
case T_COMPLEX:
{
get_dat2(self, other);
if (TYPE(adat->real) == T_FLOAT ||
TYPE(adat->image) == T_FLOAT ||
TYPE(bdat->real) == T_FLOAT ||
TYPE(bdat->image) == T_FLOAT) {
VALUE magn = m_hypot(bdat->real, bdat->image);
VALUE tmp = f_complex_new_bang2(CLASS_OF(self),
f_div(bdat->real, magn),
f_div(bdat->image, magn));
return f_div(f_mul(self, f_conjugate(tmp)), magn);
}
return f_div(f_mul(self, f_conjugate(other)), f_abs2(other));
}
default:
return rb_num_coerce_bin(self, other, '/');
}
}
static VALUE
nucomp_quo(VALUE self, VALUE other)
{
get_dat1(self);
return f_div(f_complex_new2(CLASS_OF(self),
f_quo(dat->real, ONE),
f_quo(dat->image, ONE)), other);
}
static VALUE
nucomp_fdiv(VALUE self, VALUE other)
{
get_dat1(self);
return f_div(f_complex_new2(CLASS_OF(self),
f_to_f(dat->real),
f_to_f(dat->image)), other);
}
static VALUE
nucomp_expt(VALUE self, VALUE other)
{
if (f_zero_p(other))
return f_complex_new_bang1(CLASS_OF(self), ONE);
if (k_rational_p(other) && f_one_p(f_denominator(other)))
other = f_numerator(other); /* good? */
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
if (f_gt_p(other, ZERO)) {
VALUE x, z, n;
x = self;
z = x;
n = f_sub(other, ONE);
while (!f_zero_p(n)) {
VALUE a;
while (a = f_divmod(n, TWO),
f_zero_p(RARRAY_PTR(a)[1])) {
get_dat1(x);
x = f_complex_new2(CLASS_OF(self),
f_sub(f_mul(dat->real, dat->real),
f_mul(dat->image, dat->image)),
f_mul(f_mul(TWO, dat->real), dat->image));
n = RARRAY_PTR(a)[0];
}
z = f_mul(z, x);
n = f_sub(n, ONE);
}
return z;
} else {
return f_expt(f_div(f_to_r(ONE), self), f_negate(other));
}
case T_FLOAT:
case T_RATIONAL:
{
VALUE a, r, theta;
a = f_polar(self);
r = RARRAY_PTR(a)[0];
theta = RARRAY_PTR(a)[1];
return nucomp_s_polar(CLASS_OF(self), f_expt(r, other),
f_mul(theta, other));
}
case T_COMPLEX:
{
VALUE a, r, theta, ore, oim, nr, ntheta;
get_dat1(other);
a = f_polar(self);
r = RARRAY_PTR(a)[0];
theta = RARRAY_PTR(a)[1];
ore = dat->real;
oim = dat->image;
nr = m_exp_bang(f_sub(f_mul(ore, m_log_bang(r)),
f_mul(oim, theta)));
ntheta = f_add(f_mul(theta, ore), f_mul(oim, m_log_bang(r)));
return nucomp_s_polar(CLASS_OF(self), nr, ntheta);
}
default:
return rb_num_coerce_bin(self, other, id_expt);
}
}
static VALUE
nucomp_equal_p(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
{
get_dat1(self);
return f_boolcast(f_equal_p(dat->real, other) && f_zero_p(dat->image));
}
case T_COMPLEX:
{
get_dat2(self, other);
return f_boolcast(f_equal_p(adat->real, bdat->real) &&
f_equal_p(adat->image, bdat->image));
}
default:
return f_equal_p(other, self);
}
}
static VALUE
nucomp_coerce(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
case T_FLOAT:
case T_RATIONAL:
return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
}
rb_raise(rb_eTypeError, "%s can't be coerced into %s",
rb_obj_classname(other), rb_obj_classname(self));
return Qnil;
}
static VALUE
nucomp_abs(VALUE self)
{
get_dat1(self);
return m_hypot(dat->real, dat->image);
}
static VALUE
nucomp_abs2(VALUE self)
{
get_dat1(self);
return f_add(f_mul(dat->real, dat->real),
f_mul(dat->image, dat->image));
}
static VALUE
nucomp_arg(VALUE self)
{
get_dat1(self);
return m_atan2_bang(dat->image, dat->real);
}
static VALUE
nucomp_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
static VALUE
nucomp_conjugate(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->image));
}
#if 0
static VALUE
nucomp_real_p(VALUE self)
{
return Qfalse;
}
static VALUE
nucomp_complex_p(VALUE self)
{
return Qtrue;
}
static VALUE
nucomp_exact_p(VALUE self)
{
get_dat1(self);
return f_boolcast(f_exact_p(dat->real) && f_exact_p(dat->image));
}
static VALUE
nucomp_inexact_p(VALUE self)
{
return f_boolcast(!nucomp_exact_p(self));
}
#endif
extern VALUE rb_lcm(VALUE x, VALUE y);
static VALUE
nucomp_denominator(VALUE self)
{
get_dat1(self);
return rb_lcm(f_denominator(dat->real), f_denominator(dat->image));
}
static VALUE
nucomp_numerator(VALUE self)
{
VALUE cd;
get_dat1(self);
cd = f_denominator(self);
return f_complex_new2(CLASS_OF(self),
f_mul(f_numerator(dat->real),
f_div(cd, f_denominator(dat->real))),
f_mul(f_numerator(dat->image),
f_div(cd, f_denominator(dat->image))));
}
static VALUE
nucomp_hash(VALUE self)
{
get_dat1(self);
return f_xor(dat->real, dat->image);
}
#ifndef HAVE_SIGNBIT
#ifdef signbit
#define HAVE_SIGNBIT 1
#endif
#endif
inline static VALUE
f_signbit(VALUE x)
{
switch (TYPE(x)) {
case T_FLOAT:
#ifdef HAVE_SIGNBIT
return f_boolcast(signbit(RFLOAT_VALUE(x)));
#else
{
char s[2];
(void)snprintf(s, sizeof s, "%.0f", RFLOAT_VALUE(x));
return f_boolcast(s[0] == '-');
}
#endif
}
return f_negative_p(x);
}
inline static VALUE
f_tzero_p(VALUE x)
{
return f_boolcast(f_zero_p(x) && !f_signbit(x));
}
inline static VALUE
f_tpositive_p(VALUE x)
{
return f_boolcast(!f_signbit(x));
}
static VALUE
nucomp_to_s(VALUE self)
{
VALUE s, rezero, impos;
get_dat1(self);
rezero = f_tzero_p(dat->real);
impos = f_tpositive_p(dat->image);
if (rezero)
s = rb_str_new2("");
else {
s = f_to_s(dat->real);
rb_str_cat2(s, !impos ? "-" : "+");
}
if (k_rational_p(dat->image) &&
!f_one_p(f_denominator(dat->image))) {
rb_str_cat2(s, "(");
rb_str_concat(s, f_to_s(rezero ? dat->image : f_abs(dat->image)));
rb_str_cat2(s, ")i");
} else {
rb_str_concat(s, f_to_s(rezero ? dat->image : f_abs(dat->image)));
rb_str_cat2(s, "i");
}
return s;
}
static VALUE