/* :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 LONG2FIX(v);
}
/* :nodoc: */
static VALUE
nurat_hash(VALUE self, SEL sel)
{
long v, h[2];
VALUE n;
get_dat1(self);
n = rb_hash(dat->num);
h[0] = NUM2LONG(n);
n = rb_hash(dat->den);
h[1] = NUM2LONG(n);
v = rb_memhash(h, sizeof(h));
return LONG2FIX(v);
}
/*
* 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 = f_denominator(self);
return f_complex_new2(CLASS_OF(self),
f_mul(f_numerator(dat->real),
f_div(cd, f_denominator(dat->real))),
f_mul(f_numerator(dat->imag),
f_div(cd, f_denominator(dat->imag))));
}
static VALUE
m_sin(VALUE x)
{
if (f_real_p(x))
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)));
}
}
inline static VALUE
nucomp_s_canonicalize_internal(VALUE klass, VALUE real, VALUE imag)
{
#ifdef CANON
#define CL_CANON
#ifdef CL_CANON
if (k_exact_zero_p(imag) && canonicalization)
return real;
#else
if (f_zero_p(imag) && canonicalization)
return real;
#endif
#endif
if (f_real_p(real) && f_real_p(imag))
return nucomp_s_new_internal(klass, real, imag);
else if (f_real_p(real)) {
get_dat1(imag);
return nucomp_s_new_internal(klass,
f_sub(real, dat->imag),
f_add(ZERO, dat->real));
}
else if (f_real_p(imag)) {
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:
* 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 (k_complex_p(other)) {
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_eqeq_p(other, self);
}
static VALUE
nurat_round(VALUE self)
{
get_dat1(self);
if (f_negative_p(dat->num)) {
VALUE num, den;
num = f_negate(dat->num);
num = f_add(f_mul(num, TWO), dat->den);
den = f_mul(dat->den, TWO);
return f_negate(f_idiv(num, den));
}
else {
VALUE num = f_add(f_mul(dat->num, TWO), dat->den);
VALUE den = f_mul(dat->den, TWO);
return f_idiv(num, den);
}
}
static VALUE
f_format(VALUE self, VALUE (*func)(VALUE))
{
VALUE s, 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.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
*/
static VALUE
nucomp_abs(VALUE self)
{
get_dat1(self);
if (f_zero_p(dat->real)) {
VALUE a = f_abs(dat->imag);
if (k_float_p(dat->real) && !k_float_p(dat->imag))
a = f_to_f(a);
return a;
}
if (f_zero_p(dat->imag)) {
VALUE a = f_abs(dat->real);
if (!k_float_p(dat->real) && k_float_p(dat->imag))
a = f_to_f(a);
return a;
}
return m_hypot(dat->real, dat->imag);
}
static VALUE
nucomp_sub(VALUE self, VALUE other)
{
if (k_complex_p(other)) {
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
m_sqrt(VALUE x)
{
if (f_real_p(x)) {
if (f_positive_p(x))
return m_sqrt_bang(x);
return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x)));
}
else {
get_dat1(x);
if (f_negative_p(dat->imag))
return f_conj(m_sqrt(f_conj(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)));
}
}
}
inline static VALUE
f_addsub(VALUE self, VALUE other,
VALUE (*func)(VALUE, VALUE), ID id)
{
if (k_complex_p(other)) {
VALUE real, imag;
get_dat2(self, other);
real = (*func)(adat->real, bdat->real);
imag = (*func)(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),
(*func)(dat->real, other), dat->imag);
}
return rb_num_coerce_bin(self, other, id);
}
static VALUE
nurat_round(VALUE self, SEL sel)
{
VALUE num, den, neg;
get_dat1(self);
num = dat->num;
den = dat->den;
neg = f_negative_p(num);
if (neg)
num = f_negate(num);
num = f_add(f_mul(num, TWO), den);
den = f_mul(den, TWO);
num = f_idiv(num, den);
if (neg)
num = f_negate(num);
return num;
}
static VALUE
nurat_cmp(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1)
return f_cmp(dat->num, other);
else
return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other));
}
case T_FLOAT:
return f_cmp(f_to_f(self), other);
case T_RATIONAL:
{
VALUE num1, num2;
get_dat2(self, other);
if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) &&
FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) {
num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den));
num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den));
}
else {
num1 = f_mul(adat->num, bdat->den);
num2 = f_mul(bdat->num, adat->den);
}
return f_cmp(f_sub(num1, num2), ZERO);
}
default:
return rb_num_coerce_bin(self, other, id_cmp);
}
}
/*
* call-seq:
* rat == object -> true or false
*
* Returns true if rat equals object numerically.
*
* For example:
*
* Rational(2, 3) == Rational(2, 3) #=> true
* Rational(5) == 5 #=> true
* Rational(0) == 0.0 #=> true
* Rational('1/3') == 0.33 #=> false
* Rational('1/2') == '1/2' #=> false
*/
static VALUE
nurat_eqeq_p(VALUE self, SEL sel, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
if (f_zero_p(dat->num) && f_zero_p(other))
return Qtrue;
if (!FIXNUM_P(dat->den))
return Qfalse;
if (FIX2LONG(dat->den) != 1)
return Qfalse;
if (f_eqeq_p(dat->num, other))
return Qtrue;
return Qfalse;
}
case T_FLOAT:
return f_eqeq_p(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);
if (f_zero_p(adat->num) && f_zero_p(bdat->num))
return Qtrue;
return f_boolcast(f_eqeq_p(adat->num, bdat->num) &&
f_eqeq_p(adat->den, bdat->den));
}
default:
return f_eqeq_p(other, self);
}
}
/*
* call-seq:
* cmp.imag -> real
* cmp.imaginary -> real
*
* Returns the imaginary part.
*
* Complex(7).imaginary #=> 0
* Complex(9, -4).imaginary #=> -4
*/
static VALUE
nucomp_imag(VALUE self)
{
get_dat1(self);
return dat->imag;
}
/*
* call-seq:
* cmp.real -> real
*
* Returns the real part.
*
* Complex(7).real #=> 7
* Complex(9, -4).real #=> 9
*/
static VALUE
nucomp_real(VALUE self)
{
get_dat1(self);
return dat->real;
}
static VALUE
nucomp_s_convert(int argc, VALUE *argv, VALUE klass)
{
VALUE a1, a2, backref;
rb_scan_args(argc, argv, "11", &a1, &a2);
if (NIL_P(a1) || (argc == 2 && NIL_P(a2)))
rb_raise(rb_eTypeError, "can't convert nil into Complex");
backref = rb_backref_get();
rb_match_busy(backref);
if (RB_TYPE_P(a1, T_STRING)) {
a1 = string_to_c_strict(a1);
}
if (RB_TYPE_P(a2, T_STRING)) {
a2 = string_to_c_strict(a2);
}
rb_backref_set(backref);
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 (argc == 1 || (k_exact_zero_p(a2)))
return a1;
}
if (argc == 1) {
if (k_numeric_p(a1) && !f_real_p(a1))
return a1;
/* should raise exception for consistency */
if (!k_numeric_p(a1))
return rb_convert_type(a1, T_COMPLEX, "Complex", "to_c");
}
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)));
}
{
VALUE argv2[2];
argv2[0] = a1;
argv2[1] = a2;
return nucomp_s_new(argc, argv2, klass);
}
}
/*
* call-seq:
* rat.denominator -> integer
*
* Returns the denominator (always positive).
*
* For example:
*
* Rational(7).denominator #=> 1
* Rational(7, 1).denominator #=> 1
* Rational(9, -4).denominator #=> 4
* Rational(-2, -10).denominator #=> 5
* rat.numerator.gcd(rat.denominator) #=> 1
*/
static VALUE
nurat_denominator(VALUE self, SEL sel)
{
get_dat1(self);
return dat->den;
}
/* :nodoc: */
static VALUE
nucomp_exact_p(VALUE self)
{
get_dat1(self);
return f_boolcast(k_exact_p(dat->real) && k_exact_p(dat->imag));
}
/*
* call-seq:
* cmp.conj -> complex
* cmp.conjugate -> complex
*
* Returns the complex conjugate.
*
* Complex(1, 2).conjugate #=> (1-2i)
*/
static VALUE
nucomp_conj(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}
/*
* 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);
}
static VALUE
nurat_ceil(VALUE self, SEL sel)
{
get_dat1(self);
return f_negate(f_idiv(f_negate(dat->num), dat->den));
}
/*
* call-seq:
* rat.to_f -> float
*
* Return the value as a float.
*
* For example:
*
* Rational(2).to_f #=> 2.0
* Rational(9, 4).to_f #=> 2.25
* Rational(-3, 4).to_f #=> -0.75
* Rational(20, 3).to_f #=> 6.666666666666667
*/
static VALUE
nurat_to_f(VALUE self, SEL sel)
{
get_dat1(self);
return f_fdiv(dat->num, dat->den);
}
VALUE
rb_rational_reciprocal(VALUE x, SEL sel)
{
get_dat1(x);
return f_rational_new_no_reduce2(CLASS_OF(x), dat->den, dat->num);
}
/*
* 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 ** numeric -> complex
*
* Performs exponentiation.
*
* Complex('i') ** 2 #=> (-1+0i)
* Complex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i)
*/
static VALUE
nucomp_expt(VALUE self, VALUE other)
{
if (k_numeric_p(other) && k_exact_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); /* c14n */
if (k_complex_p(other)) {
get_dat1(other);
if (k_exact_zero_p(dat->imag))
other = dat->real; /* c14n */
}
if (k_complex_p(other)) {
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 (k_fixnum_p(other)) {
if (f_gt_p(other, ZERO)) {
VALUE x, z;
long n;
x = self;
z = x;
n = FIX2LONG(other) - 1;
while (n) {
long q, r;
while (1) {
get_dat1(x);
q = n / 2;
r = n % 2;
if (r)
break;
x = nucomp_s_new_internal(CLASS_OF(self),
f_sub(f_mul(dat->real, dat->real),
f_mul(dat->imag, dat->imag)),
f_mul(f_mul(TWO, dat->real), dat->imag));
n = q;
}
z = f_mul(z, x);
n--;
}
return z;
}
return f_expt(f_reciprocal(self), f_negate(other));
}
if (k_numeric_p(other) && f_real_p(other)) {
VALUE r, theta;
if (k_bignum_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);
}
static VALUE
nurat_floor(VALUE self, SEL sel)
{
get_dat1(self);
return f_idiv(dat->num, dat->den);
}
/*
* 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
*/
static VALUE
nucomp_arg(VALUE self)
{
get_dat1(self);
return m_atan2_bang(dat->imag, dat->real);
}
/*
* call-seq:
* rat.numerator -> integer
*
* Returns the numerator.
*
* For example:
*
* Rational(7).numerator #=> 7
* Rational(7, 1).numerator #=> 7
* Rational(9, -4).numerator #=> -9
* Rational(-2, -10).numerator #=> 1
*/
static VALUE
nurat_numerator(VALUE self, SEL sel)
{
get_dat1(self);
return dat->num;
}
