/*
* call-seq:
* rat ** numeric -> numeric_result
*
* Performs exponentiation.
*
* For example:
*
* Rational(2) ** Rational(3) #=> (8/1)
* Rational(10) ** -2 #=> (1/100)
* Rational(10) ** -2.0 #=> 0.01
* Rational(-4) ** Rational(1,2) #=> (1.2246063538223773e-16+2.0i)
* Rational(1, 2) ** 0 #=> (1/1)
* Rational(1, 2) ** 0.0 #=> 1.0
*/
static VALUE
nurat_expt(VALUE self, SEL sel, VALUE other)
{
if (k_exact_zero_p(other))
return f_rational_new_bang1(CLASS_OF(self), ONE);
if (k_rational_p(other)) {
get_dat1(other);
if (f_one_p(dat->den))
other = dat->num; /* c14n */
}
switch (TYPE(other)) {
case T_FIXNUM:
{
VALUE num, den;
get_dat1(self);
switch (FIX2INT(f_cmp(other, ZERO))) {
case 1:
num = f_expt(dat->num, other);
den = f_expt(dat->den, other);
break;
case -1:
num = f_expt(dat->den, f_negate(other));
den = f_expt(dat->num, f_negate(other));
break;
default:
num = ONE;
den = ONE;
break;
}
return f_rational_new2(CLASS_OF(self), num, den);
}
case T_BIGNUM:
rb_warn("in a**b, b may be too big");
/* fall through */
case T_FLOAT:
case T_RATIONAL:
return f_expt(f_to_f(self), other);
default:
return rb_num_coerce_bin(self, other, id_expt);
}
}
/* :nodoc: */
static VALUE
nurat_coerce(VALUE self, SEL sel, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self);
case T_FLOAT:
return rb_assoc_new(other, f_to_f(self));
case T_RATIONAL:
return rb_assoc_new(other, self);
case T_COMPLEX:
if (k_exact_zero_p(RCOMPLEX(other)->imag))
return rb_assoc_new(f_rational_new_bang1
(CLASS_OF(self), RCOMPLEX(other)->real), self);
}
rb_raise(rb_eTypeError, "%s can't be coerced into %s",
rb_obj_classname(other), rb_obj_classname(self));
return Qnil;
}
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 ** 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
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);
}
}
static VALUE
nurat_s_convert(VALUE klass, SEL sel, int argc, VALUE *argv)
{
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 Rational");
switch (TYPE(a1)) {
case T_COMPLEX:
if (k_exact_zero_p(RCOMPLEX(a1)->imag))
a1 = RCOMPLEX(a1)->real;
}
switch (TYPE(a2)) {
case T_COMPLEX:
if (k_exact_zero_p(RCOMPLEX(a2)->imag))
a2 = RCOMPLEX(a2)->real;
}
backref = rb_backref_get();
rb_match_busy(backref);
switch (TYPE(a1)) {
case T_FIXNUM:
case T_BIGNUM:
break;
case T_FLOAT:
a1 = f_to_r(a1);
break;
case T_STRING:
a1 = string_to_r_strict(a1);
break;
}
switch (TYPE(a2)) {
case T_FIXNUM:
case T_BIGNUM:
break;
case T_FLOAT:
a2 = f_to_r(a2);
break;
case T_STRING:
a2 = string_to_r_strict(a2);
break;
}
rb_backref_set(backref);
switch (TYPE(a1)) {
case T_RATIONAL:
if (argc == 1 || (k_exact_one_p(a2)))
return a1;
}
if (argc == 1) {
if (!(k_numeric_p(a1) && k_integer_p(a1)))
return rb_convert_type(a1, T_RATIONAL, "Rational", "to_r");
}
else {
if ((k_numeric_p(a1) && k_numeric_p(a2)) &&
(!f_integer_p(a1) || !f_integer_p(a2)))
return f_div(a1, a2);
}
{
VALUE argv2[2];
argv2[0] = a1;
argv2[1] = a2;
return nurat_s_new(argc, argv2, klass);
}
}
