static VALUE
f_round_common(int argc, VALUE *argv, VALUE self, VALUE (*func)(VALUE, SEL))
{
VALUE n, b, s;
if (argc == 0)
return (*func)(self, NULL);
rb_scan_args(argc, argv, "01", &n);
if (!k_integer_p(n))
rb_raise(rb_eTypeError, "not an integer");
b = f_expt(INT2FIX(10), n);
s = f_mul(self, b);
s = (*func)(s, NULL);
s = f_div(f_rational_new_bang1(CLASS_OF(self), s), b);
if (f_lt_p(n, ONE))
s = f_to_i(s);
return s;
}
static VALUE
float_to_r(VALUE self)
{
VALUE a = float_decode(self);
return f_mul(RARRAY_AT(a, 0),
f_expt(INT2FIX(FLT_RADIX), RARRAY_AT(a, 1)));
}
/*
* 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);
}
}
static VALUE
float_to_r(VALUE self)
{
VALUE f, n;
float_decode_internal(self, &f, &n);
return f_mul(f, f_expt(INT2FIX(FLT_RADIX), n));
}
/*
* call-seq:
* flt.to_r -> rational
*
* Returns the value as a rational.
*
* NOTE: 0.3.to_r isn't the same as '0.3'.to_r. The latter is
* equivalent to '3/10'.to_r, but the former isn't so.
*
* For example:
*
* 2.0.to_r #=> (2/1)
* 2.5.to_r #=> (5/2)
* -0.75.to_r #=> (-3/4)
* 0.0.to_r #=> (0/1)
*/
static VALUE
float_to_r(VALUE self, SEL sel)
{
VALUE f, n;
float_decode_internal(self, &f, &n);
#if FLT_RADIX == 2
{
long ln = FIX2LONG(n);
if (ln == 0)
return f_to_r(f);
if (ln > 0)
return f_to_r(f_lshift(f, n));
ln = -ln;
return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln)));
}
#else
return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n)));
#endif
}
/*
* 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
string_to_r_internal(VALUE self)
{
VALUE s, m;
s = self;
if (RSTRING_LEN(s) == 0)
return rb_assoc_new(Qnil, self);
m = f_match(rat_pat, s);
if (!NIL_P(m)) {
VALUE v, ifp, exp, ip, fp;
VALUE si = f_aref(m, INT2FIX(1));
VALUE nu = f_aref(m, INT2FIX(2));
VALUE de = f_aref(m, INT2FIX(3));
VALUE re = f_post_match(m);
{
VALUE a;
a = f_split(nu, an_e_pat);
ifp = RARRAY_PTR(a)[0];
if (RARRAY_LEN(a) != 2)
exp = Qnil;
else
exp = RARRAY_PTR(a)[1];
a = f_split(ifp, a_dot_pat);
ip = RARRAY_PTR(a)[0];
if (RARRAY_LEN(a) != 2)
fp = Qnil;
else
fp = RARRAY_PTR(a)[1];
}
v = rb_rational_new1(f_to_i(ip));
if (!NIL_P(fp)) {
char *p = StringValuePtr(fp);
long count = 0;
VALUE l;
while (*p) {
if (rb_isdigit(*p))
count++;
p++;
}
l = f_expt(INT2FIX(10), LONG2NUM(count));
v = f_mul(v, l);
v = f_add(v, f_to_i(fp));
v = f_div(v, l);
}
if (!NIL_P(si) && *StringValuePtr(si) == '-')
v = f_negate(v);
if (!NIL_P(exp))
v = f_mul(v, f_expt(INT2FIX(10), f_to_i(exp)));
#if 0
if (!NIL_P(de) && (!NIL_P(fp) || !NIL_P(exp)))
return rb_assoc_new(v, rb_usascii_str_new2("dummy"));
#endif
if (!NIL_P(de))
v = f_div(v, f_to_i(de));
return rb_assoc_new(v, re);
}
return rb_assoc_new(Qnil, self);
}
static VALUE
nucomp_expt(VALUE self, VALUE other)
{
if (k_exact_p(other) && 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? */
if (k_complex_p(other)) {
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->imag;
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 f_complex_polar(CLASS_OF(self), nr, ntheta);
}
if (k_integer_p(other)) {
if (f_gt_p(other, ZERO)) {
VALUE x, z, n;
x = self;
z = x;
n = f_sub(other, ONE);
while (f_nonzero_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->imag, dat->imag)),
f_mul(f_mul(TWO, dat->real), dat->imag));
n = RARRAY_PTR(a)[0];
}
z = f_mul(z, x);
n = f_sub(n, ONE);
}
return z;
}
return f_expt(f_div(f_to_r(ONE), self), f_negate(other));
}
if (k_numeric_p(other) && f_real_p(other)) {
VALUE a, r, theta;
a = f_polar(self);
r = RARRAY_PTR(a)[0];
theta = RARRAY_PTR(a)[1];
return f_complex_polar(CLASS_OF(self), f_expt(r, other),
f_mul(theta, other));
}
return rb_num_coerce_bin(self, other, id_expt);
}
