static VALUE
rb_hack_rshift (VALUE x, VALUE y)
{
if ( rb_obj_is_carray(y) ) {
#if RUBY_VERSION_CODE >= 190
return rb_num_coerce_bin(x, y, rb_intern(">>"));
#else
return rb_num_coerce_bin(x, y);
#endif
}
else {
return rb_funcall(x, id___rshift__, 1, y);
}
}
/*
* call-seq:
* onum / integer -> oranumber
* onum / numeric -> numeric
*
* Returns the result of dividing <i>onum</i> by <i>other</i>.
*/
static VALUE onum_div(VALUE lhs, VALUE rhs)
{
OCIError *errhp = oci8_errhp;
OCINumber n;
OCINumber r;
boolean is_zero;
switch (rboci8_type(rhs)) {
case T_FIXNUM:
if (rhs == INT2FIX(0)) {
rb_num_zerodiv();
}
case T_BIGNUM:
if (set_oci_number_from_num(&n, rhs, 0, errhp)) {
chkerr(OCINumberDiv(errhp, _NUMBER(lhs), &n, &r));
return oci8_make_ocinumber(&r, errhp);
}
break;
case RBOCI8_T_ORANUMBER:
chkerr(OCINumberIsZero(errhp, _NUMBER(rhs), &is_zero));
if (is_zero) {
rb_num_zerodiv();
}
chkerr(OCINumberDiv(errhp, _NUMBER(lhs), _NUMBER(rhs), &r));
return oci8_make_ocinumber(&r, errhp);
case T_FLOAT:
return rb_funcall(onum_to_f(lhs), oci8_id_div_op, 1, rhs);
case RBOCI8_T_RATIONAL:
return rb_funcall(onum_to_r(lhs), oci8_id_div_op, 1, rhs);
case RBOCI8_T_BIGDECIMAL:
return rb_funcall(onum_to_d(lhs), oci8_id_div_op, 1, rhs);
}
return rb_num_coerce_bin(lhs, rhs, oci8_id_div_op);
}
/*
* call-seq:
* onum * other -> number
*
* Returns the product of <i>onum</i> and <i>other</i>.
*/
static VALUE onum_mul(VALUE lhs, VALUE rhs)
{
OCIError *errhp = oci8_errhp;
OCINumber n;
OCINumber r;
switch (rboci8_type(rhs)) {
case T_FIXNUM:
case T_BIGNUM:
if (set_oci_number_from_num(&n, rhs, 0, errhp)) {
chkerr(OCINumberMul(errhp, _NUMBER(lhs), &n, &r));
return oci8_make_ocinumber(&r, errhp);
}
break;
case RBOCI8_T_ORANUMBER:
chkerr(OCINumberMul(errhp, _NUMBER(lhs), _NUMBER(rhs), &r));
return oci8_make_ocinumber(&r, errhp);
case T_FLOAT:
return rb_funcall(onum_to_f(lhs), oci8_id_mul_op, 1, rhs);
case RBOCI8_T_RATIONAL:
return rb_funcall(onum_to_r(lhs), oci8_id_mul_op, 1, rhs);
case RBOCI8_T_BIGDECIMAL:
return rb_funcall(onum_to_d(lhs), oci8_id_mul_op, 1, rhs);
}
return rb_num_coerce_bin(lhs, rhs, oci8_id_mul_op);
}
static VALUE
nucomp_div(VALUE self, VALUE other)
{
if (k_complex_p(other)) {
get_dat2(self, other);
if (TYPE(adat->real) == T_FLOAT ||
TYPE(adat->imag) == T_FLOAT ||
TYPE(bdat->real) == T_FLOAT ||
TYPE(bdat->imag) == T_FLOAT) {
VALUE magn = m_hypot(bdat->real, bdat->imag);
VALUE tmp = f_complex_new_bang2(CLASS_OF(self),
f_div(bdat->real, magn),
f_div(bdat->imag, magn));
return f_div(f_mul(self, f_conj(tmp)), magn);
}
return f_div(f_mul(self, f_conj(other)), f_abs2(other));
}
if (k_numeric_p(other) && f_real_p(other)) {
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_div(dat->real, other),
f_div(dat->imag, other));
}
return rb_num_coerce_bin(self, other, '/');
}
/*
* call-seq:
* rat * numeric -> numeric_result
*
* Performs multiplication.
*
* For example:
*
* Rational(2, 3) * Rational(2, 3) #=> (4/9)
* Rational(900) * Rational(1) #=> (900/1)
* Rational(-2, 9) * Rational(-9, 2) #=> (1/1)
* Rational(9, 8) * 4 #=> (9/2)
* Rational(20, 9) * 9.8 #=> 21.77777777777778
*/
static VALUE
nurat_mul(VALUE self, SEL sel, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);
return f_muldiv(self,
dat->num, dat->den,
other, ONE, '*');
}
case T_FLOAT:
return f_mul(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);
return f_muldiv(self,
adat->num, adat->den,
bdat->num, bdat->den, '*');
}
default:
return rb_num_coerce_bin(self, other, '*');
}
}
/*
* 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_nucomp_mul(VALUE self, VALUE other)
{
if (k_complex_p(other)) {
VALUE real, imag;
VALUE areal, aimag, breal, bimag;
int arzero, aizero, brzero, bizero;
get_dat2(self, other);
arzero = !!f_zero_p(areal = adat->real);
aizero = !!f_zero_p(aimag = adat->imag);
brzero = !!f_zero_p(breal = bdat->real);
bizero = !!f_zero_p(bimag = bdat->imag);
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));
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, '*');
}
/*
* call-seq:
* rat / numeric -> numeric_result
* rat.quo(numeric) -> numeric_result
*
* Performs division.
*
* For example:
*
* Rational(2, 3) / Rational(2, 3) #=> (1/1)
* Rational(900) / Rational(1) #=> (900/1)
* Rational(-2, 9) / Rational(-9, 2) #=> (4/81)
* Rational(9, 8) / 4 #=> (9/32)
* Rational(20, 9) / 9.8 #=> 0.22675736961451246
*/
static VALUE
nurat_div(VALUE self, SEL sel, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
if (f_zero_p(other))
rb_raise_zerodiv();
{
get_dat1(self);
return f_muldiv(self,
dat->num, dat->den,
other, ONE, '/');
}
case T_FLOAT:
return rb_funcall(f_to_f(self), '/', 1, other);
case T_RATIONAL:
if (f_zero_p(other))
rb_raise_zerodiv();
{
get_dat2(self, other);
if (f_one_p(self))
return f_rational_new_no_reduce2(CLASS_OF(self),
bdat->den, bdat->num);
return f_muldiv(self,
adat->num, adat->den,
bdat->num, bdat->den, '/');
}
default:
return rb_num_coerce_bin(self, other, '/');
}
}
/*
* Using the Euclidean Algorithm (division-based):
* http://en.wikipedia.org/wiki/Euclidean_algorithm#Implementations
*
* In ruby:
* a = self
* while b != 0
* a, b = b, a % b
* end
* return a
*/
VALUE
rb_big_gcd_euclidean_division(VALUE a, VALUE b)
{
VALUE temp;
/* borrowed from bignum.c, rb_big_modulo() */
switch (TYPE(b)) {
case T_FIXNUM:
b = rb_int2big(FIX2LONG(b));
break;
case T_BIGNUM:
break;
default:
return rb_num_coerce_bin(a, b, '%');
}
while ((TYPE(b) == T_BIGNUM && !rb_bigzero_p(b)) ||
(TYPE(b) == T_FIXNUM && FIX2LONG(b) != 0)) {
if (TYPE(b) == T_BIGNUM) {
temp = rb_big_clone(b);
}
else {
temp = b;
}
//b = rb_big_modulo(a, b);
b = rb_funcall(a, mod_id, 1, b);
a = temp;
}
return a;
}
static VALUE
nurat_div(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
if (f_zero_p(other))
rb_raise(rb_eZeroDivError, "devided by zero");
{
get_dat1(self);
return f_muldiv(self,
dat->num, dat->den,
other, ONE, '/');
}
case T_FLOAT:
return rb_funcall(f_to_f(self), '/', 1, other);
case T_RATIONAL:
if (f_zero_p(other))
rb_raise(rb_eZeroDivError, "devided by zero");
{
get_dat2(self, other);
return f_muldiv(self,
adat->num, adat->den,
bdat->num, bdat->den, '/');
}
default:
return rb_num_coerce_bin(self, other, '/');
}
}
static VALUE
rb_hack_xor (VALUE x, VALUE y)
{
if ( rb_obj_is_carray(y) ) {
if ( rb_ca_is_boolean_type(y) ) {
return rb_funcall(y, rb_intern("bit_xor"), 1, x);
}
else {
#if RUBY_VERSION_CODE >= 190
return rb_num_coerce_bin(x, y, '^');
#else
return rb_num_coerce_bin(x, y);
#endif
}
}
else {
return rb_funcall(x, id___xor__, 1, y);
}
}
inline static VALUE
f_divide(VALUE self, VALUE other,
VALUE (*func)(VALUE, VALUE), ID id)
{
if (k_complex_p(other)) {
int flo;
get_dat2(self, other);
flo = (k_float_p(adat->real) || k_float_p(adat->imag) ||
k_float_p(bdat->real) || k_float_p(bdat->imag));
if (f_gt_p(f_abs(bdat->real), f_abs(bdat->imag))) {
VALUE r, n;
r = (*func)(bdat->imag, bdat->real);
n = f_mul(bdat->real, f_add(ONE, f_mul(r, r)));
if (flo)
return f_complex_new2(CLASS_OF(self),
(*func)(self, n),
(*func)(f_negate(f_mul(self, r)), n));
return f_complex_new2(CLASS_OF(self),
(*func)(f_add(adat->real,
f_mul(adat->imag, r)), n),
(*func)(f_sub(adat->imag,
f_mul(adat->real, r)), n));
}
else {
VALUE r, n;
r = (*func)(bdat->real, bdat->imag);
n = f_mul(bdat->imag, f_add(ONE, f_mul(r, r)));
if (flo)
return f_complex_new2(CLASS_OF(self),
(*func)(f_mul(self, r), n),
(*func)(f_negate(self), n));
return f_complex_new2(CLASS_OF(self),
(*func)(f_add(f_mul(adat->real, r),
adat->imag), n),
(*func)(f_sub(f_mul(adat->imag, r),
adat->real), n));
}
}
if (k_numeric_p(other) && f_real_p(other)) {
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
(*func)(dat->real, other),
(*func)(dat->imag, other));
}
return rb_num_coerce_bin(self, other, id);
}
/*
* call-seq:
* onum ** other -> oranumber
*
* Raises <i>onum</i> the <i>other</i> power.
*/
static VALUE onum_power(VALUE lhs, VALUE rhs)
{
OCIError *errhp = oci8_errhp;
OCINumber n;
OCINumber r;
if (FIXNUM_P(rhs)) {
chkerr(OCINumberIntPower(errhp, _NUMBER(lhs), FIX2INT(rhs), &r));
} else {
/* change to OCINumber */
if (!set_oci_number_from_num(&n, rhs, 0, errhp))
return rb_num_coerce_bin(lhs, rhs, id_power);
chkerr(OCINumberPower(errhp, _NUMBER(lhs), &n, &r));
}
return oci8_make_ocinumber(&r, errhp);
}
/*
* 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);
}
}
/*
* call-seq:
* onum % other -> oranumber
*
* Returns the modulo after division of <i>onum</i> by <i>other</i>.
*/
static VALUE onum_mod(VALUE lhs, VALUE rhs)
{
OCIError *errhp = oci8_errhp;
OCINumber n;
OCINumber r;
boolean is_zero;
/* change to OCINumber */
if (!set_oci_number_from_num(&n, rhs, 0, errhp))
return rb_num_coerce_bin(lhs, rhs, '%');
/* check whether argument is not zero. */
chkerr(OCINumberIsZero(errhp, &n, &is_zero));
if (is_zero)
rb_num_zerodiv();
/* modulo */
chkerr(OCINumberMod(errhp, _NUMBER(lhs), &n, &r));
return oci8_make_ocinumber(&r, errhp);
}
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, '-');
}
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_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:
* 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_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);
}
static VALUE numeric_spec_rb_num_coerce_bin(VALUE self, VALUE x, VALUE y, VALUE op) {
return rb_num_coerce_bin(x, y, SYM2ID(op));
}