/*
* call-seq:
* cmp.abs2 -> real
*
* Returns square of the absolute value.
*
* Complex(-1).abs2 #=> 1
* Complex(3.0, -4.0).abs2 #=> 25.0
*/
static VALUE
nucomp_abs2(VALUE self)
{
get_dat1(self);
return f_add(f_mul(dat->real, dat->real),
f_mul(dat->imag, dat->imag));
}
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:
* 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, '*');
}
inline static VALUE
f_complex_polar(VALUE klass, VALUE x, VALUE y)
{
assert(!k_complex_p(x));
assert(!k_complex_p(y));
return nucomp_s_canonicalize_internal(klass,
f_mul(x, m_cos(y)),
f_mul(x, m_sin(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:
* 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
f_addsub(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
{
VALUE num, den;
if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
FIXNUM_P(bnum) && FIXNUM_P(bden)) {
long an = FIX2LONG(anum);
long ad = FIX2LONG(aden);
long bn = FIX2LONG(bnum);
long bd = FIX2LONG(bden);
long ig = i_gcd(ad, bd);
VALUE g = LONG2NUM(ig);
VALUE a = f_imul(an, bd / ig);
VALUE b = f_imul(bn, ad / ig);
VALUE c;
if (k == '+')
c = f_add(a, b);
else
c = f_sub(a, b);
b = f_idiv(aden, g);
g = f_gcd(c, g);
num = f_idiv(c, g);
a = f_idiv(bden, g);
den = f_mul(a, b);
}
else {
VALUE g = f_gcd(aden, bden);
VALUE a = f_mul(anum, f_idiv(bden, g));
VALUE b = f_mul(bnum, f_idiv(aden, g));
VALUE c;
if (k == '+')
c = f_add(a, b);
else
c = f_sub(a, b);
b = f_idiv(aden, g);
g = f_gcd(c, g);
num = f_idiv(c, g);
a = f_idiv(bden, g);
den = f_mul(a, b);
}
return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
}
inline static VALUE
f_lcm(VALUE x, VALUE y)
{
if (f_zero_p(x) || f_zero_p(y))
return ZERO;
return f_abs(f_mul(f_div(x, f_gcd(x, y)), y));
}
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)));
}
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;
}
/*
* 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, '*');
}
}
inline static VALUE
f_imul(long x, long y)
{
VALUE r = f_imul_orig(x, y);
assert(f_eqeq_p(r, f_mul(LONG2NUM(x), LONG2NUM(y))));
return r;
}
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));
}
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_complex_polar(VALUE klass, VALUE x, VALUE y)
{
assert(!k_complex_p(x));
assert(!k_complex_p(y));
if (f_zero_p(x) || f_zero_p(y)) {
if (canonicalization) return x;
return nucomp_s_new_internal(klass, x, RFLOAT_0);
}
if (RB_FLOAT_TYPE_P(y)) {
const double arg = RFLOAT_VALUE(y);
if (arg == M_PI) {
x = f_negate(x);
if (canonicalization) return x;
y = RFLOAT_0;
}
else if (arg == M_PI_2) {
y = x;
x = RFLOAT_0;
}
else if (arg == M_PI_2+M_PI) {
y = f_negate(x);
x = RFLOAT_0;
}
else if (RB_FLOAT_TYPE_P(x)) {
const double abs = RFLOAT_VALUE(x);
const double real = abs * cos(arg), imag = abs * sin(arg);
x = DBL2NUM(real);
if (canonicalization && imag == 0.0) return x;
y = DBL2NUM(imag);
}
else {
x = f_mul(x, DBL2NUM(cos(arg)));
y = f_mul(y, DBL2NUM(sin(arg)));
if (canonicalization && f_zero_p(y)) return x;
}
return nucomp_s_new_internal(klass, x, y);
}
return nucomp_s_canonicalize_internal(klass,
f_mul(x, m_cos(y)),
f_mul(x, m_sin(y)));
}
static VALUE
safe_mul(VALUE a, VALUE b, int az, int bz)
{
double v;
if (!az && bz && RB_FLOAT_TYPE_P(a) && (v = RFLOAT_VALUE(a), !isnan(v))) {
a = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
}
if (!bz && az && RB_FLOAT_TYPE_P(b) && (v = RFLOAT_VALUE(b), !isnan(v))) {
b = signbit(v) ? DBL2NUM(-1.0) : DBL2NUM(1.0);
}
return f_mul(a, b);
}
inline static VALUE
f_muldiv(VALUE self, VALUE anum, VALUE aden, VALUE bnum, VALUE bden, int k)
{
VALUE num, den;
if (k == '/') {
VALUE t;
if (f_negative_p(bnum)) {
anum = f_negate(anum);
bnum = f_negate(bnum);
}
t = bnum;
bnum = bden;
bden = t;
}
if (FIXNUM_P(anum) && FIXNUM_P(aden) &&
FIXNUM_P(bnum) && FIXNUM_P(bden)) {
long an = FIX2LONG(anum);
long ad = FIX2LONG(aden);
long bn = FIX2LONG(bnum);
long bd = FIX2LONG(bden);
long g1 = i_gcd(an, bd);
long g2 = i_gcd(ad, bn);
num = f_imul(an / g1, bn / g2);
den = f_imul(ad / g2, bd / g1);
}
else {
VALUE g1 = f_gcd(anum, bden);
VALUE g2 = f_gcd(aden, bnum);
num = f_mul(f_idiv(anum, g1), f_idiv(bnum, g2));
den = f_mul(f_idiv(aden, g2), f_idiv(bden, g1));
}
return f_rational_new_no_reduce2(CLASS_OF(self), num, den);
}
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:
* 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 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)
*/
static VALUE
nucomp_mul(VALUE self, VALUE other)
{
if (k_complex_p(other)) {
VALUE real, imag;
get_dat2(self, other);
real = f_sub(f_mul(adat->real, bdat->real),
f_mul(adat->imag, bdat->imag));
imag = f_add(f_mul(adat->real, bdat->imag),
f_mul(adat->imag, bdat->real));
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:
* 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_mod(VALUE self, VALUE other)
{
VALUE val = f_floor(f_div(self, other));
return f_sub(self, f_mul(other, val));
}
static VALUE
nurat_divmod(VALUE self, VALUE other)
{
VALUE val = f_floor(f_div(self, other));
return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
}
/*
* call-seq:
* num.abs2 -> real
*
* Returns square of self.
*/
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
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_rem(VALUE self, VALUE other)
{
VALUE val = f_truncate(f_div(self, other));
return f_sub(self, f_mul(other, val));
}
/* :nodoc: */
static VALUE
nurat_quotrem(VALUE self, VALUE other)
{
VALUE val = f_truncate(f_div(self, other));
return rb_assoc_new(val, f_sub(self, f_mul(other, val)));
}
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);
}