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| | #include "complex_impl.h"
#include <fenv.h>
/* cssqsl() and csqrtl() taken from
* Kahan, W. (1987). Branch cuts for complex elementary functions.
*/
static inline long double complex _cssqsl(long double complex z) {
#pragma STDC FENV_ACCESS ON
fenv_t env;
unsigned k = 0;
long double x, y, r;
int set_excepts;
feholdexcept(&env);
x = creal(z);
y = cimag(z);
r = x * x + y * y;
if ((isinf(x) || isinf(y)) && (isnan(r) || isinf(r))) {
r = INFINITY;
} else {
set_excepts = fetestexcept(FE_OVERFLOW | FE_UNDERFLOW);
if ((set_excepts & FE_OVERFLOW) ||
((set_excepts & FE_UNDERFLOW) && isless(r, LDBL_MIN / LDBL_EPSILON))) {
k = logbl(fmaxl(fabsl(x), fabsl(y)));
x = scalbnl(x, -k);
y = scalbnl(y, -k);
r = x * x + y * y;
}
}
feupdateenv(&env);
return CMPLXL(r, k);
}
long double complex csqrtl(long double complex z) {
long double x, y, r, xi, eta;
unsigned k;
x = creal(z);
y = cimag(z);
z = _cssqsl(z);
r = creal(z);
k = cimag(z);
if (!isnan(x)) {
r = scalbnl(fabsl(x), -k) + sqrtl(r);
}
if (k & 1) {
k = (k - 1) / 2;
} else {
k = k / 2 - 1;
r *= 2;
}
r = scalbnl(sqrtl(r), k);
xi = r;
eta = y;
if (r != 0) {
if (!isinf(eta)) {
// TODO if eta underflowed, signal it
eta = (eta / r) / 2;
}
if (isless(x, 0)) {
xi = fabsl(eta);
eta = copysignl(r, y);
}
}
return CMPLX(xi, eta);
}
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