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#include <complex.h> // for I, complex, cabsf, cimagf, crealf, csqrtf
#include <math.h> // for fabsf, sqrtf
float complex csqrtf(float complex z)
{
float complex w;
float x, y, r, t, scale;
x = crealf(z);
y = cimagf(z);
if (y == 0.0f) {
if (x < 0.0f) {
return 0.0f + sqrtf(-x) * I;
}
if (x == 0.0f) {
return (0.0f + y * I);
}
return sqrtf(x) + y * I;
}
if (x == 0.0f) {
r = fabsf(y);
r = sqrtf(0.5f * r);
if (y > 0)
return r + r * I;
return r - r * I;
}
if ((fabsf(x) > 4.0f) || (fabsf(y) > 4.0f)) {
x *= 0.25f;
y *= 0.25f;
scale = 2.0f;
} else {
x *= 6.7108864e7f; /* 2^26 */
y *= 6.7108864e7f;
scale = 1.220703125e-4f; /* 2^-13 */
}
w = x + y * I;
r = cabsf(w);
if (x > 0) {
t = sqrtf(0.5f * r + 0.5f * x);
r = scale * fabsf((0.5f * y) / t);
t *= scale;
} else {
r = sqrtf(0.5f * r - 0.5f * x);
t = scale * fabsf((0.5f * y) / r);
r *= scale;
}
if (y < 0)
return t - r * I;
return t + r * I;
}
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