csqrt.c File Reference

#include "prim.h"

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Functions
complex	csqrt (complex z)
	Square root of complex number. More...

Function Documentation

csqrt()

complex csqrt

(

complex

z

)

Square root of complex number.

Definition at line 42 of file csqrt.c.

References cabs(), cimag(), cpack(), creal(), fabs(), and sqrt().

Referenced by cacos(), cacosh(), cacsc(), cacsch(), casec(), casech(), casin(), casinh(), and ComplexNumber::SquareRoot().

{
    complex w;
    double x, y, r, t, scale;

    x = creal(z);
    y = cimag(z);

    if (y == 0.0)
    {
        if (x == 0.0)
        {
            w = cpack(0.0, y);
        }
        else
        {
            r = fabs(x);
            r = sqrt(r);
            if (x < 0.0)
            {
                w = cpack(0.0, r);
            }
            else
            {
                w = cpack(r, y);
            }
        }
        return w;
    }
    if (x == 0.0)
    {
        r = fabs(y);
        r = sqrt(0.5 * r);
        if (y > 0)
            w = cpack(r, r);
        else
            w = cpack(r, -r);
        return w;
    }
    /* Rescale to avoid internal overflow or underflow.  */
    if ((fabs(x) > 4.0) || (fabs(y) > 4.0))
    {
        x *= 0.25;
        y *= 0.25;
        scale = 2.0;
    }
    else
    {
#if 1
        x *= 1.8014398509481984e16; /* 2^54 */
        y *= 1.8014398509481984e16;
        scale = 7.450580596923828125e-9; /* 2^-27 */
#else
        x *= 4.0;
        y *= 4.0;
        scale = 0.5;
#endif
    }
    w = cpack(x, y);
    r = cabs(w);
    if (x > 0)
    {
        t = sqrt(0.5 * r + 0.5 * x);
        r = scale * fabs((0.5 * y) / t);
        t *= scale;
    }
    else
    {
        r = sqrt(0.5 * r - 0.5 * x);
        t = scale * fabs((0.5 * y) / r);
        r *= scale;
    }
    if (y < 0)
        w = cpack(t, -r);
    else
        w = cpack(t, r);
    return w;
}

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