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Annotation of researchv10no/cmd/cfront/libC/complex/sqrt.c, revision 1.1

1.1     ! root        1: # include "complex.h"
        !             2: 
        !             3: 
        !             4: #define        SQRT_DANGER     1e17
        !             5: # define PERIL(t)      (t > SQRT_DANGER || (t < 1/SQRT_DANGER && t != 0))
        !             6: 
        !             7: /*
        !             8:  *
        !             9:  * 7-25-83, note from Leonie Rose -
        !            10:  * Stu Feldman says that the peril tests for the following function
        !            11:  * are "acceptable" for now, but certain things like
        !            12:  * sqrt(1e10 + 1e-30*i) will cause floating exceptions.
        !            13:  *
        !            14:  */
        !            15: 
        !            16: complex sqrt(complex z)
        !            17: {
        !            18:        complex  answer;
        !            19:        double  r_old,  partial;
        !            20: 
        !            21: /*
        !            22:        Check for possible overflow, and fixup if necessary.
        !            23: */
        !            24: 
        !            25:        double x = abs(z.re);
        !            26:        double y = abs(z.im);
        !            27: 
        !            28:        if (x > y && PERIL(x)) {
        !            29:                z.im /= x;
        !            30:                z.re /= x;  /* z.re is replaced by 1 or -1 */
        !            31:                partial = sqrt(x);
        !            32:        }
        !            33:        else if PERIL(y) { 
        !            34:                z.im /= y;  /* roles of z.re, z.im reversed from previous */
        !            35:                z.re /= y;
        !            36:                partial = sqrt(y);
        !            37:        }
        !            38:        else partial = 1;
        !            39: 
        !            40: /*
        !            41:        Main computation:
        !            42:        Use half angle formulas to compute angular part of the square root.
        !            43:        The sign of sin_old is the same as that for sin_new, which means that the
        !            44:        upper half plane gets mapped to the first quadrant, and
        !            45:        the lower half plane to the fourth quandrant.
        !            46: */
        !            47: 
        !            48: 
        !            49:        if (r_old = sqrt(z.re*z.re + z.im*z.im)) {
        !            50:                double r_new = partial * sqrt(r_old);
        !            51: 
        !            52:                double cos_old = z.re/r_old;
        !            53:                double sin_old = z.im/r_old;
        !            54:                double cos_new = sqrt( (1 + cos_old)/2 );
        !            55:                double sin_new = (cos_new == 0)? 1 : sin_old/(2*cos_new);
        !            56: 
        !            57:                answer.re = r_new * cos_new;
        !            58:                answer.im = r_new * sin_new;
        !            59:        }
        !            60: 
        !            61:        return answer;
        !            62: }

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