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Annotation of researchv10no/cmd/cfront/libC/complex/sqrt.c, revision 1.1.1.1

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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