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Annotation of researchv10no/cmd/map/libmap/complex.c, revision 1.1

1.1     ! root        1: #include "map.h"
        !             2: 
        !             3: /*complex divide, defensive against overflow from
        !             4:  *     * and /, but not from + and -
        !             5:  *     assumes underflow yields 0.0
        !             6:  *     uses identities:
        !             7:  *     (a + bi)/(c + di) = ((a + bd/c) + (b - ad/c)i)/(c + dd/c)
        !             8:  *     (a + bi)/(c + di) = (b - ai)/(d - ci)
        !             9: */
        !            10: void
        !            11: cdiv(double a, double b, double c, double d, double *u, double *v)
        !            12: {
        !            13:        double r,t;
        !            14:        if(fabs(c)<fabs(d)) {
        !            15:                t = -c; c = d; d = t;
        !            16:                t = -a; a = b; b = t;
        !            17:        }
        !            18:        r = d/c;
        !            19:        t = c + r*d;
        !            20:        *u = (a + r*b)/t;
        !            21:        *v = (b - r*a)/t;
        !            22: }
        !            23: 
        !            24: void
        !            25: cmul(double c1, double c2, double d1, double d2, double *e1, double *e2)
        !            26: {
        !            27:        *e1 = c1*d1 - c2*d2;
        !            28:        *e2 = c1*d2 + c2*d1;
        !            29: }
        !            30: 
        !            31: void
        !            32: csq(double c1, double c2, double *e1, double *e2)
        !            33: {
        !            34:        *e1 = c1*c1 - c2*c2;
        !            35:        *e2 = c1*c2*2;
        !            36: }
        !            37: 
        !            38: /* complex square root
        !            39:  *     assumes underflow yields 0.0
        !            40:  *     uses these identities:
        !            41:  *     sqrt(x+_iy) = sqrt(r(cos(t)+_isin(t))
        !            42:  *                = sqrt(r)(cos(t/2)+_isin(t/2))
        !            43:  *     cos(t/2) = sin(t)/2sin(t/2) = sqrt((1+cos(t)/2)
        !            44:  *     sin(t/2) = sin(t)/2cos(t/2) = sqrt((1-cos(t)/2)
        !            45: */
        !            46: void
        !            47: csqrt(double c1, double c2, double *e1, double *e2)
        !            48: {
        !            49:        double r,s;
        !            50:        double x,y;
        !            51:        x = fabs(c1);
        !            52:        y = fabs(c2);
        !            53:        if(x>=y) {
        !            54:                if(x==0) {
        !            55:                        *e1 = *e2 = 0;
        !            56:                        return;
        !            57:                }
        !            58:                r = x;
        !            59:                s = y/x;
        !            60:        } else {
        !            61:                r = y;
        !            62:                s = x/y;
        !            63:        }
        !            64:        r *= sqrt(1+ s*s);
        !            65:        if(c1>0) {
        !            66:                *e1 = sqrt((r+c1)/2);
        !            67:                *e2 = c2/(2* *e1);
        !            68:        } else {
        !            69:                *e2 = sqrt((r-c1)/2);
        !            70:                if(c2<0)
        !            71:                        *e2 = -*e2;
        !            72:                *e1 = c2/(2* *e2);
        !            73:        }
        !            74: }

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