1 #include <u.h>
2 #include <libc.h>
3 #include "map.h"
4 
5 /*complex divide, defensive against overflow from
6  *	* and /, but not from + and -
7  *	assumes underflow yields 0.0
8  *	uses identities:
9  *	(a + bi)/(c + di) = ((a + bd/c) + (b - ad/c)i)/(c + dd/c)
10  *	(a + bi)/(c + di) = (b - ai)/(d - ci)
11 */
12 void
13 cdiv(double a, double b, double c, double d, double *u, double *v)
14 {
15 	double r,t;
16 	if(fabs(c)<fabs(d)) {
17 		t = -c; c = d; d = t;
18 		t = -a; a = b; b = t;
19 	}
20 	r = d/c;
21 	t = c + r*d;
22 	*u = (a + r*b)/t;
23 	*v = (b - r*a)/t;
24 }
25 
26 void
27 cmul(double c1, double c2, double d1, double d2, double *e1, double *e2)
28 {
29 	*e1 = c1*d1 - c2*d2;
30 	*e2 = c1*d2 + c2*d1;
31 }
32 
33 void
34 csq(double c1, double c2, double *e1, double *e2)
35 {
36 	*e1 = c1*c1 - c2*c2;
37 	*e2 = c1*c2*2;
38 }
39 
40 /* complex square root
41  *	assumes underflow yields 0.0
42  *	uses these identities:
43  *	sqrt(x+_iy) = sqrt(r(cos(t)+_isin(t))
44  *	           = sqrt(r)(cos(t/2)+_isin(t/2))
45  *	cos(t/2) = sin(t)/2sin(t/2) = sqrt((1+cos(t)/2)
46  *	sin(t/2) = sin(t)/2cos(t/2) = sqrt((1-cos(t)/2)
47 */
48 void
49 csqrt(double c1, double c2, double *e1, double *e2)
50 {
51 	double r,s;
52 	double x,y;
53 	x = fabs(c1);
54 	y = fabs(c2);
55 	if(x>=y) {
56 		if(x==0) {
57 			*e1 = *e2 = 0;
58 			return;
59 		}
60 		r = x;
61 		s = y/x;
62 	} else {
63 		r = y;
64 		s = x/y;
65 	}
66 	r *= sqrt(1+ s*s);
67 	if(c1>0) {
68 		*e1 = sqrt((r+c1)/2);
69 		*e2 = c2/(2* *e1);
70 	} else {
71 		*e2 = sqrt((r-c1)/2);
72 		if(c2<0)
73 			*e2 = -*e2;
74 		*e1 = c2/(2* *e2);
75 	}
76 }
77 
78 
79 void cpow(double c1, double c2, double *d1, double *d2, double pwr)
80 {
81 	double theta = pwr*atan2(c2,c1);
82 	double r = pow(hypot(c1,c2), pwr);
83 	*d1 = r*cos(theta);
84 	*d2 = r*sin(theta);
85 }