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#include <u.h>
#include <libc.h>
#include "map.h"
/*complex divide, defensive against overflow from
* * and /, but not from + and -
* assumes underflow yields 0.0
* uses identities:
* (a + bi)/(c + di) = ((a + bd/c) + (b - ad/c)i)/(c + dd/c)
* (a + bi)/(c + di) = (b - ai)/(d - ci)
*/
void
cdiv(double a, double b, double c, double d, double *u, double *v)
{
double r,t;
if(fabs(c)<fabs(d)) {
t = -c; c = d; d = t;
t = -a; a = b; b = t;
}
r = d/c;
t = c + r*d;
*u = (a + r*b)/t;
*v = (b - r*a)/t;
}
void
cmul(double c1, double c2, double d1, double d2, double *e1, double *e2)
{
*e1 = c1*d1 - c2*d2;
*e2 = c1*d2 + c2*d1;
}
void
csq(double c1, double c2, double *e1, double *e2)
{
*e1 = c1*c1 - c2*c2;
*e2 = c1*c2*2;
}
/* complex square root
* assumes underflow yields 0.0
* uses these identities:
* sqrt(x+_iy) = sqrt(r(cos(t)+_isin(t))
* = sqrt(r)(cos(t/2)+_isin(t/2))
* cos(t/2) = sin(t)/2sin(t/2) = sqrt((1+cos(t)/2)
* sin(t/2) = sin(t)/2cos(t/2) = sqrt((1-cos(t)/2)
*/
void
csqrt(double c1, double c2, double *e1, double *e2)
{
double r,s;
double x,y;
x = fabs(c1);
y = fabs(c2);
if(x>=y) {
if(x==0) {
*e1 = *e2 = 0;
return;
}
r = x;
s = y/x;
} else {
r = y;
s = x/y;
}
r *= sqrt(1+ s*s);
if(c1>0) {
*e1 = sqrt((r+c1)/2);
*e2 = c2/(2* *e1);
} else {
*e2 = sqrt((r-c1)/2);
if(c2<0)
*e2 = -*e2;
*e1 = c2/(2* *e2);
}
}
void cpow(double c1, double c2, double *d1, double *d2, double pwr)
{
double theta = pwr*atan2(c2,c1);
double r = pow(hypot(c1,c2), pwr);
*d1 = r*cos(theta);
*d2 = r*sin(theta);
}
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