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# pow.c

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## File contents

```/* @(#) pow.c 1.2 1/27/86 17:47:40 */
/*ident	"@(#)cfront:lib/complex/pow.c	1.2"*/
#include "complex.h"

complex
pow(double base, complex z)
/*
real to complex power: base**z.
*/
{
register complex y;

if (base == 0) return y;	/* even for singularity */

if (0 < base) {
double lb = log(base);
y.re = z.re * lb;
y.im = z.im * lb;
return exp(y);
}

return pow(complex(base), z);	/* use complex power fct */
}

complex
pow(complex a, int n)
/*
complex to integer power: a**n.
*/
{
register complex x, p = 1;

if (n == 0) return p;

if (n < 0) {
n = -n;
x = 1/a;
}
else 	x = a;

for( ; ; ) {
if(n & 01) {
register double t = p.re * x.re - p.im * x.im;
p.im = p.re * x.im + p.im * x.re;
p.re = t;
}
if(n >>= 1) {
register double t = x.re * x.re - x.im * x.im;
x.im = 2 * x.re * x.im;
x.re = t;
}
else 	break;
}
return p;
}

complex
pow(complex a, double b)
/*
complex to real power: a**b.
*/
{
register double logr = log( abs(a) );
register double logi = atan2(a.im, a.re);
register double x = exp( b*logr );
register double y = b * logi;
return complex(x*cos(y), x*sin(y));
}

complex
pow(complex base, complex sup)
/*
complex to complex power: base**sup.
*/
{
complex result;
register double	logr, logi;
register double xx, yy;
double a = abs(base);

if (a == 0) return result;

logr = log( a );
logi = atan2(base.im, base.re);

xx = exp( logr * sup.re - logi * sup.im );
yy = logr * sup.im + logi * sup.re;

result.re = xx * cos(yy);
result.im = xx * sin(yy);

return result;
}
```
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