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# sqrt.c

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## File contents

```/* @(#) sqrt.c 1.2 1/27/86 17:47:43 */
/*ident	"@(#)cfront:lib/complex/sqrt.c	1.2"*/
# include "complex.h"

#define	SQRT_DANGER	1e17
# define PERIL(t)	(t > SQRT_DANGER || (t < 1/SQRT_DANGER && t != 0))

/*
*
* 7-25-83, note from Leonie Rose -
* Stu Feldman says that the peril tests for the following function
* are "acceptable" for now, but certain things like
* sqrt(1e10 + 1e-30*i) will cause floating exceptions.
*
*/

complex
sqrt(complex z)
{
double  r_old,  partial;

/*
Check for possible overflow, and fixup if necessary.
*/

double x = abs(z.re);
double y = abs(z.im);

if (x > y && PERIL(x)) {
z.im /= x;
z.re /= x;  /* z.re is replaced by 1 or -1 */
partial = sqrt(x);
}
else if PERIL(y) {
z.im /= y;  /* roles of z.re, z.im reversed from previous */
z.re /= y;
partial = sqrt(y);
}
else partial = 1;

/*
Main computation:
Use half angle formulas to compute angular part of the square root.
The sign of sin_old is the same as that for sin_new, which means that the
upper half plane gets mapped to the first quadrant, and
the lower half plane to the fourth quandrant.
*/

if (r_old = sqrt(z.re*z.re + z.im*z.im)) {
double r_new = partial * sqrt(r_old);

double cos_old = z.re/r_old;
double sin_old = z.im/r_old;
double cos_new = sqrt( (1 + cos_old)/2 );
double sin_new = (cos_new == 0)? 1 : sin_old/(2*cos_new);

}

}
```
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