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/* @(#)z_sqrtf.c 1.0 98/08/13 */
/*****************************************************************
* The following routines are coded directly from the algorithms
* and coefficients given in "Software Manual for the Elementary
* Functions" by William J. Cody, Jr. and William Waite, Prentice
* Hall, 1980.
*****************************************************************/
/******************************************************************
* Square Root
*
* Input:
* x - floating point value
*
* Output:
* square-root of x
*
* Description:
* This routine performs floating point square root.
*
* The initial approximation is computed as
* y0 = 0.41731 + 0.59016 * f
* where f is a fraction such that x = f * 2^exp.
*
* Three Newton iterations in the form of Heron's formula
* are then performed to obtain the final value:
* y[i] = (y[i-1] + f / y[i-1]) / 2, i = 1, 2, 3.
*
*****************************************************************/
#include "fdlibm.h"
#include "zmath.h"
float
_DEFUN (sqrtf, (float),
float x)
{
float f, y;
int exp, i, odd;
/* Check for special values. */
switch (numtestf (x))
{
case NAN:
errno = EDOM;
return (x);
case INF:
if (isposf (x))
{
errno = EDOM;
return (z_notanum_f.f);
}
else
{
errno = ERANGE;
return (z_infinity_f.f);
}
}
/* Initial checks are performed here. */
if (x == 0.0)
return (0.0);
if (x < 0)
{
errno = EDOM;
return (z_notanum_f.f);
}
/* Find the exponent and mantissa for the form x = f * 2^exp. */
f = frexpf (x, &exp);
odd = exp & 1;
/* Get the initial approximation. */
y = 0.41731 + 0.59016 * f;
f *= 0.5;
/* Calculate the remaining iterations. */
for (i = 0; i < 2; ++i)
y = y * 0.5 + f / y;
/* Calculate the final value. */
if (odd)
{
y *= __SQRT_HALF;
exp++;
}
exp >>= 1;
y = ldexpf (y, exp);
return (y);
}
#ifdef _DOUBLE_IS_32BITS
double sqrt (double x)
{
return (double) sqrtf ((float) x);
}
#endif /* _DOUBLE_IS_32BITS */
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