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/* @(#)z_sqrt.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.
*****************************************************************/
/*
FUNCTION
<<sqrt>>, <<sqrtf>>---positive square root
INDEX
sqrt
INDEX
sqrtf
ANSI_SYNOPSIS
#include <math.h>
double sqrt(double <[x]>);
float sqrtf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double sqrt(<[x]>);
float sqrtf(<[x]>);
DESCRIPTION
<<sqrt>> computes the positive square root of the argument.
RETURNS
On success, the square root is returned. If <[x]> is real and
positive, then the result is positive. If <[x]> is real and
negative, the global value <<errno>> is set to <<EDOM>> (domain error).
PORTABILITY
<<sqrt>> is ANSI C. <<sqrtf>> is an extension.
*/
/******************************************************************
* 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"
#ifndef _DOUBLE_IS_32BITS
double
_DEFUN (sqrt, (double),
double x)
{
double f, y;
int exp, i, odd;
/* Check for special values. */
switch (numtest (x))
{
case NAN:
errno = EDOM;
return (x);
case INF:
if (ispos (x))
{
errno = EDOM;
return (z_notanum.d);
}
else
{
errno = ERANGE;
return (z_infinity.d);
}
}
/* Initial checks are performed here. */
if (x == 0.0)
return (0.0);
if (x < 0)
{
errno = EDOM;
return (z_notanum.d);
}
/* Find the exponent and mantissa for the form x = f * 2^exp. */
f = frexp (x, &exp);
odd = exp & 1;
/* Get the initial approximation. */
y = 0.41731 + 0.59016 * f;
f /= 2.0;
/* Calculate the remaining iterations. */
for (i = 0; i < 3; ++i)
y = y / 2.0 + f / y;
/* Calculate the final value. */
if (odd)
{
y *= __SQRT_HALF;
exp++;
}
exp >>= 1;
y = ldexp (y, exp);
return (y);
}
#endif /* _DOUBLE_IS_32BITS */
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