125 lines
2.6 KiB
C
125 lines
2.6 KiB
C
|
|
/* @(#)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
|
|
|
|
SYNOPSIS
|
|
#include <math.h>
|
|
double sqrt(double <[x]>);
|
|
float sqrtf(float <[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 */
|