130 lines
2.7 KiB
C
130 lines
2.7 KiB
C
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/* @(#)z_sqrt.c 1.0 98/08/13 */
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/*****************************************************************
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* The following routines are coded directly from the algorithms
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* and coefficients given in "Software Manual for the Elementary
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* Functions" by William J. Cody, Jr. and William Waite, Prentice
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* Hall, 1980.
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*****************************************************************/
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/*
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FUNCTION
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<<sqrt>>, <<sqrtf>>---positive square root
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INDEX
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sqrt
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INDEX
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sqrtf
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ANSI_SYNOPSIS
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#include <math.h>
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double sqrt(double <[x]>);
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float sqrtf(float <[x]>);
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TRAD_SYNOPSIS
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#include <math.h>
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double sqrt(<[x]>);
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float sqrtf(<[x]>);
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DESCRIPTION
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<<sqrt>> computes the positive square root of the argument.
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RETURNS
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On success, the square root is returned. If <[x]> is real and
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positive, then the result is positive. If <[x]> is real and
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negative, the global value <<errno>> is set to <<EDOM>> (domain error).
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PORTABILITY
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<<sqrt>> is ANSI C. <<sqrtf>> is an extension.
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*/
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/******************************************************************
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* Square Root
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*
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* Input:
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* x - floating point value
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*
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* Output:
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* square-root of x
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*
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* Description:
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* This routine performs floating point square root.
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*
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* The initial approximation is computed as
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* y0 = 0.41731 + 0.59016 * f
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* where f is a fraction such that x = f * 2^exp.
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*
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* Three Newton iterations in the form of Heron's formula
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* are then performed to obtain the final value:
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* y[i] = (y[i-1] + f / y[i-1]) / 2, i = 1, 2, 3.
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*
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*****************************************************************/
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#include "fdlibm.h"
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#include "zmath.h"
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#ifndef _DOUBLE_IS_32BITS
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double
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_DEFUN (sqrt, (double),
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double x)
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{
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double f, y;
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int exp, i, odd;
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/* Check for special values. */
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switch (numtest (x))
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{
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case NAN:
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errno = EDOM;
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return (x);
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case INF:
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if (ispos (x))
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{
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errno = EDOM;
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return (z_notanum.d);
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}
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else
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{
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errno = ERANGE;
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return (z_infinity.d);
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}
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}
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/* Initial checks are performed here. */
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if (x == 0.0)
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return (0.0);
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if (x < 0)
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{
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errno = EDOM;
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return (z_notanum.d);
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}
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/* Find the exponent and mantissa for the form x = f * 2^exp. */
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f = frexp (x, &exp);
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odd = exp & 1;
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/* Get the initial approximation. */
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y = 0.41731 + 0.59016 * f;
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f /= 2.0;
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/* Calculate the remaining iterations. */
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for (i = 0; i < 3; ++i)
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y = y / 2.0 + f / y;
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/* Calculate the final value. */
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if (odd)
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{
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y *= __SQRT_HALF;
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exp++;
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}
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exp >>= 1;
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y = ldexp (y, exp);
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return (y);
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}
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#endif /* _DOUBLE_IS_32BITS */
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