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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 */