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/* @(#)z_exp.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

        <<exp>>, <<expf>>---exponential

INDEX

        exp

INDEX

        expf

ANSI_SYNOPSIS

        #include <math.h>

        double exp(double <[x]>);

        float expf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double exp(<[x]>);

        double <[x]>;

        float expf(<[x]>);

        float <[x]>;

DESCRIPTION

        <<exp>> and <<expf>> calculate the exponential of <[x]>, that is,

        @ifnottex

        e raised to the power <[x]> (where e

        @end ifnottex

        @tex

        $e^x$ (where $e$

        @end tex

        is the base of the natural system of logarithms, approximately 2.71828).

RETURNS

        On success, <<exp>> and <<expf>> return the calculated value.

        If the result underflows, the returned value is <<0>>.  If the

        result overflows, the returned value is <<HUGE_VAL>>.  In

        either case, <<errno>> is set to <<ERANGE>>.

PORTABILITY

        <<exp>> is ANSI C.  <<expf>> is an extension.

*/

/*****************************************************************

 * Exponential Function

 *

 * Input:

 *   x - floating point value

 *

 * Output:

 *   e raised to x.

 *

 * Description:

 *   This routine returns e raised to the xth power.

 *

 *****************************************************************/

#include <float.h>

#include "fdlibm.h"

#include "zmath.h"

#ifndef _DOUBLE_IS_32BITS

static const double INV_LN2 = 1.4426950408889634074;

static const double LN2 = 0.6931471805599453094172321;

static const double p[] = { 0.25, 0.75753180159422776666e-2,

                     0.31555192765684646356e-4 };

static const double q[] = { 0.5, 0.56817302698551221787e-1,

                     0.63121894374398504557e-3,

                     0.75104028399870046114e-6 };

double

_DEFUN (exp, (double),

        double x)

{

  int N;

  double g, z, R, P, Q;

  switch (numtest (x))

    {

      case NAN:

        errno = EDOM;

        return (x);

      case INF:

        errno = ERANGE;

        if (ispos (x))

          return (z_infinity.d);

        else

          return (0.0);

      case 0:

        return (1.0);

    }

  /* Check for out of bounds. */

  if (x > BIGX || x < SMALLX)

    {

      errno = ERANGE;

      return (x);

    }

  /* Check for a value too small to calculate. */

  if (-z_rooteps < x && x < z_rooteps)

    {

      return (1.0);

    }

  /* Calculate the exponent. */

  if (x < 0.0)

    N = (int) (x * INV_LN2 - 0.5);

  else

    N = (int) (x * INV_LN2 + 0.5);

  /* Construct the mantissa. */

  g = x - N * LN2;

  z = g * g;

  P = g * ((p[2] * z + p[1]) * z + p[0]);

  Q = ((q[3] * z + q[2]) * z + q[1]) * z + q[0];

  R = 0.5 + P / (Q - P);

  /* Return the floating point value. */

  N++;

  return (ldexp (R, N));

}

#endif /* _DOUBLE_IS_32BITS */