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/* @(#)z_logarithm.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

       <<log>>, <<logf>>, <<log10>>, <<log10f>>, <<logarithm>>, <<logarithmf>>---natural or base 10 logarithms

INDEX

    log

INDEX

    logf

INDEX

    log10

INDEX

    log10f

ANSI_SYNOPSIS

       #include <math.h>

       double log(double <[x]>);

       float logf(float <[x]>);

       double log10(double <[x]>);

       float log10f(float <[x]>);

TRAD_SYNOPSIS

       #include <math.h>

       double log(<[x]>);

       double <[x]>;

       float logf(<[x]>);

       float <[x]>;

       double log10(<[x]>);

       double <[x]>;

       float log10f(<[x]>);

       float <[x]>;

DESCRIPTION

Return the natural or base 10 logarithm of <[x]>, that is, its logarithm base e

(where e is the base of the natural system of logarithms, 2.71828@dots{}) or

base 10.

<<log>> and <<logf>> are identical save for the return and argument types.

<<log10>> and <<log10f>> are identical save for the return and argument types.

RETURNS

Normally, returns the calculated value.  When <[x]> is zero, the

returned value is <<-HUGE_VAL>> and <<errno>> is set to <<ERANGE>>.

When <[x]> is negative, the returned value is <<-HUGE_VAL>> and

<<errno>> is set to <<EDOM>>.  You can control the error behavior via

<<matherr>>.

PORTABILITY

<<log>> is ANSI, <<logf>> is an extension.

<<log10>> is ANSI, <<log10f>> is an extension.

*/

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

 * Logarithm

 *

 * Input:

 *   x - floating point value

 *   ten - indicates base ten numbers

 *

 * Output:

 *   logarithm of x

 *

 * Description:

 *   This routine calculates logarithms.

 *

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

#include "fdlibm.h"

#include "zmath.h"

#ifndef _DOUBLE_IS_32BITS

static const double a[] = { -0.64124943423745581147e+02,

                             0.16383943563021534222e+02,

                            -0.78956112887481257267 };

static const double b[] = { -0.76949932108494879777e+03,

                             0.31203222091924532844e+03,

                            -0.35667977739034646171e+02 };

static const double C1 =  22713.0 / 32768.0;

static const double C2 =  1.428606820309417232e-06;

static const double C3 =  0.43429448190325182765;

double

_DEFUN (logarithm, (double, int),

        double x _AND

        int ten)

{

  int N;

  double f, w, z;

  /* Check for domain error here. */

  if (x <= 0.0)

    {

      errno = ERANGE;

      return (z_notanum.d);

    }

  /* Get the exponent and mantissa where x = f * 2^N. */

  f = frexp (x, &N);

  z = f - 0.5;

  if (f > __SQRT_HALF)

    z = (z - 0.5) / (f * 0.5 + 0.5);

  else

    {

      N--;

      z /= (z * 0.5 + 0.5);

    }

  w = z * z;

  /* Use Newton's method with 4 terms. */

  z += z * w * ((a[2] * w + a[1]) * w + a[0]) / (((w + b[2]) * w + b[1]) * w + b[0]);

  if (N != 0)

    z = (N * C2 + z) + N * C1;

  if (ten)

    z *= C3;

  return (z);

}

#endif /* _DOUBLE_IS_32BITS */