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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
SYNOPSIS
#include <math.h>
double exp(double <[x]>);
float expf(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 */
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