134 lines
3.1 KiB
C
134 lines
3.1 KiB
C
|
|
/* @(#)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 */
|