mirror of
https://github.com/ZDoom/raze-gles.git
synced 2024-11-11 07:11:39 +00:00
207 lines
5.4 KiB
C
207 lines
5.4 KiB
C
/* exp.c
|
||
*
|
||
* Exponential function
|
||
*
|
||
*
|
||
*
|
||
* SYNOPSIS:
|
||
*
|
||
* double x, y, exp();
|
||
*
|
||
* y = exp( x );
|
||
*
|
||
*
|
||
*
|
||
* DESCRIPTION:
|
||
*
|
||
* Returns e (2.71828...) raised to the x power.
|
||
*
|
||
* Range reduction is accomplished by separating the argument
|
||
* into an integer k and fraction f such that
|
||
*
|
||
* x k f
|
||
* e = 2 e.
|
||
*
|
||
* A Pade' form 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
|
||
* of degree 2/3 is used to approximate exp(f) in the basic
|
||
* interval [-0.5, 0.5].
|
||
*
|
||
*
|
||
* ACCURACY:
|
||
*
|
||
* Relative error:
|
||
* arithmetic domain # trials peak rms
|
||
* DEC 0, MAXLOG 38000 3.0e-17 6.2e-18
|
||
* IEEE +- 708 40000 2.0e-16 5.6e-17
|
||
*
|
||
*
|
||
* Error amplification in the exponential function can be
|
||
* a serious matter. The error propagation involves
|
||
* exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
|
||
* which shows that a 1 lsb error in representing X produces
|
||
* a relative error of X times 1 lsb in the function.
|
||
* While the routine gives an accurate result for arguments
|
||
* that are exactly represented by a double precision
|
||
* computer number, the result contains amplified roundoff
|
||
* error for large arguments not exactly represented.
|
||
*
|
||
*
|
||
* ERROR MESSAGES:
|
||
*
|
||
* message condition value returned
|
||
* exp underflow x < MINLOG 0.0
|
||
* exp overflow x > MAXLOG MAXNUM
|
||
*
|
||
*/
|
||
|
||
/*
|
||
Cephes Math Library Release 2.2: January, 1991
|
||
Copyright 1984, 1991 by Stephen L. Moshier
|
||
|
||
Redistribution and use in source and binary forms, with or without
|
||
modification, are permitted provided that the following conditions are met:
|
||
|
||
1. Redistributions of source code must retain the above copyright notice,
|
||
this list of conditions and the following disclaimer.
|
||
2. Redistributions in binary form must reproduce the above copyright
|
||
notice, this list of conditions and the following disclaimer in the
|
||
documentation and/or other materials provided with the distribution.
|
||
3. Neither the name of the <ORGANIZATION> nor the names of its
|
||
contributors may be used to endorse or promote products derived from
|
||
this software without specific prior written permission.
|
||
|
||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
||
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||
POSSIBILITY OF SUCH DAMAGE.
|
||
|
||
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
|
||
*/
|
||
|
||
|
||
/* Exponential function */
|
||
|
||
#include "mconf.h"
|
||
static char fname[] = {"exp"};
|
||
|
||
#ifdef UNK
|
||
|
||
static double P[] = {
|
||
1.26177193074810590878E-4,
|
||
3.02994407707441961300E-2,
|
||
9.99999999999999999910E-1,
|
||
};
|
||
static double Q[] = {
|
||
3.00198505138664455042E-6,
|
||
2.52448340349684104192E-3,
|
||
2.27265548208155028766E-1,
|
||
2.00000000000000000009E0,
|
||
};
|
||
static double C1 = 6.93145751953125E-1;
|
||
static double C2 = 1.42860682030941723212E-6;
|
||
#endif
|
||
|
||
#ifdef DEC
|
||
static short P[] = {
|
||
0035004,0047156,0127442,0057502,
|
||
0036770,0033210,0063121,0061764,
|
||
0040200,0000000,0000000,0000000,
|
||
};
|
||
static short Q[] = {
|
||
0033511,0072665,0160662,0176377,
|
||
0036045,0070715,0124105,0132777,
|
||
0037550,0134114,0142077,0001637,
|
||
0040400,0000000,0000000,0000000,
|
||
};
|
||
static short sc1[] = {0040061,0071000,0000000,0000000};
|
||
#define C1 (*(double *)sc1)
|
||
static short sc2[] = {0033277,0137216,0075715,0057117};
|
||
#define C2 (*(double *)sc2)
|
||
#endif
|
||
|
||
#ifdef IBMPC
|
||
static short P[] = {
|
||
0x4be8,0xd5e4,0x89cd,0x3f20,
|
||
0x2c7e,0x0cca,0x06d1,0x3f9f,
|
||
0x0000,0x0000,0x0000,0x3ff0,
|
||
};
|
||
static short Q[] = {
|
||
0x5fa0,0xbc36,0x2eb6,0x3ec9,
|
||
0xb6c0,0xb508,0xae39,0x3f64,
|
||
0xe074,0x9887,0x1709,0x3fcd,
|
||
0x0000,0x0000,0x0000,0x4000,
|
||
};
|
||
static short sc1[] = {0x0000,0x0000,0x2e40,0x3fe6};
|
||
#define C1 (*(double *)sc1)
|
||
static short sc2[] = {0xabca,0xcf79,0xf7d1,0x3eb7};
|
||
#define C2 (*(double *)sc2)
|
||
#endif
|
||
|
||
#ifdef MIEEE
|
||
static short P[] = {
|
||
0x3f20,0x89cd,0xd5e4,0x4be8,
|
||
0x3f9f,0x06d1,0x0cca,0x2c7e,
|
||
0x3ff0,0x0000,0x0000,0x0000,
|
||
};
|
||
static short Q[] = {
|
||
0x3ec9,0x2eb6,0xbc36,0x5fa0,
|
||
0x3f64,0xae39,0xb508,0xb6c0,
|
||
0x3fcd,0x1709,0x9887,0xe074,
|
||
0x4000,0x0000,0x0000,0x0000,
|
||
};
|
||
static short sc1[] = {0x3fe6,0x2e40,0x0000,0x0000};
|
||
#define C1 (*(double *)sc1)
|
||
static short sc2[] = {0x3eb7,0xf7d1,0xcf79,0xabca};
|
||
#define C2 (*(double *)sc2)
|
||
#endif
|
||
|
||
extern double LOGE2, LOG2E, MAXLOG, MINLOG, MAXNUM;
|
||
|
||
double c_exp(x)
|
||
double x;
|
||
{
|
||
double px, xx;
|
||
int n;
|
||
double polevl(), floor(), ldexp();
|
||
|
||
if( x > MAXLOG)
|
||
{
|
||
mtherr( fname, OVERFLOW );
|
||
return( MAXNUM );
|
||
}
|
||
|
||
if( x < MINLOG )
|
||
{
|
||
mtherr( fname, UNDERFLOW );
|
||
return(0.0);
|
||
}
|
||
|
||
/* Express e**x = e**g 2**n
|
||
* = e**g e**( n loge(2) )
|
||
* = e**( g + n loge(2) )
|
||
*/
|
||
px = floor( LOG2E * x + 0.5 ); /* floor() truncates toward -infinity. */
|
||
n = (int)px;
|
||
x -= px * C1;
|
||
x -= px * C2;
|
||
|
||
/* rational approximation for exponential
|
||
* of the fractional part:
|
||
* e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
|
||
*/
|
||
xx = x * x;
|
||
px = x * polevl( xx, P, 2 );
|
||
x = px/( polevl( xx, Q, 3 ) - px );
|
||
x = 1.0 + ldexp( x, 1 );
|
||
|
||
/* multiply by power of 2 */
|
||
x = ldexp( x, n );
|
||
return(x);
|
||
}
|