137 lines
5.0 KiB
C
137 lines
5.0 KiB
C
/* $NetBSD: n_exp__E.c,v 1.6 2003/08/07 16:44:51 agc Exp $ */
|
|
/*
|
|
* Copyright (c) 1985, 1993
|
|
* The Regents of the University of California. All rights reserved.
|
|
*
|
|
* 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 University 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 REGENTS 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 REGENTS 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.
|
|
*/
|
|
|
|
#ifndef lint
|
|
#if 0
|
|
static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93";
|
|
#endif
|
|
#endif /* not lint */
|
|
|
|
/* exp__E(x,c)
|
|
* ASSUMPTION: c << x SO THAT fl(x+c)=x.
|
|
* (c is the correction term for x)
|
|
* exp__E RETURNS
|
|
*
|
|
* / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736
|
|
* exp__E(x,c) = |
|
|
* \ 0 , |x| < 1E-19.
|
|
*
|
|
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
|
|
* KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
|
|
* CODED IN C BY K.C. NG, 1/31/85;
|
|
* REVISED BY K.C. NG on 3/16/85, 4/16/85.
|
|
*
|
|
* Required system supported function:
|
|
* copysign(x,y)
|
|
*
|
|
* Method:
|
|
* 1. Rational approximation. Let r=x+c.
|
|
* Based on
|
|
* 2 * sinh(r/2)
|
|
* exp(r) - 1 = ---------------------- ,
|
|
* cosh(r/2) - sinh(r/2)
|
|
* exp__E(r) is computed using
|
|
* x*x (x/2)*W - ( Q - ( 2*P + x*P ) )
|
|
* --- + (c + x*[---------------------------------- + c ])
|
|
* 2 1 - W
|
|
* where P := p1*x^2 + p2*x^4,
|
|
* Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
|
|
* W := x/2-(Q-x*P),
|
|
*
|
|
* (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
|
|
* nomials P and Q may be regarded as the approximations to sinh
|
|
* and cosh :
|
|
* sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . )
|
|
*
|
|
* The coefficients were obtained by a special Remez algorithm.
|
|
*
|
|
* Approximation error:
|
|
*
|
|
* | exp(x) - 1 | 2**(-57), (IEEE double)
|
|
* | ------------ - (exp__E(x,0)+x)/x | <=
|
|
* | x | 2**(-69). (VAX D)
|
|
*
|
|
* Constants:
|
|
* The hexadecimal values are the intended ones for the following constants.
|
|
* The decimal values may be used, provided that the compiler will convert
|
|
* from decimal to binary accurately enough to produce the hexadecimal values
|
|
* shown.
|
|
*/
|
|
|
|
#define _LIBM_STATIC
|
|
#include "mathimpl.h"
|
|
|
|
vc(p1, 1.5150724356786683059E-2 ,3abe,3d78,066a,67e1, -6, .F83ABE67E1066A)
|
|
vc(p2, 6.3112487873718332688E-5 ,5b42,3984,0173,48cd, -13, .845B4248CD0173)
|
|
vc(q1, 1.1363478204690669916E-1 ,b95a,3ee8,ec45,44a2, -3, .E8B95A44A2EC45)
|
|
vc(q2, 1.2624568129896839182E-3 ,7905,3ba5,f5e7,72e4, -9, .A5790572E4F5E7)
|
|
vc(q3, 1.5021856115869022674E-6 ,9eb4,36c9,c395,604a, -19, .C99EB4604AC395)
|
|
|
|
ic(p1, 1.3887401997267371720E-2, -7, 1.C70FF8B3CC2CF)
|
|
ic(p2, 3.3044019718331897649E-5, -15, 1.15317DF4526C4)
|
|
ic(q1, 1.1110813732786649355E-1, -4, 1.C719538248597)
|
|
ic(q2, 9.9176615021572857300E-4, -10, 1.03FC4CB8C98E8)
|
|
|
|
#ifdef vccast
|
|
#define p1 vccast(p1)
|
|
#define p2 vccast(p2)
|
|
#define q1 vccast(q1)
|
|
#define q2 vccast(q2)
|
|
#define q3 vccast(q3)
|
|
#endif
|
|
|
|
double
|
|
__exp__E(double x, double c)
|
|
{
|
|
const static double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
|
|
double z,p,q,xp,xh,w;
|
|
if(copysign(x,one)>small) {
|
|
z = x*x ;
|
|
p = z*( p1 +z* p2 );
|
|
#if defined(__vax__)||defined(tahoe)
|
|
q = z*( q1 +z*( q2 +z* q3 ));
|
|
#else /* defined(__vax__)||defined(tahoe) */
|
|
q = z*( q1 +z* q2 );
|
|
#endif /* defined(__vax__)||defined(tahoe) */
|
|
xp= x*p ;
|
|
xh= x*half ;
|
|
w = xh-(q-xp) ;
|
|
p = p+p;
|
|
c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
|
|
return(z*half+c);
|
|
}
|
|
/* end of |x| > small */
|
|
|
|
else {
|
|
if(x!=zero) w=one+small; /* raise the inexact flag ??? -ragge */
|
|
return(copysign(zero,x));
|
|
}
|
|
}
|