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Diffstat (limited to 'lib/libm/common_source/exp__E.c')
| -rw-r--r-- | lib/libm/common_source/exp__E.c | 136 |
1 files changed, 136 insertions, 0 deletions
diff --git a/lib/libm/common_source/exp__E.c b/lib/libm/common_source/exp__E.c new file mode 100644 index 000000000000..ab972477a04b --- /dev/null +++ b/lib/libm/common_source/exp__E.c @@ -0,0 +1,136 @@ +/* + * 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. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. 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 +static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93"; +#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. + */ + +#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(x,c) +double x,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) one+small; /* raise the inexact flag */ + return(copysign(zero,x)); + } +} |