1 #include "FEATURE/uwin" 2 3 #if !_UWIN 4 5 void _STUB_exp__E(){} 6 7 #else 8 9 /* 10 * Copyright (c) 1985, 1993 11 * The Regents of the University of California. All rights reserved. 12 * 13 * Redistribution and use in source and binary forms, with or without 14 * modification, are permitted provided that the following conditions 15 * are met: 16 * 1. Redistributions of source code must retain the above copyright 17 * notice, this list of conditions and the following disclaimer. 18 * 2. Redistributions in binary form must reproduce the above copyright 19 * notice, this list of conditions and the following disclaimer in the 20 * documentation and/or other materials provided with the distribution. 21 * 3. Neither the name of the University nor the names of its contributors 22 * may be used to endorse or promote products derived from this software 23 * without specific prior written permission. 24 * 25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 28 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 35 * SUCH DAMAGE. 36 */ 37 38 #ifndef lint 39 static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93"; 40 #endif /* not lint */ 41 42 /* exp__E(x,c) 43 * ASSUMPTION: c << x SO THAT fl(x+c)=x. 44 * (c is the correction term for x) 45 * exp__E RETURNS 46 * 47 * / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736 48 * exp__E(x,c) = | 49 * \ 0 , |x| < 1E-19. 50 * 51 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) 52 * KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS 53 * CODED IN C BY K.C. NG, 1/31/85; 54 * REVISED BY K.C. NG on 3/16/85, 4/16/85. 55 * 56 * Required system supported function: 57 * copysign(x,y) 58 * 59 * Method: 60 * 1. Rational approximation. Let r=x+c. 61 * Based on 62 * 2 * sinh(r/2) 63 * exp(r) - 1 = ---------------------- , 64 * cosh(r/2) - sinh(r/2) 65 * exp__E(r) is computed using 66 * x*x (x/2)*W - ( Q - ( 2*P + x*P ) ) 67 * --- + (c + x*[---------------------------------- + c ]) 68 * 2 1 - W 69 * where P := p1*x^2 + p2*x^4, 70 * Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6) 71 * W := x/2-(Q-x*P), 72 * 73 * (See the listing below for the values of p1,p2,q1,q2,q3. The poly- 74 * nomials P and Q may be regarded as the approximations to sinh 75 * and cosh : 76 * sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . ) 77 * 78 * The coefficients were obtained by a special Remez algorithm. 79 * 80 * Approximation error: 81 * 82 * | exp(x) - 1 | 2**(-57), (IEEE double) 83 * | ------------ - (exp__E(x,0)+x)/x | <= 84 * | x | 2**(-69). (VAX D) 85 * 86 * Constants: 87 * The hexadecimal values are the intended ones for the following constants. 88 * The decimal values may be used, provided that the compiler will convert 89 * from decimal to binary accurately enough to produce the hexadecimal values 90 * shown. 91 */ 92 93 #include "mathimpl.h" 94 95 vc(p1, 1.5150724356786683059E-2 ,3abe,3d78,066a,67e1, -6, .F83ABE67E1066A) 96 vc(p2, 6.3112487873718332688E-5 ,5b42,3984,0173,48cd, -13, .845B4248CD0173) 97 vc(q1, 1.1363478204690669916E-1 ,b95a,3ee8,ec45,44a2, -3, .E8B95A44A2EC45) 98 vc(q2, 1.2624568129896839182E-3 ,7905,3ba5,f5e7,72e4, -9, .A5790572E4F5E7) 99 vc(q3, 1.5021856115869022674E-6 ,9eb4,36c9,c395,604a, -19, .C99EB4604AC395) 100 101 ic(p1, 1.3887401997267371720E-2, -7, 1.C70FF8B3CC2CF) 102 ic(p2, 3.3044019718331897649E-5, -15, 1.15317DF4526C4) 103 ic(q1, 1.1110813732786649355E-1, -4, 1.C719538248597) 104 ic(q2, 9.9176615021572857300E-4, -10, 1.03FC4CB8C98E8) 105 106 #ifdef vccast 107 #define p1 vccast(p1) 108 #define p2 vccast(p2) 109 #define q1 vccast(q1) 110 #define q2 vccast(q2) 111 #define q3 vccast(q3) 112 #endif 113 114 double __exp__E(x,c) 115 double x,c; 116 { 117 const static double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19; 118 double z,p,q,xp,xh,w; 119 if(copysign(x,one)>small) { 120 z = x*x ; 121 p = z*( p1 +z* p2 ); 122 #if defined(vax)||defined(tahoe) 123 q = z*( q1 +z*( q2 +z* q3 )); 124 #else /* defined(vax)||defined(tahoe) */ 125 q = z*( q1 +z* q2 ); 126 #endif /* defined(vax)||defined(tahoe) */ 127 xp= x*p ; 128 xh= x*half ; 129 w = xh-(q-xp) ; 130 p = p+p; 131 c += x*((xh*w-(q-(p+xp)))/(one-w)+c); 132 return(z*half+c); 133 } 134 /* end of |x| > small */ 135 136 else { 137 if(x!=zero) one+small; /* raise the inexact flag */ 138 return(copysign(zero,x)); 139 } 140 } 141 142 #endif 143