1 /* $NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $ */ 2 3 /* 4 * Copyright (c) 1985, 1993 5 * The Regents of the University of California. All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 3. All advertising materials mentioning features or use of this software 16 * must display the following acknowledgement: 17 * This product includes software developed by the University of 18 * California, Berkeley and its contributors. 19 * 4. Neither the name of the University nor the names of its contributors 20 * may be used to endorse or promote products derived from this software 21 * without specific prior written permission. 22 * 23 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 24 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 25 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 26 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 27 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 28 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 29 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 30 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 31 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 32 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 33 * SUCH DAMAGE. 34 */ 35 36 /* @(#)exp.c 8.1 (Berkeley) 6/4/93 */ 37 #include <sys/cdefs.h> 38 #if 0 39 __FBSDID("$FreeBSD: release/9.0.0/lib/msun/bsdsrc/b_exp.c 176449 2008-02-22 02:26:51Z das $"); 40 #else 41 __RCSID("$NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $"); 42 #endif 43 44 45 /* EXP(X) 46 * RETURN THE EXPONENTIAL OF X 47 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) 48 * CODED IN C BY K.C. NG, 1/19/85; 49 * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86. 50 * 51 * Required system supported functions: 52 * scalb(x,n) 53 * copysign(x,y) 54 * finite(x) 55 * 56 * Method: 57 * 1. Argument Reduction: given the input x, find r and integer k such 58 * that 59 * x = k*ln2 + r, |r| <= 0.5*ln2 . 60 * r will be represented as r := z+c for better accuracy. 61 * 62 * 2. Compute exp(r) by 63 * 64 * exp(r) = 1 + r + r*R1/(2-R1), 65 * where 66 * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))). 67 * 68 * 3. exp(x) = 2^k * exp(r) . 69 * 70 * Special cases: 71 * exp(INF) is INF, exp(NaN) is NaN; 72 * exp(-INF)= 0; 73 * for finite argument, only exp(0)=1 is exact. 74 * 75 * Accuracy: 76 * exp(x) returns the exponential of x nearly rounded. In a test run 77 * with 1,156,000 random arguments on a VAX, the maximum observed 78 * error was 0.869 ulps (units in the last place). 79 */ 80 81 #include "math.h" 82 #include "math_private.h" 83 84 static const double p1 = 0x1.555555555553ep-3; 85 static const double p2 = -0x1.6c16c16bebd93p-9; 86 static const double p3 = 0x1.1566aaf25de2cp-14; 87 static const double p4 = -0x1.bbd41c5d26bf1p-20; 88 static const double p5 = 0x1.6376972bea4d0p-25; 89 static const double ln2hi = 0x1.62e42fee00000p-1; 90 static const double ln2lo = 0x1.a39ef35793c76p-33; 91 static const double lnhuge = 0x1.6602b15b7ecf2p9; 92 static const double lntiny = -0x1.77af8ebeae354p9; 93 static const double invln2 = 0x1.71547652b82fep0; 94 95 /* returns exp(r = x + c) for |c| < |x| with no overlap. */ 96 97 double 98 __exp__D(double x, double c) 99 { 100 double z,hi,lo; 101 int k; 102 103 if (x != x) /* x is NaN */ 104 return(x); 105 if ( x <= lnhuge ) { 106 if ( x >= lntiny ) { 107 108 /* argument reduction : x --> x - k*ln2 */ 109 z = invln2*x; 110 k = z + copysign(.5, x); 111 112 /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */ 113 114 hi=(x-k*ln2hi); /* Exact. */ 115 x= hi - (lo = k*ln2lo-c); 116 /* return 2^k*[1+x+x*c/(2+c)] */ 117 z=x*x; 118 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); 119 c = (x*c)/(2.0-c); 120 121 return scalb(1.+(hi-(lo - c)), k); 122 } 123 /* end of x > lntiny */ 124 125 else 126 /* exp(-big#) underflows to zero */ 127 if(finite(x)) return(scalb(1.0,-5000)); 128 129 /* exp(-INF) is zero */ 130 else return(0.0); 131 } 132 /* end of x < lnhuge */ 133 134 else 135 /* exp(INF) is INF, exp(+big#) overflows to INF */ 136 return( finite(x) ? scalb(1.0,5000) : x); 137 } 138