1 /* $NetBSD: n_expm1.c,v 1.8 2013/11/24 18:50:58 martin Exp $ */ 2 /* 3 * Copyright (c) 1985, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31 #ifndef lint 32 #if 0 33 static char sccsid[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93"; 34 #endif 35 #endif /* not lint */ 36 37 /* EXPM1(X) 38 * RETURN THE EXPONENTIAL OF X MINUS ONE 39 * DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS) 40 * CODED IN C BY K.C. NG, 1/19/85; 41 * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85. 42 * 43 * Required system supported functions: 44 * scalb(x,n) 45 * copysign(x,y) 46 * finite(x) 47 * 48 * Kernel function: 49 * exp__E(x,c) 50 * 51 * Method: 52 * 1. Argument Reduction: given the input x, find r and integer k such 53 * that 54 * x = k*ln2 + r, |r| <= 0.5*ln2 . 55 * r will be represented as r := z+c for better accuracy. 56 * 57 * 2. Compute EXPM1(r)=exp(r)-1 by 58 * 59 * EXPM1(r=z+c) := z + exp__E(z,c) 60 * 61 * 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ). 62 * 63 * Remarks: 64 * 1. When k=1 and z < -0.25, we use the following formula for 65 * better accuracy: 66 * EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) ) 67 * 2. To avoid rounding error in 1-2^-k where k is large, we use 68 * EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 } 69 * when k>56. 70 * 71 * Special cases: 72 * EXPM1(INF) is INF, EXPM1(NaN) is NaN; 73 * EXPM1(-INF)= -1; 74 * for finite argument, only EXPM1(0)=0 is exact. 75 * 76 * Accuracy: 77 * EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with 78 * 1,166,000 random arguments on a VAX, the maximum observed error was 79 * .872 ulps (units of the last place). 80 * 81 * Constants: 82 * The hexadecimal values are the intended ones for the following constants. 83 * The decimal values may be used, provided that the compiler will convert 84 * from decimal to binary accurately enough to produce the hexadecimal values 85 * shown. 86 */ 87 88 #define _LIBM_STATIC 89 #include "mathimpl.h" 90 91 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 92 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 93 vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010) 94 vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1) 95 96 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 97 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) 98 ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2) 99 ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE) 100 101 #ifdef vccast 102 #define ln2hi vccast(ln2hi) 103 #define ln2lo vccast(ln2lo) 104 #define lnhuge vccast(lnhuge) 105 #define invln2 vccast(invln2) 106 #endif 107 108 #if defined(__vax__)||defined(tahoe) 109 #define PREC 56 110 #else /* defined(__vax__)||defined(tahoe) */ 111 #define PREC 53 112 #endif /* defined(__vax__)||defined(tahoe) */ 113 114 float 115 expm1f(float x) 116 { 117 return (float)expm1(x); 118 } 119 120 double 121 expm1(double x) 122 { 123 static const double one=1.0, half=1.0/2.0; 124 double z,hi,lo,c; 125 int k; 126 127 #if !defined(__vax__)&&!defined(tahoe) 128 if(x!=x) return(x); /* x is NaN */ 129 #endif /* !defined(__vax__)&&!defined(tahoe) */ 130 131 if( x <= lnhuge ) { 132 if( x >= -40.0 ) { 133 134 /* argument reduction : x - k*ln2 */ 135 k= invln2 *x+copysign(0.5,x); /* k=NINT(x/ln2) */ 136 hi=x-k*ln2hi ; 137 z=hi-(lo=k*ln2lo); 138 c=(hi-z)-lo; 139 140 if(k==0) return(z+__exp__E(z,c)); 141 if(k==1) 142 if(z< -0.25) 143 {x=z+half;x +=__exp__E(z,c); return(x+x);} 144 else 145 {z+=__exp__E(z,c); x=half+z; return(x+x);} 146 /* end of k=1 */ 147 148 else { 149 if(k<=PREC) 150 { x=one-scalb(one,-k); z += __exp__E(z,c);} 151 else if(k<100) 152 { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;} 153 else 154 { x = __exp__E(z,c)+z; z=one;} 155 156 return (scalb(x+z,k)); 157 } 158 } 159 /* end of x > lnunfl */ 160 161 else 162 /* expm1(-big#) rounded to -1 (inexact) */ 163 if(finite(x)) 164 { c=ln2hi+ln2lo; return(-one);} /* ??? -ragge */ 165 166 /* expm1(-INF) is -1 */ 167 else return(-one); 168 } 169 /* end of x < lnhuge */ 170 171 else 172 /* expm1(INF) is INF, expm1(+big#) overflows to INF */ 173 return( finite(x) ? scalb(one,5000) : x); 174 } 175
Indexes created Mon Sep 22 10:09:38 GMT 2025