n_exp.c revision 1.7
1 /* $NetBSD: n_exp.c,v 1.7 2003/08/07 16:44:50 agc 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[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93"; 34 #endif 35 #endif /* not lint */ 36 37 /* EXP(X) 38 * RETURN THE EXPONENTIAL OF X 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, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86. 42 * 43 * Required system supported functions: 44 * scalb(x,n) 45 * copysign(x,y) 46 * finite(x) 47 * 48 * Method: 49 * 1. Argument Reduction: given the input x, find r and integer k such 50 * that 51 * x = k*ln2 + r, |r| <= 0.5*ln2 . 52 * r will be represented as r := z+c for better accuracy. 53 * 54 * 2. Compute exp(r) by 55 * 56 * exp(r) = 1 + r + r*R1/(2-R1), 57 * where 58 * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))). 59 * 60 * 3. exp(x) = 2^k * exp(r) . 61 * 62 * Special cases: 63 * exp(INF) is INF, exp(NaN) is NaN; 64 * exp(-INF)= 0; 65 * for finite argument, only exp(0)=1 is exact. 66 * 67 * Accuracy: 68 * exp(x) returns the exponential of x nearly rounded. In a test run 69 * with 1,156,000 random arguments on a VAX, the maximum observed 70 * error was 0.869 ulps (units in the last place). 71 * 72 * Constants: 73 * The hexadecimal values are the intended ones for the following constants. 74 * The decimal values may be used, provided that the compiler will convert 75 * from decimal to binary accurately enough to produce the hexadecimal values 76 * shown. 77 */ 78 79 #define _LIBM_STATIC 80 #include "mathimpl.h" 81 82 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 83 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 84 vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010) 85 vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF) 86 vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1) 87 vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1) 88 vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94) 89 vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F) 90 vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84) 91 vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683) 92 93 #ifdef vccast 94 #define ln2hi vccast(ln2hi) 95 #define ln2lo vccast(ln2lo) 96 #define lnhuge vccast(lnhuge) 97 #define lntiny vccast(lntiny) 98 #define invln2 vccast(invln2) 99 #define p1 vccast(p1) 100 #define p2 vccast(p2) 101 #define p3 vccast(p3) 102 #define p4 vccast(p4) 103 #define p5 vccast(p5) 104 #endif 105 106 ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E) 107 ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93) 108 ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C) 109 ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1) 110 ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0) 111 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 112 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76) 113 ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2) 114 ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354) 115 ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE) 116 117 double 118 exp(double x) 119 { 120 double z,hi,lo,c; 121 int k; 122 123 #if !defined(__vax__)&&!defined(tahoe) 124 if(x!=x) return(x); /* x is NaN */ 125 #endif /* !defined(__vax__)&&!defined(tahoe) */ 126 if( x <= lnhuge ) { 127 if( x >= lntiny ) { 128 129 /* argument reduction : x --> x - k*ln2 */ 130 131 k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */ 132 133 /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */ 134 135 hi=x-k*ln2hi; 136 x=hi-(lo=k*ln2lo); 137 138 /* return 2^k*[1+x+x*c/(2+c)] */ 139 z=x*x; 140 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); 141 return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k); 142 143 } 144 /* end of x > lntiny */ 145 146 else 147 /* exp(-big#) underflows to zero */ 148 if(finite(x)) return(scalb(1.0,-5000)); 149 150 /* exp(-INF) is zero */ 151 else return(0.0); 152 } 153 /* end of x < lnhuge */ 154 155 else 156 /* exp(INF) is INF, exp(+big#) overflows to INF */ 157 return( finite(x) ? scalb(1.0,5000) : x); 158 } 159 160 /* returns exp(r = x + c) for |c| < |x| with no overlap. */ 161 162 double 163 __exp__D(double x, double c) 164 { 165 double z,hi,lo; 166 int k; 167 168 #if !defined(__vax__)&&!defined(tahoe) 169 if (x!=x) return(x); /* x is NaN */ 170 #endif /* !defined(__vax__)&&!defined(tahoe) */ 171 if ( x <= lnhuge ) { 172 if ( x >= lntiny ) { 173 174 /* argument reduction : x --> x - k*ln2 */ 175 z = invln2*x; 176 k = z + copysign(.5, x); 177 178 /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */ 179 180 hi=(x-k*ln2hi); /* Exact. */ 181 x= hi - (lo = k*ln2lo-c); 182 /* return 2^k*[1+x+x*c/(2+c)] */ 183 z=x*x; 184 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); 185 c = (x*c)/(2.0-c); 186 187 return scalb(1.+(hi-(lo - c)), k); 188 } 189 /* end of x > lntiny */ 190 191 else 192 /* exp(-big#) underflows to zero */ 193 if(finite(x)) return(scalb(1.0,-5000)); 194 195 /* exp(-INF) is zero */ 196 else return(0.0); 197 } 198 /* end of x < lnhuge */ 199 200 else 201 /* exp(INF) is INF, exp(+big#) overflows to INF */ 202 return( finite(x) ? scalb(1.0,5000) : x); 203 } 204
Indexes created Thu Sep 25 16:09:42 GMT 2025