1 #include "FEATURE/uwin" 2 3 #if !_UWIN 4 5 void _STUB_exp(){} 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.c 8.1 (Berkeley) 6/4/93"; 40 #endif /* not lint */ 41 42 /* EXP(X) 43 * RETURN THE EXPONENTIAL OF X 44 * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) 45 * CODED IN C BY K.C. NG, 1/19/85; 46 * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86. 47 * 48 * Required system supported functions: 49 * scalb(x,n) 50 * copysign(x,y) 51 * finite(x) 52 * 53 * Method: 54 * 1. Argument Reduction: given the input x, find r and integer k such 55 * that 56 * x = k*ln2 + r, |r| <= 0.5*ln2 . 57 * r will be represented as r := z+c for better accuracy. 58 * 59 * 2. Compute exp(r) by 60 * 61 * exp(r) = 1 + r + r*R1/(2-R1), 62 * where 63 * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))). 64 * 65 * 3. exp(x) = 2^k * exp(r) . 66 * 67 * Special cases: 68 * exp(INF) is INF, exp(NaN) is NaN; 69 * exp(-INF)= 0; 70 * for finite argument, only exp(0)=1 is exact. 71 * 72 * Accuracy: 73 * exp(x) returns the exponential of x nearly rounded. In a test run 74 * with 1,156,000 random arguments on a VAX, the maximum observed 75 * error was 0.869 ulps (units in the last place). 76 * 77 * Constants: 78 * The hexadecimal values are the intended ones for the following constants. 79 * The decimal values may be used, provided that the compiler will convert 80 * from decimal to binary accurately enough to produce the hexadecimal values 81 * shown. 82 */ 83 84 #include "mathimpl.h" 85 86 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 87 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 88 vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010) 89 vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF) 90 vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1) 91 vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1) 92 vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94) 93 vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F) 94 vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84) 95 vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683) 96 97 #ifdef vccast 98 #define ln2hi vccast(ln2hi) 99 #define ln2lo vccast(ln2lo) 100 #define lnhuge vccast(lnhuge) 101 #define lntiny vccast(lntiny) 102 #define invln2 vccast(invln2) 103 #define p1 vccast(p1) 104 #define p2 vccast(p2) 105 #define p3 vccast(p3) 106 #define p4 vccast(p4) 107 #define p5 vccast(p5) 108 #endif 109 110 ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E) 111 ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93) 112 ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C) 113 ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1) 114 ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0) 115 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 116 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76) 117 ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2) 118 ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354) 119 ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE) 120 121 #if !_lib_exp 122 123 extern double exp(x) 124 double x; 125 { 126 double z,hi,lo,c; 127 int k; 128 129 #if !defined(vax)&&!defined(tahoe) 130 if(x!=x) return(x); /* x is NaN */ 131 #endif /* !defined(vax)&&!defined(tahoe) */ 132 if( x <= lnhuge ) { 133 if( x >= lntiny ) { 134 135 /* argument reduction : x --> x - k*ln2 */ 136 137 k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */ 138 139 /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */ 140 141 hi=x-k*ln2hi; 142 x=hi-(lo=k*ln2lo); 143 144 /* return 2^k*[1+x+x*c/(2+c)] */ 145 z=x*x; 146 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); 147 return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k); 148 149 } 150 /* end of x > lntiny */ 151 152 else 153 /* exp(-big#) underflows to zero */ 154 if(finite(x)) return(scalb(1.0,-5000)); 155 156 /* exp(-INF) is zero */ 157 else return(0.0); 158 } 159 /* end of x < lnhuge */ 160 161 else 162 /* exp(INF) is INF, exp(+big#) overflows to INF */ 163 return( finite(x) ? scalb(1.0,5000) : x); 164 } 165 166 #endif 167 168 /* returns exp(r = x + c) for |c| < |x| with no overlap. */ 169 170 double __exp__D(x, c) 171 double x, c; 172 { 173 double z,hi,lo; 174 int k; 175 176 #if !defined(vax)&&!defined(tahoe) 177 if (x!=x) return(x); /* x is NaN */ 178 #endif /* !defined(vax)&&!defined(tahoe) */ 179 if ( x <= lnhuge ) { 180 if ( x >= lntiny ) { 181 182 /* argument reduction : x --> x - k*ln2 */ 183 z = invln2*x; 184 k = (int)z + copysign(.5, x); 185 186 /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */ 187 188 hi=(x-k*ln2hi); /* Exact. */ 189 x= hi - (lo = k*ln2lo-c); 190 /* return 2^k*[1+x+x*c/(2+c)] */ 191 z=x*x; 192 c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); 193 c = (x*c)/(2.0-c); 194 195 return scalb(1.+(hi-(lo - c)), k); 196 } 197 /* end of x > lntiny */ 198 199 else 200 /* exp(-big#) underflows to zero */ 201 if(finite(x)) return(scalb(1.0,-5000)); 202 203 /* exp(-INF) is zero */ 204 else return(0.0); 205 } 206 /* end of x < lnhuge */ 207 208 else 209 /* exp(INF) is INF, exp(+big#) overflows to INF */ 210 return( finite(x) ? scalb(1.0,5000) : x); 211 } 212 213 #endif 214