1 #include "FEATURE/uwin" 2 3 #if !_UWIN || _lib_expm1 4 5 void _STUB_expm1(){} 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[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93"; 40 #endif /* not lint */ 41 42 /* EXPM1(X) 43 * RETURN THE EXPONENTIAL OF X MINUS ONE 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, 3/7/85, 3/21/85, 4/16/85. 47 * 48 * Required system supported functions: 49 * scalb(x,n) 50 * copysign(x,y) 51 * finite(x) 52 * 53 * Kernel function: 54 * exp__E(x,c) 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 EXPM1(r)=exp(r)-1 by 63 * 64 * EXPM1(r=z+c) := z + exp__E(z,c) 65 * 66 * 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ). 67 * 68 * Remarks: 69 * 1. When k=1 and z < -0.25, we use the following formula for 70 * better accuracy: 71 * EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) ) 72 * 2. To avoid rounding error in 1-2^-k where k is large, we use 73 * EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 } 74 * when k>56. 75 * 76 * Special cases: 77 * EXPM1(INF) is INF, EXPM1(NaN) is NaN; 78 * EXPM1(-INF)= -1; 79 * for finite argument, only EXPM1(0)=0 is exact. 80 * 81 * Accuracy: 82 * EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with 83 * 1,166,000 random arguments on a VAX, the maximum observed error was 84 * .872 ulps (units of the last place). 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(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 96 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 97 vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010) 98 vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1) 99 100 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 101 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) 102 ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2) 103 ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE) 104 105 #ifdef vccast 106 #define ln2hi vccast(ln2hi) 107 #define ln2lo vccast(ln2lo) 108 #define lnhuge vccast(lnhuge) 109 #define invln2 vccast(invln2) 110 #endif 111 112 extern double expm1(x) 113 double x; 114 { 115 const static double one=1.0, half=1.0/2.0; 116 double z,hi,lo,c; 117 int k; 118 #if defined(vax)||defined(tahoe) 119 static prec=56; 120 #else /* defined(vax)||defined(tahoe) */ 121 static prec=53; 122 #endif /* defined(vax)||defined(tahoe) */ 123 124 #if !defined(vax)&&!defined(tahoe) 125 if(x!=x) return(x); /* x is NaN */ 126 #endif /* !defined(vax)&&!defined(tahoe) */ 127 128 if( x <= lnhuge ) { 129 if( x >= -40.0 ) { 130 131 /* argument reduction : x - k*ln2 */ 132 k= (int)(invln2*x)+copysign(0.5,x); /* k=NINT(x/ln2) */ 133 hi=x-k*ln2hi ; 134 z=hi-(lo=k*ln2lo); 135 c=(hi-z)-lo; 136 137 if(k==0) return(z+__exp__E(z,c)); 138 if(k==1) 139 if(z< -0.25) 140 {x=z+half;x +=__exp__E(z,c); return(x+x);} 141 else 142 {z+=__exp__E(z,c); x=half+z; return(x+x);} 143 /* end of k=1 */ 144 145 else { 146 if(k<=prec) 147 { x=one-scalb(one,-k); z += __exp__E(z,c);} 148 else if(k<100) 149 { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;} 150 else 151 { x = __exp__E(z,c)+z; z=one;} 152 153 return (scalb(x+z,k)); 154 } 155 } 156 /* end of x > lnunfl */ 157 158 else 159 /* expm1(-big#) rounded to -1 (inexact) */ 160 if(finite(x)) 161 { ln2hi+ln2lo; return(-one);} 162 163 /* expm1(-INF) is -1 */ 164 else return(-one); 165 } 166 /* end of x < lnhuge */ 167 168 else 169 /* expm1(INF) is INF, expm1(+big#) overflows to INF */ 170 return( finite(x) ? scalb(one,5000) : x); 171 } 172 173 #endif 174