1 /* $NetBSD: n_log1p.c,v 1.9 2024/07/16 14:52:50 riastradh 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 #include <sys/cdefs.h> 32 __RCSID("$NetBSD: n_log1p.c,v 1.9 2024/07/16 14:52:50 riastradh Exp $"); 33 34 #ifndef lint 35 #if 0 36 static char sccsid[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93"; 37 #endif 38 #endif /* not lint */ 39 40 /* LOG1P(x) 41 * RETURN THE LOGARITHM OF 1+x 42 * DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS) 43 * CODED IN C BY K.C. NG, 1/19/85; 44 * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85. 45 * 46 * Required system supported functions: 47 * scalb(x,n) 48 * copysign(x,y) 49 * logb(x) 50 * finite(x) 51 * 52 * Required kernel function: 53 * log__L(z) 54 * 55 * Method : 56 * 1. Argument Reduction: find k and f such that 57 * 1+x = 2^k * (1+f), 58 * where sqrt(2)/2 < 1+f < sqrt(2) . 59 * 60 * 2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) 61 * = 2s + 2/3 s**3 + 2/5 s**5 + ....., 62 * log(1+f) is computed by 63 * 64 * log(1+f) = 2s + s*log__L(s*s) 65 * where 66 * log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...))) 67 * 68 * See log__L() for the values of the coefficients. 69 * 70 * 3. Finally, log(1+x) = k*ln2 + log(1+f). 71 * 72 * Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers 73 * n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last 74 * 20 bits (for VAX D format), or the last 21 bits ( for IEEE 75 * double) is 0. This ensures n*ln2hi is exactly representable. 76 * 2. In step 1, f may not be representable. A correction term c 77 * for f is computed. It follows that the correction term for 78 * f - t (the leading term of log(1+f) in step 2) is c-c*x. We 79 * add this correction term to n*ln2lo to attenuate the error. 80 * 81 * 82 * Special cases: 83 * log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal; 84 * log1p(INF) is +INF; log1p(-1) is -INF with signal; 85 * only log1p(0)=0 is exact for finite argument. 86 * 87 * Accuracy: 88 * log1p(x) returns the exact log(1+x) nearly rounded. In a test run 89 * with 1,536,000 random arguments on a VAX, the maximum observed 90 * error was .846 ulps (units in the last place). 91 * 92 * Constants: 93 * The hexadecimal values are the intended ones for the following constants. 94 * The decimal values may be used, provided that the compiler will convert 95 * from decimal to binary accurately enough to produce the hexadecimal values 96 * shown. 97 */ 98 99 #include "namespace.h" 100 101 #include <errno.h> 102 #define _LIBM_STATIC 103 #include "mathimpl.h" 104 105 __weak_alias(log1pl, _log1pl) 106 __strong_alias(_log1pl, _log1p) 107 108 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 109 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 110 vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65) 111 112 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 113 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) 114 ic(sqrt2, 1.4142135623730951455E0, 0, 1.6A09E667F3BCD) 115 116 #ifdef vccast 117 #define ln2hi vccast(ln2hi) 118 #define ln2lo vccast(ln2lo) 119 #define sqrt2 vccast(sqrt2) 120 #endif 121 122 __weak_alias(log1p, _log1p) 123 double 124 log1p(double x) 125 { 126 static const double zero=0.0, negone= -1.0, one=1.0, 127 half=1.0/2.0, small=1.0E-20; /* 1+small == 1 */ 128 double z,s,t,c; 129 int k; 130 131 #if !defined(__vax__)&&!defined(tahoe) 132 if(x!=x) return(x); /* x is NaN */ 133 #endif /* !defined(__vax__)&&!defined(tahoe) */ 134 135 if(finite(x)) { 136 if( x > negone ) { 137 138 /* argument reduction */ 139 if(copysign(x,one)<small) return(x); 140 k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k); 141 if(z+t >= sqrt2 ) 142 { k += 1 ; z *= half; t *= half; } 143 t += negone; x = z + t; 144 c = (t-x)+z ; /* correction term for x */ 145 146 /* compute log(1+x) */ 147 s = x/(2+x); t = x*x*half; 148 c += (k*ln2lo-c*x); 149 z = c+s*(t+__log__L(s*s)); 150 x += (z - t) ; 151 152 return(k*ln2hi+x); 153 } 154 /* end of if (x > negone) */ 155 156 else { 157 #if defined(__vax__)||defined(tahoe) 158 if ( x == negone ) 159 return (infnan(-ERANGE)); /* -INF */ 160 else 161 return (infnan(EDOM)); /* NaN */ 162 #else /* defined(__vax__)||defined(tahoe) */ 163 /* x = -1, return -INF with signal */ 164 if ( x == negone ) return( negone/zero ); 165 166 /* negative argument for log, return NaN with signal */ 167 else return ( zero / zero ); 168 #endif /* defined(__vax__)||defined(tahoe) */ 169 } 170 } 171 /* end of if (finite(x)) */ 172 173 /* log(-INF) is NaN */ 174 else if(x<0) 175 return(zero/zero); 176 177 /* log(+INF) is INF */ 178 else return(x); 179 } 180 181 __weak_alias(log1pf, _log1pf) 182 float 183 log1pf(float x) 184 { 185 return log1p(x); 186 } 187