1 /* 2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. Oracle designates this 8 * particular file as subject to the "Classpath" exception as provided 9 * by Oracle in the LICENSE file that accompanied this code. 10 * 11 * This code is distributed in the hope that it will be useful, but WITHOUT 12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 * version 2 for more details (a copy is included in the LICENSE file that 15 * accompanied this code). 16 * 17 * You should have received a copy of the GNU General Public License version 18 * 2 along with this work; if not, write to the Free Software Foundation, 19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 20 * 21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 22 * or visit www.oracle.com if you need additional information or have any 23 * questions. 24 */ 25 26 /* __ieee754_log10(x) 27 * Return the base 10 logarithm of x 28 * 29 * Method : 30 * Let log10_2hi = leading 40 bits of log10(2) and 31 * log10_2lo = log10(2) - log10_2hi, 32 * ivln10 = 1/log(10) rounded. 33 * Then 34 * n = ilogb(x), 35 * if(n<0) n = n+1; 36 * x = scalbn(x,-n); 37 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 38 * 39 * Note 1: 40 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 41 * mode must set to Round-to-Nearest. 42 * Note 2: 43 * [1/log(10)] rounded to 53 bits has error .198 ulps; 44 * log10 is monotonic at all binary break points. 45 * 46 * Special cases: 47 * log10(x) is NaN with signal if x < 0; 48 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 49 * log10(NaN) is that NaN with no signal; 50 * log10(10**N) = N for N=0,1,...,22. 51 * 52 * Constants: 53 * The hexadecimal values are the intended ones for the following constants. 54 * The decimal values may be used, provided that the compiler will convert 55 * from decimal to binary accurately enough to produce the hexadecimal values 56 * shown. 57 */ 58 59 #include "fdlibm.h" 60 61 #ifdef __STDC__ 62 static const double 63 #else 64 static double 65 #endif 66 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 67 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 68 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 69 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 70 71 static double zero = 0.0; 72 73 #ifdef __STDC__ __ieee754_log10(double x)74 double __ieee754_log10(double x) 75 #else 76 double __ieee754_log10(x) 77 double x; 78 #endif 79 { 80 double y,z; 81 int i,k,hx; 82 unsigned lx; 83 84 hx = __HI(x); /* high word of x */ 85 lx = __LO(x); /* low word of x */ 86 87 k=0; 88 if (hx < 0x00100000) { /* x < 2**-1022 */ 89 if (((hx&0x7fffffff)|lx)==0) 90 return -two54/zero; /* log(+-0)=-inf */ 91 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 92 k -= 54; x *= two54; /* subnormal number, scale up x */ 93 hx = __HI(x); /* high word of x */ 94 } 95 if (hx >= 0x7ff00000) return x+x; 96 k += (hx>>20)-1023; 97 i = ((unsigned)k&0x80000000)>>31; 98 hx = (hx&0x000fffff)|((0x3ff-i)<<20); 99 y = (double)(k+i); 100 __HI(x) = hx; 101 z = y*log10_2lo + ivln10*__ieee754_log(x); 102 return z+y*log10_2hi; 103 } 104