1 /* @(#)e_log10.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp $"); 16 #endif 17 18 /* __ieee754_log10(x) 19 * Return the base 10 logarithm of x 20 * 21 * Method : 22 * Let log10_2hi = leading 40 bits of log10(2) and 23 * log10_2lo = log10(2) - log10_2hi, 24 * ivln10 = 1/log(10) rounded. 25 * Then 26 * n = ilogb(x), 27 * if(n<0) n = n+1; 28 * x = scalbn(x,-n); 29 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 30 * 31 * Note 1: 32 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 33 * mode must set to Round-to-Nearest. 34 * Note 2: 35 * [1/log(10)] rounded to 53 bits has error .198 ulps; 36 * log10 is monotonic at all binary break points. 37 * 38 * Special cases: 39 * log10(x) is NaN with signal if x < 0; 40 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 41 * log10(NaN) is that NaN with no signal; 42 * log10(10**N) = N for N=0,1,...,22. 43 * 44 * Constants: 45 * The hexadecimal values are the intended ones for the following constants. 46 * The decimal values may be used, provided that the compiler will convert 47 * from decimal to binary accurately enough to produce the hexadecimal values 48 * shown. 49 */ 50 51 #include "math.h" 52 #include "math_private.h" 53 54 static const double 55 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 56 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 57 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 58 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 59 60 static const double zero = 0.0; 61 62 double 63 __ieee754_log10(double x) 64 { 65 double y,z; 66 int32_t i,k,hx; 67 u_int32_t lx; 68 69 EXTRACT_WORDS(hx,lx,x); 70 71 k=0; 72 if (hx < 0x00100000) { /* x < 2**-1022 */ 73 if (((hx&0x7fffffff)|lx)==0) 74 return -two54/zero; /* log(+-0)=-inf */ 75 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 76 k -= 54; x *= two54; /* subnormal number, scale up x */ 77 GET_HIGH_WORD(hx,x); 78 } 79 if (hx >= 0x7ff00000) return x+x; 80 k += (hx>>20)-1023; 81 i = ((u_int32_t)k&0x80000000)>>31; 82 hx = (hx&0x000fffff)|((0x3ff-i)<<20); 83 y = (double)(k+i); 84 SET_HIGH_WORD(x,hx); 85 z = y*log10_2lo + ivln10*__ieee754_log(x); 86 return z+y*log10_2hi; 87 } 88