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 #ifndef lint 14 static char rcsid[] = "$Id$"; 15 #endif 16 17 /* __ieee754_log10(x) 18 * Return the base 10 logarithm of x 19 * 20 * Method : 21 * Let log10_2hi = leading 40 bits of log10(2) and 22 * log10_2lo = log10(2) - log10_2hi, 23 * ivln10 = 1/log(10) rounded. 24 * Then 25 * n = ilogb(x), 26 * if(n<0) n = n+1; 27 * x = scalbn(x,-n); 28 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 29 * 30 * Note 1: 31 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 32 * mode must set to Round-to-Nearest. 33 * Note 2: 34 * [1/log(10)] rounded to 53 bits has error .198 ulps; 35 * log10 is monotonic at all binary break points. 36 * 37 * Special cases: 38 * log10(x) is NaN with signal if x < 0; 39 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 40 * log10(NaN) is that NaN with no signal; 41 * log10(10**N) = N for N=0,1,...,22. 42 * 43 * Constants: 44 * The hexadecimal values are the intended ones for the following constants. 45 * The decimal values may be used, provided that the compiler will convert 46 * from decimal to binary accurately enough to produce the hexadecimal values 47 * shown. 48 */ 49 50 #include "math.h" 51 #include "math_private.h" 52 53 #ifdef __STDC__ 54 static const double 55 #else 56 static double 57 #endif 58 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 59 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 60 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 61 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 62 63 #ifdef __STDC__ 64 static const double zero = 0.0; 65 #else 66 static double zero = 0.0; 67 #endif 68 69 #ifdef __STDC__ 70 double __generic___ieee754_log10(double x) 71 #else 72 double __generic___ieee754_log10(x) 73 double x; 74 #endif 75 { 76 double y,z; 77 int32_t i,k,hx; 78 u_int32_t lx; 79 80 EXTRACT_WORDS(hx,lx,x); 81 82 k=0; 83 if (hx < 0x00100000) { /* x < 2**-1022 */ 84 if (((hx&0x7fffffff)|lx)==0) 85 return -two54/zero; /* log(+-0)=-inf */ 86 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 87 k -= 54; x *= two54; /* subnormal number, scale up x */ 88 GET_HIGH_WORD(hx,x); 89 } 90 if (hx >= 0x7ff00000) return x+x; 91 k += (hx>>20)-1023; 92 i = ((u_int32_t)k&0x80000000)>>31; 93 hx = (hx&0x000fffff)|((0x3ff-i)<<20); 94 y = (double)(k+i); 95 SET_HIGH_WORD(x,hx); 96 z = y*log10_2lo + ivln10*__ieee754_log(x); 97 return z+y*log10_2hi; 98 } 99