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