1 2 /* @(#)e_log10.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* __ieee754_log10(x) 15 * Return the base 10 logarithm of x 16 * 17 * Method : 18 * Let log10_2hi = leading 40 bits of ieee_log10(2) and 19 * log10_2lo = ieee_log10(2) - log10_2hi, 20 * ivln10 = 1/ieee_log(10) rounded. 21 * Then 22 * n = ieee_ilogb(x), 23 * if(n<0) n = n+1; 24 * x = ieee_scalbn(x,-n); 25 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*ieee_log(x)) 26 * 27 * Note 1: 28 * To guarantee ieee_log10(10**n)=n, where 10**n is normal, the rounding 29 * mode must set to Round-to-Nearest. 30 * Note 2: 31 * [1/ieee_log(10)] rounded to 53 bits has error .198 ulps; 32 * log10 is monotonic at all binary break points. 33 * 34 * Special cases: 35 * log10(x) is NaN with signal if x < 0; 36 * log10(+INF) is +INF with no signal; ieee_log10(0) is -INF with signal; 37 * log10(NaN) is that NaN with no signal; 38 * log10(10**N) = N for N=0,1,...,22. 39 * 40 * Constants: 41 * The hexadecimal values are the intended ones for the following constants. 42 * The decimal values may be used, provided that the compiler will convert 43 * from decimal to binary accurately enough to produce the hexadecimal values 44 * shown. 45 */ 46 47 #include "fdlibm.h" 48 49 #ifdef __STDC__ 50 static const double 51 #else 52 static double 53 #endif 54 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 55 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 56 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 57 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 58 59 static double zero = 0.0; 60 61 #ifdef __STDC__ __ieee754_log10(double x)62 double __ieee754_log10(double x) 63 #else 64 double __ieee754_log10(x) 65 double x; 66 #endif 67 { 68 double y,z; 69 int i,k,hx; 70 unsigned lx; 71 72 hx = __HI(x); /* high word of x */ 73 lx = __LO(x); /* low word of x */ 74 75 k=0; 76 if (hx < 0x00100000) { /* x < 2**-1022 */ 77 if (((hx&0x7fffffff)|lx)==0) 78 return -two54/zero; /* ieee_log(+-0)=-inf */ 79 if (hx<0) return (x-x)/zero; /* ieee_log(-#) = NaN */ 80 k -= 54; x *= two54; /* subnormal number, scale up x */ 81 hx = __HI(x); /* high word of x */ 82 } 83 if (hx >= 0x7ff00000) return x+x; 84 k += (hx>>20)-1023; 85 i = ((unsigned)k&0x80000000)>>31; 86 hx = (hx&0x000fffff)|((0x3ff-i)<<20); 87 y = (double)(k+i); 88 __HI(x) = hx; 89 z = y*log10_2lo + ivln10*__ieee754_log(x); 90 return z+y*log10_2hi; 91 } 92