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