/* @(#)e_log10.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* __ieee754_log10(x) * Return the base 10 logarithm of x * * Method : * Let log10_2hi = leading 40 bits of log10(2) and * log10_2lo = log10(2) - log10_2hi, * ivln10 = 1/log(10) rounded. * Then * n = ilogb(x), * if(n<0) n = n+1; * x = scalbn(x,-n); * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) * * Note 1: * To guarantee log10(10**n)=n, where 10**n is normal, the rounding * mode must set to Round-to-Nearest. * Note 2: * [1/log(10)] rounded to 53 bits has error .198 ulps; * log10 is monotonic at all binary break points. * * Special cases: * log10(x) is NaN with signal if x < 0; * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; * log10(NaN) is that NaN with no signal; * log10(10**N) = N for N=0,1,...,22. * * Constants: * The hexadecimal values are the intended ones for the following constants. * The decimal values may be used, provided that the compiler will convert * from decimal to binary accurately enough to produce the hexadecimal values * shown. */ #include "fdlibm.h" #ifdef __STDC__ static const double #else static double #endif two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ static double zero = 0.0; #ifdef __STDC__ double __ieee754_log10(double x) #else double __ieee754_log10(x) double x; #endif { double y,z; int i,k,hx; unsigned lx; hx = __HI(x); /* high word of x */ lx = __LO(x); /* low word of x */ k=0; if (hx < 0x00100000) { /* x < 2**-1022 */ if (((hx&0x7fffffff)|lx)==0) return -two54/zero; /* log(+-0)=-inf */ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ k -= 54; x *= two54; /* subnormal number, scale up x */ hx = __HI(x); /* high word of x */ } if (hx >= 0x7ff00000) return x+x; k += (hx>>20)-1023; i = ((unsigned)k&0x80000000)>>31; hx = (hx&0x000fffff)|((0x3ff-i)<<20); y = (double)(k+i); __HI(x) = hx; z = y*log10_2lo + ivln10*__ieee754_log(x); return z+y*log10_2hi; }