e_log2.c revision 97413
159412Smsmith/* @(#)e_log10.c 5.1 93/09/24 */ 265577Sdes/* 365577Sdes * ==================================================== 459412Smsmith * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 559412Smsmith * 659412Smsmith * Developed at SunPro, a Sun Microsystems, Inc. business. 759412Smsmith * Permission to use, copy, modify, and distribute this 859412Smsmith * software is freely granted, provided that this notice 959412Smsmith * is preserved. 1059412Smsmith * ==================================================== 1159412Smsmith */ 1259412Smsmith 1359412Smsmith#ifndef lint 1459412Smsmithstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/e_log10.c 97413 2002-05-28 18:15:04Z alfred $"; 1559412Smsmith#endif 1659412Smsmith 1759412Smsmith/* __ieee754_log10(x) 1859412Smsmith * Return the base 10 logarithm of x 1959412Smsmith * 2059412Smsmith * Method : 2159412Smsmith * Let log10_2hi = leading 40 bits of log10(2) and 2259412Smsmith * log10_2lo = log10(2) - log10_2hi, 2359412Smsmith * ivln10 = 1/log(10) rounded. 2459412Smsmith * Then 2559412Smsmith * n = ilogb(x), 2659412Smsmith * if(n<0) n = n+1; 2759412Smsmith * x = scalbn(x,-n); 2859412Smsmith * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 2959412Smsmith * 3059412Smsmith * Note 1: 3159412Smsmith * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 3259412Smsmith * mode must set to Round-to-Nearest. 3359412Smsmith * Note 2: 3459412Smsmith * [1/log(10)] rounded to 53 bits has error .198 ulps; 3559412Smsmith * log10 is monotonic at all binary break points. 3659412Smsmith * 3759412Smsmith * Special cases: 3859412Smsmith * log10(x) is NaN with signal if x < 0; 3959412Smsmith * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 4059412Smsmith * log10(NaN) is that NaN with no signal; 4159412Smsmith * log10(10**N) = N for N=0,1,...,22. 4259412Smsmith * 4359412Smsmith * Constants: 4459412Smsmith * The hexadecimal values are the intended ones for the following constants. 4559412Smsmith * The decimal values may be used, provided that the compiler will convert 4659412Smsmith * from decimal to binary accurately enough to produce the hexadecimal values 4759412Smsmith * shown. 4859412Smsmith */ 4959412Smsmith 5059412Smsmith#include "math.h" 5159412Smsmith#include "math_private.h" 5259458Smsmith 5359412Smsmithstatic const double 5459412Smsmithtwo54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 5559412Smsmithivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 5659412Smsmithlog10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 5760860Sdeslog10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 5859412Smsmith 5959412Smsmithstatic const double zero = 0.0; 6059412Smsmith 6159412Smsmithdouble 6259412Smsmith__generic___ieee754_log10(double x) 6359412Smsmith{ 6459412Smsmith double y,z; 6559412Smsmith int32_t i,k,hx; 6659412Smsmith u_int32_t lx; 6759412Smsmith 6859412Smsmith EXTRACT_WORDS(hx,lx,x); 6959412Smsmith 7059412Smsmith k=0; 7159412Smsmith if (hx < 0x00100000) { /* x < 2**-1022 */ 7259412Smsmith if (((hx&0x7fffffff)|lx)==0) 7359412Smsmith return -two54/zero; /* log(+-0)=-inf */ 7459412Smsmith if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 7559412Smsmith k -= 54; x *= two54; /* subnormal number, scale up x */ 7659412Smsmith GET_HIGH_WORD(hx,x); 7759412Smsmith } 7859412Smsmith if (hx >= 0x7ff00000) return x+x; 7959412Smsmith k += (hx>>20)-1023; 8059412Smsmith i = ((u_int32_t)k&0x80000000)>>31; 8159412Smsmith hx = (hx&0x000fffff)|((0x3ff-i)<<20); 8259412Smsmith y = (double)(k+i); 8359412Smsmith SET_HIGH_WORD(x,hx); 8459412Smsmith z = y*log10_2lo + ivln10*__ieee754_log(x); 8559412Smsmith return z+y*log10_2hi; 8660860Sdes} 8759412Smsmith