e_log10.c revision 176451
1141296Sdas 2141296Sdas/* @(#)e_log10.c 1.3 95/01/18 */ 32116Sjkh/* 42116Sjkh * ==================================================== 52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62116Sjkh * 7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 82116Sjkh * Permission to use, copy, modify, and distribute this 9141296Sdas * software is freely granted, provided that this notice 102116Sjkh * is preserved. 112116Sjkh * ==================================================== 122116Sjkh */ 132116Sjkh 14176451Sdas#include <sys/cdefs.h> 15176451Sdas__FBSDID("$FreeBSD: head/lib/msun/src/e_log10.c 176451 2008-02-22 02:30:36Z das $"); 162116Sjkh 172116Sjkh/* __ieee754_log10(x) 182116Sjkh * Return the base 10 logarithm of x 19141296Sdas * 202116Sjkh * Method : 212116Sjkh * Let log10_2hi = leading 40 bits of log10(2) and 222116Sjkh * log10_2lo = log10(2) - log10_2hi, 232116Sjkh * ivln10 = 1/log(10) rounded. 242116Sjkh * Then 25141296Sdas * n = ilogb(x), 262116Sjkh * if(n<0) n = n+1; 272116Sjkh * x = scalbn(x,-n); 282116Sjkh * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 292116Sjkh * 302116Sjkh * Note 1: 31141296Sdas * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 322116Sjkh * mode must set to Round-to-Nearest. 332116Sjkh * Note 2: 342116Sjkh * [1/log(10)] rounded to 53 bits has error .198 ulps; 352116Sjkh * log10 is monotonic at all binary break points. 362116Sjkh * 372116Sjkh * Special cases: 38141296Sdas * log10(x) is NaN with signal if x < 0; 392116Sjkh * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 402116Sjkh * log10(NaN) is that NaN with no signal; 412116Sjkh * log10(10**N) = N for N=0,1,...,22. 422116Sjkh * 432116Sjkh * Constants: 442116Sjkh * The hexadecimal values are the intended ones for the following constants. 452116Sjkh * The decimal values may be used, provided that the compiler will convert 462116Sjkh * from decimal to binary accurately enough to produce the hexadecimal values 472116Sjkh * shown. 482116Sjkh */ 492116Sjkh 502116Sjkh#include "math.h" 512116Sjkh#include "math_private.h" 522116Sjkh 532116Sjkhstatic const double 542116Sjkhtwo54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 552116Sjkhivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 562116Sjkhlog10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 572116Sjkhlog10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 582116Sjkh 592116Sjkhstatic const double zero = 0.0; 602116Sjkh 6197413Salfreddouble 62117912Speter__ieee754_log10(double x) 632116Sjkh{ 642116Sjkh double y,z; 652116Sjkh int32_t i,k,hx; 662116Sjkh u_int32_t lx; 672116Sjkh 682116Sjkh EXTRACT_WORDS(hx,lx,x); 692116Sjkh 702116Sjkh k=0; 712116Sjkh if (hx < 0x00100000) { /* x < 2**-1022 */ 722116Sjkh if (((hx&0x7fffffff)|lx)==0) 732116Sjkh return -two54/zero; /* log(+-0)=-inf */ 742116Sjkh if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 752116Sjkh k -= 54; x *= two54; /* subnormal number, scale up x */ 762116Sjkh GET_HIGH_WORD(hx,x); 772116Sjkh } 782116Sjkh if (hx >= 0x7ff00000) return x+x; 792116Sjkh k += (hx>>20)-1023; 802116Sjkh i = ((u_int32_t)k&0x80000000)>>31; 812116Sjkh hx = (hx&0x000fffff)|((0x3ff-i)<<20); 822116Sjkh y = (double)(k+i); 832116Sjkh SET_HIGH_WORD(x,hx); 842116Sjkh z = y*log10_2lo + ivln10*__ieee754_log(x); 852116Sjkh return z+y*log10_2hi; 862116Sjkh} 87