11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* @(#)e_log10.c 1.3 95/01/18 */ 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#ifndef lint 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic char rcsid[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.11 2005/02/04 18:26:06 das Exp $"; 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#endif 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* __ieee754_log10(x) 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Return the base 10 logarithm of x 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Method : 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Let log10_2hi = leading 40 bits of log10(2) and 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log10_2lo = log10(2) - log10_2hi, 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ivln10 = 1/log(10) rounded. 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Then 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * n = ilogb(x), 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * if(n<0) n = n+1; 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * x = scalbn(x,-n); 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Note 1: 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * mode must set to Round-to-Nearest. 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Note 2: 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * [1/log(10)] rounded to 53 bits has error .198 ulps; 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log10 is monotonic at all binary break points. 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Special cases: 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log10(x) is NaN with signal if x < 0; 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log10(NaN) is that NaN with no signal; 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log10(10**N) = N for N=0,1,...,22. 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Constants: 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * The hexadecimal values are the intended ones for the following constants. 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * The decimal values may be used, provided that the compiler will convert 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * from decimal to binary accurately enough to produce the hexadecimal values 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * shown. 491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttwo54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlog10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlog10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double zero = 0.0; 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project__ieee754_log10(double x) 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double y,z; 661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t i,k,hx; 671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u_int32_t lx; 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project EXTRACT_WORDS(hx,lx,x); 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k=0; 721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (hx < 0x00100000) { /* x < 2**-1022 */ 731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (((hx&0x7fffffff)|lx)==0) 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return -two54/zero; /* log(+-0)=-inf */ 751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k -= 54; x *= two54; /* subnormal number, scale up x */ 771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(hx,x); 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (hx >= 0x7ff00000) return x+x; 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k += (hx>>20)-1023; 811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project i = ((u_int32_t)k&0x80000000)>>31; 821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project hx = (hx&0x000fffff)|((0x3ff-i)<<20); 831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project y = (double)(k+i); 841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_HIGH_WORD(x,hx); 851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = y*log10_2lo + ivln10*__ieee754_log(x); 861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return z+y*log10_2hi; 871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 88