/* @(#)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. * ==================================================== */ //#include <sys/cdefs.h> //__FBSDID("$FreeBSD$"); /* * Return the base 10 logarithm of x. See e_log.c and k_log.h for most * comments. * * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) * in not-quite-routine extra precision. */ #include <float.h> #include "math_private.h" #include "k_log.h" static const double two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ static const double zero = 0.0; static volatile double vzero = 0.0; double __ieee754_log10(double x) { double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; int32_t i,k,hx; u_int32_t lx; EXTRACT_WORDS(hx,lx,x); k=0; if (hx < 0x00100000) { /* x < 2**-1022 */ if (((hx&0x7fffffff)|lx)==0) return -two54/vzero; /* log(+-0)=-inf */ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ k -= 54; x *= two54; /* subnormal number, scale up x */ GET_HIGH_WORD(hx,x); } if (hx >= 0x7ff00000) return x+x; if (hx == 0x3ff00000 && lx == 0) return zero; /* log(1) = +0 */ k += (hx>>20)-1023; hx &= 0x000fffff; i = (hx+0x95f64)&0x100000; SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ k += (i>>20); y = (double)k; f = x - 1.0; hfsq = 0.5*f*f; r = k_log1p(f); /* See e_log2.c for most details. */ hi = f - hfsq; SET_LOW_WORD(hi,0); lo = (f - hi) - hfsq + r; val_hi = hi*ivln10hi; y2 = y*log10_2hi; val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; /* * Extra precision in for adding y*log10_2hi is not strictly needed * since there is no very large cancellation near x = sqrt(2) or * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs * with some parallelism and it reduces the error for many args. */ w = y2 + val_hi; val_lo += (y2 - w) + val_hi; val_hi = w; return val_lo + val_hi; }