1a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 2a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* @(#)e_log10.c 1.3 95/01/18 */ 3a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* 4a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ==================================================== 5a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 7a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Developed at SunSoft, a Sun Microsystems, Inc. business. 8a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Permission to use, copy, modify, and distribute this 9a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * software is freely granted, provided that this notice 10a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * is preserved. 11a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ==================================================== 12a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 13a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 15a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 16a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 17a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* 18a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Return the base 10 logarithm of x. See e_log.c and k_log.h for most 19a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * comments. 20a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 21a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) 22a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * in not-quite-routine extra precision. 23a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 24a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 2578419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes#include <float.h> 2678419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes 27a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math.h" 28a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math_private.h" 29a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "k_log.h" 30a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 31a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesstatic const double 32a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughestwo54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 33a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ 34a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ 35a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hugheslog10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 36a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hugheslog10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 37a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 38a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesstatic const double zero = 0.0; 3978419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughesstatic volatile double vzero = 0.0; 40a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 41a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesdouble 42a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__ieee754_log10(double x) 43a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes{ 44a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; 45a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes int32_t i,k,hx; 46a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes u_int32_t lx; 47a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 48a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes EXTRACT_WORDS(hx,lx,x); 49a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 50a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes k=0; 51a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (hx < 0x00100000) { /* x < 2**-1022 */ 52a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (((hx&0x7fffffff)|lx)==0) 5378419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes return -two54/vzero; /* log(+-0)=-inf */ 54a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 55a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes k -= 54; x *= two54; /* subnormal number, scale up x */ 56a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes GET_HIGH_WORD(hx,x); 57a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 58a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (hx >= 0x7ff00000) return x+x; 59a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (hx == 0x3ff00000 && lx == 0) 60a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return zero; /* log(1) = +0 */ 61a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes k += (hx>>20)-1023; 62a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes hx &= 0x000fffff; 63a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes i = (hx+0x95f64)&0x100000; 64a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 65a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes k += (i>>20); 66a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes y = (double)k; 67a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes f = x - 1.0; 68a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes hfsq = 0.5*f*f; 69a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes r = k_log1p(f); 70a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 71a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* See e_log2.c for most details. */ 72a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes hi = f - hfsq; 73a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes SET_LOW_WORD(hi,0); 74a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes lo = (f - hi) - hfsq + r; 75a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes val_hi = hi*ivln10hi; 76a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes y2 = y*log10_2hi; 77a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; 78a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 79a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* 80a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Extra precision in for adding y*log10_2hi is not strictly needed 81a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * since there is no very large cancellation near x = sqrt(2) or 82a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs 83a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * with some parallelism and it reduces the error for many args. 84a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 85a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes w = y2 + val_hi; 86a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes val_lo += (y2 - w) + val_hi; 87a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes val_hi = w; 88a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 89a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return val_lo + val_hi; 90a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes} 9178419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes 9278419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes#if (LDBL_MANT_DIG == 53) 9378419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes__weak_reference(log10, log10l); 9478419467a2f88744ae2445fca5eb442877ebb1b0Elliott Hughes#endif 95