1 2 /* @(#)e_log10.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include <sys/cdefs.h> 15 __FBSDID("$FreeBSD$"); 16 17 /* 18 * Return the base 10 logarithm of x. See e_log.c and k_log.h for most 19 * comments. 20 * 21 * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) 22 * in not-quite-routine extra precision. 23 */ 24 25 #include "math.h" 26 #include "math_private.h" 27 #include "k_log.h" 28 29 static const double 30 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 31 ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ 32 ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ 33 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 34 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 35 36 static const double zero = 0.0; 37 38 double 39 __ieee754_log10(double x) 40 { 41 double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; 42 int32_t i,k,hx; 43 u_int32_t lx; 44 45 EXTRACT_WORDS(hx,lx,x); 46 47 k=0; 48 if (hx < 0x00100000) { /* x < 2**-1022 */ 49 if (((hx&0x7fffffff)|lx)==0) 50 return -two54/zero; /* log(+-0)=-inf */ 51 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 52 k -= 54; x *= two54; /* subnormal number, scale up x */ 53 GET_HIGH_WORD(hx,x); 54 } 55 if (hx >= 0x7ff00000) return x+x; 56 if (hx == 0x3ff00000 && lx == 0) 57 return zero; /* log(1) = +0 */ 58 k += (hx>>20)-1023; 59 hx &= 0x000fffff; 60 i = (hx+0x95f64)&0x100000; 61 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 62 k += (i>>20); 63 y = (double)k; 64 f = x - 1.0; 65 hfsq = 0.5*f*f; 66 r = k_log1p(f); 67 68 /* See e_log2.c for most details. */ 69 hi = f - hfsq; 70 SET_LOW_WORD(hi,0); 71 lo = (f - hi) - hfsq + r; 72 val_hi = hi*ivln10hi; 73 y2 = y*log10_2hi; 74 val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; 75 76 /* 77 * Extra precision in for adding y*log10_2hi is not strictly needed 78 * since there is no very large cancellation near x = sqrt(2) or 79 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs 80 * with some parallelism and it reduces the error for many args. 81 */ 82 w = y2 + val_hi; 83 val_lo += (y2 - w) + val_hi; 84 val_hi = w; 85 86 return val_lo + val_hi; 87 } 88