e_log10.cpp (2485B)
1 /* @(#)e_log10.c 1.3 95/01/18 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 //#include <sys/cdefs.h> 14 //__FBSDID("$FreeBSD$"); 15 16 /* 17 * Return the base 10 logarithm of x. See e_log.c and k_log.h for most 18 * comments. 19 * 20 * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) 21 * in not-quite-routine extra precision. 22 */ 23 24 #include <float.h> 25 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 static volatile double vzero = 0.0; 38 39 double 40 __ieee754_log10(double x) 41 { 42 double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; 43 int32_t i,k,hx; 44 u_int32_t lx; 45 46 EXTRACT_WORDS(hx,lx,x); 47 48 k=0; 49 if (hx < 0x00100000) { /* x < 2**-1022 */ 50 if (((hx&0x7fffffff)|lx)==0) 51 return -two54/vzero; /* log(+-0)=-inf */ 52 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 53 k -= 54; x *= two54; /* subnormal number, scale up x */ 54 GET_HIGH_WORD(hx,x); 55 } 56 if (hx >= 0x7ff00000) return x+x; 57 if (hx == 0x3ff00000 && lx == 0) 58 return zero; /* log(1) = +0 */ 59 k += (hx>>20)-1023; 60 hx &= 0x000fffff; 61 i = (hx+0x95f64)&0x100000; 62 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 63 k += (i>>20); 64 y = (double)k; 65 f = x - 1.0; 66 hfsq = 0.5*f*f; 67 r = k_log1p(f); 68 69 /* See e_log2.c for most details. */ 70 hi = f - hfsq; 71 SET_LOW_WORD(hi,0); 72 lo = (f - hi) - hfsq + r; 73 val_hi = hi*ivln10hi; 74 y2 = y*log10_2hi; 75 val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; 76 77 /* 78 * Extra precision in for adding y*log10_2hi is not strictly needed 79 * since there is no very large cancellation near x = sqrt(2) or 80 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs 81 * with some parallelism and it reduces the error for many args. 82 */ 83 w = y2 + val_hi; 84 val_lo += (y2 - w) + val_hi; 85 val_hi = w; 86 87 return val_lo + val_hi; 88 }