1 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 /* 14 * Return the base 10 logarithm of x. See e_log.c and k_log.h for most 15 * comments. 16 * 17 * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) 18 * in not-quite-routine extra precision. 19 */ 20 21 #include <float.h> 22 23 #include "math.h" 24 #include "math_private.h" 25 #include "k_log.h" 26 27 static const double 28 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 29 ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ 30 ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ 31 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 32 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 33 34 static const double zero = 0.0; 35 static volatile double vzero = 0.0; 36 37 double 38 log10(double x) 39 { 40 double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; 41 int32_t i,k,hx; 42 u_int32_t lx; 43 44 EXTRACT_WORDS(hx,lx,x); 45 46 k=0; 47 if (hx < 0x00100000) { /* x < 2**-1022 */ 48 if (((hx&0x7fffffff)|lx)==0) 49 return -two54/vzero; /* log(+-0)=-inf */ 50 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 51 k -= 54; x *= two54; /* subnormal number, scale up x */ 52 GET_HIGH_WORD(hx,x); 53 } 54 if (hx >= 0x7ff00000) return x+x; 55 if (hx == 0x3ff00000 && lx == 0) 56 return zero; /* log(1) = +0 */ 57 k += (hx>>20)-1023; 58 hx &= 0x000fffff; 59 i = (hx+0x95f64)&0x100000; 60 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 61 k += (i>>20); 62 y = (double)k; 63 f = x - 1.0; 64 hfsq = 0.5*f*f; 65 r = k_log1p(f); 66 67 /* See e_log2.c for most details. */ 68 hi = f - hfsq; 69 SET_LOW_WORD(hi,0); 70 lo = (f - hi) - hfsq + r; 71 val_hi = hi*ivln10hi; 72 y2 = y*log10_2hi; 73 val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; 74 75 /* 76 * Extra precision in for adding y*log10_2hi is not strictly needed 77 * since there is no very large cancellation near x = sqrt(2) or 78 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs 79 * with some parallelism and it reduces the error for many args. 80 */ 81 w = y2 + val_hi; 82 val_lo += (y2 - w) + val_hi; 83 val_hi = w; 84 85 return val_lo + val_hi; 86 } 87 88 #if (LDBL_MANT_DIG == 53) 89 __weak_reference(log10, log10l); 90 #endif 91