1 2 /* @(#)e_log10.c 5.1 93/09/24 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, 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 /* __ieee754_log10(x) 15 * Return the base 10 logarithm of x 16 * 17 * Method : 18 * Let log10_2hi = leading 40 bits of log10(2) and 19 * log10_2lo = log10(2) - log10_2hi, 20 * ivln10 = 1/log(10) rounded. 21 * Then 22 * n = ilogb(x), 23 * if(n<0) n = n+1; 24 * x = scalbn(x,-n); 25 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 26 * 27 * Note 1: 28 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 29 * mode must set to Round-to-Nearest. 30 * Note 2: 31 * [1/log(10)] rounded to 53 bits has error .198 ulps; 32 * log10 is monotonic at all binary break points. 33 * 34 * Special cases: 35 * log10(x) is NaN with signal if x < 0; 36 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 37 * log10(NaN) is that NaN with no signal; 38 * log10(10**N) = N for N=0,1,...,22. 39 * 40 * Constants: 41 * The hexadecimal values are the intended ones for the following constants. 42 * The decimal values may be used, provided that the compiler will convert 43 * from decimal to binary accurately enough to produce the hexadecimal values 44 * shown. 45 */ 46 47 #include "fdlibm.h" 48 49 #ifndef _DOUBLE_IS_32BITS 50 51 #ifdef __STDC__ 52 static const double 53 #else 54 static double 55 #endif 56 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 57 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 58 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 59 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 60 61 #ifdef __STDC__ 62 static const double zero = 0.0; 63 #else 64 static double zero = 0.0; 65 #endif 66 67 #ifdef __STDC__ __ieee754_log10(double x)68 double __ieee754_log10(double x) 69 #else 70 double __ieee754_log10(x) 71 double x; 72 #endif 73 { 74 double y,z; 75 __int32_t i,k,hx; 76 __uint32_t lx; 77 78 EXTRACT_WORDS(hx,lx,x); 79 80 k=0; 81 if (hx < 0x00100000) { /* x < 2**-1022 */ 82 if (((hx&0x7fffffff)|lx)==0) 83 return -two54/zero; /* log(+-0)=-inf */ 84 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 85 k -= 54; x *= two54; /* subnormal number, scale up x */ 86 GET_HIGH_WORD(hx,x); 87 } 88 if (hx >= 0x7ff00000) return x+x; 89 k += (hx>>20)-1023; 90 i = ((__uint32_t)k&0x80000000)>>31; 91 hx = (hx&0x000fffff)|((0x3ff-i)<<20); 92 y = (double)(k+i); 93 SET_HIGH_WORD(x,hx); 94 z = y*log10_2lo + ivln10*__ieee754_log(x); 95 return z+y*log10_2hi; 96 } 97 98 #endif /* defined(_DOUBLE_IS_32BITS) */ 99