e_log10.c (3110B)
1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ 13 /* C4723: potential divide by zero. */ 14 #pragma warning ( disable : 4723 ) 15 #endif 16 17 /* __ieee754_log10(x) 18 * Return the base 10 logarithm of x 19 * 20 * Method : 21 * Let log10_2hi = leading 40 bits of log10(2) and 22 * log10_2lo = log10(2) - log10_2hi, 23 * ivln10 = 1/log(10) rounded. 24 * Then 25 * n = ilogb(x), 26 * if(n<0) n = n+1; 27 * x = scalbn(x,-n); 28 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 29 * 30 * Note 1: 31 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 32 * mode must set to Round-to-Nearest. 33 * Note 2: 34 * [1/log(10)] rounded to 53 bits has error .198 ulps; 35 * log10 is monotonic at all binary break points. 36 * 37 * Special cases: 38 * log10(x) is NaN with signal if x < 0; 39 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 40 * log10(NaN) is that NaN with no signal; 41 * log10(10**N) = N for N=0,1,...,22. 42 * 43 * Constants: 44 * The hexadecimal values are the intended ones for the following constants. 45 * The decimal values may be used, provided that the compiler will convert 46 * from decimal to binary accurately enough to produce the hexadecimal values 47 * shown. 48 */ 49 50 #include "math_libm.h" 51 #include "math_private.h" 52 53 static const double 54 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ 55 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 56 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 57 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ 58 59 static const double zero = 0.0; 60 61 double attribute_hidden __ieee754_log10(double x) 62 { 63 double y,z; 64 int32_t i,k,hx; 65 u_int32_t lx; 66 67 EXTRACT_WORDS(hx,lx,x); 68 69 k=0; 70 if (hx < 0x00100000) { /* x < 2**-1022 */ 71 if (((hx&0x7fffffff)|lx)==0) 72 return -two54/zero; /* log(+-0)=-inf */ 73 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 74 k -= 54; x *= two54; /* subnormal number, scale up x */ 75 GET_HIGH_WORD(hx,x); 76 } 77 if (hx >= 0x7ff00000) return x+x; 78 k += (hx>>20)-1023; 79 i = ((u_int32_t)k&0x80000000)>>31; 80 hx = (hx&0x000fffff)|((0x3ff-i)<<20); 81 y = (double)(k+i); 82 SET_HIGH_WORD(x,hx); 83 z = y*log10_2lo + ivln10*__ieee754_log(x); 84 return z+y*log10_2hi; 85 } 86 87 /* 88 * wrapper log10(X) 89 */ 90 #ifndef _IEEE_LIBM 91 double log10(double x) 92 { 93 double z = __ieee754_log10(x); 94 if (_LIB_VERSION == _IEEE_ || isnan(x)) 95 return z; 96 if (x <= 0.0) { 97 if(x == 0.0) 98 return __kernel_standard(x, x, 18); /* log10(0) */ 99 return __kernel_standard(x, x, 19); /* log10(x<0) */ 100 } 101 return z; 102 } 103 #else 104 strong_alias(__ieee754_log10, log10) 105 #endif 106 libm_hidden_def(log10)