| 1 |
1010 |
ivang |
|
| 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__
|
| 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) */
|
