0,0 → 1,98 |
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/* @(#)e_log10.c 5.1 93/09/24 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunPro, a Sun Microsystems, Inc. business. |
* Permission to use, copy, modify, and distribute this |
* software is freely granted, provided that this notice |
* is preserved. |
* ==================================================== |
*/ |
|
/* __ieee754_log10(x) |
* Return the base 10 logarithm of x |
* |
* Method : |
* Let log10_2hi = leading 40 bits of log10(2) and |
* log10_2lo = log10(2) - log10_2hi, |
* ivln10 = 1/log(10) rounded. |
* Then |
* n = ilogb(x), |
* if(n<0) n = n+1; |
* x = scalbn(x,-n); |
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) |
* |
* Note 1: |
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding |
* mode must set to Round-to-Nearest. |
* Note 2: |
* [1/log(10)] rounded to 53 bits has error .198 ulps; |
* log10 is monotonic at all binary break points. |
* |
* Special cases: |
* log10(x) is NaN with signal if x < 0; |
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal; |
* log10(NaN) is that NaN with no signal; |
* log10(10**N) = N for N=0,1,...,22. |
* |
* Constants: |
* The hexadecimal values are the intended ones for the following constants. |
* The decimal values may be used, provided that the compiler will convert |
* from decimal to binary accurately enough to produce the hexadecimal values |
* shown. |
*/ |
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#include "fdlibm.h" |
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#ifndef _DOUBLE_IS_32BITS |
|
#ifdef __STDC__ |
static const double |
#else |
static double |
#endif |
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ |
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ |
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ |
|
#ifdef __STDC__ |
static const double zero = 0.0; |
#else |
static double zero = 0.0; |
#endif |
|
#ifdef __STDC__ |
double __ieee754_log10(double x) |
#else |
double __ieee754_log10(x) |
double x; |
#endif |
{ |
double y,z; |
__int32_t i,k,hx; |
__uint32_t lx; |
|
EXTRACT_WORDS(hx,lx,x); |
|
k=0; |
if (hx < 0x00100000) { /* x < 2**-1022 */ |
if (((hx&0x7fffffff)|lx)==0) |
return -two54/zero; /* log(+-0)=-inf */ |
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
k -= 54; x *= two54; /* subnormal number, scale up x */ |
GET_HIGH_WORD(hx,x); |
} |
if (hx >= 0x7ff00000) return x+x; |
k += (hx>>20)-1023; |
i = ((__uint32_t)k&0x80000000)>>31; |
hx = (hx&0x000fffff)|((0x3ff-i)<<20); |
y = (double)(k+i); |
SET_HIGH_WORD(x,hx); |
z = y*log10_2lo + ivln10*__ieee754_log(x); |
return z+y*log10_2hi; |
} |
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#endif /* defined(_DOUBLE_IS_32BITS) */ |