Convert log10() to use __kernel_log(), which is more accurate and simpler.
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svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=219360
@ -14,45 +14,18 @@
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/* __ieee754_log10(x)
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* Return the base 10 logarithm of x
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*
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* Method :
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* Let log10_2hi = leading 40 bits of log10(2) and
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* log10_2lo = log10(2) - log10_2hi,
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* ivln10 = 1/log(10) rounded.
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* Then
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* n = ilogb(x),
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* if(n<0) n = n+1;
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* x = scalbn(x,-n);
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* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
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*
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* Note 1:
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* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
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* mode must set to Round-to-Nearest.
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* Note 2:
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* [1/log(10)] rounded to 53 bits has error .198 ulps;
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* log10 is monotonic at all binary break points.
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*
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* Special cases:
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* log10(x) is NaN with signal if x < 0;
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* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
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* log10(NaN) is that NaN with no signal;
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* log10(10**N) = N for N=0,1,...,22.
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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/*
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* Return the base 10 logarithm of x. See k_log.c for details on the algorithm.
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*/
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#include "math.h"
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#include "math_private.h"
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#include "k_log.h"
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static const double
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two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
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ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
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ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
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log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
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@ -61,7 +34,7 @@ static const double zero = 0.0;
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double
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__ieee754_log10(double x)
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{
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double y,z;
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double f,hi,lo,y,z;
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int32_t i,k,hx;
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u_int32_t lx;
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@ -77,10 +50,15 @@ __ieee754_log10(double x)
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}
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if (hx >= 0x7ff00000) return x+x;
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k += (hx>>20)-1023;
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i = ((u_int32_t)k&0x80000000)>>31;
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hx = (hx&0x000fffff)|((0x3ff-i)<<20);
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y = (double)(k+i);
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SET_HIGH_WORD(x,hx);
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z = y*log10_2lo + ivln10*__ieee754_log(x);
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hx &= 0x000fffff;
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i = (hx+0x95f64)&0x100000;
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SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
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k += (i>>20);
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y = (double)k;
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f = __kernel_log(x);
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hi = x = x - 1;
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SET_LOW_WORD(hi,0);
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lo = x - hi;
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z = y*log10_2lo + (x+f)*ivln10lo + (lo+f)*ivln10hi + hi*ivln10hi;
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return z+y*log10_2hi;
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}
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