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| 2 | /* @(#)e_log10.c 1.3 95/01/18 */
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| 3 | /*
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| 4 | * ====================================================
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 6 | *
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| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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| 8 | * Permission to use, copy, modify, and distribute this
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| 9 | * software is freely granted, provided that this notice
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| 10 | * is preserved.
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| 11 | * ====================================================
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| 12 | */
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| 13 |
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| 14 | #ifndef lint
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| 15 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.11 2005/02/04 18:26:06 das Exp $";
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| 16 | #endif
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| 17 |
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| 18 | /* __ieee754_log10(x)
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| 19 | * Return the base 10 logarithm of x
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| 20 | *
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| 21 | * Method :
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| 22 | * Let log10_2hi = leading 40 bits of log10(2) and
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| 23 | * log10_2lo = log10(2) - log10_2hi,
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| 24 | * ivln10 = 1/log(10) rounded.
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| 25 | * Then
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| 26 | * n = ilogb(x),
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| 27 | * if(n<0) n = n+1;
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| 28 | * x = scalbn(x,-n);
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| 29 | * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
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| 30 | *
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| 31 | * Note 1:
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| 32 | * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
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| 33 | * mode must set to Round-to-Nearest.
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| 34 | * Note 2:
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| 35 | * [1/log(10)] rounded to 53 bits has error .198 ulps;
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| 36 | * log10 is monotonic at all binary break points.
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| 37 | *
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| 38 | * Special cases:
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| 39 | * log10(x) is NaN with signal if x < 0;
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| 40 | * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
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| 41 | * log10(NaN) is that NaN with no signal;
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| 42 | * log10(10**N) = N for N=0,1,...,22.
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| 43 | *
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| 44 | * Constants:
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| 45 | * The hexadecimal values are the intended ones for the following constants.
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| 46 | * The decimal values may be used, provided that the compiler will convert
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| 47 | * from decimal to binary accurately enough to produce the hexadecimal values
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| 48 | * shown.
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| 49 | */
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| 50 |
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| 51 | #include "math.h"
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| 52 | #include "math_private.h"
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| 53 |
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| 54 | static const double
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| 55 | two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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| 56 | ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
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| 57 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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| 58 | log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
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| 59 |
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| 60 | static const double zero = 0.0;
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| 61 |
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| 62 | double
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| 63 | __ieee754_log10(double x)
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| 64 | {
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| 65 | double y,z;
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| 66 | int32_t i,k,hx;
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| 67 | u_int32_t lx;
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| 68 |
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| 69 | EXTRACT_WORDS(hx,lx,x);
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| 70 |
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| 71 | k=0;
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| 72 | if (hx < 0x00100000) { /* x < 2**-1022 */
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| 73 | if (((hx&0x7fffffff)|lx)==0)
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| 74 | return -two54/zero; /* log(+-0)=-inf */
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| 75 | if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
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| 76 | k -= 54; x *= two54; /* subnormal number, scale up x */
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| 77 | GET_HIGH_WORD(hx,x);
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| 78 | }
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| 79 | if (hx >= 0x7ff00000) return x+x;
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| 80 | k += (hx>>20)-1023;
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| 81 | i = ((u_int32_t)k&0x80000000)>>31;
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| 82 | hx = (hx&0x000fffff)|((0x3ff-i)<<20);
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| 83 | y = (double)(k+i);
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| 84 | SET_HIGH_WORD(x,hx);
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| 85 | z = y*log10_2lo + ivln10*__ieee754_log(x);
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| 86 | return z+y*log10_2hi;
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| 87 | }
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