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| 2 | /* @(#)e_log10.c 5.1 93/09/24 */ |
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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 SunPro, 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 | /* __ieee754_log10(x) |
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| 15 | * Return the base 10 logarithm of x |
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| 16 | * |
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| 17 | * Method : |
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| 18 | * Let log10_2hi = leading 40 bits of log10(2) and |
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| 19 | * log10_2lo = log10(2) - log10_2hi, |
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| 20 | * ivln10 = 1/log(10) rounded. |
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| 21 | * Then |
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| 22 | * n = ilogb(x), |
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| 23 | * if(n<0) n = n+1; |
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| 24 | * x = scalbn(x,-n); |
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| 25 | * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) |
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| 26 | * |
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| 27 | * Note 1: |
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| 28 | * To guarantee log10(10**n)=n, where 10**n is normal, the rounding |
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| 29 | * mode must set to Round-to-Nearest. |
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| 30 | * Note 2: |
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| 31 | * [1/log(10)] rounded to 53 bits has error .198 ulps; |
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| 32 | * log10 is monotonic at all binary break points. |
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| 33 | * |
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| 34 | * Special cases: |
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| 35 | * log10(x) is NaN with signal if x < 0; |
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| 36 | * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; |
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| 37 | * log10(NaN) is that NaN with no signal; |
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| 38 | * log10(10**N) = N for N=0,1,...,22. |
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| 39 | * |
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| 40 | * Constants: |
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| 41 | * The hexadecimal values are the intended ones for the following constants. |
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| 42 | * The decimal values may be used, provided that the compiler will convert |
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| 43 | * from decimal to binary accurately enough to produce the hexadecimal values |
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| 44 | * shown. |
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| 45 | */ |
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| 46 | |
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| 47 | #include <libm/fdlibm.h> |
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| 48 | |
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| 49 | #ifdef __STDC__ |
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| 50 | static const double |
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| 51 | #else |
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| 52 | static double |
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| 53 | #endif |
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| 54 | one = 1.0, |
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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 double zero = 0.0; |
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| 61 | |
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| 62 | #ifdef __STDC__ |
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| 63 | double __ieee754_log10(double x) |
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| 64 | #else |
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| 65 | double __ieee754_log10(x) |
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| 66 | double x; |
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| 67 | #endif |
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| 68 | { |
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| 69 | double y,z; |
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| 70 | int i,k,n0,hx; |
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| 71 | unsigned lx; |
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| 72 | |
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| 73 | n0 = ((*(int*)&one)>>29)^1; /* high word index */ |
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| 74 | hx = *(n0+(unsigned*)&x); /* high word of x */ |
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| 75 | lx = *(1-n0+(unsigned*)&x); /* low word of x */ |
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| 76 | |
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| 77 | k=0; |
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| 78 | if (hx < 0x00100000) { /* x < 2**-1022 */ |
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| 79 | if (((hx&0x7fffffff)|lx)==0) |
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| 80 | return -two54/zero; /* log(+-0)=-inf */ |
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| 81 | if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
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| 82 | k -= 54; x *= two54; /* subnormal number, scale up x */ |
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| 83 | hx = *(n0+(int*)&x); /* high word of x */ |
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| 84 | } |
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| 85 | if (hx >= 0x7ff00000) return x+x; |
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| 86 | k += (hx>>20)-1023; |
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| 87 | i = ((unsigned)k&0x80000000)>>31; |
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| 88 | hx = (hx&0x000fffff)|((0x3ff-i)<<20); |
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| 89 | y = (double)(k+i); |
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| 90 | *(n0+(int*)&x) = hx; |
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| 91 | z = y*log10_2lo + ivln10*__ieee754_log(x); |
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| 92 | return z+y*log10_2hi; |
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| 93 | } |
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