1 | |
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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 "fdlibm.h" |
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48 | |
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49 | #ifndef _DOUBLE_IS_32BITS |
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50 | |
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51 | #ifdef __STDC__ |
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52 | static const double |
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53 | #else |
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54 | static double |
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55 | #endif |
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56 | two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ |
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57 | ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ |
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58 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
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59 | log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ |
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60 | |
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61 | #ifdef __STDC__ |
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62 | static const double zero = 0.0; |
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63 | #else |
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64 | static double zero = 0.0; |
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65 | #endif |
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66 | |
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67 | #ifdef __STDC__ |
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68 | double __ieee754_log10(double x) |
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69 | #else |
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70 | double __ieee754_log10(x) |
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71 | double x; |
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72 | #endif |
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73 | { |
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74 | double y,z; |
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75 | __int32_t i,k,hx; |
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76 | __uint32_t lx; |
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77 | |
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78 | EXTRACT_WORDS(hx,lx,x); |
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79 | |
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80 | k=0; |
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81 | if (hx < 0x00100000) { /* x < 2**-1022 */ |
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82 | if (((hx&0x7fffffff)|lx)==0) |
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83 | return -two54/zero; /* log(+-0)=-inf */ |
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84 | if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
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85 | k -= 54; x *= two54; /* subnormal number, scale up x */ |
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86 | GET_HIGH_WORD(hx,x); |
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87 | } |
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88 | if (hx >= 0x7ff00000) return x+x; |
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89 | k += (hx>>20)-1023; |
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90 | i = ((__uint32_t)k&0x80000000)>>31; |
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91 | hx = (hx&0x000fffff)|((0x3ff-i)<<20); |
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92 | y = (double)(k+i); |
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93 | SET_HIGH_WORD(x,hx); |
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94 | z = y*log10_2lo + ivln10*__ieee754_log(x); |
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95 | return z+y*log10_2hi; |
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96 | } |
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97 | |
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98 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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