1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
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2 | /*
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3 | * ====================================================
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4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 | *
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6 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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7 | * Permission to use, copy, modify, and distribute this
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8 | * software is freely granted, provided that this notice
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9 | * is preserved.
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10 | * ====================================================
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11 | */
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12 | /*
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13 | * Return the base 10 logarithm of x. See log.c for most comments.
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14 | *
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15 | * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
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16 | * as in log.c, then combine and scale in extra precision:
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17 | * log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
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18 | */
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19 |
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20 | #include <math.h>
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21 | #include <stdint.h>
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22 |
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23 | static const double
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24 | ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
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25 | ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
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26 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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27 | log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
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28 | Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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29 | Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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30 | Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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31 | Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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32 | Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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33 | Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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34 | Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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35 |
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36 | double log10(double x)
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37 | {
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38 | union {double f; uint64_t i;} u = {x};
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39 | double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
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40 | uint32_t hx;
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41 | int k;
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42 |
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43 | hx = u.i>>32;
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44 | k = 0;
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45 | if (hx < 0x00100000 || hx>>31) {
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46 | if (u.i<<1 == 0)
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47 | return -1/(x*x); /* log(+-0)=-inf */
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48 | if (hx>>31)
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49 | return (x-x)/0.0; /* log(-#) = NaN */
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50 | /* subnormal number, scale x up */
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51 | k -= 54;
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52 | x *= 0x1p54;
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53 | u.f = x;
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54 | hx = u.i>>32;
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55 | } else if (hx >= 0x7ff00000) {
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56 | return x;
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57 | } else if (hx == 0x3ff00000 && u.i<<32 == 0)
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58 | return 0;
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59 |
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60 | /* reduce x into [sqrt(2)/2, sqrt(2)] */
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61 | hx += 0x3ff00000 - 0x3fe6a09e;
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62 | k += (int)(hx>>20) - 0x3ff;
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63 | hx = (hx&0x000fffff) + 0x3fe6a09e;
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64 | u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
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65 | x = u.f;
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66 |
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67 | f = x - 1.0;
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68 | hfsq = 0.5*f*f;
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69 | s = f/(2.0+f);
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70 | z = s*s;
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71 | w = z*z;
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72 | t1 = w*(Lg2+w*(Lg4+w*Lg6));
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73 | t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
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74 | R = t2 + t1;
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75 |
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76 | /* See log2.c for details. */
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77 | /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
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78 | hi = f - hfsq;
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79 | u.f = hi;
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80 | u.i &= (uint64_t)-1<<32;
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81 | hi = u.f;
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82 | lo = f - hi - hfsq + s*(hfsq+R);
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83 |
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84 | /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
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85 | val_hi = hi*ivln10hi;
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86 | dk = k;
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87 | y = dk*log10_2hi;
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88 | val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
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89 |
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90 | /*
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91 | * Extra precision in for adding y is not strictly needed
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92 | * since there is no very large cancellation near x = sqrt(2) or
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93 | * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
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94 | * with some parallelism and it reduces the error for many args.
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95 | */
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96 | w = y + val_hi;
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97 | val_lo += (y - w) + val_hi;
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98 | val_hi = w;
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99 |
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100 | return val_lo + val_hi;
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101 | }
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