1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.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 SunPro, 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 | * See comments in log10.c.
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14 | */
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15 |
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16 | #include <math.h>
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17 | #include <stdint.h>
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18 |
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19 | static const float
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20 | ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */
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21 | ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */
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22 | log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
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23 | log10_2lo = 7.9034151668e-07, /* 0x355427db */
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24 | /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
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25 | Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
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26 | Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
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27 | Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
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28 | Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
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29 |
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30 | float log10f(float x)
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31 | {
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32 | union {float f; uint32_t i;} u = {x};
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33 | float_t hfsq,f,s,z,R,w,t1,t2,dk,hi,lo;
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34 | uint32_t ix;
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35 | int k;
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36 |
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37 | ix = u.i;
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38 | k = 0;
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39 | if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */
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40 | if (ix<<1 == 0)
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41 | return -1/(x*x); /* log(+-0)=-inf */
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42 | if (ix>>31)
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43 | return (x-x)/0.0f; /* log(-#) = NaN */
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44 | /* subnormal number, scale up x */
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45 | k -= 25;
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46 | x *= 0x1p25f;
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47 | u.f = x;
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48 | ix = u.i;
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49 | } else if (ix >= 0x7f800000) {
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50 | return x;
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51 | } else if (ix == 0x3f800000)
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52 | return 0;
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53 |
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54 | /* reduce x into [sqrt(2)/2, sqrt(2)] */
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55 | ix += 0x3f800000 - 0x3f3504f3;
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56 | k += (int)(ix>>23) - 0x7f;
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57 | ix = (ix&0x007fffff) + 0x3f3504f3;
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58 | u.i = ix;
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59 | x = u.f;
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60 |
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61 | f = x - 1.0f;
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62 | s = f/(2.0f + f);
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63 | z = s*s;
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64 | w = z*z;
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65 | t1= w*(Lg2+w*Lg4);
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66 | t2= z*(Lg1+w*Lg3);
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67 | R = t2 + t1;
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68 | hfsq = 0.5f*f*f;
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69 |
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70 | hi = f - hfsq;
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71 | u.f = hi;
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72 | u.i &= 0xfffff000;
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73 | hi = u.f;
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74 | lo = f - hi - hfsq + s*(hfsq+R);
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75 | dk = k;
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76 | return dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + dk*log10_2hi;
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77 | }
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