1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.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 log2.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 | ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */
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21 | ivln2lo = -1.7605285393e-04, /* 0xb9389ad4 */
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22 | /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
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23 | Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
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24 | Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
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25 | Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
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26 | Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
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27 |
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28 | float log2f(float x)
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29 | {
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30 | union {float f; uint32_t i;} u = {x};
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31 | float_t hfsq,f,s,z,R,w,t1,t2,hi,lo;
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32 | uint32_t ix;
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33 | int k;
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34 |
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35 | ix = u.i;
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36 | k = 0;
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37 | if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */
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38 | if (ix<<1 == 0)
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39 | return -1/(x*x); /* log(+-0)=-inf */
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40 | if (ix>>31)
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41 | return (x-x)/0.0f; /* log(-#) = NaN */
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42 | /* subnormal number, scale up x */
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43 | k -= 25;
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44 | x *= 0x1p25f;
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45 | u.f = x;
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46 | ix = u.i;
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47 | } else if (ix >= 0x7f800000) {
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48 | return x;
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49 | } else if (ix == 0x3f800000)
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50 | return 0;
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51 |
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52 | /* reduce x into [sqrt(2)/2, sqrt(2)] */
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53 | ix += 0x3f800000 - 0x3f3504f3;
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54 | k += (int)(ix>>23) - 0x7f;
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55 | ix = (ix&0x007fffff) + 0x3f3504f3;
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56 | u.i = ix;
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57 | x = u.f;
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58 |
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59 | f = x - 1.0f;
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60 | s = f/(2.0f + f);
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61 | z = s*s;
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62 | w = z*z;
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63 | t1= w*(Lg2+w*Lg4);
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64 | t2= z*(Lg1+w*Lg3);
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65 | R = t2 + t1;
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66 | hfsq = 0.5f*f*f;
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67 |
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68 | hi = f - hfsq;
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69 | u.f = hi;
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70 | u.i &= 0xfffff000;
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71 | hi = u.f;
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72 | lo = f - hi - hfsq + s*(hfsq+R);
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73 | return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + k;
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74 | }
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