[337] | 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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