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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */ |
| 2 /* |
| 3 * ==================================================== |
| 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 5 * |
| 6 * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 7 * Permission to use, copy, modify, and distribute this |
| 8 * software is freely granted, provided that this notice |
| 9 * is preserved. |
| 10 * ==================================================== |
| 11 */ |
| 12 /* |
| 13 * See comments in log2.c. |
| 14 */ |
| 15 |
| 16 #include <math.h> |
| 17 #include <stdint.h> |
| 18 |
| 19 static const float |
| 20 ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ |
| 21 ivln2lo = -1.7605285393e-04, /* 0xb9389ad4 */ |
| 22 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ |
| 23 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ |
| 24 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ |
| 25 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ |
| 26 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ |
| 27 |
| 28 float log2f(float x) |
| 29 { |
| 30 union {float f; uint32_t i;} u = {x}; |
| 31 float_t hfsq,f,s,z,R,w,t1,t2,hi,lo; |
| 32 uint32_t ix; |
| 33 int k; |
| 34 |
| 35 ix = u.i; |
| 36 k = 0; |
| 37 if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */ |
| 38 if (ix<<1 == 0) |
| 39 return -1/(x*x); /* log(+-0)=-inf */ |
| 40 if (ix>>31) |
| 41 return (x-x)/0.0f; /* log(-#) = NaN */ |
| 42 /* subnormal number, scale up x */ |
| 43 k -= 25; |
| 44 x *= 0x1p25f; |
| 45 u.f = x; |
| 46 ix = u.i; |
| 47 } else if (ix >= 0x7f800000) { |
| 48 return x; |
| 49 } else if (ix == 0x3f800000) |
| 50 return 0; |
| 51 |
| 52 /* reduce x into [sqrt(2)/2, sqrt(2)] */ |
| 53 ix += 0x3f800000 - 0x3f3504f3; |
| 54 k += (int)(ix>>23) - 0x7f; |
| 55 ix = (ix&0x007fffff) + 0x3f3504f3; |
| 56 u.i = ix; |
| 57 x = u.f; |
| 58 |
| 59 f = x - 1.0f; |
| 60 s = f/(2.0f + f); |
| 61 z = s*s; |
| 62 w = z*z; |
| 63 t1= w*(Lg2+w*Lg4); |
| 64 t2= z*(Lg1+w*Lg3); |
| 65 R = t2 + t1; |
| 66 hfsq = 0.5f*f*f; |
| 67 |
| 68 hi = f - hfsq; |
| 69 u.f = hi; |
| 70 u.i &= 0xfffff000; |
| 71 hi = u.f; |
| 72 lo = f - hi - hfsq + s*(hfsq+R); |
| 73 return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + k; |
| 74 } |
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