[352] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.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 | #include "libm.h"
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| 14 |
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| 15 | static const float
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| 16 | ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
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| 17 | ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
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| 18 | /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
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| 19 | Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
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| 20 | Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
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| 21 | Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
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| 22 | Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
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| 23 |
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| 24 | float log1pf(float x)
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| 25 | {
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| 26 | union {float f; uint32_t i;} u = {x};
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| 27 | float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
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| 28 | uint32_t ix,iu;
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| 29 | int k;
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| 30 |
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| 31 | ix = u.i;
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| 32 | k = 1;
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| 33 | if (ix < 0x3ed413d0 || ix>>31) { /* 1+x < sqrt(2)+ */
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| 34 | if (ix >= 0xbf800000) { /* x <= -1.0 */
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| 35 | if (x == -1)
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| 36 | return x/0.0f; /* log1p(-1)=+inf */
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| 37 | return (x-x)/0.0f; /* log1p(x<-1)=NaN */
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| 38 | }
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| 39 | if (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */
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| 40 | /* underflow if subnormal */
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| 41 | if ((ix&0x7f800000) == 0)
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| 42 | FORCE_EVAL(x*x);
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| 43 | return x;
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| 44 | }
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| 45 | if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
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| 46 | k = 0;
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| 47 | c = 0;
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| 48 | f = x;
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| 49 | }
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| 50 | } else if (ix >= 0x7f800000)
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| 51 | return x;
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| 52 | if (k) {
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| 53 | u.f = 1 + x;
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| 54 | iu = u.i;
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| 55 | iu += 0x3f800000 - 0x3f3504f3;
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| 56 | k = (int)(iu>>23) - 0x7f;
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| 57 | /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
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| 58 | if (k < 25) {
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| 59 | c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
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| 60 | c /= u.f;
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| 61 | } else
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| 62 | c = 0;
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| 63 | /* reduce u into [sqrt(2)/2, sqrt(2)] */
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| 64 | iu = (iu&0x007fffff) + 0x3f3504f3;
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| 65 | u.i = iu;
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| 66 | f = u.f - 1;
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| 67 | }
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| 68 | s = f/(2.0f + f);
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| 69 | z = s*s;
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| 70 | w = z*z;
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| 71 | t1= w*(Lg2+w*Lg4);
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| 72 | t2= z*(Lg1+w*Lg3);
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| 73 | R = t2 + t1;
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| 74 | hfsq = 0.5f*f*f;
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| 75 | dk = k;
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| 76 | return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
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| 77 | }
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