70 lines
1.7 KiB
C
70 lines
1.7 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <math.h>
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#include <stdint.h>
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static const float
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ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
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ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
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/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
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Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
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Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
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Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
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Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
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float logf(float x)
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{
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union {float f; uint32_t i;} u = {x};
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float_t hfsq,f,s,z,R,w,t1,t2,dk;
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uint32_t ix;
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int k;
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ix = u.i;
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k = 0;
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if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */
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if (ix<<1 == 0)
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return -1/(x*x); /* log(+-0)=-inf */
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if (ix>>31)
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return (x-x)/0.0f; /* log(-#) = NaN */
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/* subnormal number, scale up x */
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k -= 25;
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x *= 0x1p25f;
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u.f = x;
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ix = u.i;
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} else if (ix >= 0x7f800000) {
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return x;
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} else if (ix == 0x3f800000)
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return 0;
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/* reduce x into [sqrt(2)/2, sqrt(2)] */
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ix += 0x3f800000 - 0x3f3504f3;
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k += (int)(ix>>23) - 0x7f;
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ix = (ix&0x007fffff) + 0x3f3504f3;
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u.i = ix;
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x = u.f;
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f = x - 1.0f;
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s = f/(2.0f + f);
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z = s*s;
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w = z*z;
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t1= w*(Lg2+w*Lg4);
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t2= z*(Lg1+w*Lg3);
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R = t2 + t1;
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hfsq = 0.5f*f*f;
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dk = k;
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return s*(hfsq+R) + dk*ln2_lo - hfsq + f + dk*ln2_hi;
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}
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