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81 lines
2.2 KiB
C
81 lines
2.2 KiB
C
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/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.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 "libm.h"
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static const float
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half[2] = {0.5,-0.5},
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ln2hi = 6.9314575195e-1f, /* 0x3f317200 */
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ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */
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invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
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/*
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* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
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* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
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*/
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P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
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P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
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float expf(float x)
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{
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float_t hi, lo, c, xx, y;
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int k, sign;
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uint32_t hx;
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GET_FLOAT_WORD(hx, x);
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sign = hx >> 31; /* sign bit of x */
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hx &= 0x7fffffff; /* high word of |x| */
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/* special cases */
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if (hx >= 0x42aeac50) { /* if |x| >= -87.33655f or NaN */
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if (hx >= 0x42b17218 && !sign) { /* x >= 88.722839f */
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/* overflow */
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x *= 0x1p127f;
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return x;
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}
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if (sign) {
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/* underflow */
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FORCE_EVAL(-0x1p-149f/x);
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if (hx >= 0x42cff1b5) /* x <= -103.972084f */
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return 0;
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}
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}
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/* argument reduction */
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if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */
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k = invln2*x + half[sign];
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else
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k = 1 - sign - sign;
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hi = x - k*ln2hi; /* k*ln2hi is exact here */
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lo = k*ln2lo;
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x = hi - lo;
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} else if (hx > 0x39000000) { /* |x| > 2**-14 */
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k = 0;
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hi = x;
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lo = 0;
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} else {
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/* raise inexact */
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FORCE_EVAL(0x1p127f + x);
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return 1 + x;
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}
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/* x is now in primary range */
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xx = x*x;
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c = x - xx*(P1+xx*P2);
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y = 1 + (x*c/(2-c) - lo + hi);
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if (k == 0)
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return y;
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return scalbnf(y, k);
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}
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