98 lines
2.8 KiB
C
98 lines
2.8 KiB
C
/* e_expf.c -- float version of e_exp.c.
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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 "cdefs-compat.h"
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//__FBSDID("$FreeBSD: src/lib/msun/src/e_expf.c,v 1.16 2011/10/21 06:26:38 das Exp $");
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#include <float.h>
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#include <openlibm_math.h>
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#include "math_private.h"
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static const float
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one = 1.0,
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halF[2] = {0.5,-0.5,},
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huge = 1.0e+30,
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o_threshold= 8.8721679688e+01, /* 0x42b17180 */
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u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
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ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */
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-6.9314575195e-01,}, /* 0xbf317200 */
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ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
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-1.4286067653e-06,}, /* 0xb5bfbe8e */
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invln2 = 1.4426950216e+00, /* 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-1, /* 0xaaaa8f.0p-26 */
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P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
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static volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
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OLM_DLLEXPORT float
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__ieee754_expf(float x)
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{
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float y,hi=0.0,lo=0.0,c,t,twopk;
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int32_t k=0,xsb;
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u_int32_t hx;
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GET_FLOAT_WORD(hx,x);
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xsb = (hx>>31)&1; /* sign bit of x */
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hx &= 0x7fffffff; /* high word of |x| */
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/* filter out non-finite argument */
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if(hx >= 0x42b17218) { /* if |x|>=88.721... */
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if(hx>0x7f800000)
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return x+x; /* NaN */
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if(hx==0x7f800000)
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return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
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if(x > o_threshold) return huge*huge; /* overflow */
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if(x < u_threshold) return twom100*twom100; /* underflow */
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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) { /* and |x| < 1.5 ln2 */
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hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
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} else {
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k = invln2*x+halF[xsb];
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t = k;
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hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
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lo = t*ln2LO[0];
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}
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STRICT_ASSIGN(float, x, hi - lo);
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}
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else if(hx < 0x39000000) { /* when |x|<2**-14 */
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if(huge+x>one) return one+x;/* trigger inexact */
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}
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else k = 0;
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/* x is now in primary range */
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t = x*x;
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if(k >= -125)
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SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
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else
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SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
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c = x - t*(P1+t*P2);
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if(k==0) return one-((x*c)/(c-(float)2.0)-x);
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else y = one-((lo-(x*c)/((float)2.0-c))-hi);
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if(k >= -125) {
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if(k==128) return y*2.0F*0x1p127F;
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return y*twopk;
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} else {
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return y*twopk*twom100;
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}
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}
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