100 lines
2.9 KiB
C
100 lines
2.9 KiB
C
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/* @(#)e_exp.c 1.6 04/04/22 */
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/*
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* ====================================================
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* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
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*
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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 <float.h>
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#include "math.h"
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#include "math_private.h"
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static const double
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one = 1.0,
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halF[2] = {0.5,-0.5,},
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o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
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u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
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ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
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-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
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ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
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-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
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invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
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P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
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P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
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P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
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P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
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P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
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static volatile double
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huge = 1.0e+300,
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twom1000= 9.33263618503218878990e-302; /* 2**-1000=0x01700000,0*/
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double exp(double x) /* default IEEE double exp */
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{
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double 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_HIGH_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 >= 0x40862E42) { /* if |x|>=709.78... */
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if(hx>=0x7ff00000) {
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u_int32_t lx;
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GET_LOW_WORD(lx,x);
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if(((hx&0xfffff)|lx)!=0)
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return x+x; /* NaN */
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else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
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}
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if(x > o_threshold) return huge*huge; /* overflow */
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if(x < u_threshold) return twom1000*twom1000; /* underflow */
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}
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/* argument reduction */
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if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
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if(hx < 0x3FF0A2B2) { /* 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 = (int)(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(double, x, hi - lo);
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}
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else if(hx < 0x3e300000) { /* when |x|<2**-28 */
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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 >= -1021)
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INSERT_WORDS(twopk,0x3ff00000+(k<<20), 0);
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else
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INSERT_WORDS(twopk,0x3ff00000+((k+1000)<<20), 0);
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c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
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if(k==0) return one-((x*c)/(c-2.0)-x);
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else y = one-((lo-(x*c)/(2.0-c))-hi);
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if(k >= -1021) {
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if (k==1024) return y*2.0*0x1p1023;
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return y*twopk;
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} else {
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return y*twopk*twom1000;
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}
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}
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/*
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#if (LDBL_MANT_DIG == 53)
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__weak_reference(exp, expl);
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#endif
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*/
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