185 lines
5.8 KiB
C
185 lines
5.8 KiB
C
/* s_erff.c -- float version of s_erf.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/s_erff.c,v 1.8 2008/02/22 02:30:35 das Exp $");
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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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tiny = 1e-30,
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half= 5.0000000000e-01, /* 0x3F000000 */
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one = 1.0000000000e+00, /* 0x3F800000 */
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two = 2.0000000000e+00, /* 0x40000000 */
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/*
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* Coefficients for approximation to erf on [0,0.84375]
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*/
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efx = 1.2837916613e-01, /* 0x3e0375d4 */
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efx8= 1.0270333290e+00, /* 0x3f8375d4 */
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/*
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* Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]:
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* |(erf(x) - x)/x - p(x)/q(x)| < 2**-31.
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*/
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pp0 = 1.28379166e-01F, /* 0x1.06eba8p-3 */
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pp1 = -3.36030394e-01F, /* -0x1.58185ap-2 */
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pp2 = -1.86260219e-03F, /* -0x1.e8451ep-10 */
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qq1 = 3.12324286e-01F, /* 0x1.3fd1f0p-2 */
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qq2 = 2.16070302e-02F, /* 0x1.620274p-6 */
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qq3 = -1.98859419e-03F, /* -0x1.04a626p-9 */
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/*
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* Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]:
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* |(erf(x) - erx) - p(x)/q(x)| < 2**-36.
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*/
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erx = 8.42697144e-01F, /* 0x1.af7600p-1. erf(1) rounded to 16 bits. */
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pa0 = 3.64939137e-06F, /* 0x1.e9d022p-19 */
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pa1 = 4.15109694e-01F, /* 0x1.a91284p-2 */
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pa2 = -1.65179938e-01F, /* -0x1.5249dcp-3 */
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pa3 = 1.10914491e-01F, /* 0x1.c64e46p-4 */
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qa1 = 6.02074385e-01F, /* 0x1.344318p-1 */
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qa2 = 5.35934687e-01F, /* 0x1.126608p-1 */
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qa3 = 1.68576106e-01F, /* 0x1.593e6ep-3 */
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qa4 = 5.62181212e-02F, /* 0x1.cc89f2p-5 */
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/*
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* Domain [1.25,1/0.35], range ~[-7.043e-10,7.457e-10]:
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* |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-30
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*/
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ra0 = -9.87132732e-03F, /* -0x1.4376b2p-7 */
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ra1 = -5.53605914e-01F, /* -0x1.1b723cp-1 */
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ra2 = -2.17589188e+00F, /* -0x1.1683a0p+1 */
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ra3 = -1.43268085e+00F, /* -0x1.6ec42cp+0 */
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sa1 = 5.45995426e+00F, /* 0x1.5d6fe4p+2 */
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sa2 = 6.69798088e+00F, /* 0x1.acabb8p+2 */
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sa3 = 1.43113089e+00F, /* 0x1.6e5e98p+0 */
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sa4 = -5.77397496e-02F, /* -0x1.d90108p-5 */
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/*
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* Domain [1/0.35, 11], range ~[-2.264e-13,2.336e-13]:
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* |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-42
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*/
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rb0 = -9.86494310e-03F, /* -0x1.434124p-7 */
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rb1 = -6.25171244e-01F, /* -0x1.401672p-1 */
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rb2 = -6.16498327e+00F, /* -0x1.8a8f16p+2 */
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rb3 = -1.66696873e+01F, /* -0x1.0ab70ap+4 */
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rb4 = -9.53764343e+00F, /* -0x1.313460p+3 */
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sb1 = 1.26884899e+01F, /* 0x1.96081cp+3 */
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sb2 = 4.51839523e+01F, /* 0x1.6978bcp+5 */
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sb3 = 4.72810211e+01F, /* 0x1.7a3f88p+5 */
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sb4 = 8.93033314e+00F; /* 0x1.1dc54ap+3 */
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OLM_DLLEXPORT float
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erff(float x)
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{
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int32_t hx,ix,i;
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float R,S,P,Q,s,y,z,r;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix>=0x7f800000) { /* erf(nan)=nan */
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i = ((u_int32_t)hx>>31)<<1;
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return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
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}
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if(ix < 0x3f580000) { /* |x|<0.84375 */
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if(ix < 0x38800000) { /* |x|<2**-14 */
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if (ix < 0x04000000) /* |x|<0x1p-119 */
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return (8*x+efx8*x)/8; /* avoid spurious underflow */
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return x + efx*x;
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}
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z = x*x;
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r = pp0+z*(pp1+z*pp2);
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s = one+z*(qq1+z*(qq2+z*qq3));
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y = r/s;
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return x + x*y;
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}
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if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
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s = fabsf(x)-one;
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P = pa0+s*(pa1+s*(pa2+s*pa3));
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Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
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if(hx>=0) return erx + P/Q; else return -erx - P/Q;
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}
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if (ix >= 0x40800000) { /* inf>|x|>=4 */
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if(hx>=0) return one-tiny; else return tiny-one;
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}
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x = fabsf(x);
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s = one/(x*x);
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if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
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R=ra0+s*(ra1+s*(ra2+s*ra3));
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S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
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} else { /* |x| >= 1/0.35 */
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R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
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S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
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}
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SET_FLOAT_WORD(z,hx&0xffffe000);
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r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
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if(hx>=0) return one-r/x; else return r/x-one;
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}
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OLM_DLLEXPORT float
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erfcf(float x)
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{
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int32_t hx,ix;
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float R,S,P,Q,s,y,z,r;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix>=0x7f800000) { /* erfc(nan)=nan */
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/* erfc(+-inf)=0,2 */
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return (float)(((u_int32_t)hx>>31)<<1)+one/x;
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}
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if(ix < 0x3f580000) { /* |x|<0.84375 */
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if(ix < 0x33800000) /* |x|<2**-56 */
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return one-x;
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z = x*x;
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r = pp0+z*(pp1+z*pp2);
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s = one+z*(qq1+z*(qq2+z*qq3));
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y = r/s;
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if(hx < 0x3e800000) { /* x<1/4 */
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return one-(x+x*y);
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} else {
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r = x*y;
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r += (x-half);
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return half - r ;
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}
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}
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if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
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s = fabsf(x)-one;
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P = pa0+s*(pa1+s*(pa2+s*pa3));
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Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
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if(hx>=0) {
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z = one-erx; return z - P/Q;
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} else {
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z = erx+P/Q; return one+z;
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}
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}
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if (ix < 0x41300000) { /* |x|<28 */
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x = fabsf(x);
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s = one/(x*x);
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if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
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R=ra0+s*(ra1+s*(ra2+s*ra3));
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S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
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} else { /* |x| >= 1/.35 ~ 2.857143 */
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if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */
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R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
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S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
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}
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SET_FLOAT_WORD(z,hx&0xffffe000);
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r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
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if(hx>0) return r/x; else return two-r/x;
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} else {
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if(hx>0) return tiny*tiny; else return two-tiny;
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}
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}
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