258 lines
7.3 KiB
C
258 lines
7.3 KiB
C
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/*
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* This file is part of the Micro Python project, http://micropython.org/
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*
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* These math functions are taken from newlib-nano-2, the newlib/libm/math
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* directory, available from https://github.com/32bitmicro/newlib-nano-2.
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*
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* Appropriate copyright headers are reproduced below.
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*/
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/* sf_erf.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 "fdlibm.h"
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#define __ieee754_expf expf
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#ifdef __v810__
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#define const
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#endif
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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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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/* c = (subfloat)0.84506291151 */
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erx = 8.4506291151e-01, /* 0x3f58560b */
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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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pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
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pp1 = -3.2504209876e-01, /* 0xbea66beb */
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pp2 = -2.8481749818e-02, /* 0xbce9528f */
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pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
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pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
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qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
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qq2 = 6.5022252500e-02, /* 0x3d852a63 */
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qq3 = 5.0813062117e-03, /* 0x3ba68116 */
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qq4 = 1.3249473704e-04, /* 0x390aee49 */
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qq5 = -3.9602282413e-06, /* 0xb684e21a */
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/*
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* Coefficients for approximation to erf in [0.84375,1.25]
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*/
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pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
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pa1 = 4.1485610604e-01, /* 0x3ed46805 */
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pa2 = -3.7220788002e-01, /* 0xbebe9208 */
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pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
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pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
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pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
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pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
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qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
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qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
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qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
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qa4 = 1.2617121637e-01, /* 0x3e013307 */
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qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
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qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
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/*
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* Coefficients for approximation to erfc in [1.25,1/0.35]
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*/
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ra0 = -9.8649440333e-03, /* 0xbc21a093 */
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ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
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ra2 = -1.0558626175e+01, /* 0xc128f022 */
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ra3 = -6.2375331879e+01, /* 0xc2798057 */
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ra4 = -1.6239666748e+02, /* 0xc322658c */
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ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
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ra6 = -8.1287437439e+01, /* 0xc2a2932b */
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ra7 = -9.8143291473e+00, /* 0xc11d077e */
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sa1 = 1.9651271820e+01, /* 0x419d35ce */
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sa2 = 1.3765776062e+02, /* 0x4309a863 */
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sa3 = 4.3456588745e+02, /* 0x43d9486f */
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sa4 = 6.4538726807e+02, /* 0x442158c9 */
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sa5 = 4.2900814819e+02, /* 0x43d6810b */
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sa6 = 1.0863500214e+02, /* 0x42d9451f */
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sa7 = 6.5702495575e+00, /* 0x40d23f7c */
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sa8 = -6.0424413532e-02, /* 0xbd777f97 */
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/*
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* Coefficients for approximation to erfc in [1/.35,28]
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*/
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rb0 = -9.8649431020e-03, /* 0xbc21a092 */
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rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
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rb2 = -1.7757955551e+01, /* 0xc18e104b */
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rb3 = -1.6063638306e+02, /* 0xc320a2ea */
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rb4 = -6.3756646729e+02, /* 0xc41f6441 */
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rb5 = -1.0250950928e+03, /* 0xc480230b */
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rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
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sb1 = 3.0338060379e+01, /* 0x41f2b459 */
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sb2 = 3.2579251099e+02, /* 0x43a2e571 */
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sb3 = 1.5367296143e+03, /* 0x44c01759 */
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sb4 = 3.1998581543e+03, /* 0x4547fdbb */
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sb5 = 2.5530502930e+03, /* 0x451f90ce */
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sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
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sb7 = -2.2440952301e+01; /* 0xc1b38712 */
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#ifdef __STDC__
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float erff(float x)
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#else
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float erff(x)
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float x;
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#endif
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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(!FLT_UWORD_IS_FINITE(ix)) { /* erf(nan)=nan */
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i = ((__uint32_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 < 0x31800000) { /* |x|<2**-28 */
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if (ix < 0x04000000)
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/*avoid underflow */
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return (float)0.125*((float)8.0*x+efx8*x);
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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+z*(pp3+z*pp4)));
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s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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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+s*(pa4+s*(pa5+s*pa6)))));
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Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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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 >= 0x40c00000) { /* inf>|x|>=6 */
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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+s*(ra4+s*(
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ra5+s*(ra6+s*ra7))))));
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S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
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sa5+s*(sa6+s*(sa7+s*sa8)))))));
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} else { /* |x| >= 1/0.35 */
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R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
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rb5+s*rb6)))));
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S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
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sb5+s*(sb6+s*sb7))))));
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}
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GET_FLOAT_WORD(ix,x);
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SET_FLOAT_WORD(z,ix&0xfffff000);
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r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_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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#ifdef __STDC__
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float erfcf(float x)
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#else
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float erfcf(x)
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float x;
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#endif
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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(!FLT_UWORD_IS_FINITE(ix)) { /* erfc(nan)=nan */
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/* erfc(+-inf)=0,2 */
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return (float)(((__uint32_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 < 0x23800000) /* |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+z*(pp3+z*pp4)));
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s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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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+s*(pa4+s*(pa5+s*pa6)))));
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Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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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 < 0x41e00000) { /* |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+s*(ra4+s*(
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ra5+s*(ra6+s*ra7))))));
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S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
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sa5+s*(sa6+s*(sa7+s*sa8)))))));
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} else { /* |x| >= 1/.35 ~ 2.857143 */
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if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
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R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
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rb5+s*rb6)))));
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S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
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sb5+s*(sb6+s*sb7))))));
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}
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GET_FLOAT_WORD(ix,x);
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SET_FLOAT_WORD(z,ix&0xfffff000);
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r = __ieee754_expf(-z*z-(float)0.5625)*
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__ieee754_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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#ifdef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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double erf(double x)
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#else
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double erf(x)
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double x;
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#endif
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{
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return (double) erff((float) x);
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}
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#ifdef __STDC__
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double erfc(double x)
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#else
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double erfc(x)
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double x;
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#endif
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{
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return (double) erfcf((float) x);
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */
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