184 lines
5.2 KiB
C
184 lines
5.2 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.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 "libc/math/libm.h"
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static const float
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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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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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static float erfc1(float x)
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{
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float_t s,P,Q;
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s = fabsf(x) - 1;
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P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
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Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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return 1 - erx - P/Q;
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}
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static float erfc2(uint32_t ix, float x)
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{
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float_t s,R,S;
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float z;
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if (ix < 0x3fa00000) /* |x| < 1.25 */
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return erfc1(x);
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x = fabsf(x);
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s = 1/(x*x);
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if (ix < 0x4036db6d) { /* |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 = 1.0f+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 = 1.0f+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&0xffffe000);
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return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x;
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}
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float erff(float x)
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{
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float r,s,z,y;
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uint32_t ix;
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int sign;
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GET_FLOAT_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7f800000) {
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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return 1-2*sign + 1/x;
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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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/*avoid underflow */
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return 0.125f*(8*x + efx8*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 = 1+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 < 0x40c00000) /* |x| < 6 */
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y = 1 - erfc2(ix,x);
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else
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y = 1 - 0x1p-120f;
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return sign ? -y : y;
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}
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float erfcf(float x)
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{
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float r,s,z,y;
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uint32_t ix;
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int sign;
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GET_FLOAT_WORD(ix, x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7f800000) {
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/* erfc(nan)=nan, erfc(+-inf)=0,2 */
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return 2*sign + 1/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 1.0f - 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 = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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if (sign || ix < 0x3e800000) /* x < 1/4 */
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return 1.0f - (x+x*y);
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return 0.5f - (x - 0.5f + x*y);
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}
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if (ix < 0x41e00000) { /* |x| < 28 */
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return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
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}
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return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f;
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}
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