/* ef_exp.c -- float version of e_exp.c.
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/* ef_exp.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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* 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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/*
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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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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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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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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*/
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*/
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#include "fdlibm.h"
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#include "fdlibm.h"
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#ifdef __v810__
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#ifdef __v810__
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#define const
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#define const
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#endif
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#endif
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#ifdef __STDC__
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#ifdef __STDC__
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static const float
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static const float
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#else
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#else
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static float
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static float
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#endif
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#endif
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one = 1.0,
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one = 1.0,
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halF[2] = {0.5,-0.5,},
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halF[2] = {0.5,-0.5,},
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huge = 1.0e+30,
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huge = 1.0e+30,
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twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
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twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
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ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
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ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
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-6.9313812256e-01,}, /* 0xbf317180 */
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-6.9313812256e-01,}, /* 0xbf317180 */
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ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
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ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
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-9.0580006145e-06,}, /* 0xb717f7d1 */
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-9.0580006145e-06,}, /* 0xb717f7d1 */
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invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
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invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
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P1 = 1.6666667163e-01, /* 0x3e2aaaab */
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P1 = 1.6666667163e-01, /* 0x3e2aaaab */
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P2 = -2.7777778450e-03, /* 0xbb360b61 */
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P2 = -2.7777778450e-03, /* 0xbb360b61 */
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P3 = 6.6137559770e-05, /* 0x388ab355 */
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P3 = 6.6137559770e-05, /* 0x388ab355 */
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P4 = -1.6533901999e-06, /* 0xb5ddea0e */
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P4 = -1.6533901999e-06, /* 0xb5ddea0e */
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P5 = 4.1381369442e-08; /* 0x3331bb4c */
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P5 = 4.1381369442e-08; /* 0x3331bb4c */
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#ifdef __STDC__
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#ifdef __STDC__
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float __ieee754_expf(float x) /* default IEEE double exp */
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float __ieee754_expf(float x) /* default IEEE double exp */
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#else
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#else
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float __ieee754_expf(x) /* default IEEE double exp */
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float __ieee754_expf(x) /* default IEEE double exp */
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float x;
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float x;
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#endif
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#endif
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{
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{
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float y,hi,lo,c,t;
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float y,hi,lo,c,t;
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__int32_t k,xsb,sx;
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__int32_t k,xsb,sx;
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__uint32_t hx;
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__uint32_t hx;
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GET_FLOAT_WORD(sx,x);
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GET_FLOAT_WORD(sx,x);
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xsb = (sx>>31)&1; /* sign bit of x */
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xsb = (sx>>31)&1; /* sign bit of x */
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hx = sx & 0x7fffffff; /* high word of |x| */
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hx = sx & 0x7fffffff; /* high word of |x| */
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/* filter out non-finite argument */
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/* filter out non-finite argument */
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if(FLT_UWORD_IS_NAN(hx))
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if(FLT_UWORD_IS_NAN(hx))
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return x+x; /* NaN */
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return x+x; /* NaN */
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if(FLT_UWORD_IS_INFINITE(hx))
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if(FLT_UWORD_IS_INFINITE(hx))
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return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
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return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
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if(sx > FLT_UWORD_LOG_MAX)
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if(sx > FLT_UWORD_LOG_MAX)
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return huge*huge; /* overflow */
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return huge*huge; /* overflow */
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if(sx < 0 && hx > FLT_UWORD_LOG_MIN)
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if(sx < 0 && hx > FLT_UWORD_LOG_MIN)
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return twom100*twom100; /* underflow */
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return twom100*twom100; /* underflow */
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/* argument reduction */
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/* argument reduction */
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if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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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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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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hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
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} else {
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} else {
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k = invln2*x+halF[xsb];
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k = invln2*x+halF[xsb];
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t = k;
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t = k;
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hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
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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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lo = t*ln2LO[0];
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}
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}
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x = hi - lo;
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x = hi - lo;
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}
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}
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else if(hx < 0x31800000) { /* when |x|<2**-28 */
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else if(hx < 0x31800000) { /* when |x|<2**-28 */
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if(huge+x>one) return one+x;/* trigger inexact */
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if(huge+x>one) return one+x;/* trigger inexact */
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}
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}
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else k = 0;
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else k = 0;
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/* x is now in primary range */
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/* x is now in primary range */
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t = x*x;
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t = x*x;
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c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
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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-(float)2.0)-x);
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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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else y = one-((lo-(x*c)/((float)2.0-c))-hi);
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if(k >= -125) {
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if(k >= -125) {
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__uint32_t hy;
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__uint32_t hy;
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GET_FLOAT_WORD(hy,y);
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GET_FLOAT_WORD(hy,y);
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SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
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SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
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return y;
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return y;
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} else {
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} else {
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__uint32_t hy;
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__uint32_t hy;
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GET_FLOAT_WORD(hy,y);
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GET_FLOAT_WORD(hy,y);
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SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
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SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
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return y*twom100;
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return y*twom100;
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}
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}
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}
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}
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