text: /*
   * This file is part of the MicroPython project, http://micropython.org/
   *
   * These math functions are taken from newlib-nano-2, the newlib/libm/math
   * directory, available from https://github.com/32bitmicro/newlib-nano-2.
   *
   * Appropriate copyright headers are reproduced below.
   */
  
  /* sf_erf.c -- float version of s_erf.c.
   * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   */
  
  /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunPro, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice 
   * is preserved.
   * ====================================================
   */
  
  #include "fdlibm.h"
  
  #define __ieee754_expf expf
  
  #ifdef __v810__
  #define const
  #endif
  
  #ifdef __STDC__
  static const float
  #else
  static float
  #endif
  tiny	    = 1e-30f,
  half=  5.0000000000e-01f, /* 0x3F000000 */
  one =  1.0000000000e+00f, /* 0x3F800000 */
  two =  2.0000000000e+00f, /* 0x40000000 */
  	/* c = (subfloat)0.84506291151 */
  erx =  8.4506291151e-01f, /* 0x3f58560b */
  /*
   * Coefficients for approximation to  erf on [0,0.84375]
   */
  efx =  1.2837916613e-01f, /* 0x3e0375d4 */
  efx8=  1.0270333290e+00f, /* 0x3f8375d4 */
  pp0  =  1.2837916613e-01f, /* 0x3e0375d4 */
  pp1  = -3.2504209876e-01f, /* 0xbea66beb */
  pp2  = -2.8481749818e-02f, /* 0xbce9528f */
  pp3  = -5.7702702470e-03f, /* 0xbbbd1489 */
  pp4  = -2.3763017452e-05f, /* 0xb7c756b1 */
  qq1  =  3.9791721106e-01f, /* 0x3ecbbbce */
  qq2  =  6.5022252500e-02f, /* 0x3d852a63 */
  qq3  =  5.0813062117e-03f, /* 0x3ba68116 */
  qq4  =  1.3249473704e-04f, /* 0x390aee49 */
  qq5  = -3.9602282413e-06f, /* 0xb684e21a */
  /*
   * Coefficients for approximation to  erf  in [0.84375,1.25] 
   */
  pa0  = -2.3621185683e-03f, /* 0xbb1acdc6 */
  pa1  =  4.1485610604e-01f, /* 0x3ed46805 */
  pa2  = -3.7220788002e-01f, /* 0xbebe9208 */
  pa3  =  3.1834661961e-01f, /* 0x3ea2fe54 */
  pa4  = -1.1089469492e-01f, /* 0xbde31cc2 */
  pa5  =  3.5478305072e-02f, /* 0x3d1151b3 */
  pa6  = -2.1663755178e-03f, /* 0xbb0df9c0 */
  qa1  =  1.0642088205e-01f, /* 0x3dd9f331 */
  qa2  =  5.4039794207e-01f, /* 0x3f0a5785 */
  qa3  =  7.1828655899e-02f, /* 0x3d931ae7 */
  qa4  =  1.2617121637e-01f, /* 0x3e013307 */
  qa5  =  1.3637083583e-02f, /* 0x3c5f6e13 */
  qa6  =  1.1984500103e-02f, /* 0x3c445aa3 */
  /*
   * Coefficients for approximation to  erfc in [1.25,1/0.35]
   */
  ra0  = -9.8649440333e-03f, /* 0xbc21a093 */
  ra1  = -6.9385856390e-01f, /* 0xbf31a0b7 */
  ra2  = -1.0558626175e+01f, /* 0xc128f022 */
  ra3  = -6.2375331879e+01f, /* 0xc2798057 */
  ra4  = -1.6239666748e+02f, /* 0xc322658c */
  ra5  = -1.8460508728e+02f, /* 0xc3389ae7 */
  ra6  = -8.1287437439e+01f, /* 0xc2a2932b */
  ra7  = -9.8143291473e+00f, /* 0xc11d077e */
  sa1  =  1.9651271820e+01f, /* 0x419d35ce */
  sa2  =  1.3765776062e+02f, /* 0x4309a863 */
  sa3  =  4.3456588745e+02f, /* 0x43d9486f */
  sa4  =  6.4538726807e+02f, /* 0x442158c9 */
  sa5  =  4.2900814819e+02f, /* 0x43d6810b */
  sa6  =  1.0863500214e+02f, /* 0x42d9451f */
  sa7  =  6.5702495575e+00f, /* 0x40d23f7c */
  sa8  = -6.0424413532e-02f, /* 0xbd777f97 */
  /*
   * Coefficients for approximation to  erfc in [1/.35,28]
   */
  rb0  = -9.8649431020e-03f, /* 0xbc21a092 */
  rb1  = -7.9928326607e-01f, /* 0xbf4c9dd4 */
  rb2  = -1.7757955551e+01f, /* 0xc18e104b */
  rb3  = -1.6063638306e+02f, /* 0xc320a2ea */
  rb4  = -6.3756646729e+02f, /* 0xc41f6441 */
  rb5  = -1.0250950928e+03f, /* 0xc480230b */
  rb6  = -4.8351919556e+02f, /* 0xc3f1c275 */
  sb1  =  3.0338060379e+01f, /* 0x41f2b459 */
  sb2  =  3.2579251099e+02f, /* 0x43a2e571 */
  sb3  =  1.5367296143e+03f, /* 0x44c01759 */
  sb4  =  3.1998581543e+03f, /* 0x4547fdbb */
  sb5  =  2.5530502930e+03f, /* 0x451f90ce */
  sb6  =  4.7452853394e+02f, /* 0x43ed43a7 */
  sb7  = -2.2440952301e+01f; /* 0xc1b38712 */
  
  #ifdef __STDC__
  	float erff(float x) 
  #else
  	float erff(x) 
  	float x;
  #endif
  {
  	__int32_t hx,ix,i;
  	float R,S,P,Q,s,y,z,r;
  	GET_FLOAT_WORD(hx,x);
  	ix = hx&0x7fffffff;
  	if(!FLT_UWORD_IS_FINITE(ix)) {		/* erf(nan)=nan */
  	    i = ((__uint32_t)hx>>31)<<1;
  	    return (float)(1-i)+one/x;	/* erf(+-inf)=+-1 */
  	}
  
  	if(ix < 0x3f580000) {		/* |x|<0.84375 */
  	    if(ix < 0x31800000) { 	/* |x|<2**-28 */
  	        if (ix < 0x04000000) 
  		    /*avoid underflow */
  		    return (float)0.125*((float)8.0*x+efx8*x);
  		return x + efx*x;
  	    }
  	    z = x*x;
  	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
  	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
  	    y = r/s;
  	    return x + x*y;
  	}
  	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
  	    s = fabsf(x)-one;
  	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
  	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
  	    if(hx>=0) return erx + P/Q; else return -erx - P/Q;
  	}
  	if (ix >= 0x40c00000) {		/* inf>|x|>=6 */
  	    if(hx>=0) return one-tiny; else return tiny-one;
  	}
  	x = fabsf(x);
   	s = one/(x*x);
  	if(ix< 0x4036DB6E) {	/* |x| < 1/0.35 */
  	    R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
  				ra5+s*(ra6+s*ra7))))));
  	    S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
  				sa5+s*(sa6+s*(sa7+s*sa8)))))));
  	} else {	/* |x| >= 1/0.35 */
  	    R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
  				rb5+s*rb6)))));
  	    S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
  				sb5+s*(sb6+s*sb7))))));
  	}
  	GET_FLOAT_WORD(ix,x);
  	SET_FLOAT_WORD(z,ix&0xfffff000);
  	r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
  	if(hx>=0) return one-r/x; else return  r/x-one;
  }
  
  #ifdef __STDC__
  	float erfcf(float x) 
  #else
  	float erfcf(x) 
  	float x;
  #endif
  {
  	__int32_t hx,ix;
  	float R,S,P,Q,s,y,z,r;
  	GET_FLOAT_WORD(hx,x);
  	ix = hx&0x7fffffff;
  	if(!FLT_UWORD_IS_FINITE(ix)) {			/* erfc(nan)=nan */
  						/* erfc(+-inf)=0,2 */
  	    return (float)(((__uint32_t)hx>>31)<<1)+one/x;
  	}
  
  	if(ix < 0x3f580000) {		/* |x|<0.84375 */
  	    if(ix < 0x23800000)  	/* |x|<2**-56 */
  		return one-x;
  	    z = x*x;
  	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
  	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
  	    y = r/s;
  	    if(hx < 0x3e800000) {  	/* x<1/4 */
  		return one-(x+x*y);
  	    } else {
  		r = x*y;
  		r += (x-half);
  	        return half - r ;
  	    }
  	}
  	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
  	    s = fabsf(x)-one;
  	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
  	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
  	    if(hx>=0) {
  	        z  = one-erx; return z - P/Q; 
  	    } else {
  		z = erx+P/Q; return one+z;
  	    }
  	}
  	if (ix < 0x41e00000) {		/* |x|<28 */
  	    x = fabsf(x);
   	    s = one/(x*x);
  	    if(ix< 0x4036DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
  	        R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
  				ra5+s*(ra6+s*ra7))))));
  	        S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
  				sa5+s*(sa6+s*(sa7+s*sa8)))))));
  	    } else {			/* |x| >= 1/.35 ~ 2.857143 */
  		if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
  	        R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
  				rb5+s*rb6)))));
  	        S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
  				sb5+s*(sb6+s*sb7))))));
  	    }
  	    GET_FLOAT_WORD(ix,x);
  	    SET_FLOAT_WORD(z,ix&0xfffff000);
  	    r  =  __ieee754_expf(-z*z-(float)0.5625)*
  			__ieee754_expf((z-x)*(z+x)+R/S);
  	    if(hx>0) return r/x; else return two-r/x;
  	} else {
  	    if(hx>0) return tiny*tiny; else return two-tiny;
  	}
  }
  
  #ifdef _DOUBLE_IS_32BITS
  
  #ifdef __STDC__
  	double erf(double x)
  #else
  	double erf(x)
  	double x;
  #endif
  {
  	return (double) erff((float) x);
  }
  
  #ifdef __STDC__
  	double erfc(double x)
  #else
  	double erfc(x)
  	double x;
  #endif
  {
  	return (double) erfcf((float) x);
  }
  
  #endif /* defined(_DOUBLE_IS_32BITS) */
  