kc3-lang/SDL/src/libm/s_atan.c

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• Hash : 0e45984f
  Author :
  Date : 2015-06-21T17:33:46
  

  Fixed crash if initialization of EGL failed but was tried again later.
  
  The internal function SDL_EGL_LoadLibrary() did not delete and remove a mostly
  uninitialized data structure if loading the library first failed. A later try to
  use EGL then skipped initialization and assumed it was previously successful
  because the data structure now already existed. This led to at least one crash
  in the internal function SDL_EGL_ChooseConfig() because a NULL pointer was
  dereferenced to make a call to eglBindAPI().
  

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• src/libm/s_atan.c

• /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  /* atan(x)
   * Method
   *   1. Reduce x to positive by atan(x) = -atan(-x).
   *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
   *      is further reduced to one of the following intervals and the
   *      arctangent of t is evaluated by the corresponding formula:
   *
   *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
   *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
   *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
   *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
   *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
   *
   * Constants:
   * The hexadecimal values are the intended ones for the following
   * constants. The decimal values may be used, provided that the
   * compiler will convert from decimal to binary accurately enough
   * to produce the hexadecimal values shown.
   */
  
  #include "math_libm.h"
  #include "math_private.h"
  
  static const double atanhi[] = {
    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
  };
  
  static const double atanlo[] = {
    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
  };
  
  static const double aT[] = {
    3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
   -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
    1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
   -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
    9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
   -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
    6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
   -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
    4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
   -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
    1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
  };
  
  static const double
  one   = 1.0,
  huge   = 1.0e300;
  
  double atan(double x)
  {
  	double w,s1,s2,z;
  	int32_t ix,hx,id;
  
  	GET_HIGH_WORD(hx,x);
  	ix = hx&0x7fffffff;
  	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
  	    u_int32_t low;
  	    GET_LOW_WORD(low,x);
  	    if(ix>0x7ff00000||
  		(ix==0x7ff00000&&(low!=0)))
  		return x+x;		/* NaN */
  	    if(hx>0) return  atanhi[3]+atanlo[3];
  	    else     return -atanhi[3]-atanlo[3];
  	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
  	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
  		if(huge+x>one) return x;	/* raise inexact */
  	    }
  	    id = -1;
  	} else {
  	x = fabs(x);
  	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
  	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
  		id = 0; x = (2.0*x-one)/(2.0+x);
  	    } else {			/* 11/16<=|x|< 19/16 */
  		id = 1; x  = (x-one)/(x+one);
  	    }
  	} else {
  	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
  		id = 2; x  = (x-1.5)/(one+1.5*x);
  	    } else {			/* 2.4375 <= |x| < 2^66 */
  		id = 3; x  = -1.0/x;
  	    }
  	}}
      /* end of argument reduction */
  	z = x*x;
  	w = z*z;
      /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  	if (id<0) return x - x*(s1+s2);
  	else {
  	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  	    return (hx<0)? -z:z;
  	}
  }
  libm_hidden_def(atan)
  
  

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