kc3-lang/SDL/src/libm/k_tan.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/k_tan.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.
   * ====================================================
   */
  
  /* __kernel_tan( x, y, k )
   * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
   * Input x is assumed to be bounded by ~pi/4 in magnitude.
   * Input y is the tail of x.
   * Input k indicates whether tan (if k=1) or
   * -1/tan (if k= -1) is returned.
   *
   * Algorithm
   *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
   *	2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
   *	3. tan(x) is approximated by a odd polynomial of degree 27 on
   *	   [0,0.67434]
   *		  	         3             27
   *	   	tan(x) ~ x + T1*x + ... + T13*x
   *	   where
   *
   * 	        |tan(x)         2     4            26   |     -59.2
   * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
   * 	        |  x 					|
   *
   *	   Note: tan(x+y) = tan(x) + tan'(x)*y
   *		          ~ tan(x) + (1+x*x)*y
   *	   Therefore, for better accuracy in computing tan(x+y), let
   *		     3      2      2       2       2
   *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
   *	   then
   *		 		    3    2
   *		tan(x+y) = x + (T1*x + (x *(r+y)+y))
   *
   *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
   *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
   *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
   */
  
  #include "math_libm.h"
  #include "math_private.h"
  
  static const double
  one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
  pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
  T[] =  {
    3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
    1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
    5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
    2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
    8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
    3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
    1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
    5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
    2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
    7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
    7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
   -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
    2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
  };
  
  double __kernel_tan(double x, double y, int iy)
  {
  	double z,r,v,w,s;
  	int32_t ix,hx;
  	GET_HIGH_WORD(hx,x);
  	ix = hx&0x7fffffff;	/* high word of |x| */
  	if(ix<0x3e300000)			/* x < 2**-28 */
  	    {if((int)x==0) {			/* generate inexact */
  	        u_int32_t low;
  		GET_LOW_WORD(low,x);
  		if(((ix|low)|(iy+1))==0) return one/fabs(x);
  		else return (iy==1)? x: -one/x;
  	    }
  	    }
  	if(ix>=0x3FE59428) { 			/* |x|>=0.6744 */
  	    if(hx<0) {x = -x; y = -y;}
  	    z = pio4-x;
  	    w = pio4lo-y;
  	    x = z+w; y = 0.0;
  	}
  	z	=  x*x;
  	w 	=  z*z;
      /* Break x^5*(T[1]+x^2*T[2]+...) into
       *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
       *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
       */
  	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
  	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
  	s = z*x;
  	r = y + z*(s*(r+v)+y);
  	r += T[0]*s;
  	w = x+r;
  	if(ix>=0x3FE59428) {
  	    v = (double)iy;
  	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
  	}
  	if(iy==1) return w;
  	else {		/* if allow error up to 2 ulp,
  			   simply return -1.0/(x+r) here */
       /*  compute -1.0/(x+r) accurately */
  	    double a,t;
  	    z  = w;
  	    SET_LOW_WORD(z,0);
  	    v  = r-(z - x); 	/* z+v = r+x */
  	    t = a  = -1.0/w;	/* a = -1.0/w */
  	    SET_LOW_WORD(t,0);
  	    s  = 1.0+t*z;
  	    return t+a*(s+t*v);
  	}
  }
  

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