kc3-lang/SDL/src/libm/k_cos.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_cos.c

• /* @(#)k_cos.c 5.1 93/09/24 */
  /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  #if defined(LIBM_SCCS) && !defined(lint)
  static const char rcsid[] =
      "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
  #endif
  
  /*
   * __kernel_cos( x,  y )
   * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
   * Input x is assumed to be bounded by ~pi/4 in magnitude.
   * Input y is the tail of x.
   *
   * Algorithm
   *	1. Since cos(-x) = cos(x), we need only to consider positive x.
   *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
   *	3. cos(x) is approximated by a polynomial of degree 14 on
   *	   [0,pi/4]
   *		  	                 4            14
   *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
   *	   where the remez error is
   *
   * 	|              2     4     6     8     10    12     14 |     -58
   * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
   * 	|    					               |
   *
   * 	               4     6     8     10    12     14
   *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
   *	       cos(x) = 1 - x*x/2 + r
   *	   since cos(x+y) ~ cos(x) - sin(x)*y
   *			  ~ cos(x) - x*y,
   *	   a correction term is necessary in cos(x) and hence
   *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
   *	   For better accuracy when x > 0.3, let qx = |x|/4 with
   *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
   *	   Then
   *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
   *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
   *	   magnitude of the latter is at least a quarter of x*x/2,
   *	   thus, reducing the rounding error in the subtraction.
   */
  
  #include "math_libm.h"
  #include "math_private.h"
  
  #ifdef __STDC__
  static const double
  #else
  static double
  #endif
    one = 1.00000000000000000000e+00,     /* 0x3FF00000, 0x00000000 */
      C1 = 4.16666666666666019037e-02,    /* 0x3FA55555, 0x5555554C */
      C2 = -1.38888888888741095749e-03,   /* 0xBF56C16C, 0x16C15177 */
      C3 = 2.48015872894767294178e-05,    /* 0x3EFA01A0, 0x19CB1590 */
      C4 = -2.75573143513906633035e-07,   /* 0xBE927E4F, 0x809C52AD */
      C5 = 2.08757232129817482790e-09,    /* 0x3E21EE9E, 0xBDB4B1C4 */
      C6 = -1.13596475577881948265e-11;   /* 0xBDA8FAE9, 0xBE8838D4 */
  
  #ifdef __STDC__
  double attribute_hidden
  __kernel_cos(double x, double y)
  #else
  double attribute_hidden
  __kernel_cos(x, y)
       double x, y;
  #endif
  {
      double a, hz, z, r, qx;
      int32_t ix;
      GET_HIGH_WORD(ix, x);
      ix &= 0x7fffffff;           /* ix = |x|'s high word */
      if (ix < 0x3e400000) {      /* if x < 2**27 */
          if (((int) x) == 0)
              return one;         /* generate inexact */
      }
      z = x * x;
      r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
      if (ix < 0x3FD33333)        /* if |x| < 0.3 */
          return one - (0.5 * z - (z * r - x * y));
      else {
          if (ix > 0x3fe90000) {  /* x > 0.78125 */
              qx = 0.28125;
          } else {
              INSERT_WORDS(qx, ix - 0x00200000, 0);       /* x/4 */
          }
          hz = 0.5 * z - qx;
          a = one - qx;
          return a - (hz - (z * r - x * y));
      }
  }
  

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