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

Branch : - branch - v2.28 - tag -

• Show log

  Commit

• Author : Sam Lantinga
  Date : 2013-08-11 19:56:43
  Hash : 1ad936eb
  Message : Fixed bug 2027 - Full-screen appears to be broken - hang in SDL_DestroyWindow() Rainer Deyke I'm running Linux Mint 15 with the Cinnamon window manager. SDL_DestroyWindow consistently locks up for me when the window if fullscreen.

• 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));
      }
  }