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

Branch : - branch - v2.28 - tag -

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• Author : Sam Lantinga
  Date : 2017-11-04 15:53:19
  Hash : 6cf06575
  Message : Updated math code from the uClibc 0.9.33 release

• src/libm/k_cos.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_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"
  
  static const double
  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 */
  
  double attribute_hidden __kernel_cos(double x, double y)
  {
  	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));
  	}
  }