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

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• Hash : b72938c8
  Author :
  Date : 2015-04-20T12:22:44
  

  Windows: Always set the system timer resolution to 1ms by default.
  
  An existing hint lets apps that don't need the timer resolution changed avoid
  this, to save battery, etc, but this fixes several problems in timing, audio
  callbacks not firing fast enough, etc.
  
  Fixes Bugzilla #2944.
  

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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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