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

Branch : - branch - v2.28 - tag -

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  Commit

• Author : Pierre-Loup A. Griffais
  Date : 2014-09-11 19:24:42
  Hash : 24c86b55
  Message : [X11] Reconcile logical keyboard state with physical state on FocusIn since the window system doesn't do it for us like other platforms. This prevents sticky keys and missed keys when going in and out of focus, for example Alt would appear to stick if switching away from an SDL app with Alt-Tab and had to be pressed again. CR: Sam

• 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);
  	}
  }