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

Branch : - branch - v2.28 - tag -

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  Commit

• 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_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 attribute_hidden __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);
  	}
  }