src/libm/k_tan.c
author Sam Lantinga <slouken@libsdl.org>
Fri, 26 Aug 2016 12:18:08 -0700
changeset 10226 cb13d22b7f09
parent 8840 9b6ddcbdea65
child 11683 48bcba563d9c
permissions -rw-r--r--
Added SDL_PrivateJoystickAdded() and SDL_PrivateJoystickRemoved()
Updated the removal code to iterate over all joystick add messages instead of just the first one.
     1 /*
     2  * ====================================================
     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     4  *
     5  * Developed at SunPro, a Sun Microsystems, Inc. business.
     6  * Permission to use, copy, modify, and distribute this
     7  * software is freely granted, provided that this notice
     8  * is preserved.
     9  * ====================================================
    10  */
    11 
    12 /* __kernel_tan( x, y, k )
    13  * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
    14  * Input x is assumed to be bounded by ~pi/4 in magnitude.
    15  * Input y is the tail of x.
    16  * Input k indicates whether tan (if k=1) or
    17  * -1/tan (if k= -1) is returned.
    18  *
    19  * Algorithm
    20  *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
    21  *	2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
    22  *	3. tan(x) is approximated by a odd polynomial of degree 27 on
    23  *	   [0,0.67434]
    24  *		  	         3             27
    25  *	   	tan(x) ~ x + T1*x + ... + T13*x
    26  *	   where
    27  *
    28  * 	        |tan(x)         2     4            26   |     -59.2
    29  * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
    30  * 	        |  x 					|
    31  *
    32  *	   Note: tan(x+y) = tan(x) + tan'(x)*y
    33  *		          ~ tan(x) + (1+x*x)*y
    34  *	   Therefore, for better accuracy in computing tan(x+y), let
    35  *		     3      2      2       2       2
    36  *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
    37  *	   then
    38  *		 		    3    2
    39  *		tan(x+y) = x + (T1*x + (x *(r+y)+y))
    40  *
    41  *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
    42  *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
    43  *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
    44  */
    45 
    46 #include "math_libm.h"
    47 #include "math_private.h"
    48 
    49 static const double
    50 one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
    51 pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
    52 pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
    53 T[] =  {
    54   3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
    55   1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
    56   5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
    57   2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
    58   8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
    59   3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
    60   1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
    61   5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
    62   2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
    63   7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
    64   7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
    65  -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
    66   2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
    67 };
    68 
    69 double __kernel_tan(double x, double y, int iy)
    70 {
    71 	double z,r,v,w,s;
    72 	int32_t ix,hx;
    73 	GET_HIGH_WORD(hx,x);
    74 	ix = hx&0x7fffffff;	/* high word of |x| */
    75 	if(ix<0x3e300000)			/* x < 2**-28 */
    76 	    {if((int)x==0) {			/* generate inexact */
    77 	        u_int32_t low;
    78 		GET_LOW_WORD(low,x);
    79 		if(((ix|low)|(iy+1))==0) return one/fabs(x);
    80 		else return (iy==1)? x: -one/x;
    81 	    }
    82 	    }
    83 	if(ix>=0x3FE59428) { 			/* |x|>=0.6744 */
    84 	    if(hx<0) {x = -x; y = -y;}
    85 	    z = pio4-x;
    86 	    w = pio4lo-y;
    87 	    x = z+w; y = 0.0;
    88 	}
    89 	z	=  x*x;
    90 	w 	=  z*z;
    91     /* Break x^5*(T[1]+x^2*T[2]+...) into
    92      *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
    93      *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
    94      */
    95 	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
    96 	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
    97 	s = z*x;
    98 	r = y + z*(s*(r+v)+y);
    99 	r += T[0]*s;
   100 	w = x+r;
   101 	if(ix>=0x3FE59428) {
   102 	    v = (double)iy;
   103 	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
   104 	}
   105 	if(iy==1) return w;
   106 	else {		/* if allow error up to 2 ulp,
   107 			   simply return -1.0/(x+r) here */
   108      /*  compute -1.0/(x+r) accurately */
   109 	    double a,t;
   110 	    z  = w;
   111 	    SET_LOW_WORD(z,0);
   112 	    v  = r-(z - x); 	/* z+v = r+x */
   113 	    t = a  = -1.0/w;	/* a = -1.0/w */
   114 	    SET_LOW_WORD(t,0);
   115 	    s  = 1.0+t*z;
   116 	    return t+a*(s+t*v);
   117 	}
   118 }