src/libm/k_tan.c
 author Sam Lantinga Fri, 26 Aug 2016 12:18:08 -0700 changeset 10226 cb13d22b7f09 parent 8840 9b6ddcbdea65 child 11683 48bcba563d9c permissions -rw-r--r--
Updated the removal code to iterate over all joystick add messages instead of just the first one.
```     1 /*
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```     2  * ====================================================
```
```     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
```
```     4  *
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```     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
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```     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
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```    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
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```    27  *
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```    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
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```    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"
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```    48
```
```    49 static const double
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```    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 }
```