src/libm/k_cos.c
 author Sam Lantinga Wed, 19 Feb 2020 08:26:00 -0800 changeset 13540 28fcb5ef7ff1 parent 11683 48bcba563d9c permissions -rw-r--r--
Fixed support for third party Xbox 360 wireless controller dongle
```     1 /*
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```     2  * ====================================================
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```     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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```     4  *
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```     5  * Developed at SunPro, a Sun Microsystems, Inc. business.
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```     6  * Permission to use, copy, modify, and distribute this
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```     7  * software is freely granted, provided that this notice
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```     8  * is preserved.
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```     9  * ====================================================
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```    10  */
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```    11
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```    12 /*
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```    13  * __kernel_cos( x,  y )
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```    14  * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
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```    15  * Input x is assumed to be bounded by ~pi/4 in magnitude.
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```    16  * Input y is the tail of x.
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```    17  *
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```    18  * Algorithm
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```    19  *	1. Since cos(-x) = cos(x), we need only to consider positive x.
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```    20  *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
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```    21  *	3. cos(x) is approximated by a polynomial of degree 14 on
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```    22  *	   [0,pi/4]
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```    23  *		  	                 4            14
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```    24  *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
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```    25  *	   where the remez error is
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```    26  *
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```    27  * 	|              2     4     6     8     10    12     14 |     -58
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```    28  * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
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```    29  * 	|    					               |
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```    30  *
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```    31  * 	               4     6     8     10    12     14
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```    32  *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
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```    33  *	       cos(x) = 1 - x*x/2 + r
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```    34  *	   since cos(x+y) ~ cos(x) - sin(x)*y
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```    35  *			  ~ cos(x) - x*y,
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```    36  *	   a correction term is necessary in cos(x) and hence
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```    37  *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
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```    38  *	   For better accuracy when x > 0.3, let qx = |x|/4 with
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```    39  *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
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```    40  *	   Then
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```    41  *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
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```    42  *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
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```    43  *	   magnitude of the latter is at least a quarter of x*x/2,
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```    44  *	   thus, reducing the rounding error in the subtraction.
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```    45  */
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```    46
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```    47 #include "math_libm.h"
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```    48 #include "math_private.h"
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```    49
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```    50 static const double
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```    51 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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```    52 C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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```    53 C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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```    54 C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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```    55 C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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```    56 C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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```    57 C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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```    58
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```    59 double attribute_hidden __kernel_cos(double x, double y)
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```    60 {
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```    61 	double a,hz,z,r,qx;
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```    62 	int32_t ix;
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```    63 	GET_HIGH_WORD(ix,x);
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```    64 	ix &= 0x7fffffff;			/* ix = |x|'s high word*/
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```    65 	if(ix<0x3e400000) {			/* if x < 2**27 */
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```    66 	    if(((int)x)==0) return one;		/* generate inexact */
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```    67 	}
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```    68 	z  = x*x;
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```    69 	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
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```    70 	if(ix < 0x3FD33333) 			/* if |x| < 0.3 */
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```    71 	    return one - (0.5*z - (z*r - x*y));
```
```    72 	else {
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```    73 	    if(ix > 0x3fe90000) {		/* x > 0.78125 */
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```    74 		qx = 0.28125;
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```    75 	    } else {
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```    76 	        INSERT_WORDS(qx,ix-0x00200000,0);	/* x/4 */
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```    77 	    }
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```    78 	    hz = 0.5*z-qx;
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```    79 	    a  = one-qx;
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```    80 	    return a - (hz - (z*r-x*y));
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```    81 	}
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```    82 }
```