src/libm/k_cos.c
author Ryan C. Gordon <icculus@icculus.org>
Mon, 21 May 2018 12:00:21 -0400
changeset 11994 8e094f91ddab
parent 11683 48bcba563d9c
permissions -rw-r--r--
thread: fixed compiler warnings on non-Linux systems that use pthread.

(static function rtkit_setpriority was unused, moved it in with rest of
__LINUX__ section.)
     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 /*
    13  * __kernel_cos( x,  y )
    14  * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
    15  * Input x is assumed to be bounded by ~pi/4 in magnitude.
    16  * Input y is the tail of x.
    17  *
    18  * Algorithm
    19  *	1. Since cos(-x) = cos(x), we need only to consider positive x.
    20  *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
    21  *	3. cos(x) is approximated by a polynomial of degree 14 on
    22  *	   [0,pi/4]
    23  *		  	                 4            14
    24  *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
    25  *	   where the remez error is
    26  *
    27  * 	|              2     4     6     8     10    12     14 |     -58
    28  * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
    29  * 	|    					               |
    30  *
    31  * 	               4     6     8     10    12     14
    32  *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
    33  *	       cos(x) = 1 - x*x/2 + r
    34  *	   since cos(x+y) ~ cos(x) - sin(x)*y
    35  *			  ~ cos(x) - x*y,
    36  *	   a correction term is necessary in cos(x) and hence
    37  *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
    38  *	   For better accuracy when x > 0.3, let qx = |x|/4 with
    39  *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
    40  *	   Then
    41  *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
    42  *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
    43  *	   magnitude of the latter is at least a quarter of x*x/2,
    44  *	   thus, reducing the rounding error in the subtraction.
    45  */
    46 
    47 #include "math_libm.h"
    48 #include "math_private.h"
    49 
    50 static const double
    51 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
    52 C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
    53 C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
    54 C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
    55 C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
    56 C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
    57 C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
    58 
    59 double attribute_hidden __kernel_cos(double x, double y)
    60 {
    61 	double a,hz,z,r,qx;
    62 	int32_t ix;
    63 	GET_HIGH_WORD(ix,x);
    64 	ix &= 0x7fffffff;			/* ix = |x|'s high word*/
    65 	if(ix<0x3e400000) {			/* if x < 2**27 */
    66 	    if(((int)x)==0) return one;		/* generate inexact */
    67 	}
    68 	z  = x*x;
    69 	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
    70 	if(ix < 0x3FD33333) 			/* if |x| < 0.3 */
    71 	    return one - (0.5*z - (z*r - x*y));
    72 	else {
    73 	    if(ix > 0x3fe90000) {		/* x > 0.78125 */
    74 		qx = 0.28125;
    75 	    } else {
    76 	        INSERT_WORDS(qx,ix-0x00200000,0);	/* x/4 */
    77 	    }
    78 	    hz = 0.5*z-qx;
    79 	    a  = one-qx;
    80 	    return a - (hz - (z*r-x*y));
    81 	}
    82 }