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.)
slouken@2756
     1
/*
slouken@2756
     2
 * ====================================================
slouken@2756
     3
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
slouken@2756
     4
 *
slouken@2756
     5
 * Developed at SunPro, a Sun Microsystems, Inc. business.
slouken@2756
     6
 * Permission to use, copy, modify, and distribute this
slouken@2756
     7
 * software is freely granted, provided that this notice
slouken@2756
     8
 * is preserved.
slouken@2756
     9
 * ====================================================
slouken@2756
    10
 */
slouken@2756
    11
slouken@2756
    12
/*
slouken@2756
    13
 * __kernel_cos( x,  y )
slouken@2756
    14
 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
slouken@2756
    15
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
slouken@2756
    16
 * Input y is the tail of x.
slouken@2756
    17
 *
slouken@2756
    18
 * Algorithm
slouken@2756
    19
 *	1. Since cos(-x) = cos(x), we need only to consider positive x.
slouken@2756
    20
 *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
slouken@2756
    21
 *	3. cos(x) is approximated by a polynomial of degree 14 on
slouken@2756
    22
 *	   [0,pi/4]
slouken@2756
    23
 *		  	                 4            14
slouken@2756
    24
 *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
slouken@2756
    25
 *	   where the remez error is
slouken@2756
    26
 *
slouken@2756
    27
 * 	|              2     4     6     8     10    12     14 |     -58
slouken@2756
    28
 * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
slouken@2756
    29
 * 	|    					               |
slouken@2756
    30
 *
slouken@2756
    31
 * 	               4     6     8     10    12     14
slouken@2756
    32
 *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
slouken@2756
    33
 *	       cos(x) = 1 - x*x/2 + r
slouken@2756
    34
 *	   since cos(x+y) ~ cos(x) - sin(x)*y
slouken@2756
    35
 *			  ~ cos(x) - x*y,
slouken@2756
    36
 *	   a correction term is necessary in cos(x) and hence
slouken@2756
    37
 *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
slouken@2756
    38
 *	   For better accuracy when x > 0.3, let qx = |x|/4 with
slouken@2756
    39
 *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
slouken@2756
    40
 *	   Then
slouken@2756
    41
 *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
slouken@2756
    42
 *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
slouken@2756
    43
 *	   magnitude of the latter is at least a quarter of x*x/2,
slouken@2756
    44
 *	   thus, reducing the rounding error in the subtraction.
slouken@2756
    45
 */
slouken@2756
    46
slouken@6044
    47
#include "math_libm.h"
slouken@2756
    48
#include "math_private.h"
slouken@2756
    49
slouken@2756
    50
static const double
slouken@11683
    51
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
slouken@11683
    52
C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
slouken@11683
    53
C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
slouken@11683
    54
C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
slouken@11683
    55
C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
slouken@11683
    56
C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
slouken@11683
    57
C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
slouken@2756
    58
slouken@11683
    59
double attribute_hidden __kernel_cos(double x, double y)
slouken@2756
    60
{
slouken@11683
    61
	double a,hz,z,r,qx;
slouken@11683
    62
	int32_t ix;
slouken@11683
    63
	GET_HIGH_WORD(ix,x);
slouken@11683
    64
	ix &= 0x7fffffff;			/* ix = |x|'s high word*/
slouken@11683
    65
	if(ix<0x3e400000) {			/* if x < 2**27 */
slouken@11683
    66
	    if(((int)x)==0) return one;		/* generate inexact */
slouken@11683
    67
	}
slouken@11683
    68
	z  = x*x;
slouken@11683
    69
	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
slouken@11683
    70
	if(ix < 0x3FD33333) 			/* if |x| < 0.3 */
slouken@11683
    71
	    return one - (0.5*z - (z*r - x*y));
slouken@11683
    72
	else {
slouken@11683
    73
	    if(ix > 0x3fe90000) {		/* x > 0.78125 */
slouken@11683
    74
		qx = 0.28125;
slouken@11683
    75
	    } else {
slouken@11683
    76
	        INSERT_WORDS(qx,ix-0x00200000,0);	/* x/4 */
slouken@11683
    77
	    }
slouken@11683
    78
	    hz = 0.5*z-qx;
slouken@11683
    79
	    a  = one-qx;
slouken@11683
    80
	    return a - (hz - (z*r-x*y));
slouken@11683
    81
	}
slouken@2756
    82
}