src/libm/k_cos.c
 author Holmes Futrell Thu, 01 Jan 2009 23:49:28 +0000 changeset 2950 04c9f1e4c496 parent 2756 a98604b691c8 child 3162 dc1eb82ffdaa permissions -rw-r--r--
Added target testdraw2 for running the test/testdraw2.c test.
```
/* @(#)k_cos.c 5.1 93/09/24 */
/*
* ====================================================
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "\$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp \$";
#endif

/*
* __kernel_cos( x,  y )
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
*
* Algorithm
*	1. Since cos(-x) = cos(x), we need only to consider positive x.
*	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
*	3. cos(x) is approximated by a polynomial of degree 14 on
*	   [0,pi/4]
*		  	                 4            14
*	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
*	   where the remez error is
*
* 	|              2     4     6     8     10    12     14 |     -58
* 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
* 	|    					               |
*
* 	               4     6     8     10    12     14
*	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
*	       cos(x) = 1 - x*x/2 + r
*	   since cos(x+y) ~ cos(x) - sin(x)*y
*			  ~ cos(x) - x*y,
*	   a correction term is necessary in cos(x) and hence
*		cos(x+y) = 1 - (x*x/2 - (r - x*y))
*	   For better accuracy when x > 0.3, let qx = |x|/4 with
*	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
*	   Then
*		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
*	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
*	   magnitude of the latter is at least a quarter of x*x/2,
*	   thus, reducing the rounding error in the subtraction.
*/

#include "math.h"
#include "math_private.h"

#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00,     /* 0x3FF00000, 0x00000000 */
C1 = 4.16666666666666019037e-02,    /* 0x3FA55555, 0x5555554C */
C2 = -1.38888888888741095749e-03,   /* 0xBF56C16C, 0x16C15177 */
C3 = 2.48015872894767294178e-05,    /* 0x3EFA01A0, 0x19CB1590 */
C4 = -2.75573143513906633035e-07,   /* 0xBE927E4F, 0x809C52AD */
C5 = 2.08757232129817482790e-09,    /* 0x3E21EE9E, 0xBDB4B1C4 */
C6 = -1.13596475577881948265e-11;   /* 0xBDA8FAE9, 0xBE8838D4 */

#ifdef __STDC__
double attribute_hidden
__kernel_cos(double x, double y)
#else
double attribute_hidden
__kernel_cos(x, y)
double x, y;
#endif
{
double a, hz, z, r, qx;
int32_t ix;
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;           /* ix = |x|'s high word */
if (ix < 0x3e400000) {      /* if x < 2**27 */
if (((int) x) == 0)
return one;         /* generate inexact */
}
z = x * x;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
if (ix < 0x3FD33333)        /* if |x| < 0.3 */
return one - (0.5 * z - (z * r - x * y));
else {
if (ix > 0x3fe90000) {  /* x > 0.78125 */
qx = 0.28125;
} else {
INSERT_WORDS(qx, ix - 0x00200000, 0);       /* x/4 */
}
hz = 0.5 * z - qx;
a = one - qx;
return a - (hz - (z * r - x * y));
}
}
```