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/* k_cosf.c -- float version of k_cos.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* 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.
* ====================================================
*/
#ifndef lint
static char rcsid[] = "$FreeBSD$";
#endif
#include "math.h"
#include "math_private.h"
static const float
one = 1.0000000000e+00, /* 0x3f800000 */
C1 = 4.1666667908e-02, /* 0x3d2aaaab */
C2 = -1.3888889225e-03, /* 0xbab60b61 */
C3 = 2.4801587642e-05, /* 0x37d00d01 */
C4 = -2.7557314297e-07, /* 0xb493f27c */
C5 = 2.0875723372e-09, /* 0x310f74f6 */
C6 = -1.1359647598e-11; /* 0xad47d74e */
float
__kernel_cosf(float x, float y)
{
float a,hz,z,r,qx;
int32_t ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff; /* ix = |x|'s high word*/
if(ix<0x32000000) { /* 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 < 0x3e99999a) /* if |x| < 0.3 */
return one - ((float)0.5*z - (z*r - x*y));
else {
/*
* qx is an approximation to x*x/2 such that 1-qx and x*x/2-qx
* are both exact. Its implementation is optimized for
* efficiency in preference to accuracy. We use x*x/2 ~ x/4 for
* x near 0.5 and mask off just enough low bits (3) for both of
* the above differences to be exact. We use a constant for
* x > 0.78125 to keep using the same algorithm as k_cos.c,
* although this gives only a small improvement in accuracy, at
* least here. Using x*x/2 to approximate itself (masking off
* 3 low bits again) would give better accuracy.
*/
if(ix > 0x3f480000) { /* x > 0.78125 */
qx = (float)0.28125;
} else {
SET_FLOAT_WORD(qx,(ix-0x01000000)&0xfffffff8);
}
hz = (float)0.5*z-qx;
a = one-qx;
return a - (hz - (z*r-x*y));
}
}
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