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/*-
* Copyright (c) 2017 Steven G. Kargl
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* See ../src/s_cospi.c for implementation details.
*/
#ifdef __i386__
#include <ieeefp.h>
#endif
#include <stdint.h>
#include "../ld/fpmath.h"
#include "math.h"
#include "../ld/math_private.h"
static const double
pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
#include "k_cospil.h"
#include "k_sinpil.h"
volatile static const double vzero = 0;
long double
cospil(long double x)
{
long double ax, c;
uint64_t lx, m;
uint32_t j0;
uint16_t hx, ix;
EXTRACT_LDBL80_WORDS(hx, lx, x);
ix = hx & 0x7fff;
INSERT_LDBL80_WORDS(ax, ix, lx);
ENTERI();
if (ix < 0x3fff) { /* |x| < 1 */
if (ix < 0x3ffd) { /* |x| < 0.25 */
if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
if ((int)x == 0)
RETURNI(1);
}
RETURNI(__kernel_cospil(ax));
}
if (ix < 0x3ffe) /* |x| < 0.5 */
c = __kernel_sinpil(0.5 - ax);
else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
if (ax == 0.5)
RETURNI(0);
c = -__kernel_sinpil(ax - 0.5);
} else
c = -__kernel_cospil(1 - ax);
RETURNI(c);
}
if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
/* Determine integer part of ax. */
j0 = ix - 0x3fff + 1;
if (j0 < 32) {
lx = (lx >> 32) << 32;
lx &= ~(((lx << 32)-1) >> j0);
} else {
m = (uint64_t)-1 >> (j0 + 1);
if (lx & m) lx &= ~m;
}
INSERT_LDBL80_WORDS(x, ix, lx);
ax -= x;
EXTRACT_LDBL80_WORDS(ix, lx, ax);
if (ix < 0x3ffe) { /* |x| < 0.5 */
if (ix < 0x3ffd) /* |x| < 0.25 */
c = ix == 0 ? 1 : __kernel_cospil(ax);
else
c = __kernel_sinpil(0.5 - ax);
} else {
if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
if (ax == 0.5)
RETURNI(0);
c = -__kernel_sinpil(ax - 0.5);
} else
c = -__kernel_cospil(1 - ax);
}
if (j0 > 40)
x -= 0x1p40;
if (j0 > 30)
x -= 0x1p30;
j0 = (uint32_t)x;
RETURNI(j0 & 1 ? -c : c);
}
if (ix >= 0x7fff)
RETURNI(vzero / vzero);
/*
* |x| >= 0x1p63 is always an even integer, so return 1.
*/
RETURNI(1);
}
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