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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_sinpi.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 union IEEEl2bits
pi_hi_u = LD80C(0xc90fdaa200000000, 1, 3.14159265346825122833e+00L),
pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L);
#define pi_hi (pi_hi_u.e)
#define pi_lo (pi_lo_u.e)
#include "k_cospil.h"
#include "k_sinpil.h"
volatile static const double vzero = 0;
long double
sinpil(long double x)
{
long double ax, hi, lo, s;
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 (x == 0)
RETURNI(x);
INSERT_LDBL80_WORDS(hi, hx,
lx & 0xffffffff00000000ull);
hi *= 0x1p63L;
lo = x * 0x1p63L - hi;
s = (pi_lo + pi_hi) * lo + pi_lo * hi +
pi_hi * hi;
RETURNI(s * 0x1p-63L);
}
s = __kernel_sinpil(ax);
RETURNI((hx & 0x8000) ? -s : s);
}
if (ix < 0x3ffe) /* |x| < 0.5 */
s = __kernel_cospil(0.5 - ax);
else if (lx < 0xc000000000000000ull) /* |x| < 0.75 */
s = __kernel_cospil(ax - 0.5);
else
s = __kernel_sinpil(1 - ax);
RETURNI((hx & 0x8000) ? -s : s);
}
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 == 0) {
s = 0;
} else {
if (ix < 0x3ffe) { /* |x| < 0.5 */
if (ix < 0x3ffd) /* |x| < 0.25 */
s = __kernel_sinpil(ax);
else
s = __kernel_cospil(0.5 - ax);
} else {
/* |x| < 0.75 */
if (lx < 0xc000000000000000ull)
s = __kernel_cospil(ax - 0.5);
else
s = __kernel_sinpil(1 - ax);
}
if (j0 > 40)
x -= 0x1p40;
if (j0 > 30)
x -= 0x1p30;
j0 = (uint32_t)x;
if (j0 & 1) s = -s;
}
RETURNI((hx & 0x8000) ? -s : s);
}
/* x = +-inf or nan. */
if (ix >= 0x7fff)
RETURNI(vzero / vzero);
/*
* |x| >= 0x1p63 is always an integer, so return +-0.
*/
RETURNI(copysignl(0, x));
}
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