/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
/* long double sinpil(long double x),
* return long double precision sinl(pi*x).
*
* Algorithm, 10/17/2002, K.C. Ng
* ------------------------------
* Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
* 1. If y == z, then x is a multiple of pi/4. Return the following values:
* ---------------------------------------------------
* n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi)
* ---------------------------------------------------
* 000 0.00 +0 ___ +1 ___ +0
* 001 0.25 +\/0.5 +\/0.5 +1
* 010 0.50 +1 ___ +0 ___ +inf
* 011 0.75 +\/0.5 -\/0.5 -1
* 100 1.00 -0 ___ -1 ___ +0
* 101 1.25 -\/0.5 -\/0.5 +1
* 110 1.50 -1 ___ -0 ___ +inf
* 111 1.75 -\/0.5 +\/0.5 -1
* ---------------------------------------------------
* 2. Otherwise,
* ---------------------------------------------------
* n t sin(x*pi) cos(x*pi) tan(x*pi)
* ---------------------------------------------------
* 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t)
* 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t)
* 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t)
* 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t)
* 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t)
* 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t)
* 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t)
* 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t)
* ---------------------------------------------------
*
* NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
* This will return a result with error slightly more than one ulp (but less
* than 2 ulp). If one wants accurate result, one may break up pi*t in
* high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
* instead.
*/
#include "libm.h"
#include "longdouble.h"
#include <sys/isa_defs.h>
#define I(q, m) ((int *) &(q))[m]
#define U(q, m) ((unsigned *) &(q))[m]
#if defined(__i386) || defined(__amd64)
#define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
#define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
#define PREC 64
#define PRECM1 63
#define PRECM2 62
static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
#else
#define LDBL_MOST_SIGNIF_I(ld) I(ld, 0)
#define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1)
#define PREC 113
#define PRECM1 112
#define PRECM2 111
static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
#endif
static const long double
zero = 0.0L,
quater = 0.25L,
one = 1.0L,
pi = 3.141592653589793238462643383279502884197e+0000L,
sqrth = 0.707106781186547524400844362104849039284835937688474,
tiny = 1.0e-100;
long double
sinpil(long double x) {
long double y, z, t;
int hx, n, k;
unsigned lx;
hx = LDBL_MOST_SIGNIF_I(x);
lx = LDBL_LEAST_SIGNIF_U(x);
k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */
if (k >= 16384)
y = x - x;
else {
if (k >= PREC)
y = zero;
else if (k == PRECM1)
y = (lx & 1) == 0 ? zero: -zero;
else { /* k = Prec - 2 */
y = (lx & 1) == 0 ? zero : one;
if ((lx & 2) != 0)
y = -y;
}
}
}
else if (k < -2) /* |x| < 0.25 */
y = __k_sinl(pi * fabsl(x), zero);
else {
/* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
y = 4.0L * fabsl(x);
if (k < PRECM2) {
z = y + twoPRECM2;
n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
t = z - twoPRECM2;
k = 0;
if (t == y)
k = 1;
else if (t > y) {
n -= 1;
t = quater + (y - t) * quater;
}
else
t = (y - t) * quater;
}
else { /* k = Prec-3 */
n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
k = 1;
}
if (k) { /* x = N/4 */
if ((n & 1) != 0)
y = sqrth + tiny;
else
y = (n & 2) == 0 ? zero : one;
if ((n & 4) != 0)
y = -y;
}
else {
if ((n & 1) != 0)
t = quater - t;
if (((n + (n & 1)) & 2) == 0)
y = __k_sinl(pi * t, zero);
else
y = __k_cosl(pi * t, zero);
if ((n & 4) != 0)
y = -y;
}
}
return hx >= 0 ? y : -y;
}
#undef U
#undef LDBL_LEAST_SIGNIF_U
#undef I
#undef LDBL_MOST_SIGNIF_I