sincospi.c revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af
/*
* 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
* 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.
*/
/* INDENT OFF */
/*
* void sincospi(double x, double *s, double *c)
* *s = sin(pi*x); *c = cos(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)
* ---------------------------------------------------
*
* 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
* instead.
*/
#include "libm.h"
#include "libm_protos.h"
#include "libm_macros.h"
#include <math.h>
#if defined(__SUNPRO_C)
#include <sunmath.h>
#endif
static const double
sqrth_h = 0.70710678118654757273731092936941422522068023681640625,
sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17;
/* INDENT ON */
void
sincospi(double x, double *s, double *c) {
double y, z, t;
int n, ix, k;
if (n >= 51) { /* |x| >= 2**51 */
if (n >= 1024)
#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
*s = *c = ix >= 0x7ff80000 ? x : x - x;
/* assumes sparc-like QNaN */
#else
*s = *c = x - x;
#endif
else {
if (n >= 53) {
*s = 0.0;
*c = 1.0;
}
else if (n == 52) {
if ((lx & 1) == 0) {
*s = 0.0;
*c = 1.0;
}
else {
*s = -0.0;
*c = -1.0;
}
}
else { /* n == 51 */
if ((lx & 1) == 0) {
*s = 0.0;
*c = 1.0;
}
else {
*s = 1.0;
*c = 0.0;
}
if ((lx & 2) != 0) {
*s = -*s;
*c = -*c;
}
}
}
}
else if (n < -2) /* |x| < 0.25 */
else {
/* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
y = 4.0 * fabs(x);
n = (int) y; /* exact */
z = (double) n;
k = z == y;
t = (y - z) * 0.25;
}
else { /* 2**29 <= |x| < 2**51 */
y = fabs(x);
k = 50 - n;
n = lx >> k;
h = n << k;
((unsigned *) &z)[LOWORD] = h;
k = h == lx;
t = y - z;
}
if (k) { /* x = N/4 */
if ((n & 1) != 0)
else
if ((n & 2) == 0) {
*s = 0.0;
*c = 1.0;
}
else {
*s = 1.0;
*c = 0.0;
}
y = (n & 2) == 0 ? 0.0 : 1.0;
if ((n & 4) != 0)
*s = -*s;
if (((n + 1) & 4) != 0)
*c = -*c;
}
else {
if ((n & 1) != 0)
t = 0.25 - t;
if (((n + (n & 1)) & 2) == 0)
else
if ((n & 4) != 0)
*s = -*s;
if (((n + 2) & 4) != 0)
*c = -*c;
}
}
if (hx < 0)
*s = -*s;
}