sincosl.c revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * CDDL HEADER START
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * The contents of this file are subject to the terms of the
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * Common Development and Distribution License (the "License").
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * You may not use this file except in compliance with the License.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * See the License for the specific language governing permissions
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * and limitations under the License.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * When distributing Covered Code, include this CDDL HEADER in each
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * If applicable, add the following below this CDDL HEADER, with the
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * fields enclosed by brackets "[]" replaced with your own identifying
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * information: Portions Copyright [yyyy] [name of copyright owner]
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * CDDL HEADER END
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
fd21d481e26774c37a197c7cc8ab56096a21e7aaPhill Cunnington * Use is subject to license terms.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * sincosl(x)
7b3fa0c4c626865e92012ef9f885e91d945850eaCraig McDonnell * Table look-up algorithm by K.C. Ng, November, 1989.
7b3fa0c4c626865e92012ef9f885e91d945850eaCraig McDonnell * kernel function:
87d68743726585ee101ba2e7be2cf06cd34ebb80Neil Madden * __k_sincosl ... sin and cos function on [-pi/4,pi/4]
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * __rem_pio2l ... argument reduction routine
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * 1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
997d6667b8c483bf582a231b1b24f84fbe6c8390Neil Madden * [-pi/2 , +pi/2], and let n = k mod 4.
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * 2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * n sin(x) cos(x) tan(x)
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * ----------------------------------------------------------
a90aba9cbcbb8e7fe95e45590d853959efe0d354Tom Rumsey * 1 C -S -C/S
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * 2 -S -C S/C
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * 3 -C S -C/S
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * ----------------------------------------------------------
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * Special cases:
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * Let trig be any of sin, cos, or tan.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * trig(+-INF) is NaN, with signals;
3cfef899c650ea8fa23c64ad5a66b8986bf77bb2Tom Rumsey * trig(NaN) is that NaN;
72450cb9c2ca854c6d3479832c2738196c1d3282Robert Wapshott * computer TRIG(x) returns trig(x) nearly rounded.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Fostersincosl(long double x, long double *s, long double *c) {
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster /* |x| ~< pi/4 */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *s = __k_sincosl(x, z, c);
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *s = *c = x - x; /* trig(Inf or NaN) is NaN */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster else { /* argument reduction needed */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster switch (n & 3) {