sincosl.c revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af
ccf9d4a5c6453fa9f8b839baeee25147865fbb7dJames Phillpotts/*
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * CDDL HEADER START
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *
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 *
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8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * or http://www.opensolaris.org/os/licensing.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * See the License for the specific language governing permissions
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8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *
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8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster/*
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster/*
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
fd21d481e26774c37a197c7cc8ab56096a21e7aaPhill Cunnington * Use is subject to license terms.
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster/*
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster * sincosl(x)
7b3fa0c4c626865e92012ef9f885e91d945850eaCraig McDonnell * Table look-up algorithm by K.C. Ng, November, 1989.
7b3fa0c4c626865e92012ef9f885e91d945850eaCraig McDonnell *
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 *
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * Method.
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 *
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * n sin(x) cos(x) tan(x)
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * ----------------------------------------------------------
26304a2a091af368cfc16c977bcce6d17195360aTom Rumsey * 0 S C S/C
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 *
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 *
72450cb9c2ca854c6d3479832c2738196c1d3282Robert Wapshott * Accuracy:
72450cb9c2ca854c6d3479832c2738196c1d3282Robert Wapshott * computer TRIG(x) returns trig(x) nearly rounded.
3cfef899c650ea8fa23c64ad5a66b8986bf77bb2Tom Rumsey */
01a939641aeb0a095851921879620c3fab295cb2Robert Wapshott
c184142912cff04e5442d8bf70febe477285fb1cCraig McDonnell#pragma weak __sincosl = sincosl
7b3fa0c4c626865e92012ef9f885e91d945850eaCraig McDonnell
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster#include "libm.h"
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster#include "longdouble.h"
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster
8af80418ba1ec431c8027fa9668e5678658d3611Allan Fostervoid
8af80418ba1ec431c8027fa9668e5678658d3611Allan Fostersincosl(long double x, long double *s, long double *c) {
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster long double y[2], z = 0.0L;
01a939641aeb0a095851921879620c3fab295cb2Robert Wapshott int n, ix;
01a939641aeb0a095851921879620c3fab295cb2Robert Wapshott
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster ix = *(int *) &x; /* High word of x */
01a939641aeb0a095851921879620c3fab295cb2Robert Wapshott
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster /* |x| ~< pi/4 */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster ix &= 0x7fffffff;
01a939641aeb0a095851921879620c3fab295cb2Robert Wapshott if (ix <= 0x3ffe9220)
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *s = __k_sincosl(x, z, c);
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster else if (ix >= 0x7fff0000)
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *s = *c = x - x; /* trig(Inf or NaN) is NaN */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster else { /* argument reduction needed */
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster n = __rem_pio2l(x, y);
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster switch (n & 3) {
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster case 0:
0c893a059f84246bf91e2f0fbf63e4c92f8e5165Tony Bamford *s = __k_sincosl(y[0], y[1], c);
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster break;
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster case 1:
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *c = -__k_sincosl(y[0], y[1], s);
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster break;
a90aba9cbcbb8e7fe95e45590d853959efe0d354Tom Rumsey case 2:
321cc59fdbbb9b6eebdfc714f2d86b785965d50eTom Rumsey *s = -__k_sincosl(y[0], y[1], c);
321cc59fdbbb9b6eebdfc714f2d86b785965d50eTom Rumsey *c = -*c;
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster break;
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster case 3:
7b3fa0c4c626865e92012ef9f885e91d945850eaCraig McDonnell *c = __k_sincosl(y[0], y[1], s);
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster *s = -*s;
7b3fa0c4c626865e92012ef9f885e91d945850eaCraig McDonnell break;
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster }
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster }
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster}
8af80418ba1ec431c8027fa9668e5678658d3611Allan Foster