1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 
  26 /*
  27  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 /*
  32  * sincosl(x)
  33  * Table look-up algorithm by K.C. Ng, November, 1989.
  34  *
  35  * kernel function:
  36  *      __k_sincosl     ... sin and cos function on [-pi/4,pi/4]
  37  *      __rem_pio2l     ... argument reduction routine
  38  *
  39  * Method.
  40  *      Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
  41  *      1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
  42  *         [-pi/2 , +pi/2], and let n = k mod 4.
  43  *      2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
  44  *
  45  *          n        sin(x)      cos(x)        tan(x)
  46  *     ----------------------------------------------------------
  47  *          0          S           C             S/C
  48  *          1          C          -S            -C/S
  49  *          2         -S          -C             S/C
  50  *          3         -C           S            -C/S
  51  *     ----------------------------------------------------------
  52  *
  53  * Special cases:
  54  *      Let trig be any of sin, cos, or tan.
  55  *      trig(+-INF)  is NaN, with signals;
  56  *      trig(NaN)    is that NaN;
  57  *
  58  * Accuracy:
  59  *      computer TRIG(x) returns trig(x) nearly rounded.
  60  */
  61 
  62 #pragma weak __sincosl = sincosl
  63 
  64 #include "libm.h"
  65 #include "longdouble.h"
  66 
  67 void
  68 sincosl(long double x, long double *s, long double *c)
  69 {
  70         long double y[2], z = 0.0L;
  71         int n, ix;
  72 
  73         ix = *(int *)&x;            /* High word of x */
  74 
  75         /* |x| ~< pi/4 */
  76         ix &= 0x7fffffff;
  77 
  78         if (ix <= 0x3ffe9220) {
  79                 *s = __k_sincosl(x, z, c);
  80         } else if (ix >= 0x7fff0000) {
  81                 *s = *c = x - x;        /* trig(Inf or NaN) is NaN */
  82         } else {                /* argument reduction needed */
  83                 n = __rem_pio2l(x, y);
  84 
  85                 switch (n & 3) {
  86                 case 0:
  87                         *s = __k_sincosl(y[0], y[1], c);
  88                         break;
  89                 case 1:
  90                         *c = -__k_sincosl(y[0], y[1], s);
  91                         break;
  92                 case 2:
  93                         *s = -__k_sincosl(y[0], y[1], c);
  94                         *c = -*c;
  95                         break;
  96                 case 3:
  97                         *c = __k_sincosl(y[0], y[1], s);
  98                         *s = -*s;
  99                         break;
 100                 }
 101         }
 102 }