usr/src/lib/libm/common/Q/sincosl.c

   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  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29
  30 /*
  31  * sincosl(x)
  32  * Table look-up algorithm by K.C. Ng, November, 1989.
  33  *
  34  * kernel function:
  35  *      __k_sincosl     ... sin and cos function on [-pi/4,pi/4]
  36  *      __rem_pio2l     ... argument reduction routine
  37  *
  38  * Method.
  39  *      Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
  40  *      1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
  41  *         [-pi/2 , +pi/2], and let n = k mod 4.
  42  *      2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
  43  *
  44  *          n        sin(x)      cos(x)        tan(x)
  45  *     ----------------------------------------------------------
  46  *          0          S           C             S/C
  47  *          1          C          -S            -C/S
  48  *          2         -S          -C             S/C
  49  *          3         -C           S            -C/S
  50  *     ----------------------------------------------------------
  51  *
  52  * Special cases:
  53  *      Let trig be any of sin, cos, or tan.
  54  *      trig(+-INF)  is NaN, with signals;
  55  *      trig(NaN)    is that NaN;
  56  *
  57  * Accuracy:
  58  *      computer TRIG(x) returns trig(x) nearly rounded.
  59  */
  60
  61 #pragma weak __sincosl = sincosl
  62
  63 #include "libm.h"
  64 #include "longdouble.h"
  65
  66 void
  67 sincosl(long double x, long double *s, long double *c) {
  68         long double y[2], z = 0.0L;
  69         int n, ix;
  70
  71         ix = *(int *) &x;       /* High word of x */
  72
  73         /* |x| ~< pi/4 */
  74         ix &= 0x7fffffff;
  75         if (ix <= 0x3ffe9220)
  76                 *s = __k_sincosl(x, z, c);
  77         else if (ix >= 0x7fff0000)
  78                 *s = *c = x - x;        /* trig(Inf or NaN) is NaN */
  79         else {                  /* argument reduction needed */
  80                 n = __rem_pio2l(x, y);
  81                 switch (n & 3) {
  82                 case 0:
  83                         *s = __k_sincosl(y[0], y[1], c);
  84                         break;
  85                 case 1:
  86                         *c = -__k_sincosl(y[0], y[1], s);
  87                         break;
  88                 case 2:
  89                         *s = -__k_sincosl(y[0], y[1], c);
  90                         *c = -*c;
  91                         break;
  92                 case 3:
  93                         *c = __k_sincosl(y[0], y[1], s);
  94                         *s = -*s;
  95                         break;
  96                 }
  97         }
  98 }