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  * cosl(x)
  33  * Table look-up algorithm by K.C. Ng, November, 1989.
  34  *
  35  * kernel function:
  36  *      __k_sinl        ... sin function on [-pi/4,pi/4]
  37  *      __k_cosl        ... cos function on [-pi/4,pi/4]
  38  *      __rem_pio2l     ... argument reduction routine
  39  *
  40  * Method.
  41  *      Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
  42  *      1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
  43  *         [-pi/2 , +pi/2], and let n = k mod 4.
  44  *      2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
  45  *
  46  *          n        sin(x)      cos(x)        tan(x)
  47  *     ----------------------------------------------------------
  48  *          0          S           C             S/C
  49  *          1          C          -S            -C/S
  50  *          2         -S          -C             S/C
  51  *          3         -C           S            -C/S
  52  *     ----------------------------------------------------------
  53  *
  54  * Special cases:
  55  *      Let trig be any of sin, cos, or tan.
  56  *      trig(+-INF)  is NaN, with signals;
  57  *      trig(NaN)    is that NaN;
  58  *
  59  * Accuracy:
  60  *      computer TRIG(x) returns trig(x) nearly rounded.
  61  */
  62 
  63 #pragma weak __cosl = cosl
  64 
  65 #include "libm.h"
  66 #include "longdouble.h"
  67 
  68 long double
  69 cosl(long double x)
  70 {
  71         long double y[2], z = 0.0L;
  72         int n, ix;
  73 
  74         ix = *(int *)&x;            /* High word of x */
  75 
  76         ix &= 0x7fffffff;
  77 
  78         if (ix <= 0x3ffe9220) {              /* |x| ~< pi/4 */
  79                 return (__k_cosl(x, z));
  80         } else if (ix >= 0x7fff0000) {       /* trig(Inf or NaN) is NaN */
  81                 return (x - x);
  82         } else {                        /* argument reduction needed */
  83                 n = __rem_pio2l(x, y);
  84 
  85                 switch (n & 3) {
  86                 case 0:
  87                         return (__k_cosl(y[0], y[1]));
  88                 case 1:
  89                         return (-__k_sinl(y[0], y[1]));
  90                 case 2:
  91                         return (-__k_cosl(y[0], y[1]));
  92                 case 3:
  93                         return (__k_sinl(y[0], y[1]));
  94                 }
  95         }
  96 
  97         /* NOTREACHED */
  98         return (0.0L);
  99 }