usr/src/lib/libm/common/Q/sinl.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  * sinl(x)
  32  * Table look-up algorithm by K.C. Ng, November, 1989.
  33  *
  34  * kernel function:
  35  *      __k_sinl                ... sin function on [-pi/4,pi/4]
  36  *      __k_cosl                ... 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 __sinl = sinl
  63
  64 #include "libm.h"
  65 #include "longdouble.h"
  66
  67 long double
  68 sinl(long double x) {
  69         long double y[2], z = 0.0L;
  70         int n, ix;
  71
  72         ix = *(int *) &x;               /* High word of x */
  73         ix &= 0x7fffffff;
  74         if (ix <= 0x3ffe9220)           /* |x| ~< pi/4 */
  75                 return (__k_sinl(x, z));
  76         else if (ix >= 0x7fff0000)      /* sin(Inf or NaN) is NaN */
  77                 return (x - x);
  78         else {                          /* argument reduction needed */
  79                 n = __rem_pio2l(x, y);
  80                 switch (n & 3) {
  81                         case 0:
  82                                 return (__k_sinl(y[0], y[1]));
  83                         case 1:
  84                                 return (__k_cosl(y[0], y[1]));
  85                         case 2:
  86                                 return (-__k_sinl(y[0], y[1]));
  87                         case 3:
  88                                 return (-__k_cosl(y[0], y[1]));
  89                 }
  90         }
  91         /* NOTREACHED */
  92     return 0.0L;
  93 }