usr/src/lib/libm/common/LD/tanl.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 #pragma weak __tanl = tanl
  31
  32 /* INDENT OFF */
  33 /* cosl(x)
  34  * Table look-up algorithm by K.C. Ng, November, 1989.
  35  *
  36  * kernel function:
  37  *      __k_tanl        ... tangent 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 /* INDENT ON */
  63
  64 #include "libm.h"
  65 #include "longdouble.h"
  66
  67 #include <sys/isa_defs.h>
  68
  69 long double
  70 tanl(long double x) {
  71         long double y[2], z = 0.0L;
  72         int n, ix;
  73 #if defined(__i386) || defined(__amd64)
  74         int *px = (int *) &x;
  75 #endif
  76
  77         /* trig(Inf or NaN) is NaN */
  78         if (!finitel(x))
  79                 return x - x;
  80
  81         /* High word of x. */
  82 #if defined(__i386) || defined(__amd64)
  83         XTOI(px, ix);
  84 #else
  85         ix = *(int *) &x;
  86 #endif
  87
  88         /* |x| ~< pi/4 */
  89         ix &= 0x7fffffff;
  90         if (ix <= 0x3ffe9220)
  91                 return __k_tanl(x, z, 0);
  92
  93         /* argument reduction needed */
  94         else {
  95                 n = __rem_pio2l(x, y);
  96                 return __k_tanl(y[0], y[1], n & 1);
  97         }
  98 }