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/* INDENT OFF */
31/*
32 * __k_tanl( long double x;  long double y; int k )
33 * kernel tan/cotan function on [-pi/4, pi/4], pi/4 ~ 0.785398164
34 * Input x is assumed to be bounded by ~pi/4 in magnitude.
35 * Input y is the tail of x.
36 * Input k indicate -- tan if k=0; else -1/tan
37 *
38 * Table look up algorithm
39 *	1. by tan(-x) = -tan(x), need only to consider positive x
40 *	2. if x < 5/32 = [0x3ffc4000, 0] = 0.15625 , then
41 *	     if x < 2^-57 (hx < 0x3fc40000 0), set w=x with inexact if x !=  0
42 *	     else
43 *		z = x*x;
44 *		w = x + (y+(x*z)*(t1+z*(t2+z*(t3+z*(t4+z*(t5+z*t6))))))
45 *	   return (k == 0 ? w : 1/w);
46 *	3. else
47 *		ht = (hx + 0x400)&0x7ffff800	(round x to a break point t)
48 *		lt = 0
49 *		i  = (hy-0x3ffc4000)>>11;	(i<=64)
50 *		x' = (x - t)+y 			(|x'| ~<= 2^-7)
51 *	   By
52 *		tan(t+x')
53 *		  = (tan(t)+tan(x'))/(1-tan(x')tan(t))
54 *	   We have
55 *		             sin(x')+tan(t)*(tan(t)*sin(x'))
56 *		  = tan(t) + -------------------------------	for k=0
57 *			        cos(x') - tan(t)*sin(x')
58 *
59 *		             cos(x') - tan(t)*sin(x')
60 *		  = - --------------------------------------	for k=1
61 *		       tan(t) + tan(t)*(cos(x')-1) + sin(x')
62 *
63 *
64 *	   where 	tan(t) is from the table,
65 *			sin(x') = x + pp1*x^3 + ...+ pp5*x^11
66 *			cos(x') = 1 + qq1*x^2 + ...+ qq5*x^10
67 */
68
69#include "libm.h"
70
71#include <sys/isa_defs.h>
72
73extern const long double _TBL_tanl_hi[], _TBL_tanl_lo[];
74static const long double
75one	= 1.0,
76/*
77 * |sin(x) - (x+pp1*x^3+...+ pp5*x^11)| <= 2^-122.32 for |x|<1/64
78 */
79pp1	= -1.666666666666666666666666666586782940810e-0001L,
80pp2	=  8.333333333333333333333003723660929317540e-0003L,
81pp3	= -1.984126984126984076045903483778337804470e-0004L,
82pp4	=  2.755731922361906641319723106210900949413e-0006L,
83pp5	= -2.505198398570947019093998469135012057673e-0008L,
84/*
85 *                   2           10        -123.84
86 * |cos(x) - (1+qq1*x +...+ qq5*x  )| <= 2        for |x|<=1/128
87 */
88qq1	= -4.999999999999999999999999999999378373641e-0001L,
89qq2	=  4.166666666666666666666665478399327703130e-0002L,
90qq3	= -1.388888888888888888058211230618051613494e-0003L,
91qq4	=  2.480158730156105377771585658905303111866e-0005L,
92qq5	= -2.755728099762526325736488376695157008736e-0007L,
93/*
94 * |tan(x) - (x+t1*x^3+...+t6*x^13)|
95 * |------------------------------ | <= 2^-59.73 for |x|<0.15625
96 * |                x              |
97 */
98t1	=  3.333333333333333333333333333333423342490e-0001L,
99t2	=  1.333333333333333333333333333093838744537e-0001L,
100t3	=  5.396825396825396825396827906318682662250e-0002L,
101t4	=  2.186948853615520282185576976994418486911e-0002L,
102t5	=  8.863235529902196573354554519991152936246e-0003L,
103t6	=  3.592128036572480064652191427543994878790e-0003L,
104t7	=  1.455834387051455257856833807581901305474e-0003L,
105t8	=  5.900274409318599857829983256201725587477e-0004L,
106t9	=  2.391291152117265181501116961901122362937e-0004L,
107t10	=  9.691533169382729742394024173194981882375e-0005L,
108t11	=  3.927994733186415603228178184225780859951e-0005L,
109t12	=  1.588300018848323824227640064883334101288e-0005L,
110t13	=  6.916271223396808311166202285131722231723e-0006L;
111/* INDENT ON */
112long double
113__k_tanl(long double x, long double y, int k) {
114	long double a, t, z, w = 0.0, s, c;
115	int *pt = (int *) &t, *px = (int *) &x;
116	int i, j, hx, ix;
117
118	t = 1.0;
119#if defined(__i386) || defined(__amd64)
120	XTOI(px, hx);
121#else
122	hx = px[0];
123#endif
124	ix = hx & 0x7fffffff;
125	if (ix < 0x3ffc4000) {
126		if (ix < 0x3fc60000) {
127			if ((i = (int) x) == 0)	/* generate inexact */
128				w = x;
129		} else {
130			z = x * x;
131			if (ix < 0x3ff30000)	/* 2**-12 */
132				t = z * (t1 + z * (t2 + z * (t3 + z * t4)));
133			else
134				t = z * (t1 + z * (t2 + z * (t3 + z * (t4 +
135					z * (t5 + z * (t6 + z * (t7 + z *
136					(t8 + z * (t9 + z * (t10 + z * (t11 +
137					z * (t12 + z * t13))))))))))));
138			t = y + x * t;
139			w = x + t;
140		}
141		return (k == 0 ? w : -one / w);
142	}
143	j = (ix + 0x400) & 0x7ffff800;
144	i = (j - 0x3ffc4000) >> 11;
145#if defined(__i386) || defined(__amd64)
146	ITOX(j, pt);
147#else
148	pt[0] = j;
149#endif
150	if (hx > 0)
151		x = y - (t - x);
152	else
153		x = (-y) - (t + x);
154	a = _TBL_tanl_hi[i];
155	z = x * x;
156	/* cos(x)-1 */
157	t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
158	/* sin(x) */
159	s = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
160		pp5)))));
161	if (k == 0) {
162		w = a * s;
163		t = _TBL_tanl_lo[i] + (s + a * w) / (one - (w - t));
164		return (hx < 0 ? -a - t : a + t);
165	} else {
166		w = s + a * t;
167		c = w + _TBL_tanl_lo[i];
168		z = (one - (a * s - t));
169		return (hx >= 0 ? z / (-a - c) : z / (a + c));
170	}
171}
172