1*25c28e83SPiotr Jasiukajtis /*
2*25c28e83SPiotr Jasiukajtis * CDDL HEADER START
3*25c28e83SPiotr Jasiukajtis *
4*25c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the
5*25c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License").
6*25c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License.
7*25c28e83SPiotr Jasiukajtis *
8*25c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9*25c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
10*25c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions
11*25c28e83SPiotr Jasiukajtis * and limitations under the License.
12*25c28e83SPiotr Jasiukajtis *
13*25c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
14*25c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15*25c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
16*25c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
17*25c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
18*25c28e83SPiotr Jasiukajtis *
19*25c28e83SPiotr Jasiukajtis * CDDL HEADER END
20*25c28e83SPiotr Jasiukajtis */
21*25c28e83SPiotr Jasiukajtis
22*25c28e83SPiotr Jasiukajtis /*
23*25c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24*25c28e83SPiotr Jasiukajtis */
25*25c28e83SPiotr Jasiukajtis /*
26*25c28e83SPiotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27*25c28e83SPiotr Jasiukajtis * Use is subject to license terms.
28*25c28e83SPiotr Jasiukajtis */
29*25c28e83SPiotr Jasiukajtis
30*25c28e83SPiotr Jasiukajtis /* INDENT OFF */
31*25c28e83SPiotr Jasiukajtis /*
32*25c28e83SPiotr Jasiukajtis * __k_tanl( long double x; long double y; int k )
33*25c28e83SPiotr Jasiukajtis * kernel tan/cotan function on [-pi/4, pi/4], pi/4 ~ 0.785398164
34*25c28e83SPiotr Jasiukajtis * Input x is assumed to be bounded by ~pi/4 in magnitude.
35*25c28e83SPiotr Jasiukajtis * Input y is the tail of x.
36*25c28e83SPiotr Jasiukajtis * Input k indicate -- tan if k=0; else -1/tan
37*25c28e83SPiotr Jasiukajtis *
38*25c28e83SPiotr Jasiukajtis * Table look up algorithm
39*25c28e83SPiotr Jasiukajtis * 1. by tan(-x) = -tan(x), need only to consider positive x
40*25c28e83SPiotr Jasiukajtis * 2. if x < 5/32 = [0x3ffc4000, 0] = 0.15625 , then
41*25c28e83SPiotr Jasiukajtis * if x < 2^-57 (hx < 0x3fc40000 0), set w=x with inexact if x != 0
42*25c28e83SPiotr Jasiukajtis * else
43*25c28e83SPiotr Jasiukajtis * z = x*x;
44*25c28e83SPiotr Jasiukajtis * w = x + (y+(x*z)*(t1+z*(t2+z*(t3+z*(t4+z*(t5+z*t6))))))
45*25c28e83SPiotr Jasiukajtis * return (k == 0 ? w : 1/w);
46*25c28e83SPiotr Jasiukajtis * 3. else
47*25c28e83SPiotr Jasiukajtis * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t)
48*25c28e83SPiotr Jasiukajtis * lt = 0
49*25c28e83SPiotr Jasiukajtis * i = (hy-0x3ffc4000)>>11; (i<=64)
50*25c28e83SPiotr Jasiukajtis * x' = (x - t)+y (|x'| ~<= 2^-7)
51*25c28e83SPiotr Jasiukajtis * By
52*25c28e83SPiotr Jasiukajtis * tan(t+x')
53*25c28e83SPiotr Jasiukajtis * = (tan(t)+tan(x'))/(1-tan(x')tan(t))
54*25c28e83SPiotr Jasiukajtis * We have
55*25c28e83SPiotr Jasiukajtis * sin(x')+tan(t)*(tan(t)*sin(x'))
56*25c28e83SPiotr Jasiukajtis * = tan(t) + ------------------------------- for k=0
57*25c28e83SPiotr Jasiukajtis * cos(x') - tan(t)*sin(x')
58*25c28e83SPiotr Jasiukajtis *
59*25c28e83SPiotr Jasiukajtis * cos(x') - tan(t)*sin(x')
60*25c28e83SPiotr Jasiukajtis * = - -------------------------------------- for k=1
61*25c28e83SPiotr Jasiukajtis * tan(t) + tan(t)*(cos(x')-1) + sin(x')
62*25c28e83SPiotr Jasiukajtis *
63*25c28e83SPiotr Jasiukajtis *
64*25c28e83SPiotr Jasiukajtis * where tan(t) is from the table,
65*25c28e83SPiotr Jasiukajtis * sin(x') = x + pp1*x^3 + ...+ pp5*x^11
66*25c28e83SPiotr Jasiukajtis * cos(x') = 1 + qq1*x^2 + ...+ qq5*x^10
67*25c28e83SPiotr Jasiukajtis */
68*25c28e83SPiotr Jasiukajtis
69*25c28e83SPiotr Jasiukajtis #include "libm.h"
70*25c28e83SPiotr Jasiukajtis
71*25c28e83SPiotr Jasiukajtis #include <sys/isa_defs.h>
72*25c28e83SPiotr Jasiukajtis
73*25c28e83SPiotr Jasiukajtis extern const long double _TBL_tanl_hi[], _TBL_tanl_lo[];
74*25c28e83SPiotr Jasiukajtis static const long double
75*25c28e83SPiotr Jasiukajtis one = 1.0,
76*25c28e83SPiotr Jasiukajtis /*
77*25c28e83SPiotr Jasiukajtis * |sin(x) - (x+pp1*x^3+...+ pp5*x^11)| <= 2^-122.32 for |x|<1/64
78*25c28e83SPiotr Jasiukajtis */
79*25c28e83SPiotr Jasiukajtis pp1 = -1.666666666666666666666666666586782940810e-0001L,
80*25c28e83SPiotr Jasiukajtis pp2 = 8.333333333333333333333003723660929317540e-0003L,
81*25c28e83SPiotr Jasiukajtis pp3 = -1.984126984126984076045903483778337804470e-0004L,
82*25c28e83SPiotr Jasiukajtis pp4 = 2.755731922361906641319723106210900949413e-0006L,
83*25c28e83SPiotr Jasiukajtis pp5 = -2.505198398570947019093998469135012057673e-0008L,
84*25c28e83SPiotr Jasiukajtis /*
85*25c28e83SPiotr Jasiukajtis * 2 10 -123.84
86*25c28e83SPiotr Jasiukajtis * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
87*25c28e83SPiotr Jasiukajtis */
88*25c28e83SPiotr Jasiukajtis qq1 = -4.999999999999999999999999999999378373641e-0001L,
89*25c28e83SPiotr Jasiukajtis qq2 = 4.166666666666666666666665478399327703130e-0002L,
90*25c28e83SPiotr Jasiukajtis qq3 = -1.388888888888888888058211230618051613494e-0003L,
91*25c28e83SPiotr Jasiukajtis qq4 = 2.480158730156105377771585658905303111866e-0005L,
92*25c28e83SPiotr Jasiukajtis qq5 = -2.755728099762526325736488376695157008736e-0007L,
93*25c28e83SPiotr Jasiukajtis /*
94*25c28e83SPiotr Jasiukajtis * |tan(x) - (x+t1*x^3+...+t6*x^13)|
95*25c28e83SPiotr Jasiukajtis * |------------------------------ | <= 2^-59.73 for |x|<0.15625
96*25c28e83SPiotr Jasiukajtis * | x |
97*25c28e83SPiotr Jasiukajtis */
98*25c28e83SPiotr Jasiukajtis t1 = 3.333333333333333333333333333333423342490e-0001L,
99*25c28e83SPiotr Jasiukajtis t2 = 1.333333333333333333333333333093838744537e-0001L,
100*25c28e83SPiotr Jasiukajtis t3 = 5.396825396825396825396827906318682662250e-0002L,
101*25c28e83SPiotr Jasiukajtis t4 = 2.186948853615520282185576976994418486911e-0002L,
102*25c28e83SPiotr Jasiukajtis t5 = 8.863235529902196573354554519991152936246e-0003L,
103*25c28e83SPiotr Jasiukajtis t6 = 3.592128036572480064652191427543994878790e-0003L,
104*25c28e83SPiotr Jasiukajtis t7 = 1.455834387051455257856833807581901305474e-0003L,
105*25c28e83SPiotr Jasiukajtis t8 = 5.900274409318599857829983256201725587477e-0004L,
106*25c28e83SPiotr Jasiukajtis t9 = 2.391291152117265181501116961901122362937e-0004L,
107*25c28e83SPiotr Jasiukajtis t10 = 9.691533169382729742394024173194981882375e-0005L,
108*25c28e83SPiotr Jasiukajtis t11 = 3.927994733186415603228178184225780859951e-0005L,
109*25c28e83SPiotr Jasiukajtis t12 = 1.588300018848323824227640064883334101288e-0005L,
110*25c28e83SPiotr Jasiukajtis t13 = 6.916271223396808311166202285131722231723e-0006L;
111*25c28e83SPiotr Jasiukajtis /* INDENT ON */
112*25c28e83SPiotr Jasiukajtis long double
__k_tanl(long double x,long double y,int k)113*25c28e83SPiotr Jasiukajtis __k_tanl(long double x, long double y, int k) {
114*25c28e83SPiotr Jasiukajtis long double a, t, z, w = 0.0, s, c;
115*25c28e83SPiotr Jasiukajtis int *pt = (int *) &t, *px = (int *) &x;
116*25c28e83SPiotr Jasiukajtis int i, j, hx, ix;
117*25c28e83SPiotr Jasiukajtis
118*25c28e83SPiotr Jasiukajtis t = 1.0;
119*25c28e83SPiotr Jasiukajtis #if defined(__i386) || defined(__amd64)
120*25c28e83SPiotr Jasiukajtis XTOI(px, hx);
121*25c28e83SPiotr Jasiukajtis #else
122*25c28e83SPiotr Jasiukajtis hx = px[0];
123*25c28e83SPiotr Jasiukajtis #endif
124*25c28e83SPiotr Jasiukajtis ix = hx & 0x7fffffff;
125*25c28e83SPiotr Jasiukajtis if (ix < 0x3ffc4000) {
126*25c28e83SPiotr Jasiukajtis if (ix < 0x3fc60000) {
127*25c28e83SPiotr Jasiukajtis if ((i = (int) x) == 0) /* generate inexact */
128*25c28e83SPiotr Jasiukajtis w = x;
129*25c28e83SPiotr Jasiukajtis } else {
130*25c28e83SPiotr Jasiukajtis z = x * x;
131*25c28e83SPiotr Jasiukajtis if (ix < 0x3ff30000) /* 2**-12 */
132*25c28e83SPiotr Jasiukajtis t = z * (t1 + z * (t2 + z * (t3 + z * t4)));
133*25c28e83SPiotr Jasiukajtis else
134*25c28e83SPiotr Jasiukajtis t = z * (t1 + z * (t2 + z * (t3 + z * (t4 +
135*25c28e83SPiotr Jasiukajtis z * (t5 + z * (t6 + z * (t7 + z *
136*25c28e83SPiotr Jasiukajtis (t8 + z * (t9 + z * (t10 + z * (t11 +
137*25c28e83SPiotr Jasiukajtis z * (t12 + z * t13))))))))))));
138*25c28e83SPiotr Jasiukajtis t = y + x * t;
139*25c28e83SPiotr Jasiukajtis w = x + t;
140*25c28e83SPiotr Jasiukajtis }
141*25c28e83SPiotr Jasiukajtis return (k == 0 ? w : -one / w);
142*25c28e83SPiotr Jasiukajtis }
143*25c28e83SPiotr Jasiukajtis j = (ix + 0x400) & 0x7ffff800;
144*25c28e83SPiotr Jasiukajtis i = (j - 0x3ffc4000) >> 11;
145*25c28e83SPiotr Jasiukajtis #if defined(__i386) || defined(__amd64)
146*25c28e83SPiotr Jasiukajtis ITOX(j, pt);
147*25c28e83SPiotr Jasiukajtis #else
148*25c28e83SPiotr Jasiukajtis pt[0] = j;
149*25c28e83SPiotr Jasiukajtis #endif
150*25c28e83SPiotr Jasiukajtis if (hx > 0)
151*25c28e83SPiotr Jasiukajtis x = y - (t - x);
152*25c28e83SPiotr Jasiukajtis else
153*25c28e83SPiotr Jasiukajtis x = (-y) - (t + x);
154*25c28e83SPiotr Jasiukajtis a = _TBL_tanl_hi[i];
155*25c28e83SPiotr Jasiukajtis z = x * x;
156*25c28e83SPiotr Jasiukajtis /* cos(x)-1 */
157*25c28e83SPiotr Jasiukajtis t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
158*25c28e83SPiotr Jasiukajtis /* sin(x) */
159*25c28e83SPiotr Jasiukajtis s = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
160*25c28e83SPiotr Jasiukajtis pp5)))));
161*25c28e83SPiotr Jasiukajtis if (k == 0) {
162*25c28e83SPiotr Jasiukajtis w = a * s;
163*25c28e83SPiotr Jasiukajtis t = _TBL_tanl_lo[i] + (s + a * w) / (one - (w - t));
164*25c28e83SPiotr Jasiukajtis return (hx < 0 ? -a - t : a + t);
165*25c28e83SPiotr Jasiukajtis } else {
166*25c28e83SPiotr Jasiukajtis w = s + a * t;
167*25c28e83SPiotr Jasiukajtis c = w + _TBL_tanl_lo[i];
168*25c28e83SPiotr Jasiukajtis z = (one - (a * s - t));
169*25c28e83SPiotr Jasiukajtis return (hx >= 0 ? z / (-a - c) : z / (a + c));
170*25c28e83SPiotr Jasiukajtis }
171*25c28e83SPiotr Jasiukajtis }
172