xref: /illumos-gate/usr/src/lib/libm/common/LD/__tanl.c (revision 25c28e83)
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