xref: /illumos-gate/usr/src/lib/libm/common/LD/__cosl.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_cosl( long double x;  long double y )
33*25c28e83SPiotr Jasiukajtis  * kernel cos 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  *
37*25c28e83SPiotr Jasiukajtis  * Table look up algorithm
38*25c28e83SPiotr Jasiukajtis  *	1. by cos(-x) = cos(x), we may replace x by |x|
39*25c28e83SPiotr Jasiukajtis  *	2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then
40*25c28e83SPiotr Jasiukajtis  *	     if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x !=  0
41*25c28e83SPiotr Jasiukajtis  *	     z = x*x;
42*25c28e83SPiotr Jasiukajtis  *	     if x <= 1/128 = 2**-7 = 0.0078125
43*25c28e83SPiotr Jasiukajtis  *		cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))))
44*25c28e83SPiotr Jasiukajtis  *	     else
45*25c28e83SPiotr Jasiukajtis  *	        cos(x)=1.0+z*(q1+ ... z*q8)
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  *		cos(t+x')
53*25c28e83SPiotr Jasiukajtis  *		  = cos(t)cos(x')-sin(t)sin(x')
54*25c28e83SPiotr Jasiukajtis  *		  = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2))
55*25c28e83SPiotr Jasiukajtis  *		  = cos(t) + [cos(t)]*(z*(qq1+z*qq2))-
56*25c28e83SPiotr Jasiukajtis  *				[sin(t)]*x*(1+z*(pp1+z*pp2))
57*25c28e83SPiotr Jasiukajtis  *
58*25c28e83SPiotr Jasiukajtis  *	   Thus,
59*25c28e83SPiotr Jasiukajtis  *		let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i],
60*25c28e83SPiotr Jasiukajtis  *		x = (x-t)+y
61*25c28e83SPiotr Jasiukajtis  *		z = x*x;
62*25c28e83SPiotr Jasiukajtis  *		cos(t+x) = a+(b+ (-c*x*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
63*25c28e83SPiotr Jasiukajtis  */
64*25c28e83SPiotr Jasiukajtis 
65*25c28e83SPiotr Jasiukajtis #include "libm.h"
66*25c28e83SPiotr Jasiukajtis 
67*25c28e83SPiotr Jasiukajtis #include <sys/isa_defs.h>
68*25c28e83SPiotr Jasiukajtis 
69*25c28e83SPiotr Jasiukajtis extern const long double _TBL_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_hi[];
70*25c28e83SPiotr Jasiukajtis static const long double
71*25c28e83SPiotr Jasiukajtis one	= 1.0,
72*25c28e83SPiotr Jasiukajtis /*
73*25c28e83SPiotr Jasiukajtis  * |sin(x) - (x+pp1*x^3+...+ pp5*x^11 )| <= 2^-122.32 for |x|<1/64
74*25c28e83SPiotr Jasiukajtis  */
75*25c28e83SPiotr Jasiukajtis pp1	= -1.666666666666666666666666666586782940810e-0001L,
76*25c28e83SPiotr Jasiukajtis pp2	=  8.333333333333333333333003723660929317540e-0003L,
77*25c28e83SPiotr Jasiukajtis pp3	= -1.984126984126984076045903483778337804470e-0004L,
78*25c28e83SPiotr Jasiukajtis pp4	=  2.755731922361906641319723106210900949413e-0006L,
79*25c28e83SPiotr Jasiukajtis pp5	= -2.505198398570947019093998469135012057673e-0008L,
80*25c28e83SPiotr Jasiukajtis /*
81*25c28e83SPiotr Jasiukajtis  *
82*25c28e83SPiotr Jasiukajtis  * |cos(x) - (1+q1*x^2+...+q8*x^16)| <= 2^-117.11 for |x|<= 0.15625
83*25c28e83SPiotr Jasiukajtis  */
84*25c28e83SPiotr Jasiukajtis q1	=  -4.999999999999999999999999999999756416975e-0001L,
85*25c28e83SPiotr Jasiukajtis q2	=   4.166666666666666666666666664006066577258e-0002L,
86*25c28e83SPiotr Jasiukajtis q3	=  -1.388888888888888888888877700363937169637e-0003L,
87*25c28e83SPiotr Jasiukajtis q4	=   2.480158730158730158494468463031814083559e-0005L,
88*25c28e83SPiotr Jasiukajtis q5	=  -2.755731922398586276322819250356005542871e-0007L,
89*25c28e83SPiotr Jasiukajtis q6	=   2.087675698767424261441959760729854017855e-0009L,
90*25c28e83SPiotr Jasiukajtis q7	=  -1.147074481239662089072452129010790774761e-0011L,
91*25c28e83SPiotr Jasiukajtis q8	=   4.777761647399651599730663422263531034782e-0014L,
92*25c28e83SPiotr Jasiukajtis /*
93*25c28e83SPiotr Jasiukajtis  *
94*25c28e83SPiotr Jasiukajtis  * |cos(x) - (1+qq1*x^2+...+ qq5*x^10)| <= 2^-123.84 for |x|<=1/128
95*25c28e83SPiotr Jasiukajtis  */
96*25c28e83SPiotr Jasiukajtis qq1	=  -4.999999999999999999999999999999378373641e-0001L,
97*25c28e83SPiotr Jasiukajtis qq2	=   4.166666666666666666666665478399327703130e-0002L,
98*25c28e83SPiotr Jasiukajtis qq3	=  -1.388888888888888888058211230618051613494e-0003L,
99*25c28e83SPiotr Jasiukajtis qq4	=   2.480158730156105377771585658905303111866e-0005L,
100*25c28e83SPiotr Jasiukajtis qq5	=  -2.755728099762526325736488376695157008736e-0007L;
101*25c28e83SPiotr Jasiukajtis /* INDENT ON */
102*25c28e83SPiotr Jasiukajtis long double
__k_cosl(long double x,long double y)103*25c28e83SPiotr Jasiukajtis __k_cosl(long double x, long double y) {
104*25c28e83SPiotr Jasiukajtis 	long double a, t, z, w;
105*25c28e83SPiotr Jasiukajtis 	int *pt = (int *) &t, *px = (int *) &x;
106*25c28e83SPiotr Jasiukajtis 	int i, j, hx, ix;
107*25c28e83SPiotr Jasiukajtis 
108*25c28e83SPiotr Jasiukajtis 	t = 1.0;
109*25c28e83SPiotr Jasiukajtis #if defined(__i386) || defined(__amd64)
110*25c28e83SPiotr Jasiukajtis 	XTOI(px, hx);
111*25c28e83SPiotr Jasiukajtis #else
112*25c28e83SPiotr Jasiukajtis 	hx = px[0];
113*25c28e83SPiotr Jasiukajtis #endif
114*25c28e83SPiotr Jasiukajtis 	ix = hx & 0x7fffffff;
115*25c28e83SPiotr Jasiukajtis 	if (ix < 0x3ffc4000) {
116*25c28e83SPiotr Jasiukajtis 		if (ix < 0x3fc60000)
117*25c28e83SPiotr Jasiukajtis 			if ((i = (int) x) == 0)
118*25c28e83SPiotr Jasiukajtis 				return (one);	/* generate inexact */
119*25c28e83SPiotr Jasiukajtis 		z = x * x;
120*25c28e83SPiotr Jasiukajtis 
121*25c28e83SPiotr Jasiukajtis 		if (ix < 0x3ff80000)	/* 0.0078125 */
122*25c28e83SPiotr Jasiukajtis 			return (one + z * (qq1 + z * (qq2 + z * (qq3 + z *
123*25c28e83SPiotr Jasiukajtis 				(qq4 + z * qq5)))));
124*25c28e83SPiotr Jasiukajtis 		else
125*25c28e83SPiotr Jasiukajtis 			return (one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
126*25c28e83SPiotr Jasiukajtis 				z * (q5 + z * (q6 + z * (q7 + z * q8))))))));
127*25c28e83SPiotr Jasiukajtis 	}
128*25c28e83SPiotr Jasiukajtis 	j = (ix + 0x400) & 0x7ffff800;
129*25c28e83SPiotr Jasiukajtis 	i = (j - 0x3ffc4000) >> 11;
130*25c28e83SPiotr Jasiukajtis #if defined(__i386) || defined(__amd64)
131*25c28e83SPiotr Jasiukajtis 	ITOX(j, pt);
132*25c28e83SPiotr Jasiukajtis #else
133*25c28e83SPiotr Jasiukajtis 	pt[0] = j;
134*25c28e83SPiotr Jasiukajtis #endif
135*25c28e83SPiotr Jasiukajtis 	if (hx > 0)
136*25c28e83SPiotr Jasiukajtis 		x = y - (t - x);
137*25c28e83SPiotr Jasiukajtis 	else
138*25c28e83SPiotr Jasiukajtis 		x = (-y) - (t + x);
139*25c28e83SPiotr Jasiukajtis 	a = _TBL_cosl_hi[i];
140*25c28e83SPiotr Jasiukajtis 	z = x * x;
141*25c28e83SPiotr Jasiukajtis 	t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
142*25c28e83SPiotr Jasiukajtis 	w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
143*25c28e83SPiotr Jasiukajtis 		pp5)))));
144*25c28e83SPiotr Jasiukajtis 	t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t);
145*25c28e83SPiotr Jasiukajtis 	return (a + t);
146*25c28e83SPiotr Jasiukajtis }
147