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 __atanf = atanf
31
32/* INDENT OFF */
33/*
34 * float atanf(float x);
35 * Table look-up algorithm
36 * By K.C. Ng, March 9, 1989
37 *
38 * Algorithm.
39 *
40 * The algorithm is based on atan(x)=atan(y)+atan((x-y)/(1+x*y)).
41 * We use poly1(x) to approximate atan(x) for x in [0,1/8] with
42 * error (relative)
43 * 	|(atan(x)-poly1(x))/x|<= 2^-115.94 	long double
44 * 	|(atan(x)-poly1(x))/x|<= 2^-58.85	double
45 * 	|(atan(x)-poly1(x))/x|<= 2^-25.53 	float
46 * and use poly2(x) to approximate atan(x) for x in [0,1/65] with
47 * error (absolute)
48 *	|atan(x)-poly2(x)|<= 2^-122.15		long double
49 *	|atan(x)-poly2(x)|<= 2^-64.79		double
50 *	|atan(x)-poly2(x)|<= 2^-35.36		float
51 * and use poly3(x) to approximate atan(x) for x in [1/8,7/16] with
52 * error (relative, on for single precision)
53 * 	|(atan(x)-poly1(x))/x|<= 2^-25.53 	float
54 *
55 * Here poly1-3 are odd polynomial with the following form:
56 *		x + x^3*(a1+x^2*(a2+...))
57 *
58 * (0). Purge off Inf and NaN and 0
59 * (1). Reduce x to positive by atan(x) = -atan(-x).
60 * (2). For x <= 1/8, use
61 *	(2.1) if x < 2^(-prec/2-2), atan(x) =  x  with inexact
62 *	(2.2) Otherwise
63 *		atan(x) = poly1(x)
64 * (3). For x >= 8 then
65 *	(3.1) if x >= 2^(prec+2),   atan(x) = atan(inf) - pio2lo
66 *	(3.2) if x >= 2^(prec/3+2), atan(x) = atan(inf) - 1/x
67 *	(3.3) if x >  65,           atan(x) = atan(inf) - poly2(1/x)
68 *	(3.4) Otherwise,	    atan(x) = atan(inf) - poly1(1/x)
69 *
70 * (4). Now x is in (0.125, 8)
71 *      Find y that match x to 4.5 bit after binary (easy).
72 *	If iy is the high word of y, then
73 *		single : j = (iy - 0x3e000000) >> 19
74 *		(single is modified to (iy-0x3f000000)>>19)
75 *		double : j = (iy - 0x3fc00000) >> 16
76 *		quad   : j = (iy - 0x3ffc0000) >> 12
77 *
78 *	Let s = (x-y)/(1+x*y). Then
79 *	atan(x) = atan(y) + poly1(s)
80 *		= _TBL_r_atan_hi[j] + (_TBL_r_atan_lo[j] + poly2(s) )
81 *
82 *	Note. |s| <= 1.5384615385e-02 = 1/65. Maxium occurs at x = 1.03125
83 *
84 */
85
86#include "libm.h"
87
88extern const float _TBL_r_atan_hi[], _TBL_r_atan_lo[];
89static const float
90	big	=   1.0e37F,
91	one	=   1.0F,
92	p1	=  -3.333185951111688247225368498733544672172e-0001F,
93	p2	=   1.969352894213455405211341983203180636021e-0001F,
94	q1	=  -3.332921964095646819563419704110132937456e-0001F,
95	a1	=  -3.333323465223893614063523351509338934592e-0001F,
96	a2	=   1.999425625935277805494082274808174062403e-0001F,
97	a3	=  -1.417547090509737780085769846290301788559e-0001F,
98	a4	=   1.016250813871991983097273733227432685084e-0001F,
99	a5	=  -5.137023693688358515753093811791755221805e-0002F,
100	pio2hi	=   1.570796371e+0000F,
101	pio2lo	=  -4.371139000e-0008F;
102/* INDENT ON */
103
104float
105atanf(float xx) {
106	float x, y, z, r, p, s;
107	volatile double dummy __unused;
108	int ix, iy, sign, j;
109
110	x = xx;
111	ix = *(int *) &x;
112	sign = ix & 0x80000000;
113	ix ^= sign;
114
115	/* for |x| < 1/8 */
116	if (ix < 0x3e000000) {
117		if (ix < 0x38800000) {	/* if |x| < 2**(-prec/2-2) */
118			dummy = big + x;	/* get inexact flag if x != 0 */
119#ifdef lint
120			dummy = dummy;
121#endif
122			return (x);
123		}
124		z = x * x;
125		if (ix < 0x3c000000) {	/* if |x| < 2**(-prec/4-1) */
126			x = x + (x * z) * p1;
127			return (x);
128		} else {
129			x = x + (x * z) * (p1 + z * p2);
130			return (x);
131		}
132	}
133
134	/* for |x| >= 8.0 */
135	if (ix >= 0x41000000) {
136		*(int *) &x = ix;
137		if (ix < 0x42820000) {	/* x <  65 */
138			r = one / x;
139			z = r * r;
140			y = r * (one + z * (p1 + z * p2));	/* poly1 */
141			y -= pio2lo;
142		} else if (ix < 0x44800000) {	/* x <  2**(prec/3+2) */
143			r = one / x;
144			z = r * r;
145			y = r * (one + z * q1);	/* poly2 */
146			y -= pio2lo;
147		} else if (ix < 0x4c800000) {	/* x <  2**(prec+2) */
148			y = one / x - pio2lo;
149		} else if (ix < 0x7f800000) {	/* x <  inf */
150			y = -pio2lo;
151		} else {		/* x is inf or NaN */
152			if (ix > 0x7f800000) {
153				return (x * x);	/* - -> * for Cheetah */
154			}
155			y = -pio2lo;
156		}
157
158		if (sign == 0)
159			x = pio2hi - y;
160		else
161			x = y - pio2hi;
162		return (x);
163	}
164
165
166	/* now x is between 1/8 and 8 */
167	if (ix < 0x3f000000) {	/* between 1/8 and 1/2 */
168		z = x * x;
169		x = x + (x * z) * (a1 + z * (a2 + z * (a3 + z * (a4 +
170			z * a5))));
171		return (x);
172	}
173	*(int *) &x = ix;
174	iy = (ix + 0x00040000) & 0x7ff80000;
175	*(int *) &y = iy;
176	j = (iy - 0x3f000000) >> 19;
177
178	if (ix == iy)
179		p = x - y;	/* p=0.0 */
180	else {
181		if (sign == 0)
182			s = (x - y) / (one + x * y);
183		else
184			s = (y - x) / (one + x * y);
185		z = s * s;
186		p = s * (one + z * q1);
187	}
188	if (sign == 0) {
189		r = p + _TBL_r_atan_lo[j];
190		x = r + _TBL_r_atan_hi[j];
191	} else {
192		r = p - _TBL_r_atan_lo[j];
193		x = r - _TBL_r_atan_hi[j];
194	}
195	return (x);
196}
197