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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak __atan2f = atan2f
30
31 #include "libm.h"
32
33 #if defined(__i386) && !defined(__amd64)
34 extern int __swapRP(int);
35 #endif
36
37 /*
38 * For i = 0, ..., 192, let x[i] be the double precision number whose
39 * high order 32 bits are 0x3f900000 + (i << 16) and whose low order
40 * 32 bits are zero. Then TBL[i] := atan(x[i]) to double precision.
41 */
42
43 static const double TBL[] = {
44 1.56237286204768313e-02,
45 1.66000375562312640e-02,
46 1.75763148444955872e-02,
47 1.85525586258889763e-02,
48 1.95287670414137082e-02,
49 2.05049382324763683e-02,
50 2.14810703409090559e-02,
51 2.24571615089905717e-02,
52 2.34332098794675855e-02,
53 2.44092135955758099e-02,
54 2.53851708010611396e-02,
55 2.63610796402007873e-02,
56 2.73369382578244127e-02,
57 2.83127447993351995e-02,
58 2.92884974107309737e-02,
59 3.02641942386252458e-02,
60 3.12398334302682774e-02,
61 3.31909314971115949e-02,
62 3.51417768027967800e-02,
63 3.70923545503918164e-02,
64 3.90426499551669928e-02,
65 4.09926482452637811e-02,
66 4.29423346623621707e-02,
67 4.48916944623464972e-02,
68 4.68407129159696539e-02,
69 4.87893753095156174e-02,
70 5.07376669454602178e-02,
71 5.26855731431300420e-02,
72 5.46330792393594777e-02,
73 5.65801705891457105e-02,
74 5.85268325663017702e-02,
75 6.04730505641073168e-02,
76 6.24188099959573500e-02,
77 6.63088949198234884e-02,
78 7.01969710718705203e-02,
79 7.40829225490337306e-02,
80 7.79666338315423008e-02,
81 8.18479898030765457e-02,
82 8.57268757707448092e-02,
83 8.96031774848717461e-02,
84 9.34767811585894698e-02,
85 9.73475734872236709e-02,
86 1.01215441667466668e-01,
87 1.05080273416329528e-01,
88 1.08941956989865793e-01,
89 1.12800381201659389e-01,
90 1.16655435441069349e-01,
91 1.20507009691224562e-01,
92 1.24354994546761438e-01,
93 1.32039761614638762e-01,
94 1.39708874289163648e-01,
95 1.47361481088651630e-01,
96 1.54996741923940973e-01,
97 1.62613828597948568e-01,
98 1.70211925285474408e-01,
99 1.77790228992676075e-01,
100 1.85347949995694761e-01,
101 1.92884312257974672e-01,
102 2.00398553825878512e-01,
103 2.07889927202262986e-01,
104 2.15357699697738048e-01,
105 2.22801153759394521e-01,
106 2.30219587276843718e-01,
107 2.37612313865471242e-01,
108 2.44978663126864143e-01,
109 2.59629629408257512e-01,
110 2.74167451119658789e-01,
111 2.88587361894077410e-01,
112 3.02884868374971417e-01,
113 3.17055753209147029e-01,
114 3.31096076704132103e-01,
115 3.45002177207105132e-01,
116 3.58770670270572245e-01,
117 3.72398446676754202e-01,
118 3.85882669398073752e-01,
119 3.99220769575252543e-01,
120 4.12410441597387323e-01,
121 4.25449637370042266e-01,
122 4.38336559857957830e-01,
123 4.51069655988523499e-01,
124 4.63647609000806094e-01,
125 4.88333951056405535e-01,
126 5.12389460310737732e-01,
127 5.35811237960463704e-01,
128 5.58599315343562441e-01,
129 5.80756353567670414e-01,
130 6.02287346134964152e-01,
131 6.23199329934065904e-01,
132 6.43501108793284371e-01,
133 6.63202992706093286e-01,
134 6.82316554874748071e-01,
135 7.00854407884450192e-01,
136 7.18829999621624527e-01,
137 7.36257428981428097e-01,
138 7.53151280962194414e-01,
139 7.69526480405658297e-01,
140 7.85398163397448279e-01,
141 8.15691923316223422e-01,
142 8.44153986113171051e-01,
143 8.70903457075652976e-01,
144 8.96055384571343927e-01,
145 9.19719605350416858e-01,
146 9.42000040379463610e-01,
147 9.62994330680936206e-01,
148 9.82793723247329054e-01,
149 1.00148313569423464e+00,
150 1.01914134426634972e+00,
151 1.03584125300880014e+00,
152 1.05165021254837376e+00,
153 1.06663036531574362e+00,
154 1.08083900054116833e+00,
155 1.09432890732118993e+00,
156 1.10714871779409041e+00,
157 1.13095374397916038e+00,
158 1.15257199721566761e+00,
159 1.17227388112847630e+00,
160 1.19028994968253166e+00,
161 1.20681737028525249e+00,
162 1.22202532321098967e+00,
163 1.23605948947808186e+00,
164 1.24904577239825443e+00,
165 1.26109338225244039e+00,
166 1.27229739520871732e+00,
167 1.28274087974427076e+00,
168 1.29249666778978534e+00,
169 1.30162883400919616e+00,
170 1.31019393504755555e+00,
171 1.31824205101683711e+00,
172 1.32581766366803255e+00,
173 1.33970565959899957e+00,
174 1.35212738092095464e+00,
175 1.36330010035969384e+00,
176 1.37340076694501589e+00,
177 1.38257482149012589e+00,
178 1.39094282700241845e+00,
179 1.39860551227195762e+00,
180 1.40564764938026987e+00,
181 1.41214106460849531e+00,
182 1.41814699839963154e+00,
183 1.42371797140649403e+00,
184 1.42889927219073276e+00,
185 1.43373015248470903e+00,
186 1.43824479449822262e+00,
187 1.44247309910910193e+00,
188 1.44644133224813509e+00,
189 1.45368758222803240e+00,
190 1.46013910562100091e+00,
191 1.46591938806466282e+00,
192 1.47112767430373470e+00,
193 1.47584462045214027e+00,
194 1.48013643959415142e+00,
195 1.48405798811891154e+00,
196 1.48765509490645531e+00,
197 1.49096634108265924e+00,
198 1.49402443552511865e+00,
199 1.49685728913695626e+00,
200 1.49948886200960629e+00,
201 1.50193983749385196e+00,
202 1.50422816301907281e+00,
203 1.50636948736934317e+00,
204 1.50837751679893928e+00,
205 1.51204050407917401e+00,
206 1.51529782154917969e+00,
207 1.51821326518395483e+00,
208 1.52083793107295384e+00,
209 1.52321322351791322e+00,
210 1.52537304737331958e+00,
211 1.52734543140336587e+00,
212 1.52915374769630819e+00,
213 1.53081763967160667e+00,
214 1.53235373677370856e+00,
215 1.53377621092096650e+00,
216 1.53509721411557254e+00,
217 1.53632722579538861e+00,
218 1.53747533091664934e+00,
219 1.53854944435964280e+00,
220 1.53955649336462841e+00,
221 1.54139303859089161e+00,
222 1.54302569020147562e+00,
223 1.54448660954197448e+00,
224 1.54580153317597646e+00,
225 1.54699130060982659e+00,
226 1.54807296595325550e+00,
227 1.54906061995310385e+00,
228 1.54996600675867957e+00,
229 1.55079899282174605e+00,
230 1.55156792769518947e+00,
231 1.55227992472688747e+00,
232 1.55294108165534417e+00,
233 1.55355665560036682e+00,
234 1.55413120308095598e+00,
235 1.55466869295126031e+00,
236 1.55517259817441977e+00,
237 };
238
239 static const double
240 pio4 = 7.8539816339744827900e-01,
241 pio2 = 1.5707963267948965580e+00,
242 negpi = -3.1415926535897931160e+00,
243 q1 = -3.3333333333296428046e-01,
244 q2 = 1.9999999186853752618e-01,
245 zero = 0.0;
246
247 static const float two24 = 16777216.0;
248
249 float
250 atan2f(float fy, float fx)
251 {
252 double a, t, s, dbase;
253 float x, y, base;
254 int i, k, hx, hy, ix, iy, sign;
255 #if defined(__i386) && !defined(__amd64)
256 int rp;
257 #endif
258
259 iy = *(int *)&fy;
260 ix = *(int *)&fx;
261 hy = iy & ~0x80000000;
262 hx = ix & ~0x80000000;
263
264 sign = 0;
265 if (hy > hx) {
266 x = fy;
267 y = fx;
268 i = hx;
269 hx = hy;
270 hy = i;
271 if (iy < 0) {
272 x = -x;
273 sign = 1;
274 }
275 if (ix < 0) {
276 y = -y;
277 a = pio2;
278 } else {
279 a = -pio2;
280 sign = 1 - sign;
281 }
282 } else {
283 y = fy;
284 x = fx;
285 if (iy < 0) {
286 y = -y;
287 sign = 1;
288 }
289 if (ix < 0) {
290 x = -x;
291 a = negpi;
292 sign = 1 - sign;
293 } else {
294 a = zero;
295 }
296 }
297
298 if (hx >= 0x7f800000 || hx - hy >= 0x0c800000) {
299 if (hx >= 0x7f800000) {
300 if (hx > 0x7f800000) /* nan */
301 return (x * y);
302 else if (hy >= 0x7f800000)
303 a += pio4;
304 } else if ((int)a == 0) {
305 a = (double)y / x;
306 }
307 return ((float)((sign)? -a : a));
308 }
309
310 if (hy < 0x00800000) {
311 if (hy == 0)
312 return ((float)((sign)? -a : a));
313 /* scale subnormal y */
314 y *= two24;
315 x *= two24;
316 hy = *(int *)&y;
317 hx = *(int *)&x;
318 }
319
320 #if defined(__i386) && !defined(__amd64)
321 rp = __swapRP(fp_extended);
322 #endif
323 k = (hy - hx + 0x3f800000) & 0xfff80000;
324 if (k >= 0x3c800000) { /* |y/x| >= 1/64 */
325 *(int *)&base = k;
326 k = (k - 0x3c800000) >> 19;
327 a += TBL[k];
328 } else {
329 /*
330 * For some reason this is faster on USIII than just
331 * doing t = y/x in this case.
332 */
333 *(int *)&base = 0;
334 }
335 dbase = (double)base;
336 t = (y - x * dbase) / (x + y * dbase);
337 s = t * t;
338 a = (a + t) + t * s * (q1 + s * q2);
339 #if defined(__i386) && !defined(__amd64)
340 if (rp != fp_extended)
341 (void) __swapRP(rp);
342 #endif
343 return ((float)((sign)? -a : a));
344 }