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Commit | Line | Data |
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f7eac6eb | 1 | /* |
e4d82761 | 2 | * IBM Accurate Mathematical Library |
aeb25823 | 3 | * written by International Business Machines Corp. |
b168057a | 4 | * Copyright (C) 2001-2015 Free Software Foundation, Inc. |
f7eac6eb | 5 | * |
e4d82761 UD |
6 | * This program is free software; you can redistribute it and/or modify |
7 | * it under the terms of the GNU Lesser General Public License as published by | |
cc7375ce | 8 | * the Free Software Foundation; either version 2.1 of the License, or |
e4d82761 | 9 | * (at your option) any later version. |
f7eac6eb | 10 | * |
e4d82761 UD |
11 | * This program is distributed in the hope that it will be useful, |
12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
c6c6dd48 | 14 | * GNU Lesser General Public License for more details. |
f7eac6eb | 15 | * |
e4d82761 | 16 | * You should have received a copy of the GNU Lesser General Public License |
59ba27a6 | 17 | * along with this program; if not, see <http://www.gnu.org/licenses/>. |
f7eac6eb | 18 | */ |
e4d82761 UD |
19 | /************************************************************************/ |
20 | /* MODULE_NAME: atnat.c */ | |
21 | /* */ | |
22 | /* FUNCTIONS: uatan */ | |
23 | /* atanMp */ | |
24 | /* signArctan */ | |
25 | /* */ | |
26 | /* */ | |
27 | /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */ | |
28 | /* mpatan.c mpatan2.c mpsqrt.c */ | |
29 | /* uatan.tbl */ | |
30 | /* */ | |
31 | /* An ultimate atan() routine. Given an IEEE double machine number x */ | |
32 | /* it computes the correctly rounded (to nearest) value of atan(x). */ | |
33 | /* */ | |
34 | /* Assumption: Machine arithmetic operations are performed in */ | |
35 | /* round to nearest mode of IEEE 754 standard. */ | |
36 | /* */ | |
37 | /************************************************************************/ | |
f7eac6eb | 38 | |
c8b3296b | 39 | #include <dla.h> |
e4d82761 UD |
40 | #include "mpa.h" |
41 | #include "MathLib.h" | |
42 | #include "uatan.tbl" | |
43 | #include "atnat.h" | |
1ed0291c | 44 | #include <math.h> |
10e1cf6b | 45 | #include <stap-probe.h> |
e4d82761 | 46 | |
d26dd3eb SP |
47 | void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */ |
48 | static double atanMp (double, const int[]); | |
af968f62 UD |
49 | |
50 | /* Fix the sign of y and return */ | |
d26dd3eb SP |
51 | static double |
52 | __signArctan (double x, double y) | |
53 | { | |
54 | return __copysign (y, x); | |
af968f62 UD |
55 | } |
56 | ||
57 | ||
e4d82761 UD |
58 | /* An ultimate atan() routine. Given an IEEE double machine number x, */ |
59 | /* routine computes the correctly rounded (to nearest) value of atan(x). */ | |
d26dd3eb SP |
60 | double |
61 | atan (double x) | |
62 | { | |
63 | double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3, | |
c5d5d574 | 64 | v, vv, w, ww, y, yy, z, zz; |
58985aa9 | 65 | #ifndef DLA_FMS |
d26dd3eb | 66 | double t4, t5, t6; |
50944bca | 67 | #endif |
d26dd3eb SP |
68 | int i, ux, dx; |
69 | static const int pr[M] = { 6, 8, 10, 32 }; | |
e4d82761 | 70 | number num; |
e4d82761 | 71 | |
d26dd3eb SP |
72 | num.d = x; |
73 | ux = num.i[HIGH_HALF]; | |
74 | dx = num.i[LOW_HALF]; | |
e4d82761 UD |
75 | |
76 | /* x=NaN */ | |
d26dd3eb SP |
77 | if (((ux & 0x7ff00000) == 0x7ff00000) |
78 | && (((ux & 0x000fffff) | dx) != 0x00000000)) | |
79 | return x + x; | |
e4d82761 UD |
80 | |
81 | /* Regular values of x, including denormals +-0 and +-INF */ | |
a64d7e0e | 82 | u = (x < 0) ? -x : x; |
d26dd3eb SP |
83 | if (u < C) |
84 | { | |
85 | if (u < B) | |
86 | { | |
87 | if (u < A) | |
88 | return x; | |
89 | else | |
90 | { /* A <= u < B */ | |
91 | v = x * x; | |
92 | yy = d11.d + v * d13.d; | |
93 | yy = d9.d + v * yy; | |
94 | yy = d7.d + v * yy; | |
95 | yy = d5.d + v * yy; | |
96 | yy = d3.d + v * yy; | |
97 | yy *= x * v; | |
98 | ||
99 | if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x)) | |
100 | return y; | |
101 | ||
102 | EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */ | |
103 | ||
104 | s1 = f17.d + v * f19.d; | |
105 | s1 = f15.d + v * s1; | |
106 | s1 = f13.d + v * s1; | |
107 | s1 = f11.d + v * s1; | |
108 | s1 *= v; | |
109 | ||
a64d7e0e | 110 | ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); |
d26dd3eb SP |
111 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); |
112 | ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); | |
113 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
114 | ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); | |
115 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
116 | ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); | |
117 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
a64d7e0e | 118 | MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, |
d26dd3eb | 119 | t8); |
a64d7e0e | 120 | ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2); |
d26dd3eb SP |
121 | if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1)) |
122 | return y; | |
123 | ||
124 | return atanMp (x, pr); | |
125 | } | |
126 | } | |
127 | else | |
128 | { /* B <= u < C */ | |
129 | i = (TWO52 + TWO8 * u) - TWO52; | |
130 | i -= 16; | |
131 | z = u - cij[i][0].d; | |
132 | yy = cij[i][5].d + z * cij[i][6].d; | |
133 | yy = cij[i][4].d + z * yy; | |
134 | yy = cij[i][3].d + z * yy; | |
135 | yy = cij[i][2].d + z * yy; | |
136 | yy *= z; | |
137 | ||
138 | t1 = cij[i][1].d; | |
139 | if (i < 112) | |
140 | { | |
141 | if (i < 48) | |
142 | u2 = U21; /* u < 1/4 */ | |
143 | else | |
144 | u2 = U22; | |
145 | } /* 1/4 <= u < 1/2 */ | |
146 | else | |
147 | { | |
148 | if (i < 176) | |
149 | u2 = U23; /* 1/2 <= u < 3/4 */ | |
150 | else | |
151 | u2 = U24; | |
152 | } /* 3/4 <= u <= 1 */ | |
153 | if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1)) | |
154 | return __signArctan (x, y); | |
155 | ||
156 | z = u - hij[i][0].d; | |
157 | ||
158 | s1 = hij[i][14].d + z * hij[i][15].d; | |
159 | s1 = hij[i][13].d + z * s1; | |
160 | s1 = hij[i][12].d + z * s1; | |
161 | s1 = hij[i][11].d + z * s1; | |
162 | s1 *= z; | |
163 | ||
a64d7e0e SP |
164 | ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); |
165 | MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
d26dd3eb | 166 | ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); |
a64d7e0e | 167 | MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); |
d26dd3eb | 168 | ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); |
a64d7e0e | 169 | MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); |
d26dd3eb | 170 | ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); |
a64d7e0e | 171 | MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); |
d26dd3eb SP |
172 | ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); |
173 | if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2)) | |
174 | return __signArctan (x, y); | |
175 | ||
176 | return atanMp (x, pr); | |
177 | } | |
e4d82761 | 178 | } |
d26dd3eb SP |
179 | else |
180 | { | |
181 | if (u < D) | |
182 | { /* C <= u < D */ | |
c2d94018 | 183 | w = 1 / u; |
d26dd3eb | 184 | EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); |
c2d94018 | 185 | ww = w * ((1 - t1) - t2); |
d26dd3eb SP |
186 | i = (TWO52 + TWO8 * w) - TWO52; |
187 | i -= 16; | |
188 | z = (w - cij[i][0].d) + ww; | |
189 | ||
190 | yy = cij[i][5].d + z * cij[i][6].d; | |
191 | yy = cij[i][4].d + z * yy; | |
192 | yy = cij[i][3].d + z * yy; | |
193 | yy = cij[i][2].d + z * yy; | |
c5d5d574 | 194 | yy = HPI1 - z * yy; |
f7eac6eb | 195 | |
d26dd3eb SP |
196 | t1 = HPI - cij[i][1].d; |
197 | if (i < 112) | |
c5d5d574 | 198 | u3 = U31; /* w < 1/2 */ |
d26dd3eb | 199 | else |
c5d5d574 | 200 | u3 = U32; /* w >= 1/2 */ |
d26dd3eb SP |
201 | if ((y = t1 + (yy - u3)) == t1 + (yy + u3)) |
202 | return __signArctan (x, y); | |
203 | ||
c5d5d574 | 204 | DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
d26dd3eb SP |
205 | t10); |
206 | t1 = w - hij[i][0].d; | |
207 | EADD (t1, ww, z, zz); | |
208 | ||
209 | s1 = hij[i][14].d + z * hij[i][15].d; | |
210 | s1 = hij[i][13].d + z * s1; | |
211 | s1 = hij[i][12].d + z * s1; | |
212 | s1 = hij[i][11].d + z * s1; | |
213 | s1 *= z; | |
214 | ||
a64d7e0e | 215 | ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); |
d26dd3eb SP |
216 | MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); |
217 | ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); | |
218 | MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
219 | ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); | |
220 | MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
221 | ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); | |
222 | MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
223 | ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); | |
224 | SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2); | |
225 | if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7)) | |
226 | return __signArctan (x, y); | |
227 | ||
228 | return atanMp (x, pr); | |
229 | } | |
230 | else | |
231 | { | |
232 | if (u < E) | |
c5d5d574 | 233 | { /* D <= u < E */ |
c2d94018 | 234 | w = 1 / u; |
d26dd3eb SP |
235 | v = w * w; |
236 | EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); | |
237 | ||
238 | yy = d11.d + v * d13.d; | |
239 | yy = d9.d + v * yy; | |
240 | yy = d7.d + v * yy; | |
241 | yy = d5.d + v * yy; | |
242 | yy = d3.d + v * yy; | |
243 | yy *= w * v; | |
244 | ||
c2d94018 | 245 | ww = w * ((1 - t1) - t2); |
d26dd3eb SP |
246 | ESUB (HPI, w, t3, cor); |
247 | yy = ((HPI1 + cor) - ww) - yy; | |
248 | if ((y = t3 + (yy - U4)) == t3 + (yy + U4)) | |
249 | return __signArctan (x, y); | |
250 | ||
c5d5d574 | 251 | DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, |
d26dd3eb SP |
252 | t9, t10); |
253 | MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); | |
254 | ||
255 | s1 = f17.d + v * f19.d; | |
256 | s1 = f15.d + v * s1; | |
257 | s1 = f13.d + v * s1; | |
258 | s1 = f11.d + v * s1; | |
259 | s1 *= v; | |
260 | ||
a64d7e0e | 261 | ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); |
d26dd3eb SP |
262 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); |
263 | ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); | |
264 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
265 | ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); | |
266 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
267 | ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); | |
268 | MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); | |
269 | MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); | |
270 | ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2); | |
271 | SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2); | |
272 | ||
273 | if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8)) | |
274 | return __signArctan (x, y); | |
275 | ||
276 | return atanMp (x, pr); | |
277 | } | |
278 | else | |
279 | { | |
280 | /* u >= E */ | |
281 | if (x > 0) | |
282 | return HPI; | |
283 | else | |
284 | return MHPI; | |
285 | } | |
286 | } | |
287 | } | |
f7eac6eb | 288 | } |
e4d82761 | 289 | |
e4d82761 | 290 | /* Final stages. Compute atan(x) by multiple precision arithmetic */ |
d26dd3eb SP |
291 | static double |
292 | atanMp (double x, const int pr[]) | |
293 | { | |
294 | mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1; | |
295 | double y1, y2; | |
296 | int i, p; | |
297 | ||
298 | for (i = 0; i < M; i++) | |
299 | { | |
300 | p = pr[i]; | |
301 | __dbl_mp (x, &mpx, p); | |
302 | __mpatan (&mpx, &mpy, p); | |
303 | __dbl_mp (u9[i].d, &mpt1, p); | |
304 | __mul (&mpy, &mpt1, &mperr, p); | |
305 | __add (&mpy, &mperr, &mpy1, p); | |
306 | __sub (&mpy, &mperr, &mpy2, p); | |
307 | __mp_dbl (&mpy1, &y1, p); | |
308 | __mp_dbl (&mpy2, &y2, p); | |
309 | if (y1 == y2) | |
10e1cf6b SP |
310 | { |
311 | LIBC_PROBE (slowatan, 3, &p, &x, &y1); | |
312 | return y1; | |
313 | } | |
d26dd3eb | 314 | } |
10e1cf6b | 315 | LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1); |
d26dd3eb | 316 | return y1; /*if impossible to do exact computing */ |
e4d82761 UD |
317 | } |
318 | ||
cccda09f | 319 | #ifdef NO_LONG_DOUBLE |
e4d82761 | 320 | weak_alias (atan, atanl) |
cccda09f | 321 | #endif |