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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. |
2b778ceb | 4 | * Copyright (C) 2001-2021 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 |
5a82c748 | 17 | * along with this program; if not, see <https://www.gnu.org/licenses/>. |
f7eac6eb | 18 | */ |
e4d82761 UD |
19 | /*********************************************************************/ |
20 | /* MODULE_NAME: utan.c */ | |
21 | /* */ | |
22 | /* FUNCTIONS: utan */ | |
23 | /* tanMp */ | |
24 | /* */ | |
25 | /* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */ | |
26 | /* branred.c sincos32.c mptan.c */ | |
27 | /* utan.tbl */ | |
28 | /* */ | |
29 | /* An ultimate tan routine. Given an IEEE double machine number x */ | |
30 | /* it computes the correctly rounded (to nearest) value of tan(x). */ | |
31 | /* Assumption: Machine arithmetic operations are performed in */ | |
32 | /* round to nearest mode of IEEE 754 standard. */ | |
33 | /* */ | |
34 | /*********************************************************************/ | |
337c2708 UD |
35 | |
36 | #include <errno.h> | |
37550cb3 | 37 | #include <float.h> |
e4d82761 | 38 | #include "endian.h" |
c8b3296b | 39 | #include <dla.h> |
e4d82761 UD |
40 | #include "mpa.h" |
41 | #include "MathLib.h" | |
1ed0291c RH |
42 | #include <math.h> |
43 | #include <math_private.h> | |
70e2ba33 | 44 | #include <fenv_private.h> |
8f5b00d3 | 45 | #include <math-underflow.h> |
38722448 | 46 | #include <libm-alias-double.h> |
804360ed | 47 | #include <fenv.h> |
10e1cf6b | 48 | #include <stap-probe.h> |
15b3c029 | 49 | |
31d3cc00 UD |
50 | #ifndef SECTION |
51 | # define SECTION | |
52 | #endif | |
53 | ||
27ec37f1 SP |
54 | static double tanMp (double); |
55 | void __mptan (double, mp_no *, int); | |
f7eac6eb | 56 | |
31d3cc00 UD |
57 | double |
58 | SECTION | |
527cd19c | 59 | __tan (double x) |
27ec37f1 | 60 | { |
e4d82761 UD |
61 | #include "utan.h" |
62 | #include "utan.tbl" | |
f7eac6eb | 63 | |
27ec37f1 SP |
64 | int ux, i, n; |
65 | double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz, | |
e93c2643 | 66 | s, sy, t, t1, t2, t3, t4, w, x2, xn, xx2, y, ya, |
c5d5d574 | 67 | yya, z0, z, zz, z2, zz2; |
e4d82761 | 68 | int p; |
27ec37f1 SP |
69 | number num, v; |
70 | mp_no mpa, mpt1, mpt2; | |
e4d82761 | 71 | |
804360ed JM |
72 | double retval; |
73 | ||
27ec37f1 SP |
74 | int __branred (double, double *, double *); |
75 | int __mpranred (double, mp_no *, int); | |
e4d82761 | 76 | |
eb92c487 | 77 | SET_RESTORE_ROUND_53BIT (FE_TONEAREST); |
804360ed | 78 | |
e4d82761 | 79 | /* x=+-INF, x=NaN */ |
27ec37f1 SP |
80 | num.d = x; |
81 | ux = num.i[HIGH_HALF]; | |
82 | if ((ux & 0x7ff00000) == 0x7ff00000) | |
83 | { | |
84 | if ((ux & 0x7fffffff) == 0x7ff00000) | |
85 | __set_errno (EDOM); | |
86 | retval = x - x; | |
87 | goto ret; | |
88 | } | |
e4d82761 | 89 | |
27ec37f1 | 90 | w = (x < 0.0) ? -x : x; |
e4d82761 UD |
91 | |
92 | /* (I) The case abs(x) <= 1.259e-8 */ | |
27ec37f1 SP |
93 | if (w <= g1.d) |
94 | { | |
d96164c3 | 95 | math_check_force_underflow_nonneg (w); |
27ec37f1 SP |
96 | retval = x; |
97 | goto ret; | |
98 | } | |
e4d82761 UD |
99 | |
100 | /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ | |
27ec37f1 SP |
101 | if (w <= g2.d) |
102 | { | |
27ec37f1 SP |
103 | /* First stage */ |
104 | x2 = x * x; | |
e4d82761 | 105 | |
27ec37f1 SP |
106 | t2 = d9.d + x2 * d11.d; |
107 | t2 = d7.d + x2 * t2; | |
108 | t2 = d5.d + x2 * t2; | |
109 | t2 = d3.d + x2 * t2; | |
110 | t2 *= x * x2; | |
111 | ||
112 | if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2)) | |
113 | { | |
114 | retval = y; | |
115 | goto ret; | |
116 | } | |
e4d82761 UD |
117 | |
118 | /* Second stage */ | |
27ec37f1 SP |
119 | c1 = a25.d + x2 * a27.d; |
120 | c1 = a23.d + x2 * c1; | |
121 | c1 = a21.d + x2 * c1; | |
122 | c1 = a19.d + x2 * c1; | |
123 | c1 = a17.d + x2 * c1; | |
124 | c1 = a15.d + x2 * c1; | |
125 | c1 *= x2; | |
126 | ||
e93c2643 | 127 | EMULV (x, x, x2, xx2); |
27ec37f1 | 128 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); |
e93c2643 | 129 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 130 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 131 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 132 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 133 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 134 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 135 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 136 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 137 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 138 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
139 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
140 | MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
141 | ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2); |
142 | if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1)) | |
143 | { | |
144 | retval = y; | |
145 | goto ret; | |
146 | } | |
147 | retval = tanMp (x); | |
804360ed | 148 | goto ret; |
e4d82761 UD |
149 | } |
150 | ||
27ec37f1 SP |
151 | /* (III) The case 0.0608 < abs(x) <= 0.787 */ |
152 | if (w <= g3.d) | |
153 | { | |
27ec37f1 SP |
154 | /* First stage */ |
155 | i = ((int) (mfftnhf.d + TWO8 * w)); | |
156 | z = w - xfg[i][0].d; | |
157 | z2 = z * z; | |
c2d94018 | 158 | s = (x < 0.0) ? -1 : 1; |
27ec37f1 SP |
159 | pz = z + z * z2 * (e0.d + z2 * e1.d); |
160 | fi = xfg[i][1].d; | |
161 | gi = xfg[i][2].d; | |
162 | t2 = pz * (gi + fi) / (gi - pz); | |
163 | if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d)) | |
164 | { | |
165 | retval = (s * y); | |
166 | goto ret; | |
167 | } | |
168 | t3 = (t2 < 0.0) ? -t2 : t2; | |
169 | t4 = fi * ua3.d + t3 * ub3.d; | |
170 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
171 | { | |
172 | retval = (s * y); | |
173 | goto ret; | |
174 | } | |
e4d82761 | 175 | |
27ec37f1 SP |
176 | /* Second stage */ |
177 | ffi = xfg[i][3].d; | |
178 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); | |
e93c2643 | 179 | EMULV (z, z, z2, zz2); |
27ec37f1 | 180 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); |
e93c2643 | 181 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 182 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
183 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
184 | MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
185 | ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2); |
186 | ||
187 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
e93c2643 | 188 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2); |
27ec37f1 | 189 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
e93c2643 | 190 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4); |
27ec37f1 SP |
191 | |
192 | if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3)) | |
193 | { | |
194 | retval = (s * y); | |
195 | goto ret; | |
196 | } | |
197 | retval = tanMp (x); | |
198 | goto ret; | |
199 | } | |
f7eac6eb | 200 | |
27ec37f1 SP |
201 | /* (---) The case 0.787 < abs(x) <= 25 */ |
202 | if (w <= g4.d) | |
203 | { | |
204 | /* Range reduction by algorithm i */ | |
205 | t = (x * hpinv.d + toint.d); | |
206 | xn = t - toint.d; | |
207 | v.d = t; | |
208 | t1 = (x - xn * mp1.d) - xn * mp2.d; | |
209 | n = v.i[LOW_HALF] & 0x00000001; | |
210 | da = xn * mp3.d; | |
211 | a = t1 - da; | |
212 | da = (t1 - a) - da; | |
213 | if (a < 0.0) | |
214 | { | |
215 | ya = -a; | |
216 | yya = -da; | |
c2d94018 | 217 | sy = -1; |
27ec37f1 SP |
218 | } |
219 | else | |
220 | { | |
221 | ya = a; | |
222 | yya = da; | |
c2d94018 | 223 | sy = 1; |
27ec37f1 SP |
224 | } |
225 | ||
226 | /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */ | |
227 | if (ya <= gy1.d) | |
228 | { | |
229 | retval = tanMp (x); | |
230 | goto ret; | |
231 | } | |
232 | ||
233 | /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */ | |
234 | if (ya <= gy2.d) | |
235 | { | |
236 | a2 = a * a; | |
237 | t2 = d9.d + a2 * d11.d; | |
238 | t2 = d7.d + a2 * t2; | |
239 | t2 = d5.d + a2 * t2; | |
240 | t2 = d3.d + a2 * t2; | |
241 | t2 = da + a * a2 * t2; | |
242 | ||
243 | if (n) | |
244 | { | |
245 | /* First stage -cot */ | |
246 | EADD (a, t2, b, db); | |
e93c2643 | 247 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4); |
27ec37f1 SP |
248 | if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c)) |
249 | { | |
250 | retval = (-y); | |
251 | goto ret; | |
252 | } | |
253 | } | |
254 | else | |
255 | { | |
256 | /* First stage tan */ | |
257 | if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a)) | |
258 | { | |
259 | retval = y; | |
260 | goto ret; | |
261 | } | |
262 | } | |
263 | /* Second stage */ | |
264 | /* Range reduction by algorithm ii */ | |
265 | t = (x * hpinv.d + toint.d); | |
266 | xn = t - toint.d; | |
267 | v.d = t; | |
268 | t1 = (x - xn * mp1.d) - xn * mp2.d; | |
269 | n = v.i[LOW_HALF] & 0x00000001; | |
270 | da = xn * pp3.d; | |
271 | t = t1 - da; | |
272 | da = (t1 - t) - da; | |
273 | t1 = xn * pp4.d; | |
274 | a = t - t1; | |
275 | da = ((t - a) - t1) + da; | |
276 | ||
277 | /* Second stage */ | |
278 | EADD (a, da, t1, t2); | |
279 | a = t1; | |
280 | da = t2; | |
e93c2643 | 281 | MUL2 (a, da, a, da, x2, xx2, t1, t2); |
27ec37f1 SP |
282 | |
283 | c1 = a25.d + x2 * a27.d; | |
284 | c1 = a23.d + x2 * c1; | |
285 | c1 = a21.d + x2 * c1; | |
286 | c1 = a19.d + x2 * c1; | |
287 | c1 = a17.d + x2 * c1; | |
288 | c1 = a15.d + x2 * c1; | |
289 | c1 *= x2; | |
290 | ||
291 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); | |
e93c2643 | 292 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 293 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 294 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 295 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 296 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 297 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 298 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 299 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 300 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 301 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
302 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
303 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
304 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); |
305 | ||
306 | if (n) | |
307 | { | |
308 | /* Second stage -cot */ | |
e93c2643 | 309 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4); |
27ec37f1 SP |
310 | if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2)) |
311 | { | |
312 | retval = (-y); | |
313 | goto ret; | |
314 | } | |
315 | } | |
316 | else | |
317 | { | |
318 | /* Second stage tan */ | |
319 | if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1)) | |
320 | { | |
321 | retval = y; | |
322 | goto ret; | |
323 | } | |
324 | } | |
325 | retval = tanMp (x); | |
326 | goto ret; | |
327 | } | |
328 | ||
329 | /* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */ | |
330 | ||
331 | /* First stage */ | |
332 | i = ((int) (mfftnhf.d + TWO8 * ya)); | |
333 | z = (z0 = (ya - xfg[i][0].d)) + yya; | |
334 | z2 = z * z; | |
335 | pz = z + z * z2 * (e0.d + z2 * e1.d); | |
336 | fi = xfg[i][1].d; | |
337 | gi = xfg[i][2].d; | |
338 | ||
339 | if (n) | |
340 | { | |
341 | /* -cot */ | |
342 | t2 = pz * (fi + gi) / (fi + pz); | |
343 | if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d)) | |
344 | { | |
345 | retval = (-sy * y); | |
346 | goto ret; | |
347 | } | |
348 | t3 = (t2 < 0.0) ? -t2 : t2; | |
349 | t4 = gi * ua10.d + t3 * ub10.d; | |
350 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) | |
351 | { | |
352 | retval = (-sy * y); | |
353 | goto ret; | |
354 | } | |
355 | } | |
356 | else | |
357 | { | |
358 | /* tan */ | |
359 | t2 = pz * (gi + fi) / (gi - pz); | |
360 | if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d)) | |
361 | { | |
362 | retval = (sy * y); | |
363 | goto ret; | |
364 | } | |
365 | t3 = (t2 < 0.0) ? -t2 : t2; | |
366 | t4 = fi * ua9.d + t3 * ub9.d; | |
367 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
368 | { | |
369 | retval = (sy * y); | |
370 | goto ret; | |
371 | } | |
372 | } | |
e4d82761 | 373 | |
27ec37f1 SP |
374 | /* Second stage */ |
375 | ffi = xfg[i][3].d; | |
376 | EADD (z0, yya, z, zz) | |
e93c2643 | 377 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2); |
27ec37f1 SP |
378 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
379 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); | |
e93c2643 | 380 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 381 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
382 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
383 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
384 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); |
385 | ||
386 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
e93c2643 | 387 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2); |
27ec37f1 SP |
388 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
389 | ||
390 | if (n) | |
391 | { | |
392 | /* -cot */ | |
e93c2643 | 393 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4); |
27ec37f1 SP |
394 | if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3)) |
395 | { | |
396 | retval = (-sy * y); | |
397 | goto ret; | |
398 | } | |
399 | } | |
400 | else | |
401 | { | |
402 | /* tan */ | |
e93c2643 | 403 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4); |
27ec37f1 SP |
404 | if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3)) |
405 | { | |
406 | retval = (sy * y); | |
407 | goto ret; | |
408 | } | |
409 | } | |
410 | ||
411 | retval = tanMp (x); | |
412 | goto ret; | |
413 | } | |
e4d82761 UD |
414 | |
415 | /* (---) The case 25 < abs(x) <= 1e8 */ | |
27ec37f1 SP |
416 | if (w <= g5.d) |
417 | { | |
418 | /* Range reduction by algorithm ii */ | |
419 | t = (x * hpinv.d + toint.d); | |
420 | xn = t - toint.d; | |
421 | v.d = t; | |
422 | t1 = (x - xn * mp1.d) - xn * mp2.d; | |
423 | n = v.i[LOW_HALF] & 0x00000001; | |
424 | da = xn * pp3.d; | |
425 | t = t1 - da; | |
426 | da = (t1 - t) - da; | |
427 | t1 = xn * pp4.d; | |
428 | a = t - t1; | |
429 | da = ((t - a) - t1) + da; | |
430 | EADD (a, da, t1, t2); | |
431 | a = t1; | |
432 | da = t2; | |
433 | if (a < 0.0) | |
434 | { | |
435 | ya = -a; | |
436 | yya = -da; | |
c2d94018 | 437 | sy = -1; |
27ec37f1 SP |
438 | } |
439 | else | |
440 | { | |
441 | ya = a; | |
442 | yya = da; | |
c2d94018 | 443 | sy = 1; |
27ec37f1 SP |
444 | } |
445 | ||
446 | /* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */ | |
447 | if (ya <= gy1.d) | |
448 | { | |
449 | retval = tanMp (x); | |
450 | goto ret; | |
451 | } | |
452 | ||
453 | /* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */ | |
454 | if (ya <= gy2.d) | |
455 | { | |
456 | a2 = a * a; | |
457 | t2 = d9.d + a2 * d11.d; | |
458 | t2 = d7.d + a2 * t2; | |
459 | t2 = d5.d + a2 * t2; | |
460 | t2 = d3.d + a2 * t2; | |
461 | t2 = da + a * a2 * t2; | |
462 | ||
463 | if (n) | |
464 | { | |
465 | /* First stage -cot */ | |
466 | EADD (a, t2, b, db); | |
e93c2643 | 467 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4); |
27ec37f1 SP |
468 | if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c)) |
469 | { | |
470 | retval = (-y); | |
471 | goto ret; | |
472 | } | |
473 | } | |
474 | else | |
475 | { | |
476 | /* First stage tan */ | |
477 | if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a)) | |
478 | { | |
479 | retval = y; | |
480 | goto ret; | |
481 | } | |
482 | } | |
483 | ||
484 | /* Second stage */ | |
e93c2643 | 485 | MUL2 (a, da, a, da, x2, xx2, t1, t2); |
27ec37f1 SP |
486 | c1 = a25.d + x2 * a27.d; |
487 | c1 = a23.d + x2 * c1; | |
488 | c1 = a21.d + x2 * c1; | |
489 | c1 = a19.d + x2 * c1; | |
490 | c1 = a17.d + x2 * c1; | |
491 | c1 = a15.d + x2 * c1; | |
492 | c1 *= x2; | |
493 | ||
494 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); | |
e93c2643 | 495 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 496 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 497 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 498 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 499 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 500 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 501 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 502 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 503 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 504 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
505 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
506 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
507 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); |
508 | ||
509 | if (n) | |
510 | { | |
511 | /* Second stage -cot */ | |
e93c2643 | 512 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4); |
27ec37f1 SP |
513 | if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2)) |
514 | { | |
515 | retval = (-y); | |
516 | goto ret; | |
517 | } | |
518 | } | |
519 | else | |
520 | { | |
521 | /* Second stage tan */ | |
522 | if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1)) | |
523 | { | |
524 | retval = (y); | |
525 | goto ret; | |
526 | } | |
527 | } | |
528 | retval = tanMp (x); | |
529 | goto ret; | |
530 | } | |
531 | ||
532 | /* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */ | |
533 | /* First stage */ | |
534 | i = ((int) (mfftnhf.d + TWO8 * ya)); | |
535 | z = (z0 = (ya - xfg[i][0].d)) + yya; | |
536 | z2 = z * z; | |
537 | pz = z + z * z2 * (e0.d + z2 * e1.d); | |
538 | fi = xfg[i][1].d; | |
539 | gi = xfg[i][2].d; | |
540 | ||
541 | if (n) | |
542 | { | |
543 | /* -cot */ | |
544 | t2 = pz * (fi + gi) / (fi + pz); | |
545 | if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d)) | |
546 | { | |
547 | retval = (-sy * y); | |
548 | goto ret; | |
549 | } | |
550 | t3 = (t2 < 0.0) ? -t2 : t2; | |
551 | t4 = gi * ua18.d + t3 * ub18.d; | |
552 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) | |
553 | { | |
554 | retval = (-sy * y); | |
555 | goto ret; | |
556 | } | |
557 | } | |
558 | else | |
559 | { | |
560 | /* tan */ | |
561 | t2 = pz * (gi + fi) / (gi - pz); | |
562 | if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d)) | |
563 | { | |
564 | retval = (sy * y); | |
565 | goto ret; | |
566 | } | |
567 | t3 = (t2 < 0.0) ? -t2 : t2; | |
568 | t4 = fi * ua17.d + t3 * ub17.d; | |
569 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
570 | { | |
571 | retval = (sy * y); | |
572 | goto ret; | |
573 | } | |
574 | } | |
e4d82761 UD |
575 | |
576 | /* Second stage */ | |
27ec37f1 SP |
577 | ffi = xfg[i][3].d; |
578 | EADD (z0, yya, z, zz); | |
e93c2643 | 579 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2); |
27ec37f1 SP |
580 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
581 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); | |
e93c2643 | 582 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 583 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
584 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
585 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
586 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); |
587 | ||
588 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
e93c2643 | 589 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2); |
27ec37f1 SP |
590 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
591 | ||
592 | if (n) | |
593 | { | |
594 | /* -cot */ | |
e93c2643 | 595 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4); |
27ec37f1 SP |
596 | if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3)) |
597 | { | |
598 | retval = (-sy * y); | |
599 | goto ret; | |
600 | } | |
601 | } | |
602 | else | |
603 | { | |
604 | /* tan */ | |
e93c2643 | 605 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4); |
27ec37f1 SP |
606 | if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3)) |
607 | { | |
608 | retval = (sy * y); | |
609 | goto ret; | |
610 | } | |
611 | } | |
612 | retval = tanMp (x); | |
804360ed | 613 | goto ret; |
e4d82761 UD |
614 | } |
615 | ||
e4d82761 UD |
616 | /* (---) The case 1e8 < abs(x) < 2**1024 */ |
617 | /* Range reduction by algorithm iii */ | |
27ec37f1 SP |
618 | n = (__branred (x, &a, &da)) & 0x00000001; |
619 | EADD (a, da, t1, t2); | |
620 | a = t1; | |
621 | da = t2; | |
622 | if (a < 0.0) | |
623 | { | |
624 | ya = -a; | |
625 | yya = -da; | |
c2d94018 | 626 | sy = -1; |
27ec37f1 SP |
627 | } |
628 | else | |
629 | { | |
630 | ya = a; | |
631 | yya = da; | |
c2d94018 | 632 | sy = 1; |
27ec37f1 | 633 | } |
e4d82761 UD |
634 | |
635 | /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ | |
27ec37f1 SP |
636 | if (ya <= gy1.d) |
637 | { | |
638 | retval = tanMp (x); | |
639 | goto ret; | |
640 | } | |
e4d82761 UD |
641 | |
642 | /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ | |
27ec37f1 SP |
643 | if (ya <= gy2.d) |
644 | { | |
645 | a2 = a * a; | |
646 | t2 = d9.d + a2 * d11.d; | |
647 | t2 = d7.d + a2 * t2; | |
648 | t2 = d5.d + a2 * t2; | |
649 | t2 = d3.d + a2 * t2; | |
650 | t2 = da + a * a2 * t2; | |
651 | if (n) | |
652 | { | |
653 | /* First stage -cot */ | |
654 | EADD (a, t2, b, db); | |
e93c2643 | 655 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4); |
27ec37f1 SP |
656 | if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c)) |
657 | { | |
658 | retval = (-y); | |
659 | goto ret; | |
660 | } | |
661 | } | |
662 | else | |
663 | { | |
664 | /* First stage tan */ | |
665 | if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a)) | |
666 | { | |
667 | retval = y; | |
668 | goto ret; | |
669 | } | |
670 | } | |
671 | ||
672 | /* Second stage */ | |
673 | /* Reduction by algorithm iv */ | |
674 | p = 10; | |
675 | n = (__mpranred (x, &mpa, p)) & 0x00000001; | |
676 | __mp_dbl (&mpa, &a, p); | |
677 | __dbl_mp (a, &mpt1, p); | |
678 | __sub (&mpa, &mpt1, &mpt2, p); | |
679 | __mp_dbl (&mpt2, &da, p); | |
680 | ||
e93c2643 | 681 | MUL2 (a, da, a, da, x2, xx2, t1, t2); |
27ec37f1 SP |
682 | |
683 | c1 = a25.d + x2 * a27.d; | |
684 | c1 = a23.d + x2 * c1; | |
685 | c1 = a21.d + x2 * c1; | |
686 | c1 = a19.d + x2 * c1; | |
687 | c1 = a17.d + x2 * c1; | |
688 | c1 = a15.d + x2 * c1; | |
689 | c1 *= x2; | |
690 | ||
691 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); | |
e93c2643 | 692 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 693 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 694 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 695 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 696 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 697 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 698 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 699 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 | 700 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 701 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
702 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2); |
703 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
704 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); |
705 | ||
706 | if (n) | |
707 | { | |
708 | /* Second stage -cot */ | |
e93c2643 | 709 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4); |
27ec37f1 SP |
710 | if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2)) |
711 | { | |
712 | retval = (-y); | |
713 | goto ret; | |
714 | } | |
715 | } | |
716 | else | |
717 | { | |
718 | /* Second stage tan */ | |
719 | if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1)) | |
720 | { | |
721 | retval = y; | |
722 | goto ret; | |
723 | } | |
724 | } | |
725 | retval = tanMp (x); | |
726 | goto ret; | |
727 | } | |
e4d82761 UD |
728 | |
729 | /* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */ | |
730 | /* First stage */ | |
27ec37f1 SP |
731 | i = ((int) (mfftnhf.d + TWO8 * ya)); |
732 | z = (z0 = (ya - xfg[i][0].d)) + yya; | |
733 | z2 = z * z; | |
734 | pz = z + z * z2 * (e0.d + z2 * e1.d); | |
735 | fi = xfg[i][1].d; | |
736 | gi = xfg[i][2].d; | |
737 | ||
738 | if (n) | |
739 | { | |
740 | /* -cot */ | |
741 | t2 = pz * (fi + gi) / (fi + pz); | |
742 | if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d)) | |
743 | { | |
744 | retval = (-sy * y); | |
745 | goto ret; | |
746 | } | |
747 | t3 = (t2 < 0.0) ? -t2 : t2; | |
748 | t4 = gi * ua26.d + t3 * ub26.d; | |
749 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) | |
750 | { | |
751 | retval = (-sy * y); | |
752 | goto ret; | |
753 | } | |
754 | } | |
755 | else | |
756 | { | |
757 | /* tan */ | |
758 | t2 = pz * (gi + fi) / (gi - pz); | |
759 | if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d)) | |
760 | { | |
761 | retval = (sy * y); | |
762 | goto ret; | |
763 | } | |
764 | t3 = (t2 < 0.0) ? -t2 : t2; | |
765 | t4 = fi * ua25.d + t3 * ub25.d; | |
766 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
767 | { | |
768 | retval = (sy * y); | |
769 | goto ret; | |
770 | } | |
771 | } | |
e4d82761 UD |
772 | |
773 | /* Second stage */ | |
774 | ffi = xfg[i][3].d; | |
27ec37f1 | 775 | EADD (z0, yya, z, zz); |
e93c2643 | 776 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2); |
27ec37f1 SP |
777 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
778 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); | |
e93c2643 | 779 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
27ec37f1 | 780 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
e93c2643 VG |
781 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2); |
782 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2); | |
27ec37f1 SP |
783 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); |
784 | ||
785 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
e93c2643 | 786 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2); |
27ec37f1 SP |
787 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
788 | ||
789 | if (n) | |
790 | { | |
791 | /* -cot */ | |
e93c2643 | 792 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4); |
27ec37f1 SP |
793 | if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3)) |
794 | { | |
795 | retval = (-sy * y); | |
796 | goto ret; | |
797 | } | |
798 | } | |
799 | else | |
800 | { | |
801 | /* tan */ | |
e93c2643 | 802 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4); |
27ec37f1 SP |
803 | if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3)) |
804 | { | |
805 | retval = (sy * y); | |
806 | goto ret; | |
807 | } | |
808 | } | |
809 | retval = tanMp (x); | |
804360ed | 810 | goto ret; |
e4d82761 | 811 | |
27ec37f1 | 812 | ret: |
804360ed JM |
813 | return retval; |
814 | } | |
e4d82761 UD |
815 | |
816 | /* multiple precision stage */ | |
817 | /* Convert x to multi precision number,compute tan(x) by mptan() routine */ | |
818 | /* and converts result back to double */ | |
31d3cc00 UD |
819 | static double |
820 | SECTION | |
27ec37f1 | 821 | tanMp (double x) |
e4d82761 UD |
822 | { |
823 | int p; | |
824 | double y; | |
825 | mp_no mpy; | |
27ec37f1 SP |
826 | p = 32; |
827 | __mptan (x, &mpy, p); | |
828 | __mp_dbl (&mpy, &y, p); | |
10e1cf6b | 829 | LIBC_PROBE (slowtan, 2, &x, &y); |
e4d82761 | 830 | return y; |
f7eac6eb | 831 | } |
e4d82761 | 832 | |
527cd19c | 833 | #ifndef __tan |
38722448 | 834 | libm_alias_double (__tan, tan) |
cccda09f | 835 | #endif |