1 | /* |
2 | * IBM Accurate Mathematical Library |
3 | * written by International Business Machines Corp. |
4 | * Copyright (C) 2001-2018 Free Software Foundation, Inc. |
5 | * |
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 |
8 | * the Free Software Foundation; either version 2.1 of the License, or |
9 | * (at your option) any later version. |
10 | * |
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 |
14 | * GNU Lesser General Public License for more details. |
15 | * |
16 | * You should have received a copy of the GNU Lesser General Public License |
17 | * along with this program; if not, see <http://www.gnu.org/licenses/>. |
18 | */ |
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 | /*********************************************************************/ |
35 | |
36 | #include <errno.h> |
37 | #include <float.h> |
38 | #include "endian.h" |
39 | #include <dla.h> |
40 | #include "mpa.h" |
41 | #include "MathLib.h" |
42 | #include <math.h> |
43 | #include <math_private.h> |
44 | #include <libm-alias-double.h> |
45 | #include <fenv.h> |
46 | #include <stap-probe.h> |
47 | |
48 | #ifndef SECTION |
49 | # define SECTION |
50 | #endif |
51 | |
52 | static double tanMp (double); |
53 | void __mptan (double, mp_no *, int); |
54 | |
55 | double |
56 | SECTION |
57 | __tan (double x) |
58 | { |
59 | #include "utan.h" |
60 | #include "utan.tbl" |
61 | |
62 | int ux, i, n; |
63 | double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz, |
64 | s, sy, t, t1, t2, t3, t4, t7, t8, t9, t10, w, x2, xn, xx2, y, ya, |
65 | yya, z0, z, zz, z2, zz2; |
66 | #ifndef DLA_FMS |
67 | double t5, t6; |
68 | #endif |
69 | int p; |
70 | number num, v; |
71 | mp_no mpa, mpt1, mpt2; |
72 | |
73 | double retval; |
74 | |
75 | int __branred (double, double *, double *); |
76 | int __mpranred (double, mp_no *, int); |
77 | |
78 | SET_RESTORE_ROUND_53BIT (FE_TONEAREST); |
79 | |
80 | /* x=+-INF, x=NaN */ |
81 | num.d = x; |
82 | ux = num.i[HIGH_HALF]; |
83 | if ((ux & 0x7ff00000) == 0x7ff00000) |
84 | { |
85 | if ((ux & 0x7fffffff) == 0x7ff00000) |
86 | __set_errno (EDOM); |
87 | retval = x - x; |
88 | goto ret; |
89 | } |
90 | |
91 | w = (x < 0.0) ? -x : x; |
92 | |
93 | /* (I) The case abs(x) <= 1.259e-8 */ |
94 | if (w <= g1.d) |
95 | { |
96 | math_check_force_underflow_nonneg (w); |
97 | retval = x; |
98 | goto ret; |
99 | } |
100 | |
101 | /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ |
102 | if (w <= g2.d) |
103 | { |
104 | /* First stage */ |
105 | x2 = x * x; |
106 | |
107 | t2 = d9.d + x2 * d11.d; |
108 | t2 = d7.d + x2 * t2; |
109 | t2 = d5.d + x2 * t2; |
110 | t2 = d3.d + x2 * t2; |
111 | t2 *= x * x2; |
112 | |
113 | if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2)) |
114 | { |
115 | retval = y; |
116 | goto ret; |
117 | } |
118 | |
119 | /* Second stage */ |
120 | c1 = a25.d + x2 * a27.d; |
121 | c1 = a23.d + x2 * c1; |
122 | c1 = a21.d + x2 * c1; |
123 | c1 = a19.d + x2 * c1; |
124 | c1 = a17.d + x2 * c1; |
125 | c1 = a15.d + x2 * c1; |
126 | c1 *= x2; |
127 | |
128 | EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5); |
129 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); |
130 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
131 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
132 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
133 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
134 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
135 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
136 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
137 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
138 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
139 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
140 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
141 | MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
142 | ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2); |
143 | if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1)) |
144 | { |
145 | retval = y; |
146 | goto ret; |
147 | } |
148 | retval = tanMp (x); |
149 | goto ret; |
150 | } |
151 | |
152 | /* (III) The case 0.0608 < abs(x) <= 0.787 */ |
153 | if (w <= g3.d) |
154 | { |
155 | /* First stage */ |
156 | i = ((int) (mfftnhf.d + TWO8 * w)); |
157 | z = w - xfg[i][0].d; |
158 | z2 = z * z; |
159 | s = (x < 0.0) ? -1 : 1; |
160 | pz = z + z * z2 * (e0.d + z2 * e1.d); |
161 | fi = xfg[i][1].d; |
162 | gi = xfg[i][2].d; |
163 | t2 = pz * (gi + fi) / (gi - pz); |
164 | if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d)) |
165 | { |
166 | retval = (s * y); |
167 | goto ret; |
168 | } |
169 | t3 = (t2 < 0.0) ? -t2 : t2; |
170 | t4 = fi * ua3.d + t3 * ub3.d; |
171 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) |
172 | { |
173 | retval = (s * y); |
174 | goto ret; |
175 | } |
176 | |
177 | /* Second stage */ |
178 | ffi = xfg[i][3].d; |
179 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
180 | EMULV (z, z, z2, zz2, t1, t2, t3, t4, t5); |
181 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); |
182 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
183 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
184 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
185 | MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
186 | ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2); |
187 | |
188 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); |
189 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); |
190 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
191 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
192 | t10); |
193 | |
194 | if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3)) |
195 | { |
196 | retval = (s * y); |
197 | goto ret; |
198 | } |
199 | retval = tanMp (x); |
200 | goto ret; |
201 | } |
202 | |
203 | /* (---) The case 0.787 < abs(x) <= 25 */ |
204 | if (w <= g4.d) |
205 | { |
206 | /* Range reduction by algorithm i */ |
207 | t = (x * hpinv.d + toint.d); |
208 | xn = t - toint.d; |
209 | v.d = t; |
210 | t1 = (x - xn * mp1.d) - xn * mp2.d; |
211 | n = v.i[LOW_HALF] & 0x00000001; |
212 | da = xn * mp3.d; |
213 | a = t1 - da; |
214 | da = (t1 - a) - da; |
215 | if (a < 0.0) |
216 | { |
217 | ya = -a; |
218 | yya = -da; |
219 | sy = -1; |
220 | } |
221 | else |
222 | { |
223 | ya = a; |
224 | yya = da; |
225 | sy = 1; |
226 | } |
227 | |
228 | /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */ |
229 | if (ya <= gy1.d) |
230 | { |
231 | retval = tanMp (x); |
232 | goto ret; |
233 | } |
234 | |
235 | /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */ |
236 | if (ya <= gy2.d) |
237 | { |
238 | a2 = a * a; |
239 | t2 = d9.d + a2 * d11.d; |
240 | t2 = d7.d + a2 * t2; |
241 | t2 = d5.d + a2 * t2; |
242 | t2 = d3.d + a2 * t2; |
243 | t2 = da + a * a2 * t2; |
244 | |
245 | if (n) |
246 | { |
247 | /* First stage -cot */ |
248 | EADD (a, t2, b, db); |
249 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, |
250 | t9, t10); |
251 | if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c)) |
252 | { |
253 | retval = (-y); |
254 | goto ret; |
255 | } |
256 | } |
257 | else |
258 | { |
259 | /* First stage tan */ |
260 | if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a)) |
261 | { |
262 | retval = y; |
263 | goto ret; |
264 | } |
265 | } |
266 | /* Second stage */ |
267 | /* Range reduction by algorithm ii */ |
268 | t = (x * hpinv.d + toint.d); |
269 | xn = t - toint.d; |
270 | v.d = t; |
271 | t1 = (x - xn * mp1.d) - xn * mp2.d; |
272 | n = v.i[LOW_HALF] & 0x00000001; |
273 | da = xn * pp3.d; |
274 | t = t1 - da; |
275 | da = (t1 - t) - da; |
276 | t1 = xn * pp4.d; |
277 | a = t - t1; |
278 | da = ((t - a) - t1) + da; |
279 | |
280 | /* Second stage */ |
281 | EADD (a, da, t1, t2); |
282 | a = t1; |
283 | da = t2; |
284 | MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); |
285 | |
286 | c1 = a25.d + x2 * a27.d; |
287 | c1 = a23.d + x2 * c1; |
288 | c1 = a21.d + x2 * c1; |
289 | c1 = a19.d + x2 * c1; |
290 | c1 = a17.d + x2 * c1; |
291 | c1 = a15.d + x2 * c1; |
292 | c1 *= x2; |
293 | |
294 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); |
295 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
296 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
297 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
298 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
299 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
300 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
301 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
302 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
303 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
304 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
305 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
306 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
307 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); |
308 | |
309 | if (n) |
310 | { |
311 | /* Second stage -cot */ |
312 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, |
313 | t8, t9, t10); |
314 | if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2)) |
315 | { |
316 | retval = (-y); |
317 | goto ret; |
318 | } |
319 | } |
320 | else |
321 | { |
322 | /* Second stage tan */ |
323 | if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1)) |
324 | { |
325 | retval = y; |
326 | goto ret; |
327 | } |
328 | } |
329 | retval = tanMp (x); |
330 | goto ret; |
331 | } |
332 | |
333 | /* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */ |
334 | |
335 | /* First stage */ |
336 | i = ((int) (mfftnhf.d + TWO8 * ya)); |
337 | z = (z0 = (ya - xfg[i][0].d)) + yya; |
338 | z2 = z * z; |
339 | pz = z + z * z2 * (e0.d + z2 * e1.d); |
340 | fi = xfg[i][1].d; |
341 | gi = xfg[i][2].d; |
342 | |
343 | if (n) |
344 | { |
345 | /* -cot */ |
346 | t2 = pz * (fi + gi) / (fi + pz); |
347 | if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d)) |
348 | { |
349 | retval = (-sy * y); |
350 | goto ret; |
351 | } |
352 | t3 = (t2 < 0.0) ? -t2 : t2; |
353 | t4 = gi * ua10.d + t3 * ub10.d; |
354 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) |
355 | { |
356 | retval = (-sy * y); |
357 | goto ret; |
358 | } |
359 | } |
360 | else |
361 | { |
362 | /* tan */ |
363 | t2 = pz * (gi + fi) / (gi - pz); |
364 | if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d)) |
365 | { |
366 | retval = (sy * y); |
367 | goto ret; |
368 | } |
369 | t3 = (t2 < 0.0) ? -t2 : t2; |
370 | t4 = fi * ua9.d + t3 * ub9.d; |
371 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) |
372 | { |
373 | retval = (sy * y); |
374 | goto ret; |
375 | } |
376 | } |
377 | |
378 | /* Second stage */ |
379 | ffi = xfg[i][3].d; |
380 | EADD (z0, yya, z, zz) |
381 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); |
382 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
383 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); |
384 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
385 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
386 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
387 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
388 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); |
389 | |
390 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); |
391 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); |
392 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
393 | |
394 | if (n) |
395 | { |
396 | /* -cot */ |
397 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
398 | t10); |
399 | if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3)) |
400 | { |
401 | retval = (-sy * y); |
402 | goto ret; |
403 | } |
404 | } |
405 | else |
406 | { |
407 | /* tan */ |
408 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
409 | t10); |
410 | if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3)) |
411 | { |
412 | retval = (sy * y); |
413 | goto ret; |
414 | } |
415 | } |
416 | |
417 | retval = tanMp (x); |
418 | goto ret; |
419 | } |
420 | |
421 | /* (---) The case 25 < abs(x) <= 1e8 */ |
422 | if (w <= g5.d) |
423 | { |
424 | /* Range reduction by algorithm ii */ |
425 | t = (x * hpinv.d + toint.d); |
426 | xn = t - toint.d; |
427 | v.d = t; |
428 | t1 = (x - xn * mp1.d) - xn * mp2.d; |
429 | n = v.i[LOW_HALF] & 0x00000001; |
430 | da = xn * pp3.d; |
431 | t = t1 - da; |
432 | da = (t1 - t) - da; |
433 | t1 = xn * pp4.d; |
434 | a = t - t1; |
435 | da = ((t - a) - t1) + da; |
436 | EADD (a, da, t1, t2); |
437 | a = t1; |
438 | da = t2; |
439 | if (a < 0.0) |
440 | { |
441 | ya = -a; |
442 | yya = -da; |
443 | sy = -1; |
444 | } |
445 | else |
446 | { |
447 | ya = a; |
448 | yya = da; |
449 | sy = 1; |
450 | } |
451 | |
452 | /* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */ |
453 | if (ya <= gy1.d) |
454 | { |
455 | retval = tanMp (x); |
456 | goto ret; |
457 | } |
458 | |
459 | /* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */ |
460 | if (ya <= gy2.d) |
461 | { |
462 | a2 = a * a; |
463 | t2 = d9.d + a2 * d11.d; |
464 | t2 = d7.d + a2 * t2; |
465 | t2 = d5.d + a2 * t2; |
466 | t2 = d3.d + a2 * t2; |
467 | t2 = da + a * a2 * t2; |
468 | |
469 | if (n) |
470 | { |
471 | /* First stage -cot */ |
472 | EADD (a, t2, b, db); |
473 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, |
474 | t9, t10); |
475 | if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c)) |
476 | { |
477 | retval = (-y); |
478 | goto ret; |
479 | } |
480 | } |
481 | else |
482 | { |
483 | /* First stage tan */ |
484 | if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a)) |
485 | { |
486 | retval = y; |
487 | goto ret; |
488 | } |
489 | } |
490 | |
491 | /* Second stage */ |
492 | MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); |
493 | c1 = a25.d + x2 * a27.d; |
494 | c1 = a23.d + x2 * c1; |
495 | c1 = a21.d + x2 * c1; |
496 | c1 = a19.d + x2 * c1; |
497 | c1 = a17.d + x2 * c1; |
498 | c1 = a15.d + x2 * c1; |
499 | c1 *= x2; |
500 | |
501 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); |
502 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
503 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
504 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
505 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
506 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
507 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
508 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
509 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
510 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
511 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
512 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
513 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
514 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); |
515 | |
516 | if (n) |
517 | { |
518 | /* Second stage -cot */ |
519 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, |
520 | t8, t9, t10); |
521 | if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2)) |
522 | { |
523 | retval = (-y); |
524 | goto ret; |
525 | } |
526 | } |
527 | else |
528 | { |
529 | /* Second stage tan */ |
530 | if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1)) |
531 | { |
532 | retval = (y); |
533 | goto ret; |
534 | } |
535 | } |
536 | retval = tanMp (x); |
537 | goto ret; |
538 | } |
539 | |
540 | /* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */ |
541 | /* First stage */ |
542 | i = ((int) (mfftnhf.d + TWO8 * ya)); |
543 | z = (z0 = (ya - xfg[i][0].d)) + yya; |
544 | z2 = z * z; |
545 | pz = z + z * z2 * (e0.d + z2 * e1.d); |
546 | fi = xfg[i][1].d; |
547 | gi = xfg[i][2].d; |
548 | |
549 | if (n) |
550 | { |
551 | /* -cot */ |
552 | t2 = pz * (fi + gi) / (fi + pz); |
553 | if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d)) |
554 | { |
555 | retval = (-sy * y); |
556 | goto ret; |
557 | } |
558 | t3 = (t2 < 0.0) ? -t2 : t2; |
559 | t4 = gi * ua18.d + t3 * ub18.d; |
560 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) |
561 | { |
562 | retval = (-sy * y); |
563 | goto ret; |
564 | } |
565 | } |
566 | else |
567 | { |
568 | /* tan */ |
569 | t2 = pz * (gi + fi) / (gi - pz); |
570 | if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d)) |
571 | { |
572 | retval = (sy * y); |
573 | goto ret; |
574 | } |
575 | t3 = (t2 < 0.0) ? -t2 : t2; |
576 | t4 = fi * ua17.d + t3 * ub17.d; |
577 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) |
578 | { |
579 | retval = (sy * y); |
580 | goto ret; |
581 | } |
582 | } |
583 | |
584 | /* Second stage */ |
585 | ffi = xfg[i][3].d; |
586 | EADD (z0, yya, z, zz); |
587 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); |
588 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
589 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); |
590 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
591 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
592 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
593 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
594 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); |
595 | |
596 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); |
597 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); |
598 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
599 | |
600 | if (n) |
601 | { |
602 | /* -cot */ |
603 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
604 | t10); |
605 | if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3)) |
606 | { |
607 | retval = (-sy * y); |
608 | goto ret; |
609 | } |
610 | } |
611 | else |
612 | { |
613 | /* tan */ |
614 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
615 | t10); |
616 | if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3)) |
617 | { |
618 | retval = (sy * y); |
619 | goto ret; |
620 | } |
621 | } |
622 | retval = tanMp (x); |
623 | goto ret; |
624 | } |
625 | |
626 | /* (---) The case 1e8 < abs(x) < 2**1024 */ |
627 | /* Range reduction by algorithm iii */ |
628 | n = (__branred (x, &a, &da)) & 0x00000001; |
629 | EADD (a, da, t1, t2); |
630 | a = t1; |
631 | da = t2; |
632 | if (a < 0.0) |
633 | { |
634 | ya = -a; |
635 | yya = -da; |
636 | sy = -1; |
637 | } |
638 | else |
639 | { |
640 | ya = a; |
641 | yya = da; |
642 | sy = 1; |
643 | } |
644 | |
645 | /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ |
646 | if (ya <= gy1.d) |
647 | { |
648 | retval = tanMp (x); |
649 | goto ret; |
650 | } |
651 | |
652 | /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ |
653 | if (ya <= gy2.d) |
654 | { |
655 | a2 = a * a; |
656 | t2 = d9.d + a2 * d11.d; |
657 | t2 = d7.d + a2 * t2; |
658 | t2 = d5.d + a2 * t2; |
659 | t2 = d3.d + a2 * t2; |
660 | t2 = da + a * a2 * t2; |
661 | if (n) |
662 | { |
663 | /* First stage -cot */ |
664 | EADD (a, t2, b, db); |
665 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
666 | t10); |
667 | if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c)) |
668 | { |
669 | retval = (-y); |
670 | goto ret; |
671 | } |
672 | } |
673 | else |
674 | { |
675 | /* First stage tan */ |
676 | if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a)) |
677 | { |
678 | retval = y; |
679 | goto ret; |
680 | } |
681 | } |
682 | |
683 | /* Second stage */ |
684 | /* Reduction by algorithm iv */ |
685 | p = 10; |
686 | n = (__mpranred (x, &mpa, p)) & 0x00000001; |
687 | __mp_dbl (&mpa, &a, p); |
688 | __dbl_mp (a, &mpt1, p); |
689 | __sub (&mpa, &mpt1, &mpt2, p); |
690 | __mp_dbl (&mpt2, &da, p); |
691 | |
692 | MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); |
693 | |
694 | c1 = a25.d + x2 * a27.d; |
695 | c1 = a23.d + x2 * c1; |
696 | c1 = a21.d + x2 * c1; |
697 | c1 = a19.d + x2 * c1; |
698 | c1 = a17.d + x2 * c1; |
699 | c1 = a15.d + x2 * c1; |
700 | c1 *= x2; |
701 | |
702 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); |
703 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
704 | ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2); |
705 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
706 | ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2); |
707 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
708 | ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2); |
709 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
710 | ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); |
711 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
712 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
713 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
714 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
715 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); |
716 | |
717 | if (n) |
718 | { |
719 | /* Second stage -cot */ |
720 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8, |
721 | t9, t10); |
722 | if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2)) |
723 | { |
724 | retval = (-y); |
725 | goto ret; |
726 | } |
727 | } |
728 | else |
729 | { |
730 | /* Second stage tan */ |
731 | if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1)) |
732 | { |
733 | retval = y; |
734 | goto ret; |
735 | } |
736 | } |
737 | retval = tanMp (x); |
738 | goto ret; |
739 | } |
740 | |
741 | /* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */ |
742 | /* First stage */ |
743 | i = ((int) (mfftnhf.d + TWO8 * ya)); |
744 | z = (z0 = (ya - xfg[i][0].d)) + yya; |
745 | z2 = z * z; |
746 | pz = z + z * z2 * (e0.d + z2 * e1.d); |
747 | fi = xfg[i][1].d; |
748 | gi = xfg[i][2].d; |
749 | |
750 | if (n) |
751 | { |
752 | /* -cot */ |
753 | t2 = pz * (fi + gi) / (fi + pz); |
754 | if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d)) |
755 | { |
756 | retval = (-sy * y); |
757 | goto ret; |
758 | } |
759 | t3 = (t2 < 0.0) ? -t2 : t2; |
760 | t4 = gi * ua26.d + t3 * ub26.d; |
761 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) |
762 | { |
763 | retval = (-sy * y); |
764 | goto ret; |
765 | } |
766 | } |
767 | else |
768 | { |
769 | /* tan */ |
770 | t2 = pz * (gi + fi) / (gi - pz); |
771 | if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d)) |
772 | { |
773 | retval = (sy * y); |
774 | goto ret; |
775 | } |
776 | t3 = (t2 < 0.0) ? -t2 : t2; |
777 | t4 = fi * ua25.d + t3 * ub25.d; |
778 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) |
779 | { |
780 | retval = (sy * y); |
781 | goto ret; |
782 | } |
783 | } |
784 | |
785 | /* Second stage */ |
786 | ffi = xfg[i][3].d; |
787 | EADD (z0, yya, z, zz); |
788 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); |
789 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
790 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); |
791 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
792 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); |
793 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); |
794 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); |
795 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); |
796 | |
797 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); |
798 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); |
799 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); |
800 | |
801 | if (n) |
802 | { |
803 | /* -cot */ |
804 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
805 | t10); |
806 | if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3)) |
807 | { |
808 | retval = (-sy * y); |
809 | goto ret; |
810 | } |
811 | } |
812 | else |
813 | { |
814 | /* tan */ |
815 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, |
816 | t10); |
817 | if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3)) |
818 | { |
819 | retval = (sy * y); |
820 | goto ret; |
821 | } |
822 | } |
823 | retval = tanMp (x); |
824 | goto ret; |
825 | |
826 | ret: |
827 | return retval; |
828 | } |
829 | |
830 | /* multiple precision stage */ |
831 | /* Convert x to multi precision number,compute tan(x) by mptan() routine */ |
832 | /* and converts result back to double */ |
833 | static double |
834 | SECTION |
835 | tanMp (double x) |
836 | { |
837 | int p; |
838 | double y; |
839 | mp_no mpy; |
840 | p = 32; |
841 | __mptan (x, &mpy, p); |
842 | __mp_dbl (&mpy, &y, p); |
843 | LIBC_PROBE (slowtan, 2, &x, &y); |
844 | return y; |
845 | } |
846 | |
847 | #ifndef __tan |
848 | libm_alias_double (__tan, tan) |
849 | #endif |
850 | |