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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. |
bfff8b1b | 4 | * Copyright (C) 2001-2017 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: 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> | |
38722448 | 44 | #include <libm-alias-double.h> |
804360ed | 45 | #include <fenv.h> |
10e1cf6b | 46 | #include <stap-probe.h> |
15b3c029 | 47 | |
31d3cc00 UD |
48 | #ifndef SECTION |
49 | # define SECTION | |
50 | #endif | |
51 | ||
27ec37f1 SP |
52 | static double tanMp (double); |
53 | void __mptan (double, mp_no *, int); | |
f7eac6eb | 54 | |
31d3cc00 UD |
55 | double |
56 | SECTION | |
527cd19c | 57 | __tan (double x) |
27ec37f1 | 58 | { |
e4d82761 UD |
59 | #include "utan.h" |
60 | #include "utan.tbl" | |
f7eac6eb | 61 | |
27ec37f1 SP |
62 | int ux, i, n; |
63 | double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz, | |
c5d5d574 OB |
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; | |
58985aa9 | 66 | #ifndef DLA_FMS |
27ec37f1 | 67 | double t5, t6; |
a1a87169 | 68 | #endif |
e4d82761 | 69 | int p; |
27ec37f1 SP |
70 | number num, v; |
71 | mp_no mpa, mpt1, mpt2; | |
e4d82761 | 72 | |
804360ed JM |
73 | double retval; |
74 | ||
27ec37f1 SP |
75 | int __branred (double, double *, double *); |
76 | int __mpranred (double, mp_no *, int); | |
e4d82761 | 77 | |
eb92c487 | 78 | SET_RESTORE_ROUND_53BIT (FE_TONEAREST); |
804360ed | 79 | |
e4d82761 | 80 | /* x=+-INF, x=NaN */ |
27ec37f1 SP |
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 | } | |
e4d82761 | 90 | |
27ec37f1 | 91 | w = (x < 0.0) ? -x : x; |
e4d82761 UD |
92 | |
93 | /* (I) The case abs(x) <= 1.259e-8 */ | |
27ec37f1 SP |
94 | if (w <= g1.d) |
95 | { | |
d96164c3 | 96 | math_check_force_underflow_nonneg (w); |
27ec37f1 SP |
97 | retval = x; |
98 | goto ret; | |
99 | } | |
e4d82761 UD |
100 | |
101 | /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ | |
27ec37f1 SP |
102 | if (w <= g2.d) |
103 | { | |
27ec37f1 SP |
104 | /* First stage */ |
105 | x2 = x * x; | |
e4d82761 | 106 | |
27ec37f1 SP |
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 | } | |
e4d82761 UD |
118 | |
119 | /* Second stage */ | |
27ec37f1 SP |
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); | |
804360ed | 149 | goto ret; |
e4d82761 UD |
150 | } |
151 | ||
27ec37f1 SP |
152 | /* (III) The case 0.0608 < abs(x) <= 0.787 */ |
153 | if (w <= g3.d) | |
154 | { | |
27ec37f1 SP |
155 | /* First stage */ |
156 | i = ((int) (mfftnhf.d + TWO8 * w)); | |
157 | z = w - xfg[i][0].d; | |
158 | z2 = z * z; | |
c2d94018 | 159 | s = (x < 0.0) ? -1 : 1; |
27ec37f1 SP |
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 | } | |
e4d82761 | 176 | |
27ec37f1 SP |
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 | } | |
f7eac6eb | 202 | |
27ec37f1 SP |
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; | |
c2d94018 | 219 | sy = -1; |
27ec37f1 SP |
220 | } |
221 | else | |
222 | { | |
223 | ya = a; | |
224 | yya = da; | |
c2d94018 | 225 | sy = 1; |
27ec37f1 SP |
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 | } | |
e4d82761 | 377 | |
27ec37f1 SP |
378 | /* Second stage */ |
379 | ffi = xfg[i][3].d; | |
380 | EADD (z0, yya, z, zz) | |
c5d5d574 | 381 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); |
27ec37f1 SP |
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 | } | |
e4d82761 UD |
420 | |
421 | /* (---) The case 25 < abs(x) <= 1e8 */ | |
27ec37f1 SP |
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; | |
c2d94018 | 443 | sy = -1; |
27ec37f1 SP |
444 | } |
445 | else | |
446 | { | |
447 | ya = a; | |
448 | yya = da; | |
c2d94018 | 449 | sy = 1; |
27ec37f1 SP |
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 | } | |
e4d82761 UD |
583 | |
584 | /* Second stage */ | |
27ec37f1 SP |
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); | |
804360ed | 623 | goto ret; |
e4d82761 UD |
624 | } |
625 | ||
e4d82761 UD |
626 | /* (---) The case 1e8 < abs(x) < 2**1024 */ |
627 | /* Range reduction by algorithm iii */ | |
27ec37f1 SP |
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; | |
c2d94018 | 636 | sy = -1; |
27ec37f1 SP |
637 | } |
638 | else | |
639 | { | |
640 | ya = a; | |
641 | yya = da; | |
c2d94018 | 642 | sy = 1; |
27ec37f1 | 643 | } |
e4d82761 UD |
644 | |
645 | /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ | |
27ec37f1 SP |
646 | if (ya <= gy1.d) |
647 | { | |
648 | retval = tanMp (x); | |
649 | goto ret; | |
650 | } | |
e4d82761 UD |
651 | |
652 | /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ | |
27ec37f1 SP |
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 | } | |
e4d82761 UD |
740 | |
741 | /* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */ | |
742 | /* First stage */ | |
27ec37f1 SP |
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 | } | |
e4d82761 UD |
784 | |
785 | /* Second stage */ | |
786 | ffi = xfg[i][3].d; | |
27ec37f1 SP |
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); | |
804360ed | 824 | goto ret; |
e4d82761 | 825 | |
27ec37f1 | 826 | ret: |
804360ed JM |
827 | return retval; |
828 | } | |
e4d82761 UD |
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 */ | |
31d3cc00 UD |
833 | static double |
834 | SECTION | |
27ec37f1 | 835 | tanMp (double x) |
e4d82761 UD |
836 | { |
837 | int p; | |
838 | double y; | |
839 | mp_no mpy; | |
27ec37f1 SP |
840 | p = 32; |
841 | __mptan (x, &mpy, p); | |
842 | __mp_dbl (&mpy, &y, p); | |
10e1cf6b | 843 | LIBC_PROBE (slowtan, 2, &x, &y); |
e4d82761 | 844 | return y; |
f7eac6eb | 845 | } |
e4d82761 | 846 | |
527cd19c | 847 | #ifndef __tan |
38722448 | 848 | libm_alias_double (__tan, tan) |
cccda09f | 849 | #endif |