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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. |
04277e02 | 4 | * Copyright (C) 2001-2019 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> | |
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, | |
c5d5d574 OB |
66 | s, sy, t, t1, t2, t3, t4, t7, t8, t9, t10, w, x2, xn, xx2, y, ya, |
67 | yya, z0, z, zz, z2, zz2; | |
58985aa9 | 68 | #ifndef DLA_FMS |
27ec37f1 | 69 | double t5, t6; |
a1a87169 | 70 | #endif |
e4d82761 | 71 | int p; |
27ec37f1 SP |
72 | number num, v; |
73 | mp_no mpa, mpt1, mpt2; | |
e4d82761 | 74 | |
804360ed JM |
75 | double retval; |
76 | ||
27ec37f1 SP |
77 | int __branred (double, double *, double *); |
78 | int __mpranred (double, mp_no *, int); | |
e4d82761 | 79 | |
eb92c487 | 80 | SET_RESTORE_ROUND_53BIT (FE_TONEAREST); |
804360ed | 81 | |
e4d82761 | 82 | /* x=+-INF, x=NaN */ |
27ec37f1 SP |
83 | num.d = x; |
84 | ux = num.i[HIGH_HALF]; | |
85 | if ((ux & 0x7ff00000) == 0x7ff00000) | |
86 | { | |
87 | if ((ux & 0x7fffffff) == 0x7ff00000) | |
88 | __set_errno (EDOM); | |
89 | retval = x - x; | |
90 | goto ret; | |
91 | } | |
e4d82761 | 92 | |
27ec37f1 | 93 | w = (x < 0.0) ? -x : x; |
e4d82761 UD |
94 | |
95 | /* (I) The case abs(x) <= 1.259e-8 */ | |
27ec37f1 SP |
96 | if (w <= g1.d) |
97 | { | |
d96164c3 | 98 | math_check_force_underflow_nonneg (w); |
27ec37f1 SP |
99 | retval = x; |
100 | goto ret; | |
101 | } | |
e4d82761 UD |
102 | |
103 | /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ | |
27ec37f1 SP |
104 | if (w <= g2.d) |
105 | { | |
27ec37f1 SP |
106 | /* First stage */ |
107 | x2 = x * x; | |
e4d82761 | 108 | |
27ec37f1 SP |
109 | t2 = d9.d + x2 * d11.d; |
110 | t2 = d7.d + x2 * t2; | |
111 | t2 = d5.d + x2 * t2; | |
112 | t2 = d3.d + x2 * t2; | |
113 | t2 *= x * x2; | |
114 | ||
115 | if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2)) | |
116 | { | |
117 | retval = y; | |
118 | goto ret; | |
119 | } | |
e4d82761 UD |
120 | |
121 | /* Second stage */ | |
27ec37f1 SP |
122 | c1 = a25.d + x2 * a27.d; |
123 | c1 = a23.d + x2 * c1; | |
124 | c1 = a21.d + x2 * c1; | |
125 | c1 = a19.d + x2 * c1; | |
126 | c1 = a17.d + x2 * c1; | |
127 | c1 = a15.d + x2 * c1; | |
128 | c1 *= x2; | |
129 | ||
130 | EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5); | |
131 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); | |
132 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
133 | ADD2 (a11.d, aa11.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 (a9.d, aa9.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 (a7.d, aa7.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 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); | |
140 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
141 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
142 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
143 | MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
144 | ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2); | |
145 | if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1)) | |
146 | { | |
147 | retval = y; | |
148 | goto ret; | |
149 | } | |
150 | retval = tanMp (x); | |
804360ed | 151 | goto ret; |
e4d82761 UD |
152 | } |
153 | ||
27ec37f1 SP |
154 | /* (III) The case 0.0608 < abs(x) <= 0.787 */ |
155 | if (w <= g3.d) | |
156 | { | |
27ec37f1 SP |
157 | /* First stage */ |
158 | i = ((int) (mfftnhf.d + TWO8 * w)); | |
159 | z = w - xfg[i][0].d; | |
160 | z2 = z * z; | |
c2d94018 | 161 | s = (x < 0.0) ? -1 : 1; |
27ec37f1 SP |
162 | pz = z + z * z2 * (e0.d + z2 * e1.d); |
163 | fi = xfg[i][1].d; | |
164 | gi = xfg[i][2].d; | |
165 | t2 = pz * (gi + fi) / (gi - pz); | |
166 | if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d)) | |
167 | { | |
168 | retval = (s * y); | |
169 | goto ret; | |
170 | } | |
171 | t3 = (t2 < 0.0) ? -t2 : t2; | |
172 | t4 = fi * ua3.d + t3 * ub3.d; | |
173 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
174 | { | |
175 | retval = (s * y); | |
176 | goto ret; | |
177 | } | |
e4d82761 | 178 | |
27ec37f1 SP |
179 | /* Second stage */ |
180 | ffi = xfg[i][3].d; | |
181 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); | |
182 | EMULV (z, z, z2, zz2, t1, t2, t3, t4, t5); | |
183 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); | |
184 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
185 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
186 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
187 | MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
188 | ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2); | |
189 | ||
190 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
191 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); | |
192 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); | |
193 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
194 | t10); | |
195 | ||
196 | if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3)) | |
197 | { | |
198 | retval = (s * y); | |
199 | goto ret; | |
200 | } | |
201 | retval = tanMp (x); | |
202 | goto ret; | |
203 | } | |
f7eac6eb | 204 | |
27ec37f1 SP |
205 | /* (---) The case 0.787 < abs(x) <= 25 */ |
206 | if (w <= g4.d) | |
207 | { | |
208 | /* Range reduction by algorithm i */ | |
209 | t = (x * hpinv.d + toint.d); | |
210 | xn = t - toint.d; | |
211 | v.d = t; | |
212 | t1 = (x - xn * mp1.d) - xn * mp2.d; | |
213 | n = v.i[LOW_HALF] & 0x00000001; | |
214 | da = xn * mp3.d; | |
215 | a = t1 - da; | |
216 | da = (t1 - a) - da; | |
217 | if (a < 0.0) | |
218 | { | |
219 | ya = -a; | |
220 | yya = -da; | |
c2d94018 | 221 | sy = -1; |
27ec37f1 SP |
222 | } |
223 | else | |
224 | { | |
225 | ya = a; | |
226 | yya = da; | |
c2d94018 | 227 | sy = 1; |
27ec37f1 SP |
228 | } |
229 | ||
230 | /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */ | |
231 | if (ya <= gy1.d) | |
232 | { | |
233 | retval = tanMp (x); | |
234 | goto ret; | |
235 | } | |
236 | ||
237 | /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */ | |
238 | if (ya <= gy2.d) | |
239 | { | |
240 | a2 = a * a; | |
241 | t2 = d9.d + a2 * d11.d; | |
242 | t2 = d7.d + a2 * t2; | |
243 | t2 = d5.d + a2 * t2; | |
244 | t2 = d3.d + a2 * t2; | |
245 | t2 = da + a * a2 * t2; | |
246 | ||
247 | if (n) | |
248 | { | |
249 | /* First stage -cot */ | |
250 | EADD (a, t2, b, db); | |
251 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, | |
252 | t9, t10); | |
253 | if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c)) | |
254 | { | |
255 | retval = (-y); | |
256 | goto ret; | |
257 | } | |
258 | } | |
259 | else | |
260 | { | |
261 | /* First stage tan */ | |
262 | if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a)) | |
263 | { | |
264 | retval = y; | |
265 | goto ret; | |
266 | } | |
267 | } | |
268 | /* Second stage */ | |
269 | /* Range reduction by algorithm ii */ | |
270 | t = (x * hpinv.d + toint.d); | |
271 | xn = t - toint.d; | |
272 | v.d = t; | |
273 | t1 = (x - xn * mp1.d) - xn * mp2.d; | |
274 | n = v.i[LOW_HALF] & 0x00000001; | |
275 | da = xn * pp3.d; | |
276 | t = t1 - da; | |
277 | da = (t1 - t) - da; | |
278 | t1 = xn * pp4.d; | |
279 | a = t - t1; | |
280 | da = ((t - a) - t1) + da; | |
281 | ||
282 | /* Second stage */ | |
283 | EADD (a, da, t1, t2); | |
284 | a = t1; | |
285 | da = t2; | |
286 | MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); | |
287 | ||
288 | c1 = a25.d + x2 * a27.d; | |
289 | c1 = a23.d + x2 * c1; | |
290 | c1 = a21.d + x2 * c1; | |
291 | c1 = a19.d + x2 * c1; | |
292 | c1 = a17.d + x2 * c1; | |
293 | c1 = a15.d + x2 * c1; | |
294 | c1 *= x2; | |
295 | ||
296 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); | |
297 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
298 | ADD2 (a11.d, aa11.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 (a9.d, aa9.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 (a7.d, aa7.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 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); | |
305 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
306 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
307 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
308 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
309 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); | |
310 | ||
311 | if (n) | |
312 | { | |
313 | /* Second stage -cot */ | |
314 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, | |
315 | t8, t9, t10); | |
316 | if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2)) | |
317 | { | |
318 | retval = (-y); | |
319 | goto ret; | |
320 | } | |
321 | } | |
322 | else | |
323 | { | |
324 | /* Second stage tan */ | |
325 | if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1)) | |
326 | { | |
327 | retval = y; | |
328 | goto ret; | |
329 | } | |
330 | } | |
331 | retval = tanMp (x); | |
332 | goto ret; | |
333 | } | |
334 | ||
335 | /* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */ | |
336 | ||
337 | /* First stage */ | |
338 | i = ((int) (mfftnhf.d + TWO8 * ya)); | |
339 | z = (z0 = (ya - xfg[i][0].d)) + yya; | |
340 | z2 = z * z; | |
341 | pz = z + z * z2 * (e0.d + z2 * e1.d); | |
342 | fi = xfg[i][1].d; | |
343 | gi = xfg[i][2].d; | |
344 | ||
345 | if (n) | |
346 | { | |
347 | /* -cot */ | |
348 | t2 = pz * (fi + gi) / (fi + pz); | |
349 | if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d)) | |
350 | { | |
351 | retval = (-sy * y); | |
352 | goto ret; | |
353 | } | |
354 | t3 = (t2 < 0.0) ? -t2 : t2; | |
355 | t4 = gi * ua10.d + t3 * ub10.d; | |
356 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) | |
357 | { | |
358 | retval = (-sy * y); | |
359 | goto ret; | |
360 | } | |
361 | } | |
362 | else | |
363 | { | |
364 | /* tan */ | |
365 | t2 = pz * (gi + fi) / (gi - pz); | |
366 | if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d)) | |
367 | { | |
368 | retval = (sy * y); | |
369 | goto ret; | |
370 | } | |
371 | t3 = (t2 < 0.0) ? -t2 : t2; | |
372 | t4 = fi * ua9.d + t3 * ub9.d; | |
373 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
374 | { | |
375 | retval = (sy * y); | |
376 | goto ret; | |
377 | } | |
378 | } | |
e4d82761 | 379 | |
27ec37f1 SP |
380 | /* Second stage */ |
381 | ffi = xfg[i][3].d; | |
382 | EADD (z0, yya, z, zz) | |
c5d5d574 | 383 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); |
27ec37f1 SP |
384 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); |
385 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); | |
386 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
387 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
388 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
389 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
390 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); | |
391 | ||
392 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
393 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); | |
394 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); | |
395 | ||
396 | if (n) | |
397 | { | |
398 | /* -cot */ | |
399 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
400 | t10); | |
401 | if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3)) | |
402 | { | |
403 | retval = (-sy * y); | |
404 | goto ret; | |
405 | } | |
406 | } | |
407 | else | |
408 | { | |
409 | /* tan */ | |
410 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
411 | t10); | |
412 | if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3)) | |
413 | { | |
414 | retval = (sy * y); | |
415 | goto ret; | |
416 | } | |
417 | } | |
418 | ||
419 | retval = tanMp (x); | |
420 | goto ret; | |
421 | } | |
e4d82761 UD |
422 | |
423 | /* (---) The case 25 < abs(x) <= 1e8 */ | |
27ec37f1 SP |
424 | if (w <= g5.d) |
425 | { | |
426 | /* Range reduction by algorithm ii */ | |
427 | t = (x * hpinv.d + toint.d); | |
428 | xn = t - toint.d; | |
429 | v.d = t; | |
430 | t1 = (x - xn * mp1.d) - xn * mp2.d; | |
431 | n = v.i[LOW_HALF] & 0x00000001; | |
432 | da = xn * pp3.d; | |
433 | t = t1 - da; | |
434 | da = (t1 - t) - da; | |
435 | t1 = xn * pp4.d; | |
436 | a = t - t1; | |
437 | da = ((t - a) - t1) + da; | |
438 | EADD (a, da, t1, t2); | |
439 | a = t1; | |
440 | da = t2; | |
441 | if (a < 0.0) | |
442 | { | |
443 | ya = -a; | |
444 | yya = -da; | |
c2d94018 | 445 | sy = -1; |
27ec37f1 SP |
446 | } |
447 | else | |
448 | { | |
449 | ya = a; | |
450 | yya = da; | |
c2d94018 | 451 | sy = 1; |
27ec37f1 SP |
452 | } |
453 | ||
454 | /* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */ | |
455 | if (ya <= gy1.d) | |
456 | { | |
457 | retval = tanMp (x); | |
458 | goto ret; | |
459 | } | |
460 | ||
461 | /* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */ | |
462 | if (ya <= gy2.d) | |
463 | { | |
464 | a2 = a * a; | |
465 | t2 = d9.d + a2 * d11.d; | |
466 | t2 = d7.d + a2 * t2; | |
467 | t2 = d5.d + a2 * t2; | |
468 | t2 = d3.d + a2 * t2; | |
469 | t2 = da + a * a2 * t2; | |
470 | ||
471 | if (n) | |
472 | { | |
473 | /* First stage -cot */ | |
474 | EADD (a, t2, b, db); | |
475 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, | |
476 | t9, t10); | |
477 | if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c)) | |
478 | { | |
479 | retval = (-y); | |
480 | goto ret; | |
481 | } | |
482 | } | |
483 | else | |
484 | { | |
485 | /* First stage tan */ | |
486 | if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a)) | |
487 | { | |
488 | retval = y; | |
489 | goto ret; | |
490 | } | |
491 | } | |
492 | ||
493 | /* Second stage */ | |
494 | MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); | |
495 | c1 = a25.d + x2 * a27.d; | |
496 | c1 = a23.d + x2 * c1; | |
497 | c1 = a21.d + x2 * c1; | |
498 | c1 = a19.d + x2 * c1; | |
499 | c1 = a17.d + x2 * c1; | |
500 | c1 = a15.d + x2 * c1; | |
501 | c1 *= x2; | |
502 | ||
503 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); | |
504 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
505 | ADD2 (a11.d, aa11.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 (a9.d, aa9.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 (a7.d, aa7.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 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); | |
512 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
513 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
514 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
515 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
516 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); | |
517 | ||
518 | if (n) | |
519 | { | |
520 | /* Second stage -cot */ | |
521 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, | |
522 | t8, t9, t10); | |
523 | if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2)) | |
524 | { | |
525 | retval = (-y); | |
526 | goto ret; | |
527 | } | |
528 | } | |
529 | else | |
530 | { | |
531 | /* Second stage tan */ | |
532 | if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1)) | |
533 | { | |
534 | retval = (y); | |
535 | goto ret; | |
536 | } | |
537 | } | |
538 | retval = tanMp (x); | |
539 | goto ret; | |
540 | } | |
541 | ||
542 | /* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */ | |
543 | /* First stage */ | |
544 | i = ((int) (mfftnhf.d + TWO8 * ya)); | |
545 | z = (z0 = (ya - xfg[i][0].d)) + yya; | |
546 | z2 = z * z; | |
547 | pz = z + z * z2 * (e0.d + z2 * e1.d); | |
548 | fi = xfg[i][1].d; | |
549 | gi = xfg[i][2].d; | |
550 | ||
551 | if (n) | |
552 | { | |
553 | /* -cot */ | |
554 | t2 = pz * (fi + gi) / (fi + pz); | |
555 | if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d)) | |
556 | { | |
557 | retval = (-sy * y); | |
558 | goto ret; | |
559 | } | |
560 | t3 = (t2 < 0.0) ? -t2 : t2; | |
561 | t4 = gi * ua18.d + t3 * ub18.d; | |
562 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) | |
563 | { | |
564 | retval = (-sy * y); | |
565 | goto ret; | |
566 | } | |
567 | } | |
568 | else | |
569 | { | |
570 | /* tan */ | |
571 | t2 = pz * (gi + fi) / (gi - pz); | |
572 | if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d)) | |
573 | { | |
574 | retval = (sy * y); | |
575 | goto ret; | |
576 | } | |
577 | t3 = (t2 < 0.0) ? -t2 : t2; | |
578 | t4 = fi * ua17.d + t3 * ub17.d; | |
579 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
580 | { | |
581 | retval = (sy * y); | |
582 | goto ret; | |
583 | } | |
584 | } | |
e4d82761 UD |
585 | |
586 | /* Second stage */ | |
27ec37f1 SP |
587 | ffi = xfg[i][3].d; |
588 | EADD (z0, yya, z, zz); | |
589 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); | |
590 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); | |
591 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); | |
592 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
593 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
594 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
595 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
596 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); | |
597 | ||
598 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
599 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); | |
600 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); | |
601 | ||
602 | if (n) | |
603 | { | |
604 | /* -cot */ | |
605 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
606 | t10); | |
607 | if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3)) | |
608 | { | |
609 | retval = (-sy * y); | |
610 | goto ret; | |
611 | } | |
612 | } | |
613 | else | |
614 | { | |
615 | /* tan */ | |
616 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
617 | t10); | |
618 | if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3)) | |
619 | { | |
620 | retval = (sy * y); | |
621 | goto ret; | |
622 | } | |
623 | } | |
624 | retval = tanMp (x); | |
804360ed | 625 | goto ret; |
e4d82761 UD |
626 | } |
627 | ||
e4d82761 UD |
628 | /* (---) The case 1e8 < abs(x) < 2**1024 */ |
629 | /* Range reduction by algorithm iii */ | |
27ec37f1 SP |
630 | n = (__branred (x, &a, &da)) & 0x00000001; |
631 | EADD (a, da, t1, t2); | |
632 | a = t1; | |
633 | da = t2; | |
634 | if (a < 0.0) | |
635 | { | |
636 | ya = -a; | |
637 | yya = -da; | |
c2d94018 | 638 | sy = -1; |
27ec37f1 SP |
639 | } |
640 | else | |
641 | { | |
642 | ya = a; | |
643 | yya = da; | |
c2d94018 | 644 | sy = 1; |
27ec37f1 | 645 | } |
e4d82761 UD |
646 | |
647 | /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ | |
27ec37f1 SP |
648 | if (ya <= gy1.d) |
649 | { | |
650 | retval = tanMp (x); | |
651 | goto ret; | |
652 | } | |
e4d82761 UD |
653 | |
654 | /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ | |
27ec37f1 SP |
655 | if (ya <= gy2.d) |
656 | { | |
657 | a2 = a * a; | |
658 | t2 = d9.d + a2 * d11.d; | |
659 | t2 = d7.d + a2 * t2; | |
660 | t2 = d5.d + a2 * t2; | |
661 | t2 = d3.d + a2 * t2; | |
662 | t2 = da + a * a2 * t2; | |
663 | if (n) | |
664 | { | |
665 | /* First stage -cot */ | |
666 | EADD (a, t2, b, db); | |
667 | DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
668 | t10); | |
669 | if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c)) | |
670 | { | |
671 | retval = (-y); | |
672 | goto ret; | |
673 | } | |
674 | } | |
675 | else | |
676 | { | |
677 | /* First stage tan */ | |
678 | if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a)) | |
679 | { | |
680 | retval = y; | |
681 | goto ret; | |
682 | } | |
683 | } | |
684 | ||
685 | /* Second stage */ | |
686 | /* Reduction by algorithm iv */ | |
687 | p = 10; | |
688 | n = (__mpranred (x, &mpa, p)) & 0x00000001; | |
689 | __mp_dbl (&mpa, &a, p); | |
690 | __dbl_mp (a, &mpt1, p); | |
691 | __sub (&mpa, &mpt1, &mpt2, p); | |
692 | __mp_dbl (&mpt2, &da, p); | |
693 | ||
694 | MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8); | |
695 | ||
696 | c1 = a25.d + x2 * a27.d; | |
697 | c1 = a23.d + x2 * c1; | |
698 | c1 = a21.d + x2 * c1; | |
699 | c1 = a19.d + x2 * c1; | |
700 | c1 = a17.d + x2 * c1; | |
701 | c1 = a15.d + x2 * c1; | |
702 | c1 *= x2; | |
703 | ||
704 | ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2); | |
705 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
706 | ADD2 (a11.d, aa11.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 (a9.d, aa9.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 (a7.d, aa7.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 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2); | |
713 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
714 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
715 | MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
716 | MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
717 | ADD2 (a, da, c2, cc2, c1, cc1, t1, t2); | |
718 | ||
719 | if (n) | |
720 | { | |
721 | /* Second stage -cot */ | |
722 | DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8, | |
723 | t9, t10); | |
724 | if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2)) | |
725 | { | |
726 | retval = (-y); | |
727 | goto ret; | |
728 | } | |
729 | } | |
730 | else | |
731 | { | |
732 | /* Second stage tan */ | |
733 | if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1)) | |
734 | { | |
735 | retval = y; | |
736 | goto ret; | |
737 | } | |
738 | } | |
739 | retval = tanMp (x); | |
740 | goto ret; | |
741 | } | |
e4d82761 UD |
742 | |
743 | /* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */ | |
744 | /* First stage */ | |
27ec37f1 SP |
745 | i = ((int) (mfftnhf.d + TWO8 * ya)); |
746 | z = (z0 = (ya - xfg[i][0].d)) + yya; | |
747 | z2 = z * z; | |
748 | pz = z + z * z2 * (e0.d + z2 * e1.d); | |
749 | fi = xfg[i][1].d; | |
750 | gi = xfg[i][2].d; | |
751 | ||
752 | if (n) | |
753 | { | |
754 | /* -cot */ | |
755 | t2 = pz * (fi + gi) / (fi + pz); | |
756 | if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d)) | |
757 | { | |
758 | retval = (-sy * y); | |
759 | goto ret; | |
760 | } | |
761 | t3 = (t2 < 0.0) ? -t2 : t2; | |
762 | t4 = gi * ua26.d + t3 * ub26.d; | |
763 | if ((y = gi - (t2 - t4)) == gi - (t2 + t4)) | |
764 | { | |
765 | retval = (-sy * y); | |
766 | goto ret; | |
767 | } | |
768 | } | |
769 | else | |
770 | { | |
771 | /* tan */ | |
772 | t2 = pz * (gi + fi) / (gi - pz); | |
773 | if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d)) | |
774 | { | |
775 | retval = (sy * y); | |
776 | goto ret; | |
777 | } | |
778 | t3 = (t2 < 0.0) ? -t2 : t2; | |
779 | t4 = fi * ua25.d + t3 * ub25.d; | |
780 | if ((y = fi + (t2 - t4)) == fi + (t2 + t4)) | |
781 | { | |
782 | retval = (sy * y); | |
783 | goto ret; | |
784 | } | |
785 | } | |
e4d82761 UD |
786 | |
787 | /* Second stage */ | |
788 | ffi = xfg[i][3].d; | |
27ec37f1 SP |
789 | EADD (z0, yya, z, zz); |
790 | MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8); | |
791 | c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d)); | |
792 | ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2); | |
793 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
794 | ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2); | |
795 | MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8); | |
796 | MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8); | |
797 | ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2); | |
798 | ||
799 | ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2); | |
800 | MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8); | |
801 | SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2); | |
802 | ||
803 | if (n) | |
804 | { | |
805 | /* -cot */ | |
806 | DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
807 | t10); | |
808 | if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3)) | |
809 | { | |
810 | retval = (-sy * y); | |
811 | goto ret; | |
812 | } | |
813 | } | |
814 | else | |
815 | { | |
816 | /* tan */ | |
817 | DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9, | |
818 | t10); | |
819 | if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3)) | |
820 | { | |
821 | retval = (sy * y); | |
822 | goto ret; | |
823 | } | |
824 | } | |
825 | retval = tanMp (x); | |
804360ed | 826 | goto ret; |
e4d82761 | 827 | |
27ec37f1 | 828 | ret: |
804360ed JM |
829 | return retval; |
830 | } | |
e4d82761 UD |
831 | |
832 | /* multiple precision stage */ | |
833 | /* Convert x to multi precision number,compute tan(x) by mptan() routine */ | |
834 | /* and converts result back to double */ | |
31d3cc00 UD |
835 | static double |
836 | SECTION | |
27ec37f1 | 837 | tanMp (double x) |
e4d82761 UD |
838 | { |
839 | int p; | |
840 | double y; | |
841 | mp_no mpy; | |
27ec37f1 SP |
842 | p = 32; |
843 | __mptan (x, &mpy, p); | |
844 | __mp_dbl (&mpy, &y, p); | |
10e1cf6b | 845 | LIBC_PROBE (slowtan, 2, &x, &y); |
e4d82761 | 846 | return y; |
f7eac6eb | 847 | } |
e4d82761 | 848 | |
527cd19c | 849 | #ifndef __tan |
38722448 | 850 | libm_alias_double (__tan, tan) |
cccda09f | 851 | #endif |