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1 | .file "libm_sincos.s" |
2 | ||
3 | ||
4 | // Copyright (c) 2002 - 2005, Intel Corporation | |
5 | // All rights reserved. | |
6 | // | |
7 | // Contributed 2002 by the Intel Numerics Group, Intel Corporation | |
8 | // | |
9 | // Redistribution and use in source and binary forms, with or without | |
10 | // modification, are permitted provided that the following conditions are | |
11 | // met: | |
12 | // | |
13 | // * Redistributions of source code must retain the above copyright | |
14 | // notice, this list of conditions and the following disclaimer. | |
15 | // | |
16 | // * Redistributions in binary form must reproduce the above copyright | |
17 | // notice, this list of conditions and the following disclaimer in the | |
18 | // documentation and/or other materials provided with the distribution. | |
19 | // | |
20 | // * The name of Intel Corporation may not be used to endorse or promote | |
21 | // products derived from this software without specific prior written | |
22 | // permission. | |
23 | ||
24 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
25 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
26 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
27 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS | |
28 | // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, | |
29 | // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, | |
30 | // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR | |
31 | // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY | |
32 | // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING | |
33 | // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS | |
34 | // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
35 | // | |
36 | // Intel Corporation is the author of this code, and requests that all | |
37 | // problem reports or change requests be submitted to it directly at | |
38 | // http://www.intel.com/software/products/opensource/libraries/num.htm. | |
39 | // | |
40 | // History | |
41 | //============================================================== | |
42 | // 02/01/02 Initial version | |
43 | // 02/18/02 Large arguments processing routine is excluded. | |
44 | // External interface entry points are added | |
45 | // 03/13/02 Corrected restore of predicate registers | |
46 | // 03/19/02 Added stack unwind around call to __libm_cis_large | |
47 | // 09/05/02 Work range is widened by reduction strengthen (3 parts of Pi/16) | |
48 | // 02/10/03 Reordered header: .section, .global, .proc, .align | |
49 | // 08/08/03 Improved performance | |
50 | // 02/11/04 cis is moved to the separate file. | |
51 | // 03/31/05 Reformatted delimiters between data tables | |
52 | // | |
53 | // API | |
54 | //============================================================== | |
55 | // 1) void sincos(double, double*s, double*c) | |
56 | // 2) __libm_sincos - internal LIBM function, that accepts | |
57 | // argument in f8 and returns cosine through f8, sine through f9 | |
58 | // | |
59 | // Overview of operation | |
60 | //============================================================== | |
61 | // | |
62 | // Step 1 | |
63 | // ====== | |
64 | // Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k where k=4 | |
65 | // divide x by pi/2^k. | |
66 | // Multiply by 2^k/pi. | |
67 | // nfloat = Round result to integer (round-to-nearest) | |
68 | // | |
69 | // r = x - nfloat * pi/2^k | |
70 | // Do this as ((((x - nfloat * HIGH(pi/2^k))) - | |
71 | // nfloat * LOW(pi/2^k)) - | |
72 | // nfloat * LOWEST(pi/2^k) for increased accuracy. | |
73 | // pi/2^k is stored as two numbers that when added make pi/2^k. | |
74 | // pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k) | |
75 | // HIGH and LOW parts are rounded to zero values, | |
76 | // and LOWEST is rounded to nearest one. | |
77 | // | |
78 | // x = (nfloat * pi/2^k) + r | |
79 | // r is small enough that we can use a polynomial approximation | |
80 | // and is referred to as the reduced argument. | |
81 | // | |
82 | // Step 3 | |
83 | // ====== | |
84 | // Take the unreduced part and remove the multiples of 2pi. | |
85 | // So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits | |
86 | // | |
87 | // nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1) | |
88 | // N * 2^(k+1) | |
89 | // nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k | |
90 | // nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k | |
91 | // nfloat * pi/2^k = N2pi + M * pi/2^k | |
92 | // | |
93 | // | |
94 | // Sin(x) = Sin((nfloat * pi/2^k) + r) | |
95 | // = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r) | |
96 | // | |
97 | // Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k) | |
98 | // = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k) | |
99 | // = Sin(Mpi/2^k) | |
100 | // | |
101 | // Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k) | |
102 | // = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k) | |
103 | // = Cos(Mpi/2^k) | |
104 | // | |
105 | // Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) | |
106 | // | |
107 | // | |
108 | // Step 4 | |
109 | // ====== | |
110 | // 0 <= M < 2^(k+1) | |
111 | // There are 2^(k+1) Sin entries in a table. | |
112 | // There are 2^(k+1) Cos entries in a table. | |
113 | // | |
114 | // Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup. | |
115 | // | |
116 | // | |
117 | // Step 5 | |
118 | // ====== | |
119 | // Calculate Cos(r) and Sin(r) by polynomial approximation. | |
120 | // | |
121 | // Cos(r) = 1 + r^2 q1 + r^4 q2 + r^6 q3 + ... = Series for Cos | |
122 | // Sin(r) = r + r^3 p1 + r^5 p2 + r^7 p3 + ... = Series for Sin | |
123 | // | |
124 | // and the coefficients q1, q2, ... and p1, p2, ... are stored in a table | |
125 | // | |
126 | // | |
127 | // Calculate | |
128 | // Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) | |
129 | // | |
130 | // as follows | |
131 | // | |
132 | // S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k) | |
133 | // rsq = r*r | |
134 | // | |
135 | // | |
136 | // P = p1 + r^2p2 + r^4p3 + r^6p4 | |
137 | // Q = q1 + r^2q2 + r^4q3 + r^6q4 | |
138 | // | |
139 | // rcub = r * rsq | |
140 | // Sin(r) = r + rcub * P | |
141 | // = r + r^3p1 + r^5p2 + r^7p3 + r^9p4 + ... = Sin(r) | |
142 | // | |
143 | // The coefficients are not exactly these values, but almost. | |
144 | // | |
145 | // p1 = -1/6 = -1/3! | |
146 | // p2 = 1/120 = 1/5! | |
147 | // p3 = -1/5040 = -1/7! | |
148 | // p4 = 1/362889 = 1/9! | |
149 | // | |
150 | // P = r + rcub * P | |
151 | // | |
152 | // Answer = S[m] Cos(r) + C[m] P | |
153 | // | |
154 | // Cos(r) = 1 + rsq Q | |
155 | // Cos(r) = 1 + r^2 Q | |
156 | // Cos(r) = 1 + r^2 (q1 + r^2q2 + r^4q3 + r^6q4) | |
157 | // Cos(r) = 1 + r^2q1 + r^4q2 + r^6q3 + r^8q4 + ... | |
158 | // | |
159 | // S[m] Cos(r) = S[m](1 + rsq Q) | |
160 | // S[m] Cos(r) = S[m] + S[m] rsq Q | |
161 | // S[m] Cos(r) = S[m] + s_rsq Q | |
162 | // Q = S[m] + s_rsq Q | |
163 | // | |
164 | // Then, | |
165 | // | |
166 | // Answer = Q + C[m] P | |
167 | ||
168 | // Registers used | |
169 | //============================================================== | |
170 | // general input registers: | |
171 | // r14 -> r39 | |
172 | ||
173 | // predicate registers used: | |
174 | // p6 -> p14 | |
175 | // | |
176 | // floating-point registers used | |
177 | // f9 -> f15 | |
178 | // f32 -> f67 | |
179 | ||
180 | // Assembly macros | |
181 | //============================================================== | |
182 | ||
183 | cis_Arg = f8 | |
184 | ||
185 | cis_Sin_res = f9 | |
186 | cis_Cos_res = f8 | |
187 | ||
188 | cis_NORM_f8 = f10 | |
189 | cis_W = f11 | |
190 | cis_int_Nfloat = f12 | |
191 | cis_Nfloat = f13 | |
192 | ||
193 | cis_r = f14 | |
194 | cis_rsq = f15 | |
195 | cis_rcub = f32 | |
196 | ||
197 | cis_Inv_Pi_by_16 = f33 | |
198 | cis_Pi_by_16_hi = f34 | |
199 | cis_Pi_by_16_lo = f35 | |
200 | ||
201 | cis_Inv_Pi_by_64 = f36 | |
202 | cis_Pi_by_16_lowest = f37 | |
203 | cis_r_exact = f38 | |
204 | ||
205 | ||
206 | cis_P1 = f39 | |
207 | cis_Q1 = f40 | |
208 | cis_P2 = f41 | |
209 | cis_Q2 = f42 | |
210 | cis_P3 = f43 | |
211 | cis_Q3 = f44 | |
212 | cis_P4 = f45 | |
213 | cis_Q4 = f46 | |
214 | ||
215 | cis_P_temp1 = f47 | |
216 | cis_P_temp2 = f48 | |
217 | ||
218 | cis_Q_temp1 = f49 | |
219 | cis_Q_temp2 = f50 | |
220 | ||
221 | cis_P = f51 | |
222 | ||
223 | cis_SIG_INV_PI_BY_16_2TO61 = f52 | |
224 | cis_RSHF_2TO61 = f53 | |
225 | cis_RSHF = f54 | |
226 | cis_2TOM61 = f55 | |
227 | cis_NFLOAT = f56 | |
228 | cis_W_2TO61_RSH = f57 | |
229 | ||
230 | cis_tmp = f58 | |
231 | ||
232 | cis_Sm_sin = f59 | |
233 | cis_Cm_sin = f60 | |
234 | ||
235 | cis_Sm_cos = f61 | |
236 | cis_Cm_cos = f62 | |
237 | ||
238 | cis_srsq_sin = f63 | |
239 | cis_srsq_cos = f64 | |
240 | ||
241 | cis_Q_sin = f65 | |
242 | cis_Q_cos = f66 | |
243 | cis_Q = f67 | |
244 | ||
245 | ///////////////////////////////////////////////////////////// | |
246 | ||
247 | cis_pResSin = r33 | |
248 | cis_pResCos = r34 | |
249 | ||
250 | cis_GR_sig_inv_pi_by_16 = r14 | |
251 | cis_GR_rshf_2to61 = r15 | |
252 | cis_GR_rshf = r16 | |
253 | cis_GR_exp_2tom61 = r17 | |
254 | cis_GR_n = r18 | |
255 | cis_GR_n_sin = r19 | |
256 | cis_exp_limit = r20 | |
257 | cis_r_signexp = r21 | |
258 | cis_AD_1 = r22 | |
259 | cis_r_sincos = r23 | |
260 | cis_r_exp = r24 | |
261 | cis_r_17_ones = r25 | |
262 | cis_GR_m_sin = r26 | |
263 | cis_GR_32m_sin = r26 | |
264 | cis_GR_n_cos = r27 | |
265 | cis_GR_m_cos = r28 | |
266 | cis_GR_32m_cos = r28 | |
267 | cis_AD_2_sin = r29 | |
268 | cis_AD_2_cos = r30 | |
269 | cis_gr_tmp = r31 | |
270 | ||
271 | GR_SAVE_B0 = r35 | |
272 | GR_SAVE_GP = r36 | |
273 | rB0_SAVED = r37 | |
274 | GR_SAVE_PFS = r38 | |
275 | GR_SAVE_PR = r39 | |
276 | ||
277 | RODATA | |
278 | ||
279 | .align 16 | |
280 | // Pi/16 parts | |
281 | LOCAL_OBJECT_START(double_cis_pi) | |
282 | data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part | |
283 | data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part | |
284 | data8 0xA4093822299F31D0, 0x00003F7A // pi/16 3rd part | |
285 | LOCAL_OBJECT_END(double_cis_pi) | |
286 | ||
287 | // Coefficients for polynomials | |
288 | LOCAL_OBJECT_START(double_cis_pq_k4) | |
289 | data8 0x3EC71C963717C63A // P4 | |
290 | data8 0x3EF9FFBA8F191AE6 // Q4 | |
291 | data8 0xBF2A01A00F4E11A8 // P3 | |
292 | data8 0xBF56C16C05AC77BF // Q3 | |
293 | data8 0x3F8111111110F167 // P2 | |
294 | data8 0x3FA555555554DD45 // Q2 | |
295 | data8 0xBFC5555555555555 // P1 | |
296 | data8 0xBFDFFFFFFFFFFFFC // Q1 | |
297 | LOCAL_OBJECT_END(double_cis_pq_k4) | |
298 | ||
299 | // Sincos table (S[m], C[m]) | |
300 | LOCAL_OBJECT_START(double_sin_cos_beta_k4) | |
301 | data8 0x0000000000000000 , 0x00000000 // sin( 0 pi/16) S0 | |
302 | data8 0x8000000000000000 , 0x00003fff // cos( 0 pi/16) C0 | |
303 | // | |
304 | data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin( 1 pi/16) S1 | |
305 | data8 0xfb14be7fbae58157 , 0x00003ffe // cos( 1 pi/16) C1 | |
306 | // | |
307 | data8 0xc3ef1535754b168e , 0x00003ffd // sin( 2 pi/16) S2 | |
308 | data8 0xec835e79946a3146 , 0x00003ffe // cos( 2 pi/16) C2 | |
309 | // | |
310 | data8 0x8e39d9cd73464364 , 0x00003ffe // sin( 3 pi/16) S3 | |
311 | data8 0xd4db3148750d181a , 0x00003ffe // cos( 3 pi/16) C3 | |
312 | // | |
313 | data8 0xb504f333f9de6484 , 0x00003ffe // sin( 4 pi/16) S4 | |
314 | data8 0xb504f333f9de6484 , 0x00003ffe // cos( 4 pi/16) C4 | |
315 | // | |
316 | data8 0xd4db3148750d181a , 0x00003ffe // sin( 5 pi/16) C3 | |
317 | data8 0x8e39d9cd73464364 , 0x00003ffe // cos( 5 pi/16) S3 | |
318 | // | |
319 | data8 0xec835e79946a3146 , 0x00003ffe // sin( 6 pi/16) C2 | |
320 | data8 0xc3ef1535754b168e , 0x00003ffd // cos( 6 pi/16) S2 | |
321 | // | |
322 | data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 7 pi/16) C1 | |
323 | data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos( 7 pi/16) S1 | |
324 | // | |
325 | data8 0x8000000000000000 , 0x00003fff // sin( 8 pi/16) C0 | |
326 | data8 0x0000000000000000 , 0x00000000 // cos( 8 pi/16) S0 | |
327 | // | |
328 | data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 9 pi/16) C1 | |
329 | data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos( 9 pi/16) -S1 | |
330 | // | |
331 | data8 0xec835e79946a3146 , 0x00003ffe // sin(10 pi/16) C2 | |
332 | data8 0xc3ef1535754b168e , 0x0000bffd // cos(10 pi/16) -S2 | |
333 | // | |
334 | data8 0xd4db3148750d181a , 0x00003ffe // sin(11 pi/16) C3 | |
335 | data8 0x8e39d9cd73464364 , 0x0000bffe // cos(11 pi/16) -S3 | |
336 | // | |
337 | data8 0xb504f333f9de6484 , 0x00003ffe // sin(12 pi/16) S4 | |
338 | data8 0xb504f333f9de6484 , 0x0000bffe // cos(12 pi/16) -S4 | |
339 | // | |
340 | data8 0x8e39d9cd73464364 , 0x00003ffe // sin(13 pi/16) S3 | |
341 | data8 0xd4db3148750d181a , 0x0000bffe // cos(13 pi/16) -C3 | |
342 | // | |
343 | data8 0xc3ef1535754b168e , 0x00003ffd // sin(14 pi/16) S2 | |
344 | data8 0xec835e79946a3146 , 0x0000bffe // cos(14 pi/16) -C2 | |
345 | // | |
346 | data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin(15 pi/16) S1 | |
347 | data8 0xfb14be7fbae58157 , 0x0000bffe // cos(15 pi/16) -C1 | |
348 | // | |
349 | data8 0x0000000000000000 , 0x00000000 // sin(16 pi/16) S0 | |
350 | data8 0x8000000000000000 , 0x0000bfff // cos(16 pi/16) -C0 | |
351 | // | |
352 | data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(17 pi/16) -S1 | |
353 | data8 0xfb14be7fbae58157 , 0x0000bffe // cos(17 pi/16) -C1 | |
354 | // | |
355 | data8 0xc3ef1535754b168e , 0x0000bffd // sin(18 pi/16) -S2 | |
356 | data8 0xec835e79946a3146 , 0x0000bffe // cos(18 pi/16) -C2 | |
357 | // | |
358 | data8 0x8e39d9cd73464364 , 0x0000bffe // sin(19 pi/16) -S3 | |
359 | data8 0xd4db3148750d181a , 0x0000bffe // cos(19 pi/16) -C3 | |
360 | // | |
361 | data8 0xb504f333f9de6484 , 0x0000bffe // sin(20 pi/16) -S4 | |
362 | data8 0xb504f333f9de6484 , 0x0000bffe // cos(20 pi/16) -S4 | |
363 | // | |
364 | data8 0xd4db3148750d181a , 0x0000bffe // sin(21 pi/16) -C3 | |
365 | data8 0x8e39d9cd73464364 , 0x0000bffe // cos(21 pi/16) -S3 | |
366 | // | |
367 | data8 0xec835e79946a3146 , 0x0000bffe // sin(22 pi/16) -C2 | |
368 | data8 0xc3ef1535754b168e , 0x0000bffd // cos(22 pi/16) -S2 | |
369 | // | |
370 | data8 0xfb14be7fbae58157 , 0x0000bffe // sin(23 pi/16) -C1 | |
371 | data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos(23 pi/16) -S1 | |
372 | // | |
373 | data8 0x8000000000000000 , 0x0000bfff // sin(24 pi/16) -C0 | |
374 | data8 0x0000000000000000 , 0x00000000 // cos(24 pi/16) S0 | |
375 | // | |
376 | data8 0xfb14be7fbae58157 , 0x0000bffe // sin(25 pi/16) -C1 | |
377 | data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos(25 pi/16) S1 | |
378 | // | |
379 | data8 0xec835e79946a3146 , 0x0000bffe // sin(26 pi/16) -C2 | |
380 | data8 0xc3ef1535754b168e , 0x00003ffd // cos(26 pi/16) S2 | |
381 | // | |
382 | data8 0xd4db3148750d181a , 0x0000bffe // sin(27 pi/16) -C3 | |
383 | data8 0x8e39d9cd73464364 , 0x00003ffe // cos(27 pi/16) S3 | |
384 | // | |
385 | data8 0xb504f333f9de6484 , 0x0000bffe // sin(28 pi/16) -S4 | |
386 | data8 0xb504f333f9de6484 , 0x00003ffe // cos(28 pi/16) S4 | |
387 | // | |
388 | data8 0x8e39d9cd73464364 , 0x0000bffe // sin(29 pi/16) -S3 | |
389 | data8 0xd4db3148750d181a , 0x00003ffe // cos(29 pi/16) C3 | |
390 | // | |
391 | data8 0xc3ef1535754b168e , 0x0000bffd // sin(30 pi/16) -S2 | |
392 | data8 0xec835e79946a3146 , 0x00003ffe // cos(30 pi/16) C2 | |
393 | // | |
394 | data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(31 pi/16) -S1 | |
395 | data8 0xfb14be7fbae58157 , 0x00003ffe // cos(31 pi/16) C1 | |
396 | // | |
397 | data8 0x0000000000000000 , 0x00000000 // sin(32 pi/16) S0 | |
398 | data8 0x8000000000000000 , 0x00003fff // cos(32 pi/16) C0 | |
399 | LOCAL_OBJECT_END(double_sin_cos_beta_k4) | |
400 | ||
401 | .section .text | |
402 | ||
403 | GLOBAL_IEEE754_ENTRY(sincos) | |
404 | // cis_GR_sig_inv_pi_by_16 = significand of 16/pi | |
405 | { .mlx | |
406 | getf.exp cis_r_signexp = cis_Arg | |
407 | movl cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A | |
408 | ||
409 | } | |
410 | // cis_GR_rshf_2to61 = 1.1000 2^(63+63-2) | |
411 | { .mlx | |
412 | addl cis_AD_1 = @ltoff(double_cis_pi), gp | |
413 | movl cis_GR_rshf_2to61 = 0x47b8000000000000 | |
414 | };; | |
415 | ||
416 | { .mfi | |
417 | ld8 cis_AD_1 = [cis_AD_1] | |
418 | fnorm.s1 cis_NORM_f8 = cis_Arg | |
419 | cmp.eq p13, p14 = r0, r0 // p13 set for sincos | |
420 | } | |
421 | // cis_GR_exp_2tom61 = exponent of scaling factor 2^-61 | |
422 | { .mib | |
423 | mov cis_GR_exp_2tom61 = 0xffff-61 | |
424 | nop.i 0 | |
425 | br.cond.sptk _CIS_COMMON | |
426 | };; | |
427 | GLOBAL_IEEE754_END(sincos) | |
428 | ||
429 | GLOBAL_LIBM_ENTRY(__libm_sincos) | |
430 | // cis_GR_sig_inv_pi_by_16 = significand of 16/pi | |
431 | { .mlx | |
432 | getf.exp cis_r_signexp = cis_Arg | |
433 | movl cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A | |
434 | } | |
435 | // cis_GR_rshf_2to61 = 1.1000 2^(63+63-2) | |
436 | { .mlx | |
437 | addl cis_AD_1 = @ltoff(double_cis_pi), gp | |
438 | movl cis_GR_rshf_2to61 = 0x47b8000000000000 | |
439 | };; | |
440 | ||
441 | // p14 set for __libm_sincos and cis | |
442 | { .mfi | |
443 | ld8 cis_AD_1 = [cis_AD_1] | |
444 | fnorm.s1 cis_NORM_f8 = cis_Arg | |
445 | cmp.eq p14, p13 = r0, r0 | |
446 | } | |
447 | // cis_GR_exp_2tom61 = exponent of scaling factor 2^-61 | |
448 | { .mib | |
449 | mov cis_GR_exp_2tom61 = 0xffff-61 | |
450 | nop.i 0 | |
451 | nop.b 0 | |
452 | };; | |
453 | ||
454 | _CIS_COMMON: | |
455 | // Form two constants we need | |
456 | // 16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand | |
457 | // 1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand | |
458 | // fcmp used to set denormal, and invalid on snans | |
459 | { .mfi | |
460 | setf.sig cis_SIG_INV_PI_BY_16_2TO61 = cis_GR_sig_inv_pi_by_16 | |
461 | fclass.m p6,p0 = cis_Arg, 0xe7 // if x=0,inf,nan | |
462 | addl cis_gr_tmp = -1, r0 | |
463 | } | |
464 | // 1.1000 2^63 for right shift | |
465 | { .mlx | |
466 | setf.d cis_RSHF_2TO61 = cis_GR_rshf_2to61 | |
467 | movl cis_GR_rshf = 0x43e8000000000000 | |
468 | };; | |
469 | ||
470 | // Form another constant | |
471 | // 2^-61 for scaling Nfloat | |
472 | // 0x1001a is register_bias + 27. | |
473 | // So if f8 >= 2^27, go to large arguments routine | |
474 | { .mfi | |
475 | alloc GR_SAVE_PFS = ar.pfs, 3, 5, 0, 0 | |
476 | fclass.m p11,p0 = cis_Arg, 0x0b // Test for x=unorm | |
477 | mov cis_exp_limit = 0x1001a | |
478 | } | |
479 | { .mib | |
480 | setf.exp cis_2TOM61 = cis_GR_exp_2tom61 | |
481 | nop.i 0 | |
482 | (p6) br.cond.spnt _CIS_SPECIAL_ARGS | |
483 | };; | |
484 | ||
485 | // Load the two pieces of pi/16 | |
486 | // Form another constant | |
487 | // 1.1000...000 * 2^63, the right shift constant | |
488 | { .mmb | |
489 | ldfe cis_Pi_by_16_hi = [cis_AD_1],16 | |
490 | setf.d cis_RSHF = cis_GR_rshf | |
491 | (p11) br.cond.spnt _CIS_UNORM // Branch if x=unorm | |
492 | };; | |
493 | ||
494 | _CIS_COMMON2: | |
495 | // Return here if x=unorm | |
496 | // Create constant inexact set | |
497 | { .mmi | |
498 | ldfe cis_Pi_by_16_lo = [cis_AD_1],16 | |
499 | setf.sig cis_tmp = cis_gr_tmp | |
500 | nop.i 0 | |
501 | };; | |
502 | ||
503 | // Select exponent (17 lsb) | |
504 | { .mfi | |
505 | ldfe cis_Pi_by_16_lowest = [cis_AD_1],16 | |
506 | nop.f 0 | |
507 | dep.z cis_r_exp = cis_r_signexp, 0, 17 | |
508 | };; | |
509 | ||
510 | // Start loading P, Q coefficients | |
511 | // p10 is true if we must call routines to handle larger arguments | |
512 | // p10 is true if f8 exp is > 0x1001a | |
513 | { .mmb | |
514 | ldfpd cis_P4,cis_Q4 = [cis_AD_1],16 | |
515 | cmp.ge p10, p0 = cis_r_exp, cis_exp_limit | |
516 | (p10) br.cond.spnt _CIS_LARGE_ARGS // go to |x| >= 2^27 path | |
517 | };; | |
518 | ||
519 | // cis_W = x * cis_Inv_Pi_by_16 | |
520 | // Multiply x by scaled 16/pi and add large const to shift integer part of W to | |
521 | // rightmost bits of significand | |
522 | { .mfi | |
523 | ldfpd cis_P3,cis_Q3 = [cis_AD_1],16 | |
524 | fma.s1 cis_W_2TO61_RSH = cis_NORM_f8,cis_SIG_INV_PI_BY_16_2TO61,cis_RSHF_2TO61 | |
525 | nop.i 0 | |
526 | };; | |
527 | ||
528 | // get N = (int)cis_int_Nfloat | |
529 | // cis_NFLOAT = Round_Int_Nearest(cis_W) | |
530 | { .mmf | |
531 | getf.sig cis_GR_n = cis_W_2TO61_RSH | |
532 | ldfpd cis_P2,cis_Q2 = [cis_AD_1],16 | |
533 | fms.s1 cis_NFLOAT = cis_W_2TO61_RSH,cis_2TOM61,cis_RSHF | |
534 | };; | |
535 | ||
536 | // cis_r = -cis_Nfloat * cis_Pi_by_16_hi + x | |
537 | { .mfi | |
538 | ldfpd cis_P1,cis_Q1 = [cis_AD_1], 16 | |
539 | fnma.s1 cis_r = cis_NFLOAT,cis_Pi_by_16_hi,cis_NORM_f8 | |
540 | nop.i 0 | |
541 | };; | |
542 | ||
543 | // Add 2^(k-1) (which is in cis_r_sincos) to N | |
544 | { .mmi | |
545 | add cis_GR_n_cos = 0x8, cis_GR_n | |
546 | ;; | |
547 | //Get M (least k+1 bits of N) | |
548 | and cis_GR_m_sin = 0x1f,cis_GR_n | |
549 | and cis_GR_m_cos = 0x1f,cis_GR_n_cos | |
550 | };; | |
551 | ||
552 | { .mmi | |
553 | nop.m 0 | |
554 | nop.m 0 | |
555 | shl cis_GR_32m_sin = cis_GR_m_sin,5 | |
556 | };; | |
557 | ||
558 | // Add 32*M to address of sin_cos_beta table | |
559 | // cis_r = cis_r -cis_Nfloat * cis_Pi_by_16_lo | |
560 | { .mfi | |
561 | add cis_AD_2_sin = cis_GR_32m_sin, cis_AD_1 | |
562 | fnma.s1 cis_r = cis_NFLOAT, cis_Pi_by_16_lo, cis_r | |
563 | shl cis_GR_32m_cos = cis_GR_m_cos,5 | |
564 | };; | |
565 | ||
566 | // Add 32*M to address of sin_cos_beta table | |
567 | { .mmf | |
568 | ldfe cis_Sm_sin = [cis_AD_2_sin],16 | |
569 | add cis_AD_2_cos = cis_GR_32m_cos, cis_AD_1 | |
570 | fclass.m.unc p10,p0 = cis_Arg,0x0b // den. input - uflow | |
571 | };; | |
572 | ||
573 | { .mfi | |
574 | ldfe cis_Sm_cos = [cis_AD_2_cos], 16 | |
575 | nop.i 0 | |
576 | };; | |
577 | ||
578 | { .mfi | |
579 | ldfe cis_Cm_sin = [cis_AD_2_sin] | |
580 | fma.s1 cis_rsq = cis_r, cis_r, f0 // get r^2 | |
581 | nop.i 0 | |
582 | } | |
583 | // fmpy forces inexact flag | |
584 | { .mfi | |
585 | nop.m 0 | |
586 | fmpy.s0 cis_tmp = cis_tmp,cis_tmp | |
587 | nop.i 0 | |
588 | };; | |
589 | ||
590 | { .mfi | |
591 | nop.m 0 | |
592 | fnma.s1 cis_r_exact = cis_NFLOAT, cis_Pi_by_16_lowest, cis_r | |
593 | nop.i 0 | |
594 | };; | |
595 | ||
596 | { .mfi | |
597 | ldfe cis_Cm_cos = [cis_AD_2_cos] | |
598 | fma.s1 cis_P_temp1 = cis_rsq, cis_P4, cis_P3 | |
599 | nop.i 0 | |
600 | } | |
601 | ||
602 | { .mfi | |
603 | nop.m 0 | |
604 | fma.s1 cis_Q_temp1 = cis_rsq, cis_Q4, cis_Q3 | |
605 | nop.i 0 | |
606 | };; | |
607 | ||
608 | { .mfi | |
609 | nop.m 0 | |
610 | fmpy.s1 cis_srsq_sin = cis_Sm_sin, cis_rsq | |
611 | nop.i 0 | |
612 | } | |
613 | { .mfi | |
614 | nop.m 0 | |
615 | fmpy.s1 cis_srsq_cos = cis_Sm_cos,cis_rsq | |
616 | nop.i 0 | |
617 | };; | |
618 | ||
619 | { .mfi | |
620 | nop.m 0 | |
621 | fma.s1 cis_Q_temp2 = cis_rsq, cis_Q_temp1, cis_Q2 | |
622 | nop.i 0 | |
623 | } | |
624 | { .mfi | |
625 | nop.m 0 | |
626 | fma.s1 cis_P_temp2 = cis_rsq, cis_P_temp1, cis_P2 | |
627 | nop.i 0 | |
628 | };; | |
629 | ||
630 | { .mfi | |
631 | nop.m 0 | |
632 | fmpy.s1 cis_rcub = cis_r_exact, cis_rsq // get r^3 | |
633 | nop.i 0 | |
634 | };; | |
635 | ||
636 | { .mfi | |
637 | nop.m 0 | |
638 | fma.s1 cis_Q = cis_rsq, cis_Q_temp2, cis_Q1 | |
639 | nop.i 0 | |
640 | } | |
641 | { .mfi | |
642 | nop.m 0 | |
643 | fma.s1 cis_P = cis_rsq, cis_P_temp2, cis_P1 | |
644 | nop.i 0 | |
645 | };; | |
646 | ||
647 | { .mfi | |
648 | nop.m 0 | |
649 | fma.s1 cis_Q_sin = cis_srsq_sin,cis_Q, cis_Sm_sin | |
650 | nop.i 0 | |
651 | } | |
652 | { .mfi | |
653 | nop.m 0 | |
654 | fma.s1 cis_Q_cos = cis_srsq_cos,cis_Q, cis_Sm_cos | |
655 | nop.i 0 | |
656 | };; | |
657 | ||
658 | { .mfi | |
659 | nop.m 0 | |
660 | fma.s1 cis_P = cis_rcub,cis_P, cis_r_exact // final P | |
661 | nop.i 0 | |
662 | };; | |
663 | ||
664 | // If den. arg, force underflow to be set | |
665 | { .mfi | |
666 | nop.m 0 | |
667 | (p10) fmpy.d.s0 cis_tmp = cis_Arg,cis_Arg | |
668 | nop.i 0 | |
669 | };; | |
670 | ||
671 | { .mfi | |
672 | nop.m 0 | |
673 | fma.d.s0 cis_Sin_res = cis_Cm_sin,cis_P,cis_Q_sin//Final sin | |
674 | nop.i 0 | |
675 | } | |
676 | { .mfb | |
677 | nop.m 0 | |
678 | fma.d.s0 cis_Cos_res = cis_Cm_cos,cis_P,cis_Q_cos//Final cos | |
679 | (p14) br.ret.sptk b0 // common exit for __libm_sincos and cis main path | |
680 | };; | |
681 | ||
682 | { .mmb | |
683 | stfd [cis_pResSin] = cis_Sin_res | |
684 | stfd [cis_pResCos] = cis_Cos_res | |
685 | br.ret.sptk b0 // common exit for sincos main path | |
686 | };; | |
687 | ||
688 | _CIS_SPECIAL_ARGS: | |
689 | // sin(+/-0) = +/-0 | |
690 | // sin(Inf) = NaN | |
691 | // sin(NaN) = NaN | |
692 | { .mfi | |
693 | nop.m 999 | |
694 | fma.d.s0 cis_Sin_res = cis_Arg, f0, f0 // sinf(+/-0,NaN,Inf) | |
695 | nop.i 999 | |
696 | };; | |
697 | // cos(+/-0) = 1.0 | |
698 | // cos(Inf) = NaN | |
699 | // cos(NaN) = NaN | |
700 | { .mfb | |
701 | nop.m 999 | |
702 | fma.d.s0 cis_Cos_res = cis_Arg, f0, f1 // cosf(+/-0,NaN,Inf) | |
703 | (p14) br.ret.sptk b0 //spec exit for __libm_sincos and cis main path | |
704 | };; | |
705 | ||
706 | { .mmb | |
707 | stfd [cis_pResSin] = cis_Sin_res | |
708 | stfd [cis_pResCos] = cis_Cos_res | |
709 | br.ret.sptk b0 // common exit for sincos main path | |
710 | };; | |
711 | ||
712 | _CIS_UNORM: | |
713 | // Here if x=unorm | |
714 | { .mfb | |
715 | getf.exp cis_r_signexp = cis_NORM_f8 // Get signexp of x | |
716 | fcmp.eq.s0 p11,p0 = cis_Arg, f0 // Dummy op to set denorm | |
717 | br.cond.sptk _CIS_COMMON2 // Return to main path | |
718 | };; | |
719 | ||
720 | GLOBAL_LIBM_END(__libm_sincos) | |
721 | ||
722 | //// |x| > 2^27 path /////// | |
723 | .proc _CIS_LARGE_ARGS | |
724 | _CIS_LARGE_ARGS: | |
725 | .prologue | |
726 | { .mfi | |
727 | nop.m 0 | |
728 | nop.f 0 | |
729 | .save ar.pfs, GR_SAVE_PFS | |
730 | mov GR_SAVE_PFS = ar.pfs | |
731 | } | |
732 | ;; | |
733 | ||
734 | { .mfi | |
735 | mov GR_SAVE_GP = gp | |
736 | nop.f 0 | |
737 | .save b0, GR_SAVE_B0 | |
738 | mov GR_SAVE_B0 = b0 | |
739 | };; | |
740 | ||
741 | .body | |
742 | // Call of huge arguments sincos | |
743 | { .mib | |
744 | nop.m 0 | |
745 | mov GR_SAVE_PR = pr | |
746 | br.call.sptk b0 = __libm_sincos_large | |
747 | };; | |
748 | ||
749 | { .mfi | |
750 | mov gp = GR_SAVE_GP | |
751 | nop.f 0 | |
752 | mov pr = GR_SAVE_PR, 0x1fffe | |
753 | } | |
754 | ;; | |
755 | ||
756 | { .mfi | |
757 | nop.m 0 | |
758 | nop.f 0 | |
759 | mov b0 = GR_SAVE_B0 | |
760 | } | |
761 | ;; | |
762 | ||
763 | { .mfi | |
764 | nop.m 0 | |
765 | fma.d.s0 cis_Cos_res = cis_Cos_res, f1, f0 | |
766 | mov ar.pfs = GR_SAVE_PFS | |
767 | } | |
768 | { .mfb | |
769 | nop.m 0 | |
770 | fma.d.s0 cis_Sin_res = cis_Sin_res, f1, f0 | |
771 | (p14) br.ret.sptk b0 // exit for |x| > 2^27 path (__libm_sincos and cis) | |
772 | };; | |
773 | ||
774 | { .mmb | |
775 | stfd [cis_pResSin] = cis_Sin_res | |
776 | stfd [cis_pResCos] = cis_Cos_res | |
777 | br.ret.sptk b0 // exit for sincos |x| > 2^27 path | |
778 | };; | |
779 | .endp _CIS_LARGE_ARGS | |
780 | ||
781 | .type __libm_sincos_large#,@function | |
782 | .global __libm_sincos_large# | |
783 |