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1 .file "cbrtl.s"
4 // Copyright (c) 2000 - 2004, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2000 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.
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 // 04/28/00 Initial version
43 // 05/20/02 Cleaned up namespace and sf0 syntax
44 // 02/06/03 Reordered header:.section,.global,.proc,.align
45 // 11/23/04 Reformatted routine and improved speed
46 //
47 // API
48 //==============================================================
49 // long double cbrtl(long double)
50 //
51 // Overview of operation
52 //==============================================================
53 // Background
54 //
55 // Implementation
56 //
57 // The result is computed as
58 // cbrt(x)= cbrt(1 - (1 - x*y)) * (1/cbrt(y))
59 // where y = frcpa(x) = (-1)^sgn_y * 2^(3*k+j) * m_y,
60 // m_y in [1,2), j in {0,1,2}
61 //
62 // cbrt(1 - (1 - x*y)) is approximated by a degree-6 polynomial
63 // in r= 1 - x*y :
64 // P = 1 - c_1 r - c_2 * r^2 - c_3 * r^3 - c_4 * r^4 - c_5 * r^5 - c_6 * r^6
65 //
66 //
67 // The values (1/cbrt(y)) are stored as two tables of constants T_hi
68 // (double-extended precision) and D (single precision) as follows:
69 // T_hi (1 + D)= 1/cbrt(y) to about 80 bits of accuracy
70 //
71 // The tables are only stored for three exponent values (i.e.
72 // only for 2^j * m_y, where j in {0,1,2} and m_y covers the 256
73 // possible mantissas for an frcpa result); the index is formed
74 // by the 8 leading mantissa bits of x, which is the same index used
75 // by the hardware to get frcpa(x).
76 //
77 // The table values are multiplied by 2^k where e is the exponent of
78 // the input number. This multiplication is carried out in parallel with
79 // the polynomial evaluation:
80 // T= 2^(k) * T_hi
81 //
82 //=======================================================================
84 //===============
85 // Special values
86 //==============================================================
88 // Registers used
89 //==============================================================
90 // p6, p7, p12
91 FR_R = f6
92 FR_C1 = f7
93 FR_C2 = f9
94 FR_C3 = f10
95 FR_C4 = f11
96 FR_C5 = f12
97 FR_C6 = f13
98 FR_XNORM = f14
99 FR_D = f15
100 FR_SPECIAL = f32
101 FR_RCP = f33
102 FR_R2 = f34
103 FR_P1 = f35
104 FR_P2 = f36
105 FR_P3 = f37
106 FR_P4 = f38
107 FR_P5 = f39
108 FR_R3 = f40
109 FR_T = f41
110 FR_TF = f42
111 FR_P = f43
112 FR_SGNEXP = f44
114 GR_ADDR = r2
115 GR_C_START = r2
116 GR_ARGSIG = r3
117 GR_NORMSIG = r15
118 GR_D_ADDR = r16
119 GR_D_START = r16
120 GR_INDEX2 = r17
121 GR_IX2 = r17
122 GR_NORMEXP = r18
123 GR_EXP5 = r19
124 GR_EXP3 = r20
125 GR_EXP6 = r20
126 GR_EXP17 = r21
127 GR_TMP1 = r21
128 GR_SGNMASK = r22
129 GR_T_INDEX = r23
130 GR_IX_T = r23
131 GR_IX_D = r24
132 GR_D_INDEX = r24
133 GR_TMP2 = r25
134 GR_TMP3 = r25
135 GR_TMP4 = r25
136 GR_EXP_RES = r26
137 GR_BIAS23 = r27
138 GR_EXPBIAS = r27
139 GR_EXP_MOD_3 = r28
140 GR_SIGN = r29
141 GR_EXPSIGNRES = r29
142 GR_REMTMP = r30
143 GR_NORMEXPSGN = r31
146 // Data tables
147 //==============================================================
149 RODATA
151 .align 16
153 LOCAL_OBJECT_START(poly_coeffs)
155 data8 0xaaaaaaaaaaaaaab1, 0x00003ffd // C_1
156 data8 0xe38e38e38e38e3e0, 0x00003ffb // C_2
157 data8 0x3faf9add3c0be9a6, 0x3fa511e8d2b1f749 // C_3, C_4
158 data8 0x3f9ee71b2c6ebe99, 0x3f9809180fd0340c // C_5, C_6
159 LOCAL_OBJECT_END(poly_coeffs)
162 LOCAL_OBJECT_START(T_table)
164 data8 0x80155c748c374836, 0x8040404b0879f7f9
165 data8 0x806b5dce4b405c10, 0x8096b586974669b1
166 data8 0x80bcd273d952a028, 0x80e898c52813f2f3
167 data8 0x81149add67c2d208, 0x813b4e2c856b6e9a
168 data8 0x8167c1dde03de7aa, 0x818ed973b811135e
169 data8 0x81bbc0c33e13ec98, 0x81e33e69fbe7504a
170 data8 0x820aec524e3c23e9, 0x823880f78e70b805
171 data8 0x826097a62a8e5200, 0x8288dfe00e9b5eaf
172 data8 0x82b15a10c5371624, 0x82da06a527b18937
173 data8 0x8302e60b635ab394, 0x832bf8b2feec2f0e
174 data8 0x83553f0ce00e276b, 0x837eb98b50f8322a
175 data8 0x83a270f44c84f699, 0x83cc4d7cfcfac5ca
176 data8 0x83f65f78a8872b4c, 0x8420a75f2f7b53c8
177 data8 0x844510461ff14209, 0x846fbd91b930bed2
178 data8 0x84947e18234f3294, 0x84bf92755825045a
179 data8 0x84e4ac0ee112ba51, 0x8509ef44b86f20be
180 data8 0x85359d5d91768427, 0x855b3bd5b7384357
181 data8 0x858104f0c415f79a, 0x85a6f90390d29864
182 data8 0x85d3772fcd56a1dd, 0x85f9c982fcc002f3
183 data8 0x862047e0e7ea554b, 0x8646f2a26f7f5852
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199 data8 0x8ace0d6bbe2cb316, 0x8af301688ab33558
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201 data8 0x8b62cb603bb2fad0, 0x8b80d7d6bc4104de
202 data8 0x8ba68bf73ac74f39, 0x8bcc68fb9f9f7335
203 data8 0x8bf26f31c534fca2, 0x8c10f86e13a1a1f9
204 data8 0x8c3749916cc6abb5, 0x8c5dc4c4f7706032
205 data8 0x8c7cac3a8c42e3e0, 0x8ca373f1b7bf2716
206 data8 0x8cc29907fb951294, 0x8ce9ae4e9492aac8
207 data8 0x8d0911dddbfdad0e, 0x8d3075c4f20f04ee
208 data8 0x8d5018a9d4de77d5, 0x8d77cc47dd143515
209 data8 0x8d97af6352739cb7, 0x8db7af523167800f
210 data8 0x8ddfd80bc68c32ff, 0x8e00197e1e7c88fe
211 data8 0x8e207859f77e20e7, 0x8e40f4ce60c9f8e2
212 data8 0x8e69ba46cf2fde4d, 0x8e8a7a00bd7ae63e
213 data8 0x8eab57ef1cf2f529, 0x8ecc5442cffb1dad
214 data8 0x8eed6f2d2a4acbfe, 0x8f0ea8dff24441ff
215 data8 0x8f385c95d696b817, 0x8f59dc43edd930f3
216 data8 0x8f7b7b5f5ffad1c4, 0x8f9d3a1bea165f38
217 data8 0x8fbf18adc34b66da, 0x8fe117499e356095
218 data8 0x90033624aa685f8d, 0x9025757495f36b86
219 data8 0x903f3a5dcc091203, 0x9061b2fceb2bdbab
220 data8 0x90844ca7211032a7, 0x90a7079403e6a15d
221 data8 0x90c9e3fbafd63799, 0x90ece216c8a16ee4
222 data8 0x9110021e7b516f0a, 0x912a708a39be9075
223 data8 0x914dcc7b31146370, 0x91714af8cfe984d5
224 data8 0x918c00a6f3795e97, 0x91afbc299ed0295d
225 data8 0x91d39add3e958db0, 0x91ee9920a8974d92
226 data8 0x9212b5fcac537c19, 0x9236f6b256923fcf
227 data8 0x92523ee6f90dcfc3, 0x9276bef031e6eb79
228 data8 0x929236ec237a24ad, 0x92b6f70b7efe9dc3
229 data8 0x92d29f61eec7dc2b, 0x92f7a05d5b8ba92f
230 data8 0x931379a403be5c16, 0x9338bc44de2e3f34
231 data8 0x9354c71412c69486, 0x937a4c273907e262
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233 data8 0x93d8c123d9be59b2, 0x93f546c955e60076
234 data8 0x941b70a65879079f, 0x943829f337410591
235 data8 0x9454f995765bc4d2, 0x947b86b57f5842ed
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238 data8 0x95175019a503d89e, 0x9534cefa625fcb3a
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240 data8 0x9597ca4119525184, 0x95b5af6fb5aa4d3c
241 data8 0x95d3ac9273aafd7a, 0x95f1c1cafdfd3684
242 data8 0x960fef3b430b8d5f, 0x962e350575b409c5
243 data8 0x964c934c0dfc1708, 0x966b0a31c9c6bc7d
244 data8 0x968999d9ad8d264e, 0x96a8426705198795
245 data8 0x96c703fd64445ee5, 0x96e5dec0a7b4268d
246 data8 0x9704d2d4f59f79f3, 0x9723e05ebe91b9b0
247 data8 0x97430782be323831, 0x97624865fc0df8bf
248 data8 0x9781a32dcc640b2a, 0x97a117ffd0f48e46
249 data8 0x97c0a701f9d263c9, 0x97e0505a8637a036
250 data8 0x97f57a9fb0b08c6e, 0x9815503365914a9d
251 data8 0x98354085054fd204, 0x98554bbbf8a77902
252 data8 0x987571fffb7f94f6, 0x9895b3791dd03c23
253 data8 0x98ab43a5fc65d0c8, 0x98cbb2d196bd713d
254 data8 0x98ec3d9ec7b6f21a, 0x990ce436db5e8344
255 data8 0x9922b8218160967a, 0x99438d686f75779d
256 data8 0x99647eea131fa20b, 0x997a85045a47c6d0
257 data8 0x999ba5f14f8add02, 0x99bce38b5465ecae
258 data8 0x99d31ca0887f30f9, 0x99f48a669c74c09e
259 data8 0x9a16154eb445c873, 0x9a2c822ec198d667
260 data8 0x9a4e3e080cd91b78, 0x9a70177afe52322e
261 data8 0x9a86b8fa94eebe10, 0x9aa8c42866ae2958
262 data8 0x9abf86f9e12fc45e, 0x9ae1c462fc05f49d
263 data8 0x9af8a8dc936b84d0, 0x9b1b19033be35730
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266 data8 0x9ba60e6a5ca133b6, 0x9bc919ea66a151a4
267 data8 0x9be0887c09ef82bb, 0x9c03c8d5fffc3503
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271 data8 0x9ccdeca60e80b5f8, 0x9ce5f9d4653d4902
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283 data8 0x9f6c52426a39d003, 0x9f860593d42fd7f3
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334 data8 0xb158bf8e4cb04055, 0xb189fd69d56b238f
335 data8 0xb1b189958e8108e4, 0xb1e32a8165b09832
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337 data8 0xb26538b2db8420dc, 0xb28d89e339ceca14
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340 data8 0xb36ddbc5ea70ec55, 0xb3971e9b39264023
341 data8 0xb3c0877ecc18e24a, 0xb3ea16ae3a6c905f
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343 data8 0xb47233773b84d425, 0xb49c6825430fe730
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358 data8 0xb94de2d841a184c2, 0xb97cd4c36c92693c
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375 data8 0xbe93f5b41d047cf7, 0xbebb5630bae4c15f
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377 data8 0xbf323c217be2bc8c, 0xbf5a203a09342bbb
378 data8 0xbf74cad1c14ebfc4, 0xbf9ce6a497a89f78
379 data8 0xbfc52428bec6e72f, 0xbfed838fddab024b
380 data8 0xc016050c0420981a, 0xc03ea8cfabddc330
381 data8 0xc059d3cbd65ddbce, 0xc082b122a3c78c9d
382 data8 0xc0abb1499ae736c4, 0xc0d4d474c3aedaaf
383 data8 0xc0f054ca33eb3437, 0xc119b2c67e600ed0
384 data8 0xc1433453de2033ff, 0xc15ef3e44e10032d
385 data8 0xc188b130431d80e6, 0xc1b2929d6067730e
386 data8 0xc1ce9268f31cc734, 0xc1f8b0877c1b0c08
387 data8 0xc222f35a87b415ba, 0xc23f3467349e5c88
388 data8 0xc269b4e40e088c01, 0xc2945aac24daaf6e
389 data8 0xc2b0de05e43c1d66, 0xc2dbc275e1229d09
390 data8 0xc2f86fca9d80eeff, 0xc323938449a2587e
391 data8 0xc3406b40a538ed20, 0xc36bcee8211d15e0
392 data8 0xc397593adf2ba366, 0xc3b475b6206155d5
393 data8 0xc3e0410243b97383, 0xc3fd890709833d37
394 data8 0xc41ae295f7e7fa06, 0xc44709f7bb8a4dd2
395 data8 0xc4648fb0e0bec4c1, 0xc490f9a94695ba14
396 data8 0xc4aeac0173b7d390, 0xc4db5941007aa853
397 data8 0xc4f938aec206291a, 0xc52629e899dfd622
398 data8 0xc54436e44043b965, 0xc562563abf9ea07f
399 data8 0xc58fa7d1dc42921c, 0xc5adf561b91e110a
400 data8 0xc5cc5591bdbd82fa, 0xc5fa08f1ff20593c
401 data8 0xc618980a79ce6862, 0xc6373a09e34b50fa
402 data8 0xc66550a6e0baaf35, 0xc6842241926342c9
403 data8 0xc6a3070b7c93bb9e, 0xc6d18260bb84081b
404 data8 0xc6f0977c9416828b, 0xc70fc0117c641630
405 data8 0xc72efc34d7e615be, 0xc75dfb441594141e
406 data8 0xc77d68aa019bda4c, 0xc79ce9ea478dbc4f
407 data8 0xc7bc7f1ae453219d, 0xc7ec0476e15e141a
408 data8 0xc80bcbe16f1d540f, 0xc82ba78a5d349735
409 data8 0xc84b978847a06b87, 0xc86b9bf1ee817bc6
410 data8 0xc88bb4de3667cdf4, 0xc8bc00e7fe9e23a3
411 data8 0xc8dc4d7ff2d25232, 0xc8fcaeebcb40eb47
412 data8 0xc91d25431426a663, 0xc93db09d7fdb2949
413 data8 0xc95e5112e721582a, 0xc97f06bb49787677
414 data8 0xc99fd1aecd6e1b06, 0xc9d12a3e27bb1625
415 data8 0xc9f22ad82ba3d5f0, 0xca134113105e67b2
416 data8 0xca346d07b045a876, 0xca55aecf0e94bb88
417 data8 0xca77068257be9bab, 0xca98743ae1c693a8
418 data8 0xcab9f8122c99a101, 0xcadb9221e268c3b5
419 data8 0xcafd4283d8043dfd, 0xcb1f09520d37c6fb
420 data8 0xcb51ddcb9e93095e, 0xcb95f333968ad59b
421 data8 0xcbda64292d3ffd97, 0xcc1f3184af961596
422 data8 0xcc5bb1ac954d33e2, 0xcca12e9831fc6402
423 data8 0xcce70a67b64f24ad, 0xcd24794726477ea5
424 data8 0xcd6b096a0b70ee87, 0xcda9177738b15a90
425 data8 0xcdf05f2247dffab9, 0xce2f0f347f96f906
426 data8 0xce6e0be0cd551a61, 0xceb666b2c347d1de
427 data8 0xcef609b0cb874f00, 0xcf35fb5447e5c765
428 data8 0xcf763c47ee869f00, 0xcfb6cd3888d71785
429 data8 0xcff7aed4fbfbb447, 0xd038e1ce5167e3c6
430 data8 0xd07a66d7bfa0ebba, 0xd0bc3ea6b32d1b21
431 data8 0xd0f4f0e8f36c1bf8, 0xd1376458e34b037e
432 data8 0xd17a2ca133f78572, 0xd1bd4a80301c5715
433 data8 0xd1f71682b2fa4575, 0xd23ad555f773f059
434 data8 0xd2752c7039a5bf73, 0xd2b98ee008c06b59
435 data8 0xd2f4735ffd700280, 0xd32f99ed6d9ac0e1
436 data8 0xd374f0666c75d51c, 0xd3b0a7d13618e4a1
437 data8 0xd3eca2ea53bcec0c, 0xd428e23874f13a17
438 data8 0xd46f82fe293bc6d3, 0xd4ac57e9b7186420
439 data8 0xd4e972becb04e8b8, 0xd526d40a7a9b43a3
440 data8 0xd5647c5b73917370, 0xd5a26c4201bd6d13
441 data8 0xd5e0a45015350a7e, 0xd614b539c6194104
442 data8 0xd6537310e224283f, 0xd6927ab62244c917
443 data8 0xd6d1ccc1fc4ef4b7, 0xd71169cea98fdded
444 data8 0xd746a66a5bc9f6d9, 0xd786ce8f0fae5317
445 data8 0xd7bc7ff214c4e75a, 0xd7fd35467a517ed1
446 data8 0xd83e38838648d815, 0xd874a1db598b8951
447 data8 0xd8ab42205b80edaf, 0xd8ed1849d202f965
448 data8 0xd92432bd5a173685, 0xd9669ca45b03c23e
449 data8 0xd99e3327cf89574e, 0xd9d602b19b100466
450 data8 0xda0e0ba86c096841, 0xda5195fcdb1c3dce
451 data8 0xda8a1eb87a491f6c, 0xdac2e230b91c3f84
452 data8 0xdafbe0d0b66aea30, 0xdb351b04a8fafced
453 data8 0xdb6e9139e33cdd8e, 0xdba843ded7151ea1
454 data8 0xdbe2336319b61fc8, 0xdc1c60376789fa68
455 data8 0xdc56cacda82d0cd5, 0xdc917398f2797814
456 data8 0xdccc5b0d90a3e628, 0xdd0781a10469f0f2
457 data8 0xdd42e7ca0b52838f, 0xdd729ad01c69114d
458 data8 0xddae749c001fbf5e, 0xddea8f50a51c69b1
459 data8 0xde26eb69a0f0f111, 0xde576480262399bc
460 data8 0xde943789645933c8, 0xded14d58139a28af
461 data8 0xdf025c00bbf2b5c7, 0xdf3feb44d723a713
462 data8 0xdf715bc16c159be0, 0xdfaf66240e29cda8
463 data8 0xdfe139cbf6e19bdc, 0xe01fc0fe94d9fc52
464 data8 0xe051f92ffcc0bd60, 0xe090feec9c9a06ac
465 data8 0xe0c39d0c9ff862d6, 0xe0f668eeb99f188d
466 data8 0xe1362890eb663139, 0xe1695c7212aecbaa
467 data8 0xe19cbf0391bbbbe9, 0xe1d050901c531e85
468 data8 0xe2110903b4f4047a, 0xe2450559b4d80b6d
469 data8 0xe27931a231554ef3, 0xe2ad8e2ac3c5b04b
470 data8 0xe2e21b41b9694cce, 0xe316d93615862714
471 data8 0xe3590bd86a0d30f9, 0xe38e38e38e38e38e
472 data8 0xe3c397d1e6db7839, 0xe3f928f5953feb9e
473 data8 0xe42eeca17c62886c, 0xe464e32943446305
474 data8 0xe49b0ce15747a8a2, 0xe4d16a1eee94e9d4
475 data8 0xe4fa52107353f67d, 0xe5310a471f4d2dc3
476 data8 0xe567f6f1c2b9c224, 0xe59f18689a9e4c9a
477 data8 0xe5d66f04b8a68ecf, 0xe60dfb2005c192e9
478 data8 0xe645bd1544c7ea51, 0xe66fb21b505b20a0
479 data8 0xe6a7d32af4a7c59a, 0xe6e02b129c6a5ae4
480 data8 0xe70a9136a7403039, 0xe74349fb2d92a589
481 data8 0xe77c3a9c86ed7d42, 0xe7a713f88151518a
482 data8 0xe7e067453317ed2b, 0xe819f37a81871bb5
483 data8 0xe8454236bfaeca14, 0xe87f32f24c3fc90e
484 data8 0xe8aacd8688892ba6, 0xe8e523fd32f606f7
485 data8 0xe9110b5311407927, 0xe94bc8bf0c108fa3
486 data8 0xe977fdc439c2ca3c, 0xe9b3236528fc349e
487 data8 0xe9dfa70b745ac1b4, 0xea1b36268d0eaa38
488 data8 0xea480963fd394197, 0xea84034425f27484
489 data8 0xeab12713138dd1cc, 0xeade6db73a5e503b
490 data8 0xeb1b0268343b121b, 0xeb489b0b2bdb5f14
491 data8 0xeb765721e85f03d0, 0xebb389645f222f62
492 data8 0xebe198f090607e0c, 0xec0fcc9321024509
493 data8 0xec3e247da8b82f61, 0xec7c27d21321c9f7
494 data8 0xecaad5278824e453, 0xecd9a76d097d4e77
495 data8 0xed089ed5dcd99446, 0xed37bb95add09a1c
496 data8 0xed76c70508f904b6, 0xeda63bb05e7f93c6
497 data8 0xedd5d661daed2dc4, 0xee05974eef86b903
498 data8 0xee357ead791fc670, 0xee658cb3c134a463
499 data8 0xee95c1987f080211, 0xeec61d92d8c4314f
500 data8 0xeef6a0da64a014ac, 0xef274ba72a07c811
501 data8 0xef581e31a2c91260, 0xef8918b2bc43aec6
502 data8 0xefba3b63d89d7cbf, 0xefeb867ecffaa607
503 data8 0xf01cfa3df1b9c9fa, 0xf04e96dc05b43e2d
504 data8 0xf0805c944d827454, 0xf0b24ba285c495cb
505 data8 0xf0e46442e76f6569, 0xf116a6b2291d7896
506 data8 0xf1383fa9e9b5b381, 0xf16ac84f90083b9b
507 data8 0xf19d7b686dcb03d7, 0xf1d0593311db1757
508 data8 0xf20361ee8f1c711e, 0xf23695da7de51d3f
509 data8 0xf258d095e465cc35, 0xf28c4d0bfc982b34
510 data8 0xf2bff55eb3f0ea71, 0xf2f3c9cf9884636e
511 data8 0xf31670135ab9cc0f, 0xf34a8e9f0b54cdfb
512 data8 0xf37ed9fa6b8add3f, 0xf3a1cfe884ef6bb6
513 data8 0xf3d66689dcc8e8d3, 0xf40b2ab069d5c96a
514 data8 0xf42e718b90c8bc16, 0xf463822a0a3b4b00
515 data8 0xf498c1076015faf8, 0xf4bc5a19a33990b5
516 data8 0xf4f1e6a7d6f5425f, 0xf527a232cf6be334
517 data8 0xf54b8ecdcda90851, 0xf5819949c7ad87b4
518 data8 0xf5a5bac9213b48a9, 0xf5dc1501f324a812
519 data8 0xf6006bee86b5589e, 0xf63716b2fa067fa4
520 data8 0xf66df22fb6132b9c, 0xf6929fb98225deb1
521 data8 0xf6c9cd13021e3fea, 0xf6eeb177472cedae
522 data8 0xf713abf4cb0b3afb, 0xf74b4d5333684ef1
523 data8 0xf7707f75a72f8e94, 0xf7a874b97927af44
524 data8 0xf7cddf140aedf1d8, 0xf806291bacb7f7a9
525 data8 0xf82bcc43b92eafef, 0xf8646bf0defb759e
526 data8 0xf88a487dfc3ff5f7, 0xf8b03c2b46cdc17f
527 data8 0xf8e95541c152ae7a, 0xf90f832c2700c160
528 data8 0xf935c88e0c7f419b, 0xf96f5cd84fd86873
529 data8 0xf995dd53ebdd9d6d, 0xf9bc75a034436a41
530 data8 0xf9f686f26d5518de, 0xfa1d5b39b910a8c5
531 data8 0xfa4447acc4ecbfd2, 0xfa7ed7e51e6fdfb4
532 data8 0xfaa601394d49a1a0, 0xfacd431644ce0e40
533 data8 0xfaf49d96f7a75909, 0xfb2fd3c65e562fd5
534 data8 0xfb576c5762024805, 0xfb7f1debc22c4040
535 data8 0xfba6e89f32d0190a, 0xfbe2c803a0894893
536 data8 0xfc0ad1ff0ed9ecf0, 0xfc32f57bdfbcbe7f
537 data8 0xfc5b32968f99b21c, 0xfc83896bc861ab08
538 data8 0xfcabfa1861ed4815, 0xfce8d3cea7d3163e
539 data8 0xfd118595143ee273, 0xfd3a519943d4865a
540 data8 0xfd6337f8e1ae5a4b, 0xfd8c38d1c8e927eb
541 data8 0xfdb5544205095a53, 0xfdde8a67d2613531
542 data8 0xfe07db619e781611, 0xfe460768d80bf758
543 data8 0xfe6f9bfb06cd32f6, 0xfe994bcd3d14fcc2
544 data8 0xfec316fecaf3f2ab, 0xfeecfdaf33fadb80
545 data8 0xff16fffe2fa8fad6, 0xff411e0ba9db886d
546 data8 0xff6b57f7c33e4e9a, 0xff95ade2d1bd7358
547 data8 0xffc01fed60f86fb5, 0xffeaae3832b63956
548 LOCAL_OBJECT_END(T_table)
551 LOCAL_OBJECT_START(D_table)
553 data4 0x1e50f488, 0x1ebdc559, 0x1e649ec1, 0x9eed9b2c
554 data4 0x9e511c44, 0x9ec6d551, 0x9eefe248, 0x9e313854
555 data4 0x9f54ff18, 0x9d231411, 0x1ee5d63c, 0x9edf6b95
556 data4 0x9f332aaa, 0x1dc92a84, 0x1f73fb7b, 0x1e32f100
557 data4 0x9ea636f5, 0x9f6c3353, 0x9f405552, 0x1f33fd97
558 data4 0x1e975291, 0x9e59a11e, 0x1e47b0ba, 0x9d8ad33e
559 data4 0x1ea51bf6, 0x1f25d782, 0x9ecf534d, 0x1f55436f
560 data4 0x1d0975e4, 0x9f0633a1, 0x1f3e840a, 0x1f523a4c
561 data4 0x9f53cbbc, 0x9c8b5661, 0x9f6bc8eb, 0x1f4f6c7b
562 data4 0x9ed9b376, 0x9f5b30b6, 0x1f64fa5e, 0x1cbcc3e0
563 data4 0x1f343548, 0x1f62a6a2, 0x9f336abb, 0x9f1d15af
564 data4 0x1f476c83, 0x1ea86421, 0x1f33b2cf, 0x9e8f1348
565 data4 0x1f6fa829, 0x9f30ee3a, 0x9ebd6146, 0x1f2db598
566 data4 0x1ef9600d, 0x1f5b1427, 0x9edd741b, 0x1f51ef4e
567 data4 0x9f1aa57d, 0x9ee9b5e0, 0x9f17ecd7, 0x1ead71ff
568 data4 0x1f6c910e, 0x9e1837df, 0x9f0f17d9, 0x9e8350dd
569 data4 0x9d292f1b, 0x9e33b3ab, 0x9d6f0fe8, 0x9ed8c7cc
570 data4 0x9ec598c8, 0x9d56758c, 0x1e090c1e, 0x9ed4b941
571 data4 0x9f1fc4cf, 0x1f63513a, 0x9edd0abc, 0x1e3924dd
572 data4 0x1f60d56f, 0x1ea84424, 0x9e88f4fb, 0x1f205c09
573 data4 0x1ec9ae4e, 0x1d2d5738, 0x9f2c9f6d, 0x1e0765c2
574 data4 0x1e8bbdd7, 0x9f16d9f1, 0x9ea62627, 0x1f13904c
575 data4 0x1e566ab8, 0x9dca3d1a, 0x9e91f2a1, 0x9f14641c
576 data4 0x9f278946, 0x1f490c1e, 0x1f575eb6, 0x1f50b3fd
577 data4 0x9da32efb, 0x1ea95e59, 0x9e41e058, 0x9eada15f
578 data4 0x9e4fe66c, 0x1f3abc98, 0x1f1b8d1e, 0x9ece97e4
579 data4 0x1d188aed, 0x9e89b6ee, 0x1f287478, 0x9e8a161a
580 data4 0x1e4749f7, 0x9e68084a, 0x1e867f33, 0x9f462b63
581 data4 0x1db30792, 0x1f59a767, 0x9d1da4ae, 0x9f472a33
582 data4 0x1d1e91cd, 0x9f414824, 0x9f473d4f, 0x1f4b5783
583 data4 0x9f5b04b8, 0x9f5c205b, 0x1f309617, 0x9f0d6852
584 data4 0x9d96a609, 0x9f0965c2, 0x9e23f467, 0x9f089884
585 data4 0x9ec71458, 0x9ed6e955, 0x1e5e8691, 0x1f5b2bbc
586 data4 0x9f128268, 0x1ed40f5b, 0x1dc430ce, 0x1f345986
587 data4 0x1d778f72, 0x1e9b11d6, 0x9f5a40be, 0x9e07f61a
588 data4 0x9ed641a7, 0x9f334787, 0x1e952fd0, 0x1edeb5e2
589 data4 0x9e9f3eb1, 0x9e379fd9, 0x1f13102a, 0x9e5e80e1
590 data4 0x1c757944, 0x1dae2260, 0x1f183ab7, 0x1e55d576
591 data4 0x9e6bb99f, 0x9f52d7cb, 0x9e73a0f5, 0x1d4e1d14
592 data4 0x9dd05b53, 0x1f2261e4, 0x9d4ee73d, 0x1ede515e
593 data4 0x1f22a573, 0x9ecac348, 0x1e6a2ac0, 0x1e2787d2
594 data4 0x9eb64b87, 0x1f0c69c6, 0x9f470a01, 0x9d7c1686
595 data4 0x1e468ebe, 0x9f21ee2f, 0x9ee52116, 0x9e20f715
596 data4 0x1ed18533, 0x9f005b38, 0x9f20cb95, 0x1da72967
597 data4 0x1f1ba5d7, 0x1e2f8b16, 0x9c794f96, 0x9ca74ea3
598 data4 0x1f410555, 0x9eff2b96, 0x1ce8f0b1, 0x1f0cee77
599 data4 0x1f191edd, 0x9ed5fcbc, 0x1f30f242, 0x9e0ad369
600 data4 0x1ed8f3c8, 0x1f52bb0e, 0x9e9ce408, 0x1f18907f
601 data4 0x9ecdad40, 0x9e8af91d, 0x1d46698a, 0x9f4b93d6
602 data4 0x9f3f5d33, 0x1e2e52f7, 0x9f13aeec, 0x9f3b1969
603 data4 0x1f0996f4, 0x9f2a03df, 0x1e264767, 0x1f3ab1fb
604 data4 0x9f3193c9, 0x9f21ce22, 0x9eab624c, 0x9ecd8fb1
605 data4 0x1eaf9a85, 0x1f0c6a2c, 0x1eecbe61, 0x1f3fead9
606 data4 0x1f1d3a29, 0x1e9099ce, 0x1eadd875, 0x1e4dbfb8
607 data4 0x9dc640d2, 0x1f413680, 0x9f3f57b3, 0x1dfa1553
608 data4 0x1ec71c6b, 0x1e00cc00, 0x9f271e55, 0x1e5a88bb
609 data4 0x1f46cc2b, 0x1ee80ff9, 0x9e29c6f3, 0x1f15e229
610 data4 0x9ea83d66, 0x1f37408e, 0x9dacb66e, 0x1e6f6259
611 data4 0x9f106973, 0x1dd4e5ac, 0x1cbfdcc8, 0x9f231c9f
612 data4 0x9e8677e4, 0x9e9e695a, 0x1efd782b, 0x9dd26959
613 data4 0x9e80af69, 0x1f386fb3, 0x1f022e8c, 0x9e839967
614 data4 0x1ce6796f, 0x1e4c22c2, 0x1e57ef24, 0x1e919804
615 data4 0x9d7ea090, 0x1e40140a, 0x1f261b46, 0x1db75be2
616 data4 0x1f145019, 0x9e3102b9, 0x9e22507b, 0x1eae813c
617 data4 0x1f117e97, 0x1f282296, 0x1f3814b3, 0x1e17977b
618 data4 0x1f39d6ff, 0x9f1c81b9, 0x9eb5bcad, 0x1f0f596e
619 data4 0x1e757fd5, 0x9f090daa, 0x9f2532fc, 0x9eebafbb
620 data4 0x1f086556, 0x9eeedde8, 0x9f32e174, 0x1e33c030
621 data4 0x1f1f145a, 0x1e6e556c, 0x1e419ffb, 0x9eb6019a
622 data4 0x9e872a2e, 0x1e113136, 0x1e93096f, 0x1f39be40
623 data4 0x1f1665ad, 0x9db81d7d, 0x9cd29091, 0x1e3f4af7
624 data4 0x9f23176c, 0x9eccf9b3, 0x1f34fc6c, 0x9ed36894
625 data4 0x1ef08e06, 0x9f3b46bb, 0x9f2c850b, 0x1f1565a4
626 data4 0x1e887bc3, 0x1e92629c, 0x9f11ac9e, 0x9e5579f3
627 data4 0x1e4d5790, 0x9ee1c3d1, 0x9e916aec, 0x9eb8d9b8
628 data4 0x1db46105, 0x1e168663, 0x1f26a942, 0x9f0f0383
629 data4 0x9f079032, 0x9ecae1d8, 0x1ed3b34c, 0x9edc5ee6
630 data4 0x9e8a75a7, 0x1f3c3de2, 0x9ee5041e, 0x1f08c727
631 data4 0x1d02d7ae, 0x9f36adda, 0x9ef9a857, 0x9ef5cb3a
632 data4 0x9eee73da, 0x9da5d629, 0x1e0e99be, 0x1e5159b9
633 data4 0x1f2eac89, 0x9e8eedc5, 0x1dd0ec90, 0x1f229aff
634 data4 0x1ed9c3e6, 0x1e95c55a, 0x9f0c24e4, 0x1e8afed6
635 data4 0x1e599a96, 0x1e881b21, 0x1eab84b9, 0x9ba2bb0e
636 data4 0x9e33ab10, 0x1f1710b5, 0x1ebfa271, 0x9e90bbc5
637 data4 0x9f32515b, 0x9b32aae8, 0x1eda455c, 0x1da8186e
638 data4 0x9e8917ff, 0x1ec4d08e, 0x1c90069d, 0x9f2f1d29
639 data4 0x9ecee86d, 0x9f234d1f, 0x1f370724, 0x1da87496
640 data4 0x1e7959f0, 0x9e8ada34, 0x1f1c7f6f, 0x1edd576b
641 data4 0x9de91e8b, 0x1ec4ef89, 0x1f32078a, 0x1e9925e2
642 data4 0x9d8eeccb, 0x9ea3d011, 0x1f231fdf, 0x9f1dbdfa
643 data4 0x1e7507a3, 0x1ec42614, 0x9e8693cb, 0x9ec68398
644 data4 0x1d5b05fb, 0x1de32119, 0x9f003429, 0x9ec16d92
645 data4 0x9f095315, 0x9f119d2c, 0x9ed0c984, 0x9f090662
646 data4 0x9e59aa1f, 0x9ed4e64a, 0x9f2798a7, 0x9f23624d
647 data4 0x1e0467d9, 0x1f22e7e7, 0x1e915256, 0x9cb4df70
648 data4 0x9e6f687c, 0x9e3c35e5, 0x9e5757ab, 0x9f031fa1
649 data4 0x1f25bff7, 0x1f0e58c2, 0x1ef3ce04, 0x1f002ecb
650 data4 0x9ebdc836, 0x9ed657dd, 0x9f149441, 0x9e8544b2
651 data4 0x1cd8ff1e, 0x1e9bb463, 0x1eaa1c5c, 0x1f200c1a
652 data4 0x1edbfbaf, 0x1f18724d, 0x9ed63c22, 0x9f08e045
653 data4 0x1f13ad07, 0x9e949311, 0x9f0c50d4, 0x1e824516
654 data4 0x1d5e52ba, 0x1d583fbd, 0x1e3b60a9, 0x9effe6d3
655 data4 0x1f0d0508, 0x1f00be77, 0x9e404bfa, 0x9e1ca381
656 data4 0x9f084dd8, 0x9e6db85d, 0x1db698e4, 0x9ebd1871
657 data4 0x9ecc2679, 0x1ee68442, 0x1edb1050, 0x9dbc96a4
658 data4 0x9f27c1f4, 0x1c99b756, 0x1eb4400a, 0x9f24390a
659 data4 0x1d927875, 0x9f074faa, 0x1e9dc2c3, 0x1f13c0d2
660 data4 0x1e3c9685, 0x9e6b6f75, 0x9db9cb31, 0x1ea5f3aa
661 data4 0x9d992c61, 0x1f1015e4, 0x1f194f70, 0x9e19d2b3
662 data4 0x9d89116c, 0x1f23cd35, 0x1e33d3a2, 0x1ee331b8
663 data4 0x1d5ba7ec, 0x9f273788, 0x9e6907f4, 0x9ed5f912
664 data4 0x9edd458d, 0x1e2ca7b2, 0x1ef81fe4, 0x1dc7ade6
665 data4 0x1e876e51, 0x9f04ec89, 0x1f1da63a, 0x1ec02bd0
666 data4 0x9e71326f, 0x1e7847b4, 0x1f0de618, 0x9e036cb6
667 data4 0x1eec61e2, 0x1ef1758b, 0x9ee880a3, 0x1ed269d7
668 data4 0x1e27edd3, 0x9e8a81a1, 0x1eacb84d, 0x9e1aad37
669 data4 0x1f1aa8f7, 0x1e9bbd90, 0x1ea1b61f, 0x9ed41c2f
670 data4 0x1dbb5dd6, 0x1f0ec733, 0x9df06b1b, 0x1e06fef1
671 data4 0x9edede3a, 0x1edeb5e2, 0x1f0e63ee, 0x9db316bb
672 data4 0x9efc1ad3, 0x1f01fbb5, 0x9cc0d078, 0x1ea28b36
673 data4 0x9e9dd205, 0x9e791534, 0x1da1c8d5, 0x9e8195cc
674 data4 0x1f0681a4, 0x1eeaf1e2, 0x9ef83b37, 0x9f22a92b
675 data4 0x1eabc4ce, 0x1f10eefb, 0x1e06d9aa, 0x1e7cacd5
676 data4 0x1f1ea087, 0x1eb21983, 0x9f100c78, 0x1e840abe
677 data4 0x9efab66c, 0x1f183fa8, 0x9e84ee68, 0x9eea083d
678 data4 0x9ee23a74, 0x1f1351d7, 0x9ec5d42a, 0x9f071f57
679 data4 0x9ef578d9, 0x9f1aa7e7, 0x1eb02044, 0x1f151a2e
680 data4 0x9c0dc8b2, 0x9ef4087a, 0x1ec12b93, 0x1c1a946b
681 data4 0x1e89946f, 0x9dafe8c3, 0x1d295288, 0x9e8497ab
682 data4 0x1ec000c6, 0x1e102f29, 0x1e542256, 0x1e67d44d
683 data4 0x1ef688d8, 0x1f0e0f29, 0x1e67861f, 0x1e869748
684 data4 0x1ee6aa6e, 0x9e4d228b, 0x9e50be5b, 0x1e9fe225
685 data4 0x9ea34102, 0x9e628a3b, 0x9ed9fd83, 0x1ecd7109
686 data4 0x1f1864ff, 0x1ea19b76, 0x1db0d1c9, 0x9dff519b
687 data4 0x1e8fea71, 0x9ee82e9a, 0x9f08919b, 0x9ef5c8ae
688 data4 0x9ee446a4, 0x1ea59444, 0x1eb74230, 0x1ea13fbf
689 data4 0x9ea6a3ea, 0x1e5f2797, 0x9e0adb07, 0x9d3adadd
690 data4 0x1ebf2ee2, 0x1da19bfa, 0x1e8dea6d, 0x1ec4fea9
691 data4 0x1e669f22, 0x1dc5f919, 0x9ed25caa, 0x1ee475b1
692 data4 0x1ed0603e, 0x9eacb35c, 0x1dc00b27, 0x1e2f9991
693 data4 0x1e7b0406, 0x1eaa3387, 0x9d865bde, 0x1eb78a48
694 data4 0x1c40ae2e, 0x1ee9838b, 0x9f0f0d7f, 0x1e3e5d26
695 data4 0x1e99e7a6, 0x9e681ccf, 0x9e93ed65, 0x9eeb6a66
696 data4 0x1e29e9af, 0x9e96f923, 0x9e74f11d, 0x9f1474da
697 data4 0x1eec2ea7, 0x1ebf7aa3, 0x9c25dcca, 0x9f0553c2
698 data4 0x9e599efd, 0x1d2ab490, 0x1e95d7cd, 0x9ee4b20e
699 data4 0x9d988ce5, 0x9ef9787e, 0x9dbbba5b, 0x9f12c304
700 data4 0x1e3b9d70, 0x1e7bcae8, 0x9d98bb6e, 0x9e8e6b01
701 data4 0x9f07d03b, 0x9d67c822, 0x9f0ef69e, 0x1c7c0fe3
702 data4 0x9e9bfbb9, 0x9e83b84b, 0x1efbf15e, 0x9ecfa6a6
703 data4 0x9c91158e, 0x9ecf6770, 0x1ee1e3a8, 0x9dc95ec0
704 data4 0x1ef603f7, 0x1d5e52ba, 0x1c477d1b, 0x9e955cd8
705 data4 0x1ed665b0, 0x9e8376c4, 0x9c0ee88e, 0x1e8c989e
706 data4 0x1ea2df29, 0x9d961e5c, 0x1e101813, 0x1e7fffff
707 data4 0x9e5abff4, 0x1dbddd71, 0x1eb69100, 0x1e71f114
708 data4 0x1e9ca798, 0x1ef62c8d, 0x9db4e55a, 0x1dbe69ce
709 data4 0x9ef1c01f, 0x1f044a2a, 0x9eb9e0d7, 0x9ee59745
710 data4 0x9e874803, 0x1ea0b418, 0x9e13572a, 0x1ddbb3a2
711 data4 0x9ec0e391, 0x1e89fba1, 0x1ee8b261, 0x9e5d25f0
712 data4 0x9ef222cb, 0x9ef135ec, 0x1ea04b9a, 0x9f04291f
713 data4 0x9e969254, 0x9ee32f08, 0x9ed909d3, 0x9e362640
714 data4 0x9ec20735, 0x1e50131b, 0x9ed4e049, 0x1ee8e817
715 data4 0x1e1e09c0, 0x9ea643c5, 0x9e5a1ab6, 0x9e389059
716 data4 0x1e560947, 0x1d02b877, 0x1e4475ab, 0x9ea9aaf6
717 data4 0x1e95bc5e, 0x1eaf6afd, 0x1d43067d, 0x9d043821
718 data4 0x9e97baa9, 0x1de5c4f9, 0x9e9a0069, 0x9e1b9944
719 data4 0x1eb13686, 0x9eb907eb, 0x1e059589, 0x1cbd0f93
720 data4 0x9eb7e6ae, 0x1e9fa175, 0x1ee5bdf4, 0x1e8052f7
721 data4 0x9c80d1e3, 0x1bfbe28e, 0x9e672b3b, 0x9ecacf19
722 data4 0x9e3c04be, 0x1dfe8c5c, 0x1e1ba9cb, 0x1eb40b1e
723 data4 0x1ec7e7f6, 0x9d0d45b3, 0x1ef0113b, 0x9a155fa3
724 data4 0x1e28ec3b, 0x1e7ca8df, 0x9d2f91b4, 0x1eccd9ed
725 data4 0x9ed943bc, 0x9ccaab19, 0x9e8a5c58, 0x1ec3bca8
726 data4 0x1ed78dc7, 0x9ed391a8, 0x9e938f6e, 0x9ec4a030
727 data4 0x9e80346e, 0x1e7a4686, 0x9e284315, 0x9e39584c
728 data4 0x1ebdc9b4, 0x9e9cfce5, 0x9ef55c65, 0x1e2941e7
729 data4 0x9efbe59f, 0x1d87c41b, 0x1e40befc, 0x1e3d05b5
730 data4 0x1de9ea67, 0x1ec9a21c, 0x1decb69a, 0x1df6e75a
731 data4 0x9e8030ab, 0x9db20540, 0x9ef1e977, 0x1e3cdc43
732 data4 0x1e0492b0, 0x9e91d872, 0x1e775346, 0x9e939978
733 data4 0x1eb2714e, 0x1e49a203, 0x9e10195a, 0x1ef1ffc3
734 data4 0x9ea8b709, 0x9e832e27, 0x1ed5ac3b, 0x1edb20a6
735 data4 0x1e4dbd4e, 0x1efbb932, 0x1d8170ec, 0x1e6c4849
736 data4 0x1f008e17, 0x1e8000c4, 0x1d855ecf, 0x9e37cb85
737 data4 0x1ecffdf5, 0x1eba6519, 0x9edbe600, 0x1ea3e5e7
738 data4 0x1ed4fb39, 0x1f00be77, 0x1e6f4484, 0x9e9e7107
739 data4 0x9e30b29d, 0x9ee6e174, 0x1e3a2656, 0x9dd72f3f
740 data4 0x9ee12138, 0x1ed16fed, 0x9ece8a02, 0x9ca5b249
741 data4 0x9eafd508, 0x9ef0e9fc, 0x1d1307ac, 0x1eecee20
742 data4 0x1cf60c6f, 0x9d556216, 0x9eaed175, 0x9ec919f4
743 data4 0x1ec2c988, 0x1cd82772, 0x9dc99456, 0x1eab0467
744 data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d
745 LOCAL_OBJECT_END(D_table)
748 .section .text
749 GLOBAL_LIBM_ENTRY(cbrtl)
751 { .mfi
752 getf.sig GR_ARGSIG = f8
753 // will continue on main path only for normal/denormal numbers
754 // all other values will be filtered out and will exit early
755 fclass.nm.unc p12, p7 = f8, 0x1b
756 // GR_ADDR = pointer to C_1...C_6 followed by T_table
757 addl GR_ADDR = @ltoff(poly_coeffs), gp
758 }
759 { .mfi
760 // GR_BIAS23 = 2/3*bias -63 = 0xaaaa-0x3f = 0xaa6b
761 mov GR_BIAS23 = 0xaa6b
762 // normalize a
763 fma.s1 FR_XNORM = f8, f1, f0
764 // GR_D_ADDR = pointer to D table
765 addl GR_D_ADDR = @ltoff(D_table), gp
766 }
767 ;;
769 { .mmf
770 // load start address for C_1...C_6 followed by T_table
771 ld8 GR_C_START = [ GR_ADDR ]
772 // load start address of D table
773 ld8 GR_D_START = [ GR_D_ADDR ]
774 // y = frcpa(a)
775 frcpa.s1 FR_RCP, p6 = f1, f8
776 }
777 ;;
779 { .mmi
780 // get normalized significand
781 getf.sig GR_NORMSIG = FR_XNORM
782 // get exponent
783 getf.exp GR_NORMEXPSGN = FR_XNORM
784 (p7) cmp.eq p12, p0 = GR_ARGSIG, r0
785 }
786 ;;
788 { .mii
789 // load C_1
790 ldfe FR_C1 = [ GR_C_START ], 16
791 mov GR_SGNMASK = 0x20000
792 nop.i 0
793 }
794 ;;
796 { .mfb
797 // load C_2
798 ldfe FR_C2 = [ GR_C_START ], 16
799 (p12) fma.s0 f8 = f8, f1, f0
800 // NaN/Infinities exit early
801 (p12) br.ret.spnt b0
802 }
803 ;;
805 { .mfi
806 // load C_3, C_4
807 ldfpd FR_C3, FR_C4 = [ GR_C_START ], 16
808 // y = frcpa(a), set flags and result when argument is 0
809 // only used when p6=0
810 frcpa.s0 f8, p0 = f1, f8
811 nop.i 0
812 }
813 ;;
815 { .mii
816 // get GR_SIGN = sign
817 and GR_SIGN = GR_NORMEXPSGN, GR_SGNMASK
818 // eliminate leading 1 from GR_NORMSIG = 2nd table index
819 shl GR_INDEX2 = GR_NORMSIG, 1
820 // eliminate sign from exponent
821 andcm GR_NORMEXP = GR_NORMEXPSGN, GR_SGNMASK
822 }
823 ;;
825 { .mfi
826 // load C_5, C_6
827 (p6) ldfpd FR_C5, FR_C6 = [ GR_C_START ], 16
828 // r = 1-a*y
829 (p6) fnma.s1 FR_R = FR_RCP, FR_XNORM, f1
830 // Start computation of floor(exponent/3) by
831 // computing (2^20+2)/3*exponent = exponent*0x55556
832 // 1: exponent* = 5;
833 // (2^{16}-1)/3 = 0x5555:
834 // will form 0x5555*exponent by using shladd's
835 shladd GR_EXP5 = GR_NORMEXP, 2, GR_NORMEXP
836 }
837 ;;
839 { .mib
840 // Next several integer steps compute floor(exponent/3)
841 // GR_TMP1 = (5*expon)*16
842 shladd GR_TMP1 = GR_EXP5, 4, r0
843 // GR_EXP3 = 3*exponent
844 shladd GR_EXP3 = GR_NORMEXP, 1, GR_NORMEXP
845 nop.b 0
846 }
847 ;;
849 { .mmi
850 // GR_EXP6 = 6*exponent
851 shladd GR_EXP6 = GR_EXP3, 1, r0
852 // GR_EXP17 = 17*expon
853 add GR_EXP17 = GR_EXP5, GR_TMP1
854 // GR_IX2 = 2nd table index (8 bits)
855 shr.u GR_IX2 = GR_INDEX2, 56
856 }
857 ;;
859 { .mmi
860 // adjust T_table pointer by 2nd index
861 shladd GR_T_INDEX = GR_IX2, 3, GR_C_START
862 // adjust D_table pointer by 2nd index
863 shladd GR_D_INDEX = GR_IX2, 2, GR_D_START
864 // GR_TMP2 = (17*expon)*16^2
865 shl GR_TMP2 = GR_EXP17, 8
866 }
867 ;;
869 { .mmi
870 // GR_TMP3 = expon*(2^16-1)/3
871 add GR_TMP3 = GR_EXP17, GR_TMP2
872 ;;
873 // GR_TMP4 = expon*(2^20+2)/3 = expon*0x55556
874 shladd GR_TMP4 = GR_TMP3, 4, GR_EXP6
875 nop.i 0
876 }
877 ;;
879 { .mii
880 nop.m 0
881 // GR_EXP_RES = floor(expon/3)
882 shr.u GR_EXP_RES = GR_TMP4, 20
883 nop.i 0
884 }
885 ;;
887 { .mmi
888 nop.m 0
889 // r16 = 3*exponent
890 shladd r16 = GR_EXP_RES, 1, GR_EXP_RES
891 // bias exponent
892 add GR_EXPBIAS = GR_BIAS23, GR_EXP_RES
893 }
894 ;;
896 { .mmi
897 // get remainder of exponent/3
898 sub GR_EXP_MOD_3 = GR_NORMEXP, r16
899 ;;
900 // add sign to exponent
901 or GR_EXPSIGNRES = GR_EXPBIAS, GR_SIGN
902 // remainder << = 8
903 shl GR_REMTMP = GR_EXP_MOD_3, 8
904 }
905 ;;
907 { .mfi
908 // adjust D_table pointer by 1st index
909 shladd GR_IX_D = GR_REMTMP, 2, GR_D_INDEX
910 // P_1 = C_1+C_2*r
911 (p6) fma.s1 FR_P1 = FR_C2, FR_R, FR_C1
912 // adjust T_table pointer by 1st index
913 shladd GR_IX_T = GR_REMTMP, 3, GR_T_INDEX
914 }
915 { .mfi
916 // FR_SGNEXP = sign*2^{exponent/3}
917 (p6) setf.exp FR_SGNEXP = GR_EXPSIGNRES
918 // r^2 = r*r
919 (p6) fma.s1 FR_R2 = FR_R, FR_R, f0
920 nop.i 0
921 }
922 ;;
924 { .mfi
925 // load D
926 (p6) ldfs FR_D = [ GR_IX_D ]
927 // P_2 = C_3+C_4*r
928 (p6) fma.s1 FR_P2 = FR_C4, FR_R, FR_C3
929 nop.i 0
930 }
931 { .mfi
932 // load T
933 (p6) ldf8 FR_T = [ GR_IX_T ]
934 // P_3 = C_5+C_6*r
935 (p6) fma.s1 FR_P3 = FR_C6, FR_R, FR_C5
936 nop.i 0
937 }
938 ;;
940 { .mfi
941 nop.m 0
942 // P_4 = D-r*P_1
943 (p6) fnma.s1 FR_P4 = FR_R, FR_P1, FR_D
944 nop.i 0
945 }
946 { .mfi
947 nop.m 0
948 // r^3 = r*r^2
949 (p6) fma.s1 FR_R3 = FR_R, FR_R2, f0
950 nop.i 0
951 }
952 ;;
954 { .mfi
955 nop.m 0
956 // P_5 = P_2+r2*P_3
957 (p6) fma.s1 FR_P5 = FR_R2, FR_P3, FR_P2
958 nop.i 0
959 }
960 ;;
962 { .mfi
963 nop.m 0
964 // T = T*(sign*2^{exponent/3})
965 (p6) fma.s1 FR_TF = FR_T, FR_SGNEXP, f0
966 nop.i 0
967 }
968 { .mfi
969 nop.m 0
970 // P = P_4-r3*P_5
971 (p6) fnma.s1 FR_P = FR_R3, FR_P5, FR_P4
972 nop.i 0
973 }
974 ;;
976 { .mfb
977 nop.m 0
978 // result = T+T*p
979 (p6) fma.s0 f8 = FR_TF, FR_P, FR_TF
980 br.ret.sptk b0
981 }
982 ;;
984 GLOBAL_LIBM_END(cbrtl)