-
Notifications
You must be signed in to change notification settings - Fork 6
/
grisu_exact.h
2686 lines (2474 loc) · 97.2 KB
/
grisu_exact.h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
// Copyright 2020 Junekey Jeon
//
// The contents of this file may be used under the terms of
// the Apache License v2.0 with LLVM Exceptions.
//
// (See accompanying file LICENSE-Apache or copy at
// https://llvm.org/foundation/relicensing/LICENSE.txt)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
#ifndef JKJ_GRISU_EXACT
#define JKJ_GRISU_EXACT
//#include <bit> // We don't have C++20 <bit> yet
#include <bitset> // Payload of NaN's is of type std::bitset
#include <cassert>
#include <cstddef> // std::size_t, etc
#include <cstdint> // std::uint32_t, etc.
#include <cstring> // std::memcpy; not needed if C++20 std::bit_cast is used instead
#include <limits>
#include <type_traits> // std::remove_cv, etc
#if defined(_MSC_VER)
#include <intrin.h>
#include <immintrin.h>
// Suppress additional buffer overrun check
// I have no idea why MSVC thinks some functions here are vulnerable to the buffer overrun attacks
// No, they aren't.
#ifndef __clang__
#define JKJ_SAFEBUFFERS __declspec(safebuffers)
#else
#define JKJ_SAFEBUFFERS
#endif
#else
#define JKJ_SAFEBUFFERS
#endif
namespace jkj {
namespace grisu_exact_detail {
////////////////////////////////////////////////////////////////////////////////////////
// Utilities for 128-bit arithmetic
////////////////////////////////////////////////////////////////////////////////////////
// Get 128-bit result of multiplication of two 64-bit unsigned integers
struct uint128 {
uint128() = default;
#if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__)
unsigned __int128 internal_;
constexpr uint128(std::uint64_t high, std::uint64_t low) noexcept :
internal_{ ((unsigned __int128)low) | (((unsigned __int128)high) << 64) } {}
constexpr uint128(unsigned __int128 u) : internal_{ u } {}
constexpr std::uint64_t high() const noexcept {
return std::uint64_t(internal_ >> 64);
}
constexpr std::uint64_t low() const noexcept {
return std::uint64_t(internal_);
}
#else
std::uint64_t high_;
std::uint64_t low_;
constexpr uint128(std::uint64_t high, std::uint64_t low) noexcept :
high_{ high }, low_{ low } {}
constexpr std::uint64_t high() const noexcept {
return high_;
}
constexpr std::uint64_t low() const noexcept {
return low_;
}
#endif
};
static inline std::uint64_t umul64(std::uint32_t x, std::uint32_t y) noexcept {
#if defined(_MSC_VER)
return __emulu(x, y);
#else
return x * (std::uint64_t)y;
#endif
}
JKJ_SAFEBUFFERS
inline uint128 umul128(std::uint64_t x, std::uint64_t y) noexcept {
#if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__)
return (unsigned __int128)(x) * (unsigned __int128)(y);
#elif defined(_MSC_VER) && defined(_M_X64)
uint128 result;
result.low_ = _umul128(x, y, &result.high_);
return result;
#else
auto a = std::uint32_t(x >> 32);
auto b = std::uint32_t(x);
auto c = std::uint32_t(y >> 32);
auto d = std::uint32_t(y);
auto ac = umul64(a, c);
auto bc = umul64(b, c);
auto ad = umul64(a, d);
auto bd = umul64(b, d);
auto intermediate = (bd >> 32) + std::uint32_t(ad) + std::uint32_t(bc);
return{ ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32),
(intermediate << 32) + std::uint32_t(bd) };
#endif
}
JKJ_SAFEBUFFERS
inline std::uint64_t umul128_upper64(std::uint64_t x, std::uint64_t y) noexcept {
#if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__)
auto p = (unsigned __int128)(x) * (unsigned __int128)(y);
return std::uint64_t(p >> 64);
#elif defined(_MSC_VER) && defined(_M_X64)
return __umulh(x, y);
#else
auto a = std::uint32_t(x >> 32);
auto b = std::uint32_t(x);
auto c = std::uint32_t(y >> 32);
auto d = std::uint32_t(y);
auto ac = umul64(a, c);
auto bc = umul64(b, c);
auto ad = umul64(a, d);
auto bd = umul64(b, d);
auto intermediate = (bd >> 32) + std::uint32_t(ad) + std::uint32_t(bc);
return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32);
#endif
}
// Get upper 64-bits of multiplication of a 64-bit unsigned integer and a 128-bit unsigned integer
JKJ_SAFEBUFFERS
inline std::uint64_t umul192_upper64(std::uint64_t x, uint128 y) noexcept {
auto g0 = umul128(x, y.high());
auto g10 = umul128_upper64(x, y.low());
#if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__)
return uint128{ g0.internal_ + g10 }.high();
#elif defined(_MSC_VER) && defined(_M_X64)
std::uint64_t high, low;
auto carry = _addcarry_u64(0, g0.low(), g10, &low);
_addcarry_u64(carry, g0.high(), 0, &high);
return high;
#else
auto intermediate = g0.low() + g10;
return g0.high() + (intermediate < g10);
#endif
}
// Get upper 32-bits of multiplication of a 32-bit unsigned integer and a 64-bit unsigned integer
inline std::uint32_t umul96_upper32(std::uint32_t x, std::uint64_t y) noexcept {
#if defined(__x86_64__) || defined(_M_X64)
return std::uint32_t(umul128_upper64(x, y));
#else
//std::uint32_t a = 0;
auto b = x;
auto c = std::uint32_t(y >> 32);
auto d = std::uint32_t(y);
//std::uint64_t ac = 0;
auto bc = umul64(b, c);
//std::uint64_t ad = 0;
auto bd = umul64(b, d);
auto intermediate = (bd >> 32) + bc;
return std::uint32_t(intermediate >> 32);
#endif
}
// Compute b^e in compile-time
template <class UInt>
constexpr UInt compute_power(UInt b, unsigned int e) noexcept {
UInt r = 1;
for (unsigned int i = 0; i < e; ++i) {
r *= b;
}
return r;
}
// Check if a number is a multiple of 2^exp
template <class UInt>
inline bool divisible_by_power_of_2(UInt x, int exp) noexcept {
static_assert(std::is_same_v<UInt, std::uint32_t> || std::is_same_v<UInt, std::uint64_t>);
assert(exp >= 1);
assert(x != 0);
#if (defined(__GNUC__) || defined(__clang__)) && defined(__x86_64__)
int index;
if constexpr (std::is_same_v<UInt, std::uint32_t>) {
if constexpr (sizeof(unsigned long) == 4) {
index = __builtin_ctzl((unsigned long)x);
}
else {
static_assert(sizeof(unsigned int) == 4,
"jkj::grisu_exact: at least one of unsigned int and unsigned long should be 4 bytes long");
index = __builtin_ctz((unsigned int)x);
}
}
else {
static_assert(sizeof(unsigned long long) == 8,
"jkj::grisu_exact: unsigned long long should be 8 bytes long");
index = __builtin_ctzll((unsigned long long)x);
}
return index >= exp;
#elif defined(_MSC_VER) && defined(_M_X64)
unsigned long index;
if constexpr (std::is_same_v<UInt, std::uint32_t>) {
_BitScanForward(&index, x);
}
else {
_BitScanForward64(&index, x);
}
return int(index) >= exp;
#else
if (exp >= int(sizeof(UInt) * 8)) {
return false;
}
auto mask = UInt((UInt(1) << exp) - 1);
return (x & mask) == 0;
#endif
}
// Check if a number is a multiple of 5^exp
// Use the algorithm introduced in Section 9 of Granlund-Montgomery
template <class UInt>
constexpr UInt compute_modular_inverse_of_5() noexcept {
// Use Euler's theorem
// phi(p^k) = p^(k-1) * (p-1), so phi(2^n) = 2^(n-1).
// Hence, we need to compute 5^(2^(n-1) - 1), which is equal to
// 5^1 * 5^2 * 5^4 * 5^8 * ... * 5^(2^(n-2)),
// which can be computed as:
constexpr unsigned int n = std::numeric_limits<UInt>::digits;
UInt r = 5;
for (unsigned int e = 1; e <= n - 2; ++e) {
r = 5 * r * r;
}
return r;
}
template <class UInt>
struct divisibility_test_table_entry {
UInt max_quotient;
UInt mod_inv;
};
// std::array might be an overkill
template <class UInt, unsigned int N>
struct divisibility_test_table {
static constexpr auto size = N;
divisibility_test_table_entry<UInt> value[N];
};
template <class UInt, std::size_t size>
constexpr auto generate_divisibility_test_table() noexcept {
using return_type = divisibility_test_table<UInt, size>;
return_type table{};
for (unsigned int i = 0; i < size; ++i) {
table.value[i].max_quotient =
std::numeric_limits<UInt>::max() / compute_power(UInt(5), i);
table.value[i].mod_inv =
compute_power(compute_modular_inverse_of_5<UInt>(), i);
}
return table;
}
template <class UInt>
struct divisibility_test_table_holder {
static constexpr auto table = generate_divisibility_test_table<UInt,
std::is_same_v<UInt, std::uint32_t> ? 12 : 24>();
};
template <class UInt>
constexpr bool divisible_by_power_of_5(UInt x, unsigned int exp) noexcept {
assert(exp < divisibility_test_table_holder<UInt>::table.size);
auto const& entry = divisibility_test_table_holder<UInt>::table.value[exp];
return (x * entry.mod_inv) <= entry.max_quotient;
}
////////////////////////////////////////////////////////////////////////////////////////
// Fast and accurate log floor calculation
////////////////////////////////////////////////////////////////////////////////////////
// This function is accurate if e is in the range [-1650,1650]
template <bool should_assert = true>
constexpr int floor_log10_pow2(int e) noexcept {
if constexpr (should_assert) {
assert(e >= -1650 && e <= 1650);
}
// The next 12 digits are 0xd27
constexpr std::int32_t log10_2_up_to_20 = 0x4d104;
return int(
// Calculate 0x0.4d104 * exp * 2^20
(std::int32_t(e) * log10_2_up_to_20)
// Perform arithmetic-shift
>> 20);
}
// This function is accurate if e is in the range [-642,642]
template <bool should_assert = true>
constexpr int floor_log2_pow10(int e) noexcept {
if constexpr (should_assert) {
assert(e >= -642 && e <= 642);
}
// The next 12 digits are 0x12f
constexpr std::int32_t log2_5_over_4_up_to_20 = 0x35269e;
return int(
// Calculate 0x3.5269e * exp * 2^20
(std::int32_t(e) * log2_5_over_4_up_to_20)
// Perform arithmetic-shift
>> 20);
}
// This function is accurate if e is in the range [-65536,+65536]
// This function is only executed at compile-time,
// and never executed at runtime.
template <bool should_assert = true>
constexpr int floor_log5_pow2(int e) noexcept {
if constexpr (should_assert) {
assert(e >= -65536 && e <= 65536);
}
// The next 32 digits are 0x143dcb94
constexpr std::uint32_t log5_2_up_to_32 = 0x6e40d1a4;
return int(
// Calculate 0x0.6e40d1a4 * exp * 2^32
(std::int64_t(e) * log5_2_up_to_32)
// Perform arithmetic-shift
>> 32);
}
////////////////////////////////////////////////////////////////////////////////////////
// Collection of relevent information about IEEE-754 and precision settings
////////////////////////////////////////////////////////////////////////////////////////
template <class Float>
struct common_info {
using float_type = Float;
static_assert(std::numeric_limits<Float>::is_iec559 &&
std::numeric_limits<Float>::radix == 2 &&
(sizeof(Float) == 4 || sizeof(Float) == 8),
"Grisu-Exact algorithm only applies to IEEE-754 binary32 and binary64 formats!");
static constexpr std::size_t precision = std::numeric_limits<Float>::digits - 1;
using extended_significand_type = std::conditional_t<
sizeof(Float) == 4,
std::uint32_t,
std::uint64_t>;
static_assert(sizeof(extended_significand_type) == sizeof(Float));
static constexpr std::size_t extended_precision =
sizeof(extended_significand_type) * std::numeric_limits<unsigned char>::digits;
static constexpr auto sign_bit_mask =
(extended_significand_type(1) << (extended_precision - 1));
static constexpr std::size_t exponent_bits =
extended_precision - precision - 1;
static constexpr int exponent_bias = 1 - (1 << (exponent_bits - 1));
static constexpr auto exponent_bits_mask =
((extended_significand_type(1) << exponent_bits) - 1) << precision;
static constexpr auto boundary_bit =
(extended_significand_type(1) << (extended_precision - precision - 2));
static constexpr auto normal_interval_length = boundary_bit << 1;
static constexpr auto edge_case_boundary_bit = boundary_bit >> 1;
static constexpr int min_exponent =
std::numeric_limits<Float>::min_exponent - int(extended_precision);
static constexpr int max_exponent =
std::numeric_limits<Float>::max_exponent - int(extended_precision);
static_assert(min_exponent < 0 && max_exponent > 0 && -min_exponent >= max_exponent);
static_assert(min_exponent == 1 + exponent_bias - int(extended_precision) + 1);
static constexpr int alpha = sizeof(Float) == 4 ? -5 : -5;
static constexpr int gamma = alpha + 3;
static_assert(alpha >= -(int(extended_precision - precision) - 4) && gamma <= 0);
static constexpr int min_kappa =
-floor_log10_pow2(-(int(extended_precision - precision) - 3 + alpha)) - 1;
static constexpr int max_kappa =
-floor_log10_pow2(-(int(extended_precision) + gamma)) - 1;
static_assert(0 <= min_kappa && min_kappa <= max_kappa);
static constexpr int initial_kappa = sizeof(Float) == 4 ? 2 : 3;
static_assert(min_kappa <= initial_kappa && initial_kappa <= max_kappa);
// Ensure delta cannot overflow
// delta is upper bounded by 2^(q-p-1+gamma), and
// during the decreasing search, it would get multiplied by 10^(initial_kappa-min_kappa-1)
static_assert(floor_log2_pow10(initial_kappa - min_kappa - 1) <
32 - int(extended_precision - precision - 1) - gamma);
// Ensure 10^initial_kappa fits inside 32 bits
static_assert(initial_kappa < floor_log10_pow2(32));
static constexpr int min_k = -floor_log10_pow2(max_exponent + 1 - alpha);
static constexpr int max_k = -floor_log10_pow2(min_exponent + 1 - alpha);
static constexpr std::size_t cache_precision = extended_precision * 2;
using cache_entry_type = std::conditional_t<
sizeof(Float) == 4,
std::uint64_t,
uint128>;
static constexpr int integer_check_exponent_lower_bound_for_q_mp_m3 =
floor_log5_pow2(-(int(extended_precision - precision) - 3 + alpha)) -
(int(extended_precision - precision) - 3);
static constexpr int integer_check_exponent_lower_bound_for_q_mp_m2 =
floor_log5_pow2(-(int(extended_precision - precision) - 2 + alpha)) -
(int(extended_precision - precision) - 2);
static constexpr int integer_check_exponent_lower_bound_for_q_mp_m1 =
floor_log5_pow2(-(int(extended_precision - precision) - 1 + alpha)) -
(int(extended_precision - precision) - 1);
static constexpr int integer_check_exponent_lower_bound_for_q_mp =
floor_log5_pow2(-(int(extended_precision - precision) + alpha)) -
(int(extended_precision - precision));
static constexpr int max_exponent_for_k_geq_0 = alpha + 2;
static constexpr int max_exponent_for_k_geq_m1 = alpha + 5;
static constexpr int integer_check_exponent_upper_bound_for_p_p2 =
(alpha - 2) - floor_log2_pow10(-floor_log5_pow2(precision + 2) - 1);
static constexpr int integer_check_exponent_upper_bound_for_p_p1 =
(alpha - 2) - floor_log2_pow10(-floor_log5_pow2(precision + 1) - 1);
// Ensure that fractional parts cannot vanish when exponent is the minimum
static_assert(min_exponent < integer_check_exponent_lower_bound_for_q_mp_m3);
static constexpr int zero_fractional_part_min_exponent_normal =
floor_log5_pow2(-(int(extended_precision - precision) - 2 + alpha)) -
(int(extended_precision - precision) - 2);
static constexpr int zero_fractional_part_min_exponent_edge =
floor_log5_pow2(-(int(extended_precision - precision) - 3 + alpha)) -
(int(extended_precision - precision) - 3);
static constexpr int zero_fractional_part_max_exponent_normal =
alpha - 2 - floor_log2_pow10(-floor_log5_pow2(precision + 2) - 1);
static constexpr int max_exponent_for_nonnegative_k = alpha + 2;
static constexpr int zero_fractional_part_min_exponent_delta_normal =
floor_log5_pow2(-(int(extended_precision - precision) - 1 + alpha)) -
(int(extended_precision - precision) - 1);
};
////////////////////////////////////////////////////////////////////////////////////////
// Computed cache entries
// !! You SHOULD regenerate the cache if you modify alpha and gamma !!
////////////////////////////////////////////////////////////////////////////////////////
template <class Float>
struct cache_holder;
template <>
struct cache_holder<float> {
static constexpr std::uint64_t cache[] = {
0xa2425ff75e14fc32,
0xcad2f7f5359a3b3f,
0xfd87b5f28300ca0e,
0x9e74d1b791e07e49,
0xc612062576589ddb,
0xf79687aed3eec552,
0x9abe14cd44753b53,
0xc16d9a0095928a28,
0xf1c90080baf72cb2,
0x971da05074da7bef,
0xbce5086492111aeb,
0xec1e4a7db69561a6,
0x9392ee8e921d5d08,
0xb877aa3236a4b44a,
0xe69594bec44de15c,
0x901d7cf73ab0acda,
0xb424dc35095cd810,
0xe12e13424bb40e14,
0x8cbccc096f5088cc,
0xafebff0bcb24aaff,
0xdbe6fecebdedd5bf,
0x89705f4136b4a598,
0xabcc77118461cefd,
0xd6bf94d5e57a42bd,
0x8637bd05af6c69b6,
0xa7c5ac471b478424,
0xd1b71758e219652c,
0x83126e978d4fdf3c,
0xa3d70a3d70a3d70b,
0xcccccccccccccccd,
0x8000000000000000,
0xa000000000000000,
0xc800000000000000,
0xfa00000000000000,
0x9c40000000000000,
0xc350000000000000,
0xf424000000000000,
0x9896800000000000,
0xbebc200000000000,
0xee6b280000000000,
0x9502f90000000000,
0xba43b74000000000,
0xe8d4a51000000000,
0x9184e72a00000000,
0xb5e620f480000000,
0xe35fa931a0000000,
0x8e1bc9bf04000000,
0xb1a2bc2ec5000000,
0xde0b6b3a76400000,
0x8ac7230489e80000,
0xad78ebc5ac620000,
0xd8d726b7177a8000,
0x878678326eac9000,
0xa968163f0a57b400,
0xd3c21bcecceda100,
0x84595161401484a0,
0xa56fa5b99019a5c8,
0xcecb8f27f4200f3a,
0x813f3978f8940984,
0xa18f07d736b90be5,
0xc9f2c9cd04674ede,
0xfc6f7c4045812296,
0x9dc5ada82b70b59d,
0xc5371912364ce305,
0xf684df56c3e01bc6,
0x9a130b963a6c115c,
0xc097ce7bc90715b3,
0xf0bdc21abb48db20,
0x96769950b50d88f4,
0xbc143fa4e250eb31,
0xeb194f8e1ae525fd,
0x92efd1b8d0cf37be,
0xb7abc627050305ad,
0xe596b7b0c643c719,
0x8f7e32ce7bea5c6f,
0xb35dbf821ae4f38b,
0xe0352f62a19e306e
};
};
template <>
struct cache_holder<double> {
static constexpr uint128 cache[] = {
{ 0xc795830d75038c1d, 0xd59df5b9ef6a2418 },
{ 0xf97ae3d0d2446f25, 0x4b0573286b44ad1e },
{ 0x9becce62836ac577, 0x4ee367f9430aec33 },
{ 0xc2e801fb244576d5, 0x229c41f793cda740 },
{ 0xf3a20279ed56d48a, 0x6b43527578c11110 },
{ 0x9845418c345644d6, 0x830a13896b78aaaa },
{ 0xbe5691ef416bd60c, 0x23cc986bc656d554 },
{ 0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9 },
{ 0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa },
{ 0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54 },
{ 0xe858ad248f5c22c9, 0xd1b3400f8f9cff69 },
{ 0x91376c36d99995be, 0x23100809b9c21fa2 },
{ 0xb58547448ffffb2d, 0xabd40a0c2832a78b },
{ 0xe2e69915b3fff9f9, 0x16c90c8f323f516d },
{ 0x8dd01fad907ffc3b, 0xae3da7d97f6792e4 },
{ 0xb1442798f49ffb4a, 0x99cd11cfdf41779d },
{ 0xdd95317f31c7fa1d, 0x40405643d711d584 },
{ 0x8a7d3eef7f1cfc52, 0x482835ea666b2573 },
{ 0xad1c8eab5ee43b66, 0xda3243650005eed0 },
{ 0xd863b256369d4a40, 0x90bed43e40076a83 },
{ 0x873e4f75e2224e68, 0x5a7744a6e804a292 },
{ 0xa90de3535aaae202, 0x711515d0a205cb37 },
{ 0xd3515c2831559a83, 0x0d5a5b44ca873e04 },
{ 0x8412d9991ed58091, 0xe858790afe9486c3 },
{ 0xa5178fff668ae0b6, 0x626e974dbe39a873 },
{ 0xce5d73ff402d98e3, 0xfb0a3d212dc81290 },
{ 0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a },
{ 0xa139029f6a239f72, 0x1c1fffc1ebc44e81 },
{ 0xc987434744ac874e, 0xa327ffb266b56221 },
{ 0xfbe9141915d7a922, 0x4bf1ff9f0062baa9 },
{ 0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa },
{ 0xc4ce17b399107c22, 0xcb550fb4384d21d4 },
{ 0xf6019da07f549b2b, 0x7e2a53a146606a49 },
{ 0x99c102844f94e0fb, 0x2eda7444cbfc426e },
{ 0xc0314325637a1939, 0xfa911155fefb5309 },
{ 0xf03d93eebc589f88, 0x793555ab7eba27cb },
{ 0x96267c7535b763b5, 0x4bc1558b2f3458df },
{ 0xbbb01b9283253ca2, 0x9eb1aaedfb016f17 },
{ 0xea9c227723ee8bcb, 0x465e15a979c1cadd },
{ 0x92a1958a7675175f, 0x0bfacd89ec191eca },
{ 0xb749faed14125d36, 0xcef980ec671f667c },
{ 0xe51c79a85916f484, 0x82b7e12780e7401b },
{ 0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811 },
{ 0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16 },
{ 0xdfbdcece67006ac9, 0x67a791e093e1d49b },
{ 0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1 },
{ 0xaecc49914078536d, 0x58fae9f773886e19 },
{ 0xda7f5bf590966848, 0xaf39a475506a899f },
{ 0x888f99797a5e012d, 0x6d8406c952429604 },
{ 0xaab37fd7d8f58178, 0xc8e5087ba6d33b84 },
{ 0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a65 },
{ 0x855c3be0a17fcd26, 0x5cf2eea09a550680 },
{ 0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f },
{ 0xd0601d8efc57b08b, 0xf13b94daf124da27 },
{ 0x823c12795db6ce57, 0x76c53d08d6b70859 },
{ 0xa2cb1717b52481ed, 0x54768c4b0c64ca6f },
{ 0xcb7ddcdda26da268, 0xa9942f5dcf7dfd0a },
{ 0xfe5d54150b090b02, 0xd3f93b35435d7c4d },
{ 0x9efa548d26e5a6e1, 0xc47bc5014a1a6db0 },
{ 0xc6b8e9b0709f109a, 0x359ab6419ca1091c },
{ 0xf867241c8cc6d4c0, 0xc30163d203c94b63 },
{ 0x9b407691d7fc44f8, 0x79e0de63425dcf1e },
{ 0xc21094364dfb5636, 0x985915fc12f542e5 },
{ 0xf294b943e17a2bc4, 0x3e6f5b7b17b2939e },
{ 0x979cf3ca6cec5b5a, 0xa705992ceecf9c43 },
{ 0xbd8430bd08277231, 0x50c6ff782a838354 },
{ 0xece53cec4a314ebd, 0xa4f8bf5635246429 },
{ 0x940f4613ae5ed136, 0x871b7795e136be9a },
{ 0xb913179899f68584, 0x28e2557b59846e40 },
{ 0xe757dd7ec07426e5, 0x331aeada2fe589d0 },
{ 0x9096ea6f3848984f, 0x3ff0d2c85def7622 },
{ 0xb4bca50b065abe63, 0x0fed077a756b53aa },
{ 0xe1ebce4dc7f16dfb, 0xd3e8495912c62895 },
{ 0x8d3360f09cf6e4bd, 0x64712dd7abbbd95d },
{ 0xb080392cc4349dec, 0xbd8d794d96aacfb4 },
{ 0xdca04777f541c567, 0xecf0d7a0fc5583a1 },
{ 0x89e42caaf9491b60, 0xf41686c49db57245 },
{ 0xac5d37d5b79b6239, 0x311c2875c522ced6 },
{ 0xd77485cb25823ac7, 0x7d633293366b828c },
{ 0x86a8d39ef77164bc, 0xae5dff9c02033198 },
{ 0xa8530886b54dbdeb, 0xd9f57f830283fdfd },
{ 0xd267caa862a12d66, 0xd072df63c324fd7c },
{ 0x8380dea93da4bc60, 0x4247cb9e59f71e6e },
{ 0xa46116538d0deb78, 0x52d9be85f074e609 },
{ 0xcd795be870516656, 0x67902e276c921f8c },
{ 0x806bd9714632dff6, 0x00ba1cd8a3db53b7 },
{ 0xa086cfcd97bf97f3, 0x80e8a40eccd228a5 },
{ 0xc8a883c0fdaf7df0, 0x6122cd128006b2ce },
{ 0xfad2a4b13d1b5d6c, 0x796b805720085f82 },
{ 0x9cc3a6eec6311a63, 0xcbe3303674053bb1 },
{ 0xc3f490aa77bd60fc, 0xbedbfc4411068a9d },
{ 0xf4f1b4d515acb93b, 0xee92fb5515482d45 },
{ 0x991711052d8bf3c5, 0x751bdd152d4d1c4b },
{ 0xbf5cd54678eef0b6, 0xd262d45a78a0635e },
{ 0xef340a98172aace4, 0x86fb897116c87c35 },
{ 0x9580869f0e7aac0e, 0xd45d35e6ae3d4da1 },
{ 0xbae0a846d2195712, 0x8974836059cca10a },
{ 0xe998d258869facd7, 0x2bd1a438703fc94c },
{ 0x91ff83775423cc06, 0x7b6306a34627ddd0 },
{ 0xb67f6455292cbf08, 0x1a3bc84c17b1d543 },
{ 0xe41f3d6a7377eeca, 0x20caba5f1d9e4a94 },
{ 0x8e938662882af53e, 0x547eb47b7282ee9d },
{ 0xb23867fb2a35b28d, 0xe99e619a4f23aa44 },
{ 0xdec681f9f4c31f31, 0x6405fa00e2ec94d5 },
{ 0x8b3c113c38f9f37e, 0xde83bc408dd3dd05 },
{ 0xae0b158b4738705e, 0x9624ab50b148d446 },
{ 0xd98ddaee19068c76, 0x3badd624dd9b0958 },
{ 0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d7 },
{ 0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4d },
{ 0xd47487cc8470652b, 0x7647c32000696720 },
{ 0x84c8d4dfd2c63f3b, 0x29ecd9f40041e074 },
{ 0xa5fb0a17c777cf09, 0xf468107100525891 },
{ 0xcf79cc9db955c2cc, 0x7182148d4066eeb5 },
{ 0x81ac1fe293d599bf, 0xc6f14cd848405531 },
{ 0xa21727db38cb002f, 0xb8ada00e5a506a7d },
{ 0xca9cf1d206fdc03b, 0xa6d90811f0e4851d },
{ 0xfd442e4688bd304a, 0x908f4a166d1da664 },
{ 0x9e4a9cec15763e2e, 0x9a598e4e043287ff },
{ 0xc5dd44271ad3cdba, 0x40eff1e1853f29fe },
{ 0xf7549530e188c128, 0xd12bee59e68ef47d },
{ 0x9a94dd3e8cf578b9, 0x82bb74f8301958cf },
{ 0xc13a148e3032d6e7, 0xe36a52363c1faf02 },
{ 0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac2 },
{ 0x96f5600f15a7b7e5, 0x29ab103a5ef8c0ba },
{ 0xbcb2b812db11a5de, 0x7415d448f6b6f0e8 },
{ 0xebdf661791d60f56, 0x111b495b3464ad22 },
{ 0x936b9fcebb25c995, 0xcab10dd900beec35 },
{ 0xb84687c269ef3bfb, 0x3d5d514f40eea743 },
{ 0xe65829b3046b0afa, 0x0cb4a5a3112a5113 },
{ 0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ac },
{ 0xb3f4e093db73a093, 0x59ed216765690f57 },
{ 0xe0f218b8d25088b8, 0x306869c13ec3532d },
{ 0x8c974f7383725573, 0x1e414218c73a13fc },
{ 0xafbd2350644eeacf, 0xe5d1929ef90898fb },
{ 0xdbac6c247d62a583, 0xdf45f746b74abf3a },
{ 0x894bc396ce5da772, 0x6b8bba8c328eb784 },
{ 0xab9eb47c81f5114f, 0x066ea92f3f326565 },
{ 0xd686619ba27255a2, 0xc80a537b0efefebe },
{ 0x8613fd0145877585, 0xbd06742ce95f5f37 },
{ 0xa798fc4196e952e7, 0x2c48113823b73705 },
{ 0xd17f3b51fca3a7a0, 0xf75a15862ca504c6 },
{ 0x82ef85133de648c4, 0x9a984d73dbe722fc },
{ 0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebbb },
{ 0xcc963fee10b7d1b3, 0x318df905079926a9 },
{ 0xffbbcfe994e5c61f, 0xfdf17746497f7053 },
{ 0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa634 },
{ 0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc1 },
{ 0xf9bd690a1b68637b, 0x3dfdce7aa3c673b1 },
{ 0x9c1661a651213e2d, 0x06bea10ca65c084f },
{ 0xc31bfa0fe5698db8, 0x486e494fcff30a63 },
{ 0xf3e2f893dec3f126, 0x5a89dba3c3efccfb },
{ 0x986ddb5c6b3a76b7, 0xf89629465a75e01d },
{ 0xbe89523386091465, 0xf6bbb397f1135824 },
{ 0xee2ba6c0678b597f, 0x746aa07ded582e2d },
{ 0x94db483840b717ef, 0xa8c2a44eb4571cdd },
{ 0xba121a4650e4ddeb, 0x92f34d62616ce414 },
{ 0xe896a0d7e51e1566, 0x77b020baf9c81d18 },
{ 0x915e2486ef32cd60, 0x0ace1474dc1d122f },
{ 0xb5b5ada8aaff80b8, 0x0d819992132456bb },
{ 0xe3231912d5bf60e6, 0x10e1fff697ed6c6a },
{ 0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2 },
{ 0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb3 },
{ 0xddd0467c64bce4a0, 0xac7cb3f6d05ddbdf },
{ 0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96c },
{ 0xad4ab7112eb3929d, 0x86c16c98d2c953c7 },
{ 0xd89d64d57a607744, 0xe871c7bf077ba8b8 },
{ 0x87625f056c7c4a8b, 0x11471cd764ad4973 },
{ 0xa93af6c6c79b5d2d, 0xd598e40d3dd89bd0 },
{ 0xd389b47879823479, 0x4aff1d108d4ec2c4 },
{ 0x843610cb4bf160cb, 0xcedf722a585139bb },
{ 0xa54394fe1eedb8fe, 0xc2974eb4ee658829 },
{ 0xce947a3da6a9273e, 0x733d226229feea33 },
{ 0x811ccc668829b887, 0x0806357d5a3f5260 },
{ 0xa163ff802a3426a8, 0xca07c2dcb0cf26f8 },
{ 0xc9bcff6034c13052, 0xfc89b393dd02f0b6 },
{ 0xfc2c3f3841f17c67, 0xbbac2078d443ace3 },
{ 0x9d9ba7832936edc0, 0xd54b944b84aa4c0e },
{ 0xc5029163f384a931, 0x0a9e795e65d4df12 },
{ 0xf64335bcf065d37d, 0x4d4617b5ff4a16d6 },
{ 0x99ea0196163fa42e, 0x504bced1bf8e4e46 },
{ 0xc06481fb9bcf8d39, 0xe45ec2862f71e1d7 },
{ 0xf07da27a82c37088, 0x5d767327bb4e5a4d },
{ 0x964e858c91ba2655, 0x3a6a07f8d510f870 },
{ 0xbbe226efb628afea, 0x890489f70a55368c },
{ 0xeadab0aba3b2dbe5, 0x2b45ac74ccea842f },
{ 0x92c8ae6b464fc96f, 0x3b0b8bc90012929e },
{ 0xb77ada0617e3bbcb, 0x09ce6ebb40173745 },
{ 0xe55990879ddcaabd, 0xcc420a6a101d0516 },
{ 0x8f57fa54c2a9eab6, 0x9fa946824a12232e },
{ 0xb32df8e9f3546564, 0x47939822dc96abfa },
{ 0xdff9772470297ebd, 0x59787e2b93bc56f8 },
{ 0x8bfbea76c619ef36, 0x57eb4edb3c55b65b },
{ 0xaefae51477a06b03, 0xede622920b6b23f2 },
{ 0xdab99e59958885c4, 0xe95fab368e45ecee },
{ 0x88b402f7fd75539b, 0x11dbcb0218ebb415 },
{ 0xaae103b5fcd2a881, 0xd652bdc29f26a11a },
{ 0xd59944a37c0752a2, 0x4be76d3346f04960 },
{ 0x857fcae62d8493a5, 0x6f70a4400c562ddc },
{ 0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb953 },
{ 0xd097ad07a71f26b2, 0x7e2000a41346a7a8 },
{ 0x825ecc24c873782f, 0x8ed400668c0c28c9 },
{ 0xa2f67f2dfa90563b, 0x728900802f0f32fb },
{ 0xcbb41ef979346bca, 0x4f2b40a03ad2ffba },
{ 0xfea126b7d78186bc, 0xe2f610c84987bfa9 },
{ 0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7ca },
{ 0xc6ede63fa05d3143, 0x91503d1c79720dbc },
{ 0xf8a95fcf88747d94, 0x75a44c6397ce912b },
{ 0x9b69dbe1b548ce7c, 0xc986afbe3ee11abb },
{ 0xc24452da229b021b, 0xfbe85badce996169 },
{ 0xf2d56790ab41c2a2, 0xfae27299423fb9c4 },
{ 0x97c560ba6b0919a5, 0xdccd879fc967d41b },
{ 0xbdb6b8e905cb600f, 0x5400e987bbc1c921 },
{ 0xed246723473e3813, 0x290123e9aab23b69 },
{ 0x9436c0760c86e30b, 0xf9a0b6720aaf6522 },
{ 0xb94470938fa89bce, 0xf808e40e8d5b3e6a },
{ 0xe7958cb87392c2c2, 0xb60b1d1230b20e05 },
{ 0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c3 },
{ 0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af4 },
{ 0xe2280b6c20dd5232, 0x25c6da63c38de1b1 },
{ 0x8d590723948a535f, 0x579c487e5a38ad0f },
{ 0xb0af48ec79ace837, 0x2d835a9df0c6d852 },
{ 0xdcdb1b2798182244, 0xf8e431456cf88e66 },
{ 0x8a08f0f8bf0f156b, 0x1b8e9ecb641b5900 },
{ 0xac8b2d36eed2dac5, 0xe272467e3d222f40 },
{ 0xd7adf884aa879177, 0x5b0ed81dcc6abb10 },
{ 0x86ccbb52ea94baea, 0x98e947129fc2b4ea },
{ 0xa87fea27a539e9a5, 0x3f2398d747b36225 },
{ 0xd29fe4b18e88640e, 0x8eec7f0d19a03aae },
{ 0x83a3eeeef9153e89, 0x1953cf68300424ad },
{ 0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd8 },
{ 0xcdb02555653131b6, 0x3792f412cb06794e },
{ 0x808e17555f3ebf11, 0xe2bbd88bbee40bd1 },
{ 0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec5 },
{ 0xc8de047564d20a8b, 0xf245825a5a445276 },
{ 0xfb158592be068d2e, 0xeed6e2f0f0d56713 },
{ 0x9ced737bb6c4183d, 0x55464dd69685606c },
{ 0xc428d05aa4751e4c, 0xaa97e14c3c26b887 },
{ 0xf53304714d9265df, 0xd53dd99f4b3066a9 },
{ 0x993fe2c6d07b7fab, 0xe546a8038efe402a },
{ 0xbf8fdb78849a5f96, 0xde98520472bdd034 },
{ 0xef73d256a5c0f77c, 0x963e66858f6d4441 },
{ 0x95a8637627989aad, 0xdde7001379a44aa9 },
{ 0xbb127c53b17ec159, 0x5560c018580d5d53 },
{ 0xe9d71b689dde71af, 0xaab8f01e6e10b4a7 },
{ 0x9226712162ab070d, 0xcab3961304ca70e9 },
{ 0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d23 },
{ 0xe45c10c42a2b3b05, 0x8cb89a7db77c506b },
{ 0x8eb98a7a9a5b04e3, 0x77f3608e92adb243 },
{ 0xb267ed1940f1c61c, 0x55f038b237591ed4 },
{ 0xdf01e85f912e37a3, 0x6b6c46dec52f6689 },
{ 0x8b61313bbabce2c6, 0x2323ac4b3b3da016 },
{ 0xae397d8aa96c1b77, 0xabec975e0a0d081b },
{ 0xd9c7dced53c72255, 0x96e7bd358c904a22 },
{ 0x881cea14545c7575, 0x7e50d64177da2e55 },
{ 0xaa242499697392d2, 0xdde50bd1d5d0b9ea },
{ 0xd4ad2dbfc3d07787, 0x955e4ec64b44e865 },
{ 0x84ec3c97da624ab4, 0xbd5af13bef0b113f },
{ 0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58f },
{ 0xcfb11ead453994ba, 0x67de18eda5814af3 },
{ 0x81ceb32c4b43fcf4, 0x80eacf948770ced8 },
{ 0xa2425ff75e14fc31, 0xa1258379a94d028e },
{ 0xcad2f7f5359a3b3e, 0x096ee45813a04331 },
{ 0xfd87b5f28300ca0d, 0x8bca9d6e188853fd },
{ 0x9e74d1b791e07e48, 0x775ea264cf55347e },
{ 0xc612062576589dda, 0x95364afe032a819e },
{ 0xf79687aed3eec551, 0x3a83ddbd83f52205 },
{ 0x9abe14cd44753b52, 0xc4926a9672793543 },
{ 0xc16d9a0095928a27, 0x75b7053c0f178294 },
{ 0xf1c90080baf72cb1, 0x5324c68b12dd6339 },
{ 0x971da05074da7bee, 0xd3f6fc16ebca5e04 },
{ 0xbce5086492111aea, 0x88f4bb1ca6bcf585 },
{ 0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6 },
{ 0x9392ee8e921d5d07, 0x3aff322e62439fd0 },
{ 0xb877aa3236a4b449, 0x09befeb9fad487c3 },
{ 0xe69594bec44de15b, 0x4c2ebe687989a9b4 },
{ 0x901d7cf73ab0acd9, 0x0f9d37014bf60a11 },
{ 0xb424dc35095cd80f, 0x538484c19ef38c95 },
{ 0xe12e13424bb40e13, 0x2865a5f206b06fba },
{ 0x8cbccc096f5088cb, 0xf93f87b7442e45d4 },
{ 0xafebff0bcb24aafe, 0xf78f69a51539d749 },
{ 0xdbe6fecebdedd5be, 0xb573440e5a884d1c },
{ 0x89705f4136b4a597, 0x31680a88f8953031 },
{ 0xabcc77118461cefc, 0xfdc20d2b36ba7c3e },
{ 0xd6bf94d5e57a42bc, 0x3d32907604691b4d },
{ 0x8637bd05af6c69b5, 0xa63f9a49c2c1b110 },
{ 0xa7c5ac471b478423, 0x0fcf80dc33721d54 },
{ 0xd1b71758e219652b, 0xd3c36113404ea4a9 },
{ 0x83126e978d4fdf3b, 0x645a1cac083126ea },
{ 0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4 },
{ 0xcccccccccccccccc, 0xcccccccccccccccd },
{ 0x8000000000000000, 0x0000000000000000 },
{ 0xa000000000000000, 0x0000000000000000 },
{ 0xc800000000000000, 0x0000000000000000 },
{ 0xfa00000000000000, 0x0000000000000000 },
{ 0x9c40000000000000, 0x0000000000000000 },
{ 0xc350000000000000, 0x0000000000000000 },
{ 0xf424000000000000, 0x0000000000000000 },
{ 0x9896800000000000, 0x0000000000000000 },
{ 0xbebc200000000000, 0x0000000000000000 },
{ 0xee6b280000000000, 0x0000000000000000 },
{ 0x9502f90000000000, 0x0000000000000000 },
{ 0xba43b74000000000, 0x0000000000000000 },
{ 0xe8d4a51000000000, 0x0000000000000000 },
{ 0x9184e72a00000000, 0x0000000000000000 },
{ 0xb5e620f480000000, 0x0000000000000000 },
{ 0xe35fa931a0000000, 0x0000000000000000 },
{ 0x8e1bc9bf04000000, 0x0000000000000000 },
{ 0xb1a2bc2ec5000000, 0x0000000000000000 },
{ 0xde0b6b3a76400000, 0x0000000000000000 },
{ 0x8ac7230489e80000, 0x0000000000000000 },
{ 0xad78ebc5ac620000, 0x0000000000000000 },
{ 0xd8d726b7177a8000, 0x0000000000000000 },
{ 0x878678326eac9000, 0x0000000000000000 },
{ 0xa968163f0a57b400, 0x0000000000000000 },
{ 0xd3c21bcecceda100, 0x0000000000000000 },
{ 0x84595161401484a0, 0x0000000000000000 },
{ 0xa56fa5b99019a5c8, 0x0000000000000000 },
{ 0xcecb8f27f4200f3a, 0x0000000000000000 },
{ 0x813f3978f8940984, 0x4000000000000000 },
{ 0xa18f07d736b90be5, 0x5000000000000000 },
{ 0xc9f2c9cd04674ede, 0xa400000000000000 },
{ 0xfc6f7c4045812296, 0x4d00000000000000 },
{ 0x9dc5ada82b70b59d, 0xf020000000000000 },
{ 0xc5371912364ce305, 0x6c28000000000000 },
{ 0xf684df56c3e01bc6, 0xc732000000000000 },
{ 0x9a130b963a6c115c, 0x3c7f400000000000 },
{ 0xc097ce7bc90715b3, 0x4b9f100000000000 },
{ 0xf0bdc21abb48db20, 0x1e86d40000000000 },
{ 0x96769950b50d88f4, 0x1314448000000000 },
{ 0xbc143fa4e250eb31, 0x17d955a000000000 },
{ 0xeb194f8e1ae525fd, 0x5dcfab0800000000 },
{ 0x92efd1b8d0cf37be, 0x5aa1cae500000000 },
{ 0xb7abc627050305ad, 0xf14a3d9e40000000 },
{ 0xe596b7b0c643c719, 0x6d9ccd05d0000000 },
{ 0x8f7e32ce7bea5c6f, 0xe4820023a2000000 },
{ 0xb35dbf821ae4f38b, 0xdda2802c8a800000 },
{ 0xe0352f62a19e306e, 0xd50b2037ad200000 },
{ 0x8c213d9da502de45, 0x4526f422cc340000 },
{ 0xaf298d050e4395d6, 0x9670b12b7f410000 },
{ 0xdaf3f04651d47b4c, 0x3c0cdd765f114000 },
{ 0x88d8762bf324cd0f, 0xa5880a69fb6ac800 },
{ 0xab0e93b6efee0053, 0x8eea0d047a457a00 },
{ 0xd5d238a4abe98068, 0x72a4904598d6d880 },
{ 0x85a36366eb71f041, 0x47a6da2b7f864750 },
{ 0xa70c3c40a64e6c51, 0x999090b65f67d924 },
{ 0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d },
{ 0x82818f1281ed449f, 0xbff8f10e7a8921a4 },
{ 0xa321f2d7226895c7, 0xaff72d52192b6a0d },
{ 0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490 },
{ 0xfee50b7025c36a08, 0x02f236d04753d5b4 },
{ 0x9f4f2726179a2245, 0x01d762422c946590 },
{ 0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5 },
{ 0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2 },
{ 0x9b934c3b330c8577, 0x63cc55f49f88eb2f },
{ 0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb },
{ 0xf316271c7fc3908a, 0x8bef464e3945ef7a },
{ 0x97edd871cfda3a56, 0x97758bf0e3cbb5ac },
{ 0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317 },
{ 0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd },
{ 0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a },
{ 0xb975d6b6ee39e436, 0xb3e2fd538e122b44 },
{ 0xe7d34c64a9c85d44, 0x60dbbca87196b616 },
{ 0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd },
{ 0xb51d13aea4a488dd, 0x6babab6398bdbe41 },
{ 0xe264589a4dcdab14, 0xc696963c7eed2dd1 },
{ 0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2 },
{ 0xb0de65388cc8ada8, 0x3b25a55f43294bcb },
{ 0xdd15fe86affad912, 0x49ef0eb713f39ebe },
{ 0x8a2dbf142dfcc7ab, 0x6e3569326c784337 },
{ 0xacb92ed9397bf996, 0x49c2c37f07965404 },
{ 0xd7e77a8f87daf7fb, 0xdc33745ec97be906 },
{ 0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3 },
{ 0xa8acd7c0222311bc, 0xc40832ea0d68ce0c },
{ 0xd2d80db02aabd62b, 0xf50a3fa490c30190 },
{ 0x83c7088e1aab65db, 0x792667c6da79e0fa },
{ 0xa4b8cab1a1563f52, 0x577001b891185938 },
{ 0xcde6fd5e09abcf26, 0xed4c0226b55e6f86 },
{ 0x80b05e5ac60b6178, 0x544f8158315b05b4 },
{ 0xa0dc75f1778e39d6, 0x696361ae3db1c721 },
{ 0xc913936dd571c84c, 0x03bc3a19cd1e38e9 },
{ 0xfb5878494ace3a5f, 0x04ab48a04065c723 },
{ 0x9d174b2dcec0e47b, 0x62eb0d64283f9c76 },
{ 0xc45d1df942711d9a, 0x3ba5d0bd324f8394 },
{ 0xf5746577930d6500, 0xca8f44ec7ee36479 },
{ 0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb },
{ 0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e },
{ 0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e },
{ 0x95d04aee3b80ece5, 0xbba1f1d158724a12 },
{ 0xbb445da9ca61281f, 0x2a8a6e45ae8edc97 },
{ 0xea1575143cf97226, 0xf52d09d71a3293bd },
{ 0x924d692ca61be758, 0x593c2626705f9c56 },
{ 0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c },
{ 0xe498f455c38b997a, 0x0b6dfb9c0f956447 },
{ 0x8edf98b59a373fec, 0x4724bd4189bd5eac },
{ 0xb2977ee300c50fe7, 0x58edec91ec2cb657 },
{ 0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed },
{ 0x8b865b215899f46c, 0xbd79e0d20082ee74 },
{ 0xae67f1e9aec07187, 0xecd8590680a3aa11 },
{ 0xda01ee641a708de9, 0xe80e6f4820cc9495 },
{ 0x884134fe908658b2, 0x3109058d147fdcdd },
{ 0xaa51823e34a7eede, 0xbd4b46f0599fd415 },
{ 0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a },
{ 0x850fadc09923329e, 0x03e2cf6bc604ddb0 },
{ 0xa6539930bf6bff45, 0x84db8346b786151c },
{ 0xcfe87f7cef46ff16, 0xe612641865679a63 },
{ 0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e },
{ 0xa26da3999aef7749, 0xe3be5e330f38f09d },
{ 0xcb090c8001ab551c, 0x5cadf5bfd3072cc5 },
{ 0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6 },
{ 0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa },
{ 0xc646d63501a1511d, 0xb281e1fd541501b8 },
{ 0xf7d88bc24209a565, 0x1f225a7ca91a4226 },
{ 0x9ae757596946075f, 0x3375788de9b06958 },
{ 0xc1a12d2fc3978937, 0x0052d6b1641c83ae },
{ 0xf209787bb47d6b84, 0xc0678c5dbd23a49a },
{ 0x9745eb4d50ce6332, 0xf840b7ba963646e0 },
{ 0xbd176620a501fbff, 0xb650e5a93bc3d898 },
{ 0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe },
{ 0x93ba47c980e98cdf, 0xc66f336c36b10137 },
{ 0xb8a8d9bbe123f017, 0xb80b0047445d4184 },
{ 0xe6d3102ad96cec1d, 0xa60dc059157491e5 },
{ 0x9043ea1ac7e41392, 0x87c89837ad68db2f },
{ 0xb454e4a179dd1877, 0x29babe4598c311fb },
{ 0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a },
{ 0x8ce2529e2734bb1d, 0x1899e4a65f58660c },
{ 0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f },
{ 0xdc21a1171d42645d, 0x76707543f4fa1f73 },
{ 0x899504ae72497eba, 0x6a06494a791c53a8 },
{ 0xabfa45da0edbde69, 0x0487db9d17636892 },
{ 0xd6f8d7509292d603, 0x45a9d2845d3c42b6 },
{ 0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2 },
{ 0xa7f26836f282b732, 0x8e6cac7768d7141e },
{ 0xd1ef0244af2364ff, 0x3207d795430cd926 },
{ 0x8335616aed761f1f, 0x7f44e6bd49e807b8 },
{ 0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6 },
{ 0xcd036837130890a1, 0x36dba887c37a8c0f },
{ 0x802221226be55a64, 0xc2494954da2c9789 },
{ 0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c },
{ 0xc83553c5c8965d3d, 0x6f92829494e5acc7 },
{ 0xfa42a8b73abbf48c, 0xcb772339ba1f17f9 },
{ 0x9c69a97284b578d7, 0xff2a760414536efb },
{ 0xc38413cf25e2d70d, 0xfef5138519684aba },
{ 0xf46518c2ef5b8cd1, 0x7eb258665fc25d69 },
{ 0x98bf2f79d5993802, 0xef2f773ffbd97a61 },
{ 0xbeeefb584aff8603, 0xaafb550ffacfd8fa },
{ 0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38 },