I've used rotated numbers too and this appears to work well. Very useful for designs that demand minimal memory or lookup tables.Zach Wegner wrote:Random idea:
zobrist[piece][square] = rotate_left(deBruijn[piece], square);
Cheers,
Steffan
Moderators: hgm, Rebel, chrisw
I've used rotated numbers too and this appears to work well. Very useful for designs that demand minimal memory or lookup tables.Zach Wegner wrote:Random idea:
zobrist[piece][square] = rotate_left(deBruijn[piece], square);
What is not possible is to use the values you gave, upper half ones, lower half ones, and all ones, and then generate other numbers that only have a hamming distance of 32 or higher, including those three, to fill the 788 element array. I've tried way over 4,000,000,000 64 bit random numbers and have only gotten to 23 as the min between any pair. 24 might be possible, and perhaps 25 or 26. But 32 seems well out of reachhgm wrote:I don't understand what you are saying here. What exactly do you consider to be impossible? It can't be that the keys I gave are dependent (because they obviously are). And if three keys are dependent, thety do spoil the entire set, no matter how large the set is. But a 12-bit example can of course not be projected to a real chess board needing 788 keys.bob wrote:Actually that is not possible, and the "why" is trivial to see. You have 785 _other_ numbers that have to have 32 different bits from all 3 of the above keys, which is not possible at all...hgm wrote:... With 12-bit keys 0xFF0, 0xF0F and 0x0FF all have hamming distance 8, which is pretty good for 12-bit keys, and they also all have distance 8 to 0x000. Nevertheless they are dependent, and would spoil any set that containst them.
But that is overlooking my original constraint that _all_ pairs of numbers in the set have to have a hamming distance >= N. So far N is at least 23...
So to not discuss too much in abstracto, let me revise the example to 64-bit:
Having keys
In terms of hamming distance, we haveCode: Select all
k1 = 0xFFFFFFFFFFC00000 k2 = 0xFFFFF800003FFFFF k3 = 0x000007FFFFFFFFFF
d(k1,k2) = 42
d(k2,k3) = 42
d(k1,k3) = 43
d(k1,0) = 42
d(k2,0) = 43
d(k3,0) = 43
Furthermore, each of the keys would have a hamming distance of on the average 32 to any random 64-bit number drawn from a homogeneous distribution. So in terms of hamming distance, they don't spoil anything, and are in fact very likely to drive up the average, despite the effort you take to maximize the distance within the remaining 785 keys.
I don't disagree. But purely random numbers with no checks at all offer plenty of room for that or worse. When I first looked at this, a classic PRNG produced two numbers that were the _same_ in these numbers, and they just happened to cause an odd book move to be played that lost a game instantly.
But they would make the set totally useless if they were used such that they could appear together in a key, such as Pawn keys for f2, g2, h2. No matter what the other 785 keys are, positions with a full Pawn shield for the King on g1 would be constantly confused with those where the king is totally bare, all other pieces being positioned identically.
Code: Select all
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bob wrote:What is not possible is to use the values you gave, upper half ones, lower half ones, and all ones, and then generate other numbers that only have a hamming distance of 32 or higher, including those three, to fill the 788 element array. I've tried way over 4,000,000,000 64 bit random numbers and have only gotten to 23 as the min between any pair. 24 might be possible, and perhaps 25 or 26. But 32 seems well out of reach
I never said that it was possible to give all keys a distance of 32, nor is this needed. I only wanted to point out that a set of keys with a very good hamming distance can easily hide dependincies of the worst possible kind. (Well, perhaps except having two equal keys, which would be worse.) And the offending keys could be amongst those with the best hamming distance to all other keys, and each other.But that is overlooking my original constraint that _all_ pairs of numbers in the set have to have a hamming distance >= N. So far N is at least 23...
Code: Select all
/*
A C-program for MT19937-64 (2004/9/29 version).
Coded by Takuji Nishimura and Makoto Matsumoto.
This is a 64-bit version of Mersenne Twister pseudorandom number
generator.
Before using, initialize the state by using init_genrand64(seed)
or init_by_array64(init_key, key_length).
Copyright (C) 2004, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The names of its contributors may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
References:
T. Nishimura, ``Tables of 64-bit Mersenne Twisters''
ACM Transactions on Modeling and
Computer Simulation 10. (2000) 348--357.
M. Matsumoto and T. Nishimura,
``Mersenne Twister: a 623-dimensionally equidistributed
uniform pseudorandom number generator''
ACM Transactions on Modeling and
Computer Simulation 8. (Jan. 1998) 3--30.
Any feedback is very welcome.
http://www.math.hiroshima-u.ac.jp/~m-mat/MT/emt.html
email: m-mat @ math.sci.hiroshima-u.ac.jp (remove spaces)
*/
#include <stdlib.h>
#include <stdio.h>
#define NN 312
#define MM 156
#define MATRIX_A 0xB5026F5AA96619E9ULL
#define UM 0xFFFFFFFF80000000ULL/* Most significant 33 bits */
#define LM 0x7FFFFFFFULL /* Least significant 31 bits */
/* The array for the state vector */
static unsigned long long mt[NN];
/* mti==NN+1 means mt[NN] is not initialized */
static int mti = NN + 1;
/* initializes mt[NN] with a seed */
void init_genrand64(unsigned long long seed)
{
mt[0] = seed;
for (mti = 1; mti < NN; mti++)
mt[mti] = (6364136223846793005ULL * (mt[mti - 1] ^ (mt[mti - 1] >> 62)) + mti);
}
/* initialize by an array with array-length */
/* init_key is the array for initializing keys */
/* key_length is its length */
void init_by_array64(unsigned long long init_key[],
unsigned long long key_length)
{
unsigned long long i,
j,
k;
init_genrand64(19650218ULL);
i = 1;
j = 0;
k = (NN > key_length ? NN : key_length);
for (; k; k--) {
mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >> 62)) * 3935559000370003845ULL))
+ init_key[j] + j; /* non linear */
i++;
j++;
if (i >= NN) {
mt[0] = mt[NN - 1];
i = 1;
}
if (j >= key_length)
j = 0;
}
for (k = NN - 1; k; k--) {
mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >> 62)) * 2862933555777941757ULL))
- i; /* non linear */
i++;
if (i >= NN) {
mt[0] = mt[NN - 1];
i = 1;
}
}
mt[0] = 1ULL << 63; /* MSB is 1; assuring non-zero initial array */
}
/* generates a random number on [0, 2^64-1]-interval */
unsigned long long genrand64_int64(void)
{
int i;
unsigned long long x;
static unsigned long long mag01[2] = {0ULL, MATRIX_A};
if (mti >= NN) { /* generate NN words at one time */
/* if init_genrand64() has not been called, */
/* a default initial seed is used */
if (mti == NN + 1)
init_genrand64(5489ULL);
for (i = 0; i < NN - MM; i++) {
x = (mt[i] & UM) | (mt[i + 1] & LM);
mt[i] = mt[i + MM] ^ (x >> 1) ^ mag01[(int) (x & 1ULL)];
}
for (; i < NN - 1; i++) {
x = (mt[i] & UM) | (mt[i + 1] & LM);
mt[i] = mt[i + (MM - NN)] ^ (x >> 1) ^ mag01[(int) (x & 1ULL)];
}
x = (mt[NN - 1] & UM) | (mt[0] & LM);
mt[NN - 1] = mt[MM - 1] ^ (x >> 1) ^ mag01[(int) (x & 1ULL)];
mti = 0;
}
x = mt[mti++];
x ^= (x >> 29) & 0x5555555555555555ULL;
x ^= (x << 17) & 0x71D67FFFEDA60000ULL;
x ^= (x << 37) & 0xFFF7EEE000000000ULL;
x ^= (x >> 43);
return x;
}
/* generates a random number on [0, 2^63-1]-interval */
long long genrand64_int63(void)
{
return (long long) (genrand64_int64() >> 1);
}
/* generates a random number on [0,1]-real-interval */
double genrand64_real1(void)
{
return (genrand64_int64() >> 11) * (1.0 / 9007199254740991.0);
}
/* generates a random number on [0,1)-real-interval */
double genrand64_real2(void)
{
return (genrand64_int64() >> 11) * (1.0 / 9007199254740992.0);
}
/* generates a random number on (0,1)-real-interval */
double genrand64_real3(void)
{
return ((genrand64_int64() >> 12) + 0.5) * (1.0 / 4503599627370496.0);
}
unsigned long long hamdist(unsigned long long x, unsigned long long y)
{
unsigned long long dist = 0,
val = x ^ y;
while (val) {
++dist;
val &= val - 1;
}
return dist;
}
unsigned long long ullData[1001] = {0x7d497d2f7a15eaf8};
unsigned long long dist_distrib[64];
unsigned long long bigdiff[1360070 * 2 + 1];
int main(void)
{
size_t i;
size_t nsofar = 0;
size_t ulldatadim = sizeof ullData / sizeof ullData[0];
unsigned long long init[4] = {0x12345ULL, 0x23456ULL, 0x34567ULL, 0x45678ULL}, length = 4;
unsigned long long total = 0;
unsigned long long hdmin = 64;
unsigned long long hdmax = 0;
unsigned long long popsize = 1;
unsigned oksofar = 1;
init_by_array64(init, length);
while (popsize < 1000) {
unsigned long long q = genrand64_int64();
oksofar = 1;
for (i = 0; i < popsize; i++) {
unsigned long long h;
if ((h=hamdist(q, ullData[i])) < 24) {
oksofar = 0;
break;
}
}
if (oksofar) {
ullData[popsize++] = q;
printf("%llu,\n", q);
}
}
}
Code: Select all
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3531472405562073275,
15668286819122906112,
15427477814700549439,
12073839964796618661,
17507605560077946920,
2455365195181918791,
5964998669248654874,
15447880721255769419,
4469176972055685202,
15211694042356568608,
3759814231605665372,
18168445266382181794,
6509891475561581108,
12124751967199354237,
17848311530842249744,
17627624472618765247,
1223563903634178192,
2918849287364629264,
2746577282574245190,
18249210529947804762,
1387152020856480609,
3855972378689829637,
14111119528432513185,
6580174121676077055,
18265787066455576602,
10691648861204636862,
6833173963338540739,
8454814670236484282,
15036345140247192881,
9105289581939367919,
16703249455563584555,
10569135442141345919,
397017240905668054,
126198906736958735,
16591722875182706201,
5736319088835606273,
15916827908810835259,
16321683770365590218,
4536445586451618173,
9199827198413403170,
2588029247400550403,
1504353623037103694,
Got an email from someone that is more familiar with this stuff. He first told me that it is possible to produce 788 numbers with a min hamming distance of 28. But that this will be a linear code where XORing any two of the numbers will produce another number in the set. Which is not so desirable. So I am taking that data point and trying to decide what it means with respect to Zobrist numbers...hgm wrote:bob wrote:What is not possible is to use the values you gave, upper half ones, lower half ones, and all ones, and then generate other numbers that only have a hamming distance of 32 or higher, including those three, to fill the 788 element array. I've tried way over 4,000,000,000 64 bit random numbers and have only gotten to 23 as the min between any pair. 24 might be possible, and perhaps 25 or 26. But 32 seems well out of reachI never said that it was possible to give all keys a distance of 32, nor is this needed. I only wanted to point out that a set of keys with a very good hamming distance can easily hide dependincies of the worst possible kind. (Well, perhaps except having two equal keys, which would be worse.) And the offending keys could be amongst those with the best hamming distance to all other keys, and each other.But that is overlooking my original constraint that _all_ pairs of numbers in the set have to have a hamming distance >= N. So far N is at least 23...
Try the following:
Take the "best" set of 788 you were able to generate, and select the three keys from it that had the largest minimum hamming distance to all others. I.e., if the keys are k_i {0<i<=778}, define the "isolation" of a key i as min(d(k_i,k_j) over all j != i, and d(x,y) the hamming distance between x and y, and pick the three keys with the largest isolation. Call these k_a, k_b and k_c.
Now calculate M = k_a ^ k_b ^ k_c.
Then transform all keys in the set to K_i = M^k_i. This transformation leaves the hamming distance invariant, as x^y = (M^x)^(M^y). So the transformed set is just as "optimal" with respect to minimum hamming distance as your original one.
But
K_a^K_b^K_c = (M^k_a) ^ (M^k_b) ^ (M^k^c) = (M^M^M) ^ (k_a^k_b^k_c)
= (M) ^ (M) = 0.
So your "best" three keys in terms of hamming distance w.r.t. all other keys are now in fact the worst 3 keys, causing collisions between boards with just 3 mutations between them, and rendering the set with this large minimal hamming distance totally useless.
Someone who knows the theory behind this sent me an email stating that 28 is possible. But the numbers would be highly undesirable as XORing any two would produce another number in the set which is not so hot...Dann Corbit wrote:There is an exponential slowdown with my method. For 26 bits, I have more or less frozen on 347 distinct values (so I will have to try for a smaller set):Code: Select all
7266447313870364031, 4946485549665804864, 16945909448695747420, 16394063075524226720, 4873882236456199058, 14877448043947020171, 13857871200353263164, 5249110015610582907, 1235879089597390050, 17320312680810499042, 8942268601720066061, 14226945236717732373, 9383926873555417063, 11510704754157191257, 6489677788245343319, 236502320419669032, 13670483975188204088, 8904234204977263924, 17251681303478610375, 13075804672185204371, 10831805955733617705, 1074659097419704618, 17119870085051257224, 10949279256701751503, 17618792803942051220, 957923366004347591, 1012818702180800310, 974125122787311712, 1861591264068118966, 3809841506498447207, 13408683141069553686, 13900005529547645957, 16475327524349230602, 13554353441017344755, 4738086532119935073, 6788940719869959076, 11670856244972073775, 2488756775360218862, 11016608897122070904, 13978444093099579683, 11628184459157386459, 4249175367970221090, 7306216312942796257, 2889379661594013754, 17310575136995821873, 3435082195390932486, 7444710627467609883, 11216615872596820107, 5770016989916553752, 1845293119018433391, 1259990987526807294, 15531278677382192198, 16317667579273275294, 9134927878875794005, 9030000260502624168, 3115849849651526279, 10637177623943913351, 16428252083632828910, 15722061259110909195, 1524477318846038424, 3443401252003315103, 9689406052675046032, 3609534220891499022, 9281161952002617309, 147649915388326849, 10131486500045494660, 8517521928922081563, 2836463788873877488, 9570032848237657586, 10863668391515109722, 1552803150609742001, 2790375502200557313, 9038024825497430573, 91888768090624853, 18145740993490813283, 12654149022202498759, 4206418103243872757, 7233523623977397383, 16215672393055652545, 10738887894178969425, 18204068107936511697, 14383128117587060157, 15849831596023436356, 17675390291979846750, 2977578850677699908, 4893323648315952120, 1286466090879300568, 9888911152046881084, 3183884142852054126, 13772224761560358678, 9094920381744576493, 16129742540997802980, 16945398958854163835, 17650197551112766205, 4852422776459831315, 9362357443732597760, 2374087830147132659, 15000861190071109560, 2902081674035190433, 15810933559568492050, 12678167969995957047, 1798389442866720091, 14599659047605763816, 17782026137486407602, 3027116614594121997, 6496187495111652573, 9859717582333494749, 5930885232297252456, 4061277839767617930, 12035499765197893420, 4370560942875640999, 5634383789002676726, 8907175724738102010, 16593287713411177161, 3325238609365118367, 17125462708636491154, 10188578131352743024, 15161949016576385831, 6657699133553403854, 2352226978179009098, 3859532089524191730, 17631674258545638758, 17581014988572303447, 7458819045178438285, 5488240155574034654, 7788457792396395633, 1234217808918573134, 10045923023026503261, 2803693151878023143, 15042951576086758915, 1809970995609003345, 6472832596573079460, 10531013421297635766, 9687689322966646953, 5309220766259687196, 16099895359080387221, 15463291357721078947, 14892243053368326929, 15913028219213787856, 17114854711077298999, 6881183452302138939, 9743703211409053724, 6120184892838179370, 4488025338083630045, 6932643716586102064, 7085729815153112724, 2577286319771781656, 3212578193372804795, 7140055923216537951, 11545784650358033961, 15097420044622846756, 9577429288174440901, 1651506457155992685, 17206783877956047023, 4977537220776361209, 16799175153209517804, 17623046094747753280, 16695848152965592420, 807005292018537624, 5694219642130963465, 17782774995076800672, 5025236171457631467, 11601588411391151733, 13800826249802546619, 8320715347883164621, 15765965395656039061, 9783656346475123313, 15660593116602060011, 12686638988178810220, 4601829680043422926, 13649469918759116343, 11072681934824066811, 3484285465118294452, 5250162757012130834, 11822278712571422607, 16820676274862823347, 2258483262623939360, 18059638503665417019, 4038533795659869059, 9217581272623145121, 10474525469047663535, 1704011107366220345, 15761773994985082820, 1396662462031085091, 11499399103501446733, 8253913244279442889, 18014518805502248392, 10766750626076003259, 13347551569433141972, 12285514714001968960, 12601751059746685848, 4088019966658540820, 7550841428494759028, 14457212971848820997, 16415384305117522006, 3274893893751255634, 10659638677637579954, 6338371175383690179, 18162230369769586150, 428321177825102899, 15817001710821818046, 12235635129931490851, 13527122555395203005, 2178128838908381672, 14367385536076681562, 12915933956577960132, 4652351249928028414, 4951391482976146214, 7296771005593252278, 14127467184305310300, 16956161371242220606, 2288730399829329044, 10224299563023357164, 15302392990651373659, 5732367270286632815, 7889985811968217208, 5521408468444455621, 3010954896914979971, 14717388125128732814, 17543622707664214218, 16699503790769821674, 5300069125018992847, 4491717662350224528, 6179887503359229642, 10444048407325898982, 12310419282952883445, 9615039512616912255, 8912906368760218223, 2736639230152280465, 1466229153547721039, 2954109638740141000, 11746874332443504878, 10637552291778782845, 17962194647643634986, 7190730870912935711, 15378933026600388229, 7415343666878271746, 4247889442676475641, 17929428741300739597, 6205303292541642307, 11123091740953949733, 784117286214737662, 11137709922435249100, 14725228923085766997, 10386402860586212951, 13143405698908382732, 196620903144528027, 10705589578384286810, 13817879522456382188, 9229688921939842696, 16633756859233364337, 1032072982178823495, 6370454774064667856, 12850106475877076817, 12267618954701302483, 8145470530489095863, 1814673802044807488, 9225545243819924881, 14884320946805680190, 7015855463293451660, 15665030223840195079, 17002420156823161993, 3049382545994967746, 17417472035022723033, 12396544237084354931, 6725541218060571039, 9710463154252506414, 9950389178902628715, 2371212431907900846, 18374266211527465082, 14109608474880409885, 10041272077912916256, 5726527053967358581, 11966583246028264826, 16565423595231842294, 4787603906131836800, 2358971807316617129, 701848729445873300, 7462412777600825764, 17256139670461659054, 18098924730684751225, 503596689135387308, 17615667363549849844, 3787023102090135939, 10889153560001930160, 9630600983458854043, 14840676362451429709, 15285971904287568249, 760130182760799549, 18273147886613016929, 17988260782976079957, 10576771164953308062, 1374404921073484550, 5711543178872819554, 7267384182398429791, 3847053869966350600, 11350390488874863454, 18034667604288436754, 15728235335976939570, 1690501778949613150, 10549826829132374141, 8187654266517442902, 14570575066764711251, 8330819712241433781, 17436220147483706956, 1259157189813452226, 13025642373655069123, 14356472637065835570, 16222490068333456653, 2485152632185027389, 2742816983698754277, 2661133492768338581, 2301215659926313223, 13233097894633159274, 12656717602888925661, 10165318829475529952, 17104609321564382922, 10325932561555029770, 6413244029449044455, 8191767193394389622, 10270929734388613920, 12291445944674790578, 10802320535004165936, 3928453647719019674, 10318533838179330761, 18290228294878833931, 17117845830988322373, 12942239967337847160, 11380882416157141219, 13460991881535950924, 3587389546577196427, 5111810686918228644, 4114159579120732836, 8946597124993059928, 5207951741791249331, 1411671654137597246, 7702399104537211022, 4568625842739988035, 563893241007464401, 17187067130913047100, 11828988545797689038, 11702908455376917457, 8794147767634410081, 10079173818009207539, 125881399269187320, 5230839931433374219, 1531203087033921236,
Well, that illustrates my point in an even more dramatic way than I ever could have imagined. So maximum hamming distance actually produces a totally useless set of keys.bob wrote:Got an email from someone that is more familiar with this stuff. He first told me that it is possible to produce 788 numbers with a min hamming distance of 28. But that this will be a linear code where XORing any two of the numbers will produce another number in the set. Which is not so desirable. So I am taking that data point and trying to decide what it means with respect to Zobrist numbers...
Code: Select all
static const unsigned long long hv[] =
{
7266447313870364031,
4946485549665804864,
16945909448695747420,
16394063075524226720,
4873882236456199058,
14877448043947020171,
6740343660852211943,
13857871200353263164,
5249110015610582907,
1235879089597390050,
17320312680810499042,
16489141110565194782,
13520575722002588570,
14226945236717732373,
9383926873555417063,
11510704754157191257,
15864264574919463609,
6489677788245343319,
5112602299894754389,
10828930062652518694,
15942305434158995996,
236502320419669032,
14931360615268175698,
8904234204977263924,
12836915408046564963,
12120302420213647524,
15755110976537356441,
17251681303478610375,
18286145806977825275,
13075804672185204371,
12903857913610213846,
560691676108914154,
1074659097419704618,
14266121283820281686,
11696403736022963346,
12893913769120703138,
2511068401785704737,
3774730664208216065,
5083371700846102796,
9583498264570933637,
17119870085051257224,
5217910858257235075,
10949279256701751503,
15596196964072664893,
14097948002655599357,
5636498760852923045,
17618792803942051220,
13212228678420887626,
6210242862396777185,
1012818702180800310,
15299383925974515757,
974125122787311712,
1861591264068118966,
997568339582634050,
17981867688435687790,
9460108917638135678,
16172980638639374310,
15773550354402817866,
16475327524349230602,
13554353441017344755,
6788940719869959076,
11670856244972073775,
2488756775360218862,
2061695363573180185,
3566345954323888697,
6864898938209826895,
7198730565322227090,
10827695224855383989,
11016608897122070904,
3956319990205097495,
5804870313319323478,
8017203611194497730,
3310931575584983808,
5009341981771541845,
14415278059151389495,
6715939435439735925,
411419160297131328,
4522402260441335284,
3381955501804126859,
9219789505504949817,
11628184459157386459,
7242398879359936370,
13965005347172621081,
5806488997649497146,
10724207982663648949,
957364844878149318,
8197027112357634782,
12052913535387714920,
2889379661594013754,
10511508162402504492,
6801855569284252424,
16465954421598296115,
5975570403614438776,
3688303938005101774,
2210483654336887556,
6558785204455557683,
16822351800343061990,
7444710627467609883,
3200233909833521327,
3612068790453735040,
18266943104929747076,
1620389818516182276,
3906668377244742888,
5770016989916553752,
6384853777489155236,
10311708346636548706,
17771199061862790062,
12121348462972638971,
1257976447679270605,
3664184785462160180,
10718876134480663664,
3611366553819264523,
14492630642488100979,
2903980458593894032,
12026985381690317404,
15535375191850690266,
10333316143274529509,
16565481511572123421,
14237704570091006662,
6454343485137106900,
18107191819981188154,
3559348759319842667,
18059264986425101074,
3139684427605102737,
4715785502295754870,
11077531235278014145,
10637177623943913351,
10137911902863059694,
13719113891065284171,
13776316799690285717,
8687650838094264665,
3028124591188972359,
3982930188609442149,
13815150225221307677,
16924127046922196149,
5437280487207382147,
10760687291786964354,
216630713752669403,
10655207865433859491,
1524477318846038424,
3443401252003315103,
16860120454903458341,
15362920279125264094,
14358245326238118181,
4224273587485638227,
13919998707305829132,
14473305049457001422,
12955027028676000544,
17930425515478182741,
7466411836095405617,
10879629128927506091,
11502219301371200635,
4978473890680876319,
845759387067546611,
9092379465737744314,
7562781050481886043,
3514744284158856431,
14980707022065991200,
18294903201142729875,
8979482998667235743,
16495638000603654629,
17504300515449231559,
1406052433297386355,
3296968762229741153,
6214378374180465222,
11439178472613251620,
10972816599561388940,
10020049344596426576,
9381977959648494876,
15282520250746126790,
4891472444796201742,
4564628942836375772,
12627401038822728242,
8515217303152165705,
2836463788873877488,
5327734953288310341,
4193447453292207765,
8727015815475533844,
1794828640516310551,
839109216263472222,
11003569267662299508,
14818712892121773001,
11341937060697364828,
16294497818497013091,
7938847863410484112,
12460847944021797729,
8608832166868962581,
17282690963297781165,
5236305832299547005,
13653613720566641032,
12795694179935286147,
3619745730869440312,
7023474619158759074,
6411707388950674382,
11610566205662556902,
12720426256176311341,
963006111335524252,
12602026180005991793,
10977961698003017025,
14314905386630121264,
593861932304949197,
1759320944513001478,
9844433545111928009,
7516448510961597387,
6979677882708694852,
2623982553786190271,
10956409229583802704,
10773480483945135813,
15589196139318714477,
13992302356379003709,
4144556090023237143,
2683982833995814204,
14174237260119144415,
5498804830346368935,
10015422821119519276,
14006884420982275271,
15325155849418805462,
2337041946913300563,
17100624240218191776,
9703324598394127586,
17019689424591946956,
5780649476454802027,
14414929270030064142,
18404798721277276349,
13727527782081926783,
14049840052842737870,
13090081540345862947,
9489259826421593604,
11339178955354061847,
2431380992571392509,
13011028955371218345,
17577910823749512297,
6646205212361830820,
6563389574948647110,
5615534989929158531,
5753528745081333993,
1974805642753365513,
2848156987029842825,
17613615095014857579,
2011506583012245120,
2444313452813434980,
295943014965754495,
9882162289524262117,
12675922461078850762,
3834401558737001127,
866051294803417039,
2724626095286417021,
18307426813116457025,
17948009628770529172,
6685233615168851649,
13500066391123604136,
12479713940936428223,
9424117665582424405,
6039353791193701794,
6601976231243625663,
15224447585169584601,
2728973181524205713,
3462528993083828381,
11340412255977527276,
16097257884801829806,
15873188707503643756,
13772224761560358678,
13111754990776650992,
96905898085114986,
11176895769597467160,
600926880159025491,
17204915804540124261,
1144214061925539673,
6442316514250842898,
12890767762330780561,
1678595440397729949,
17555837092409264409,
11850798096946224952,
18347395534780169545,
2902301657143828160,
4513207106323818436,
7208587791955414370,
14036122687726750680,
5845312298939252013,
8658865064369425702,
17865168032283289844,
4257028217766215264,
6122026574733783975,
9170295234685582608,
4625842927060587645,
10364408876534383966,
3160614275850263182,
4048844641307615001,
9202228564570972667,
10244349660455576579,
4365624743606344104,
7914034060710558862,
14082118313143494030,
13893540545824007220,
12557303001492689466,
18034204128425921887,
340230915844217824,
13885363215660853141,
182790206115731779,
10275690770029126957,
2207732794522698303,
4015366832566852941,
3344126814245426647,
3418909431246792130,
18170060564269107324,
16825303559054309655,
3076199647024046233,
8592572442492131294,
13847613594546126389,
8025098507225669679,
9851016542364179299,
10069389887474709588,
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1447976981583137012,
3047035707044200937,
5779039202666699403,
641739833565391248,
16580648647756784598,
16754708488282152628
};
unsigned long long hamdist(unsigned long long x, unsigned long long y)
{
unsigned long long dist = 0,
val = x ^ y;
while (val) {
++dist;
val &= val - 1;
}
return dist;
}
#include <stdio.h>
#include <stdlib.h>
int main(void)
{
unsigned long long i,
j;
unsigned long long maxbad = 211,
totbad = 0;
unsigned long long len = sizeof hv / sizeof hv[0];
for (i = 0; i < len; i++) {
unsigned long long badcount = 0;
for (j = 0; j < len; j++) {
unsigned long long hd;
if (j == i)
continue;
hd = hamdist(hv[i], hv[j]);
if (hd < 23) {
badcount++;
printf("(%llu,%llu), hamdist(%llu,%llu)=%llu\n", i, j, hv[i], hv[j], hd);
}
}
if ((len - badcount) < 788) {
printf("hv[%llu]=%llu is bad\n", i, hv[i]);
totbad++;
}
}
if (totbad > maxbad)
printf("Too many bad values.\nMaximum 211 bad values can be tolerated but there were %llu.\n", totbad);
return 0;
}
Code: Select all
static const unsigned long long ham23bit[999] = {
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};
unsigned long long zobvalh23(unsigned i)
{
return ham23bit[i % 999];
}
#ifdef UNIT_TEST
#include <stdio.h>
int main(void)
{
unsigned index;
for (index = 0; index < 2000; index++)
printf("zobvalh23(%u)=%llu\n", index, zobvalh23(index));
return 0;
}
#endif