public static BigInteger Height(int n, int m)
{
if (n == 0 || m == 0)
{
return(0);
}
if (n == 1)
{
return(m);
}
BigInteger[] Prev = Enumerable.Range(1, m - n + 1).Select(x => (BigInteger)x).ToArray();
BigInteger sum = 1;
var startSum = Seed().GetEnumerator();
startSum.MoveNext();
startSum.MoveNext();
BigInteger[] Next = null;
for (int i = 2; i < n; i++)
{
Next = new BigInteger[m - n + 1];
Next[0] = startSum.Current;
sum = Prev[0];
for (int j = 1; j < Next.Length; j++)
{
sum += Prev[j];
Next[j] = sum + j + i;
}
Prev = Next;
//Console.WriteLine(Next.Aggregate("", (a, next) => a += " " + next.ToString()));
startSum.MoveNext();
}
return(Next.Aggregate(new BigInteger(0), (agg, next) => agg += next) + m);
}
/// <summary>
/// Возвращает следующее простое число.
/// </summary>
/// <returns></returns>
public static BigInteger GetNext()
{
BigInteger[] CurrentSet = new BigInteger[Misc.Misc.Data.PrimeNumbers.Length + GeneratedNums.Count];
Array.Copy(Misc.Misc.Data.PrimeNumbers.Select(num => (BigInteger)num).ToArray(), CurrentSet,
Misc.Misc.Data.PrimeNumbers.Length);
Array.Copy(GeneratedNums.ToArray(), 0, CurrentSet, Misc.Misc.Data.PrimeNumbers.Length, GeneratedNums.Count);
while (true)
{
BigInteger ElementF = CurrentSet.Aggregate <BigInteger, BigInteger>(1, (Current, KnownPrime) => Current * BigInteger.Pow(KnownPrime, RD.Rand.Next(1, 11)));
}
return(0);
}
public void Test100BCSResultsReduced() //takes too long...
{
int seed = 1;
int n = 100000; //100000
int l = 7;
int t_min = 29;
int t_max = 31;
IEnumerable <Tuple <ulong, long> > S = Generator.CreateStreamLong(n, l, seed);
HashTableChaining <long> tableMS = new HashTableChaining <long>(
HashFunction.MultiplyShift(BitConverter.ToUInt64(Generator.MakeOdd(Generator.GenerateBits(64, seed))), l),
1UL << l
);
foreach (Tuple <ulong, long> elem in S)
{
tableMS.increment(elem.Item1, (NumberLong)elem.Item2);
}
BigInteger Real_S = Generator.RealCount <long>(tableMS);
string path = Directory.GetCurrentDirectory();
DirectoryInfo di = new DirectoryInfo(path);
while (di.Name != "XUnit_RAD")
{
di = di.Parent;
}
if (!Directory.Exists(Path.Combine(di.FullName, "TestResult")))
{
Directory.CreateDirectory(Path.Combine(di.FullName, "TestResult"));
}
string testfilePath = Path.Combine(di.FullName, "TestResult", "Test100BCSResultsReduced.csv");
if (File.Exists(testfilePath))
{
File.Delete(testfilePath);
}
File.Create(testfilePath).Close();
for (int t = t_min; t <= t_max; t++)
{
BigInteger[] unsortedResults = new BigInteger[100];
for (int i = 0; i < 100; i++)
{
BasicCountSketch bcs = new BasicCountSketch(t);
foreach (Tuple <ulong, long> elem in S)
{
bcs.Process(elem);
}
unsortedResults[i] = bcs.Estimate2ndMoment();
}
BigInteger[] manyResults = unsortedResults.OrderBy(val => val).ToArray();
BigInteger meansquare = unsortedResults.Aggregate(BigInteger.Zero, (acc, x) => acc + (BigInteger)Math.Pow((long)x - (long)Real_S, 2)) / 100;
BigInteger[] medianResults = new BigInteger[9];
for (int i = 0; i < 9; i++)
{
medianResults[i] = unsortedResults.Skip(i * 11).Take(11).OrderBy(val => val).ElementAt(5);
}
medianResults = medianResults.OrderBy(val => val).ToArray();
StringBuilder sb = new StringBuilder();
sb.AppendLine("Real S;" + Real_S + ";Expectation;" + Real_S + "\nVariance;" + Math.Round(2 * Math.Pow((long)Real_S, 2) / (1 << t), 2) + ";Value of t;" + t + "\nValue of m;" + (1 << t) + ";;");
sb.Append("MeanSquareErrors");
BigInteger average = 0;
sb.Append(";" + meansquare);
average += meansquare;
sb.Append(";" + average / 10);
sb.AppendLine();
sb.AppendLine("#Estimate;1st run;Average run;Real S");
for (int i = 0; i < 100; i++)
{
sb.Append(i + 1);
average = 0;
sb.Append(";" + manyResults[i]);
average += manyResults[i];
sb.Append(";" + average / 10);
sb.Append(";" + Real_S);
sb.AppendLine();
}
sb.AppendLine("#Estimate;1st run;Average run;Real S");
for (int i = 0; i < 9; i++)
{
sb.Append(i + 1);
average = 0;
sb.Append(";" + medianResults[i]);
average += medianResults[i];
sb.Append(";" + average / 10);
sb.Append(";" + Real_S);
sb.AppendLine();
}
sb.AppendLine(";;;");
File.AppendAllText(testfilePath, sb.ToString());
}
}
public string GetSolution()
{
var largeNumbers = new BigInteger[100] {
BigInteger.Parse("37107287533902102798797998220837590246510135740250"),
BigInteger.Parse("46376937677490009712648124896970078050417018260538"),
BigInteger.Parse("74324986199524741059474233309513058123726617309629"),
BigInteger.Parse("91942213363574161572522430563301811072406154908250"),
BigInteger.Parse("23067588207539346171171980310421047513778063246676"),
BigInteger.Parse("89261670696623633820136378418383684178734361726757"),
BigInteger.Parse("28112879812849979408065481931592621691275889832738"),
BigInteger.Parse("44274228917432520321923589422876796487670272189318"),
BigInteger.Parse("47451445736001306439091167216856844588711603153276"),
BigInteger.Parse("70386486105843025439939619828917593665686757934951"),
BigInteger.Parse("62176457141856560629502157223196586755079324193331"),
BigInteger.Parse("64906352462741904929101432445813822663347944758178"),
BigInteger.Parse("92575867718337217661963751590579239728245598838407"),
BigInteger.Parse("58203565325359399008402633568948830189458628227828"),
BigInteger.Parse("80181199384826282014278194139940567587151170094390"),
BigInteger.Parse("35398664372827112653829987240784473053190104293586"),
BigInteger.Parse("86515506006295864861532075273371959191420517255829"),
BigInteger.Parse("71693888707715466499115593487603532921714970056938"),
BigInteger.Parse("54370070576826684624621495650076471787294438377604"),
BigInteger.Parse("53282654108756828443191190634694037855217779295145"),
BigInteger.Parse("36123272525000296071075082563815656710885258350721"),
BigInteger.Parse("45876576172410976447339110607218265236877223636045"),
BigInteger.Parse("17423706905851860660448207621209813287860733969412"),
BigInteger.Parse("81142660418086830619328460811191061556940512689692"),
BigInteger.Parse("51934325451728388641918047049293215058642563049483"),
BigInteger.Parse("62467221648435076201727918039944693004732956340691"),
BigInteger.Parse("15732444386908125794514089057706229429197107928209"),
BigInteger.Parse("55037687525678773091862540744969844508330393682126"),
BigInteger.Parse("18336384825330154686196124348767681297534375946515"),
BigInteger.Parse("80386287592878490201521685554828717201219257766954"),
BigInteger.Parse("78182833757993103614740356856449095527097864797581"),
BigInteger.Parse("16726320100436897842553539920931837441497806860984"),
BigInteger.Parse("48403098129077791799088218795327364475675590848030"),
BigInteger.Parse("87086987551392711854517078544161852424320693150332"),
BigInteger.Parse("59959406895756536782107074926966537676326235447210"),
BigInteger.Parse("69793950679652694742597709739166693763042633987085"),
BigInteger.Parse("41052684708299085211399427365734116182760315001271"),
BigInteger.Parse("65378607361501080857009149939512557028198746004375"),
BigInteger.Parse("35829035317434717326932123578154982629742552737307"),
BigInteger.Parse("94953759765105305946966067683156574377167401875275"),
BigInteger.Parse("88902802571733229619176668713819931811048770190271"),
BigInteger.Parse("25267680276078003013678680992525463401061632866526"),
BigInteger.Parse("36270218540497705585629946580636237993140746255962"),
BigInteger.Parse("24074486908231174977792365466257246923322810917141"),
BigInteger.Parse("91430288197103288597806669760892938638285025333403"),
BigInteger.Parse("34413065578016127815921815005561868836468420090470"),
BigInteger.Parse("23053081172816430487623791969842487255036638784583"),
BigInteger.Parse("11487696932154902810424020138335124462181441773470"),
BigInteger.Parse("63783299490636259666498587618221225225512486764533"),
BigInteger.Parse("67720186971698544312419572409913959008952310058822"),
BigInteger.Parse("95548255300263520781532296796249481641953868218774"),
BigInteger.Parse("76085327132285723110424803456124867697064507995236"),
BigInteger.Parse("37774242535411291684276865538926205024910326572967"),
BigInteger.Parse("23701913275725675285653248258265463092207058596522"),
BigInteger.Parse("29798860272258331913126375147341994889534765745501"),
BigInteger.Parse("18495701454879288984856827726077713721403798879715"),
BigInteger.Parse("38298203783031473527721580348144513491373226651381"),
BigInteger.Parse("34829543829199918180278916522431027392251122869539"),
BigInteger.Parse("40957953066405232632538044100059654939159879593635"),
BigInteger.Parse("29746152185502371307642255121183693803580388584903"),
BigInteger.Parse("41698116222072977186158236678424689157993532961922"),
BigInteger.Parse("62467957194401269043877107275048102390895523597457"),
BigInteger.Parse("23189706772547915061505504953922979530901129967519"),
BigInteger.Parse("86188088225875314529584099251203829009407770775672"),
BigInteger.Parse("11306739708304724483816533873502340845647058077308"),
BigInteger.Parse("82959174767140363198008187129011875491310547126581"),
BigInteger.Parse("97623331044818386269515456334926366572897563400500"),
BigInteger.Parse("42846280183517070527831839425882145521227251250327"),
BigInteger.Parse("55121603546981200581762165212827652751691296897789"),
BigInteger.Parse("32238195734329339946437501907836945765883352399886"),
BigInteger.Parse("75506164965184775180738168837861091527357929701337"),
BigInteger.Parse("62177842752192623401942399639168044983993173312731"),
BigInteger.Parse("32924185707147349566916674687634660915035914677504"),
BigInteger.Parse("99518671430235219628894890102423325116913619626622"),
BigInteger.Parse("73267460800591547471830798392868535206946944540724"),
BigInteger.Parse("76841822524674417161514036427982273348055556214818"),
BigInteger.Parse("97142617910342598647204516893989422179826088076852"),
BigInteger.Parse("87783646182799346313767754307809363333018982642090"),
BigInteger.Parse("10848802521674670883215120185883543223812876952786"),
BigInteger.Parse("71329612474782464538636993009049310363619763878039"),
BigInteger.Parse("62184073572399794223406235393808339651327408011116"),
BigInteger.Parse("66627891981488087797941876876144230030984490851411"),
BigInteger.Parse("60661826293682836764744779239180335110989069790714"),
BigInteger.Parse("85786944089552990653640447425576083659976645795096"),
BigInteger.Parse("66024396409905389607120198219976047599490197230297"),
BigInteger.Parse("64913982680032973156037120041377903785566085089252"),
BigInteger.Parse("16730939319872750275468906903707539413042652315011"),
BigInteger.Parse("94809377245048795150954100921645863754710598436791"),
BigInteger.Parse("78639167021187492431995700641917969777599028300699"),
BigInteger.Parse("15368713711936614952811305876380278410754449733078"),
BigInteger.Parse("40789923115535562561142322423255033685442488917353"),
BigInteger.Parse("44889911501440648020369068063960672322193204149535"),
BigInteger.Parse("41503128880339536053299340368006977710650566631954"),
BigInteger.Parse("81234880673210146739058568557934581403627822703280"),
BigInteger.Parse("82616570773948327592232845941706525094512325230608"),
BigInteger.Parse("22918802058777319719839450180888072429661980811197"),
BigInteger.Parse("77158542502016545090413245809786882778948721859617"),
BigInteger.Parse("72107838435069186155435662884062257473692284509516"),
BigInteger.Parse("20849603980134001723930671666823555245252804609722"),
BigInteger.Parse("53503534226472524250874054075591789781264330331690")
};
return(new string(largeNumbers.Aggregate(new BigInteger(0), (acc, n) => acc += n).ToString().Take(10).ToArray()));
}
public static void SumHPCsharpExamples()
{
int[] arrInt = new int[] { 5, 7, 16, 3, Int32.MaxValue, 1 };
int sumInt;
long sumLong;
//sumInt = arrInt.Sum(); // standard C# usage, single-core, will throw overflow exception
//sumInt = arrInt.AsParallel().Sum(); // standard C# usage, multi-core, will throw overflow exception
// No overflow exception thrown by HPCsharp .Sum(), producing a perfectly accurate sum
sumLong = arrInt.SumToLong(); // serial
sumLong = arrInt.SumToLongSse(); // data-parallel, single-core (many times faster)
sumLong = arrInt.SumToLongSsePar(); // data-parallel, multi-core (even faster)
long[] arrLong = new long[] { 5, 7, 16, 3, Int64.MaxValue, 1 };
decimal sumDecimal;
BigInteger sumBigInteger;
//sumLong = arrLong.Sum(); // standard C# usage, single-core, throws an overflow exception
//sumLong = arrLong.AsParallel().Sum(); // standard C# usage, multi-core, throws an overflow exception
//sumLong = arrLong.SumCheckedSse(); // data parallel (SSE), single-core, throws an overflow exception
// No overflow exception thrown by HPCsharp .Sum(), producing a perfectly accurate sum
sumDecimal = arrLong.SumToDecimal(); // scalar, single-core
sumDecimal = arrLong.SumToDecimalPar(); // scalar, multi-core
sumDecimal = arrLong.SumToDecimalFast(); // scalar, single-core, faster when a few overflow exceptions occur
sumDecimal = arrLong.SumToDecimalFaster(); // scalar, single-core, much faster when lots of overflows can occur
sumDecimal = arrLong.SumToDecimalSseFaster(); // data parallel (SSE), single-core, much faster when lots of overflows can occur
sumDecimal = arrLong.SumToDecimalFasterPar(); // scalar, multi-core, much faster when lots of overflows can occur
sumDecimal = arrLong.SumToDecimalSseFasterPar(); // data parallel (SSE), multi-core, much faster when lots of overflows can occur
// No overflow exception thrown by HPCsharp .Sum(), producing a perfectly accurate sum
sumBigInteger = arrLong.SumToBigIntegerFast(); // scalar, single-core
sumBigInteger = arrLong.SumToBigIntegerFaster(); // scalar, single-core (much faster when lots of overflows can occur)
sumBigInteger = arrLong.SumToBigIntegerSseFaster(); // data parallel (SSE), single-core, much faster when lots of overflows can occur
sumBigInteger = arrLong.SumToBigIntegerFasterPar(); // scalar, multi-core, much faster when lots of overflows can occur
sumBigInteger = arrLong.SumToBigIntegerSseFasterPar(); // data parallel (SSE), multi-core, much faster when lots of overflows can occur
float[] arrFloat = new float[] { 5.0f, 7.3f, 16.3f, 3.1f };
float sumFloat;
double sumDouble;
sumFloat = arrFloat.Sum(); // standard C# usage
sumDouble = arrFloat.SumHpc(); // serial
sumDouble = arrFloat.SumSse(); // data-parallel (SSE), single-core
sumDouble = arrFloat.SumSsePar(); // data-parallel (SSE), multi-core (Par)
// More accurate floati-point .Sum()
double[] arrDouble = new double[] { 1, 10.0e100, 1, -10e100 };
sumDouble = arrDouble.Sum(); // standard C#
var sumDoublePar = arrDouble.AsParallel().Sum(); // standard C#, multi-core
var sumDoubleKahan = arrDouble.SumMostAccurate(); // HPCsharp more accurate, serial
var sumDoubleKahanSse = arrDouble.SumSseMostAccurate(); // HPCsharp more accurate, data-parallel (SSE), single-core
var sumDoubleKahanSsePar = arrDouble.SumSseParMostAccurate(); // HPCsharp more accurate, data-parallel (SSE), multi-core
Console.WriteLine("Sum Naive (for loop) = {0}, correct answer is 2.0", sumDouble);
Console.WriteLine("Sum Kahan = {0}, correct answer is 2.0", sumDoubleKahan);
Console.WriteLine("Sum Kahan (SSE) = {0}, correct answer is 2.0", sumDoubleKahanSse);
Console.WriteLine("Sum Kahan (SSE & multi-core) = {0}, correct answer is 2.0", sumDoubleKahanSse);
ulong[] arrUlong = new ulong[] { 5, 7, 16, 3, UInt64.MaxValue, 1 };
long sumUlong;
//sumULong = arrUlong.Sum(); // standard C# usage, single-core, throws an overflow exception
//sumUlong = arrUlong.AsParallel().Sum(); // standard C# usage, multi-core, throws an overflow exception
//sumUlong = arrLong.SumCheckedSse(); // data parallel (SSE), single-core, throws an overflow exception
// No overflow exception thrown by HPCsharp .Sum(), producing a perfectly accurate sum
sumDecimal = arrUlong.SumToDecimal(); // scalar, single-core
sumDecimal = arrUlong.SumToDecimalPar(); // scalar, multi-core
// No overflow exception thrown by HPCsharp .Sum(), producing a perfectly accurate sum
sumDecimal = arrUlong.SumToDecimalFast(); // scalar, single-core, faster when a few overflow exceptions occur
sumDecimal = arrUlong.SumToDecimalFaster(); // scalar, single-core, much faster when many overflows can occur
sumDecimal = arrUlong.SumToDecimalSseFaster(); // data parallel (SSE), single-core, much faster when many overflows can occur
sumDecimal = arrUlong.SumToDecimalFasterPar(); // scalar, multi-core, much faster when many overflows can occur
sumDecimal = arrUlong.SumToDecimalSseFasterPar(); // data parallel (SSE), multi-core, much faster when many overflows can occur
// No overflow exception thrown by HPCsharp .Sum(), producing a perfectly accurate sum
sumBigInteger = arrUlong.SumToBigIntegerFast(); // scalar, single-core
sumBigInteger = arrUlong.SumToBigIntegerFaster(); // scalar, single-core (much faster when many overflows can occur)
sumBigInteger = arrUlong.SumToBigIntegerSseFaster(); // data parallel (SSE), single-core, much faster when many overflows can occur
sumBigInteger = arrUlong.SumToBigIntegerFasterPar(); // scalar, multi-core, much faster when many overflows can occur
sumBigInteger = arrUlong.SumToBigIntegerSseFasterPar(); // data parallel (SSE), multi-core, much faster when many overflows can occur
BigInteger[] arrBigInteger = new BigInteger[] { 5, 7, 16, 3, UInt64.MaxValue, 1 };
// Linq does not have BigInteger array .Sum()
sumBigInteger = arrBigInteger.Aggregate(sumBigInteger, (current, i) => current + i); // another way to accomplish .Sum() using Linq
sumBigInteger = arrBigInteger.SumHpc(); // HPCsharp implements scalar, single-core .Sum()
sumBigInteger = arrBigInteger.SumPar(); // HPCsharp implements scalar, multi-core .Sum()
}