public static mpz_t MersennePrime(mpz_t n, ulong exponent, mpz_t mersenneNumber)
{
mpz_t s = n;
for (; s.BitLength > (int)exponent; s = (s & mersenneNumber) + (s >> (int)exponent))
{
;
}
return(s == mersenneNumber ? 0 : s);
}
static void MakePrimes()
{
var primesList = new List <mpz_t>();
for (mpz_t p = 2; p <= rbmax; p = p.NextPrimeGMP())
{
primesList.Add(p);
}
Primes = primesList.ToArray();
}
public static bool Start06(ulong exponent)//3421
{
mpz_t mersenneNumber = mpz_t.One.ShiftLeft((int)exponent) - 1, s = 3;
for (ulong i = 1; i < exponent; i++)
{
s = (s * s) % mersenneNumber;
}
return(s == mersenneNumber - 3);
}
static int smpf(mpz_t n)
{
for (mpz_t p = 2; ; p = p.NextPrimeGMP())
{
if (n % p == 0)
{
return((int)p);
}
}
}
public static bool Start05(ulong exponent)//3313
{
mpz_t mersenneNumber = mpz_t.One.ShiftLeft((int)exponent) - 1, s = 4;
for (ulong i = 2; i < exponent; i++)
{
s = ((s * s) - 2) % mersenneNumber;
}
return(s == 0);
}
public void Init2()
{
using mpz_t a = new mpz_t("222509832503450298345029835740293845720");
mpz.init2(a, 20);
string AsString = a.ToString();
Assert.AreEqual("0", AsString);
}
public static bool Start04(ulong exponent)//3441
{
mpz_t mersenneNumber = mpz_t.One.ShiftLeft((int)exponent) - 1, s = 3;
for (ulong i = 1; i < exponent; i++)
{
s = Mod.MersennePrime(s * s, exponent, mersenneNumber);
}
return(s == mersenneNumber - 3);
}
public static bool Start01(ulong exponent)//2669
{
mpz_t mersenneNumber = mpz_t.One.ShiftLeft((int)exponent) - 1, s = 4;
for (ulong i = 2; i < exponent; s = s < 2 ? mersenneNumber : s - 2, i++)
{
mpir.mpz_powm(s, s, 2, mersenneNumber);
}
return(s == 0);
}
public static bool Test(ulong exponent, ref ulong startI, ref mpz_t startS)
{
if (!Collection.Primes.IsPrime((int)exponent) || ((exponent & 3) == 3 && Collection.Primes.IsPrime(((int)exponent << 1) + 1)))
{
return(false);
}
mpz_t mersenneNumber = mpz_t.One.ShiftLeft((int)exponent) - 1;
return(TrialDivision(exponent, mersenneNumber) && LucasLehmerTest.Fastest(exponent, mersenneNumber, ref startI, ref startS));
}
/// <summary>
/// Initializes a new instance of the <see cref="mpq_t"/> class.
/// </summary>
/// <param name="numerator">The numerator.</param>
/// <param name="denominator">The denominator.</param>
/// <param name="canonicalize">True if the new instance should use canonical numerator and denominator.</param>
public mpq_t(mpz_t numerator, mpz_t denominator, bool canonicalize = false)
{
mpq_init(ref Value);
mpq_set_num(ref Value, ref numerator.Value);
mpq_set_den(ref Value, ref denominator.Value);
if (canonicalize)
{
mpq_canonicalize(ref Value);
}
}
public mpz_t RandomZStarN(mpz_t n)
{
mpz_t r;
do
{
r = GetRandomNumber();
}while (r.CompareTo(n) >= 0 || mpz_t.Gcd(r, n) != 1);
return(r);
}
/// <summary>
/// Return a random integer in Z*_{n^2}
/// </summary>
public mpz_t RandomZStarNSquare(mpz_t nsquare)
{
mpz_t r;
do
{
r = GetRandomNumber();
}while (r.CompareTo(nsquare) >= 0 || mpz_t.Gcd(r, nsquare) != 1);
return(r);
}
static void Bar()
{
// [using-sample]
using (mpz_t a = new mpz_t(12345678901234567890))
using (mpz_t b = new mpz_t(9876543210987654321))
using (mpz_t c = a * b)
{
System.Console.WriteLine("{0}", c.ToString());
}
// [/using-sample]
}
//1,3
public static bool Start11(ulong exponent, ref ulong startI, ref mpz_t startS)//3969
{
mpz_t mersenneNumber = mpz_t.One.ShiftLeft((int)exponent) - 1, s = startS, e = mpz_t.One.ShiftLeft((int)(exponent - startI));
if (s < mersenneNumber)
{
startI++;
startS *= startS;
}
return(s.PowerMod(e, mersenneNumber) == mersenneNumber - 3);
}
public void Out()
{
string AsString;
using mpz_t a = new mpz_t("622288097498926496141095869268883999563096063592498055290461");
AsString = a.ToString();
Assert.AreEqual("622288097498926496141095869268883999563096063592498055290461", AsString);
using (MemoryStream Stream = new MemoryStream())
{
using (StreamWriter Writer = new StreamWriter(Stream, default, -1, leaveOpen: true))
public void PerfectPower()
{
string AsString;
using mpz_t a = new mpz_t("936995247845762439229916837840025004943963737679442023171062337518037547173883302933966320549");
AsString = a.ToString();
Assert.AreEqual("936995247845762439229916837840025004943963737679442023171062337518037547173883302933966320549", AsString);
bool IsPerfectPower = a.IsPerfectPower();
Assert.IsTrue(IsPerfectPower);
}
static int NumPrimes(int a, int b)
{
for (int n = 0; ; n++)
{
mpz_t bign = new mpz_t(n);
mpz_t p = bign.Power(2) + bign.Multiply(a) + b;
if (!p.IsProbablyPrimeRabinMiller(10))
{
return(n);
}
}
}
public void PopCount()
{
string AsString;
using mpz_t a = new mpz_t("10123456789ABCDEF0123456789ABCDEF0123456789ABCDEF", 16);
AsString = a.ToString(16).ToUpper();
Assert.AreEqual("10123456789ABCDEF0123456789ABCDEF0123456789ABCDEF", AsString);
ulong Count = mpz.popcount(a);
Assert.AreEqual(Count, 97UL);
}
public void PerfectSquare()
{
string AsString;
using mpz_t a = new mpz_t("95754294066634670780206802290671646680930214410991689632113801");
AsString = a.ToString();
Assert.AreEqual("95754294066634670780206802290671646680930214410991689632113801", AsString);
bool IsPerfectSquare = a.IsPerfectSquare();
Assert.IsTrue(IsPerfectSquare);
}
public void Sign()
{
string AsString;
bool IsNegative;
using mpz_t a = new mpz_t("-622288097498926496141095869268883999563096063592498055290461");
AsString = a.ToString();
Assert.AreEqual("-622288097498926496141095869268883999563096063592498055290461", AsString);
IsNegative = mpz.sgn(a) < 0;
Assert.IsTrue(IsNegative);
}
public void AddNonCanonicOperator()
{
string AsString;
using mpz_t n0 = new mpz_t("222509832503450298345029835740293845720");
using mpz_t d0 = new mpz_t("115756986668303657898962467957");
using mpq_t a = new mpq_t(n0, d0);
AsString = a.ToString();
Assert.AreEqual("222509832503450298345029835740293845720/115756986668303657898962467957", AsString);
using mpz_t n1 = new mpz_t("222987435987982730594288574029879874539");
using mpz_t d1 = new mpz_t("590872612825179551336102196593");
using mpq_t b = new mpq_t(n1, d1);
AsString = b.ToString();
Assert.AreEqual("222987435987982730594288574029879874539/590872612825179551336102196593", AsString);
using mpz_t n2 = n0 * 2;
using mpz_t d2 = d0 * 17;
using mpq_t c = new mpq_t(n2, d2);
AsString = c.ToString();
Assert.AreEqual("445019665006900596690059671480587691440/1967868773361162184282361955269", AsString);
c.Canonicalize();
AsString = c.ToString();
Assert.AreEqual("445019665006900596690059671480587691440/1967868773361162184282361955269", AsString);
using mpz_t n3 = n1 * 2;
using mpz_t d3 = d1 * 17;
using mpq_t d = new mpq_t(n3, d3);
AsString = d.ToString();
Assert.AreEqual("445974871975965461188577148059759749078/10044834418028052372713737342081", AsString);
d.Canonicalize();
AsString = d.ToString();
Assert.AreEqual("445974871975965461188577148059759749078/10044834418028052372713737342081", AsString);
using mpq_t e = c + d;
AsString = e.ToString();
Assert.AreEqual("314574639530933745596599719402044828752321603866779219489192838557566/1162759763812990990673034143436978981948983216731205310198517", AsString);
using mpz_t Numerator = c.GetNumerator() * d.GetDenominator() + d.GetNumerator() * c.GetDenominator();
AsString = Numerator.ToString();
Assert.AreNotEqual("314574639530933745596599719402044828752321603866779219489192838557566", AsString);
}
public void DivNonCanonicOperator()
{
string AsString;
using mpz_t n0 = new mpz_t("222509832503450298345029835740293845720");
using mpz_t d0 = new mpz_t("115756986668303657898962467957");
using mpq_t a = new mpq_t(n0, d0);
AsString = a.ToString();
Assert.AreEqual("222509832503450298345029835740293845720/115756986668303657898962467957", AsString);
using mpz_t n1 = new mpz_t("590872612825179551336102196593");
using mpz_t d1 = new mpz_t("222987435987982730594288574029879874539");
using mpq_t b = new mpq_t(n1, d1);
AsString = b.ToString();
Assert.AreEqual("590872612825179551336102196593/222987435987982730594288574029879874539", AsString);
using mpz_t n2 = n0 * 2;
using mpz_t d2 = d0 * 17;
using mpq_t c = new mpq_t(n2, d2);
AsString = c.ToString();
Assert.AreEqual("445019665006900596690059671480587691440/1967868773361162184282361955269", AsString);
c.Canonicalize();
AsString = c.ToString();
Assert.AreEqual("445019665006900596690059671480587691440/1967868773361162184282361955269", AsString);
using mpz_t n3 = n1 * 2;
using mpz_t d3 = d1 * 17;
using mpq_t d = new mpq_t(n3, d3);
AsString = d.ToString();
Assert.AreEqual("1181745225650359102672204393186/3790786411795706420102905758507957867163", AsString);
d.Canonicalize();
AsString = d.ToString();
Assert.AreEqual("1181745225650359102672204393186/3790786411795706420102905758507957867163", AsString);
using mpq_t e = c / d;
AsString = e.ToString();
Assert.AreEqual("49616897032059882578779559314539403611774953165369490340046561577107422123080/68397633165470058274884361378645822467587248043012077070501", AsString);
using mpz_t Numerator = c.GetNumerator() * d.GetDenominator();
AsString = Numerator.ToString();
Assert.AreNotEqual("49616897032059882578779559314539403611774953165369490340046561577107422123080", AsString);
}
public FactorPair(mpz_t p1, mpz_t p2)
{
if (p1 > p2)
{
Lower = p2;
Higher = p1;
}
else
{
Lower = p1;
Higher = p2;
}
}
public void BasicRoot()
{
string AsString;
using mpz_t a = new mpz_t("936995247845762439229916837840025004943963737679442023171062337518037547173883302933966320549");
AsString = a.ToString();
Assert.AreEqual("936995247845762439229916837840025004943963737679442023171062337518037547173883302933966320549", AsString);
mpz_t b = a.NthRoot(3);
AsString = b.ToString();
Assert.AreEqual("9785412309485720938412983404349", AsString);
}
public void NegateOperator()
{
string AsString;
using mpz_t a = new mpz_t("222987435987982730594288574029879874539");
AsString = a.ToString();
Assert.AreEqual("222987435987982730594288574029879874539", AsString);
using mpz_t b = -a;
AsString = b.ToString();
Assert.AreEqual("-222987435987982730594288574029879874539", AsString);
}
public void Sqrt()
{
string AsString;
using mpz_t a = new mpz_t("95754294066634670780206802290671646680930214410991689632113801");
AsString = a.ToString();
Assert.AreEqual("95754294066634670780206802290671646680930214410991689632113801", AsString);
mpz_t b = a.Sqrt();
AsString = b.ToString();
Assert.AreEqual("9785412309485720938412983404349", AsString);
}
public void AddUint()
{
string AsString;
using mpz_t a = new mpz_t("222509832503450298345029835740293845720");
AsString = a.ToString();
Assert.AreEqual("222509832503450298345029835740293845720", AsString);
using mpz_t b = new();
mpz.add_ui(b, a, 1);
AsString = b.ToString();
Assert.AreEqual("222509832503450298345029835740293845721", AsString);
}
public void AddIntOperator3()
{
string AsString;
using mpz_t a = new mpz_t("222509832503450298345029835740293845720");
AsString = a.ToString();
Assert.AreEqual("222509832503450298345029835740293845720", AsString);
int MinusOne = -1;
using mpz_t b = MinusOne + a;
AsString = b.ToString();
Assert.AreEqual("222509832503450298345029835740293845719", AsString);
}
public void AddIntOperator2()
{
string AsString;
using mpz_t a = new mpz_t("222509832503450298345029835740293845720");
AsString = a.ToString();
Assert.AreEqual("222509832503450298345029835740293845720", AsString);
int Two = 2;
using mpz_t b = a + Two;
AsString = b.ToString();
Assert.AreEqual("222509832503450298345029835740293845722", AsString);
}
public void AddUIntOperator1()
{
string AsString;
using mpz_t a = new mpz_t("222509832503450298345029835740293845720");
AsString = a.ToString();
Assert.AreEqual("222509832503450298345029835740293845720", AsString);
uint One = 1;
using mpz_t b = One + a;
AsString = b.ToString();
Assert.AreEqual("222509832503450298345029835740293845721", AsString);
}