public BigNumber Sqrt()
{
BigNumber res = 0;
BigNumber.Sqrt(this, res, numDefaultPlaces);
return(res);
}
public BigNumber Sqrt(int places)
{
BigNumber res = 0;
BigNumber.Sqrt(this, res, places);
return(res);
}
/****************************************************************************/
/*
* Calculate PI using the AGM (Arithmetic-Geometric Mean)
*
* Init : A0 = 1
* B0 = 1 / sqrt(2)
* Sum = 1
*
* Iterate: n = 1...
*
*
* A = 0.5 * [ A + B ]
* n n-1 n-1
*
*
* B = sqrt [ A * B ]
* n n-1 n-1
*
*
* C = 0.5 * [ A - B ]
* n n-1 n-1
*
*
* 2 n+1
* Sum = Sum - C * 2
* n
*
*
* At the end when C is 'small enough' :
* n
*
* 2
* PI = 4 * A / Sum
* n+1
*
* -OR-
*
* 2
* PI = ( A + B ) / Sum
* n n
*
*/
static private void CalculatePiAGM(BigNumber outv, int places)
{
int dplaces, nn;
BigNumber tmp1 = new BigNumber();
BigNumber tmp2 = new BigNumber();
BigNumber a0 = new BigNumber();
BigNumber b0 = new BigNumber();
BigNumber c0 = new BigNumber();
BigNumber a1 = new BigNumber();
BigNumber b1 = new BigNumber();
BigNumber sum = new BigNumber();
BigNumber pow_2 = new BigNumber();
dplaces = places + 16;
BigNumber.Copy(BigNumber.One, a0);
BigNumber.Copy(BigNumber.One, sum);
BigNumber.Copy(BigNumber.Four, pow_2);
BigNumber.Sqrt(BigNumber.BN_OneHalf, b0, dplaces);
while (true)
{
BigNumber.Add(a0, b0, tmp1);
BigNumber.Mul(tmp1, BigNumber.BN_OneHalf, a1);
BigNumber.Mul(a0, b0, tmp1);
BigNumber.Sqrt(tmp1, b1, dplaces);
BigNumber.Sub(a0, b0, tmp1);
BigNumber.Mul(BigNumber.BN_OneHalf, tmp1, c0);
BigNumber.Mul(c0, c0, tmp1);
BigNumber.Mul(tmp1, pow_2, tmp2);
BigNumber.Sub(sum, tmp2, tmp1);
BigNumber.Round(tmp1, sum, dplaces);
nn = -4 * c0.exponent;
if (nn >= dplaces)
{
break;
}
BigNumber.Copy(a1, a0);
BigNumber.Copy(b1, b0);
BigNumber.Mul(pow_2, BigNumber.Two, tmp1);
BigNumber.Copy(tmp1, pow_2);
}
BigNumber.Add(a1, b1, tmp1);
BigNumber.Mul(tmp1, tmp1, tmp2);
BigNumber.Div(tmp2, sum, tmp1, dplaces);
BigNumber.Round(tmp1, outv, places);
}
/****************************************************************************/
/*
* define a notation for a function 'R' :
*
*
*
* 1
* R (a0, b0) = ------------------------------
*
* ----
* \
* \ n-1 2 2
* 1 - | 2 * (a - b )
* / n n
* /
* ----
* n >= 0
*
*
* where a, b are the classic AGM iteration :
*
*
* a = 0.5 * (a + b )
* n+1 n n
*
*
* b = sqrt(a * b )
* n+1 n n
*
*
*
* define a variable 'c' for more efficient computation :
*
* 2 2 2
* c = 0.5 * (a - b ) , c = a - b
* n+1 n n n n n
*
*/
/****************************************************************************/
static void LogAGMRFunc(BigNumber aa, BigNumber bb, BigNumber rr, int places)
{
BigNumber tmp1, tmp2, tmp3, tmp4, tmpC2, sum, pow_2, tmpA0, tmpB0;
int tolerance, dplaces;
tmpA0 = new BigNumber();
tmpB0 = new BigNumber();
tmpC2 = new BigNumber();
tmp1 = new BigNumber();
tmp2 = new BigNumber();
tmp3 = new BigNumber();
tmp4 = new BigNumber();
sum = new BigNumber();
pow_2 = new BigNumber();
tolerance = places + 8;
dplaces = places + 16;
BigNumber.Copy(aa, tmpA0);
BigNumber.Copy(bb, tmpB0);
BigNumber.Copy(BigNumber.BN_OneHalf, pow_2);
BigNumber.Mul(aa, aa, tmp1); /* 0.5 * [ a ^ 2 - b ^ 2 ] */
BigNumber.Mul(bb, bb, tmp2);
BigNumber.Sub(tmp1, tmp2, tmp3);
BigNumber.Mul(BigNumber.BN_OneHalf, tmp3, sum);
while (true)
{
BigNumber.Sub(tmpA0, tmpB0, tmp1); /* C n+1 = 0.5 * [ An - Bn ] */
BigNumber.Mul(BigNumber.BN_OneHalf, tmp1, tmp4); /* C n+1 */
BigNumber.Mul(tmp4, tmp4, tmpC2); /* C n+1 ^ 2 */
/* do the AGM */
BigNumber.Add(tmpA0, tmpB0, tmp1);
BigNumber.Mul(BigNumber.BN_OneHalf, tmp1, tmp3);
BigNumber.Mul(tmpA0, tmpB0, tmp2);
BigNumber.Sqrt(tmp2, tmpB0, dplaces);
BigNumber.Round(tmp3, tmpA0, dplaces);
/* end AGM */
BigNumber.Mul(BigNumber.Two, pow_2, tmp2);
BigNumber.Copy(tmp2, pow_2);
BigNumber.Mul(tmpC2, pow_2, tmp1);
BigNumber.Add(sum, tmp1, tmp3);
if ((tmp1.signum == 0) || ((-2 * tmp1.exponent) > tolerance))
{
break;
}
BigNumber.Round(tmp3, sum, dplaces);
}
BigNumber.Sub(BigNumber.One, tmp3, tmp4);
BigNumber.Reziprocal(tmp4, rr, places);
}
public static void DoTest()
{
BigNumber A = 0, B = 0, C = 0;
BigNumber PI = new BigNumber();
// assignment by string
A = "12345";
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
// assignment from hexadecimal string
A = "0xff";
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
A = "0x1ff";
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
A = "0x123456789";
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
A = "0xFeDcBafedcba";
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
// assignment from binary string
A = "%10001000";
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
A = "%11011011100111000111000111100011010101010101";
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
// assignment by double
A = 123.45;
B = 0.12345;
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
// assignment by string in exponential form x = a*10^y. 10E3 = 10*10^^3 = 10000
A = "10E3"; // 10E3 = 10*10^3 = 10000
B = "1E4"; // 1E4 = 1*10^4 = 10000
C = 10000;
Console.WriteLine("assigned value was: " + A.ToFullString() + "(" + A.ToString() + ")");
Console.WriteLine("10000 = " + A.ToFullString() + " = " + B.ToFullString() + " = " + C.ToFullString());
A = 1; B = 2; C = 0;
C = A + B;
Console.WriteLine("the result of " + A.ToFullString() + "+" + B.ToFullString() + "=" + C.ToFullString());
// addition of BigNumber + double
C = A + 3.2;
// addition of double + BigNumber
C = 3.1 + B;
A = "5.141592"; B = "2.91827";
C = A - B;
Console.WriteLine("the result of " + A.ToFullString() + "-" + B.ToFullString() + "=" + C.ToFullString());
C = A * B;
Console.WriteLine("the result of " + A.ToFullString() + "*" + B.ToFullString() + "=" + C.ToFullString());
A = 5.0; B = 3.0;
C = A * B;
Console.WriteLine("the result of " + A.ToFullString() + "*" + B.ToFullString() + "=" + C.ToFullString());
A = 4; B = 0.5;
C = A.Pow(B);
Console.WriteLine("the result of " + A.ToFullString() + " pow " + B.ToFullString() + "=" + C.ToFullString());
A = 0.5; B = "5E-1";
C = A.Pow(B, 16);
Console.WriteLine("the result of " + A.ToFullString() + " pow " + B.ToFullString() + "=" + C.ToFullString());
A = "1e3"; // "10E2"; // "1E3 = 1000";
C = A.Log10();
Console.WriteLine("the result of " + A.ToFullString() + " Log10 =" + C.ToFullString());
A = "10E3"; B = "1E4"; C = 10000;
A = BigNumber.BN_E;
C = A.Log();
Console.WriteLine("the result of " + A.ToString() + " Log =" + C.ToFullString());
A = 3.0;
C = A.Rez();
Console.WriteLine("the result of " + A.ToString() + " Rez =" + C.ToFullString());
int NumPlaces = 4;
A = 1.53456;
C = A.Round(NumPlaces);
Console.WriteLine("the result of " + A.ToString() + " Round(" + NumPlaces + ") =" + C.ToFullString());
NumPlaces = 2;
C = A.Round(NumPlaces);
Console.WriteLine("the result of " + A.ToString() + " Round(" + NumPlaces + ") =" + C.ToFullString());
NumPlaces = 0;
C = A.Round(NumPlaces);
Console.WriteLine("the result of " + A.ToString() + " Round(" + NumPlaces + ") =" + C.ToFullString());
NumPlaces = 16;
A = 2.0;
C = A.Sqrt(NumPlaces);
Console.WriteLine("the result of " + A.ToString() + " Sqrt(" + NumPlaces + ") =" + C.ToFullString());
A = 1.0; B = 0;
try
{
C = A / B;
}
catch (BigNumberException ex)
{
Console.WriteLine("Exception in operation: " + ex.Message);
}
A = 1.0;
for (int i = 1; i <= 1000; i++)
{
A = A * i;
}
Console.WriteLine("the result of 1000!=" + A.ToFullString());
A = A.Round(numDefaultPlaces);
Console.WriteLine("the result of 1000!=" + A.ToString());
DateTime before = DateTime.Now;
NumPlaces = 5000;
CalculatePiAGM(PI, NumPlaces);
TimeSpan ts = DateTime.Now - before;
Console.WriteLine("time for " + NumPlaces + " digits of PI: " + ts.TotalMilliseconds + "[ms]");
Console.WriteLine(PI.ToFullString());
Console.WriteLine("Press 'x' key to quit test");
//while (true)
//{
// ConsoleKeyInfo i = Console.ReadKey();
// if (i.KeyChar == 'x') break;
//}
}