public BigNumber Round(int places)
{
BigNumber res = 0;
BigNumber.Round(this, res, places);
return(res);
}
static void M_log_basic_iteration(BigNumber nn, BigNumber rr, int places)
{
BigNumber tmp0, tmp1, tmp2, tmpX;
if (places < 360)
{
BigNumber.M_log_solve_cubic(nn, rr, places);
}
else
{
tmp0 = new BigNumber();
tmp1 = new BigNumber();
tmp2 = new BigNumber();
tmpX = new BigNumber();
BigNumber.M_log_solve_cubic(nn, tmpX, 110);
BigNumber.Neg(tmpX, tmp0);
BigNumber.Exp(tmp0, tmp1, (places + 8));
BigNumber.Mul(tmp1, nn, tmp2);
BigNumber.Sub(tmp2, BigNumber.One, tmp1);
BigNumber.M_log_near_1(tmp1, tmp0, (places - 104));
BigNumber.Add(tmpX, tmp0, tmp1);
BigNumber.Round(tmp1, rr, places);
}
}
static void Log10(BigNumber src, BigNumber dst, int places)
{
BigNumber tmp8 = new BigNumber();
BigNumber tmp9 = new BigNumber();
int dplaces = places + 4;
BigNumber.CheckLogPlaces(dplaces + 45);
BigNumber.Log(src, tmp9, dplaces);
BigNumber.Mul(tmp9, BN_lc_log10R, tmp8);
BigNumber.Round(tmp8, dst, places);
}
static void M_log_solve_cubic(BigNumber nn, BigNumber rr, int places)
{
BigNumber tmp0, tmp1, tmp2, tmp3, guess;
int ii, maxp, tolerance, local_precision;
guess = new BigNumber();
tmp0 = new BigNumber();
tmp1 = new BigNumber();
tmp2 = new BigNumber();
tmp3 = new BigNumber();
BigNumber.M_get_log_guess(nn, guess);
tolerance = -(places + 4);
maxp = places + 16;
local_precision = 18;
ii = 0;
while (true)
{
BigNumber.Exp(guess, tmp1, local_precision);
BigNumber.Sub(tmp1, nn, tmp3);
BigNumber.Add(tmp1, nn, tmp2);
BigNumber.Div(tmp3, tmp2, tmp1, local_precision);
BigNumber.Mul(BigNumber.Two, tmp1, tmp0);
BigNumber.Sub(guess, tmp0, tmp3);
if (ii != 0)
{
if (((3 * tmp0.exponent) < tolerance) || (tmp0.signum == 0))
{
break;
}
}
BigNumber.Round(tmp3, guess, local_precision);
local_precision *= 3;
if (local_precision > maxp)
{
local_precision = maxp;
}
ii = 1;
}
BigNumber.Round(tmp3, rr, places);
}
/****************************************************************************/
/*
* 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);
}
static public void RoundFix(BigNumber src, BigNumber dst, int places)
{
string srcStr = src.ToFullString();
int dotIndex = srcStr.IndexOf(".");
if (dotIndex >= 0)
{
BigNumber.Round(src, dst, dotIndex + places - 1);
}
else
{
}
}
/****************************************************************************/
/*
* calculate log (1 + x) with the following series:
*
* x
* y = ----- ( |y| < 1 )
* x + 2
*
*
* [ 1 + y ] y^3 y^5 y^7
* log [-------] = 2 * [ y + --- + --- + --- ... ]
* [ 1 - y ] 3 5 7
*
*/
static void M_log_near_1(BigNumber xx, BigNumber rr, int places)
{
BigNumber tmp0, tmp1, tmp2, tmpS, term;
int tolerance, dplaces, local_precision;
long m1;
tmp0 = new BigNumber();
tmp1 = new BigNumber();
tmp2 = new BigNumber();
tmpS = new BigNumber();
term = new BigNumber();
tolerance = xx.exponent - (places + 6);
dplaces = (places + 12) - xx.exponent;
BigNumber.Add(xx, BigNumber.Two, tmp0);
BigNumber.Div(xx, tmp0, tmpS, (dplaces + 6));
BigNumber.Copy(tmpS, term);
BigNumber.Mul(tmpS, tmpS, tmp0);
BigNumber.Round(tmp0, tmp2, (dplaces + 6));
m1 = 3L;
while (true)
{
BigNumber.Mul(term, tmp2, tmp0);
if ((tmp0.exponent < tolerance) || (tmp0.signum == 0))
{
break;
}
local_precision = dplaces + tmp0.exponent;
if (local_precision < 20)
{
local_precision = 20;
}
BigNumber.SetFromLong(tmp1, m1);
BigNumber.Round(tmp0, term, local_precision);
BigNumber.Div(term, tmp1, tmp0, local_precision);
BigNumber.Add(tmpS, tmp0, tmp1);
BigNumber.Copy(tmp1, tmpS);
m1 += 2;
}
BigNumber.Mul(BigNumber.Two, tmpS, tmp0);
BigNumber.Round(tmp0, rr, places);
}
static private void Exp(BigNumber src, BigNumber dst, int places)
{
BigNumber A = 0, B = 0, C = 0;
int dplaces, nn = 0, ii = 0;
if (src.signum == 0)
{
BigNumber.Copy(BigNumber.One, dst);
return;
}
if (src.exponent <= -3)
{
M_raw_exp(src, C, (places + 6));
BigNumber.Round(C, dst, places);
return;
}
if (M_exp_compute_nn(ref nn, A, src) != 0)
{
throw new BigNumberException("'Exp', Input too large, Overflow");
}
dplaces = places + 8;
BigNumber.CheckLogPlaces(dplaces);
BigNumber.Mul(A, BN_lc_log2, B);
BigNumber.Sub(src, B, A);
while (true)
{
if (A.signum != 0)
{
if (A.exponent == 0)
{
break;
}
}
if (A.signum >= 0)
{
nn++;
BigNumber.Sub(A, BN_lc_log2, B);
BigNumber.Copy(B, A);
}
else
{
nn--;
BigNumber.Add(A, BN_lc_log2, B);
BigNumber.Copy(B, A);
}
}
BigNumber.Mul(A, BN_exp_512R, C);
M_raw_exp(C, B, dplaces);
ii = 9;
while (true)
{
BigNumber.Mul(B, B, C);
BigNumber.Round(C, B, dplaces);
if (--ii == 0)
{
break;
}
}
BigNumber.IntPow(dplaces, BigNumber.Two, nn, A);
BigNumber.Mul(A, B, C);
BigNumber.Round(C, dst, places);
}
static void Sqrt(BigNumber src, BigNumber dst, int places)
{
int ii, nexp, tolerance, dplaces;
bool bflag;
if (src.signum <= 0)
{
if (src.signum == -1)
{
throw new BigNumberException("'Sqrt',Invalid Argument");
}
}
BigNumber last_x = new BigNumber();
BigNumber guess = new BigNumber();
BigNumber tmpN = new BigNumber();
BigNumber tmp7 = new BigNumber();
BigNumber tmp8 = new BigNumber();
BigNumber tmp9 = new BigNumber();
BigNumber.Copy(src, tmpN);
nexp = src.exponent / 2;
tmpN.exponent -= 2 * nexp;
BigNumber.SQrtGuess(tmpN, guess);
tolerance = places + 4;
dplaces = places + 16;
bflag = false;
BigNumber.Neg(BigNumber.Ten, last_x);
ii = 0;
while (true)
{
BigNumber.Mul(tmpN, guess, tmp9);
BigNumber.Mul(tmp9, guess, tmp8);
BigNumber.Round(tmp8, tmp7, dplaces);
BigNumber.Sub(BigNumber.Three, tmp7, tmp9);
BigNumber.Mul(tmp9, guess, tmp8);
BigNumber.Mul(tmp8, BigNumber.BN_OneHalf, tmp9);
if (bflag)
{
break;
}
BigNumber.Round(tmp9, guess, dplaces);
if (ii != 0)
{
BigNumber.Sub(guess, last_x, tmp7);
if (tmp7.signum == 0)
{
break;
}
/*
* if we are within a factor of 4 on the error term,
* we will be accurate enough after the *next* iteration
* is complete. (note that the sign of the exponent on
* the error term will be a negative number).
*/
if ((-4 * tmp7.exponent) > tolerance)
{
bflag = true;
}
}
BigNumber.Copy(guess, last_x);
ii++;
}
BigNumber.Mul(tmp9, tmpN, tmp8);
BigNumber.Round(tmp8, dst, places);
dst.exponent += nexp;
}
static private void IntPow(int places, BigNumber src, int mexp, BigNumber dst)
{
BigNumber A, B, C;
int nexp, ii, signflag, local_precision;
if (mexp == 0)
{
BigNumber.Copy(BigNumber.One, dst);
return;
}
else
{
if (mexp > 0)
{
signflag = 0;
nexp = mexp;
}
else
{
signflag = 1;
nexp = -mexp;
}
}
if (src.signum == 0)
{
BigNumber.SetZero(dst);
return;
}
A = new BigNumber();
B = new BigNumber();
C = new BigNumber();
local_precision = places + 8;
BigNumber.Copy(BigNumber.One, B);
BigNumber.Copy(src, C);
while (true)
{
ii = nexp & 1;
nexp = nexp >> 1;
if (ii != 0) /* exponent -was- odd */
{
BigNumber.Mul(B, C, A);
BigNumber.Round(A, B, local_precision);
if (nexp == 0)
{
break;
}
}
BigNumber.Mul(C, C, A);
BigNumber.Round(A, C, local_precision);
}
if (signflag > 0)
{
BigNumber.Reziprocal(B, dst, places);
}
else
{
BigNumber.Round(B, dst, places);
}
}
static void Log(BigNumber src, BigNumber dst, int places)
{
BigNumber tmp0, tmp1, tmp2;
int mexp, dplaces;
if (src.signum <= 0)
{
throw new BigNumberException(" 'Log', Negative argument");
}
tmp0 = new BigNumber();
tmp1 = new BigNumber();
tmp2 = new BigNumber();
dplaces = places + 8;
mexp = src.exponent;
if (mexp == 0 || mexp == 1)
{
BigNumber.Sub(src, BigNumber.One, tmp0);
if (tmp0.signum == 0) /* is input exactly 1 ?? */
{ /* if so, result is 0 */
BigNumber.SetZero(dst);
return;
}
if (tmp0.exponent <= -4)
{
M_log_near_1(tmp0, dst, places);
return;
}
}
/* make sure our log(10) is accurate enough for this calculation */
/* (and log(2) which is called from M_log_basic_iteration) */
BigNumber.CheckLogPlaces(dplaces + 25);
if (Math.Abs(mexp) <= 3)
{
M_log_basic_iteration(src, dst, places);
}
else
{
/*
* use log (x * y) = log(x) + log(y)
*
* here we use y = exponent of our base 10 number.
*
* let 'C' = log(10) = 2.3025850929940....
*
* then log(x * y) = log(x) + ( C * base_10_exponent )
*/
BigNumber.Copy(src, tmp2);
mexp = tmp2.exponent - 2;
tmp2.exponent = 2;
M_log_basic_iteration(tmp2, tmp0, dplaces);
BigNumber.SetFromLong(tmp1, (long)mexp);
BigNumber.Mul(tmp1, BN_lc_log10, tmp2);
BigNumber.Add(tmp2, tmp0, tmp1);
BigNumber.Round(tmp1, dst, 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);
}
static private void CalculatePiMachin(BigNumber outv, int places)
{
BigNumber curanswer;
BigNumber lastanswer;
BigNumber term5;
BigNumber term239;
BigNumber term5m;
BigNumber term239m;
BigNumber diff;
BigNumber lim;
int n5;
int n239;
bool b5termdone = false;
bool b239termdone = false;
lim = 1;
lim /= (Math.Pow(10, places));
n5 = 0;
n239 = 0;
term5 = 16;
term5 /= 5;
term239 = 4;
term239 /= 239;
curanswer = 0;
lastanswer = 0;
while (b5termdone == false && b239termdone == false)
{
lastanswer = curanswer;
term5m = term5;
term5m /= n5 * 2 + 1;
term239m = term239;
term239m /= n239 * 2 + 1;
if (n5 % 2 == 0)
{
curanswer += term5m; /* n5 is even */
}
else
{
curanswer -= term5m; /* n5 is odd */
}
if (n239 % 2 == 0)
{
curanswer -= term239m; /* n239 is even */
}
else
{
curanswer += term239m; /* n239 is odd */
}
term5 /= 25; // 5*5
n5++;
term239 /= 57121; // 239 * 239;
n239++;
diff = lastanswer - curanswer;
BigNumber.Abs(diff, diff);
if (diff < lim)
{
break;
}
}
BigNumber.Round(curanswer, outv, 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;
//}
}
static private String ToExpString(BigNumber atm, int digits)
{
int i, index, first, max_i, num_digits, dec_places;
byte numdiv = 0, numrem = 0;
BigNumber ctmp = new BigNumber();
String res = "";
dec_places = digits;
if (dec_places < 0)
{
BigNumber.Copy(atm, ctmp);
}
else
{
BigNumber.Round(atm, ctmp, dec_places);
}
if (ctmp.signum == 0)
{
if (dec_places < 0)
{
res = "0.0E+0";
}
else
{
res = "0";
if (dec_places > 0)
{
res += ".";
}
for (i = 0; i < dec_places; i++)
{
res += "0";
}
res += "E+0";
}
return(res);
}
max_i = (ctmp.dataLength + 1) >> 1;
if (dec_places < 0)
{
num_digits = ctmp.dataLength;
}
else
{
num_digits = dec_places + 1;
}
if (ctmp.signum == -1)
{
res += '-';
}
first = 1;
i = 0;
index = 0;
while (true)
{
if (index >= max_i)
{
numdiv = 0;
numrem = 0;
}
else
{
Unpack(ctmp.mantissa[index], ref numdiv, ref numrem);
}
index++;
res += (char)('0' + numdiv);
if (++i == num_digits)
{
break;
}
if (first != 0)
{
first = 0;
res += '.';
}
res += (char)('0' + numrem);
if (++i == num_digits)
{
break;
}
}
i = ctmp.exponent - 1;
if (i >= 0)
{
res += "E+" + i;
}
else if (i < 0)
{
res += "E" + i;
}
return(res);
}
