public static BigNumber operator +(BigNumber c1, BigNumber c2)
{
BigNumber res = new BigNumber();
BigNumber.Add(c1, c2, res);
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 public void Round(BigNumber src, BigNumber dst, int places)
{
BigNumber t0_5 = new BigNumber();
BigNumber.Copy(Five, t0_5);
int ii = places + 1;
if (src.dataLength <= ii)
{
Copy(src, dst);
return;
}
t0_5.exponent = src.exponent - ii;
if (src.signum > 0)
{
BigNumber.Add(src, t0_5, dst);
}
else
{
BigNumber.Sub(src, t0_5, dst);
}
dst.dataLength = ii;
BigNumber.Normalize(dst);
}
public static BigNumber operator +(BigNumber c1, long c2)
{
BigNumber res = new BigNumber();
BigNumber C2 = c2;
BigNumber.Add(c1, C2, res);
return(res);
}
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);
}
/****************************************************************************/
/*
* 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 M_raw_exp(BigNumber xx, BigNumber rr, int places)
{
BigNumber tmp0, digit, term;
int tolerance, local_precision, prev_exp;
long m1;
tmp0 = new BigNumber();
term = new BigNumber();
digit = new BigNumber();
local_precision = places + 8;
tolerance = -(places + 4);
prev_exp = 0;
BigNumber.Add(BigNumber.One, xx, rr);
BigNumber.Copy(xx, term);
m1 = 2L;
while (true)
{
BigNumber.SetFromLong(digit, m1);
BigNumber.Mul(term, xx, tmp0);
BigNumber.Div(tmp0, digit, term, local_precision);
BigNumber.Add(rr, term, tmp0);
BigNumber.Copy(tmp0, rr);
if ((term.exponent < tolerance) || (term.signum == 0))
{
break;
}
if (m1 != 2L)
{
local_precision = local_precision + term.exponent - prev_exp;
if (local_precision < 20)
{
local_precision = 20;
}
}
prev_exp = term.exponent;
m1++;
}
}
static void Floor(BigNumber dst, BigNumber src)
{
BigNumber.Copy(src, dst);
if (BigNumber.IsInteger(dst) > 0)
{
return;
}
if (dst.exponent <= 0) /* if |bb| < 1, result is -1 or 0 */
{
if (dst.signum < 0)
{
BigNumber.Neg(BigNumber.One, dst);
}
else
{
BigNumber.SetZero(dst);
}
return;
}
if (dst.signum < 0)
{
BigNumber mtmp = new BigNumber();
BigNumber.Neg(dst, mtmp);
mtmp.dataLength = mtmp.exponent;
BigNumber.Normalize(mtmp);
BigNumber.Add(mtmp, BigNumber.One, dst);
dst.signum = -1;
}
else
{
dst.dataLength = dst.exponent;
BigNumber.Normalize(dst);
}
}
static void Ceil(BigNumber dst, BigNumber src)
{
BigNumber mtmp;
BigNumber.Copy(src, dst);
if (IsInteger(dst) > 0) /* if integer, we're done */
{
return;
}
if (dst.exponent <= 0) /* if |bb| < 1, result is 0 or 1 */
{
if (dst.signum < 0)
{
BigNumber.SetZero(dst);
}
else
{
BigNumber.Copy(BigNumber.One, dst);
}
return;
}
if (dst.signum < 0)
{
dst.dataLength = dst.exponent;
BigNumber.Normalize(dst);
}
else
{
mtmp = new BigNumber();
BigNumber.Copy(dst, mtmp);
mtmp.dataLength = mtmp.exponent;
BigNumber.Normalize(mtmp);
BigNumber.Add(mtmp, BigNumber.One, dst);
}
}
static int M_exp_compute_nn(ref int n, BigNumber b, BigNumber a)
{
BigNumber tmp0, tmp1;
String cp = "";
int kk;
n = 0;
tmp0 = new BigNumber();
tmp1 = new BigNumber();
BigNumber.Mul(BN_exp_log2R, a, tmp1);
if (tmp1.signum >= 0)
{
BigNumber.Add(tmp1, BigNumber.BN_OneHalf, tmp0);
BigNumber.Floor(tmp1, tmp0);
}
else
{
BigNumber.Sub(tmp1, BigNumber.BN_OneHalf, tmp0);
BigNumber.Ceil(tmp1, tmp0);
}
kk = tmp1.exponent;
cp = BigNumber.ToIntString(tmp1);
n = Convert.ToInt32(cp);
BigNumber.SetFromLong(b, (long)(n));
kk = BigNumber.Compare(b, tmp1);
return(kk);
}
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 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);
}
