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);
}
static private void FastMul(BigNumber aa, BigNumber bb, BigNumber rr)
{
int ii, k, nexp, sign;
BigNumber M_ain = new BigNumber();
BigNumber M_bin = new BigNumber();
BigNumber.Copy(aa, M_ain);
BigNumber.Copy(bb, M_bin);
int size_flag = GetSizeofInt();
int bit_limit = 8 * size_flag + 1;
sign = M_ain.signum * M_bin.signum;
nexp = M_ain.exponent + M_bin.exponent;
if (M_ain.dataLength >= M_bin.dataLength)
{
ii = M_ain.dataLength;
}
else
{
ii = M_bin.dataLength;
}
ii = (ii + 1) >> 1;
ii = NextPowerOfTwo(ii);
k = 2 * ii; /* required size of result, in bytes */
BigNumber.Pad(M_ain, k); /* fill out the data so the number of */
BigNumber.Pad(M_bin, k); /* bytes is an exact power of 2 */
if (k > rr.mantissa.Length)
{
BigNumber.Expand(rr, (k + 32));
}
BigNumber.FastMulFFT(rr.mantissa, M_ain.mantissa, M_bin.mantissa, ii);
rr.signum = (sbyte)sign;
rr.exponent = nexp;
rr.dataLength = 4 * ii;
BigNumber.Normalize(rr);
}
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 public void Sub(BigNumber src, BigNumber dst, BigNumber result)
{
int itmp, j, ChangeOrderFlag, icompare, aexp, bexp, borrow, adigits, bdigits;
sbyte sign;
BigNumber A = 0, B = 0;
if (dst.signum == 0)
{
BigNumber.Copy(src, result);
return;
}
if (src.signum == 0)
{
BigNumber.Copy(dst.Neg(), result);
return;
}
if (src.signum == 1 && dst.signum == -1)
{
dst.signum = 1;
Add(src, dst, result);
dst.signum = -1;
return;
}
if (src.signum == -1 && dst.signum == 1)
{
dst.signum = -1;
Add(src, dst, result);
dst.signum = 1;
return;
}
BigNumber.Abs(A, src);
BigNumber.Abs(B, dst);
if ((icompare = Compare(A, B)) == 0)
{
SetZero(result);
return;
}
if (icompare == 1) /* |a| > |b| (do A-B) */
{
ChangeOrderFlag = 1;
sign = src.signum;
}
else /* |b| > |a| (do B-A) */
{
ChangeOrderFlag = 0;
sign = (sbyte)-(src.signum);
}
aexp = A.exponent;
bexp = B.exponent;
if (aexp > bexp)
{
Scale(B, (aexp - bexp));
}
if (aexp < bexp)
{
Scale(A, (bexp - aexp));
}
adigits = A.dataLength;
bdigits = B.dataLength;
if (adigits > bdigits)
{
Pad(B, adigits);
}
if (adigits < bdigits)
{
Pad(A, bdigits);
}
if (ChangeOrderFlag == 1) // |a| > |b| (do A-B)
{
Copy(A, result);
j = (result.dataLength + 1) >> 1;
borrow = 0;
while (true)
{
j--;
itmp = ((int)result.mantissa[j] - ((int)B.mantissa[j] + borrow));
if (itmp >= 0)
{
result.mantissa[j] = (byte)itmp;
borrow = 0;
}
else
{
result.mantissa[j] = (byte)(100 + itmp);
borrow = 1;
}
if (j == 0)
{
break;
}
}
}
else // |b| > |a| (do B-A) instead
{
Copy(B, result);
j = (result.dataLength + 1) >> 1;
borrow = 0;
while (true)
{
j--;
itmp = (int)result.mantissa[j] - ((int)A.mantissa[j] + borrow);
if (itmp >= 0)
{
result.mantissa[j] = (byte)itmp;
borrow = 0;
}
else
{
result.mantissa[j] = (byte)(100 + itmp);
borrow = 1;
}
if (j == 0)
{
break;
}
}
}
result.signum = sign;
BigNumber.Normalize(result);
}
static private void Div(BigNumber aa, BigNumber bb, BigNumber rr, int places)
{
int j, k, m, b0, nexp, indexr, icompare, iterations;
sbyte sign;
long trial_numer;
BigNumber M_div_worka = new BigNumber();
BigNumber M_div_workb = new BigNumber();
BigNumber M_div_tmp7 = new BigNumber();
BigNumber M_div_tmp8 = new BigNumber();
BigNumber M_div_tmp9 = new BigNumber();
sign = (sbyte)(aa.signum * bb.signum);
if (sign == 0) /* one number is zero, result is zero */
{
if (bb.signum == 0)
{
throw new BigNumberException("Division by Zero");
}
BigNumber.SetZero(rr);
return;
}
if (bb.mantissa[0] >= 50)
{
BigNumber.Abs(M_div_worka, aa);
BigNumber.Abs(M_div_workb, bb);
}
else /* 'normal' step D1 */
{
k = 100 / (bb.mantissa[0] + 1);
BigNumber.SetFromLong(M_div_tmp9, (long)k);
BigNumber.Mul(M_div_tmp9, aa, M_div_worka);
BigNumber.Mul(M_div_tmp9, bb, M_div_workb);
M_div_worka.signum = 1;
M_div_workb.signum = 1;
}
b0 = 100 * (int)M_div_workb.mantissa[0];
if (M_div_workb.dataLength >= 3)
{
b0 += M_div_workb.mantissa[1];
}
nexp = M_div_worka.exponent - M_div_workb.exponent;
if (nexp > 0)
{
iterations = nexp + places + 1;
}
else
{
iterations = places + 1;
}
k = (iterations + 1) >> 1; /* required size of result, in bytes */
if (k > rr.mantissa.Length)
{
BigNumber.Expand(rr, k + 32);
}
/* clear the exponent in the working copies */
M_div_worka.exponent = 0;
M_div_workb.exponent = 0;
/* if numbers are equal, ratio == 1.00000... */
if ((icompare = BigNumber.Compare(M_div_worka, M_div_workb)) == 0)
{
iterations = 1;
rr.mantissa[0] = 10;
nexp++;
}
else /* ratio not 1, do the real division */
{
if (icompare == 1) /* numerator > denominator */
{
nexp++; /* to adjust the final exponent */
M_div_worka.exponent += 1; /* multiply numerator by 10 */
}
else /* numerator < denominator */
{
M_div_worka.exponent += 2; /* multiply numerator by 100 */
}
indexr = 0;
m = 0;
while (true)
{
/*
* Knuth step D3. Only use the 3rd -> 6th digits if the number
* actually has that many digits.
*/
trial_numer = 10000L * (long)M_div_worka.mantissa[0];
if (M_div_worka.dataLength >= 5)
{
trial_numer += 100 * M_div_worka.mantissa[1] + M_div_worka.mantissa[2];
}
else
{
if (M_div_worka.dataLength >= 3)
{
trial_numer += 100 * M_div_worka.mantissa[1];
}
}
j = (int)(trial_numer / b0);
/*
* Since the library 'normalizes' all the results, we need
* to look at the exponent of the number to decide if we
* have a lead in 0n or 00.
*/
if ((k = 2 - M_div_worka.exponent) > 0)
{
while (true)
{
j /= 10;
if (--k == 0)
{
break;
}
}
}
if (j == 100) /* qhat == base ?? */
{
j = 99; /* if so, decrease by 1 */
}
BigNumber.SetFromLong(M_div_tmp8, (long)j);
BigNumber.Mul(M_div_tmp8, M_div_workb, M_div_tmp7);
/*
* Compare our q-hat (j) against the desired number.
* j is either correct, 1 too large, or 2 too large
* per Theorem B on pg 272 of Art of Compter Programming,
* Volume 2, 3rd Edition.
*
* The above statement is only true if using the 2 leading
* digits of the numerator and the leading digit of the
* denominator. Since we are using the (3) leading digits
* of the numerator and the (2) leading digits of the
* denominator, we eliminate the case where our q-hat is
* 2 too large, (and q-hat being 1 too large is quite remote).
*/
if (BigNumber.Compare(M_div_tmp7, M_div_worka) == 1)
{
j--;
BigNumber.Sub(M_div_tmp7, M_div_workb, M_div_tmp8);
BigNumber.Copy(M_div_tmp8, M_div_tmp7);
}
/*
* Since we know q-hat is correct, step D6 is unnecessary.
*
* Store q-hat, step D5. Since D6 is unnecessary, we can
* do D5 before D4 and decide if we are done.
*/
rr.mantissa[indexr++] = (byte)j; /* j == 'qhat' */
m += 2;
if (m >= iterations)
{
break;
}
/* step D4 */
BigNumber.Sub(M_div_worka, M_div_tmp7, M_div_tmp9);
/*
* if the subtraction yields zero, the division is exact
* and we are done early.
*/
if (M_div_tmp9.signum == 0)
{
iterations = m;
break;
}
/* multiply by 100 and re-save */
M_div_tmp9.exponent += 2;
BigNumber.Copy(M_div_tmp9, M_div_worka);
}
}
rr.signum = sign;
rr.exponent = nexp;
rr.dataLength = iterations;
BigNumber.Normalize(rr);
}
static private void Mul(BigNumber aa, BigNumber bb, BigNumber rr)
{
int ai, itmp, nexp, ii, jj, indexa, indexb, index0, numdigits;
sbyte sign;
sign = (sbyte)(aa.signum * bb.signum);
nexp = aa.exponent + bb.exponent;
if (sign == 0)
{
BigNumber.SetZero(rr);
return;
}
numdigits = aa.dataLength + bb.dataLength;
indexa = (aa.dataLength + 1) >> 1;
indexb = (bb.dataLength + 1) >> 1;
if (indexa >= 48 && indexb >= 48)
{
BigNumber.FastMul(aa, bb, rr);
return;
}
ii = (numdigits + 1) >> 1;
if (ii >= rr.mantissa.Length)
{
BigNumber.Expand(rr, ii + 32);
}
index0 = indexa + indexb;
for (int i = 0; i < index0; i++)
{
rr.mantissa[i] = 0;
}
ii = indexa;
while (true)
{
index0--;
int crp = index0;
jj = indexb;
ai = (int)aa.mantissa[--ii];
while (true)
{
itmp = ai * bb.mantissa[--jj];
rr.mantissa[crp - 1] += s_MsbLookupMult[itmp];
rr.mantissa[crp] += s_LsbLookupMult[itmp];
if (rr.mantissa[crp] >= 100)
{
rr.mantissa[crp] -= 100;
rr.mantissa[crp - 1] += 1;
}
crp--;
if (rr.mantissa[crp] >= 100)
{
rr.mantissa[crp] -= 100;
rr.mantissa[crp - 1] += 1;
}
if (jj == 0)
{
break;
}
}
if (ii == 0)
{
break;
}
}
rr.signum = sign;
rr.exponent = nexp;
rr.dataLength = numdigits;
BigNumber.Normalize(rr);
}
