public static BigNumber operator *(BigNumber c1, BigNumber c2)
{
BigNumber res = new BigNumber();
BigNumber.Mul(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);
}
}
public static BigNumber operator *(BigNumber c1, double c2)
{
BigNumber res = new BigNumber();
BigNumber C2 = c2;
BigNumber.Mul(c1, C2, res);
return(res);
}
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 public void Power(BigNumber xx, BigNumber yy, BigNumber rr, int places)
{
int iflag;
BigNumber tmp8 = new BigNumber();
BigNumber tmp9 = new BigNumber();
int M_size_flag = BigNumber.GetSizeofInt();
if (yy.signum == 0)
{
BigNumber.Copy(BigNumber.One, rr);
return;
}
if (xx.signum == 0)
{
BigNumber.SetZero(rr);
return;
}
if (BigNumber.IsInteger(yy) > 0)
{
iflag = 0;
if (M_size_flag == 2) /* 16 bit compilers */
{
if (yy.exponent <= 4)
{
iflag = 1;
}
}
else /* >= 32 bit compilers */
{
if (yy.exponent <= 7)
{
iflag = 1;
}
}
if (iflag > 0)
{
String sbuf = BigNumber.ToIntString(yy);
int Exp = Convert.ToInt32(sbuf);
BigNumber.IntPow(places, xx, Exp, rr);
return;
}
}
tmp8 = new BigNumber();
tmp9 = new BigNumber();
BigNumber.Log(xx, tmp9, (places + 8));
BigNumber.Mul(tmp9, yy, tmp8);
BigNumber.Exp(tmp8, rr, 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);
}
/****************************************************************************/
/*
* 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 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 void CheckLogPlaces(int places)
{
BigNumber tmp6, tmp7, tmp8, tmp9;
int dplaces;
dplaces = places + 4;
if (dplaces > MM_lc_log_digits)
{
MM_lc_log_digits = dplaces + 4;
tmp6 = new BigNumber();
tmp7 = new BigNumber();
tmp8 = new BigNumber();
tmp9 = new BigNumber();
dplaces += 6 + (int)Math.Log10((double)places);
BigNumber.Copy(BigNumber.One, tmp7);
tmp7.exponent = -places;
BigNumber.LogAGMRFunc(BigNumber.One, tmp7, tmp8, dplaces);
BigNumber.Mul(tmp7, BigNumber.BN_OneHalf, tmp6);
BigNumber.LogAGMRFunc(BigNumber.One, tmp6, tmp9, dplaces);
BigNumber.Sub(tmp9, tmp8, BN_lc_log2);
tmp7.exponent -= 1;
BigNumber.LogAGMRFunc(BigNumber.One, tmp7, tmp9, dplaces);
BigNumber.Sub(tmp9, tmp8, BN_lc_log10);
BigNumber.Reziprocal(BN_lc_log10R, BN_lc_log10, dplaces);
}
}
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 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 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);
}
}
/****************************************************************************/
/*
* 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 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);
}
}
