/// <summary>
/// MPUnit constructor that clones an MPUnit for
/// use within math functions
/// </summary>
/// <param name="mpclone"></param>
public MPUnit(MPUnit mpclone)
{
digitBlocks = new System.UInt16[mpclone.maxDigits];
Array.Copy(mpclone.digitBlocks,0,this.digitBlocks,0,mpclone.digitBlocks.Length);
numDigits = mpclone.numDigits;
maxDigits = mpclone.maxDigits;
}
private string FormatDec()
{
MPUnit tempUnit = new MPUnit(this);
MPUnit q=null;
MPUnit r=null;
ArrayList cc = new ArrayList();
while(tempUnit.Digits>0)
{
MPUnit.Div(tempUnit, 10, ref q, ref r);
if(r.Digits>0)
cc.Add(r[0].ToString());
tempUnit = q;
}
cc.Reverse();
StringBuilder sb = new StringBuilder();
foreach(string digstring in cc)
{
sb.Append(digstring);
}
return sb.ToString();
}
static void Main(string[] args)
{
Console.WriteLine("Simple addition test");
MPUnit mpu1 = new MPUnit();
mpu1 = MPUnit.Add(mpu1,(ushort)65535);
MPUnit mpu2 = new MPUnit();
mpu2 = MPUnit.Add(mpu2,1);
Console.WriteLine("mpu1: {0}",mpu1);
for(int i = 0; i<20; i++)
{
mpu1 = MPUnit.Add(mpu1,mpu2);
Console.WriteLine("i: {0}, mpu1: {1}",i, mpu1);
}
for(int i=0; i<20; i++)
{
mpu1 = MPUnit.Sub(mpu1,mpu2);
Console.WriteLine("i: {0}, mpu1: {1}",i, mpu1);
}
Console.WriteLine("Simple multiplication test");
MPUnit mpu3 = new MPUnit();
mpu3[1]=1;
MPUnit mpu4 = new MPUnit();
mpu4[0]=1;
for(int i=0; i<10; i++)
{
mpu3 = MPUnit.Mult(mpu3,mpu4);
mpu3.Trim();
mpu4[0]= (ushort)(mpu4[0] + (ushort)1);
Console.WriteLine("mpu3 {0} :: mpu4 {1}",mpu3, mpu4);
Console.WriteLine("mpu3 digits {0}, mpu4 digits {1}",mpu3.Digits,mpu4.Digits);
Console.WriteLine(mpu3.FormatDec());
}
Console.WriteLine("\nCompound division test");
MPUnit dividend = new MPUnit();
dividend[0]=15;
dividend[1]=43202;
dividend[2]=32720;
dividend[3]=12;
dividend[4]=4;
dividend[5]=27;
MPUnit divisor = new MPUnit();
divisor[0]=65535;
divisor[1]=16;
MPUnit quotient=null,remainder=null;
MPUnit.Div(dividend, divisor ,ref quotient, ref remainder);
Console.WriteLine("Dividend {0}",dividend);
Console.WriteLine("Divisor {0}",divisor);
Console.WriteLine("Quotient {0}",quotient);
Console.WriteLine(quotient.FormatDec());
Console.WriteLine("Remainder {0}",remainder);
MPUnit partialproduct = MPUnit.Mult(quotient,divisor);
Console.WriteLine("Quotient * Divisor = {0}",partialproduct);
Console.WriteLine("Quotient * Divisor + Remainder = {0}",MPUnit.Add(partialproduct,remainder));
Console.WriteLine("\nSimple division test");
int littledivisor = 25;
MPUnit.Div(dividend,littledivisor, ref quotient, ref remainder);
Console.WriteLine("Dividend {0}",dividend);
Console.WriteLine("little Divisor {0}",littledivisor);
Console.WriteLine("Quotient {0}",quotient);
Console.WriteLine("Remainder {0}",remainder);
Console.WriteLine("Quotient * Divisor = {0}",MPUnit.Mult(quotient,new MPUnit(littledivisor)));
partialproduct = MPUnit.Mult(quotient,new MPUnit(littledivisor));
Console.WriteLine("Quotient * Divisor = {0}",partialproduct);
Console.WriteLine("Quotient * Divisor + Remainder = {0}",MPUnit.Add(partialproduct,remainder));
}
/// <summary>
/// Multiplies current MPUnit with mpu1
/// </summary>
/// <param name="mpu1"></param>
/// <returns>MPUnit</returns>
public static MPUnit Mult(MPUnit factor1, MPUnit factor2)
{
UInt16[] productdigits = new UInt16[MPUnit.NormalSize*2];
MPUnit product = new MPUnit();
int i=0;
int carry=0;
foreach(UInt16 ui in factor1.digitBlocks)
{
int j=0;
foreach(UInt16 vj in factor2.digitBlocks)
{
System.UInt32 up = (UInt32)(ui*vj+carry+productdigits[i+j]);
productdigits[i+j] = (UInt16)(up & 0xffff);
carry=(UInt16)(up>>16);
j++;
}
i++;
}
int ndig = factor1.Digits+factor2.Digits;
#if UNDONE
while(ndig>0 && productdigits[ndig-1]==0)
ndig--;
#endif
product.numDigits=ndig;
Array.Copy(productdigits,0,product.digitBlocks,0,Math.Min(ndig,MPUnit.NormalSize));
// overflow
if(ndig > MPUnit.NormalSize)
throw new ArithmeticException();
return product;
}
public static MPUnit Sub(MPUnit minuend, MPUnit subtrahend)
{
// subtrahend >= minuend
int compares = minuend.CompareTo(subtrahend);
if(compares == 0)
{
MPUnit retval = new MPUnit();
retval.numDigits = minuend.numDigits;
return retval;
}
if(compares<0)
throw new ArithmeticException();
MPUnit difference = new MPUnit();
int maxdigits = minuend.Digits;
subtrahend.Digits=maxdigits;
int carry=0;
for(int i=0; i<maxdigits; i++)
{
int resdigit = minuend[i]-subtrahend[i]+carry;
if(resdigit<0)
{
resdigit+=MPUnit.BASE;
carry=-1;
}
else
carry=0;
difference[i]=(UInt16)resdigit;
}
while(difference.Digits >0 && difference[difference.Digits-1]==0)
{ difference.Digits = difference.Digits-1; }
// underflow exception
if(carry==-1)
throw new ArithmeticException();
return difference;
}
/// <summary>
/// Multiplies current MPUnit with um1
/// </summary>
/// <param name="um1"></param>
/// <returns>MPUnit</returns>
public static MPUnit Mult(MPUnit s1, System.UInt16 um1)
{
MPUnit product = new MPUnit(s1.maxDigits);
System.UInt16 carry = 0;
System.UInt32 um2 = 0;
int i=0;
for(i=0; i < s1.Digits; i++)
{
um2 = (UInt32)(s1[i]*um1)+carry;
carry=(UInt16)(um2>>16);
product[i]=(System.UInt16)(um2 & 0xffff);
}
if(carry!=0)
{
if(i==s1.maxDigits)
throw new ArithmeticException();
product[i++]=carry;
}
#if UNDONE
while(i >0 && product[i-1]==0)
i--;
#endif
product.numDigits=i;
return product;
}
/// <summary>
/// Divides current MPUnit by short int ui, Quotient in q, Remainder in r
/// </summary>
/// <param name="i"></param>
/// <param name="q"></param>
/// <param name="r"></param>
/// <returns></returns>
public static void Div(MPUnit dividend, int i, ref MPUnit q, ref MPUnit r)
{
if(i < 0 || i > BASE)
throw new ArgumentOutOfRangeException();
MPUnit pseudodividend = new MPUnit(dividend);
pseudodividend.ASL(1);
MPUnit divisor = new MPUnit(i);
MPUnit pseudodivisor = new MPUnit(divisor);
pseudodivisor.ASL(1);
Div(pseudodividend, pseudodivisor, ref q, ref r);
r = MPUnit.Sub(dividend, MPUnit.Mult(q,divisor));
}
/// <summary>
/// Divides current MPUnit by mpu1, Quotient in q, Remainder in r
/// </summary>
/// <param name="mpu1"></param>
/// <param name="q"></param>
/// <param name="r"></param>
/// <returns></returns>
public static void Div(MPUnit dividend, MPUnit divisor, ref MPUnit q, ref MPUnit r)
{
MPUnit mpuInter = new MPUnit();
MPUnit u = new MPUnit(dividend);
MPUnit v = new MPUnit(divisor);
q = new MPUnit();
// Can't divide by zero
if(v.numDigits == 0)
throw new ArgumentException();
// dividing zero by something else equals zero
if(u.numDigits == 0)
{
q.numDigits=0;
r.numDigits=0;
return;
}
// if the v only has one digit, use the simple routine
// BUGBUG, how about pretending v has two digits, then postshifting?
if(v.numDigits == 1)
{
Div(u, v[0], ref q , ref r);
return;
}
// ok, long route
// normalize to give better qhat estimates
// this raises number of digits in u by one
// (top digit may be zero) and does not raise the number
// of digits in v (since we've just scaled its top
// digit to be between BASE/2 and BASE
UInt16 scale = 1;
int n = v.Digits;
int m = u.Digits-n;
int v_msd = v[n-1];
// scale up v
while(v_msd < BASE/2)
{
v_msd <<= 1;
scale <<= 1;
}
// if no shift occurs, or if the multiplication
// doesn't cause a carry into a higher digit
// we will add an additional 0 digit anyway
int u_inc_digits = u.Digits+1;
if(scale != 1)
{
// This may or may not increment the number of digits in u...
// must check this
int digits = u.Digits;
u = MPUnit.Mult(u,scale);
v = MPUnit.Mult(v,scale);
}
u.Digits=u_inc_digits;
// initialize j
for(int j=m; j>=0; j--)
{
// generate qhat
// From Knuth (Uj+nB + Uj+n-1)/(Vn-1)
long uhat = (((long)u[j+n]) << 16) + ((long)u[j+n-1]) ;
long vhat = (long)v[n-1];
long qhat = uhat / vhat ;
long rhat = uhat - (qhat * vhat);
long test1 = qhat*v[n-2];
long test2 = (BASE * rhat) + ( (j+n-2) >=0 ? (int)u[j+n-2] : (int)0);
// Make sure we didn't overflow in
// creating the test values
Debug.Assert(test1>=0 && test2>=0);
// decrease qhat by one if it is BASE or test fails
if(qhat == BASE || test1 > test2)
{
qhat--;
rhat += v[n-1];
test1 = qhat*v[n-2];
test2 = (BASE * rhat) + ( (j+n-2) >=0 ? (int)u[j+n-2] : (int)0);
// qhat is still 1 too great
if(rhat < BASE && (qhat == BASE || test1>test2))
{
qhat--;
}
}
Debug.Assert(qhat < BASE && qhat>=0 && rhat>=0);
// Multiply and subtract
// subtract term from top term.Digits digits of u
// easiest done as a shift of term?
MPUnit term = MPUnit.Mult(v,(ushort)qhat);
term.ASL(j);
// if the result would be negative, then
// we oopsd again
if(u.CompareTo(term)<0)
{
qhat--;
term = MPUnit.Mult(v,(ushort)qhat);
term.ASL(j);
}
u = MPUnit.Sub(u,term);
// set quotient digit
q[j]=(ushort)qhat;
}
q.Trim();
r = MPUnit.Sub(dividend,MPUnit.Mult(divisor,q));
r.Trim();
return;
}
/// <summary>
/// Adds an MPUnit to current MPUnit
/// </summary>
/// <param name="mps"></param>
/// <returns>MPUnit</returns>
public static MPUnit Add(MPUnit s1, MPUnit s2)
{
System.UInt16 carry=0;
int maxdigits = Math.Max(s2.numDigits, s1.numDigits);
MPUnit summand1 = new MPUnit(s1);
MPUnit summand2 = new MPUnit(s2);
summand1.Digits = maxdigits+1;
summand2.Digits = maxdigits+1;
MPUnit sum = new MPUnit();
sum.Digits = maxdigits+1;
int i=0;
// The result may be 1 greater than
// maxdigits because of carry, this is overflow
for(i=0; i<=maxdigits; i++)
{
System.UInt32 us = (UInt32)(summand1[i]+summand2[i]+carry);
carry = (UInt16)(us >> 16);
sum[i] = (UInt16)(us & 0xffff);
}
while(i>0 && sum[i-1]==0)
{ i--; }
sum.numDigits = i;
// overflow
if(carry != 0)
throw new ArithmeticException();
return sum;
}
/// <summary>
/// Adds short to current MPUnit, returns sum in new MPUnit
/// </summary>
/// <param name="us1"></param>
/// <returns></returns>
public static MPUnit Add(MPUnit s1, System.UInt16 us1)
{
MPUnit sum = new MPUnit(s1);
sum.Digits=s1.Digits+1;
int i=0;
System.UInt32 us2=0;
System.UInt16 carry=us1;
do
{
us2 = (UInt32)(sum[i] + carry);
carry = (System.UInt16)(us2 >> 16);
sum[i] = (System.UInt16)(us2&0xffff);
i++;
}while(carry > 0 && i < sum.maxDigits);
// overflow
if(i == sum.maxDigits)
throw new ArithmeticException();
// Notice that, upon finishing the loop, i may be one greater
// than the original sum.numDigits. This shows a carry
// that propagated all the way through s1
sum.Digits=Math.Max(i,s1.numDigits);
return sum;
}
