public static IntegerNumber Inverse(IntegerNumber number, out IntegerNumber remainder)
{
int n = number.Digits;
if (n <= IntegerDigitsBreakPoint)
{
ulong[] a = new ulong[(n + 1) * 2];
a[n * 2] = 1UL;
IntegerNumber b = number.ExtendTo(n + 1);
ulong[] q = new ulong[(n + 1) * 2];
AsmX64Operations.GetDivMod(a, b.bits, n + 1, q, true);
remainder = new IntegerNumber(a, false);
shrink(remainder);
IntegerNumber result = new IntegerNumber(q, false);
shrink(result);
return(result);
}
bool isNegative = false;
if (number.IsNegative)
{
number = -number;
isNegative = true;
n = number.Digits;
}
//Newton iteration: x <- x + x * (1 - d * x^2)
int m = (n + 5) >> 1;
IntegerNumber dx, dhi = number.GetDigits(n - m, m, false);
IntegerNumber x = Inverse(dhi, out dx);
//IntegerNumber test = x * d + dx;
//shrink(ref test);
//if (test.Digits != d.Digits * 2 + 1 || test.bits[d.Digits * 2] != 1UL || Enumerable.Range(0, d.Digits * 2).Any(idx => test.bits[idx] != 0UL))
//{
// System.Diagnostics.Debugger.Break();
//}
const int CorrectionDigits = 4;
IntegerNumber dlo = number.GetDigits(0, n - m, true);
IntegerNumber dp = (dx << ((n - m) * 64)) - dlo * x;
IntegerNumber delta = dp >> ((m - CorrectionDigits) * 64); //keep one additional correction digit.
shrink(delta);
delta *= x;
delta >>= (m + CorrectionDigits) * 64;
shrink(delta);
x <<= (n - m) * 64;
x += delta;
//FACT: number * x == (IntegerNumber.One << (n * 128)) - ((dp << ((n - m) * 64)) - delta * number);
//but : remainder = number * x;
//then: Array.Resize(ref remainder.bits, n * 2);
//then: shrink(ref remainder);
//then: remainder = -remainder;
remainder = ((dp - delta * dhi) << ((n - m) * 64)) - delta * dlo;
shrink(remainder);
int count = 0;
while (remainder.IsNegative)
{
remainder += number;
x -= One;
count++;
if (count >= 2)
{
System.Diagnostics.Debugger.Break();
}
}
while (remainder >= number)
{
remainder -= number;
x += One;
count++;
if (count >= 2)
{
System.Diagnostics.Debugger.Break();
}
}
if (isNegative)
{
x = -x;
remainder = -remainder;
}
return(x);
}
public static IntegerNumber DivRem(IntegerNumber dividend, IntegerNumber divisor, out IntegerNumber remainder)
{
shrink(dividend);
shrink(divisor);
int dividendDigits = dividend.Digits;
int divisorDigits = divisor.Digits;
IntegerNumber quotient;
int n = Math.Max(divisorDigits, (dividendDigits + 1) >> 1);
if (divisorDigits <= IntegerDigitsBreakPoint)
{
dividend = dividend.ExtendTo(n * 2);
divisor = divisor.ExtendTo(n);
quotient = new IntegerNumber(new ulong[n * 2], false);
remainder = new IntegerNumber(dividend.bits, true);
AsmX64Operations.GetDivMod(remainder.bits, divisor.bits, n, quotient.bits, true);
shrink(quotient);
shrink(remainder);
return(quotient);
}
bool sign = false;
if (dividend.IsNegative != divisor.IsNegative)
{
dividend = IntegerNumber.Abs(dividend);
divisor = IntegerNumber.Abs(divisor);
sign = true;
}
else if (dividend.IsNegative && divisor.IsNegative)
{
dividend = -dividend;
divisor = -divisor;
}
int delta = n - divisorDigits;
IntegerNumber x = (divisor << (delta * 128)).Inverse();
quotient = dividend * x >> (n * 128);
shrink(quotient);
remainder = dividend - quotient * divisor;
shrink(remainder);
int count = 0;
while (remainder.IsNegative)
{
remainder += divisor;
quotient -= One;
count++;
if (count >= 2)
{
System.Diagnostics.Debugger.Break();
}
}
while (remainder >= divisor)
{
remainder -= divisor;
quotient += One;
count++;
if (count >= 2)
{
System.Diagnostics.Debugger.Break();
}
}
if (sign)
{
quotient = -quotient;
remainder = -remainder;
}
return(quotient);
}
