/// <summary>Computes the nearest number greater than or equal to the
/// specified start value that is coprime to another specified value.
/// Returns 0 if no coprime was found in the range start to MaxValue.</summary>
/// <param name="start">The start value.</param>
/// <param name="value2">The value to test against.</param>
/// <returns>The largest value that is less than or equal to the start value
/// and also coprime to the other specified value.</returns>
public static long NearestCoprimeCeiling(this long start, long value2)
{
ulong v1, v2;
v2 = (value2 >= 0) ? (ulong)value2 : value2.AbsU();
if ((value2 == 0) && (start <= -1))
{
return(-1);
}
if ((start == int.MaxValue) || ((value2 == 0) && (start > 1)))
{
return(0);
}
v1 = start.AbsU();
if (start >= 0)
{
while (!IsCoprime(v1, v2))
{
if (v1 == long.MaxValue)
{
return(0);
}
v1++;
}
return((long)v1);
}
else
{
while (!IsCoprime(v1, v2))
{
v1--;
}
return(-(long)v1);
}
}
/// <summary>Computes the greatest common divisor of two values.</summary>
/// <param name="value1">The first value.</param>
/// <param name="value2">The other value.</param>
/// <returns>The greatest common divisor of the two values.</returns>
public static long Gcd(this long value1, long value2)
{
if ((value1 | value2) < 0)
{
return((long)Gcd(value1.AbsU(), value2.AbsU()));
}
return((long)Gcd((ulong)value1, (ulong)value2));
}
/// <summary>Compute the modulo (division remainder) of a number multiplied by another number.</summary>
/// <remarks>Overflow safe for all input values. </remarks>
/// <param name="value1">The number to be multiplied by value2.</param>
/// <param name="value2">The number to be multiplied by value1.</param>
/// <param name="modulus">The number by which to divide value raised to the exponent power.</param>
/// <returns>The remainder after dividing the product of multiplying value1 and value2.</returns>
public static long MulMod(this long value1, long value2, long modulus)
{
if (modulus <= 0)
{
return(0);
}
unchecked {
if ((value1 | value2) >= 0)
{
return((long)MulMod((ulong)value1, (ulong)value2, (ulong)modulus));
}
return(((1 | (value1 ^ value2) >> 63)) * (long)MulMod(value1.AbsU(), value2.AbsU(), (ulong)modulus));
}
}
/// <summary>Computes the nearest number less than or equal to the
/// specified start value that is coprime to another specified value.
/// Returns 0 if no coprime was found in the range MinValue to start.</summary>
/// <param name="start">The start value.</param>
/// <param name="value2">The value to test against.</param>
/// <returns>The largest value that is less than or equal to the start value
/// and also coprime to the other specified value.</returns>
public static long NearestCoprimeFloor(this long start, long value2)
{
ulong v1, v2;
v2 = (value2 >= 0) ? (ulong)value2 : value2.AbsU();
if (start > 0)
{
return((long)NearestCoprimeFloor((ulong)start, v2));
}
if ((v2 == 0) && (start < -1))
{
return(0);
}
for (v1 = start.AbsU(); v1 <= (ulong)(-(long.MinValue + 1)) + 1; v1++)
{
if (v1.IsCoprime(v2))
{
return(-(long)v1);
}
}
return(0);
}