/* CALCULATION -- MULTIPLICATION */
private static IntervalStruct IntervalMultiplication(IntervalStruct x, IntervalStruct y)
{
// Comparing a1 * a2 and a1 * b2
double min = System.Math.Min(x.GetMinBound() * y.GetMinBound(), x.GetMinBound() * y.GetMaxBound());
double max = System.Math.Max(x.GetMinBound() * y.GetMinBound(), x.GetMinBound() * y.GetMaxBound());
// Comparing the previous results to b1 * a2
min = System.Math.Min(min, x.GetMaxBound() * y.GetMinBound());
max = System.Math.Max(max, x.GetMaxBound() * y.GetMinBound());
// Comparing the previous results to b1 * b2
min = System.Math.Min(min, x.GetMaxBound() * y.GetMaxBound());
max = System.Math.Max(max, x.GetMaxBound() * y.GetMaxBound());
return(new IntervalStruct("", min, max, true, true));
}
/* CALCULATION -- EXPONENTS */
private static IntervalStruct IntervalExponents(IntervalStruct x, IntervalStruct y)
{
IntervalStruct exp = null;
if (x.GetMinBound() == x.GetMaxBound())
{
exp = IntervalAsExponent(x.GetMinBound(), y);
}
else if (y.GetMinBound() == y.GetMaxBound())
{
exp = IntervalAsBase(x, y.GetMinBound());
}
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Exponents)." + System.Environment.NewLine);
}
return(exp);
}
private static IntervalStruct IntervalDivisionNegativeDivisor(IntervalStruct x, IntervalStruct y)
{
double min = 0;
double max = 0;
// 0 < a1 <= b1
if (x.GetMinBound() > 0)
{
min = x.GetMaxBound() / y.GetMaxBound();
max = x.GetMinBound() / y.GetMinBound();
}
// a1 = 0, a1 <= b1
else if (x.GetMinBound() == 0)
{
min = x.GetMaxBound() / y.GetMaxBound();
max = 0;
}
// a1 < 0 < b1
else if (x.GetMaxBound() > 0)
{
min = x.GetMaxBound() / y.GetMaxBound();
max = x.GetMinBound() / y.GetMaxBound();
}
// b1 = 0, a1 <= b1
else if (x.GetMaxBound() == 0)
{
min = 0;
max = x.GetMinBound() / y.GetMaxBound();
}
//a1 <= b1 < 0
else if (x.GetMaxBound() < 0)
{
min = x.GetMaxBound() / y.GetMinBound();
max = x.GetMinBound() / y.GetMaxBound();
}
return(new IntervalStruct("", min, max, true, true));
}
private static IntervalStruct IntervalAsBase(IntervalStruct x, double n)
{
IntervalStruct exp = null;
double roundedN = System.Math.Round(n);
if (n >= 0)
{
if (n != roundedN)
{
frm_Main.UpdateLog("Warning: The value provided for the exponent" + System.Convert.ToString(n) + "is not a natural number. It has been rounded to " + System.Convert.ToString(roundedN) + System.Environment.NewLine);
}
if (roundedN % 2 != 0)
{
exp = new IntervalStruct("", System.Math.Pow(x.GetMinBound(), roundedN), System.Math.Pow(x.GetMaxBound(), roundedN), true, true);
}
else if (x.GetMinBound() >= 0)
{
exp = new IntervalStruct("", System.Math.Pow(x.GetMinBound(), roundedN), System.Math.Pow(x.GetMaxBound(), roundedN), true, true);
}
else if (x.GetMaxBound() < 0)
{
exp = new IntervalStruct("", System.Math.Pow(x.GetMaxBound(), roundedN), System.Math.Pow(x.GetMinBound(), roundedN), true, true);
}
else
{
exp = new IntervalStruct("", 0, System.Math.Max(System.Math.Pow(x.GetMinBound(), roundedN), System.Math.Pow(x.GetMaxBound(), roundedN)), true, true);
}
}
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Exponent < 0)." + System.Environment.NewLine);
}
return(exp);
}
private static IntervalStruct IntervalAsExponent(double b, IntervalStruct x)
{
IntervalStruct exp = null;
if (b > 1)
{
exp = new IntervalStruct("", System.Math.Pow(b, x.GetMinBound()), System.Math.Pow(b, x.GetMaxBound()), true, true);
}
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Exponent base <= 1)." + System.Environment.NewLine);
}
return(exp);
}
/* CALCULATION -- DIVISION */
private static IntervalStruct IntervalDivision(IntervalStruct x, IntervalStruct y)
{
IntervalStruct divInterval = null;
// 0 < a2 <= b2
if (y.GetMinBound() > 0)
{
divInterval = IntervalDivisionPositiveDivisor(x, y);
}
// a2 <= b2 < 0
else if (y.GetMaxBound() < 0)
{
divInterval = IntervalDivisionNegativeDivisor(x, y);
}
// a2 = 0 v b2 = 0
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Mixed interval division)." + System.Environment.NewLine);
}
return(divInterval);
}
/* CALCULATION -- SUBTRACTION */
private static IntervalStruct IntervalSubtraction(IntervalStruct x, IntervalStruct y)
{
return(new IntervalStruct("", x.GetMinBound() - y.GetMinBound(), x.GetMaxBound() - y.GetMaxBound(), true, true));
}