/// <summary>
/// Add two rationals
/// </summary>
public static Rational32 Add(Rational32 a, Rational32 b)
{
// self = a/b, other = c/d
var a_sign = a.Sign();
var b_sign = b.Sign();
var num = (a.Numerator64() * a_sign) * b.Denominator64();
num += a.Denominator64() * (b.Numerator64() * b_sign);
var den = a.Denominator64() * b.Denominator64();
var sign = num < 0;
if (sign)
{
num = -num;
}
// Try to find an exact result
var gcd = GCD(num, den);
num /= gcd;
den /= gcd;
// Reduce precision until it fits
while (num > MaxInt || WouldOverflow((uint)num, (uint)den))
{
gcd = GCD(num, den);
if (gcd == 1)
{
num /= 2;
den /= 2;
}
else
{
num /= gcd;
den /= gcd;
}
if (den < 1)
{
den = 1;
break;
}
}
return(new Rational32(sign, (uint)num, (uint)den));
}
/// <summary>
///
/// </summary>
/// <param name="f"></param>
/// <returns></returns>
public static Rational32 FromFloat(double f)
{
// The plan: split float into int and frac parts
// With frac, invert and build rational. Invert that rational and add int part
var sign = f < 0;
if (sign)
{
f = -f;
}
var num = (long)f;
var frac = f - num;
if (Math.Abs(frac) < Sigma)
{
return(new Rational32(sign, (uint)num, 1)); // close enough to an integer
}
var top = new Rational32(sign, (uint)num, 1);
var inv = new Rational32(sign, 1, (uint)(1 / frac));
return(Add(top, inv));
}
