public void Abs(int n, int d)
{
var actual = BigRational.Abs(new BigRational(n, d));
var expected = new BigRational(Math.Abs(n), Math.Abs(d));
AssertEqual(expected, actual);
}
public void E()
{
var expected = Math.E;
var actual = BigRational.E;
Assert.True(BigRational.Abs(expected - actual) < new BigRational(1, 100000000000000));
}
public void SqrtIrrational()
{
var expected = BigRational.SqrtAsRationals(2).Skip(100).First();
var actual = BigRational.Sqrt(new(2), 13);
Assert.True(BigRational.Abs(expected - actual) < new BigRational(1, 1000000000));
}
public static object Abs(object a)
{
if (a is int)
{
return(Math.Abs((int)a));
}
else if (a is long)
{
return(Math.Abs((long)a));
}
else if (a is decimal)
{
return(Math.Abs((decimal)a));
}
else if (a is double)
{
return(Math.Abs((double)a));
}
else if (a is BigInteger)
{
return(BigInteger.Abs((BigInteger)a));
}
else if (a is BigRational)
{
return(BigRational.Abs((BigRational)a));
}
else
{
return(Complex.Abs(AsComplex(a)));
}
}
public bool HasValueNear(BigRational value, BigRational?epsilon = null)
{
var eps = epsilon ?? new BigRational(1, 1000000);
var y = BigRational.Abs(Constraint.EvaluateAt(value));
return(y < eps);
}
private static string GetMixedFormat(BigRational value, char separator)
{
StringBuilder sb = new();
BigInteger whole = value.GetWholePart();
BigRational fractionPart = value.GetFractionPart();
if (!whole.IsZero)
{
sb.Append(whole.ToString("R", CultureInfo.CurrentCulture));
if (separator != DisplaySeparator)
{
sb.Append(separator);
}
else
{
// When the DisplaySeparator is being used,
// then the whole and fractional parts need
// to be separated by whitespace.
sb.Append(' ');
}
// If the rational number was negative, then the
// whole part will have been rendered as a negative
// number, so we need to ensure that the fractional
// part doesn't render as a negative value too.
fractionPart = BigRational.Abs(fractionPart);
}
AppendCommonFormat(sb, fractionPart, separator);
return(sb.ToString());
}
public void BigRational_Abs_ReturnsAbsoluteValue()
{
var value1 = new BigRational((BigInteger)10);
Assert.Equal("10/1", value1.Abs().ToString("B", null));
var value2 = new BigRational(-(BigInteger)10);
Assert.Equal("10/1", value2.Abs().ToString("B", null));
var value3 = BigRational.Zero;
Assert.Equal("0/1", value3.Abs().ToString("B", null));
var value4 = BigRational.Create(VeryBigNumber);
Assert.Equal($"{VeryBigNumber}/1", value4.Abs().ToString("B", null));
var value5 = BigRational.Create($"-{VeryBigNumber}");
Assert.Equal($"{VeryBigNumber}/1", value4.Abs().ToString("B", null));
}
private Value decimalToFraction(BigRational Decimal)
{
BigInteger fractionNumerator = int.MaxValue;
BigInteger fractionDenominator = 1;
BigRational accuracyFactor = .0000001;
int decimalSign;
BigRational Z;
BigInteger previousDenominator;
BigInteger scratchValue;
if (Decimal < 0)
{
decimalSign = -1;
}
else
{
decimalSign = 1;
}
Decimal = BigRational.Abs(Decimal);
if (Decimal == (BigInteger)Decimal)
{
fractionNumerator = (int)Decimal * decimalSign;
fractionDenominator = 1;
return(new Value(fractionDenominator, fractionNumerator, NumberType.rational));
}
Z = Decimal;
previousDenominator = 0;
while (!(Z == (BigInteger)Z) && (BigRational.Abs((Decimal - ((BigRational)fractionNumerator / fractionDenominator))) > accuracyFactor))
{
Z = 1 / (Z - (BigInteger)Z);
scratchValue = fractionDenominator;
fractionDenominator = fractionDenominator * (BigInteger)Z + previousDenominator;
previousDenominator = scratchValue;
fractionNumerator = (BigInteger)(Decimal * fractionDenominator + .5);
}
fractionNumerator = decimalSign * fractionNumerator;
return(new Value(fractionNumerator, fractionDenominator, NumberType.rational));
}
public static BigRational IntegralSinX2Row(int a)
{
BigRational sum = 0;
BigRational previous;
BigRational factorial = 1;
var minus = 1;
var n = 0;
do
{
var member = minus
* BigRational.Pow(a, 4 * n + 3)
/ (factorial * (4 * n + 3));
n++;
minus *= -1;
factorial *= (2 * n + 1) * (2 * n);
previous = sum;
sum += member;
} while (BigRational.Abs(sum - previous) > Error);
return(sum);
}
public void big_rational_static_methods()
{
Assert.True(0.5 == BigRational.Abs(0.5d));
Assert.True(0.5 == BigRational.Abs(-0.5d));
Assert.False(0.5 == BigRational.Abs(-1));
Assert.False(0.5 == BigRational.Abs(1));
Assert.True(-0.5 == BigRational.Negate(0.5d));
Assert.True(0.5 == BigRational.Negate(-0.5d));
Assert.False(0.5 == BigRational.Negate(-1));
Assert.False(-0.5 == BigRational.Negate(1));
//Doesn't work great... testing with equals doubles fails
Assert.True(new BigRational(1, 2) == BigRational.Invert(new BigRational(2, 1)));
Assert.True(new BigRational(2, 1) == BigRational.Invert(new BigRational(1, 2)));
Assert.True(new BigRational(-1, 2) == BigRational.Invert(new BigRational(-2, 1)));
Assert.True(new BigRational(-2, 1) == BigRational.Invert(new BigRational(-1, 2)));
Assert.True(new BigRational(BigInteger.One) + new BigRational(BigInteger.One) == 2);
Assert.True(BigRational.Add(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 2);
//Not working for me
//BigRational big1 = new BigRational(1.0);
//big1++;
//Assert.AreEqual(new BigRational(2, 1), big1);
//Not working for me
//BigRational big2 = new BigRational(1.0);
//big2--;
//Assert.True(0 == big2);
Assert.True(new BigRational(BigInteger.One) - new BigRational(BigInteger.One) == 0);
Assert.True(BigRational.Subtract(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 0);
BigRational big3 = new BigRational(1.0);
Assert.True(-1.0 == -big3);
BigRational big4 = new BigRational(1.0);
Assert.True(1.0 == +big3);
Assert.True(new BigRational(BigInteger.One) * new BigRational(BigInteger.One) == 1);
Assert.True(BigRational.Multiply(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 1);
Assert.True(new BigRational(BigInteger.One) * new BigRational(2.0) == 2.0);
Assert.True(BigRational.Multiply(new BigRational(BigInteger.One), new BigRational(2.0)) == 2.0);
Assert.True(new BigRational(BigInteger.One) / new BigRational(BigInteger.One) == 1);
Assert.True(BigRational.Divide(new BigRational(BigInteger.One), new BigRational(BigInteger.One)) == 1);
Assert.AreEqual(new BigRational(1, 2), new BigRational(new BigInteger(1)) / new BigRational(new BigInteger(2))); //Again, mixing consructors doesn't work well.
Assert.AreEqual(new BigRational(1, 2), BigRational.Divide(new BigRational(new BigInteger(1)), new BigRational(new BigInteger(2)))); //Again, mixing consructors doesn't work well. Testing with equals double 0.5 fails
//Assert.True(new BigRational(BigInteger.One) < new BigRational(2.0)); //Don't mix the constructors for comparison!!!
Assert.True(new BigRational(1.0) < new BigRational(2.0));
Assert.False(new BigRational(2.0) < new BigRational(1.0));
Assert.False(new BigRational(1.0) < new BigRational(1.0));
Assert.True(new BigRational(1.0) <= new BigRational(2.0));
Assert.True(new BigRational(1.0) <= new BigRational(1.0));
Assert.False(new BigRational(2.0) <= new BigRational(1.0));
Assert.True(new BigRational(1.0) == new BigRational(1.0));
Assert.True(new BigRational(1.0) != new BigRational(2.0));
Assert.False(new BigRational(1.0) > new BigRational(2.0));
Assert.True(new BigRational(2.0) > new BigRational(1.0));
Assert.False(new BigRational(BigInteger.One) > new BigRational(BigInteger.One));
Assert.False(new BigRational(1.0) >= new BigRational(2.0));
Assert.True(new BigRational(BigInteger.One) >= new BigRational(BigInteger.One));
Assert.True(new BigRational(2.0) >= new BigRational(1.0));
//Modulus doesn't seem to work well
//Assert.AreEqual(BigRational.Zero, new BigRational(2.0) % new BigRational(1.0));
//Assert.AreEqual(BigRational.One, new BigRational(3.0) % new BigRational(2.0));
//Assert.True(new BigRational(1.5) % new BigRational(1.0) == new BigRational(0.5));
//Assert.True(new BigRational(1.0) % new BigRational(2.0) == 0);
}
