public static BigRational ArcTan(BigRational x, int digits, int maxNumberOfIterations)
{
iterations = 0;
// Later needed variable:
int digitCheck = digits * 100;
bool subtract = true;
BigRational result = x;
int iteration = 0;
var divisor = new BigInteger(3);
while (iteration < maxNumberOfIterations)
{
var dividend = BigRational.Pow(x, divisor);
result = (subtract) ? (result - (dividend / divisor)) : (result + (dividend / divisor));
// Optimation hack:
// Check only every two calls if end is reached.
if (!subtract && (result / digitCheck > 100))
{
iterations = iteration;
break;
}
divisor += 2;
subtract = !subtract;
iteration++;
}
return result;
}
/// <summary>
/// Возводить текущее число в квадрат
/// </summary>
public void t_sqr()
{
BigRational i = Imagine;
Imagine *= Real * _twice;
Real *= Real;
Real -= i * i;
}
public static BigRational[] RemoveUselessZeros(BigRational[] source)
{
int numOfLeadingZero = 0;
Array.Reverse(source);
foreach (var i in source)
{
if (i == 0 )
{
numOfLeadingZero++;
}
else
{
break;
}
}
if (numOfLeadingZero == 0)
{
Array.Reverse(source);
return source;
}
BigRational[] arrayBuffer = new BigRational[source.Length - numOfLeadingZero];
Array.Copy(source, numOfLeadingZero, arrayBuffer, 0, arrayBuffer.Length);
Array.Reverse(arrayBuffer);
return arrayBuffer;
}
internal override ParsedSyntax CombineForPlus(PowerSyntax other, BigRational thisValue)
{
if(Left.CompareTo(other.Left) == 0 && Right.CompareTo(other.Right) == 0)
return Times(thisValue + 1);
return null;
}
public Value(BigRational realPart, BigRational imaginaryPart, NumberType type)
{
switch (type) {
case NumberType.imaginary:
InitComplexNum(realPart, imaginaryPart);
break;
}
}
public Value(BigRational baseVal, BigRational exponent, NumberType type, Restrictions restrictions)
{
switch (type) {
case NumberType.exponent:
InitExp(baseVal, exponent, restrictions);
break;
}
}
public BigNumber(double val)
{
if (val == Math.Floor(val)) {
integerVal = new BigInt((int)val);
Type = NumberType2.integer;
} else {
rationalVal = new BigRational(val);
Type = NumberType2.rational;
}
}
public static BigRational[] ArraySubtrInts(BigRational[] from, BigRational[] subAmount)
{
BigRational[] result = new BigRational[from.Length];
for (int i = 0; i < from.Length - 1; i++)
{
result[i] = from[i] - subAmount[i];
}
return result;
}
public void CheckModBigIntegerConsistency(int left, int right)
{
var leftInt = (BigInteger)left;
var rightInt = (BigInteger)right;
var expected = new BigRational(leftInt % rightInt);
var leftRational = new BigRational(leftInt);
var rightRational = new BigRational(rightInt);
var actual = leftRational % rightRational;
AssertEqual(expected, actual);
}
public void CastToDoubleRoundToInfinity()
{
BigRational toRound = BigInteger.Pow(2, 1024) - BigInteger.One;
Assert.AreEqual(
double.PositiveInfinity,
(double)toRound);
Assert.AreEqual(
double.NegativeInfinity,
(double)-toRound);
}
public void RoundWithRuleWithDecimals(MidpointRounding decimalMode, RationalRounding rationalMode)
{
for (int d = 0; d < 4; d++)
{
for (var v = -2.5M; v <= 2.5M; v += 0.0001M)
{
Compare(
Math.Round(v, d, decimalMode),
BigRational.Round(v, d, rationalMode));
}
}
}
public void Sqrt_Test()
{
var r = new BigRational(2, 1);
Assert.AreEqual(r, BigRational.Sqrt(4));
r = new BigRational(3, 1);
Assert.AreEqual(r, BigRational.Sqrt(9));
r = new BigRational(BigInteger.Parse("2168488286494085478154297235187389205761"), BigInteger.Parse("685736206471705483022831680917430579904"));
Assert.AreEqual(r, BigRational.Sqrt(10));
}
public void RoundWithDecimals()
{
for (var v = -2.5M; v <= 2.5M; v += 0.0001M)
{
for (int d = 0; d < 4; d++)
{
Compare(
Math.Round(v, d),
BigRational.Round(v, d));
}
}
}
private static string FormatBigRational(BigRational x, int digits)
{
// Let the magic begin:
BigInteger shiftedBigInteger = x.Numerator * BigInteger.Pow(10, digits);
string formatString = (shiftedBigInteger / x.Denominator).ToString();
var sb = new StringBuilder(digits);
sb.Append(x.GetWholePart().ToString());
int wholePart = sb.Length;
sb.Append('.');
sb.Append(formatString.Substring(1, formatString.Length - wholePart));
return sb.ToString();
}
static string InternalToString(BigRational r, int precision)
{
var fraction = r.GetFractionPart();
// Case where the rational number is a whole number
// Niko: Incorrect check? F**k it... This works...
if (fraction.Numerator == 0 && fraction.Denominator == 1)
{
return(r.GetWholePart().ToString());
}
BigInteger adjustedNumerator = fraction.Numerator * BigInteger.Pow(10, precision);
// Abs fixes decimals having minuses in front of them
BigInteger decimalPlaces = BigInteger.Abs(adjustedNumerator / fraction.Denominator);
// Case where precision wasn't large enough.
if (decimalPlaces == 0)
{
return(null);
}
// Give it the capacity for around what we should need for
// the whole part and total precision
// (this is kinda sloppy, but does the trick)
var sb = new StringBuilder(precision + r.ToString().Length);
bool noMoreTrailingZeros = false;
for (int i = precision; i > 0; i--)
{
if (!noMoreTrailingZeros)
{
if ((decimalPlaces % 10) == 0)
{
decimalPlaces /= 10;
continue;
}
noMoreTrailingZeros = true;
}
// Add the right most decimal to the string
sb.Insert(0, decimalPlaces % 10);
decimalPlaces /= 10;
}
// Insert the whole part and decimal
sb.Insert(0, ",");
sb.Insert(0, r.GetWholePart());
return(sb.ToString());
}
public bool Intersects(Line2BR other, out Point2BR?intersection, out bool parallel)
{
if (this.direction.IsZero)
{
parallel = false;
bool flag;
if (flag = other.Contains(this.origin))
{
intersection = new Point2BR?(this.origin);
}
else
{
intersection = new Point2BR?();
}
return(flag);
}
if (other.Direction.IsZero)
{
parallel = false;
bool flag;
if (flag = this.Contains(other.origin))
{
intersection = new Point2BR?(other.origin);
}
else
{
intersection = new Point2BR?();
}
return(flag);
}
BigRational bigRational1 = this.direction.X * other.direction.Y - this.direction.Y * other.direction.X;
if (bigRational1.IsZero)
{
parallel = true;
bool flag;
if (flag = other.Contains(this.origin))
{
intersection = new Point2BR?(this.origin);
}
else
{
intersection = new Point2BR?();
}
return(flag);
}
parallel = false;
BigRational bigRational2 = Vector2BR.CrossProduct(other.Origin - this.origin, other.Direction) / bigRational1;
intersection = new Point2BR?(this.origin + bigRational2 * this.direction);
return(true);
}
public override byte[] Split(byte[] secretClear, int shareCount, int threshold)
{
// var primeArr = ComputeRandomePrime();
// var prime = new BigInteger(primeArr);
var primeMinusOne = _prime - 1;
var number = new BigInteger(secretClear);
var coef = new BigInteger[threshold];
coef[0] = number;
// TODO: rewrite this to use cryptographically-secure RNG
var rng = new Random();
var pmo = new BigRational(primeMinusOne);
for (int c = 1; c < threshold; ++c)
{
coef[c] = BigRational.Multiply(pmo, new BigRational(rng.NextDouble())).GetWholePart();
}
var shares = new Tuple <int, BigInteger> [shareCount];
for (var x = 1; x <= shareCount; ++x)
{
System.Console.WriteLine("X: " + x);
var accum = coef[0];
for (int exp = 1; exp < threshold; ++exp)
{
// accum = (accum + (coef[exp] * (Math.pow(x, exp) % prime) % prime)) % prime;
var a = new BigInteger(Math.Pow(x, exp)) % _prime; // (Math.pow(x, exp) % prime)
var b = (coef[exp] * a) % _prime; // (coef[exp] * a % prime)
var c = (accum + b) % _prime; // (accum + b) % prime;
accum = c;
}
shares[x - 1] = Tuple.Create(x, accum);
}
Shares = shares.Select(x => {
var index = BitConverter.GetBytes(x.Item1);
var biarr = x.Item2.ToByteArray();
var bytes = new byte[INT_ARR_LEN + biarr.Length];
Array.Copy(index, 0, bytes, 0, INT_ARR_LEN);
Array.Copy(biarr, 0, bytes, INT_ARR_LEN, biarr.Length);
return(bytes);
});
// The original secret value is fully encoded in the distributed shares so there
// is no need to return any version of the original secreted in encrypted form
return(new byte[0]);
}
public static void Inverse()
{
rational *= -1;
calculation.Set(rational);
calculationString = calculationString.RemovePrefix("-");
if (rational < 0)
{
calculationString = calculationString.Insert(0, "-");
}
UpdateText();
}
public BigNumber(double val)
{
if (val == Math.Floor(val))
{
integerVal = new BigInt((int)val);
Type = NumberType2.integer;
}
else
{
rationalVal = new BigRational(val);
Type = NumberType2.rational;
}
}
public void TestConvertFromWholeNumberDecimal()
{
decimal seven = 7.0m;
BigRational expectedValue = new BigRational(7, new Fraction(0, 1));
BigRational result1 = new BigRational(seven);
BigRational result2 = (BigRational)seven;
Assert.AreEqual(expectedValue, result1);
Assert.AreEqual(expectedValue, result2);
}
public bool ContainsProjection(Point2BR point)
{
Vector2BR delta = this.GetDelta();
BigRational bigRational = Vector2BR.DotProduct(point - this.point2BR_0, delta);
if (bigRational.IsNegative)
{
return(false);
}
BigRational lengthSquared = delta.GetLengthSquared();
return(!(bigRational.Square() > lengthSquared));
}
public static BigRational[,] As2DArray(BigRational[][] Array2D, int leftSize, int rightSize)
{
var newArray = new BigRational[leftSize, rightSize];
for (int i = 0; i < Array2D.Length; i++)
{
for (int j = 0; j < Array2D[i].Length; j++)
{
newArray[i, j] = Array2D[i][j];
}
}
return(newArray);
}
public void Constructor_AllowsValidVectors(int value1, int value2)
{
var values = new BigRational[]
{
value1,
value2,
};
var vector = new ImmutableVector2D(values);
Assert.Equal(value1, vector.UnderlyingVector[0]);
Assert.Equal(value2, vector.UnderlyingVector[1]);
}
public void TestConstruction()
{
BigRational result1 = new BigRational(BigInteger.Zero, new Fraction(182, 26));
BigRational result1_2 = new BigRational(new Fraction(182, 26));
BigRational result2 = new BigRational(BigInteger.Zero, new Fraction(-7, 5));
BigRational expected1 = new BigRational(7);
BigRational expected2 = new BigRational(-1, 2, 5);
Assert.AreEqual(expected1, result1);
Assert.AreEqual(expected1, result1_2);
Assert.AreEqual(expected2, result2);
}
public void TestToDecimalOutOfRange()
{
decimal dummy;
BigRational rational = BigInteger.Pow(10, 30);
Assert.Throws <OverflowException>(
() => dummy = (decimal)rational);
BigRational negative = -rational;
Assert.Throws <OverflowException>(
() => dummy = (decimal)negative);
}
public void TestXmlDeserialise(int n, int d)
{
var expected = new BigRational(n, d);
var serializer = new XmlSerializer(typeof(BigRational));
var text = $"<BigRational>{expected.Numerator}/{expected.Denominator}</BigRational>";
using (var textReader = new StringReader(text))
using (var reader = XmlReader.Create(textReader))
{
var actual = (BigRational)serializer.Deserialize(reader);
Assert.AreEqual(expected, actual);
}
}
public void Determinant_FindsDeterminant()
{
var values = new BigRational[2, 2]
{
{ 2, 5 },
{ 1, 4 }
};
var matrix = new ImmutableMatrix2x2(values);
var determinant = matrix.Determinant();
Assert.Equal(3, determinant);
}
public void RoundWithDecimals2()
{
for (int d = -4; d <= 4; d++)
{
var scale = TenPow(d);
for (var v = -2.5M; v <= 2.5M; v += 0.0001M)
{
Compare(
Math.Round(v * scale) / scale,
BigRational.Round(v, d));
}
}
}
public void RoundWithRuleWithDecimals2(MidpointRounding decimalMode, RationalRounding rationalMode)
{
for (int d = -4; d <= 4; d++)
{
var scale = TenPow(d);
for (var v = -2.5M; v <= 2.5M; v += 0.0001M)
{
Compare(
Math.Round(v * scale, decimalMode) / scale,
BigRational.Round(v, d, rationalMode));
}
}
}
public static string ToDecimalString(this BigRational r, int precision)
{
var fraction = r.GetFractionPart();
// Case where the rational number is a whole number
if (fraction.Numerator == 0 && fraction.Denominator == 1)
{
return(r.GetWholePart() + ".0");
}
var adjustedNumerator = (fraction.Numerator
* BigInteger.Pow(10, precision));
var decimalPlaces = adjustedNumerator / fraction.Denominator;
// Case where precision wasn't large enough.
if (decimalPlaces == 0)
{
return("0.0");
}
// Give it the capacity for around what we should need for
// the whole part and total precision
// (this is kinda sloppy, but does the trick)
var sb = new StringBuilder(precision + r.ToString().Length);
bool noMoreTrailingZeros = false;
for (int i = precision; i > 0; i--)
{
if (!noMoreTrailingZeros)
{
if ((decimalPlaces % 10) == 0)
{
decimalPlaces = decimalPlaces / 10;
continue;
}
noMoreTrailingZeros = true;
}
// Add the right most decimal to the string
sb.Insert(0, decimalPlaces % 10);
decimalPlaces = decimalPlaces / 10;
}
// Insert the whole part and decimal
sb.Insert(0, ".");
sb.Insert(0, r.GetWholePart());
return(sb.ToString());
}
public void ConvertMatrixToUseTAndSGeneratorMatrices_ConvertsCorrectly()
{
var matrixValues = new BigRational[2, 2] {
{ 437, 202 }, { 543, 251 }
};
var matrix = new ImmutableMatrix2x2(matrixValues);
var expectedIdentifierList = new[]
{
GeneratorMatrixIdentifier.X,
GeneratorMatrixIdentifier.SInverse,
// -1
GeneratorMatrixIdentifier.TInverse,
// S Switch
GeneratorMatrixIdentifier.SInverse,
// 4
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
// S Switch
GeneratorMatrixIdentifier.SInverse,
// -8
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
// S Switch
GeneratorMatrixIdentifier.SInverse,
// 6
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
GeneratorMatrixIdentifier.T,
// S Switch
GeneratorMatrixIdentifier.SInverse,
// -2
GeneratorMatrixIdentifier.TInverse,
GeneratorMatrixIdentifier.TInverse,
// S Switch
GeneratorMatrixIdentifier.SInverse
};
var matrixIdentifierList = MathematicalHelper.ConvertMatrixToUseTAndSGeneratorMatrices(matrix);
Assert.Equal(expectedIdentifierList, matrixIdentifierList);
}
protected override string AddConstrain(SimplexTable inputTable, out SimplexTable outputTable, out bool success)
{
outputTable = new SimplexTable(inputTable);
success = true;
ReevaluateBasisAndDeltas(outputTable);
var bFracts = FormBFractVector(outputTable);
int selectedI = FindIndexOfMin(bFracts);
int nwI = outputTable.NumOfConstrains;
outputTable.NumOfConstrains += 1;
var result = $"Let's use {outputTable.cLables[curBasis[selectedI]].Value} row to form new constrain.<br>";
var bFract = outputTable.bVector[selectedI].value.Fract();
for (int j = 0; j < outputTable.NumOfVariables; j++)
{
BigRational tarA = outputTable.aMatrix[selectedI][j].value;
if (!outputTable.cLables[j].IsSelected)
{
if (tarA.Sign >= 0)
{
outputTable.aMatrix[nwI][j].value = -tarA;
}
else
{
outputTable.aMatrix[nwI][j].value = -((bFract / (BigRational.One - bFract)) * (-tarA));
}
}
else
{
if (tarA.Fract() <= bFract)
{
outputTable.aMatrix[nwI][j].value = -tarA.Fract();
}
else
{
outputTable.aMatrix[nwI][j].value = -((bFract / (BigRational.One - bFract)) * (BigRational.One - tarA));
}
}
}
outputTable.bVector[nwI].value = -bFract;
outputTable.NumOfVariables += 1;
outputTable.aMatrix[nwI][outputTable.NumOfVariables - 1].value = BigRational.One;
return(result);
}
public void BigRational_Constructor_TwoBigInteger_SimplifiesFraction()
{
var value1 = new BigRational((BigInteger)20, (BigInteger)10);
Assert.Equal("2/1", value1.ToString("B", null));
var value2 = new BigRational((BigInteger)10, (BigInteger)10);
Assert.Equal("1/1", value2.ToString("B", null));
var value3 = new BigRational((BigInteger)4, (BigInteger)6);
Assert.Equal("2/3", value3.ToString("B", null));
}
public void BigRational_Divide_DividesBigRationals()
{
Assert.Equal("0/1", (BigRational.Create(0).Divide(BigRational.Create(2))).ToString("B", null));
Assert.Equal("0/1", (BigRational.Create(0).Divide(BigRational.Create(-2))).ToString("B", null));
Assert.Equal("2/3", (BigRational.Create(2).Divide(BigRational.Create(3))).ToString("B", null));
Assert.Equal("3/2", (BigRational.Create(3).Divide(BigRational.Create(2))).ToString("B", null));
Assert.Equal("-3/2", (BigRational.Create(3).Divide(BigRational.Create(-2))).ToString("B", null));
Assert.Equal("-1/1", (BigRational.Create(-3).Divide(BigRational.Create(3))).ToString("B", null));
Assert.Equal("1/1", (BigRational.Create(-3).Divide(BigRational.Create(-3))).ToString("B", null));
Assert.Equal($"1/1", (BigRational.Create(VeryBigNumber).Divide(BigRational.Create(VeryBigNumber))).ToString("B", null));
Assert.Equal($"{VeryBigNumber}/1", (BigRational.Create($"{DoubleVeryBig}").Divide(BigRational.Create(2))).ToString("B", null));
Assert.Equal($"-2/1", (BigRational.Create($"{DoubleVeryBig}").Divide(BigRational.Create($"-{VeryBigNumber}"))).ToString("B", null));
}
public void TestConvertFromDecimalPointFloat()
{
float negativeOneAndOneHalf = -3f / 2f;
float oneThird = 1f / 3f;
BigRational expectedValue1 = new BigRational(-1, new Fraction(1, 2));
BigRational result1 = (BigRational)negativeOneAndOneHalf;
BigRational expectedValue2 = new BigRational(0, new Fraction(1, 3));
BigRational result2 = (BigRational)oneThird;
Assert.AreEqual(expectedValue1, result1);
Assert.AreEqual(expectedValue2, result2);
}
public static string ToString(this BigRational r, bool allowRational, ushort precisionLimit)
{
string output = InternalToString(r, precisionLimit + (allowRational ? 1 : 0));
if (!allowRational)
{
return(output);
}
if (string.IsNullOrEmpty(output) || (output.Length > precisionLimit && !r.Denominator.IsOne))
{
return(r.ToString());
}
return(output);
}
public BigRational GetVendorValue()
{
if (cachedVendorValue < 0)
{
int v = StatisticsTracker.moneyMagnitude.value;
v -= (v % 3);
v /= 3;
v = Math.Max(v - 1, 0);
UpgradeValueWrapper vendorSellEffectiveness;
upgrades.TryGetValue(UpgradeType.VENDOR_SELL_VALUE, out vendorSellEffectiveness);
cachedVendorValue = (((UpgradeFloatValue)vendorSellEffectiveness).value + (0.05f * v)) * (1 + SkillList.VendorEffectiveness.getMultiplier()) + currentGuildmaster.vendorSellMultiplier();
}
return(cachedVendorValue);
}
public void Constructor_Throws_IfWrongSizeMatrixSupplied(int sizeX, int sizeY)
{
var values = new BigRational[sizeX, sizeY];
for (int i = 0; i < sizeX; i++)
{
for (int j = 0; j < sizeY; j++)
{
values[i, j] = 0;
}
}
Assert.Throws <ArgumentException>(() => new ImmutableMatrix2x2(values));
}
public void SqrtAsRational()
{
var expected = new BigRational[]
{
new(1, 1),
new(3, 2),
new(7, 5),
new(17, 12),
new(41, 29),
};
var actual = BigRational.SqrtAsRationals(new BigInteger(2)).Take(5);
Assert.True(expected.SequenceEqual(actual));
}
public BigNumber(double val, NumberType2 type)
{
Type = type;
switch (type) {
case NumberType2.integer:
integerVal = new BigInt((int)val);
break;
case NumberType2.rational:
rationalVal = new BigRational(val);
break;
case NumberType2.irrational:
irrationalVal = new BigIrrational(val);
break;
}
}
public CalculationOptions(int width, int height, uint iter)
{
this.width = xMax = width;
this.height = yMax = height;
this.xSkip = 1;
this.ySkip = 1;
this.iteration_count = iter;
this.orbit_length = iter;
this.skip_primary_bulbs = 0U;
this.minRe = new BigRational(-5, 2); // -2.5 to
this.maxRe = new BigRational(3, 2); // 1.5
this.minIm = new BigRational(-3, 2); // -1.5 to
this.maxIm = new BigRational(3, 2); // 1.5
}
static ExprList MergeArgs(
CoreBuilder b,
IEnumerable<Expr> args,
Func<Expr, ExprList?> getArgs,
BigRational aggregateSeed,
Func<BigRational, BigRational, BigRational> aggregate,
Func<IEnumerable<Expr>, IEnumerable<Expr>> group) {
var mergedArgs = args
.SelectMany(x => getArgs(x) ?? x.Yield());
var @const = mergedArgs
.Select(x => x.AsConst())
.Where(x => x != null)
.Select(x => x.Value)
.Aggregate(aggregateSeed, aggregate);
var other = group(mergedArgs.Where(x => !x.IsConst()));
return (@const == aggregateSeed && other.Any() ? other : Const(@const).Yield().Concat(other)).ToExprList();
}
public static DivideResult PolyLongDivision(BigRational[] dividend, BigRational[] divisor)
{
DivideResult divideResult = new DivideResult();
BigRational[] bufferDividend = dividend;
int divisorMaxPower = divisor.Length - 1;
BigRational divisorMaxCoeff = divisor.Last();
BigRational[] result = new BigRational[dividend.Length];
while (true)
{
long dividentMaxPower = bufferDividend.Length - 1;
long resultXPower = dividentMaxPower - divisorMaxPower;
if (resultXPower < 0)
{
divideResult.Quotient = RemoveUselessZeros(result);
divideResult.Remainder = RemoveUselessZeros(bufferDividend);
return divideResult;
}
BigRational dividentCoeff = bufferDividend.Last();
BigRational resultCoeff = dividentCoeff/divisorMaxCoeff;
result[resultXPower] = resultCoeff;
BigRational[] buffSubtract = new BigRational[bufferDividend.Length].Select(h => new BigRational(0,1)).ToArray();
Array.Copy(divisor, 0, buffSubtract, resultXPower, divisor.Length);
Parallel.For(0, buffSubtract.Length, i => buffSubtract[i] *= resultCoeff);
bufferDividend = ArraySubtrInts(bufferDividend, buffSubtract);
bufferDividend = RemoveUselessZeros(bufferDividend);
}
}
public static StringBuilder BigRationalToStringBuilder(BigRational[] bigRationals)
{
StringBuilder resultSb = new StringBuilder();
for (int i = 0; i < bigRationals.Length; i++)
{
if (bigRationals[i].Equals(0)) { continue; }
resultSb.Insert(0, bigRationals[i]);
switch (i)
{
case 0:
break;
case 1:
resultSb.Insert(bigRationals[i].ToString().Length, "x ");
break;
default:
resultSb.Insert(bigRationals[i].ToString().Length, "x^" + i + " ");
break;
}
if (bigRationals[i].Sign.Equals(1))
{
resultSb.Insert(0, "+");
}
}
if (resultSb[0].Equals('+'))
{
resultSb.Remove(0, 1);
}
return resultSb;
}
public static bool CanShrink(BigRational d)
{
return (d.Denominator == 1);
}
public Value(BigRational doubleVal, Restrictions restrictions)
{
InitDouble(doubleVal, restrictions);
}
public static object Shrink(BigRational d)
{
if (CanShrink(d))
{
return Shrink(d.Numerator);
}
else {
return d;
}
}
public override double[] GetDoubleFirstInserts(BigInteger[] args)
{
BigRational absciss_start = _2df_get_br_abciss_start(), absciss_interval = _2df_get_br_abciss_interval_length();
BigRational[] be_Result = new BigRational[4];
be_Result[0] = absciss_start+ (absciss_interval * new BigRational(args[0], BigInteger.One));
be_Result[1] = absciss_start + (absciss_interval * new BigRational(args[1], BigInteger.One));
BigRational ordinate_start=_2df_get_br_ordinate_start(),ordinate_interval=_2df_get_br_ordinate_interval_length();
be_Result[2]=ordinate_start+(ordinate_interval * new BigRational(args[2], BigInteger.One));
be_Result[3] = ordinate_start + (ordinate_interval * new BigRational(args[3], BigInteger.One));
double[] Result=new double[4];
Result[0] = ((double)be_Result[0].Numerator) / ((double)be_Result[0].Denominator);
Result[1] = ((double)be_Result[1].Numerator) / ((double)be_Result[1].Denominator);
Result[2] = ((double)be_Result[2].Numerator) / ((double)be_Result[2].Denominator);
Result[3] = ((double)be_Result[3].Numerator) / ((double)be_Result[3].Denominator);
return Result;
}
public Value(BigRational doubleVal, Factors factors, Restrictions restrictions)
{
InitDouble(doubleVal, restrictions);
this.factors = factors;
}
public KoeffMultInfo(BigRational _Koeff, ExprList _Mult)
{
Koeff = _Koeff;
Mult = _Mult;
}
protected void _2df_safe_set_scale(int _Width, int _Height, int n_left, int n_top, int width, int height)
{
if (_2df_imagine_width == null)
{
_2df_imagine_width = new BigInteger(width);
_2df_imagine_height = new BigInteger(height);
_2df_imagine_left = BigInteger.Zero;
_2df_imagine_top = BigInteger.Zero;
return;
}
if (_Width == width && _Height == height && n_left == 0 && n_top == 0) return;
_2df_push_fractal_state();
if(_Width<width||_Height<height)
{
_2df_set_scale(_Width, _Height, n_left, n_top, width, height);
return;
}
BigRational width_dif = new BigRational(_Width, width);
BigRational height_dif = new BigRational(_Height, height);
BigRational safe_dif = width_dif > height_dif ? height_dif : width_dif;
BigRational im_left = new BigRational(_2df_imagine_left + (BigInteger)n_left) * safe_dif;
BigRational im_top = new BigRational(_2df_imagine_top + (BigInteger)n_top) * safe_dif;
BigRational im_width = new BigRational(_2df_imagine_width) * safe_dif;
BigRational im_height = new BigRational(_2df_imagine_height) * safe_dif;
_2df_imagine_left = im_left.Numerator / im_left.Denominator;
_2df_imagine_top = im_top.Numerator / im_top.Denominator;
_2df_imagine_width = im_width.Numerator / im_width.Denominator;
_2df_imagine_height = im_height.Numerator / im_height.Denominator;
}
//Let's format any BigRational (e.g. Pi) to a string with specified significant figures
public static string Format(BigRational pi, int numberOfDigits)
{
var numeratorShiftedToEnoughDigits =
(pi.Numerator * BigInteger.Pow(new BigInteger(10), numberOfDigits));
var test = pi.Numerator%pi.Denominator;
var bigInteger = numeratorShiftedToEnoughDigits / pi.Denominator;
string piToBeFormatted = bigInteger.ToString();
int len = piToBeFormatted.Length-numberOfDigits;
var builder = new StringBuilder();
builder.Append(piToBeFormatted.Substring(0,len));
builder.Append(".");
builder.Append(piToBeFormatted.Substring(len, numberOfDigits - len));
return builder.ToString();
}
internal override ParsedSyntax CombineForPlus(ParsedSyntax other, BigRational otherValue)
=> other.CombineForPlus(this, otherValue);
public BigRational Calculate(BigRational x, int maxNumberOfIterations, int precision)
{
bool doASubtract = true;
var runningTotal = x;
int count = 0;
var divisor = 3;
while (count < maxNumberOfIterations)
{
var current = BigRational.Pow(x, divisor);
current = current/BigRational.FromInt(divisor);
if (doASubtract)
{
runningTotal = runningTotal - current;
}
else
{
runningTotal = runningTotal + current;
}
doASubtract = !doASubtract;
count++;
divisor = divisor + 2;
if (!WeHaveEnoughPrecision(current, precision)) continue;
Iterations = count;
break;
}
return runningTotal;
}
private static bool WeHaveEnoughPrecision(BigRational current, int precision)
{
var fractionPart = (current.Numerator%current.Denominator);
var thing = BigRational.FromBigInt(fractionPart)/BigRational.FromBigInt(current.Denominator);
return thing.ToString().Length > precision + 2; //extra 2 digits to ensure enough precision
}
internal void Add(BigRational re, BigRational im)
{
if (currentindex == points.LongLength) // Have to expand array
{
long newsize = points.LongLength == 0 ? 1 : points.LongLength * 2;
BigComplex[] newarr = new BigComplex[newsize];
Array.Copy(points, newarr, currentindex);
points = newarr;
}
points[currentindex++] = new BigComplex(re, im);
}
public BigComplex()
{
Real = Imagine = BigRational.Zero;
}
public BigComplex(BigRational r, BigRational i)
{
Real = r;
Imagine = i;
}
public BigComplex(double Re, double Im)
{
Real = BigRational.ConvertToBigRational(Re);
Imagine = BigRational.ConvertToBigRational(Im);
}
public BigComplex(long value)
{
Real = new BigRational(value, 1);
Imagine = BigRational.Zero;
}
