C# Arbitrary Precision Signed Big Rational Numbers
Updated: Jun-11,2021
using System;
using System.Diagnostics;
using System.Globalization;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
[DebuggerDisplay("{" + nameof(DDisplay) + "}")]
[Serializable]
public struct BigRational : IComparable, IComparable<BigRational>, IEquatable<BigRational>
{
[StructLayout(LayoutKind.Explicit)]
internal struct DoubleUlong
{
[FieldOffset(0)] public double dbl;
[FieldOffset(0)] public ulong uu;
}
/// <summary>
/// Change here if more then 2048 bits are specified
/// </summary>
private const float DecimalMaxScale = 2048f / 64f * 20f;
private static readonly BigInteger DecimalPrecision = BigInteger.Pow(10, (int)DecimalMaxScale);
private const int DoubleMaxScale = 308;
public static BigRational Pi = new(
"3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798162478513934506898440362801792706010179987216806726188740140466033567581311679376075335101609659171030644576233653027450257182803484658351860927270133809030914436823660262931162576284703194589395221866245992710817555393680237554917047871708932985106840785074833639247080859264327721882027979677397953754604196915619381410505600288856897761875941052867609089114345150157869223684881643245943313338421018485091403977277400743970527492816321894223953257584787737337170568053925027217102844351208765657302025589127695185039186644597240030541171074757870137431100579097277905612641495178817964173941740654985445918326928220945355416048444887050935562696866696019631573868714587428709669938320262709342763");
public static BigRational E = GetE(MaxFactorials);
private static readonly BigInteger DoublePrecision = BigInteger.Pow(10, DoubleMaxScale);
private static readonly BigInteger DoubleMaxValue = (BigInteger)double.MaxValue;
private static readonly BigInteger DoubleMinValue = (BigInteger)double.MinValue;
private static BigRational[] Factorials;
static BigRational()
{
}
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private string DDisplay => AsDecimal(this);
[StructLayout(LayoutKind.Explicit)]
internal struct DecimalUInt32
{
[FieldOffset(0)] public decimal dec;
[FieldOffset(0)] public int flags;
}
private const int DecimalScaleMask = 0x00FF0000;
private const int DecimalSignMask = unchecked((int)0x80000000);
private const int MaxFactorials = 100;
private static readonly BigInteger DecimalMaxValue = (BigInteger)decimal.MaxValue;
private static readonly BigInteger DecimalMinValue = (BigInteger)decimal.MinValue;
private const string Solidus = @"/";
public static BigRational Zero
{
get;
} = new(BigInteger.Zero);
public static BigRational One
{
get;
} = new(BigInteger.One);
public static BigRational MinusOne
{
get;
} = new(BigInteger.MinusOne);
public int Sign => Numerator.Sign;
public BigInteger Numerator
{
get;
private set;
}
public BigInteger Denominator
{
get;
private set;
}
public BigInteger WholePart => BigInteger.Divide(Numerator, Denominator);
public bool IsFractionalPart
{
get
{
var fp = FractionPart;
return fp.Numerator != 0 || fp.Denominator != 1;
}
}
public BigInteger GetUnscaledAsDecimal => Numerator * DecimalPrecision / Denominator;
public BigInteger Remainder => Numerator % Denominator;
public int DecimalPlaces
{
get
{
var a = GetUnscaledAsDecimal;
var dPlaces = 0;
if (a.Sign == 0)
return 1;
if (a.Sign < 0)
try
{
a = -a;
}
catch (Exception ex)
{
return 0;
}
var biRadix = new BigInteger(10);
while (a > 0)
try
{
a /= biRadix;
dPlaces++;
}
catch (Exception ex)
{
break;
}
return dPlaces;
}
}
public static string AsDecimal(BigRational value)
{
var asd = new BigDecimal(value);
return asd.ToString();
}
public static string CleanAsDecimal(BigRational value)
{
var fpas = AsDecimal(value);
var rs = fpas.Reverse();
var fas = "";
foreach (var c in rs)
if (c == '0')
continue;
else
fas += c;
return fas.Reverse();
}
public BigRational FractionPart
{
get
{
var rem = BigInteger.Remainder(Numerator, Denominator);
return new BigRational(rem, Denominator);
}
}
public override bool Equals(object obj)
{
if (obj == null)
return false;
if (!(obj is BigRational))
return false;
return Equals((BigRational)obj);
}
public override int GetHashCode()
{
return (Numerator / Denominator).GetHashCode();
}
int IComparable.CompareTo(object obj)
{
if (obj == null)
return 1;
if (!(obj is BigRational))
throw new ArgumentException();
return Compare(this, (BigRational)obj);
}
public int CompareTo(BigRational other)
{
return Compare(this, other);
}
public bool Equals(BigRational other)
{
if (Denominator == other.Denominator)
return Numerator == other.Numerator;
return Numerator * other.Denominator == Denominator * other.Numerator;
}
public BigRational(BigInteger numerator)
{
Numerator = numerator;
Denominator = BigInteger.One;
}
public BigRational(string n, string d)
{
Numerator = new BigInteger().BigIntegerBase10(n);
Denominator = new BigInteger().BigIntegerBase10(d);
}
public BigRational(string value)
{
if (!value.ContainsOnly("0123456789+-.eE"))
throw new Exception(
$"Input value must only contain these '0123456789+-.eE', value'{value}");
var v1 = new BigDecimal(value);
var (unscaledValue, scale) = v1.ToByteArrays();
if (v1 == BigDecimal.Zero)
{
this = Zero;
return;
}
Numerator = new BigInteger(unscaledValue);
Denominator = BigInteger.Pow(10, BitConverter.ToInt32(scale, 0));
Simplify();
}
public static bool TryParse(string parse, out BigRational result)
{
result = default;
if (!parse.ContainsOnly("0123456789+-.eE"))
throw new Exception(
$"Input value must only contain these '0123456789+-.eE', value'{parse}");
try
{
result = new BigRational(parse);
}
catch
{
return false;
}
return true;
}
public BigRational(double value) : this((decimal)value)
{
}
public BigRational(BigDecimal value)
{
var bits = value.ToByteArrays();
if (value == BigDecimal.Zero)
{
this = Zero;
return;
}
Numerator = new BigInteger(bits.unscaledValue);
Denominator = BigInteger.Pow(10, BitConverter.ToInt32(bits.scale, 0));
Simplify();
}
public BigRational(decimal value)
{
var bits = decimal.GetBits(value);
if (bits == null || bits.Length != 4 ||
(bits[3] & ~(DecimalSignMask | DecimalScaleMask)) != 0 ||
(bits[3] & DecimalScaleMask) > 28 << 16)
throw new ArgumentException();
if (value == decimal.Zero)
{
this = Zero;
return;
}
var ul = ((ulong)(uint)bits[2] << 32) | (uint)bits[1];
Numerator = (new BigInteger(ul) << 32) | (uint)bits[0];
var isNegative = (bits[3] & DecimalSignMask) != 0;
if (isNegative)
Numerator = BigInteger.Negate(Numerator);
var scale = (bits[3] & DecimalScaleMask) >> 16;
Denominator = BigInteger.Pow(10, scale);
Simplify();
}
public BigRational(BigInteger numerator, BigInteger denominator)
{
if (denominator.Sign == 0)
throw new DivideByZeroException();
if (numerator.Sign == 0)
{
Numerator = BigInteger.Zero;
Denominator = BigInteger.One;
}
else if (denominator.Sign < 0)
{
Numerator = BigInteger.Negate(numerator);
Denominator = BigInteger.Negate(denominator);
}
else
{
Numerator = numerator;
Denominator = denominator;
}
Simplify();
}
public BigRational(BigInteger whole, BigInteger numerator, BigInteger denominator)
{
if (denominator.Sign == 0)
throw new DivideByZeroException();
if (numerator.Sign == 0 && whole.Sign == 0)
{
Numerator = BigInteger.Zero;
Denominator = BigInteger.One;
}
else if (denominator.Sign < 0)
{
Denominator = BigInteger.Negate(denominator);
Numerator = BigInteger.Negate(whole) * Denominator + BigInteger.Negate(numerator);
}
else
{
Denominator = denominator;
Numerator = whole * denominator + numerator;
}
Simplify();
}
public static BigRational Abs(BigRational r)
{
return r.Numerator.Sign < 0
? new BigRational(BigInteger.Abs(r.Numerator), r.Denominator)
: r;
}
public static BigRational Negate(BigRational r)
{
return new BigRational(BigInteger.Negate(r.Numerator), r.Denominator);
}
public static BigRational Invert(BigRational r)
{
return new BigRational(r.Denominator, r.Numerator);
}
public static BigRational Add(BigRational x, BigRational y)
{
return x + y;
}
public static BigRational Subtract(BigRational x, BigRational y)
{
return x - y;
}
public static BigRational Multiply(BigRational x, BigRational y)
{
return x * y;
}
public static BigRational Divide(BigRational dividend, BigRational divisor)
{
return dividend / divisor;
}
public static BigRational DivRem(BigRational dividend,
BigRational divisor,
out BigRational remainder)
{
var ad = dividend.Numerator * divisor.Denominator;
var bc = dividend.Denominator * divisor.Numerator;
var bd = dividend.Denominator * divisor.Denominator;
remainder = new BigRational(ad % bc, bd);
return new BigRational(ad, bc);
}
public static BigInteger LeastCommonDenominator(BigRational x, BigRational y)
{
return x.Denominator * y.Denominator /
BigInteger.GreatestCommonDivisor(x.Denominator, y.Denominator);
}
public static int Compare(BigRational r1, BigRational r2)
{
return BigInteger.Compare(r1.Numerator * r2.Denominator, r2.Numerator * r1.Denominator);
}
public static bool operator ==(BigRational x, BigRational y)
{
return Compare(x, y) == 0;
}
public static bool operator !=(BigRational x, BigRational y)
{
return Compare(x, y) != 0;
}
public static bool operator <(BigRational x, BigRational y)
{
return Compare(x, y) < 0;
}
public static bool operator <=(BigRational x, BigRational y)
{
return Compare(x, y) <= 0;
}
public static bool operator >(BigRational x, BigRational y)
{
return Compare(x, y) > 0;
}
public static bool operator >=(BigRational x, BigRational y)
{
return Compare(x, y) >= 0;
}
public static BigRational operator +(BigRational r)
{
return r;
}
public static BigRational operator -(BigRational r)
{
return new BigRational(-r.Numerator, r.Denominator);
}
public static BigRational operator ++(BigRational r)
{
return r + One;
}
public static BigRational operator --(BigRational r)
{
return r - One;
}
public static BigRational operator +(BigRational r1, BigRational r2)
{
return new BigRational(r1.Numerator * r2.Denominator + r1.Denominator * r2.Numerator,
r1.Denominator * r2.Denominator);
}
public static BigRational operator -(BigRational r1, BigRational r2)
{
return new BigRational(r1.Numerator * r2.Denominator - r1.Denominator * r2.Numerator,
r1.Denominator * r2.Denominator);
}
public static BigRational operator *(BigRational r1, BigRational r2)
{
return new BigRational(r1.Numerator * r2.Numerator, r1.Denominator * r2.Denominator);
}
public static BigRational operator /(BigRational r1, BigRational r2)
{
return new BigRational(r1.Numerator * r2.Denominator, r1.Denominator * r2.Numerator);
}
public static BigRational operator %(BigRational r1, BigRational r2)
{
return new BigRational(r1.Numerator * r2.Denominator % (r1.Denominator * r2.Numerator),
r1.Denominator * r2.Denominator);
}
public static explicit operator sbyte(BigRational value)
{
return (sbyte)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator ushort(BigRational value)
{
return (ushort)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator uint(BigRational value)
{
return (uint)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator ulong(BigRational value)
{
return (ulong)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator byte(BigRational value)
{
return (byte)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator short(BigRational value)
{
return (short)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator int(BigRational value)
{
return (int)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator long(BigRational value)
{
return (long)BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator BigInteger(BigRational value)
{
return BigInteger.Divide(value.Numerator, value.Denominator);
}
public static explicit operator float(BigRational value)
{
return (float)(double)value;
}
public static explicit operator double(BigRational value)
{
if (SafeCastToDouble(value.Numerator) && SafeCastToDouble(value.Denominator))
return (double)value.Numerator / (double)value.Denominator;
var denormalized = value.Numerator * DoublePrecision / value.Denominator;
if (denormalized.IsZero)
return value.Sign < 0
? BitConverter.Int64BitsToDouble(unchecked((long)0x8000000000000000))
: 0d;
double result = 0;
var isDouble = false;
var scale = DoubleMaxScale;
while (scale > 0)
{
if (!isDouble)
if (SafeCastToDouble(denormalized))
{
result = (double)denormalized;
isDouble = true;
}
else
{
denormalized = denormalized / 10;
}
result = result / 10;
scale--;
}
if (!isDouble)
return value.Sign < 0 ? double.NegativeInfinity : double.PositiveInfinity;
return result;
}
public static explicit operator BigDecimal(BigRational value)
{
var denormalized = value.Numerator * DecimalPrecision / value.Denominator;
return new BigDecimal(denormalized, (int)DecimalMaxScale);
}
public static explicit operator decimal(BigRational value)
{
if (SafeCastToDecimal(value.Numerator) && SafeCastToDecimal(value.Denominator))
return (decimal)value.Numerator / (decimal)value.Denominator;
var denormalized = value.Numerator * DecimalPrecision / value.Denominator;
if (denormalized.IsZero)
return decimal.Zero;
for (var scale = (int)DecimalMaxScale; scale >= 0; scale--)
if (!SafeCastToDecimal(denormalized))
{
denormalized /= 10;
}
else
{
var dec = new DecimalUInt32();
dec.dec = (decimal)denormalized;
dec.flags = (dec.flags & ~DecimalScaleMask) | (scale << 16);
return dec.dec;
}
throw new OverflowException();
}
public static implicit operator BigRational(sbyte value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(ushort value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(uint value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(ulong value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(byte value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(short value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(int value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(long value)
{
return new BigRational((BigInteger)value);
}
public static implicit operator BigRational(BigInteger value)
{
return new BigRational(value);
}
public static implicit operator BigRational(string value)
{
return new BigRational(value);
}
public static implicit operator BigRational(float value)
{
return new BigRational(value);
}
public static implicit operator BigRational(double value)
{
return new BigRational(value);
}
public static implicit operator BigRational(decimal value)
{
return new BigRational(value);
}
public static implicit operator BigRational(BigDecimal value)
{
return new BigRational(value);
}
private void Simplify()
{
if (Numerator == BigInteger.Zero)
Denominator = BigInteger.One;
var gcd = BigInteger.GreatestCommonDivisor(Numerator, Denominator);
if (gcd > BigInteger.One)
{
Numerator = Numerator / gcd;
Denominator = Denominator / gcd;
}
}
private static bool SafeCastToDouble(BigInteger value)
{
return DoubleMinValue <= value && value <= DoubleMaxValue;
}
private static bool SafeCastToDecimal(BigInteger value)
{
return DecimalMinValue <= value && value <= DecimalMaxValue;
}
private static void SplitDoubleIntoParts(double dbl,
out int sign,
out int exp,
out ulong man,
out bool isFinite)
{
DoubleUlong du;
du.uu = 0;
du.dbl = dbl;
sign = 1 - ((int)(du.uu >> 62) & 2);
man = du.uu & 0x000FFFFFFFFFFFFF;
exp = (int)(du.uu >> 52) & 0x7FF;
if (exp == 0)
{
isFinite = true;
if (man != 0)
exp = -1074;
}
else if (exp == 0x7FF)
{
isFinite = false;
exp = int.MaxValue;
}
else
{
isFinite = true;
man |= 0x0010000000000000;
exp -= 1075;
}
}
public static double GetDoubleFromParts(int sign, int exp, ulong man)
{
DoubleUlong du;
du.dbl = 0;
if (man == 0)
{
du.uu = 0;
}
else
{
var cbitShift = CbitHighZero(man) - 11;
if (cbitShift < 0)
man >>= -cbitShift;
else
man <<= cbitShift;
exp += 1075;
if (exp >= 0x7FF)
{
du.uu = 0x7FF0000000000000;
}
else if (exp <= 0)
{
exp--;
if (exp < -52)
du.uu = 0;
else
du.uu = man >> -exp;
}
else
{
du.uu = (man & 0x000FFFFFFFFFFFFF) | ((ulong)exp << 52);
}
}
if (sign < 0)
du.uu |= 0x8000000000000000;
return du.dbl;
}
private static int CbitHighZero(ulong uu)
{
if ((uu & 0xFFFFFFFF00000000) == 0)
return 32 + CbitHighZero((uint)uu);
return CbitHighZero((uint)(uu >> 32));
}
private static int CbitHighZero(uint u)
{
if (u == 0)
return 32;
var cbit = 0;
if ((u & 0xFFFF0000) == 0)
{
cbit += 16;
u <<= 16;
}
if ((u & 0xFF000000) == 0)
{
cbit += 8;
u <<= 8;
}
if ((u & 0xF0000000) == 0)
{
cbit += 4;
u <<= 4;
}
if ((u & 0xC0000000) == 0)
{
cbit += 2;
u <<= 2;
}
if ((u & 0x80000000) == 0)
cbit += 1;
return cbit;
}
private static (BigRational High, BigRational Low) SqrtLimits(BigInteger number)
{
if (number == BigInteger.Zero) return (0, 0);
var high = number >> 1;
var low = BigInteger.Zero;
while (high > low + 1)
{
var n = (high + low) >> 1;
var p = n * n;
if (number < p)
high = n;
else if (number > p)
low = n;
else
break;
}
return (high, low);
}
public static BigRational Sqrt(BigRational value)
{
if (value == 0) return 0;
var hl = SqrtLimits(value.WholePart);
BigRational n = 0, p = 0;
if (hl.High == 0 && hl.Low == 0)
return 0;
var high = hl.High;
var low = hl.Low;
var d = DecimalPrecision;
var pp = 1 / (BigRational)d;
while (high > low + pp)
{
n = (high + low) / 2;
p = n * n;
if (value < p)
high = n;
else if (value > p)
low = n;
else
break;
}
var r = value == p ? n : low;
return r;
}
public BigRational Sqrt()
{
return Sqrt(this);
}
public static BigRational ArcTangent(BigRational v, int n)
{
var retVal = v;
for (var i = 1; i < n; i++)
{
var powRat = Pow(v, 2 * i + 1);
retVal += new BigRational(powRat.Numerator * (BigInteger)Math.Pow(-1d, i),
(2 * i + 1) * powRat.Denominator);
}
return retVal;
}
public static BigRational Reciprocal(BigRational v)
{
return new BigRational(v.Denominator, v.Numerator);
}
public static BigRational Round(BigRational number, int decimalPlaces)
{
BigRational power = BigInteger.Pow(10, decimalPlaces);
number *= power;
return number >= 0 ? (BigInteger)(number + 0.5) / power : (BigInteger)(number - 0.5) / power;
}
public void Round(int decimalPlaces)
{
var number = this;
BigRational power = BigInteger.Pow(10, decimalPlaces);
number *= power;
var n = number >= 0 ? (BigInteger)(number + 0.5) / power : (BigInteger)(number - 0.5) / power;
Numerator = n.Numerator;
Denominator = n.Denominator;
}
public static BigRational Pow(BigRational v, int e)
{
if (e < 1) throw new ArgumentException("Powers must be greater than or equal to one.");
var retVal = new BigRational(v.Numerator, v.Denominator);
for (var i = 1; i < e; i++)
{
retVal.Numerator *= v.Numerator;
retVal.Denominator *= v.Denominator;
}
return retVal;
}
public static BigRational Min(BigRational r, BigRational l)
{
return l < r ? l : r;
}
public static BigRational Max(BigRational r, BigRational l)
{
return l > r ? l : r;
}
/// <summary>
/// Set Pi before call
/// </summary>
public static BigRational ToRadians(BigRational degrees)
{
return degrees * Pi / 180;
}
/// <summary>
/// Set Pi before call
/// </summary>
public static BigRational ToDegrees(BigRational rads)
{
return rads * 180 / Pi;
}
private static BigRational Factorial(BigRational x)
{
BigRational r = 1;
BigRational c = 1;
while (c <= x)
{
r *= c;
c++;
}
return r;
}
public static BigRational Exp(BigRational x)
{
BigRational r = 0;
BigRational r1 = 0;
var k = 0;
while (true)
{
r += Pow(x, k) / Factorial(k);
if (r == r1)
break;
r1 = r;
k++;
}
return r;
}
public static BigRational Sine(BigRational ar, int n)
{
if (Factorials == null)
{
Factorials = new BigRational[MaxFactorials];
for (var i = 0; i < MaxFactorials; i++)
Factorials[i] = new BigRational();
for (var i = 1; i < MaxFactorials + 1; i++)
Factorials[i - 1] = Factorial(i);
}
var sin = ar;
for (var i = 1; i <= n; i++)
{
var trm = Pow(ar, i * 2 + 1);
trm /= Factorials[i * 2];
if ((i & 1) == 1)
sin -= trm;
else
sin += trm;
}
return sin;
}
public static BigRational Atan(BigRational ar, int n)
{
var atan = ar;
for (var i = 1; i <= n; i++)
{
var trm = Pow(ar, i * 2 + 1);
trm /= i * 2;
if ((i & 1) == 1)
atan -= trm;
else
atan += trm;
}
return atan;
}
public static BigRational Cosine(BigRational ar, int n)
{
if (Factorials == null)
{
Factorials = new BigRational[MaxFactorials];
for (var i = 0; i < MaxFactorials; i++)
Factorials[i] = new BigRational();
for (var i = 1; i < MaxFactorials + 1; i++)
Factorials[i - 1] = Factorial(i);
}
BigRational cos = 1.0;
for (var i = 1; i <= n; i++)
{
var trm = Pow(ar, i * 2);
trm /= Factorials[i * 2 - 1];
if ((i & 1) == 1)
cos -= trm;
else
cos += trm;
}
return cos;
}
public static BigRational Tangent(BigRational ar, int n)
{
return Sine(ar, n) / Cosine(ar, n);
}
public static BigRational CoTangent(BigRational ar, int n)
{
return Cosine(ar, n) / Sine(ar, n);
}
public static BigRational Secant(BigRational ar, int n)
{
return 1.0 / Cosine(ar, n);
}
public static BigRational CoSecant(BigRational ar, int n)
{
return 1.0 / Sine(ar, n);
}
private static BigRational GetE(int n)
{
BigRational e = 1.0;
var c = n;
while (c > 0)
{
BigRational f = 0;
if (c == 1)
{
f = 1;
}
else
{
var i = c - 1;
f = c;
while (i > 0)
{
f *= i;
i--;
}
}
c--;
e += 1.0 / f;
}
return e;
}
public static BigRational NthRoot(BigRational value, int nth)
{
BigRational lx;
var a = value;
var n = nth;
BigRational s = 1.0;
do
{
var t = s;
lx = a / Pow(s, n - 1);
var r = (n - 1) * s;
s = (lx + r) / n;
} while (lx != s);
return s;
}
public static BigRational LogN(BigRational value)
{
BigRational a;
var p = value;
BigRational n = 0.0;
while (p >= E)
{
p /= E;
n++;
}
n += p / E;
p = value;
do
{
a = n;
var lx = p / Exp(n - 1.0);
var r = (n - 1.0) * E;
n = (lx + r) / E;
} while (n != a);
return n;
}
public static BigRational Log(BigRational n, int b)
{
return LogN(n) / LogN(b);
}
private static int ConversionIterations(BigRational v)
{
return (int)((DecimalMaxScale + 1) / (2 * Math.Log10((double)Reciprocal(v))));
}
public static BigRational GetPI()
{
var oneFifth = new BigRational(1, 5);
var oneTwoThirtyNine = new BigRational(1, 239);
var arcTanOneFifth = ArcTangent(oneFifth, ConversionIterations(oneFifth));
var arcTanOneTwoThirtyNine =
ArcTangent(oneTwoThirtyNine, ConversionIterations(oneTwoThirtyNine));
return arcTanOneFifth * 16 - arcTanOneTwoThirtyNine * 4;
}
public override string ToString()
{
var ret = new StringBuilder();
ret.Append(Numerator.ToString("R", CultureInfo.InvariantCulture));
ret.Append(Solidus);
ret.Append(Denominator.ToString("R", CultureInfo.InvariantCulture));
return ret.ToString();
}
}