InfiniteDecimal 0.2.1

Infinite Decimal

This repository provides a powerful tool for numerical computation and analysis. It offers a decimal data type with potentially infinite precision, enabling complex mathematical operations where high accuracy is required without any limitation on the number of digits after the decimal point. The flexibility and versatility of this repository make it an essential tool for anyone who deals with high-level numerical computations.

It represents a number as a * 10^-b, where a is a BigInteger mantissa, and b is an int greater than or equal to 0.

Examples

Initializing variables and construction

var precision = 5;
var a = new BigDec(1, precision);
var b = new BigDec(1m, precision + 1);
var c = new BigDec(0.3d, precision + 2);
var d = new BigDec(0.3);
var f = a.WithPrecision(1337);
var g = new BigDec(BigInteger.One);

var h = new BigDec(1000, 3, 500); // 1 because 1000 * 10^-3 = 1
var i = new BigDec(1000m, 4, 500); // 0.1 because 1000 * 10^-4 = 0.1
...

Deconstruction

var b = new BigDec(1001, 3, 500);
Console.WriteLine(
    "{0} {1}\n{2} {3}",
    b.Mantissa.GetType(),
    b.Mantissa,
    b.Offset.GetType(),
    b.Offset
);
// System.Numerics.BigInteger 1001
// System.Int32 3

var a = new BigDec(1000, 3, 500);
Console.WriteLine(
    "{0} {1}\n{2} {3}",
    a.Mantissa.GetType(),
    a.Mantissa,
    a.Offset.GetType(),
    a.Offset
);
// System.Numerics.BigInteger 1
// System.Int32 0

Primitive arithmetic operations

var g = a + b;
var h = a * new BigDec(156);
var i = new BigDec(148, 1000) / g;
var j = a - b;

var k1 = new BigDec(10, 2) / 3; // 3.333333333333333333, because 3 parsed with default precision = 18
var k2 = new BigDec(10, 2) / new BigDec(3, 2); // 3.33

Power and Sqrt

var a = new BigDec(12.34);
var b = a.Sqrt();
Console.WriteLine("{0}", b); // 3.51283361405005916
var c = b * b;
Console.WriteLine("{0}", c - a); // -0.000000000000000005

Ln & Exp

var a = new BigDec(12.34);
var b = a.Pow(15.58m);
Console.WriteLine("{0}", a); // 12.34
Console.WriteLine("{0}", b); // 100621361186662831.979620536026973505
var c = a.Ln();
var d = c.Exp();
Console.WriteLine("{0}", a - d); // 0.000000000000000005

Parsing

var a = BigDec.Parse("-12.34");
Console.WriteLine("{0}", a); // -12.34
var b = BigDec.Parse("13.e+1");
var c = BigDec.Parse("13.37e+1");
Console.WriteLine("{0}", b); // 130
Console.WriteLine("{0}", c); // 133.7

Comparision

Console.WriteLine("{0}", new BigDec(12.34) / 2 == new BigDec(6.17m)); // True
Console.WriteLine("{0}", new BigDec(0.1) + new BigDec(0.2) == new BigDec(0.3)); // True
Console.WriteLine("{0}", new BigDec(0.1m) + new BigDec(0.2m) == new BigDec(0.3m)); // True
Console.WriteLine("{0}", new BigDec(0.1m) <= new BigDec(0.2m)); // True
Console.WriteLine("{0}", new BigDec(0.1m) > new BigDec(0.2m)); // False

Included constants

var diff = (BigDec.E - Math.E).Abs();
Console.WriteLine("{0}", diff <= 0.000_000_001m); // True

Console.WriteLine("{0}", BigDec.E);
Console.WriteLine("{0}", BigDec.PI);
Console.WriteLine("{0}", (new BigDec(1, 1000).Exp() - BigDec.E).Abs()); // 0.000...0002 (999 zeroes)
Console.WriteLine("{0}", new BigDec(1, 10000).ExpWithBigPrecision()); // can correctly calculate Euler's number to the demanded 10000 digits

Console.WriteLine("{0}", new BigDec(0).Pow(0)); // 1
var epsilon = BigDec.PowFractionOfTen(3); // 0.001
BigInteger a = BigDec.Pow10BigInt(5); // 100000

License

Licensed under the Apache License.

This software is provided "AS IS" WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.