ktsu.io.SignificantNumber

The SignificantNumber class represents a number with a significand and an exponent, enabling high-precision arithmetic operations that comply with calculation rules for significant figures. It provides a robust set of functionalities for mathematical computations and formatting.

Features

• High-precision arithmetic operations (addition, subtraction, multiplication, division)
• Support for significant figures and exponents
• Integration with .NET numerical interfaces
• Comprehensive error handling and validation

Table of Contents

• Installation
• Usage
  • Creating a SignificantNumber
    • Supported Numeric Types
    • Examples
  • Arithmetic Operations
  • Comparison Operations
  • Formatting and Parsing
  • Extension Methods
  • Conversion
• Precision
  • Significand and Exponent
  • Precision Handling
  • Example of Precision
• API Reference
• Contributing
• License

Installation

To install the SignificantNumber library, you can use the .NET CLI:

dotnet add package ktsu.io.SignificantNumber

Or, add the package reference directly in your project file:

<PackageReference Include="ktsu.io.SignificantNumber" Version="x.x.x" />

Usage

Creating a SignificantNumber

You can create a SignificantNumber from various numeric types using the ToSignificantNumber extension method:

Supported Numeric Types

The SignificantNumber class supports a wide range of numeric types through the ToSignificantNumber extension method, leveraging the INumber interface for conversions. The following types are supported:

• Integer Types:

  • int
  • long
  • short
  • sbyte
  • uint
  • ulong
  • ushort
  • byte
  • BigInteger

• Floating-Point Types:

  • double
  • float
  • Half
  • decimal

Examples

You can convert various numeric types to SignificantNumber using the ToSignificantNumber extension method:

using ktsu.io.SignificantNumber;

// Integer types
int intValue = 12345;
SignificantNumber significantNumberFromInt = intValue.ToSignificantNumber();

BigInteger bigIntValue = new BigInteger(9876543210);
SignificantNumber significantNumberFromBigInt = bigIntValue.ToSignificantNumber();

// Floating-point types
double doubleValue = 123.45;
SignificantNumber significantNumberFromDouble = doubleValue.ToSignificantNumber();

Half halfValue = (Half)123.45;
SignificantNumber significantNumberFromHalf = halfValue.ToSignificantNumber();

float floatValue = 123.45f;
SignificantNumber significantNumberFromFloat = floatValue.ToSignificantNumber();

decimal decimalValue = 123.45m;
SignificantNumber significantNumberFromDecimal = decimalValue.ToSignificantNumber();

Arithmetic Operations

You can perform various arithmetic operations on SignificantNumber instances:

var result1 = number1 + number2;
var result2 = number1 - number2;
var result3 = number1 * number2;
var result4 = number1 / number2;

// Square and cube operations
var squared = number1.Squared();
var cubed = number1.Cubed();

// Power operation
var powerResult = number1.Pow(3); // number1 raised to the power of 3

Comparison Operations

You can compare SignificantNumber instances using comparison operators:

bool isEqual = number1 == number2;
bool isGreater = number1 > number2;
bool isLessOrEqual = number1 <= number2;

Formatting and Parsing

You can format a SignificantNumber as a string:

string formatted = number1.ToString("G", CultureInfo.InvariantCulture);
Console.WriteLine(formatted);  // Outputs the formatted number

Parsing is not supported and will throw NotSupportedException:

try
{
    var parsedNumber = SignificantNumber.Parse("123.45", CultureInfo.InvariantCulture);
}
catch (NotSupportedException ex)
{
    Console.WriteLine(ex.Message);
}

Instead, you should parse the number as another numeric type and convert it to a SignificantNumber:

double parsedDouble = double.Parse("123.45", CultureInfo.InvariantCulture);
SignificantNumber significantNumberFromDouble = parsedDouble.ToSignificantNumber();

Extension Methods

ToSignificantNumber

Converts various numeric types to a SignificantNumber.

Usage:

public static SignificantNumber ToSignificantNumber<TInput>(this INumber<TInput> input)
    where TInput : INumber<TInput>

Parameters:

• input: The input number to convert.

Returns:

• SignificantNumber: The converted SignificantNumber.

Example:

double floatingPointValue = 123.45;
SignificantNumber significantNumberFromFloat = floatingPointValue.ToSignificantNumber();

int integerValue = 12345;
SignificantNumber significantNumberFromInt = integerValue.ToSignificantNumber();

SignificantNumber result = significantNumberFromFloat + significantNumberFromInt;
// result = 12468.45

Conversion

To<TOutput>

Converts a SignificantNumber to the specified numeric type.

Usage:

public TOutput To<TOutput>()
    where TOutput : INumber<TOutput>

Parameters:

• None

Returns:

• TOutput: The converted value of the SignificantNumber.

Example:

SignificantNumber significantNumber = new SignificantNumber(3, 12345); // 12345e3
double result = significantNumber.To<double>();
Console.WriteLine(result);  // Outputs 12345000

Precision

The SignificantNumber class is designed to handle high-precision arithmetic operations with significant figures and exponents.

Here's how it ensures precision:

Significand and Exponent

A SignificantNumber consists of two main components:

• Significand: This is the significant part of the number, stored as a BigInteger to accommodate a wide range of values with high precision.
• Exponent: This is the exponent part of the number, which scales the significand by a power of ten.

Precision Handling

• Maximum Significant Digits: When converting from a floating-point number to a SignificantNumber maximum number of significant digits is limited to 7 for float values, and 16 for double values.
• Trailing Zero Removal: The class automatically sanitizes the significand by removing trailing zeros, ensuring that the number is stored in its most compact and precise form.
• Rounding: You can round a SignificantNumber to a specified number of decimal digits, ensuring that you can control the precision of your calculations.

Example of Precision

Consider the number 123.456000:

• When stored as a SignificantNumber, it will be represented as 123456e-3 after removing the trailing zeros and adjusting the exponent accordingly.
• This ensures that the number is represented with the exact precision required for your calculations, without unnecessary trailing zeros.

By using the SignificantNumber class, you can perform high-precision arithmetic operations and maintain control over the significant figures and exponent, ensuring accurate and efficient mathematical computations.

API Reference

Properties

• static SignificantNumber NegativeOne - Gets the value -1 for the type.
• static SignificantNumber One - Gets the value 1 for the type.
• static SignificantNumber Zero - Gets the value 0 for the type.
• static int Radix - Gets the radix, or base, for the type.
• static SignificantNumber AdditiveIdentity - Gets the additive identity of the current type.
• static SignificantNumber MultiplicativeIdentity - Gets the multiplicative identity of the current type.

Methods

• bool Equals(SignificantNumber other) - Determines whether the specified object is equal to the current object.
• int CompareTo(object? obj) - Compares the current instance with another object.
• int CompareTo(SignificantNumber other) - Compares the current instance with another significant number.
• int CompareTo<TInput>(TInput other) where TInput : INumber<TInput> - Compares the current instance with another number.
• SignificantNumber Abs() - Returns the absolute value of the current instance.
• SignificantNumber Round(int decimalDigits) - Rounds the current instance to the specified number of decimal digits.
• SignificantNumber Clamp<TNumber>(TNumber min, TNumber max) where TNumber : INumber<TNumber> - Clamps the specified value between the minimum and maximum values.
• string ToString(string? format, IFormatProvider? formatProvider) - Converts the current instance to its equivalent string representation using the specified format and format provider.
• bool TryFormat(Span<char> destination, out int charsWritten, ReadOnlySpan<char> format, IFormatProvider? provider) - Attempts to format the current instance into the provided span.
• TOutput To<TOutput>() where TOutput : INumber<TOutput> - Converts the current significant number to the specified numeric type.

Static Methods

• static SignificantNumber Abs(SignificantNumber value) - Returns the absolute value of a SignificantNumber.
• static bool IsCanonical(SignificantNumber value) - Determines whether the specified value is canonical.
• static bool IsComplexNumber(SignificantNumber value) - Determines whether the specified value is a complex number.
• static bool IsEvenInteger(SignificantNumber value) - Determines whether the specified value is an even integer.
• static bool IsFinite(SignificantNumber value) - Determines whether the specified value is finite.
• static bool IsImaginaryNumber(SignificantNumber value) - Determines whether the specified value is an imaginary number.
• static bool IsInfinity(SignificantNumber value) - Determines whether the specified value is infinite.
• static bool IsInteger(SignificantNumber value) - Determines whether the specified value is an integer.
• static bool IsNaN(SignificantNumber value) - Determines whether the specified value is NaN.
• static bool IsNegative(SignificantNumber value) - Determines whether the specified value is negative.
• static bool IsNegativeInfinity(SignificantNumber value) - Determines whether the specified value is negative infinity.
• static bool IsNormal(SignificantNumber value) - Determines whether the specified value is normal.
• static bool IsOddInteger(SignificantNumber value) - Determines whether the specified value is an odd integer.
• static bool IsPositive(SignificantNumber value) - Determines whether the specified value is positive.
• static bool IsPositiveInfinity(SignificantNumber value) - Determines whether the specified value is positive infinity.
• static bool IsRealNumber(SignificantNumber value) - Determines whether the specified value is a real number.
• static bool IsSubnormal(SignificantNumber value) - Determines whether the specified value is subnormal.
• static bool IsZero(SignificantNumber value) - Determines whether the specified value is zero.
• static SignificantNumber MaxMagnitude(SignificantNumber x, SignificantNumber y) - Returns the larger of the magnitudes of two significant numbers.
• static SignificantNumber MaxMagnitudeNumber(SignificantNumber x, SignificantNumber y) - Returns the larger of the magnitudes of two significant numbers.
• static SignificantNumber MinMagnitude(SignificantNumber x, SignificantNumber y) - Returns the smaller of the magnitudes of two significant numbers.
• static SignificantNumber MinMagnitudeNumber(SignificantNumber x, SignificantNumber y) - Returns the smaller of the magnitudes of two significant numbers.

Operators

• static SignificantNumber operator -(SignificantNumber value) - Negates a significant number.
• static SignificantNumber operator -(SignificantNumber left, SignificantNumber right) - Subtracts one significant number from another.
• static bool operator !=(SignificantNumber left, SignificantNumber right) - Determines whether two significant numbers are not equal.
• static SignificantNumber operator *(SignificantNumber left, SignificantNumber right) - Multiplies two significant numbers.
• static SignificantNumber operator /(SignificantNumber left, SignificantNumber right) - Divides one significant number by another.
• static SignificantNumber operator +(SignificantNumber value) - Returns the unary plus of a significant number.
• static SignificantNumber operator +(SignificantNumber left, SignificantNumber right) - Adds two significant numbers.
• static bool operator ==(SignificantNumber left, SignificantNumber right) - Determines whether two significant numbers are equal.
• static bool operator >(SignificantNumber left, SignificantNumber right) - Determines whether one significant number is greater than another.
• static bool operator <(SignificantNumber left, SignificantNumber right) - Determines whether one significant number is less than another.
• static bool operator >=(SignificantNumber left, SignificantNumber right) - Determines whether one significant number is greater than or equal to another.
• static bool operator <=(SignificantNumber left, SignificantNumber right) - Determines whether one significant number is less than or equal to another.

Contributing

Contributions are welcome! Please feel free to submit a pull request or open an issue.

License

This project is licensed under the MIT License. See the LICENSE file for details.