ktsu.SignificantNumber

SignificantNumber is a numeric value type whose arithmetic follows the rules for significant figures. It holds a ktsu.PreciseNumber and rounds every result to the precision its operands justify.

Features

• Addition and subtraction round to the fewest decimal places among the operands, and multiplication, division, and modulus round to the fewest significant digits
• Operands of exactly -1, 0, or 1 have unlimited precision, so they never limit a result
• A readonly record struct whose default is zero, holding a PreciseNumber that it converts to implicitly
• Implements INumber<SignificantNumber>, including CreateChecked, CreateSaturating, and CreateTruncating for every built-in numeric type, BigInteger, and PreciseNumber

Upgrading from 1.x? See the 2.0 migration guide.

Table of contents

• Performance
• 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

Performance

Every release measures a fixed set of benchmarks and adds a point to the chart; the numbers behind it are in docs/benchmarks/history.json, and the suite is SignificantNumber.Benchmarks.

Read the two halves differently. Allocation is exact — the same code allocates the same bytes on any machine, so a step in the top row is always a real change. Time is measured on shared CI runners, where the host a job happens to land on varies more than most releases do, so each time is divided by a reference workload measured in the same job. That cancels most of the difference between machines; what is left is indicative rather than precise.

The step at 2.0 is the type becoming a readonly record struct over PreciseNumber instead of deriving from it. A 200-digit addition went from 54,688 bytes and 128 μs to 112 bytes and 340 ns.

Installation

Install the package with the .NET CLI:

dotnet add package ktsu.SignificantNumber

Or add the package reference directly in your project file:

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

Usage

Creating a SignificantNumber

Create a SignificantNumber from any supported numeric type with the ToSignificantNumber extension method, from text with Parse, or from a PreciseNumber with an explicit cast.

Supported numeric types

ToSignificantNumber converts through INumber<T>. These types are supported:

• Integer types:

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

• Floating point types:

  • double
  • float
  • Half
  • decimal

• ktsu types:

  • PreciseNumber
  • SignificantNumber

Examples

using System.Numerics;
using ktsu.PreciseNumber;
using ktsu.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();

// A PreciseNumber, with an explicit cast because it opts into the significant figure rules
PreciseNumber precise = 12.5.ToPreciseNumber();
SignificantNumber significantNumberFromPrecise = (SignificantNumber)precise;

Arithmetic operations

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

// Square and cube operations, which return the unrounded PreciseNumber
PreciseNumber squared = number1.Squared();
PreciseNumber cubed = number1.Cubed();

// Power operation
SignificantNumber powerResult = number1.Pow(3.ToPreciseNumber());

The operators also accept a PreciseNumber on either side, and the result is a SignificantNumber.

Comparison operations

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

Ordering operators compare values exactly. SignificantNumber.CompareTo(left, right) and CompareTo(SignificantNumber) compare both numbers at the lower of their significant digit counts.

Formatting and parsing

Format a SignificantNumber as a string:

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

Parse one from text, including scientific notation:

SignificantNumber parsed = SignificantNumber.Parse("1.23E4", NumberStyles.Float, CultureInfo.InvariantCulture);

if (SignificantNumber.TryParse("123.45", CultureInfo.InvariantCulture, out SignificantNumber result))
{
    Console.WriteLine(result);
}

TryParse yields zero when parsing fails.

Extension methods

ToSignificantNumber

Converts a supported numeric type to a SignificantNumber. An overload takes the number of significant digits to keep.

Usage

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

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

Parameters

• input: The number to convert.
• significantDigits: The number of significant digits to keep. It must be greater than zero.

Returns

• SignificantNumber: The converted number.

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>

Returns

• TOutput: The converted value of the SignificantNumber.

Example

SignificantNumber significantNumber = SignificantNumber.Parse("12345E3", NumberStyles.Float, CultureInfo.InvariantCulture);
double result = significantNumber.To<double>();
Console.WriteLine(result);  // Outputs 12345000

Generic code converts the same way through CreateChecked, CreateSaturating, and CreateTruncating:

static T ToMeters<T>(T feet) where T : INumber<T> => feet * T.CreateChecked(0.3048);

SignificantNumber meters = ToMeters(10.ToSignificantNumber());
double asDouble = double.CreateChecked(meters);

A SignificantNumber converts to a PreciseNumber implicitly, and Value returns the PreciseNumber it holds.

Precision

Significand and exponent

A SignificantNumber holds a PreciseNumber, which stores two components:

• Significand: The significant digits of the number, stored as a BigInteger.
• Exponent: The power of ten that scales the significand.

Significand, Exponent, and SignificantDigits are available directly on SignificantNumber.

Precision handling

• Floating point input: A float keeps up to 8 significant digits, and a double up to 16.
• Trailing zero removal: Trailing zeros move from the significand into the exponent, so every value is stored in its most compact form.
• Rounding: Round rounds to a number of decimal digits, and ReduceSignificance to a number of significant digits.

Example of precision

Consider the number 123.456000:

• As a SignificantNumber, it's stored as 123456e-3 after removing the trailing zeros and adjusting the exponent.
• Adding 1.2 to it rounds the sum to one decimal place, giving 124.7, because 1.2 has the fewest decimal places.

API reference

Properties

• PreciseNumber Value - Gets the PreciseNumber the number holds.
• int Exponent, BigInteger Significand, and int SignificantDigits - Get the components of the held value.
• static SignificantNumber NegativeOne, One, and Zero - Get -1, 1, and 0. Zero is also default.
• static SignificantNumber E, Pi, and Tau - Get the mathematical constants.
• static int Radix - Gets the radix, or base, for the type.
• static SignificantNumber AdditiveIdentity - Gets the additive identity of the type.
• static SignificantNumber MultiplicativeIdentity - Gets the multiplicative identity of the type.

Methods

• bool Equals(SignificantNumber other) - Determines whether two numbers have the same significand and exponent.
• int CompareTo(object? obj) - Compares the current instance with another object.
• int CompareTo(SignificantNumber other) - Compares the current instance with another significant number at the lower of their significant digit counts.
• int CompareTo<TInput>(TInput other) where TInput : INumber<TInput> - Compares the value of the current instance with another number.
• PreciseNumber Abs() - Returns the absolute value of the current instance.
• PreciseNumber Round(int decimalDigits) - Rounds the current instance to the specified number of decimal digits.
• PreciseNumber ReduceSignificance(int significantDigits) - Reduces the current instance to the specified number of significant digits.
• PreciseNumber Clamp<TNumber>(TNumber min, TNumber max) where TNumber : INumber<TNumber> - Clamps the current instance between the minimum and maximum values.
• SignificantNumber Pow(PreciseNumber power) - Raises the current instance to a power.
• PreciseNumber ToPreciseNumber() - Returns the PreciseNumber the number holds.
• string ToString(string? format, IFormatProvider? formatProvider) - Converts the current instance to a string 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 FromPreciseNumber(PreciseNumber value) - Creates a significant number that holds a PreciseNumber.
• static SignificantNumber Add, Subtract, Multiply, Divide, and Mod(PreciseNumber left, PreciseNumber right) - Apply the significant figure rules to two numbers.
• static SignificantNumber Exp(PreciseNumber power) - Raises e to a power.
• static SignificantNumber Max, Min(SignificantNumber x, SignificantNumber y), and Clamp(SignificantNumber value, SignificantNumber min, SignificantNumber max) - Compare by value.
• static SignificantNumber Round(SignificantNumber value, int decimalDigits) - Rounds a number to the specified number of decimal digits.
• 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 implicit operator PreciseNumber(SignificantNumber value) - Converts to the held PreciseNumber.
• static explicit operator SignificantNumber(PreciseNumber value) - Creates a significant number that holds a PreciseNumber.
• static SignificantNumber operator -(SignificantNumber value) - Negates a significant number.
• static SignificantNumber operator +, -, *, /, and % - Apply the significant figure rules. Each also accepts a PreciseNumber on either side.
• static SignificantNumber operator +(SignificantNumber value) - Returns the unary plus of a significant number.
• static SignificantNumber operator ++ and -- - Increment and decrement by one.
• static bool operator == and != - Determine whether two numbers are equal, including against a PreciseNumber.
• static bool operator >, <, >=, and <= - Compare two numbers, including against a PreciseNumber.

Contributing

Contributions are welcome. Submit a pull request or open an issue.

License

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