BigInteger Structure

Represents an integer of arbitrary size.

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4

[SerializableAttribute]
public readonly struct BigInteger : IComparable, 
	IFormattable, IConvertible, IEquatable<BigInteger>, IComparable<BigInteger>, 
	IEquatable<int>, IComparable<int>, IBinaryInteger<BigInteger>, 
	IParsable<BigInteger>, ISpanFormattable, ISpanParsable<BigInteger>, 
	IAdditionOperators<BigInteger, BigInteger, BigInteger>, IAdditiveIdentity<BigInteger, BigInteger>, 
	IBinaryNumber<BigInteger>, IBitwiseOperators<BigInteger, BigInteger, BigInteger>, 
	IComparisonOperators<BigInteger, BigInteger, bool>, IEqualityOperators<BigInteger, BigInteger, bool>, 
	IDecrementOperators<BigInteger>, IDivisionOperators<BigInteger, BigInteger, BigInteger>, 
	IIncrementOperators<BigInteger>, IModulusOperators<BigInteger, BigInteger, BigInteger>, 
	IMultiplicativeIdentity<BigInteger, BigInteger>, IMultiplyOperators<BigInteger, BigInteger, BigInteger>, 
	INumber<BigInteger>, INumberBase<BigInteger>, IUtf8SpanFormattable, 
	IUtf8SpanParsable<BigInteger>, ISubtractionOperators<BigInteger, BigInteger, BigInteger>, 
	IUnaryNegationOperators<BigInteger, BigInteger>, IUnaryPlusOperators<BigInteger, BigInteger>, 
	IShiftOperators<BigInteger, int, BigInteger>, ISignedNumber<BigInteger>

Visual Basic

<SerializableAttribute>
Public Structure BigInteger
	Implements IComparable, IFormattable, IConvertible, IEquatable(Of BigInteger), 
	IComparable(Of BigInteger), IEquatable(Of Integer), 
	IComparable(Of Integer), IBinaryInteger(Of BigInteger), 
	IParsable(Of BigInteger), ISpanFormattable, ISpanParsable(Of BigInteger), 
	IAdditionOperators(Of BigInteger, BigInteger, BigInteger), IAdditiveIdentity(Of BigInteger, BigInteger), 
	IBinaryNumber(Of BigInteger), IBitwiseOperators(Of BigInteger, BigInteger, BigInteger), 
	IComparisonOperators(Of BigInteger, BigInteger, Boolean), IEqualityOperators(Of BigInteger, BigInteger, Boolean), 
	IDecrementOperators(Of BigInteger), IDivisionOperators(Of BigInteger, BigInteger, BigInteger), 
	IIncrementOperators(Of BigInteger), IModulusOperators(Of BigInteger, BigInteger, BigInteger), 
	IMultiplicativeIdentity(Of BigInteger, BigInteger), IMultiplyOperators(Of BigInteger, BigInteger, BigInteger), 
	INumber(Of BigInteger), INumberBase(Of BigInteger), IUtf8SpanFormattable, 
	IUtf8SpanParsable(Of BigInteger), ISubtractionOperators(Of BigInteger, BigInteger, BigInteger), 
	IUnaryNegationOperators(Of BigInteger, BigInteger), IUnaryPlusOperators(Of BigInteger, BigInteger), 
	IShiftOperators(Of BigInteger, Integer, BigInteger), ISignedNumber(Of BigInteger)

C++/CLI

[SerializableAttribute]
public value class BigInteger : IComparable, 
	IFormattable, IConvertible, IEquatable<BigInteger>, IComparable<BigInteger>, 
	IEquatable<int>, IComparable<int>, IBinaryInteger<BigInteger>, 
	IParsable<BigInteger>, ISpanFormattable, ISpanParsable<BigInteger>, 
	IAdditionOperators<BigInteger, BigInteger, BigInteger>, IAdditiveIdentity<BigInteger, BigInteger>, 
	IBinaryNumber<BigInteger>, IBitwiseOperators<BigInteger, BigInteger, BigInteger>, 
	IComparisonOperators<BigInteger, BigInteger, bool>, IEqualityOperators<BigInteger, BigInteger, bool>, 
	IDecrementOperators<BigInteger>, IDivisionOperators<BigInteger, BigInteger, BigInteger>, 
	IIncrementOperators<BigInteger>, IModulusOperators<BigInteger, BigInteger, BigInteger>, 
	IMultiplicativeIdentity<BigInteger, BigInteger>, IMultiplyOperators<BigInteger, BigInteger, BigInteger>, 
	INumber<BigInteger>, INumberBase<BigInteger>, IUtf8SpanFormattable, 
	IUtf8SpanParsable<BigInteger>, ISubtractionOperators<BigInteger, BigInteger, BigInteger>, 
	IUnaryNegationOperators<BigInteger, BigInteger>, IUnaryPlusOperators<BigInteger, BigInteger>, 
	IShiftOperators<BigInteger, int, BigInteger>, ISignedNumber<BigInteger>

[<SealedAttribute>]
[<SerializableAttribute>]
type BigInteger = 
    struct
        inherit ValueType
        interface IComparable
        interface IFormattable
        interface IConvertible
        interface IEquatable<BigInteger>
        interface IComparable<BigInteger>
        interface IEquatable<int>
        interface IComparable<int>
        interface IBinaryInteger<BigInteger>
        interface IParsable<BigInteger>
        interface ISpanFormattable
        interface ISpanParsable<BigInteger>
        interface IAdditionOperators<BigInteger, BigInteger, BigInteger>
        interface IAdditiveIdentity<BigInteger, BigInteger>
        interface IBinaryNumber<BigInteger>
        interface IBitwiseOperators<BigInteger, BigInteger, BigInteger>
        interface IComparisonOperators<BigInteger, BigInteger, bool>
        interface IEqualityOperators<BigInteger, BigInteger, bool>
        interface IDecrementOperators<BigInteger>
        interface IDivisionOperators<BigInteger, BigInteger, BigInteger>
        interface IIncrementOperators<BigInteger>
        interface IModulusOperators<BigInteger, BigInteger, BigInteger>
        interface IMultiplicativeIdentity<BigInteger, BigInteger>
        interface IMultiplyOperators<BigInteger, BigInteger, BigInteger>
        interface INumber<BigInteger>
        interface INumberBase<BigInteger>
        interface IUtf8SpanFormattable
        interface IUtf8SpanParsable<BigInteger>
        interface ISubtractionOperators<BigInteger, BigInteger, BigInteger>
        interface IUnaryNegationOperators<BigInteger, BigInteger>
        interface IUnaryPlusOperators<BigInteger, BigInteger>
        interface IShiftOperators<BigInteger, int, BigInteger>
        interface ISignedNumber<BigInteger>
    end

Inheritance: Object → ValueType → BigInteger

Implements: IComparable, IComparable<BigInteger>, IComparable<Int32>, IConvertible, IEquatable<BigInteger>, IEquatable<Int32>, IFormattable, IParsable<BigInteger>, ISpanFormattable, ISpanParsable<BigInteger>, IUtf8SpanFormattable, IUtf8SpanParsable<BigInteger>, IAdditionOperators<BigInteger, BigInteger, BigInteger>, IAdditiveIdentity<BigInteger, BigInteger>, IBinaryInteger<BigInteger>, IBinaryNumber<BigInteger>, IBitwiseOperators<BigInteger, BigInteger, BigInteger>, IComparisonOperators<BigInteger, BigInteger, Boolean>, IDecrementOperators<BigInteger>, IDivisionOperators<BigInteger, BigInteger, BigInteger>, IEqualityOperators<BigInteger, BigInteger, Boolean>, IIncrementOperators<BigInteger>, IModulusOperators<BigInteger, BigInteger, BigInteger>, IMultiplicativeIdentity<BigInteger, BigInteger>, IMultiplyOperators<BigInteger, BigInteger, BigInteger>, INumber<BigInteger>, INumberBase<BigInteger>, IShiftOperators<BigInteger, Int32, BigInteger>, ISignedNumber<BigInteger>, ISubtractionOperators<BigInteger, BigInteger, BigInteger>, IUnaryNegationOperators<BigInteger, BigInteger>, IUnaryPlusOperators<BigInteger, BigInteger>

Remarks

Use the BigInteger structure to represent integers that may be too large to fit into the built-in integer types. The BigInteger structure can exactly represent numbers up to about 646 million decimal digits.

Big integers can be constructed in a variety of ways, including from other numerical types and from strings. Implicit (widening) conversions are available for all built-in unsigned integer types. Explicit conversions from signed integer types as well as Single, Double and Decimal are also available.

The BigInteger structure provides methods for all the common operations on integers. Overloaded versions of the major arithmetic operators are provided for languages that support them. For languages that don't support operator overloading, equivalent static methods are supplied.

When performing a binary operation, if one of the operands is a BigInteger, then the other operand is required to also be an integral type. Prior to performing the operation, if the other operand is not a BigInteger, it is converted to BigInteger.

Constructors

BigInteger(Byte[])	Constructs a new BigInteger from a byte array containing a two's complement representation of the number.
BigInteger(Decimal)	Constructs a new BigInteger for a Decimal value.
BigInteger(Double)	Constructs a new BigInteger.
BigInteger(Int128)	Constructs a new BigInteger.
BigInteger(Int32)	Constructs a new BigInteger.
BigInteger(Int64)	Constructs a new BigInteger.
BigInteger(UInt128)	Constructs a new BigInteger.
BigInteger(UInt32)	Constructs a new BigInteger.
BigInteger(UInt32[])	Constructs a new BigInteger from raw data.
BigInteger(UInt64)	Constructs a new BigInteger.
BigInteger(Int32, Byte[])	Constructs a new BigInteger from a sign and a byte array.

Properties

BitCount	Gets the number of bits in the number.
DecimalDigitCount	Gets the number of decimal digits in the number.
IsEven	Gets whether the number is even.
IsOdd	Gets whether the number is odd.
IsOne	Gets whether the number equals 1.
IsPowerOfTwo	Gets whether the number is a power of two..
IsZero	Gets whether the number is zero.
Limbs
Sign	Gets the sign of this BigInteger: -1, 0, or 1.

Methods

Abs	Returns the absolute value of a number.
Add	Returns the sum of two BigInteger numbers.
BinomialCoefficients	Enumerates over the binomial coefficients of a specified degree.
Clamp	Clamps a value to an inclusive minimum and maximum value.
Compare	Compares two numbers.
CompareTo(BigInteger)	Compares a number to another number.
CompareTo(Int32)	Compares a number to another number.
CompareTo(Int64)	Compares a number to another number.
CopySign	Copies the sign of a value to the sign of another value.
Divide	Divides one BigInteger by another and returns the result.
DivRem(BigInteger, BigInteger)	Computes the quotient and remainder of two values.
DivRem(BigInteger, BigInteger, BigInteger)	Computes the quotient and remainder of two BigInteger numbers.
Equals(BigInteger)	Tests whether a number equals another number.
Equals(Int32)	Tests whether a number equals another number.
Equals(Object)	Returns whether this instance is equal to a specified object. (Overrides ValueType.Equals(Object))
ExtendedGreatestCommonDivisor	Returns the greatest common divisor (GCD) of two BigInteger numbers.
Factorial	Gets the factorial of a number.
Factorial2	Gets the double factorial of a number.
GetHashCode	Returns the hash code for this instance. (Overrides ValueType.GetHashCode())
GetType	Gets the Type of the current instance. (Inherited from Object)
GreatestCommonDivisor	Returns the greatest common divisor (GCD) of two BigInteger numbers.
IsBitSet
IsNegative	Determines if a value represents a negative real number.
IsPositive	Determines if a value represents zero or a positive real number.
IsPseudoPrime	Uses the Rabin-Miller test to determine if a number is pseudo-prime.
LeastCommonMultiple	Returns the least common multiple (LCM) of two BigInteger numbers.
LeftShift	Shifts the bits to the left, padding the right with zeros.
Log2	Computes the log2 of a value.
Max	Returns the largest of two numbers.
MaxMagnitude	Compares two values to compute which has the greater magnitude.
Min	Returns the smallest of two numbers.
MinMagnitude	Compares two values to compute which has the lesser magnitude.
Mod	Returns the remainder after dividing one BigInteger by another and returns the result.
ModularInverse	Computes the modular inverse of an integer with respect to the specified modulus.
ModularPow(BigInteger, BigInteger, BigInteger)	Raises a number to a power modulo another number.
ModularPow(BigInteger, Int32, BigInteger)	Raises a number to a power modulo another number.
Modulus	Returns the remainder after dividing one BigInteger by another and returns the result.
Multiply(BigInteger, BigInteger)	Returns the product of two BigInteger numbers.
Multiply(BigInteger, Int32)	Returns the product of a BigInteger number and an integer.
Multiply(BigInteger, UInt32)	Returns the product of a BigInteger number and an unsigned integer.
Multiply(Int32, BigInteger)	Returns the product of an integer and a BigInteger number.
Multiply(UInt32, BigInteger)	Returns the product of an unsigned integer and a BigInteger number.
Negate	Returns a BigInteger with the opposite sign.
Parse(String)	Converts the string representation of a number to its BigInteger equivalent.
Parse(ReadOnlySpan<Char>, IFormatProvider)	Parses a span of characters into a value.
Parse(String, NumberStyles)	Converts the string representation of a number in a specified style to its BigInteger equivalent.
Parse(String, IFormatProvider)	Converts the string representation of a number in a specified culture-specific format to its BigInteger equivalent.
Parse(ReadOnlySpan<Char>, NumberStyles, IFormatProvider)	Parses a span of characters into a value.
Parse(String, NumberStyles, IFormatProvider)	Converts the string representation of a number in a specified style and culture-specific format to its BigInteger equivalent.
Pow(BigInteger, Int32)	Raises a number to the specified power and returns the result as a BigInteger number.
Pow(Int32, Int32)	Raises a number to the specified power and returns the result as a BigInteger number.
Random	Returns a random BigInteger number with the specified number of bits.
RightShift(BigInteger, Int32)	Shifts the bits to the right, discarding bits on the right.
RightShift(BigInteger, Int32, RoundingMode)	Shifts the bits to the right with rounding.
Sqrt	Computes the integer square root of a number.
Square	Returns the square of a BigInteger number.
Subtract	Returns the difference between two BigInteger numbers.
ToByteArray	Converts a BigInteger value to a byte array.
ToString()	Returns a string representation of the number. (Overrides ValueType.ToString())
ToString(String)	Formats the value of the current instance using the specified format.
ToString(String, IFormatProvider)	Formats the value of the current instance using the specified format.
TryFormat	Tries to format the value of the current instance into the provided span of characters.
TryParse(String, BigInteger)	Converts the string representation of a number to its BigInteger equivalent. A return value indicates whether the conversion succeeded or failed.
TryParse(ReadOnlySpan<Char>, IFormatProvider, BigInteger)	Tries to parse a span of characters into a value.
TryParse(String, IFormatProvider, BigInteger)	Tries to parse a string into a value.
TryParse(ReadOnlySpan<Char>, NumberStyles, IFormatProvider, BigInteger)	Tries to parse a span of characters into a value.
TryParse(String, NumberStyles, IFormatProvider, BigInteger)	Converts the string representation of a number in a specified style and culture-specific format to its BigInteger equivalent. A return value indicates whether the conversion succeeded or failed.
Xor	Computes the bitwise exclusive or of two BigInteger values.

Operators

Addition(BigInteger, BigInteger)	Returns the sum of two BigInteger numbers.
Addition(BigInteger, Int32)	Returns the sum of a BigInteger and a 32 bit integer.
Addition(Int32, BigInteger)	Returns the sum of a 32 bit integer and a BigInteger.
BitwiseAnd(BigInteger, BigInteger)	Computes the bitwise and of two BigInteger values.
BitwiseOr(BigInteger, BigInteger)	Computes the bitwise and of two BigInteger values.
Decrement(BigInteger)	Decrements a value.
Division(BigInteger, BigInteger)	Divides one BigInteger by another and returns the result.
Division(BigInteger, Int32)	Divides one BigInteger by another and returns the result.
Equality(BigInteger, BigInteger)	Returns whether a BigInteger is equal to another and returns the result.
Equality(BigInteger, Int32)	Returns whether a BigInteger is equal to an integer.
Equality(Int32, BigInteger)	Returns whether a BigInteger is equal to an integer.
ExclusiveOr(BigInteger, BigInteger)	Computes the bitwise exclusive or of two BigInteger values.
Explicit(BigInteger to Byte)	Converts a BigInteger to a Byte value.
Explicit(BigInteger to Decimal)	Converts a BigInteger to a Decimal number.
Explicit(BigInteger to Double)	Converts a BigInteger to a double-precision floating-point number.
Explicit(BigInteger to Int16)	Converts a BigInteger to a Int16 value.
Explicit(BigInteger to Int32)	Converts a BigInteger to a Int32 value.
Explicit(BigInteger to Int64)	Converts a BigInteger to a long integer.
Explicit(BigInteger to SByte)	Converts a BigInteger to a SByte value.
Explicit(BigInteger to Single)	Converts a BigInteger to a single-precision floating-point number.
Explicit(BigInteger to UInt16)	Converts a BigInteger to a UInt16 value.
Explicit(BigInteger to UInt32)	Converts a BigInteger to an unsigned integer.
Explicit(BigInteger to UInt64)	Converts a BigInteger to a long unsigned integer.
Explicit(Decimal to BigInteger)	Converts a Decimal number to a BigInteger value.
Explicit(Double to BigInteger)	Converts a double-precision floating-point number to a BigInteger value.
Explicit(Single to BigInteger)	Converts a single-precision floating-point number to a BigInteger value.
Exponent(BigInteger, Int32)	Represents the exponentiation operator.
Exponentiation(BigInteger, Int32)	Represents the exponentiation operator.
GreaterThan(BigInteger, BigInteger)	Returns whether a BigInteger is greater than another and returns the result.
GreaterThan(BigInteger, Int32)	Returns whether an integer is greater than a BigInteger.
GreaterThan(Int32, BigInteger)	Returns whether an integer is greater than a BigInteger.
GreaterThanOrEqual(BigInteger, BigInteger)	Returns whether a BigInteger is greater than or equal to another and returns the result.
GreaterThanOrEqual(BigInteger, Int32)	Returns whether an integer is greater than or equal to a BigInteger.
GreaterThanOrEqual(Int32, BigInteger)	Returns whether an integer is greater than or equal to a BigInteger.
Implicit(Byte to BigInteger)	Converts a Byte value to a BigInteger number.
Implicit(Int128 to BigInteger)	Converts a 128 bit signed integer to a BigInteger value.
Implicit(Int16 to BigInteger)	Converts a 16 bit signed integer to a BigInteger value.
Implicit(Int32 to BigInteger)	Converts a 32 bit signed integer to a BigInteger value.
Implicit(Int64 to BigInteger)	Converts a 64 bit signed integer to a BigInteger value.
Implicit(SByte to BigInteger)	Converts a signed byte to a BigInteger value.
Implicit(UInt128 to BigInteger)	Converts a 128 bit unsigned integer to a BigInteger value.
Implicit(UInt16 to BigInteger)	Converts a 16 bit unsigned integer to a BigInteger value.
Implicit(UInt32 to BigInteger)	Converts a 32 bit unsigned integer to a BigInteger value.
Implicit(UInt64 to BigInteger)	Converts a 64 bit unsigned integer to a BigInteger value.
Increment(BigInteger)	Increments a value.
Inequality(BigInteger, BigInteger)	Returns whether a BigInteger is not equal to another and returns the result.
Inequality(BigInteger, Int32)	Returns whether a BigInteger is not equal to an integer.
Inequality(Int32, BigInteger)	Returns whether a BigInteger is not equal to an integer.
LeftShift(BigInteger, Int32)	Shifts the bits to the left, padding the right with zeros.
LessThan(BigInteger, BigInteger)	Returns whether a BigInteger is less than another and returns the result.
LessThan(BigInteger, Int32)	Returns whether an integer is less than a BigInteger.
LessThan(Int32, BigInteger)	Returns whether an integer is less than a BigInteger.
LessThanOrEqual(BigInteger, BigInteger)	Returns whether a BigInteger is less than or equal to another and returns the result.
LessThanOrEqual(BigInteger, Int32)	Returns whether an integer is less than or equal to a BigInteger.
LessThanOrEqual(Int32, BigInteger)	Returns whether an integer is less than or equal to a BigInteger.
Modulus(BigInteger, BigInteger)	Returns the remainder after dividing one BigInteger by another and returns the result.
Multiply(BigInteger, BigInteger)	Returns the product of two BigInteger numbers.
Multiply(BigInteger, Int32)	Returns the product of a BigInteger number and an integer.
Multiply(BigInteger, UInt32)	Returns the product of a BigInteger number and an unsigned integer.
Multiply(Int32, BigInteger)	Returns the product of an integer and a BigInteger number.
Multiply(UInt32, BigInteger)	Returns the product of an unsigned integer and a BigInteger number.
OnesComplement(BigInteger)	Returns the one's complement of a BigInteger.
RightShift(BigInteger, Int32)	Shifts the bits to the right, discarding bits on the right.
Subtraction(BigInteger, BigInteger)	Returns the difference between two BigInteger numbers.
Subtraction(BigInteger, Int32)
UnaryNegation(BigInteger)	Returns a BigInteger with the opposite sign.
UnaryPlus(BigInteger)	Returns the value of a BigInteger.

Fields

MaxValue	The largest possible BigInteger.
MinusOne	The number -1 as a BigInteger.
MinValue	The smallest possible BigInteger.
One	The number one as a BigInteger.
Zero	The number zero as a BigInteger.