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BigInteger Structure

Represents an arbitrarily large signed integer.

Namespace:  System.Numerics
Assemblies:   System.Runtime.Numerics (in System.Runtime.Numerics.dll)
  System.Numerics (in System.Numerics.dll)

public struct BigInteger : IComparable, 
	IComparable<BigInteger>, IEquatable<BigInteger>, IFormattable

The BigInteger type exposes the following members.

  NameDescription
Public methodSupported by Portable Class LibraryBigInteger(Byte[])Initializes a new instance of the BigInteger structure using the values in a byte array.
Public methodSupported by Portable Class LibraryBigInteger(Decimal)Initializes a new instance of the BigInteger structure using a Decimal value.
Public methodSupported by Portable Class LibraryBigInteger(Double)Initializes a new instance of the BigInteger structure using a double-precision floating-point value.
Public methodSupported by Portable Class LibraryBigInteger(Int32)Initializes a new instance of the BigInteger structure using a 32-bit signed integer value.
Public methodSupported by Portable Class LibraryBigInteger(Int64)Initializes a new instance of the BigInteger structure using a 64-bit signed integer value.
Public methodSupported by Portable Class LibraryBigInteger(Single)Initializes a new instance of the BigInteger structure using a single-precision floating-point value.
Public methodSupported by Portable Class LibraryBigInteger(UInt32)Initializes a new instance of the BigInteger structure using an unsigned 32-bit integer value.
Public methodSupported by Portable Class LibraryBigInteger(UInt64)Initializes a new instance of the BigInteger structure with an unsigned 64-bit integer value.
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  NameDescription
Public propertySupported by Portable Class LibraryIsEvenIndicates whether the value of the current BigInteger object is an even number.
Public propertySupported by Portable Class LibraryIsOneIndicates whether the value of the current BigInteger object is BigInteger.One.
Public propertySupported by Portable Class LibraryIsPowerOfTwoIndicates whether the value of the current BigInteger object is a power of two.
Public propertySupported by Portable Class LibraryIsZeroIndicates whether the value of the current BigInteger object is BigInteger.Zero.
Public propertyStatic memberSupported by Portable Class LibraryMinusOneGets a value that represents the number negative one (-1).
Public propertyStatic memberSupported by Portable Class LibraryOneGets a value that represents the number one (1).
Public propertySupported by Portable Class LibrarySignGets a number that indicates the sign (negative, positive, or zero) of the current BigInteger object.
Public propertyStatic memberSupported by Portable Class LibraryZeroGets a value that represents the number 0 (zero).
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  NameDescription
Public methodStatic memberSupported by Portable Class LibraryAbsGets the absolute value of a BigInteger object.
Public methodStatic memberSupported by Portable Class LibraryAddAdds two BigInteger values and returns the result.
Public methodStatic memberSupported by Portable Class LibraryCompareCompares two BigInteger values and returns an integer that indicates whether the first value is less than, equal to, or greater than the second value.
Public methodSupported by Portable Class LibraryCompareTo(BigInteger)Compares this instance to a second BigInteger and returns an integer that indicates whether the value of this instance is less than, equal to, or greater than the value of the specified object.
Public methodSupported by Portable Class LibraryCompareTo(Int64)Compares this instance to a signed 64-bit integer and returns an integer that indicates whether the value of this instance is less than, equal to, or greater than the value of the signed 64-bit integer.
Public methodCompareTo(Object)Compares this instance to a specified object and returns an integer that indicates whether the value of this instance is less than, equal to, or greater than the value of the specified object.
Public methodSupported by Portable Class LibraryCompareTo(UInt64)Compares this instance to an unsigned 64-bit integer and returns an integer that indicates whether the value of this instance is less than, equal to, or greater than the value of the unsigned 64-bit integer.
Public methodStatic memberSupported by Portable Class LibraryDivideDivides one BigInteger value by another and returns the result.
Public methodStatic memberSupported by Portable Class LibraryDivRemDivides one BigInteger value by another, returns the result, and returns the remainder in an output parameter.
Public methodSupported by Portable Class LibraryEquals(BigInteger)Returns a value that indicates whether the current instance and a specified BigInteger object have the same value.
Public methodSupported by Portable Class LibraryEquals(Int64)Returns a value that indicates whether the current instance and a signed 64-bit integer have the same value.
Public methodSupported by Portable Class LibraryEquals(Object)Returns a value that indicates whether the current instance and a specified object have the same value. (Overrides ValueType.Equals(Object).)
Public methodSupported by Portable Class LibraryEquals(UInt64)Returns a value that indicates whether the current instance and an unsigned 64-bit integer have the same value.
Public methodSupported by Portable Class LibraryGetHashCodeReturns the hash code for the current BigInteger object. (Overrides ValueType.GetHashCode().)
Public methodSupported by Portable Class LibraryGetTypeGets the Type of the current instance. (Inherited from Object.)
Public methodStatic memberSupported by Portable Class LibraryGreatestCommonDivisorFinds the greatest common divisor of two BigInteger values.
Public methodStatic memberSupported by Portable Class LibraryLog(BigInteger)Returns the natural (base e) logarithm of a specified number.
Public methodStatic memberSupported by Portable Class LibraryLog(BigInteger, Double)Returns the logarithm of a specified number in a specified base.
Public methodStatic memberSupported by Portable Class LibraryLog10Returns the base 10 logarithm of a specified number.
Public methodStatic memberSupported by Portable Class LibraryMaxReturns the larger of two BigInteger values.
Public methodStatic memberSupported by Portable Class LibraryMinReturns the smaller of two BigInteger values.
Public methodStatic memberSupported by Portable Class LibraryModPowPerforms modulus division on a number raised to the power of another number.
Public methodStatic memberSupported by Portable Class LibraryMultiplyReturns the product of two BigInteger values.
Public methodStatic memberSupported by Portable Class LibraryNegateNegates a specified BigInteger value.
Public methodStatic memberParse(String)Converts the string representation of a number to its BigInteger equivalent.
Public methodStatic memberParse(String, NumberStyles)Converts the string representation of a number in a specified style to its BigInteger equivalent.
Public methodStatic memberParse(String, IFormatProvider)Converts the string representation of a number in a specified culture-specific format to its BigInteger equivalent.
Public methodStatic memberParse(String, NumberStyles, IFormatProvider)Converts the string representation of a number in a specified style and culture-specific format to its BigInteger equivalent.
Public methodStatic memberSupported by Portable Class LibraryPowRaises a BigInteger value to the power of a specified value.
Public methodStatic memberSupported by Portable Class LibraryRemainderPerforms integer division on two BigInteger values and returns the remainder.
Public methodStatic memberSupported by Portable Class LibrarySubtractSubtracts one BigInteger value from another and returns the result.
Public methodSupported by Portable Class LibraryToByteArrayConverts a BigInteger value to a byte array.
Public methodSupported by Portable Class LibraryToString()Converts the numeric value of the current BigInteger object to its equivalent string representation. (Overrides ValueType.ToString().)
Public methodSupported by Portable Class LibraryToString(IFormatProvider)Converts the numeric value of the current BigInteger object to its equivalent string representation by using the specified culture-specific formatting information.
Public methodSupported by Portable Class LibraryToString(String)Converts the numeric value of the current BigInteger object to its equivalent string representation by using the specified format.
Public methodSupported by Portable Class LibraryToString(String, IFormatProvider)Converts the numeric value of the current BigInteger object to its equivalent string representation by using the specified format and culture-specific format information.
Public methodStatic memberTryParse(String, BigInteger)Tries to convert the string representation of a number to its BigInteger equivalent, and returns a value that indicates whether the conversion succeeded.
Public methodStatic memberTryParse(String, NumberStyles, IFormatProvider, BigInteger)Tries to convert the string representation of a number in a specified style and culture-specific format to its BigInteger equivalent, and returns a value that indicates whether the conversion succeeded.
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  NameDescription
Public operatorStatic memberSupported by Portable Class LibraryAdditionAdds the values of two specified BigInteger objects.
Public operatorStatic memberSupported by Portable Class LibraryBitwiseAndPerforms a bitwise And operation on two BigInteger values.
Public operatorStatic memberSupported by Portable Class LibraryBitwiseOrPerforms a bitwise Or operation on two BigInteger values.
Public operatorStatic memberSupported by Portable Class LibraryDecrementDecrements a BigInteger value by 1.
Public operatorStatic memberSupported by Portable Class LibraryDivisionDivides a specified BigInteger value by another specified BigInteger value by using integer division.
Public operatorStatic memberSupported by Portable Class LibraryEquality(BigInteger, Int64)Returns a value that indicates whether a BigInteger value and a signed long integer value are equal.
Public operatorStatic memberSupported by Portable Class LibraryEquality(BigInteger, BigInteger)Returns a value that indicates whether the values of two BigInteger objects are equal.
Public operatorStatic memberSupported by Portable Class LibraryEquality(BigInteger, UInt64)Returns a value that indicates whether a BigInteger value and an unsigned long integer value are equal.
Public operatorStatic memberSupported by Portable Class LibraryEquality(Int64, BigInteger)Returns a value that indicates whether a signed long integer value and a BigInteger value are equal.
Public operatorStatic memberSupported by Portable Class LibraryEquality(UInt64, BigInteger)Returns a value that indicates whether an unsigned long integer value and a BigInteger value are equal.
Public operatorStatic memberSupported by Portable Class LibraryExclusiveOrPerforms a bitwise exclusive Or (XOr) operation on two BigInteger values.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to Int16)Defines an explicit conversion of a BigInteger object to a 16-bit signed integer value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to Decimal)Defines an explicit conversion of a BigInteger object to a Decimal value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to Double)Defines an explicit conversion of a BigInteger object to a Double value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to Byte)Defines an explicit conversion of a BigInteger object to an unsigned byte value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to UInt64)Defines an explicit conversion of a BigInteger object to an unsigned 64-bit integer value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to Int32)Defines an explicit conversion of a BigInteger object to a 32-bit signed integer value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to SByte)Defines an explicit conversion of a BigInteger object to a signed 8-bit value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to Int64)Defines an explicit conversion of a BigInteger object to a 64-bit signed integer value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to Single)Defines an explicit conversion of a BigInteger object to a single-precision floating-point value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to UInt32)Defines an explicit conversion of a BigInteger object to an unsigned 32-bit integer value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(BigInteger to UInt16)Defines an explicit conversion of a BigInteger object to an unsigned 16-bit integer value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(Decimal to BigInteger)Defines an explicit conversion of a Decimal object to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(Double to BigInteger)Defines an explicit conversion of a Double value to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryExplicit(Single to BigInteger)Defines an explicit conversion of a Single object to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThan(BigInteger, Int64)Returns a value that indicates whether a BigInteger is greater than a 64-bit signed integer value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThan(BigInteger, BigInteger)Returns a value that indicates whether a BigInteger value is greater than another BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThan(BigInteger, UInt64)Returns a value that indicates whether a BigInteger value is greater than a 64-bit unsigned integer.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThan(Int64, BigInteger)Returns a value that indicates whether a 64-bit signed integer is greater than a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThan(UInt64, BigInteger)Returns a value that indicates whether a BigInteger value is greater than a 64-bit unsigned integer.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThanOrEqual(BigInteger, Int64)Returns a value that indicates whether a BigInteger value is greater than or equal to a 64-bit signed integer value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThanOrEqual(BigInteger, BigInteger)Returns a value that indicates whether a BigInteger value is greater than or equal to another BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThanOrEqual(BigInteger, UInt64)Returns a value that indicates whether a BigInteger value is greater than or equal to a 64-bit unsigned integer value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThanOrEqual(Int64, BigInteger)Returns a value that indicates whether a 64-bit signed integer is greater than or equal to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryGreaterThanOrEqual(UInt64, BigInteger)Returns a value that indicates whether a 64-bit unsigned integer is greater than or equal to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(Byte to BigInteger)Defines an implicit conversion of an unsigned byte to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(Int16 to BigInteger)Defines an implicit conversion of a signed 16-bit integer to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(Int32 to BigInteger)Defines an implicit conversion of a signed 32-bit integer to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(Int64 to BigInteger)Defines an implicit conversion of a signed 64-bit integer to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(SByte to BigInteger)Defines an implicit conversion of an 8-bit signed integer to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(UInt16 to BigInteger)Defines an implicit conversion of a 16-bit unsigned integer to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(UInt32 to BigInteger)Defines an implicit conversion of a 32-bit unsigned integer to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryImplicit(UInt64 to BigInteger)Defines an implicit conversion of a 64-bit unsigned integer to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryIncrementIncrements a BigInteger value by 1.
Public operatorStatic memberSupported by Portable Class LibraryInequality(BigInteger, Int64)Returns a value that indicates whether a BigInteger value and a 64-bit signed integer are not equal.
Public operatorStatic memberSupported by Portable Class LibraryInequality(BigInteger, BigInteger)Returns a value that indicates whether two BigInteger objects have different values.
Public operatorStatic memberSupported by Portable Class LibraryInequality(BigInteger, UInt64)Returns a value that indicates whether a BigInteger value and a 64-bit unsigned integer are not equal.
Public operatorStatic memberSupported by Portable Class LibraryInequality(Int64, BigInteger)Returns a value that indicates whether a 64-bit signed integer and a BigInteger value are not equal.
Public operatorStatic memberSupported by Portable Class LibraryInequality(UInt64, BigInteger)Returns a value that indicates whether a 64-bit unsigned integer and a BigInteger value are not equal.
Public operatorStatic memberSupported by Portable Class LibraryLeftShiftShifts a BigInteger value a specified number of bits to the left.
Public operatorStatic memberSupported by Portable Class LibraryLessThan(BigInteger, Int64)Returns a value that indicates whether a BigInteger value is less than a 64-bit signed integer.
Public operatorStatic memberSupported by Portable Class LibraryLessThan(BigInteger, BigInteger)Returns a value that indicates whether a BigInteger value is less than another BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryLessThan(BigInteger, UInt64)Returns a value that indicates whether a BigInteger value is less than a 64-bit unsigned integer.
Public operatorStatic memberSupported by Portable Class LibraryLessThan(Int64, BigInteger)Returns a value that indicates whether a 64-bit signed integer is less than a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryLessThan(UInt64, BigInteger)Returns a value that indicates whether a 64-bit unsigned integer is less than a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryLessThanOrEqual(BigInteger, Int64)Returns a value that indicates whether a BigInteger value is less than or equal to a 64-bit signed integer.
Public operatorStatic memberSupported by Portable Class LibraryLessThanOrEqual(BigInteger, BigInteger)Returns a value that indicates whether a BigInteger value is less than or equal to another BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryLessThanOrEqual(BigInteger, UInt64)Returns a value that indicates whether a BigInteger value is less than or equal to a 64-bit unsigned integer.
Public operatorStatic memberSupported by Portable Class LibraryLessThanOrEqual(Int64, BigInteger)Returns a value that indicates whether a 64-bit signed integer is less than or equal to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryLessThanOrEqual(UInt64, BigInteger)Returns a value that indicates whether a 64-bit unsigned integer is less than or equal to a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryModulusReturns the remainder that results from division with two specified BigInteger values.
Public operatorStatic memberSupported by Portable Class LibraryMultiplyMultiplies two specified BigInteger values.
Public operatorStatic memberSupported by Portable Class LibraryOnesComplementReturns the bitwise one's complement of a BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryRightShiftShifts a BigInteger value a specified number of bits to the right.
Public operatorStatic memberSupported by Portable Class LibrarySubtractionSubtracts a BigInteger value from another BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryUnaryNegationNegates a specified BigInteger value.
Public operatorStatic memberSupported by Portable Class LibraryUnaryPlusReturns the value of the BigInteger operand. (The sign of the operand is unchanged.)
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  NameDescription
Explicit interface implemetationPrivate methodSupported by Portable Class LibraryIComparable.CompareToCompares the current instance with another object of the same type and returns an integer that indicates whether the current instance precedes, follows, or occurs in the same position in the sort order as the other object.
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The BigInteger type is an immutable type that represents an arbitrarily large integer whose value in theory has no upper or lower bounds. The members of the BigInteger type closely parallel those of other integral types (the Byte, Int16, Int32, Int64, SByte, UInt16, UInt32, and UInt64 types). This type differs from the other integral types in the .NET Framework, which have a range indicated by their MinValue and MaxValue properties.

NoteNote

Because the BigInteger type is immutable (see Mutability and the BigInteger Structure) and because it has no upper or lower bounds, an OutOfMemoryException can be thrown for any operation that causes a BigInteger value to grow too large.

Instantiating a BigInteger Object

You can instantiate a BigInteger object in several ways:

  • You can use the new keyword and provide any integral or floating-point value as a parameter to the BigInteger constructor. (Floating-point values are truncated before they are assigned to the BigInteger.) The following example illustrates how to use the new keyword to instantiate BigInteger values.

    BigInteger bigIntFromDouble = new BigInteger(179032.6541);
    Console.WriteLine(bigIntFromDouble);
    BigInteger bigIntFromInt64 = new BigInteger(934157136952);
    Console.WriteLine(bigIntFromInt64);
    // The example displays the following output: 
    //   179032 
    //   934157136952		
    
  • You can declare a BigInteger variable and assign it a value just as you would any numeric type, as long as that value is an integral type. The following example uses assignment to create a BigInteger value from an Int64.

    long longValue = 6315489358112;      
    BigInteger assignedFromLong = longValue;
    Console.WriteLine(assignedFromLong);
    // The example displays the following output: 
    //   6315489358112
    
  • You can assign a decimal or floating-point value to a BigInteger object if you cast the value or convert it first. The following example explicitly casts (in C#) or converts (in Visual Basic) a Double and a Decimal value to a BigInteger.

    BigInteger assignedFromDouble = (BigInteger) 179032.6541;
    Console.WriteLine(assignedFromDouble);   
    BigInteger assignedFromDecimal = (BigInteger) 64312.65m;      
    Console.WriteLine(assignedFromDecimal);
    // The example displays the following output: 
    //   179032 
    //   64312      
    

These methods enable you to instantiate a BigInteger object whose value is in the range of one of the existing numeric types only. You can instantiate a BigInteger object whose value can exceed the range of the existing numeric types in one of three ways:

  • You can use the new keyword and provide a byte array of any size to the BigInteger.BigInteger constructor. For example:

    byte[] byteArray = { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0};
    BigInteger newBigInt = new BigInteger(byteArray);
    Console.WriteLine("The value of newBigInt is {0} (or 0x{0:x}).", newBigInt);    
    // The example displays the following output: 
    //   The value of newBigInt is 4759477275222530853130 (or 0x102030405060708090a).
    
  • You can call the Parse or TryParse methods to convert the string representation of a number to a BigInteger. For example:

    string positiveString = "91389681247993671255432112000000";
    string negativeString = "-90315837410896312071002088037140000";
    BigInteger posBigInt = 0;
    BigInteger negBigInt = 0;
    
    try {
       posBigInt = BigInteger.Parse(positiveString);
       Console.WriteLine(posBigInt);
    }
    catch (FormatException)
    {
       Console.WriteLine("Unable to convert the string '{0}' to a BigInteger value.", 
                         positiveString);
    }
    
    if (BigInteger.TryParse(negativeString, out negBigInt))
      Console.WriteLine(negBigInt);
    else
       Console.WriteLine("Unable to convert the string '{0}' to a BigInteger value.", 
                          negativeString);
    
    // The example displays the following output: 
    //   9.1389681247993671255432112E+31 
    //   -9.0315837410896312071002088037E+34
    
  • You can call a static (Shared in Visual Basic) BigInteger method that performs some operation on a numeric expression and returns a calculated BigInteger result. The following example does this by cubing UInt64.MaxValue and assigning the result to a BigInteger.

    BigInteger number = BigInteger.Pow(UInt64.MaxValue, 3);
    Console.WriteLine(number);
    // The example displays the following output: 
    //    6277101735386680762814942322444851025767571854389858533375
    

The uninitialized value of a BigInteger is Zero.

Performing Operations on BigInteger Values

You can use a BigInteger instance as you would use any other integral type. BigInteger overloads the standard numeric operators to enable you to perform basic mathematical operations such as addition, subtraction, division, multiplication, subtraction, negation, and unary negation. You can also use the standard numeric operators to compare two BigInteger values with each other. Like the other integral types, BigInteger also supports the bitwise And, Or, XOr, left shift, and right shift operators. For languages that do not support custom operators, the BigInteger structure also provides equivalent methods for performing mathematical operations. These include Add, Divide, Multiply, Negate, Subtract, and several others.

Many members of the BigInteger structure correspond directly to members of the other integral types. In addition, BigInteger adds members such as the following:

  • Sign, which returns a value that indicates the sign of a BigInteger value.

  • Abs, which returns the absolute value of a BigInteger value.

  • DivRem, which returns both the quotient and remainder of a division operation.

  • GreatestCommonDivisor, which returns the greatest common divisor of two BigInteger values.

Many of these additional members correspond to the members of the Math class, which provides the functionality to work with the primitive numeric types.

Mutability and the BigInteger Structure

The following example instantiates a BigInteger object and then increments its value by one.

BigInteger number = BigInteger.Multiply(Int64.MaxValue, 3);
number++;
Console.WriteLine(number);

Although this example appears to modify the value of the existing object, this is not the case. BigInteger objects are immutable, which means that internally, the common language runtime actually creates a new BigInteger object and assigns it a value one greater than its previous value. This new object is then returned to the caller.

NoteNote

The other numeric types in the .NET Framework are also immutable. However, because the BigInteger type has no upper or lower bounds, its values can grow extremely large and have a measurable impact on performance.

Although this process is transparent to the caller, it does incur a performance penalty. In some cases, especially when repeated operations are performed in a loop on very large BigInteger values, that performance penalty can be significant. For example, in the following example, an operation is performed repetitively up to a million times, and a BigInteger value is incremented by one every time the operation succeeds.

BigInteger number = Int64.MaxValue ^ 5;
int repetitions = 1000000;
// Perform some repetitive operation 1 million times. 
for (int ctr = 0; ctr <= repetitions; ctr++)
{
   // Perform some operation. If it fails, exit the loop. 
   if (! SomeOperationSucceeds()) break;
   // The following code executes if the operation succeeds.
   number++;
}

In such a case, you can improve performance by performing all intermediate assignments to an Int32 variable. The final value of the variable can then be assigned to the BigInteger object when the loop exits. The following example provides an illustration.

BigInteger number = Int64.MaxValue ^ 5;
int repetitions = 1000000;
int actualRepetitions = 0;
// Perform some repetitive operation 1 million times. 
for (int ctr = 0; ctr <= repetitions; ctr++)
{
   // Perform some operation. If it fails, exit the loop. 
   if (! SomeOperationSucceeds()) break;
   // The following code executes if the operation succeeds.
   actualRepetitions++;
}
number += actualRepetitions;

Working with Byte Arrays and Hexadecimal Strings

If you convert BigInteger values to byte arrays, or if you convert byte arrays to BigInteger values, you must consider the order of bytes. The BigInteger structure expects the individual bytes in a byte array to appear in little-endian order (that is, the lower-order bytes of the value precede the higher-order bytes). You can round-trip a BigInteger value by calling the ToByteArray method and then passing the resulting byte array to the BigInteger(Byte[]) constructor, as the following example shows.

BigInteger number = BigInteger.Pow(Int64.MaxValue, 2);     
Console.WriteLine(number);

// Write the BigInteger value to a byte array. 
byte[] bytes = number.ToByteArray();

// Display the byte array. 
foreach (byte byteValue in bytes)
   Console.Write("0x{0:X2} ", byteValue);
Console.WriteLine();

// Restore the BigInteger value from a Byte array.
BigInteger newNumber = new BigInteger(bytes);
Console.WriteLine(newNumber);
// The example displays the following output: 
//    8.5070591730234615847396907784E+37 
//    0x01 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0xFF 0xFF 0xFF 0xFF 0xFF 0xFF 0xFF 0x3F 
//     
//    8.5070591730234615847396907784E+37

To instantiate a BigInteger value from a byte array that represents a value of some other integral type, you can pass the integral value to the BitConverter.GetBytes method, and then pass the resulting byte array to the BigInteger(Byte[]) constructor. The following example instantiates a BigInteger value from a byte array that represents an Int16 value.

short originalValue = 30000;
Console.WriteLine(originalValue);

// Convert the Int16 value to a byte array. 
byte[] bytes = BitConverter.GetBytes(originalValue);

// Display the byte array. 
foreach (byte byteValue in bytes)
   Console.Write("0x{0} ", byteValue.ToString("X2"));
Console.WriteLine();

// Pass byte array to the BigInteger constructor.
BigInteger number = new BigInteger(bytes);
Console.WriteLine(number);
// The example displays the following output: 
//       30000 
//       0x30 0x75 
//       30000

The BigInteger structure assumes that negative values are stored by using two's complement representation. Because the BigInteger structure represents a numeric value with no fixed length, the BigInteger(Byte[]) constructor always interprets the most significant bit of the last byte in the array as a sign bit. To prevent the BigInteger(Byte[]) constructor from confusing the two's complement representation of a negative value with the sign and magnitude representation of a positive value, positive values in which the most significant bit of the last byte in the byte array would ordinarily be set should include an additional byte whose value is 0. For example, 0xC0 0xBD 0xF0 0xFF is the little-endian hexadecimal representation of either -1,000,000 or 4,293,967,296. Because the most significant bit of the last byte in this array is on, the value of the byte array would be interpreted by the BigInteger(Byte[]) constructor as -1,000,000. To instantiate a BigInteger whose value is positive, a byte array whose elements are 0xC0 0xBD 0xF0 0xFF 0x00 must be passed to the constructor. The following example illustrates this.

int negativeNumber = -1000000;
uint positiveNumber = 4293967296;

byte[] negativeBytes = BitConverter.GetBytes(negativeNumber); 
BigInteger negativeBigInt = new BigInteger(negativeBytes);
Console.WriteLine(negativeBigInt.ToString("N0"));

byte[] tempPosBytes = BitConverter.GetBytes(positiveNumber);
byte[] positiveBytes = new byte[tempPosBytes.Length + 1];
Array.Copy(tempPosBytes, positiveBytes, tempPosBytes.Length);
BigInteger positiveBigInt = new BigInteger(positiveBytes);
Console.WriteLine(positiveBigInt.ToString("N0")); 
// The example displays the following output: 
//    -1,000,000 
//    4,293,967,296      

Byte arrays created by the ToByteArray method from positive values include this extra zero-value byte. Therefore, the BigInteger structure can successfully round-trip values by assigning them to, and then restoring them from, byte arrays, as the following example shows.

BigInteger positiveValue = 15777216;
BigInteger negativeValue  = -1000000;

Console.WriteLine("Positive value: " + positiveValue.ToString("N0"));
byte[] bytes = positiveValue.ToByteArray();

foreach (byte byteValue in bytes)
   Console.Write("{0:X2} ", byteValue);
Console.WriteLine();
positiveValue = new BigInteger(bytes);
Console.WriteLine("Restored positive value: " + positiveValue.ToString("N0"));

Console.WriteLine();

Console.WriteLine("Negative value: " + negativeValue.ToString("N0"));
bytes = negativeValue.ToByteArray();
foreach (byte byteValue in bytes)
   Console.Write("{0:X2} ", byteValue);
Console.WriteLine();
negativeValue = new BigInteger(bytes);
Console.WriteLine("Restored negative value: " + negativeValue.ToString("N0"));
// The example displays the following output: 
//       Positive value: 15,777,216 
//       C0 BD F0 00 
//       Restored positive value: 15,777,216 
//        
//       Negative value: -1,000,000 
//       C0 BD F0 
//       Restored negative value: -1,000,000

However, you may need to add this additional zero-value byte to byte arrays that are created dynamically by the developer or that are returned by methods that convert unsigned integers to byte arrays (such as BitConverter.GetBytes(UInt16), BitConverter.GetBytes(UInt32), and BitConverter.GetBytes(UInt64)).

When parsing a hexadecimal string, the BigInteger.Parse(String, NumberStyles) and BigInteger.Parse(String, NumberStyles, IFormatProvider) methods assume that if the most significant bit of the first byte in the string is set, or if the first hexadecimal digit of the string represents the lower four bits of a byte value, the value is represented by using two's complement representation. For example, both "FF01" and "F01" represent the decimal value -255. To differentiate positive from negative values, positive values should include a leading zero. The relevant overloads of the ToString method, when they are passed the "X" format string, add a leading zero to the returned hexadecimal string for positive values. This makes it possible to round-trip BigInteger values by using the ToString and Parse methods, as the following example shows.

BigInteger negativeNumber = -1000000;
BigInteger positiveNumber  = 15777216;

string negativeHex = negativeNumber.ToString("X");
string positiveHex = positiveNumber.ToString("X");

BigInteger negativeNumber2, positiveNumber2;  
negativeNumber2 = BigInteger.Parse(negativeHex, 
                                   NumberStyles.HexNumber);
positiveNumber2 = BigInteger.Parse(positiveHex,
                                   NumberStyles.HexNumber);

Console.WriteLine("Converted {0:N0} to {1} back to {2:N0}.", 
                   negativeNumber, negativeHex, negativeNumber2);                                         
Console.WriteLine("Converted {0:N0} to {1} back to {2:N0}.", 
                   positiveNumber, positiveHex, positiveNumber2);                                         
// The example displays the following output: 
//       Converted -1,000,000 to F0BDC0 back to -1,000,000. 
//       Converted 15,777,216 to 0F0BDC0 back to 15,777,216.

However, the hexadecimal strings created by calling the ToString methods of the other integral types or the overloads of the ToString method that include a toBase parameter do not indicate the sign of the value or the source data type from which the hexadecimal string was derived. Successfully instantiating a BigInteger value from such a string requires some additional logic. The following example provides one possible implementation.

using System;
using System.Globalization;
using System.Numerics;

public struct HexValue
{
   public int Sign;
   public string Value;
}

public class Example
{
   public static void Main()
   {
      uint positiveNumber = 4039543321;
      int negativeNumber = -255423975;

      // Convert the numbers to hex strings.
      HexValue hexValue1, hexValue2;
      hexValue1.Value = positiveNumber.ToString("X");
      hexValue1.Sign = Math.Sign(positiveNumber);

      hexValue2.Value = Convert.ToString(negativeNumber, 16);
      hexValue2.Sign = Math.Sign(negativeNumber);

      // Round-trip the hexadecimal values to BigInteger values. 
      string hexString;
      BigInteger positiveBigInt, negativeBigInt;

      hexString = (hexValue1.Sign == 1 ? "0" : "") + hexValue1.Value;
      positiveBigInt = BigInteger.Parse(hexString, NumberStyles.HexNumber);      
      Console.WriteLine("Converted {0} to {1} and back to {2}.", 
                        positiveNumber, hexValue1.Value, positiveBigInt);

      hexString = (hexValue2.Sign == 1 ? "0" : "") + hexValue2.Value;
      negativeBigInt = BigInteger.Parse(hexString, NumberStyles.HexNumber);      
      Console.WriteLine("Converted {0} to {1} and back to {2}.", 
                        negativeNumber, hexValue2.Value, negativeBigInt);
   }
}
// The example displays the following output: 
//       Converted 4039543321 to F0C68A19 and back to 4039543321. 
//       Converted -255423975 to f0c68a19 and back to -255423975.

.NET Framework

Supported in: 4.6, 4.5, 4

.NET Framework Client Profile

Supported in: 4

Portable Class Library

Supported in: Portable Class Library

Supported in: Windows Phone 8.1

Any public static (Shared in Visual Basic) members of this type are thread safe. Any instance members are not guaranteed to be thread safe.
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