Crypto++  5.6.4
Free C++ class library of cryptographic schemes
Classes | List of all members
Integer Class Reference

Multiple precision integer with arithmetic operations. More...

+ Inheritance diagram for Integer:

Classes

class  DivideByZero
 Exception thrown when division by 0 is encountered. More...
 
class  OpenPGPDecodeErr
 Exception thrown when an error is encountered decoding an OpenPGP integer. More...
 
class  RandomNumberNotFound
 Exception thrown when a random number cannot be found that satisfies the condition. More...
 

ENUMS, EXCEPTIONS, and TYPEDEFS

enum  Sign { POSITIVE =0, NEGATIVE =1 }
 Used internally to represent the integer. More...
 
enum  Signedness { UNSIGNED, SIGNED }
 Used when importing and exporting integers. More...
 
enum  RandomNumberType { ANY, PRIME }
 Properties of a random integer. More...
 

CREATORS

 Integer ()
 Creates the zero integer.
 
 Integer (const Integer &t)
 copy constructor
 
 Integer (signed long value)
 Convert from signed long.
 
 Integer (Sign sign, lword value)
 Convert from lword. More...
 
 Integer (Sign sign, word highWord, word lowWord)
 Convert from two words. More...
 
 Integer (const char *str, ByteOrder order=BIG_ENDIAN_ORDER)
 Convert from a C-string. More...
 
 Integer (const wchar_t *str, ByteOrder order=BIG_ENDIAN_ORDER)
 Convert from a wide C-string. More...
 
 Integer (const byte *encodedInteger, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order=BIG_ENDIAN_ORDER)
 Convert from a big-endian byte array. More...
 
 Integer (BufferedTransformation &bt, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order=BIG_ENDIAN_ORDER)
 Convert from a big-endian array. More...
 
 Integer (BufferedTransformation &bt)
 Convert from a BER encoded byte array. More...
 
 Integer (RandomNumberGenerator &rng, size_t bitCount)
 Create a random integer. More...
 
 Integer (RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One())
 Create a random integer of special form. More...
 
static const IntegerZero ()
 Integer representing 0. More...
 
static const IntegerOne ()
 Integer representing 1. More...
 
static const IntegerTwo ()
 Integer representing 2. More...
 
static Integer Power2 (size_t e)
 Exponentiates to a power of 2. More...
 

ENCODE/DECODE

size_t MinEncodedSize (Signedness sign=UNSIGNED) const
 The minimum number of bytes to encode this integer. More...
 
void Encode (byte *output, size_t outputLen, Signedness sign=UNSIGNED) const
 Encode in big-endian format. More...
 
void Encode (BufferedTransformation &bt, size_t outputLen, Signedness sign=UNSIGNED) const
 Encode in big-endian format. More...
 
void DEREncode (BufferedTransformation &bt) const
 Encode in DER format. More...
 
void DEREncodeAsOctetString (BufferedTransformation &bt, size_t length) const
 encode absolute value as big-endian octet string More...
 
size_t OpenPGPEncode (byte *output, size_t bufferSize) const
 Encode absolute value in OpenPGP format. More...
 
size_t OpenPGPEncode (BufferedTransformation &bt) const
 Encode absolute value in OpenPGP format. More...
 
void Decode (const byte *input, size_t inputLen, Signedness sign=UNSIGNED)
 Decode from big-endian byte array. More...
 
void Decode (BufferedTransformation &bt, size_t inputLen, Signedness sign=UNSIGNED)
 Decode nonnegative value from big-endian byte array. More...
 
void BERDecode (const byte *input, size_t inputLen)
 Decode from BER format. More...
 
void BERDecode (BufferedTransformation &bt)
 Decode from BER format. More...
 
void BERDecodeAsOctetString (BufferedTransformation &bt, size_t length)
 Decode nonnegative value from big-endian octet string. More...
 
void OpenPGPDecode (const byte *input, size_t inputLen)
 Decode from OpenPGP format. More...
 
void OpenPGPDecode (BufferedTransformation &bt)
 Decode from OpenPGP format. More...
 

ACCESSORS

bool IsConvertableToLong () const
 Determines if the Integer is convertable to Long. More...
 
signed long ConvertToLong () const
 Convert the Integer to Long. More...
 
unsigned int BitCount () const
 Determines the number of bits required to represent the Integer. More...
 
unsigned int ByteCount () const
 Determines the number of bytes required to represent the Integer. More...
 
unsigned int WordCount () const
 Determines the number of words required to represent the Integer. More...
 
bool GetBit (size_t i) const
 Provides the i-th bit of the Integer. More...
 
byte GetByte (size_t i) const
 Provides the i-th byte of the Integer. More...
 
lword GetBits (size_t i, size_t n) const
 Provides the low order bits of the Integer. More...
 
bool IsZero () const
 Determines if the Integer is 0. More...
 
bool NotZero () const
 Determines if the Integer is non-0. More...
 
bool IsNegative () const
 Determines if the Integer is negative. More...
 
bool NotNegative () const
 Determines if the Integer is non-negative. More...
 
bool IsPositive () const
 Determines if the Integer is positive. More...
 
bool NotPositive () const
 Determines if the Integer is non-positive. More...
 
bool IsEven () const
 Determines if the Integer is even parity. More...
 
bool IsOdd () const
 Determines if the Integer is odd parity. More...
 

MANIPULATORS

Integeroperator= (const Integer &t)
 
Integeroperator+= (const Integer &t)
 
Integeroperator-= (const Integer &t)
 
Integeroperator*= (const Integer &t)
 
Integeroperator/= (const Integer &t)
 
Integeroperator%= (const Integer &t)
 
Integeroperator/= (word t)
 
Integeroperator%= (word t)
 
Integeroperator<<= (size_t)
 
Integeroperator>>= (size_t)
 
void Randomize (RandomNumberGenerator &rng, size_t bitCount)
 Set this Integer to random integer. More...
 
void Randomize (RandomNumberGenerator &rng, const Integer &min, const Integer &max)
 Set this Integer to random integer. More...
 
bool Randomize (RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One())
 Set this Integer to random integer of special form. More...
 
bool GenerateRandomNoThrow (RandomNumberGenerator &rng, const NameValuePairs &params=g_nullNameValuePairs)
 
void GenerateRandom (RandomNumberGenerator &rng, const NameValuePairs &params=g_nullNameValuePairs)
 
void SetBit (size_t n, bool value=1)
 Set the n-th bit to value. More...
 
void SetByte (size_t n, byte value)
 Set the n-th byte to value. More...
 
void Negate ()
 Reverse the Sign of the Integer.
 
void SetPositive ()
 Sets the Integer to positive.
 
void SetNegative ()
 Sets the Integer to negative.
 
void swap (Integer &a)
 Swaps this Integer with another Integer.
 

UNARY OPERATORS

bool operator! () const
 
Integer operator+ () const
 
Integer operator- () const
 
Integeroperator++ ()
 
Integeroperator-- ()
 
Integer operator++ (int)
 
Integer operator-- (int)
 

BINARY OPERATORS

int Compare (const Integer &a) const
 Perform signed comparison. More...
 
Integer Plus (const Integer &b) const
 
Integer Minus (const Integer &b) const
 
Integer Times (const Integer &b) const
 
Integer DividedBy (const Integer &b) const
 
Integer Modulo (const Integer &b) const
 
Integer DividedBy (word b) const
 
word Modulo (word b) const
 
Integer operator>> (size_t n) const
 
Integer operator<< (size_t n) const
 

OTHER ARITHMETIC FUNCTIONS

Integer AbsoluteValue () const
 
Integer Doubled () const
 
Integer Squared () const
 
Integer SquareRoot () const
 extract square root, if negative return 0, else return floor of square root
 
bool IsSquare () const
 return whether this integer is a perfect square
 
bool IsUnit () const
 is 1 or -1
 
Integer MultiplicativeInverse () const
 return inverse if 1 or -1, otherwise return 0
 
Integer InverseMod (const Integer &n) const
 calculate multiplicative inverse of *this mod n More...
 
word InverseMod (word n) const
 
static void Divide (Integer &r, Integer &q, const Integer &a, const Integer &d)
 calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))
 
static void Divide (word &r, Integer &q, const Integer &a, word d)
 use a faster division algorithm when divisor is short
 
static void DivideByPowerOf2 (Integer &r, Integer &q, const Integer &a, unsigned int n)
 returns same result as Divide(r, q, a, Power2(n)), but faster
 
static Integer Gcd (const Integer &a, const Integer &n)
 greatest common divisor
 

INPUT/OUTPUT

std::istream & operator>> (std::istream &in, Integer &a)
 Extraction operator. More...
 
std::ostream & operator<< (std::ostream &out, const Integer &a)
 Insertion operator. More...
 

Additional Inherited Members

- Public Member Functions inherited from ASN1Object
virtual void BEREncode (BufferedTransformation &bt) const
 Encode this object into a BufferedTransformation. More...
 

Detailed Description

Multiple precision integer with arithmetic operations.

The Integer class can represent positive and negative integers with absolute value less than (256**sizeof(word))(256**sizeof(int)).

Internally, the library uses a sign magnitude representation, and the class has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is used to hold the representation. The second is a Sign, and its is used to track the sign of the Integer.

Definition at line 45 of file integer.h.

Member Enumeration Documentation

Used internally to represent the integer.

Sign is used internally to represent the integer. It is also used in a few API functions.

See also
Signedness
Enumerator
POSITIVE 

the value is positive or 0

NEGATIVE 

the value is negative

Definition at line 69 of file integer.h.

Used when importing and exporting integers.

Signedness is usually used in API functions.

See also
Sign
Enumerator
UNSIGNED 

an unsigned value

SIGNED 

a signed value

Definition at line 79 of file integer.h.

Properties of a random integer.

Enumerator
ANY 

a number with no special properties

PRIME 

a number which is probabilistically prime

Definition at line 87 of file integer.h.

Constructor & Destructor Documentation

Integer::Integer ( Sign  sign,
lword  value 
)

Convert from lword.

Parameters
signenumeration indicating Sign
valuethe long word

Definition at line 2894 of file integer.cpp.

Integer::Integer ( Sign  sign,
word  highWord,
word  lowWord 
)

Convert from two words.

Parameters
signenumeration indicating Sign
highWordthe high word
lowWordthe low word

Definition at line 2915 of file integer.cpp.

Integer::Integer ( const char *  str,
ByteOrder  order = BIG_ENDIAN_ORDER 
)
explicit

Convert from a C-string.

Parameters
strC-string value
orderbyte order

str can be in base 2, 8, 10, or 16. Base is determined by a case insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 3254 of file integer.cpp.

Integer::Integer ( const wchar_t *  str,
ByteOrder  order = BIG_ENDIAN_ORDER 
)
explicit

Convert from a wide C-string.

Parameters
strwide C-string value
orderbyte order

str can be in base 2, 8, 10, or 16. Base is determined by a case insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 3260 of file integer.cpp.

Integer::Integer ( const byte *  encodedInteger,
size_t  byteCount,
Signedness  sign = UNSIGNED,
ByteOrder  order = BIG_ENDIAN_ORDER 
)

Convert from a big-endian byte array.

Parameters
encodedIntegerbig-endian byte array
byteCountlength of the byte array
signenumeration indicating Signedness
orderbyte order

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 2962 of file integer.cpp.

Integer::Integer ( BufferedTransformation bt,
size_t  byteCount,
Signedness  sign = UNSIGNED,
ByteOrder  order = BIG_ENDIAN_ORDER 
)

Convert from a big-endian array.

Parameters
btBufferedTransformation object with big-endian byte array
byteCountlength of the byte array
signenumeration indicating Signedness
orderbyte order

Byte order was added at Crypto++ 5.7 to allow use of little-endian integers with curve25519, Poly1305 and Microsoft CAPI.

Definition at line 2945 of file integer.cpp.

Integer::Integer ( BufferedTransformation bt)
explicit

Convert from a BER encoded byte array.

Parameters
btBufferedTransformation object with BER encoded byte array

Definition at line 2982 of file integer.cpp.

Integer::Integer ( RandomNumberGenerator rng,
size_t  bitCount 
)

Create a random integer.

Parameters
rngRandomNumberGenerator used to generate material
bitCountthe number of bits in the resulting integer

The random integer created is uniformly distributed over [0, 2bitCount].

Definition at line 2987 of file integer.cpp.

Integer::Integer ( RandomNumberGenerator rng,
const Integer min,
const Integer max,
RandomNumberType  rnType = ANY,
const Integer equiv = Zero(),
const Integer mod = One() 
)

Create a random integer of special form.

Parameters
rngRandomNumberGenerator used to generate material
minthe minimum value
maxthe maximum value
rnTypeRandomNumberType to specify the type
equivthe equivalence class based on the parameter mod
modthe modulus used to reduce the equivalence class
Exceptions
RandomNumberNotFoundif the set is empty.

Ideally, the random integer created should be uniformly distributed over {x | min <= x <= max and x is of rnType and x % mod == equiv}. However the actual distribution may not be uniform because sequential search is used to find an appropriate number from a random starting point.

May return (with very small probability) a pseudoprime when a prime is requested and max > lastSmallPrime*lastSmallPrime. lastSmallPrime is declared in nbtheory.h.

Definition at line 2992 of file integer.cpp.

Member Function Documentation

const Integer & Integer::Zero ( )
static

Integer representing 0.

Returns
an Integer representing 0

Zero() avoids calling constructors for frequently used integers

Definition at line 3014 of file integer.cpp.

const Integer & Integer::One ( )
static

Integer representing 1.

Returns
an Integer representing 1

One() avoids calling constructors for frequently used integers

Definition at line 3019 of file integer.cpp.

const Integer & Integer::Two ( )
static

Integer representing 2.

Returns
an Integer representing 2

Two() avoids calling constructors for frequently used integers

Definition at line 3024 of file integer.cpp.

Integer Integer::Power2 ( size_t  e)
static

Exponentiates to a power of 2.

Returns
the Integer 2e
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 2998 of file integer.cpp.

size_t Integer::MinEncodedSize ( Signedness  sign = UNSIGNED) const

The minimum number of bytes to encode this integer.

Parameters
signenumeration indicating Signedness
Note
The MinEncodedSize() of 0 is 1.

Definition at line 3329 of file integer.cpp.

void Integer::Encode ( byte *  output,
size_t  outputLen,
Signedness  sign = UNSIGNED 
) const

Encode in big-endian format.

Parameters
outputbig-endian byte array
outputLenlength of the byte array
signenumeration indicating Signedness

Unsigned means encode absolute value, signed means encode two's complement if negative.

outputLen can be used to ensure an Integer is encoded to an exact size (rather than a minimum size). An exact size is useful, for example, when encoding to a field element size.

Definition at line 3341 of file integer.cpp.

void Integer::Encode ( BufferedTransformation bt,
size_t  outputLen,
Signedness  sign = UNSIGNED 
) const

Encode in big-endian format.

Parameters
btBufferedTransformation object
outputLenlength of the encoding
signenumeration indicating Signedness

Unsigned means encode absolute value, signed means encode two's complement if negative.

outputLen can be used to ensure an Integer is encoded to an exact size (rather than a minimum size). An exact size is useful, for example, when encoding to a field element size.

Definition at line 3348 of file integer.cpp.

void Integer::DEREncode ( BufferedTransformation bt) const
virtual

Encode in DER format.

Parameters
btBufferedTransformation object

Encodes the Integer using Distinguished Encoding Rules The result is placed into a BufferedTransformation object

Implements ASN1Object.

Definition at line 3363 of file integer.cpp.

void Integer::DEREncodeAsOctetString ( BufferedTransformation bt,
size_t  length 
) const

encode absolute value as big-endian octet string

Parameters
btBufferedTransformation object
lengththe number of mytes to decode

Definition at line 3385 of file integer.cpp.

size_t Integer::OpenPGPEncode ( byte *  output,
size_t  bufferSize 
) const

Encode absolute value in OpenPGP format.

Parameters
outputbig-endian byte array
bufferSizelength of the byte array
Returns
length of the output

OpenPGPEncode places result into a BufferedTransformation object and returns the number of bytes used for the encoding

Definition at line 3401 of file integer.cpp.

size_t Integer::OpenPGPEncode ( BufferedTransformation bt) const

Encode absolute value in OpenPGP format.

Parameters
btBufferedTransformation object
Returns
length of the output

OpenPGPEncode places result into a BufferedTransformation object and returns the number of bytes used for the encoding

Definition at line 3407 of file integer.cpp.

void Integer::Decode ( const byte *  input,
size_t  inputLen,
Signedness  sign = UNSIGNED 
)

Decode from big-endian byte array.

Parameters
inputbig-endian byte array
inputLenlength of the byte array
signenumeration indicating Signedness

Definition at line 3289 of file integer.cpp.

void Integer::Decode ( BufferedTransformation bt,
size_t  inputLen,
Signedness  sign = UNSIGNED 
)

Decode nonnegative value from big-endian byte array.

Parameters
btBufferedTransformation object
inputLenlength of the byte array
signenumeration indicating Signedness
Note
bt.MaxRetrievable() >= inputLen.

Definition at line 3295 of file integer.cpp.

void Integer::BERDecode ( const byte *  input,
size_t  inputLen 
)

Decode from BER format.

Parameters
inputbig-endian byte array
inputLenlength of the byte array

Definition at line 3370 of file integer.cpp.

void Integer::BERDecode ( BufferedTransformation bt)
virtual

Decode from BER format.

Parameters
btBufferedTransformation object

Implements ASN1Object.

Definition at line 3376 of file integer.cpp.

void Integer::BERDecodeAsOctetString ( BufferedTransformation bt,
size_t  length 
)

Decode nonnegative value from big-endian octet string.

Parameters
btBufferedTransformation object
lengthlength of the byte array

Definition at line 3392 of file integer.cpp.

void Integer::OpenPGPDecode ( const byte *  input,
size_t  inputLen 
)

Decode from OpenPGP format.

Parameters
inputbig-endian byte array
inputLenlength of the byte array

Definition at line 3416 of file integer.cpp.

void Integer::OpenPGPDecode ( BufferedTransformation bt)

Decode from OpenPGP format.

Parameters
btBufferedTransformation object

Definition at line 3422 of file integer.cpp.

bool Integer::IsConvertableToLong ( ) const

Determines if the Integer is convertable to Long.

Returns
true if *this can be represented as a signed long
See also
ConvertToLong()

Definition at line 2922 of file integer.cpp.

signed long Integer::ConvertToLong ( ) const

Convert the Integer to Long.

Returns
equivalent signed long if possible, otherwise undefined
See also
IsConvertableToLong()

Definition at line 2936 of file integer.cpp.

unsigned int Integer::BitCount ( ) const

Determines the number of bits required to represent the Integer.

Returns
number of significant bits = floor(log2(abs(*this))) + 1

Definition at line 3280 of file integer.cpp.

unsigned int Integer::ByteCount ( ) const

Determines the number of bytes required to represent the Integer.

Returns
number of significant bytes = ceiling(BitCount()/8)

Definition at line 3271 of file integer.cpp.

unsigned int Integer::WordCount ( ) const

Determines the number of words required to represent the Integer.

Returns
number of significant words = ceiling(ByteCount()/sizeof(word))

Definition at line 3266 of file integer.cpp.

bool Integer::GetBit ( size_t  i) const

Provides the i-th bit of the Integer.

Returns
the i-th bit, i=0 being the least significant bit

Definition at line 3046 of file integer.cpp.

byte Integer::GetByte ( size_t  i) const

Provides the i-th byte of the Integer.

Returns
the i-th byte

Definition at line 3068 of file integer.cpp.

lword Integer::GetBits ( size_t  i,
size_t  n 
) const

Provides the low order bits of the Integer.

Returns
n lowest bits of *this >> i

Definition at line 3083 of file integer.cpp.

bool Integer::IsZero ( ) const
inline

Determines if the Integer is 0.

Returns
true if the Integer is 0, false otherwise

Definition at line 326 of file integer.h.

bool Integer::NotZero ( ) const
inline

Determines if the Integer is non-0.

Returns
true if the Integer is non-0, false otherwise

Definition at line 329 of file integer.h.

bool Integer::IsNegative ( ) const
inline

Determines if the Integer is negative.

Returns
true if the Integer is negative, false otherwise

Definition at line 332 of file integer.h.

bool Integer::NotNegative ( ) const
inline

Determines if the Integer is non-negative.

Returns
true if the Integer is non-negative, false otherwise

Definition at line 335 of file integer.h.

bool Integer::IsPositive ( ) const
inline

Determines if the Integer is positive.

Returns
true if the Integer is positive, false otherwise

Definition at line 338 of file integer.h.

bool Integer::NotPositive ( ) const
inline

Determines if the Integer is non-positive.

Returns
true if the Integer is non-positive, false otherwise

Definition at line 341 of file integer.h.

bool Integer::IsEven ( ) const
inline

Determines if the Integer is even parity.

Returns
true if the Integer is even, false otherwise

Definition at line 344 of file integer.h.

bool Integer::IsOdd ( ) const
inline

Determines if the Integer is odd parity.

Returns
true if the Integer is odd, false otherwise

Definition at line 347 of file integer.h.

Integer& Integer::operator*= ( const Integer t)
inline
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 361 of file integer.h.

Integer& Integer::operator%= ( const Integer t)
inline
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 366 of file integer.h.

Integer& Integer::operator%= ( word  t)
inline
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 371 of file integer.h.

void Integer::Randomize ( RandomNumberGenerator rng,
size_t  bitCount 
)

Set this Integer to random integer.

Parameters
rngRandomNumberGenerator used to generate material
bitCountthe number of bits in the resulting integer

The random integer created is uniformly distributed over [0, 2bitCount].

Definition at line 3430 of file integer.cpp.

void Integer::Randomize ( RandomNumberGenerator rng,
const Integer min,
const Integer max 
)

Set this Integer to random integer.

Parameters
rngRandomNumberGenerator used to generate material
minthe minimum value
maxthe maximum value

The random integer created is uniformly distributed over [min, max].

Definition at line 3440 of file integer.cpp.

bool Integer::Randomize ( RandomNumberGenerator rng,
const Integer min,
const Integer max,
RandomNumberType  rnType,
const Integer equiv = Zero(),
const Integer mod = One() 
)

Set this Integer to random integer of special form.

Parameters
rngRandomNumberGenerator used to generate material
minthe minimum value
maxthe maximum value
rnTypeRandomNumberType to specify the type
equivthe equivalence class based on the parameter mod
modthe modulus used to reduce the equivalence class
Exceptions
RandomNumberNotFoundif the set is empty.

Ideally, the random integer created should be uniformly distributed over {x | min <= x <= max and x is of rnType and x % mod == equiv}. However the actual distribution may not be uniform because sequential search is used to find an appropriate number from a random starting point.

May return (with very small probability) a pseudoprime when a prime is requested and max > lastSmallPrime*lastSmallPrime. lastSmallPrime is declared in nbtheory.h.

Definition at line 3457 of file integer.cpp.

void Integer::SetBit ( size_t  n,
bool  value = 1 
)

Set the n-th bit to value.

0-based numbering.

Definition at line 3054 of file integer.cpp.

void Integer::SetByte ( size_t  n,
byte  value 
)

Set the n-th byte to value.

0-based numbering.

Definition at line 3076 of file integer.cpp.

int Integer::Compare ( const Integer a) const

Perform signed comparison.

Parameters
athe Integer to comapre
Return values
-1if *this < a
0if *this = a
1if *this > a

Definition at line 4130 of file integer.cpp.

Integer Integer::Times ( const Integer b) const
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 3916 of file integer.cpp.

Integer Integer::Modulo ( const Integer b) const
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4027 of file integer.cpp.

word Integer::Modulo ( word  b) const
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4078 of file integer.cpp.

Integer Integer::Squared ( ) const
inline
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 496 of file integer.h.

Integer Integer::InverseMod ( const Integer n) const

calculate multiplicative inverse of *this mod n

See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4198 of file integer.cpp.

word Integer::InverseMod ( word  n) const
See also
a_times_b_mod_c() and a_exp_b_mod_c()

Definition at line 4223 of file integer.cpp.

Friends And Related Function Documentation

std::istream& operator>> ( std::istream &  in,
Integer a 
)
friend

Extraction operator.

Parameters
ina reference to a std::istream
aa reference to an Integer
Returns
a reference to a std::istream reference

Definition at line 3576 of file integer.cpp.

std::ostream& operator<< ( std::ostream &  out,
const Integer a 
)
friend

Insertion operator.

Parameters
outa reference to a std::ostream
aa constant reference to an Integer
Returns
a reference to a std::ostream reference

The output integer responds to std::hex, std::oct, std::hex, std::upper and std::lower. The output includes the suffix h (for hex), . (dot, for dec) and o (for octal). There is currently no way to supress the suffix.

If you want to print an Integer without the suffix or using an arbitrary base, then use IntToString<Integer>().

See also
IntToString<Integer>

Definition at line 3601 of file integer.cpp.


The documentation for this class was generated from the following files: