FBB::BigInt(3bobcat)
Big Integers
(libbobcat-dev_6.06.02)
2005-2024
NAME
FBB::BigInt - Arithmetic on Integers of Unlimited Size
SYNOPSIS
    #include <bobcat/bigint>
    Linking option: -lbobcat -lcrypto
DESCRIPTION
This class is defined as a wrapper class around the openSSL BN series
of functions, offering members to perform arithmetic on integral values of
unlimited sizes. Members are offered to generate primes and to perform all
kinds of common arithmetic operations on BigInt objects. Also, conversions
to characters and standard numerical value types are offered.
Below, the phrase the object may also refer to the object's value. The
context in which this occurs will make clear that the object's value rather
than the object as-is is referred to.
Various constructors accept BIGNUM arguments. Type BIGNUM is the type
containing an integer of unlimited precision as defined by OpenSSL.
BIGNUM's definition is
        
    typedef struct bignum_st BIGNUM;
    struct bignum_st
    {
        BN_ULONG *d;    // Pointer to an array of 'BN_BITS2' bit chunks.
        int top;        // Index of last used d +1.
        // The next are internal book keeping for bn_expand.
        int dmax;       // Size of the d array.
        int neg;        // one if the number is negative
        int flags;
    };
        
Signs of BigInt are handled in a special way. Whether a BigInt is
negative or positive is determined by its sign-flag, and not by a sign bit as
is the case with int typed values. Since BigInt values have unlimited
precision shifting values to the left won't change their signs.
Operators return either a reference to the current (modified) object or return
a BigInt object containing the computed value. The rule followed here was
to implement the operators analogously to the way the operators work on
int type values and variables. E.g., operator+() returns a BigInt
value whereas operator+=() returns a BigInt & reference.
All members modifying their objects return a reference to the current
(modified) object. All members not modifying the current object return a
BigInt object. If both members exists performing the same
functionality the name of the member returning a BigInt object ends
in a c (const) (e.g., addMod and addModc).
Almost all operators, members and constructors (except for the default
constructor) throw Exception exceptions on failure.
INHERITS FROM
    -
TYPE
The class BigInt defines the type Word, which is equal to the type
BN_ULONG used by OpenSSL to store integral values of unlimited
precision. A Word is an unsigned long, which is, depending on the
architecture, usually 64 or 32 bits long.
ENUMERATIONS
    Msb
    This (most significant bit) enumeration is used when generating a
        cryptographically strong random number. Its values are:
    
    -  MSB_UNKNOWN:
 The most significant bit may be 0 or 1.
-  MSB_IS_ONE:
 The most significant bit is guaranteed to be 1.
-  TOP_TWO_BITS_ONE:
 The two most significant bits are guaranteed to be 1, resulting in a
        product of two values each containing nBits having 2 * nBits
        bits.
Lsb
    This (least significant bit) enumeration is used when generating random
        numbers, ensuring that the resulting value is either odd or even.
    
    -  EVEN:
 The random value will be an even value;
-  ODD:
 The random value will be an odd value.
CONSTRUCTORS
    -  BigInt():
 The default constructor initializes a BigInt value to 0;
-  explicit BigInt(BIGNUM const &value):
 This constructor initializes a BigInt from a const BIGNUM;
-  explicit BigInt(BIGNUM const *value):
 This constructor initializes a BigInt from a pointer to a
        const BIGNUM;
-  explicit BigInt(BIGNUM *value):
 This constructor initializes a
        BigInt from a pointer to a BIGNUM (the BIGNUM value
        pointed to by value is not mondified by the constructor.
        This constructor is a mere wrapper around the previous
        constructor). Note that none of the constructors expecting a
        BIGNUM argument modify their argument. If the memory used by the
        BIGNUM argument must be returned to the common pool an explicit
        BN_free(3ssl) call is required;
-  BigInt(Type value):
 This constructor is defined as a member template. Any type that can be
        converted using a static cast to an unsigned long can be used as
        argument to this constructor. Promotion is allowed, so in many
        situations where BigInts are expected a plain numerical value can
        be used as well;
-  BigInt(char const *bigEndian, size_t length, bool negative = false):
 This constructor initializes a BigInt from length big-endian
        encoded bytes stored in bigEndian (having its most significant
        value at index 0). This constructor interprets the char values
        pointed at by bigEndian as unsigned values. Use this constructor
        to reconstruct a BigInt object from the data made available by the
        bigEndian member (most significant byte at index 0). If the number
        represents a negative value, then provide a third argument true;
-  explicit BigInt(std::string const &bigEndian, bool negative = false):
 This constructor initializes a BigInt from the bytes stored in
        bigEndian, which must be big-endian encoded (having its most
        significant value at index 0). This constructor interprets the
        char values stored in bigEndian as unsigned values. If the
        number that is stored in bigEndian represents a negative value,
        then provide a second argument true;
-  BigInt(size_t length, char const *littleEndian, bool negative = false):
 This constructor initializes a BigInt from length little-endian
        encoded bytes stored in littleEndian (having its least significant
        value at index 0). This constructor interprets the char
        values pointed at by littleEndian as unsigned values. Use this
        constructor to reconstruct a BigInt object from the data made
        available by the littleEndian member (most significant byte at
        index 0). If the number represents a negative value, then provide a
        third argument true;
-  explicit BigInt(BigInt::Little endian, std::string littleEndian, bool
        negative = false):
 This constructor initializes a BigInt from the bytes stored in
        littleEndian, which must be little-endian encoded (having its
        least significant value at index 0). This constructor interprets the
        char values stored in littleEndian as unsigned values. If the
        number that is stored in littleEndian represents a negative value,
        then provide a third argument true. The consructor's first
        parameter is used to distinguish this constructor from the constructor
        expecting a t(string) whose bytes represent a big-endian encoded
        value, and is not used by this constructor itself. It can be specified
        as BigInt::Little{}.
Copy and move constructors (and assignment operators) are available.
MEMBER FUNCTIONS
    
    -  BigInt &addMod(BigInt const &rhs, BigInt const &mod) :
 Rhs is added (modulo mod) to the current object;
 
-  BigInt addModc(BigInt const &rhs, BigInt const &mod) :
 The sum (modulo mod) of the current object and rhs is returned;
 
-  BigInt::Word at(size_t index) const:
 Returns the Word at index. E.g., on a 32 bit architecture, if
        the BigInt value equals 233, then at(0) returns 0, and
        at(1) returns 2. If index equals or exceeds the value returned
        by nWords an FBB::Exception is thrown;
 
-  BIGNUM const &bignum() const:
 A reference to the BIGNUM value maintained by the current
        BigInt object is returned;
 
-  char *bigEndian() const:
 The value represented by the current object is stored in a series of
        char typed values in big-endian order. If a value consists of 5
        chars the eight most significant bits will be stored in the
        char having index value 0, the eight least significant bits will
        be stored in the char having index value 4. When needed simply
        swap char[i] with char[j] (i = 0 .. nBytes/2, j = nBytes-1
        .. nBytes/2) to convert to little-endian order or use the member
        littleEndian to receive the representation in little-endian
        order. The return value consists of a series of sizeInBytes() (see
        below) dynamically allocated char values. The caller of
        bigEndian owns the allocated memory and should eventually delete
        it again using delete[]. Note that the current object's sign
        cannot be inferred from the return value;
 
-  BigInt &clearBit(size_t index):
 The current object's bit at index position index is cleared;
 
-  BigInt clearBit(size_t index) const:
 A copy of the current object having its bit at index position
        index cleared;
 
-  BigInt &div(BigInt *remainder, BigInt const &rhs):
 The current object is divided by rhs. The division's remainder
        is returned in *remainder;
 
-  BigInt divc(BigInt *remainder, BigInt const &rhs) const:
 The quotient of the current object and rhs is returned. The
        division's remainder is returned in *remainder;
 
-  int compare(BigInt const &rsh) const:
 Using signed values, if the current object is smaller than rhs -1
        is returned; if they are equal 0 is returned; if the current object is
        larger than ths 1 is returned (see also uCompare);
 
-  BigInt &exp(BigInt const &exponent):
 The current object is raised to the power exponent;
 
-  BigInt expc(BigInt const &exponent) const:
 The current object raised to the power exponent is returned;
 
-  BigInt &expMod(BigInt const &exponent, BigInt const &mod):
 The current object is raised to the power exponent modulo mod;
 
-  BigInt expModc(BigInt const &exponent, BigInt const &mod) const:
 The current object raised to the power exponent modulo mod is
        returned;
 
-  BigInt &gcd(BigInt const &rhs):
 The greatest common divisor (gcd) of the current object and rhs is
        assigned to the current object. To compute the least common multiple
        (lcm) the following relationship can be used:
    lcm(a, b) = a * b / a.gcd(b)
        
 
-  BigInt gcdc(BigInt const &rhs) const:
 The greatest common divisor (gcd) of the current object and rhs is
        returned. To compute the least common multiple (lcm) the following
        relationship can be used:
    lcm(a, b) = a * b / a.gcd(b)
        
 
-  bool hasBit(size_t index):
 True is returned if the bit at index position index has been
        set, false otherwise;
 
-  BigInt &inverseMod(BigInt const &mod):
 The inverse of the current object modulo mod is assigned to the
        current object. This is the value ret for which the following
        expression holds true:
        (*this * ret) % mod = 1
       
 
-  BigInt inverseModc(BigInt const &mod) const:
 This  inverse of the current object modulo mod is returned;
 
-  bool isNegative() const:
 Returns true if the current object contains a negative value;
 
-  bool isOdd() const:
 Returns true if the current object is an odd value;
 
-  bool isOne() const:
 Returns true if the current object equals one (1);
 
-  BigInt &isqrt():
 The current object's integer square root value is assigned to the
        current object. The integer square root of a value x is the
        biggest integral value whose square does not exceed x. E.g.,
        isqrt(17) == 4. An Exception exception is thrown if the current
        object's value is smaller than one;
 
-  BigInt isqrtc() const:
 The integer square root of the current object is returned. An
        Exception exception is thrown if the current object's value is
        smaller than one;
 
-  bool isZero() const:
 Returns true if the current object equals zero (0);
 
-  char *littleEndian() const:
 The value represented by the current object is stored in a series of
        char typed values in little-endian order. If a value consists of 5
        chars the eight least significant bits will be stored in the
        char having index value 0. To receive the bytes in big-endian
        order the member bigEndian can be used. The return value consists
        of a series of sizeInBytes() (see below) dynamically allocated
        char values. The caller of littleEndian owns the allocated
        memory and should eventually delete it again using delete[]. Note
        that the current object's sign cannot be inferred from the return
        value;
 
-  BigInt &lshift():
 The current object's bits are shifted one bit to the left. The object's
        sign remains unaltered;
 
-  BigInt lshiftc():
 The current object's bits shifted one bit to the left are returned. The
        object's sign will be equal to the current object's sign;
 
-  BigInt &lshift(size_t nBits):
 The current object's bits are shifted nBits to the left. The
        object's sign remains unaltered;
 
-  BigInt lshiftc(size_t nBits) const:
 The current object's bits shifted nBits bit to the left are
        returned. The object's sign will be equal to the current object's
        sign;
 
-  BigInt &maskBits(size_t lowerNBits):
 The  current object's lowerNBits lower bits are kept, its
        higher order bits are cleared. The object's sign is not affected;
 
-  BigInt maskBitsc(size_t lowerNBits) const:
 A copy of the current object is returned having all but its
        lowerNBits lower bits cleared. The sign of the returned object
        will be equal to the current object's sign;
 
-  size_t maxWordIndex() const:
 Returns the maximum Word-index that can be used with the at
        and setWord members for the current BigInt value;
 
-  BigInt &mulMod(BigInt const &rhs, BigInt const &mod):
 The current object is multiplied  (modulo mod) by rhs;
 
-  BigInt mulModc(BigInt const &rhs, BigInt const &mod) const:
 The current object multiplied (modulo mod) by rhs is returned;
 
-  BigInt &negate():
 The current object's value is negated (i.e., the value changes its
        sign);
 
-  BigInt negatec() const:
 The  negated value of the current object is returned;
 
-  size_t nWords() const:
 The number of `words' required to store the BigInt value is
        returned. Note that the returned value depends on the architecture's
        number of bytes per word. For 32-bit architectures there are four
        bytes per word, for 64-bit architectures eight bytes per word;
 
-  BigInt &rshift():
 The current object's bits are shifted one bit to the right. The object's
        sign remains unaltered;
 
-  BigInt rshiftc():
 The current object's bits shifted one bit to the right are returned. The
        object's sign will be equal to the current object's sign;
 
-  BigInt &rshift(size_t nBits):
 The current object's bits are shifted nBits to the right. The
        object's sign remains unaltered;
 
-  BigInt rshiftc(size_t nBits) const:
 The current object's bits shifted nBits bit to the right are
        returned. The object's sign will be equal to the current object's
        sign;
 
-  BigInt &setBit(size_t index):
 The bit at index position index is set;
 
-  BigInt setBitc(size_t index) const:
 A copy of the current object is returned having its bit at index
        position index set;
 
-  BigInt &setBit(size_t index, bool value):
 The bit at index position index is set to value;
 
-  BigInt setBitc(size_t index, bool value) const:
 A copy of the current object is returned having its bit at index
        position index set to value;
 
-  BigInt &setNegative(bool negative):
 The current object's sign will be set to negative if the function's
        argument is true, it will be set to positive if the function's
        argument is false;
 
-  BigInt setNegativec(bool negative) const:
 A copy of the current object is return having a negative sign if the
        function's argument is true and a positive sign if the function's
        argument is false;
 
-  void setWord(size_t index, BigInt::Word value):
 Assigns value to the Word at index. E.g., on a 32 bit
        architecture, if the BigInt value equals 233, then
        after setWord(1, 1) the value has become 232. If index
        exceeds the value returned by nWords an FBB::Exception is
        thrown;
 
-  size_t size() const:
 The number of significant bits required to store the current
        BIGNUM value is returned;
 
-  size_t sizeInBytes() const:
 The number of bytes required to store the current BIGNUM value is
        returned;
 
-  size_t constexpr sizeOfWord() const:
 BigInt values are stored in units of `words', which are unsigned
        long values. These values may consist of, e.g., 32 or 64 bits. The
        number of bytes occupied by a `word' is returned: 4 for a 32 bit
        value, 8 for a 64 bit value, and possibly other values, depending on
        specific architecture peculiarities. The value returned by this
        member, therefore, is architecture dependent;
 
-  BigInt &sqr():
 The current object's value is squared;
 
-  BigInt sqrc() const:
 The square of the current object is returned;
 
-  BigInt &sqrMod(BigInt const &mod) const:
 The current object's value is squared modulo mod;
 
-  BigInt sqrModc(BigInt const &mod) const:
 The square (modulo mod) of the current object is returned;
 
-  BigInt &subMod(BigInt const &rhs, BigInt const &mod):
 Rhs is subtracted modulo mod from the current object;
 
-  BigInt subModc(BigInt const &rhs, BigInt const &mod) const:
 The difference (modulo mod) of the current object and rhs is
        returned;
 
-  void swap(BigInt &other):
 The current object swaps its value with other;
 
-  BigInt &tildeBits():
 All the bits in
        the bytes of the current object and the sign of the current object
        are toggled.
       So, after
        Bigint b(5);
        b.tildeBits();
            
b contains the value -250. Also see the discussion with
        operator~() below;
 
-  BigInt tildeBitsc() const:
 A copy of the current object whose bits are toggled is returned;
 
-  BigInt &tildeInt():
 The `tilde' operation is performed on the current object using the
        standard int semantics. E.g., ~5 results in -6.  Also see the
        discussion with operator~() below;
 
-  BigInt tildeIntc() const:
 A copy of the current object is returned to which the `tilde' operation
        has been performed using the standard int semantics;
 
-  unsigned long ulong() const:
 The absolute value stored in the current object is returned as an
        unsigned long. If it cannot be represented by an unsigned long it
        returns 0xffffffffL;
 
-  int uCompare(BigInt const &rsh) const:
 Using absolute values, if the current object is smaller than rhs -1
        is returned; if they are equal 0 is returned; if the current object is
        larger than ths 1 is returned (see also uCompare).
OVERLOADED OPERATORS
Except for some operators all operators perform their intuitive
operations. Where that isn't completely true an explanatory remark is
provided. E.g., operator*() multiplies two BigInts, possibly promoting
one of the operands; operator*=() multiplies the lhs by the rhs
BigInt, possibly promoting the rhs operand.
Here are the available operators:
Unary operators:
    -  bool operator bool() const:
 Returns true if the BigInt value is unequal zero, otherwise
        false is returned;
 
-  BigInt &operator++():
 Unary prefix increment operator;
-  BigInt operator++(int):
 Unary postfix increment operator;
-  BigInt &operator--():
 Unary prefix decrement operator;
-  BigInt operator--(int):
 Unary postfix decrement operator;
-  BigInt operator-():
 Unary negation operator;
-  int operator[](size_t idx) const:
 With BigInt objects it returns the bit-value of the object's
        idxth bit as the value 0 or 1;
 
-  BigInt::Bit operator[](size_t idx):
 With non-const BigInt objects it returns a reference to the
        bit-value of the object's idxth bit. When used as lvalue
        assigning a 0 or non-zero value to the operator's return value will
        either clear or set the bit.  Likewise, the following arithmetic
        assignment operators may be used: binary or (|=), binary and
        (&=) or binary xor (^=). When used as rvalue the value of
        the object's idxth bit is returned as a bool value. When
        inseerted into a std::ostream the bit's value is displayed as 0 or
        1;
 
-  BigInt operator~():
 This operator is not implemented as it cannot be implemented so
        that it matches the actions of this operator when applied to int
        type values;
When used on int values this operator toggles all the int's
        bits. E.g., ~5 represents -6, and ~-6 again equals five. The -6 is the
        result of the sign bit of int values. The obvious implementation
        of BigInt::operator~() is to toggle all the value's bits and to
        toggle its sign bit. For 5 this would result in -250: 5, being 101
        (binary), fits in one byte, so ~5 becomes 11111010 (binary), which is
        250. Its sign must be reversed as well, so it becomes -250.  This
        clearly differs from the value represented by the int constant ~5:
        when constructing BigInt(~5), the value -6 is obtained.
 
It is possible to change the implementation. E.g., after
             
        Bigint b(5);
        b = ~b;
            
~b could be implemented so that it results in the value -6. But
        this too leads to unexpected results. While 5 & ~5 == 0, this
        would no longer hold true for BigInt objects: Assuming b
        contains 5 then b & ~b would expand to (binary) 101 &
        (negative)110 which equals (binary) 100;
Since either implementation produces unexpected results
        BigInt::operator~() was not implemented. Instead two members are
        offered: tildeBits(), toggling all the bits of all the
       BigInt bytes and toggling its sign (so
             
        Bigint b(5);
        b.tildeBits();
            
changes b's value into -250), and tildeInt() changing the
        object's value into the value that would have been obtained if a
       BigInt was a mere int (so
        Bigint b(5);
        b.tildeInt();
            
changes b's value into -6).
Binary operators:
    -  BigInt operator*(BigInt const &lhs, BigInt const &rhs):
 
-  BigInt operator/(BigInt const &lhs, BigInt const &rhs):
 This operator returns the quotient of the lhs object divided by the
        rhs object. The remainder is lost (The member div performs the
        division and makes the remainder available as well);
-  BigInt operator%(BigInt const &lhs, BigInt const &rhs):
 
-  BigInt operator+(BigInt const &lhs, BigInt const &rhs):
 
-  BigInt operator-(BigInt const &lhs, BigInt const &rhs):
 
-  BigInt operator<<(BigInt const &lhs, size_t nBits):
 See also the lshift member;
-  BigInt operator>>=(BigInt const &lhs, size_t nBits):
 See also the rshift member;
-  BigInt operator&(BigInt const &lhs, BigInt const &rhs):
 This operator returns a BigInt value consisting of the
        bit_and-ed bits and sign flags of lhs and rhs
        operands. Consequently, if one operand is positive, the resulting
        value will be positive;
-  BigInt operator|(BigInt const &lhs, BigInt const &rhs):
 This operator returns a BigInt value consisting of the
        bit_or-ed bits and sign flags of lhs and rhs
        operands. Consequently, if either operand is negative, the result will
        be negative;
-  BigInt operator^(BigInt const &lhs, BigInt const &rhs):
 This operator returns a BigInt value consisting of the
        bit_xor-ed bits and sign flags of lhs and rhs
        operands. Consequently, if exactly one operand is negative, the result
        will be negative.
(Arithmetic) assignment operator(s):
    -  BigInt &operator*=(BigInt const &rhs):
 
-  BigInt &operator/=(BigInt const &rhs):
 This operator assigns the result of the (integer) division of the current
        BigInt object by ths to the current object. The remainder is
        lost. The member div divides and makes the remainder available as
        well;
-  BigInt &operator%=(BigInt const &rhs):
 
-  BigInt &operator+=(BigInt const &rhs):
 
-  BigInt &operator-=(BigInt const &rhs):
 
-  BigInt &operator<<=(size_t nBits):
 See also the lshift members;
-  BigInt &operator>>=(size_t nBits):
 See also the rshift members;
-  BigInt &operator&=(BigInt const &rhs):
 This operator bit_ands the bits and sign flags of the current
        object and the rhs operand;
-  BigInt &operator|=(BigInt const &rhs):
 This operator bit_ors the bits and sign flags of the current
        object and the rhs operand;
-  BigInt &operator^=(BigInt const &rhs):
 This operator bit_xors the bits and sign flags of the current
        object and the rhs operand.
STATIC MEMBERS
All members returning a BigInt computed from a set of arguments and
not requiring an existing BigInt object are defined as static members.
The first diophantus member, returning a long long value, also is a
static member.
    -  long long diophantus(long long *factor1, long long *factor2,
                             long long value1, long long value2):
 The integral solution of factor1 * value1 + factor2 * value2 = gcd
        is computed. The function returns the greatest common divisor
        (gcd) of value1 and value2, and returns their
        multiplication factors in, respectively, *factor1 and
        *factor2. The solution is not unique: another solution is obtained
        by adding k * value2 to factor1 and subtracting k * value1
        from factor2. For values exceeding std::numeric_limits<long,
        long>::max() the next member can be used;
 
-  BigInt diophantus(BigInt *factor1, BigInt *factor2,
                            BigInt const &value1, BigInt const &value2):
 The integral solution of factor1 * value1 + factor2 * value2 = gcd
        is computed. The function returns the greatest common divisor
        (gcd) of value1 and value2, and returns their
        multiplication factors in, respectively, *factor1 and
        *factor2. The solution is not unique: another solution is obtained
        by adding k * value2 to factor1 and subtracting k * value1
        from factor2;
 
-  BigInt fromText(std::string text, int mode = 0):
 This member converts a textual representation of a number to a
        BigInt value. Conversion continues until the end of text or
        until a character outside of an expected range is encountered;
The expected range may be preset by specifying mode as ios::dec,
        ios::oct, or ios::hex or (the default) the expected range is
        determined by fromText itself by inspecting the characters in
        text.
 
By default if text contains hexadecimal characters then
        fromText assumes that the number is represented as a hexadecimal
        value (e.g., "abc" is converted to the (decimal) value 2748); if
        text starts with 0 and contains only characters in the range 0
        until (including) 7 then fromText assumes the number is
        represented as an octal value (e.g., "01234" is converted to the
        (decimal) value 668). Otherwise a decimal value is assumed.
 
If the text does not represent a valid numerical value (of the
        given extraction mode) then a FBB::Exception exception is thrown
        (fromText: text does not represent a BigInt value);
 
 
-  BigInt rand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb = ODD):
 This member returns a cryptographically strong pseudo-random number
        of size bits. The most significant bit(s) can be controlled by
        msb (by default MSB_IS_ONE), the least significant bit can be
        controlled by lsb (by default ODD). Before calling this
        member for real the random number generator must have been seeded.
From the RAND_add(3ssl) man-page:
 
OpenSSL makes sure that the PRNG state is unique for each thread. On
        systems that provide /dev/urandom, the randomness device is used
        to seed the PRNG transparently. However, on all other systems, the
        application is responsible for seeding the PRNG by calling
        RAND_add(3ssl), RAND_egd(3ssl), RAND_load_file(3ssl), or
        RAND_seed(3ssl);
 
 
-  BigInt randRange(BigInt const &max):
 This member returns a cryptographically strong pseudo-random number in
        the range 0 <= number < max. Before calling this member for real
        the random number generator must have been seeded (see also rand,
        described above);
 
-  BigInt setBigEndian(std::string const &bytes):
 The bytes.length() bytes of bytes are used to compute a
        BigInt object which is returned by this function. The characters
        in bytes are interpreted as a series of bytes in big-endian
        order. See also the member function bigEndian() above. The
        returned BigInt has a positive value;
 
-  BigInt prime(size_t nBits,
                            BigInt const *mod = 0, BigInt const *rem = 0,
                            PrimeType primeType = ANY):
 This member returns a prime number of bBits bits. If both mod
        and rem are non-zero, the condition prime % mod == rem.
        (E.g., use prime % mod == 1 in order to suit a given
        generator). The parameter primeType can be ANY, (prime - 1)
        / 2 may or may not be a prime. If it is SAFE then  (prime - 1)
        / 2 will be a (so-called safe) prime;
 
-  BigInt pseudoRand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb =
            ODD):
 This member merely calls BigInt::rand;
 
-  BigInt pseudoRandRange(BigInt const &max):
 This member merely calls BigInt::randRange.
FREE FUNCTIONS IN THE FBB NAMESPACE
    -  std::ostream &operator<<(ostream &out, BigInt const &value):
 Inserts value into the provided ostream. If the hex
        manipulator has been inserted into the stream before inserting the
        BigInt value the value will be displayed as a hexadecimal value
        (without a leading 0x); if the oct manipulator has been
        inserted the value will be represented as an octal value (starting
        with a 0). The value will be displayed as a decimal value if the
        dec manipulator is active. If the BigInt value is negative its
        value will be preceded by a minus character.
This conversion isn't very fast. For faster conversion consider using
        the LDC class (cf. ldc(3bobcat)) in statements like
        
BigInt value;           // contains a positive value
                        // insert value using decimal digits:
std::cout << LDC{ value };
        
 
-  std::istream &operator>>(istream &in, BigInt &value):
 Extracts value from the provided istream. Depending on the
        currently set extraction mode (dec, oct, or hex) the matching
        set of characters will be extracted from in and converted to a
        number which is stored in value. Extraction stops at EOF or at the
        first character outside of the range of characters matching the
        extraction mode. if no numerical characters were extracted the
        stream's failbit is set. The extracted value may be preceded
        by a minus character, resulting in an extracted negative value.
EXAMPLE
        
#include <iostream>
#include <bobcat/bigint>
using namespace std;
using namespace FBB;
int main()
{
    BigInt value(BigInt::prime(100));
    BigInt mod(BigInt::rand(50));
    BigInt inverse(value.inverseModc(mod));
    cout << '(' << value << " * " << inverse << ") % " << mod << " = " <<
             (    value       *      inverse     ) %      mod << '\n';
}
// shows:
// (1258586273445895786081124957771 * 828997573545038) %
//                                                  1007205247048889 = 1
FILES
    bobcat/bigint - defines the class interface
SEE ALSO
    bobcat(7), diffiehellman(3bobcat), ldc(3bobcat),
    RAND_add(3ssl), RAND_egd(3ssl),
    RAND_load_file(3ssl), RAND_seed(3).
For BIGNUM:
    https://www.openssl.org/docs/man1.0.2/man3/bn_sub_words.html
BUGS
    None Reported.
BOBCAT PROJECT FILES
    -  https://fbb-git.gitlab.io/bobcat/: gitlab project page;
    
-  bobcat_6.06.02-x.dsc: detached signature;
    
-  bobcat_6.06.02-x.tar.gz: source archive;
    
-  bobcat_6.06.02-x_i386.changes: change log;
    
-  libbobcat1_6.06.02-x_*.deb: debian package containing the
            libraries;
    
-  libbobcat1-dev_6.06.02-x_*.deb: debian package containing the
            libraries, headers and manual pages;
    
BOBCAT
    Bobcat is an acronym of `Brokken's Own Base Classes And Templates'.
COPYRIGHT
    This is free software, distributed under the terms of the
    GNU General Public License (GPL).
AUTHOR
    Frank B. Brokken (f.b.brokken@rug.nl).