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<html><head>
<title>FBB::BigInt</title>
<link rev="made" href="mailto:Frank B. Brokken: f.b.brokken@rug.nl">
</head>
<body text="#27408B" bgcolor="#FFFAF0">
<hr>
<h1>FBB::BigInt</h1>
<h2>libbobcat-dev_3.19.01-x.tar.gz</h2>
<h2>2005-2013</h2>

<html><head>
<link rev="made" href="mailto:Frank B. Brokken: f.b.brokken@rug.nl">
</head>
<body text="#27408B" bgcolor="#FFFAF0">
<hr>
<h1></h1>

<html><head>
<title>FBB::BigInt(3bobcat)</title>
<link rev="made" href="mailto:Frank B. Brokken: f.b.brokken@rug.nl">
</head>
<body text="#27408B" bgcolor="#FFFAF0">
<hr>
<h1>FBB::BigInt(3bobcat)</h1>
<h2>libbobcat-dev_3.19.01-x.tar.gz Big Integers</h2>
<h2>2005-2013</h2>


<p>
<h2>NAME</h2>FBB::BigInt - Arithmetic on Integers of Unlimited Size
<p>
<h2>SYNOPSIS</h2>
    <strong>#include &lt;bobcat/bigint&gt;</strong><br>
    Linking option: <em>-lbobcat -lcrypto</em> 
<p>
<h2>DESCRIPTION</h2>
<p>
This class is defined as a wrapper class around the <em>openSSL</em> <em>BN</em> 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 <em>BigInt</em> objects. Also, conversions
to characters and standard numerical value types are offered.
<p>
Below, the phrase <em>the object</em> 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.
<p>
Various constructors accept <em>BIGNUM</em> arguments. Type <em>BIGNUM</em> is the type
containing an integer of unlimited precision as defined by OpenSSL.
<p>
Signs of <em>BigInt</em> are handled in a special way. Whether a <em>BigInt</em> is
negative or positive is determined by its sign-flag, and not by a sign bit as
is the case with <em>int</em> typed values. Since <em>BigInt</em> values have unlimited
precision shifting values to the left won't change their signs.
<p>
Operators return either a reference to the current (modified) object or return
a <em>BigInt</em> object containing the computed value. The rule followed here was
to implement the operators analogously to the way the operators work on
<em>int</em> type values and variables. E.g., <em>operator+()</em> returns a <em>BigInt</em>
value whereas <em>operator+=()</em> returns a <em>BigInt &amp;</em> reference.
<p>
All members modifying their objects return a reference to the current
(modified) object. All members not modifying the current object return a
<em>BigInt</em> object. If both members exists performing the same
functionality the name of the member returning a <em>BigInt</em> object ends
in a <em>c</em> (const) (e.g., <em>addMod</em> and <em>addModc</em>.
<p>
Almost all operators, members and constructors (except for the default
constructor) throw <em>Exception</em> exceptions on failure.
<p>
<h2>INHERITS FROM</h2>
    -
<p>
<h2>TYPE</h2>
<p>
The class <strong>BigInt</strong> defines the type <em>Word</em>, which is equal to the type
<em>BN_ULONG</em> used by <em>OpenSSL</em> to store integral values of unlimited
precision. A <em>Word</em> is an <em>unsigned long</em>, which is, depending on the
architecture, usually 64 or 32 bits long. 
<p>
<h2>ENUMERATIONS</h2>
    <strong>Msb</strong><br>
    This (most significant bit) enumeration is used when generating a
        cryptographically strong random number. Its values are:
    <ul>
    <li> <strong>MSB_UNKNOWN</strong>:<br>
       The most significant bit may be 0 or 1.
    <li> <strong>MSB_IS_ONE</strong>:<br>
        The most significant bit is guaranteed to be 1.
    <li> <strong>TOP_TWO_BITS_ONE</strong>:<br>
        The two most significant bits are guaranteed to be 1, resulting in a
        product of two values each containing <em>nBits</em> having <em>2 * nBits</em>
        bits.
    </ul>
<p>
<strong>Lsb</strong><br>
    This (least significant bit) enumeration is used when generating random
        numbers, ensuring that the resulting value is either odd or even.
    <ul>
    <li> <strong>EVEN</strong>:<br>
        The random value will be an even value;
    <li> <strong>ODD</strong>:<br>
        The random value will be an odd value.
    </ul>
<p>
<h2>CONSTRUCTORS</h2>
<p>
<ul>
    <li> <strong>BigInt()</strong>:<br>
        The default constructor initializes a <em>BigInt</em> value to 0.
    <li> <strong>explicit BigInt(BIGNUM const &amp;value)</strong>:<br>
        This constructor initializes a <em>BigInt</em> from a <em>const BIGNUM</em>. 
    <li> <strong>explicit BigInt(BIGNUM const *value)</strong>:<br>
        This constructor initializes a <em>BigInt</em> from a pointer to a 
        <em>const BIGNUM</em>.
    <li> <strong>BigInt(Type value)</strong>:<br>
        This constructor is defined as a member template. Any type that can be
converted using a static cast to an <em>unsigned long</em> can be used as argument
to this constructor. Promotion is allowed, so in many situations where
<em>BigInt</em>s are expected a plain numerical value can be used as well.
    <li> <strong>BigInt(char const *bigEndian, size_t length, bool negative = false)</strong>:<br>
        This constructor initializes a <em>BigInt</em> from <em>length</em>
big-endian encoded bytes stored in <em>bigEndian</em>. This constructor interprets
the <em>char</em> values pointed at by <em>bigEndian</em> as unsigned values. Use this
constructor to reconstruct a <em>BigInt</em> object from the data made available by
the <em>bigEndian</em> member. If the number represents a negative value, then
provide a third argument <em>true</em>.
    <li> <strong>explicit BigInt(std::string const &amp;bigEndian, bool negative = false)</strong>:<br>
        This constructor initializes a <em>BigInt</em> from the bytes stored in
<em>bigEndian</em>, which must be big-endian encoded. This constructor interprets
the <em>char</em> values stored in <em>bigEndian</em> as unsigned values. If the number
that is stored in <em>bigEndian</em> represents a negative value, then provide a
second argument <em>true</em>.
    </ul>
<p>
The standard copy constructor is available, the move constructor is not
available. 
<p>
<h2>MEMBER FUNCTIONS</h2>
    <ul>
    <li> <strong>BigInt &amp;addMod(BigInt const &amp;rhs, BigInt const &amp;mod) </strong>:<br>
       <em>Rhs</em> is added (modulo <em>mod</em>) to the current object.
<p>
<li> <strong>BigInt addModc(BigInt const &amp;rhs, BigInt const &amp;mod) </strong>:<br>
       The sum (modulo <em>mod</em>) of the current object and <em>rhs</em> is returned.
<p>
<li> <strong>BigInt::Word at(size_t index) const</strong>:<br>
       Returns the <em>Word</em> at <em>index</em>. E.g., on a 32 bit architecture, if
        the <strong>BigInt</strong> value equals 2<sup>33</sup>, then <em>at(0)</em> returns 0, and
        <em>at(1)</em> returns 2. If <em>index</em> equals or exceeds the value returned
        by <em>nWords</em> an <em>FBB::Exception</em> is thrown.
<p>
<li> <strong>BIGNUM const &amp;bignum() const</strong>:<br>
       A reference to the <em>BIGNUM</em> value maintained by the current
        <em>BigInt</em> object is returned.
<p>
<li> <strong>char *bigEndian() const</strong>:<br> The value represented by the current object
        is stored in a series of <em>char</em> typed values in big-endian order. If
        a value consists of 5 <em>char</em>s the eight most significant bits will
        be stored in the <em>char</em> having index value 0, the eight least
        significant bits will be stored in the <em>char</em> having index value
        4. When needed simply swap <em>char[i]</em> with <em>char[j]</em> (i = 0
        .. nBytes/2, j = nBytes-1 .. nBytes/2) to convert to little-endian
        order. The return value consists of a series of <em>sizeInBytes()</em> (see
        below) dynamically allocated <em>char</em> values. The caller of
        <em>bigEndian</em> owns the allocated memory and should eventually delete
        it again using <em>delete[]</em>. Note that the current object's <em>sign</em>
        cannot be inferred from the return value.
<p>
<li> <strong>BigInt &amp;clearBit(size_t index)</strong>:<br>
       The current object's bit at index position <em>index</em> is cleared.
<p>
<li> <strong>BigInt clearBit(size_t index) const</strong>:<br>
       A copy of the current object having its bit at index position
        <em>index</em> cleared.
<p>
<li> <strong>long long diophantus(long long *factor1, long long *factor2, 
                             long long value1, long long value2)</strong>:<br>
       The integral solution of <em>factor1 * value1 + factor2 * value2 = gcd</em>
        is computed. The function returns the greatest common divisor
        (<em>gcd</em>) of <em>value1</em> and <em>value2</em>, and returns their
        multiplication factors in, respectively, <em>*factor1</em> and
        <em>*factor2</em>. The solution is not unique: another solution is obtained
        by adding <em>k * value2</em> to <em>factor1</em> and subtracting <em>k * value1</em>
        from <em>factor2</em>. For values exceeding <em>std::numeric_limits&lt;long,
        long&gt;::max()</em> the next member can be used.
<p>
<li> <strong>BigInt diophantus(BigInt *factor1, BigInt *factor2, 
                            BigInt const &amp;value1, BigInt const &amp;value2)</strong>:<br>
       The integral solution of <em>factor1 * value1 + factor2 * value2 = gcd</em>
        is computed. The function returns the greatest common divisor
        (<em>gcd</em>) of <em>value1</em> and <em>value2</em>, and returns their
        multiplication factors in, respectively, <em>*factor1</em> and
        <em>*factor2</em>. The solution is not unique: another solution is obtained
        by adding <em>k * value2</em> to <em>factor1</em> and subtracting <em>k * value1</em>
        from <em>factor2</em>.
<p>
<li> <strong>BigInt &amp;div(BigInt *remainder, BigInt const &amp;rhs)</strong>:<br>
       The current object is divided by <em>rhs</em>. The division's remainder
        is returned in <em>*remainder</em>.
<p>
<li> <strong>BigInt divc(BigInt *remainder, BigInt const &amp;rhs) const</strong>:<br>
       The quotient of the current object and <em>rhs</em> is returned. The
        division's remainder is returned in <em>*remainder</em>.
<p>
<li> <strong>int compare(BigInt const &amp;rsh) const</strong>:<br>
       Using signed values, if the current object is smaller than <em>rhs</em> -1
        is returned; if they are equal 0 is returned; if the current object is
        larger than <em>ths</em> 1 is returned (see also <em>uCompare</em>). 
<p>
<li> <strong>BigInt &amp;exp(BigInt const &amp;exponent)</strong>:<br>
       The current object is raised to the power <em>exponent</em>.
<p>
<li> <strong>BigInt expc(BigInt const &amp;exponent) const</strong>:<br>
       The current object raised to the power <em>exponent</em> is returned.
<p>
<li> <strong>BigInt &amp;expMod(BigInt const &amp;exponent, BigInt const &amp;mod)</strong>:<br>
       The current object is raised to the power <em>exponent</em> modulo <em>mod</em>.
<p>
<li> <strong>BigInt expModc(BigInt const &amp;exponent, BigInt const &amp;mod) const</strong>:<br>
       The current object raised to the power <em>exponent</em> modulo <em>mod</em> is
        returned.
<p>
<li> <strong>BigInt &amp;gcd(BigInt const &amp;rhs)</strong>:<br>
       The greatest common divisor (gcd) of the current object and <em>rhs</em> is
        assigned to the current object. To compute the least common multiple
        (lcm) the following relationship can be used:
       <pre>

    lcm(a, b) = a * b / a.gcd(b)
        
</pre>

<p>
<li> <strong>BigInt gcdc(BigInt const &amp;rhs) const</strong>:<br>
       The greatest common divisor (gcd) of the current object and <em>rhs</em> is
        returned. To compute the least common multiple (lcm) the following
        relationship can be used: 
       <pre>

    lcm(a, b) = a * b / a.gcd(b)
        
</pre>

<p>
<li> <strong>bool hasBit(size_t index)</strong>:<br>
        <em>True</em> is returned if the bit at index position <em>index</em> has been
        set, <em>false</em> otherwise.
<p>
<li> <strong>BigInt &amp;inverseMod(BigInt const &amp;mod)</strong>:<br>
       The inverse of the current object modulo <em>mod</em> is assigned to the
        current object. This is the value <em>ret</em> for which the following
        expression holds true:
       <pre>
 
        (*this * ret) % mod = 1 
       
</pre>

<p>
<li> <strong>BigInt inverseModc(BigInt const &amp;mod) const</strong>:<br>
       This  inverse of the current object modulo <em>mod</em> is returned.
<p>
<li> <strong>bool isNegative() const</strong>:<br>
       Returns <em>true</em> if the current object contains a negative value.
<p>
<li> <strong>bool isOdd() const</strong>:<br>
       Returns <em>true</em> if the current object is an odd value.
<p>
<li> <strong>bool isOne() const</strong>:<br>
       Returns <em>true</em> if the current object equals one (1).
<p>
<li> <strong>BigInt &amp;isqrt()</strong>:<br>
       The current object's integer square root value is assigned to the
        current object. The integer square root of a value <em>x</em> is the
        biggest integral value whose square does not exceed <em>x</em>. E.g.,
        <em>isqrt(17) == 4</em>. An <em>Exception</em> exception is thrown if the current
        object's value is smaller than one.
<p>
<li> <strong>BigInt isqrtc() const</strong>:<br>
        The integer square root of the current object is returned. An
        <em>Exception</em> exception is thrown if the current object's value is smaller
        than one.  
<p>
<li> <strong>bool isZero() const</strong>:<br>
       Returns <em>true</em> if the current object equals zero (0).
<p>
<li> <strong>BigInt &amp;lshift()</strong>:<br> 
       The current object's bits are shifted one bit to the left. The object's
        sign remains unaltered.
<p>
<li> <strong>BigInt lshiftc()</strong>:<br> 
       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.
<p>
<li> <strong>BigInt &amp;lshift(size_t nBits)</strong>:<br> 
       The current object's bits are shifted <em>nBits</em> to the left. The
        object's sign remains unaltered.
<p>
<li> <strong>BigInt lshiftc(size_t nBits) const</strong>:<br> 
       The current object's bits shifted <em>nBits</em> bit to the left are
        returned. The object's sign will be equal to the current object's
        sign.
<p>
<li> <strong>BigInt &amp;maskBits(size_t lowerNBits)</strong>:<br>
        The  current object's <em>lowerNBits</em> lower bits are kept, its
        higher order bits are cleared. The object's sign is not affected.
<p>
<li> <strong>BigInt maskBitsc(size_t lowerNBits) const</strong>:<br>
       A copy of the current object is returned having all but its
        <em>lowerNBits</em> lower bits cleared. The sign of the returned object
        will be equal to the current object's sign.
<p>
<li> <strong>size_t maxWordIndex() const</strong>:<br>
       Returns the maximum <em>Word</em>-index that can be used with the <em>at</em>
        and <em>setWord</em> members for the current <strong>BigInt</strong> value.
<p>
<li> <strong>BigInt &amp;mulMod(BigInt const &amp;rhs, BigInt const &amp;mod)</strong>:<br> 
       The current object is multiplied  (modulo <em>mod</em>) by <em>rhs</em>.
<p>
<li> <strong>BigInt mulModc(BigInt const &amp;rhs, BigInt const &amp;mod) const</strong>:<br> 
       The current object multiplied (modulo <em>mod</em>) by <em>rhs</em> is returned.
<p>
<li> <strong>BigInt &amp;negate()</strong>:<br> 
       The current object's value is negated (i.e., the value changes its
        sign).
<p>
<li> <strong>BigInt negatec() const</strong>:<br> 
       The  negated value of the current object is returned.
<p>
<li> <strong>BigInt &amp;rshift()</strong>:<br> 
       The current object's bits are shifted one bit to the right. The object's
        sign remains unaltered.
<p>
<li> <strong>BigInt rshiftc()</strong>:<br> 
       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.
<p>
<li> <strong>BigInt &amp;rshift(size_t nBits)</strong>:<br> 
       The current object's bits are shifted <em>nBits</em> to the right. The
        object's sign remains unaltered.
<p>
<li> <strong>BigInt rshiftc(size_t nBits) const</strong>:<br> 
       The current object's bits shifted <em>nBits</em> bit to the right are
        returned. The object's sign will be equal to the current object's
        sign.
<p>
<li> <strong>BigInt &amp;setBit(size_t index)</strong>:<br>
       The bit at index position <em>index</em> is set. 
<p>
<li> <strong>BigInt setBitc(size_t index) const</strong>:<br> 
       A copy of the current object is returned having its bit at index
        position <em>index</em> set.
<p>
<li> <strong>BigInt &amp;setBit(size_t index, bool value)</strong>:<br>
       The bit at index position <em>index</em> is set to <em>value</em>.
<p>
<li> <strong>BigInt setBitc(size_t index, bool value) const</strong>:<br>
       A copy of the current object is returned having its bit at index
        position <em>index</em> set to <em>value</em>.
<p>
<li> <strong>BigInt &amp;setNegative(bool negative)</strong>:<br>
       The current object's sign will be set to negative if the function's
        argument is <em>true</em>, it will be set to positive if the function's
        argument is <em>false</em>.
<p>
<li> <strong>BigInt setNegativec(bool negative) const</strong>:<br>
       A copy of the current object is return having a negative sign if the
        function's argument is <em>true</em> and a positive sign if the function's
        argument is <em>false</em>.
<p>
<li> <strong>void setWord(size_t index, BigInt::Word value)</strong>:<br>
       Assigns <em>value</em> to the <em>Word</em> at <em>index</em>. E.g., on a 32 bit
        architecture, if the <strong>BigInt</strong> value equals 2<sup>33</sup>, then
        after <em>setWord(1, 1)</em> the value has become 2<sup>32</sup>. If <em>index</em>
        exceeds the value returned by <em>nWords</em> an <em>FBB::Exception</em> is
        thrown.
<p>
<li> <strong>size_t size() const</strong>:<br>
       The number of bytes required to store the current <em>BIGNUM</em> value is
        returned. 
<p>
<li> <strong>size_t sizeInBits() const</strong>:<br>
       The number of bits required to represent the current <em>BIGNUM</em> value
        is returned. 
<p>
<li> <strong>size_t sizeInBytes() const</strong>:<br>
       The number of bytes required to store the current <em>BIGNUM</em> value is
        returned (returns the same value as the <em>size</em> memeber does).
<p>
<li> <strong>size_t constexpr sizeOfWord() const</strong>:<br>
       <strong>BigInt</strong> 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.
<p>
<li> <strong>BigInt &amp;sqr()</strong>:<br>
      The current object's value is squared.
<p>
<li> <strong>BigInt sqrc() const</strong>:<br>
      The square of the current object is returned.
<p>
<li> <strong>BigInt &amp;sqrMod(BigInt const &amp;mod) const</strong>:<br>
      The current object's value is squared modulo <em>mod</em>.
<p>
<li> <strong>BigInt sqrModc(BigInt const &amp;mod) const</strong>:<br>
      The square (modulo <em>mod</em>) of the current object is returned.
<p>
<li> <strong>BigInt &amp;subMod(BigInt const &amp;rhs, BigInt const &amp;mod)</strong>:<br> 
       <em>Rhs</em> is subtracted modulo <em>mod</em> from the current object.
<p>
<li> <strong>BigInt subModc(BigInt const &amp;rhs, BigInt const &amp;mod) const</strong>:<br> 
      The difference (modulo <em>mod</em>) of the current object and <em>rhs</em> is
        returned.
<p>
<li> <strong>void swap(BigInt &amp;other)</strong>:<br>
       The current object swaps its value with <em>other</em>.
<p>
<li> <strong>BigInt &amp;tildeBits()</strong>:<br>
       All the bits in
        the bytes of the current object and the sign of the current object
        are toggled.
       So, after
            <pre>

        Bigint b(5);
        b.tildeBits();
            
</pre>

       <em>b</em> contains the value -250. Also see the discussion with
        <em>operator~()</em> below.
<p>
<li> <strong>BigInt tildeBitsc() const</strong>:<br>
       A copy of the current object whose bits are toggled is returned.
<p>
<li> <strong>BigInt &amp;tildeInt()</strong>:<br>
       The `tilde' operation is performed on the current object using the
        standard <em>int</em> semantics. E.g., ~5 results in -6.  Also see the
        discussion with <em>operator~()</em> below.
<p>
<li> <strong>BigInt tildeIntc() const</strong>:<br>
       A copy of the current object is returned to which the `tilde' operation
        has been performed using the standard <em>int</em> semantics.
<p>
<li> <strong>unsigned long ulong() const</strong>:<br> 
       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 <em>0xffffffffL</em>.
<p>
<li> <strong>int uCompare(BigInt const &amp;rsh) const</strong>:<br>
       Using absolute values, if the current object is smaller than <em>rhs</em> -1
        is returned; if they are equal 0 is returned; if the current object is
        larger than <em>ths</em> 1 is returned (see also <em>uCompare</em>).
    </ul>
<p>
<h2>OVERLOADED OPERATORS</h2>
<p>
Except for some operators all operators perform their intuitive
operations. Where that isn't completely true an explanatory remark is
provided. E.g., <em>operator*()</em> multiplies two <em>BigInt</em>s, possibly promoting
one of the operands; <em>operator*=()</em> multiplies the lhs by the rhs
<em>BigInt</em>, possibly promoting the rhs operand.
<p>
Here are the available operators:
<p>
<strong>Unary operators:</strong>
<p>
<ul>
    <li> <strong>bool operator bool() const</strong>:<br>
       Returns <em>true</em> if the <em>BigInt</em> value is unequal zero, otherwise
        <em>false</em> is returned.
<p>
<li> <strong>BigInt &amp;operator++()</strong>:<br>
    <li> <strong>BigInt operator++(int)</strong>:<br>
    <li> <strong>BigInt &amp;operator--()</strong>:<br>
    <li> <strong>BigInt operator--(int)</strong>:<br>
    <li> <strong>BigInt operator-()</strong>:<br>
    <li> <strong>int operator[](size_t idx) const</strong>:<br>
       With <em>BigInt</em> objects it returns the bit-value of the object's
        <em>idx</em>th bit as the value 0 or 1.
<p>
<li> <strong>BigInt::Bit operator[](size_t idx)</strong>:<br>
       With non-const <em>BigInt</em> objects it returns a reference to the
        bit-value of the object's <em>idx</em>th bit. When used as <em>lvalue</em>
        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 (<em>|=</em>), binary and
        (<em>&amp;=</em>) or binary xor (<em>^=</em>). When used as <em>rvalue</em> the value of
        the object's <em>idx</em>th bit is returned as a <em>bool</em> value. When
        inseerted into a <em>std::ostream</em> the bit's value is displayed as 0 or
        1. 
<p>
<li> <strong>BigInt operator~()</strong>:<br>
       This operator is <em>not</em> implemented as it cannot be implemented so
        that it matches the actions of this operator when applied to <em>int</em>
        type values.
<p>
When used on <em>int</em> values this operator toggles all the <em>int</em>'s
        bits. E.g., ~5 represents -6, and ~-6 again equals five. The -6 is the
        result of the sign bit of <em>int</em> values. The obvious implementation
        of <em>BigInt::operator~()</em> 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 <em>int</em> constant ~5:
        when constructing <em>BigInt(~5)</em>, the value -6 is obtained.
<p>
It is possible to change the implementation. E.g., after
            <pre>

        Bigint b(5);
        b = ~b;
            
</pre>

       <em>~b</em> could be implemented so that it results in the value -6. But
        this too leads to unexpected results. While <em>5 &amp; ~5 == 0</em>, this
        would no longer hold true for <em>BigInt</em> objects: Assuming <em>b</em>
        contains 5 then <em>b &amp; ~b</em> would expand to (binary) <em>101 &amp;
        (negative)110</em> which equals (binary) 100.
<p>
Since either implementation produces unexpected results
        <em>BigInt::operator~()</em> was not implemented. Instead two members are
        offered: <em>tildeBits()</em>, toggling all the bits of all the
       <em>BigInt</em> bytes and toggling its sign (so
            <pre>

        Bigint b(5);
        b.tildeBits();
            
</pre>

       changes <em>b</em>'s value into -250), and <em>tildeInt()</em> changing the
        object's value into the value that would have been obtained if a
       <em>BigInt</em> was a mere <em>int</em> (so    
        <pre>

        Bigint b(5);
        b.tildeInt();
            
</pre>

       changes <em>b</em>'s value into -6).
    </ul>
<p>
<strong>Binary operators:</strong>
<p>
<ul>
    <li> <strong>BigInt operator*(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt operator/(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br>
       This operator returns the quotient of the <em>lhs</em> object divided by the
        <em>rhs</em> object. The remainder is lost (The member <em>div</em> performs the
        division and makes the remainder available as well).
    <li> <strong>BigInt operator%(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt operator+(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt operator-(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br> 
    <li> <strong>BigInt operator&lt;&lt;(BigInt const &amp;lhs, size_t nBits)</strong>:<br>
        See also the <em>lshift</em> members. If <em>lhs</em> is positive, 
    <li> <strong>BigInt operator&gt;&gt;=(BigInt const &amp;lhs, size_t nBits)</strong>:<br>
       See also the <em>rshift</em> members.
    <li> <strong>BigInt operator&amp;(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br> 
        This operator returns a <em>BigInt</em> value consisting of the
        <em>bit_and</em>-ed bits and sign flags of lhs and rhs
        operands. Consequently, if one operand is positive, the resulting
        value will be positive. 
    <li> <strong>BigInt operator|(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br> 
        This operator returns a <em>BigInt</em> value consisting of the
        <em>bit_or</em>-ed bits and sign flags of lhs and rhs
        operands. Consequently, if either operand is negative, the result will
        be negative. 
    <li> <strong>BigInt operator^(BigInt const &amp;lhs, BigInt const &amp;rhs)</strong>:<br> 
        This operator returns a <em>BigInt</em> value consisting of the
        <em>bit_xor</em>-ed bits and sign flags of lhs and rhs
        operands. Consequently, if exactly one operand is negative, the result
        will be negative. 
    </ul>
<p>
<strong>(Arithmetic) assignment operator(s):</strong>
<p>
<ul>
    <li> <strong>BigInt &amp;operator=(BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt &amp;operator*=(BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt &amp;operator/=(BigInt const &amp;rhs)</strong>:<br>
       This operator assigns the result of the (integer) division of the current
        <em>BigInt</em> object by <em>ths</em> to the current object. The remainder is
        lost. The member <em>div</em> divides and makes the remainder available as
        well.
    <li> <strong>BigInt &amp;operator%=(BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt &amp;operator+=(BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt &amp;operator-=(BigInt const &amp;rhs)</strong>:<br>
    <li> <strong>BigInt &amp;operator&lt;&lt;=(size_t nBits)</strong>:<br>
        See also the <em>lshift</em> members.
    <li> <strong>BigInt &amp;operator&gt;&gt;=(size_t nBits)</strong>:<br>
        See also the <em>rshift</em> members.
    <li> <strong>BigInt &amp;operator&amp;=(BigInt const &amp;rhs)</strong>:<br> 
        This operator <em>bit_and</em>s the bits and sign flags of the current
        object and the rhs operand.
    <li> <strong>BigInt &amp;operator|=(BigInt const &amp;rhs)</strong>:<br> 
        This operator <em>bit_or</em>s the bits and sign flags of the current
        object and the rhs operand.
    <li> <strong>BigInt &amp;operator^=(BigInt const &amp;rhs)</strong>:<br> 
        This operator <em>bit_xor</em>s the bits and sign flags of the current
        object and the rhs operand.
    </ul>
<p>
Note that the move operator is not available
<p>
<h2>STATIC MEMBERS</h2>
<p>
All members returning a <em>BigInt</em> computed from a set of arguments and
not requiring an existing <em>BigInt</em> object are defined as static members.
<p>
<ul>
    <li> <strong>BigInt fromText(std::string text, int mode = 0)</strong>:<br>
       This member converts a textual representation of a number to a
        <em>BigInt</em> value. Conversion continues until the end of <em>text</em> or
        until a character outside of an expected range is encountered.  
<p>
The expected range may be preset by specifying <em>mode</em> as <em>ios::dec,
        ios::oct,</em> or <em>ios::hex</em> or (the default) the expected range is
        determined by <em>fromText</em> itself by inspecting the characters in
        <em>text</em>.
<p>
By default if <em>text</em> contains hexadecimal characters then
        <em>fromText</em> assumes that the number is represented as a hexadecimal
        value (e.g., <em>"abc"</em> is converted to the (decimal) value 2748); if
        <em>text</em> starts with 0 and contains only characters in the range 0
        until (including) 7 then <em>fromText</em> assumes the number is
        represented as an octal value (e.g., <em>"01234"</em> is converted to the
        (decimal) value 668). Otherwise a decimal value is assumed. 
<p>
If the text does not represent a valid numerical value (of the
        given extraction mode) then a <em>FBB::Exception</em> exception is thrown
        (<em>fromText: text does not represent a BigInt value</em>).
<p>
<li> <strong>BigInt rand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb = ODD)</strong>:<br>
       This member returns a cryptographically strong pseudo-random number
        of <em>size</em> bits. The most significant bit(s) can be controlled by
        <em>msb</em> (by default <strong>MSB_IS_ONE</strong>), the least significant bit can be
        controlled by <em>lsb</em> (by default <strong>ODD</strong>). Before calling this
        member the random number generator must have been seeded.
<p>
From the <strong>RAND_add</strong>(3ssl) man-page:
<p>
OpenSSL makes sure that the PRNG state is unique for each thread. On
        systems that provide <em>/dev/urandom</em>, 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
        <strong>RAND_add</strong>(3ssl), <strong>RAND_egd</strong>(3ssl), <strong>RAND_load_file</strong>(3ssl), or
        <strong>RAND_seed</strong>(3ssl).
<p>
<li> <strong>BigInt randRange(BigInt const &amp;max)</strong>:<br>
       This member returns a cryptographically strong pseudo-random
        number in the range <em>0 &lt;= number &lt; max</em>. Before calling this
        member the random number generator must have been seeded (see also
        <strong>rand</strong>, described above).
<p>
<li> <strong>BigInt setBigEndian(std::string const &amp;bytes)</strong>:<br> 
       The <em>bytes.length()</em> bytes of <em>bytes</em> are used to compute a
        <em>BigInt</em> object which is returned by this function. The characters
        in <em>bytes</em> are interpreted as a series of bytes in big-endian
        order. See also the member function <em>bigEndian()</em> above. The
        returned <em>BigInt</em> has a positive value.
<p>
<li> <strong>BigInt prime(size_t nBits, 
                            BigInt const *mod = 0, BigInt const *rem = 0,
                            PrimeType primeType = ANY)</strong>:<br>
       This member returns a prime number of <em>bBits</em> bits. If both <em>mod</em>
        and <em>rem</em> are non-zero, the condition prime % mod == rem.
        (E.g., use <em>prime % mod == 1</em> in order to suit a given
        generator). The parameter <em>primeType</em> can be <em>ANY</em>, <em>(prime - 1)
        / 2</em> may or may not be a prime. If it is <em>SAFE</em> then  <em>(prime - 1)
        / 2</em> will be a (so-called <em>safe</em>) prime.
<p>
<li> <strong>BigInt pseudoRand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb =
            ODD)</strong>:<br> 
       This member returns a potentially predictable pseudo-random number of
        <em>size</em> bits. The most significant bit(s) can be controlled by
        <em>msb</em> (by default <strong>MSB_IS_ONE</strong>), the least significant bit can be
        controlled by <em>lsb</em> (by default <strong>ODD</strong>). It can be used for
        non-cryptographic purposes and for certain purposes in cryptographic
        protocols, but usually not for key generation.
<p>
<li> <strong>BigInt pseudoRandRange(BigInt const &amp;max)</strong>:<br>
       This member returns a potentially predictable  pseudo-random
       number in the range <em>0 &lt;= number &lt; max</em>.
    </ul>
<p>
<h2>FREE FUNCTIONS IN THE FBB NAMESPACE</h2>
<p>
<ul>
    <li> <strong>std::ostream &amp;operator&lt;&lt;(ostream &amp;out, BigInt const &amp;value)</strong>:<br>
        Inserts <em>value</em> into the provided <em>ostream</em>. If the <em>hex</em>
manipulator has been inserted into the stream before inserting the <em>BigInt</em>
value the value will be displayed as a hexadecimal value (without a leading
<em>0x</em>); if the <em>oct</em> 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 <em>dec</em> manipulator is active. If the
<em>BigInt</em> value is negative its value will be preceded by a minus
character. 
    <li> <strong>std::istream &amp;operator&gt;&gt;(istream &amp;in, BigInt &amp;value)</strong>:<br>
       Extracts <em>value</em> from the provided <em>istream</em>. Depending on the
        currently set extraction mode (<em>dec, oct,</em> or <em>hex</em>) the matching
        set of characters will be extracted from <em>in</em> and converted to a
        number which is stored in <em>value</em>. 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 <em>failbit</em> is set. The extracted value may be preceded
        by a minus character, resulting in an extracted negative value.
    </ul>
<p>
<h2>EXAMPLE</h2>
        <pre>

#include &lt;iostream&gt;
#include &lt;bobcat/bigint&gt;

using namespace std;
using namespace FBB;

int main()
{
    BigInt value(BigInt::prime(100));
    BigInt mod(BigInt::rand(50));
    BigInt inverse(value.inverseModc(mod));

    cout &lt;&lt; '(' &lt;&lt; value &lt;&lt; " * " &lt;&lt; inverse &lt;&lt; ") % " &lt;&lt; mod &lt;&lt; " = " &lt;&lt;
             (    value       *      inverse     ) %      mod &lt;&lt; endl;
}
        
</pre>
 
<p>
<h2>FILES</h2>
    <em>bobcat/bigint</em> - defines the class interface
<p>
<h2>SEE ALSO</h2>
    <strong>bobcat</strong>(7), <strong>diffiehellman</strong>(3bobcat), 
    <strong>RAND_add</strong>(3ssl), <strong>RAND_egd</strong>(3ssl),
    <strong>RAND_load_file</strong>(3ssl), <strong>RAND_seed</strong>(3).
<p>
<h2>BUGS</h2>
<p>
Sep/Oct 2013: due to a change in library handling by the linker
(cf. <a href="http://fedoraproject.org/wiki/UnderstandingDSOLinkChange">http://fedoraproject.org/wiki/UnderstandingDSOLinkChange</a> and
<a href="https://wiki.debian.org/ToolChain/DSOLinking">https://wiki.debian.org/ToolChain/DSOLinking</a>) libraries that are
indirectly required are no longer automatically linked to your program. With
<strong>BigInt</strong> this is <em>libcrypto</em>, which requires programs to link to both
<em>bobcat</em> and <em>crypto</em>.
<p>

<h2>DISTRIBUTION FILES</h2>
    <ul>
    <li> <em>bobcat_3.19.01-x.dsc</em>: detached signature;
    <li> <em>bobcat_3.19.01-x.tar.gz</em>: source archive;
    <li> <em>bobcat_3.19.01-x_i386.changes</em>: change log;
    <li> <em>libbobcat1_3.19.01-x_*.deb</em>: debian package holding the
            libraries;
    <li> <em>libbobcat1-dev_3.19.01-x_*.deb</em>: debian package holding the
            libraries, headers and manual pages;
    <li> <em>http://sourceforge.net/projects/bobcat</em>: public archive location;
    </ul>
<p>
<h2>BOBCAT</h2>
    Bobcat is an acronym of `Brokken's Own Base Classes And Templates'.
<p>
<h2>COPYRIGHT</h2>
    This is free software, distributed under the terms of the 
    GNU General Public License (GPL).
<p>
<h2>AUTHOR</h2>
    Frank B. Brokken (<strong>f.b.brokken@rug.nl</strong>).
<p>