lib/tommath/bn.tex

346 Where ``mp\_digit'' is a data type that represents individual digits of the integer.  By default, an mp\_digit is the
515 default number of digits.  By default, all initializers allocate \textbf{MP\_PREC} digits.  This function lets
524 to have $size$ digits (which are all initially zero).
549 digits can be removed to return memory to the heap with the mp\_shrink() function.
556 This will remove excess digits of the mp\_int $a$.  If the operation fails the mp\_int should be intact without the
557 excess digits being removed.  Note that you can use a shrunk mp\_int in further computations, however, such operations
592 \subsection{Adding additional digits}
594 Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
595 the integer the mp\_int is meant to equal.   The \textit{used} parameter dictates how many digits are significant, that is,
596 contribute to the value of the mp\_int.  The \textit{alloc} parameter dictates how many digits are currently available in
597 the array.  If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
605 This will grow the array of digits of $a$ to $size$.  If the \textit{alloc} parameter is already bigger than
622    /* We need to add 20 digits to the number  */
692 accept a 32-bit input regardless of the size of a single digit.  However, since the value may span several digits
809 An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the
811 mp\_int variables based on their digits only.
875 differ it will return immediately based on their signs.  If the signs are equal then it will compare the digits
1067 $f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be
1070 To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place.  The
1078 This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes
1079 in the least significant digits.  Similarly to divide by a power of $x$ the following function is provided.
1086 in place and no new digits are required to complete it.
1239 GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4).  That is, at
1240 110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.
1396 setup for instance, the limit is $127$ digits ($3556$--bits).   Note that this function is not limited to
1397 $127$ digits just that it falls back to a baseline algorithm after that point.
1400 where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).