lib/tommath/tommath.tex

392                      & new theory from the perspective of a student. \\
407 devising new theory.  These problems are quick tests to see if the material is understood.  Problems at the second level
413 involve devising a new algorithm or implementing a variation of another algorithm previously presented.  Readers who can
543 dependent function mp\_exptmod() was written.  Adding the new multiplication algorithms did not require changes to the
545 for new algorithms.  This methodology allows new algorithms to be tested in a complete framework with relative ease.
783 iteration the variable $a$ is substituted for a new integer that lies inclusively between $b$ and $c$.  If $b > c$ occured
1171 \textbf{Remark.}  This algorithm also introduces a new idiosyncrasy that will be used throughout the rest of the
1708 of the two inputs.  The original \textbf{used} count of $c$ is copied and set to the new used count.
1753 For this algorithm a new variable is required to make the description simpler.  Recall from section 1.3.1 that a mp\_digit must be able to represent
1933 The source code follows the algorithm fairly closely.  The most notable new source code addition is the usage of the $res$ integer variable which
2612 \textbf{MP\_WARRAY}.  This new constant is used to control the stack usage in the Comba routines.  By default it is
2817 slower and also often doesn't exist.  This new algorithm only performs two reads per iteration under the assumption that the
3011 The new coding element in this routine, not  seen in previous routines, is the usage of goto statements.  The conventional
3682 $a = 180388626447$ modulo $b$ using the above reduction equation.  The quotient using the new formula is $\lfloor (a \cdot \mu) / 2^q \rfloor = 152913$.
3722 With the new observation the multiplicand for the quotient is equal to $q_0 = \lfloor a / \beta^{m - 1} \rfloor = 99929$.  The quotient is then
3994 previous algorithm re-written to compute the Montgomery reduction in this new fashion.
4026 In each iteration of the loop on step 1 a new value of $\mu$ must be calculated.  The value of $-1/n_0 \mbox{ (mod }\beta\mbox{)}$ is used
4535 In general the restricted Diminished Radix reduction algorithm is much faster since it has considerably lower overhead.  However, this new
4822 of $b$ is shifted left one bit to make the next bit down from the most signficant bit the new most significant bit.  In effect each
5021 the modular inverse of $G$ and $tmpX$ is assigned the absolute value of $X$.  The algorithm will recuse with these new values with a positive
5154    \item When $mode = 1$ a non-zero bit has been seen before and a new $winsize$-bit window has not been formed yet.  In this mode leading $0$ bits
5155          are read and a single squaring is performed.  If a non-zero bit is read a new window is created.
5156    \item When $mode = 2$ the algorithm is in the middle of forming a window and new bits are appended to the window from the most significant bit
5159 \item The variable $bitcnt$ indicates how many bits are left in the current digit of the exponent left to be read.  When it reaches zero a new digit
5169 inside this loop is to extract a new digit if no more bits are available in the current digit.  If there are no bits left a new digit is