hcrypto/libtommath/tommath.tex

281 the reader how the algorithms fit together as well as where to start on various taskings.
424 Often problems will be tied together.  The purpose of this is to start a chain of thought that will be discussed in future chapters.  The reader
537 Usually when I start a project I will begin with the header files.  I define the data types I think I will need and
549 \includegraphics{pics/design_process.ps}
1049 though, with no final carry into the last position.  However, suppose the destination had to be first expanded
1086 the most.  For example, this will happen in cases where there is not a carry to fill the last position.  Step two fixes the sign for
1502 positions.  If any leading digit of one integer is greater than a digit in the same position of another integer then obviously it must be greater.
1548 By step three both inputs must have the same number of digits so its safe to start from either $a.used - 1$ or $b.used - 1$ and count down to
1632 One significant difference between a logical shift and the way decimals are shifted is that digits below the zero'th position are removed
1822 10 will ensure that any leading digits of $c$ above the $max$'th position are zeroed.
2190 \includegraphics{pics/sliding_window.ps}
2910 \item  To a lesser extent memory bandwidth and function call overheads.  Provided the values are in the processor cache this is less of an
3396 only to even outputs and it is the square of the term at the $\lfloor ix / 2 \rfloor$ position.
3805 Recall that the multiplication for the quotient on step 3 must only produce digits at or above the $m-1$'th position.  An algorithm called
4439 the term at the $m+i$'th position which is subsequently multiplied by $k$ and added to the term at the $i$'th position.  After the loop the $m$'th
5182 \includegraphics{pics/expt_state.ps}
5259 let $r$ represent the remainder $r = y - x \lfloor y / x \rfloor$.  The following simple algorithm will be used to start the discussion.
5513 above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}.
5725 The initial value of the approximation is t$2 = 2$ which allows the algorithm to start with very small values and quickly converge on the
5833 \hspace{3mm}6.1  Let $y$ denote the position in the map of $str_{iy}$. \\