lib/tommath/tommath.tex

455 MPI library was used as a API template for all the basic functions.  MPI was chosen because it is another library that fits
487 functions share the same parameter passing convention.  The learning curve is fairly shallow with the API provided
531 That is, to implement the lowest level dependencies first and work towards the most abstract functions last.  For example,
538 prototype the initial functions that are not dependent on other functions (within the library).  After I
539 implement these base functions I prototype more dependent functions and implement them.   The process repeats until
540 I implement all of the functions I require.  For example, in the case of LibTomMath I implemented functions such as
555 Only after the majority of the functions were in place did I pursue a less hierarchical approach to auditing and optimizing
556 the source code.  For example, one day I may audit the multipliers and the next day the polynomial basis functions.
619 many digits are available in the array to use by functions before it has to increase in size.  When the \textbf{used} count
636 The only exceptions are when the structure is passed to initialization functions such as mp\_init() and mp\_init\_copy().
654 In LibTomMath the multiple precision integer functions accept parameters from left to right as pointers to mp\_int
664 The left to right order is a fairly natural way to implement the functions since it lets the developer read aloud the
665 functions and make sense of them.  For example, the first function would read ``multiply a and b and store in c''.
674 feature to implement since it allows the calling functions to cut down on the number of variables it must maintain.
720 The logical starting point when actually writing multiple precision integer functions is the initialization and
772 heap operations later functions will have to perform in the future.  If \textbf{MP\_PREC} is set correctly the slack
812 mp\_int structure has been properly initialized and is safe to use with other functions within the library.
933 to re-allocate the memory.  As per the other functions XREALLOC is actually a macro which evaluates to realloc by default.  The realloc
996 functions to work with.
1040 The function uses the ``stdarg.h'' \textit{va} functions to step portably through the arguments to the function.  A count
1201 be used considerably in other functions.  Technically, a pointer alias is simply a short hand alias used to lower the
1257 useful within functions that need to modify an argument but do not wish to actually modify the original copy.  The
1494 as well as the  call to mp\_clamp() on line 41.  Both functions will clamp excess leading digits which keeps
1508 To facilitate working with the results of the comparison functions three constants are required.
1651 Historically that convention stems from the MPI library where ``s\_'' stood for static functions that were hidden from the developer entirely.
1936 level functions do so.  Returning their return code is sufficient.
5148 Now that the table is available the sliding window may begin.  The following list describes the functions of all the variables in the window.
5521 the helper functions assume the single digit input is positive and will treat them as such.
6127 The least common multiple arises often in coding theory as well as number theory.  If two functions have periods of $a$ and $b$ respectively they will