commitbf8dfe5a718f7daa96d918367f30a3c272533b40parent6b97020bdbdc5eb08aaa638d0649013ce9c65188Author:Mattias Andrée <maandree@kth.se>Date:Tue, 14 Jun 2016 12:39:19 +0200 Fix typos found by Marc Signed-off-by: Mattias Andrée <maandree@kth.se>Diffstat:

doc/not-implemented.tex | | | 28 | ++++++++++++++-------------- |

1 file changed, 14 insertions(+), 14 deletions(-)diff --git a/doc/not-implemented.tex b/doc/not-implemented.tex@@ -2,30 +2,30 @@ \label{chap:Not implemented} In this chapter we maintain a list of -features we have choosen not to implement, +features we have chosen not to implement, but would fit into libzahl had we not have our priorities straight. Functions listed -herein will only be implemented if there -is shown that it would be overwhelmingly +herein will only be implemented if it is +shown that it would be overwhelmingly advantageous. For each feature, a sample implementation or a mathematical expression on which you can base your implemention is included. The sample implementations create temporary integer references, this is to -simplify in the examples. You should try to +simplify the examples. You should try to use dedicated variables; in case of recursion, a robust program should store temporary variables on a stack, so they can be -clean up of something happens. +clean up if something happens. Research problems, like prime-factorisation and discrete logarithms do not fit in the scope of bignum libraries. % Unless they are extraordinarily bloated with vague mission-scope, like systemd. -And therefore does not fit into libzahl, +And therefore do not fit into libzahl, and will not be included in this chapter. Operators and functions that grow so ridiculously fast that a tiny lookup table -constructed to cover all practicle input +constructed to cover all practical input will also not be included in this chapter, nor in libzahl. @@ -196,7 +196,7 @@ TODO % Square: Cipolla's algorithm, Pocklington's algorithm, Tonelli–Shanks al \( \displaystyle{ n! = \left \lbrace \begin{array}{ll} - \displaystyle{\prod_{i = 0}^n i} & \textrm{if}~ n \ge 0 \\ + \displaystyle{\prod_{i = 1}^n i} & \textrm{if}~ n \ge 0 \\ \textrm{undefined} & \textrm{otherwise} \end{array} \right . }\) @@ -463,7 +463,7 @@ Each call to {\tt fib\_ll} returns $F_n$ and $F_{n - 1}$ for any input $n$. $F_{k}$ is only correctly returned for $k \ge 0$. $F_n$ and $F_{n - 1}$ is used for calculating $F_{2n}$ or $F_{2n + 1}$. The algorithm -can be speed up with a larger lookup table than one +can be sped up with a larger lookup table than one covering just the base cases. Alternatively, a naïve calculation could be used for sufficiently small input. @@ -596,8 +596,8 @@ a fully unrolled \label{sec:Hamming distance} A simple way to compute the Hamming distance, -the number of differing bits, between two number -is with the function +the number of differing bits, between two +numbers is with the function \begin{alltt} size_t @@ -615,8 +615,8 @@ is with the function \noindent The performance of this function could -be improve by comparing character by -character manually with using {\tt zxor}. +be improved by comparing character by +character manually using {\tt zxor}. \newpage @@ -658,7 +658,7 @@ side-effects. This could be useful for creating duplicates with modified sign. But only if neither -{\tt r} or {\tt a} will be modified whilst +{\tt r} nor {\tt a} will be modified whilst both are in use. Because it is unsafe, fairly simple to create an implementation with acceptable performance — {\tt *r = *a},