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\documentclass[10pt,draft]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath, amssymb, mathtools}
\DeclarePairedDelimiter\ab{\lvert}{\rvert}
\begin{document}
{\Huge libzahl}
\\
Unless specified otherwise, all times are of type {\tt z\_t}.
\\ \\
\begin{tabular}{lll}
\textbf{Initialisation} & {} & {} \\
Initialise libzahl & {\tt zsetup(env)} & must be called before any other function is used, \\
{} & {} & $~~~~~$ {\tt env} is a {\tt jmp\_buf} all
functions will {\tt longjmp} \\
{} & {} & $~~~~~$ to --- with value 1 --- on error \\
Deinitialise libzahl & {\tt zunsetup()} & will free any pooled memory \\
Initialise $a$ & {\tt zinit(a)} & must be called before used in any other function \\
Deinitialise $a$ & {\tt zfree(a)} & must not be used again before reinitialisation \\
\\
\textbf{Error handling} & {} & {} \\
Get error code & {\tt zerror(a)} & returns {\tt enum zerror},
and stores description in \\
{} & {} & $~~~~~$ {\tt const char **a} \\
Print error description & {\tt zperror(a)} & behaves like {\tt perror(a)}, {\tt a} is a,
possibly {\tt NULL}, \\
{} & {} & $~~~~~$ {\tt const char *} \\
\\
\textbf{Arithmetic} & {} & {} \\
$a \gets b + c$ & {\tt zadd(a, b, c)} & \\
$a \gets b - c$ & {\tt zsub(a, b, c)} & \\
$a \gets b \cdot c$ & {\tt zmul(a, b, c)} & \\
$a \gets b \cdot c \mod d$ & {\tt zmodmul(a, b, c, d)} & $0 \le a < \ab{d}$ \\
$a \gets [b / c]$ & {\tt zdiv(a, b, c)} & rounded towards zero \\
$a \gets [c / d]$ & {\tt zdivmod(a, b, c, d)} & rounded towards zero \\
$b \gets c \mod d$ & {\tt zdivmod(a, b, c, d)} & $0 \le b < \ab{d}$ \\
$a \gets b \mod c$ & {\tt zmod(a, b, c)} & $0 \le a < \ab{c}$ \\
%$a \gets b / c$ & {\tt zdiv\_exact(a, b, c)} & assumes $c \vert d$ \\ %%
$a \gets b^2$ & {\tt zsqr(a, b)} & \\
$a \gets b^2 \mod c$ & {\tt zmodsqr(a, b, c)} & $0 \le a < \ab{c}$ \\
$a \gets b^2$ & {\tt zsqr(a, b)} & \\
$a \gets b^c$ & {\tt zpow(a, b, c)} & \\
$a \gets b^c$ & {\tt zpowu(a, b, c)} & {\tt c} is an {\tt unsigned long long int} \\
$a \gets b^c \mod d$ & {\tt zmodpow(a, b, c, d)} & $0 \le a < \ab{d}$ \\
$a \gets b^c \mod d$ & {\tt zmodpowu(a, b, c, d)} & ditto, {\tt c} is an {\tt unsigned long long int} \\
$a \gets \ab{b}$ & {\tt zabs(a, b)} & \\
$a \gets -b$ & {\tt zneg(a, b)} & \\
\\
\textbf{Assignment} & {} & {} \\
$a \gets b$ & {\tt zset(a, b)} & \\
$a \gets b$ & {\tt zseti(a, b)} & {\tt b} is an {\tt int64\_t} \\
$a \gets b$ & {\tt zsetu(a, b)} & {\tt b} is a {\tt uint64\_t} \\
$a \gets b$ & {\tt zsets(a, b)} & {\tt b} is a decimal {\tt const char *} \\
%$a \gets b$ & {\tt zsets\_radix(a, b, c)} & {\tt b} is a radix $c$ {\tt const char *}, \\ %%
%{} & {} & $~~~~~$ {\tt c} is an {\tt unsigned long long int} \\ %%
$a \leftrightarrow b$ & {\tt zswap(a, b)} & \\
\\
\textbf{Comparison} & {} & {} \\
Compare $a$ and $b$ & {\tt zcmp(a, b)} & returns {\tt int} $\mbox{sgn}(a - b)$ \\
Compare $a$ and $b$ & {\tt zcmpi(a, b)} & ditto, {\tt b} is an {\tt int64\_t} \\
Compare $a$ and $b$ & {\tt zcmpu(a, b)} & ditto, {\tt b} is a {\tt uint64\_t} \\
Compare $\ab{a}$ and $\ab{b}$ & {\tt zcmpmag(a, b)} & returns {\tt int} $\mbox{sgn}(\ab{a} - \ab{b})$ \\
\\
\end{tabular}
\newpage
\begin{tabular}{lll}
\textbf{Bit operations} & {} & {} \\
$a \gets b \wedge c$ & {\tt zand(a, b, c)} & bitwise \\
$a \gets b \vee c$ & {\tt zor(a, b, c)} & bitwise \\
$a \gets b \oplus c$ & {\tt zxor(a, b, c)} & bitwise \\
$a \gets \lnot b$ & {\tt znot(a, b, c)} & bitwise, cut at highest set bit \\
$a \gets b \cdot 2^c$ & {\tt zlsh(a, b, c)} & {\tt c} is a {\tt size\_t} \\
$a \gets [b / 2^c]$ & {\tt zrsh(a, b, c)} & ditto, rounded towards zero \\
$a \gets b \mod 2^c$ & {\tt ztrunc(a, b, c)} & ditto, {\tt a} shares signum with {\tt b} \\
Get index of highest set bit & {\tt zbits(a)} & returns {\tt size\_t}, 1 if $a = 0$ \\
Get index of lowest set bit & {\tt zlsb(a)} & returns {\tt size\_t}, {\tt SIZE\_MAX} if $a = 0$ \\
Is bit $b$ in $a$ set? & {\tt zbtest(a, b)} & {\tt b} is a {\tt size\_t}, returns {\tt int} \\
$a \gets b$, set bit $c$ & {\tt zbset(a, b, c, 1)} & {\tt c} is a {\tt size\_t} \\
$a \gets b$, clear bit $c$ & {\tt zbset(a, b, c, 0)} & ditto \\
$a \gets b$, flip bit $c$ & {\tt zbset(a, b, c, -1)} & ditto \\
$a \gets [c / 2^d]$ & {\tt zsplit(a, b, c, d)} & {\tt d} is a {\tt size\_t}, rounded towards zero \\
$b \gets c \mod 2^d$ & {\tt zsplit(a, b, c, d)} & ditto, {\tt b} shares signum with {\tt c} \\
\\
\textbf{Conversion to string} & {} & {} \\
Convert $a$ to decimal & {\tt zstr(a, b, c)} & returns the resulting {\tt const char *} \\
{} & {} & $~~~~~$ --- {\tt b} unless {\tt b} is {\tt NULL},
--- {\tt c} must be \\
{} & {} & $~~~~~$ either 0 or at least the length of the \\
{} & {} & $~~~~~$ resulting string but at most the \\
{} & {} & $~~~~~$ allocation size of {\tt b} minus 1 \\
%Convert $a$ to radix $d$ & {\tt zstr\_radix(a, b, c, d)} & ditto,
% {\tt d} is an {\tt unsigned long long int}\\ %%
Get string length of $a$ & {\tt zstr\_length(a, b)} & returns {\tt size\_t} length of $a$ in radix $b$ \\
\\
\textbf{Marshallisation} & {} & {} \\
Marshal $a$ into $b$ & {\tt zsave(a, b)} & returns {\tt size\_t} number of saved bytes, \\
{} & {} & $~~~~~$ {\tt b} is a {\tt char *\_t} \\
Get marshal-size of $a$ & {\tt zsave(a, NULL)} & returns {\tt size\_t} \\
Unmarshal $a$ from $b$ & {\tt zload(a, b)} & returns {\tt size\_t} number of read bytes, \\
{} & {} & $~~~~~$ {\tt b} is a {\tt const char *\_t} \\
\\
\textbf{Number theory} & {} & {} \\
$a \gets \mbox{sgn}(b)$ & {\tt zsignum(a, b)} & \\
Is $a$ even? & {\tt zeven(a)} & returns {\tt int} 1 (true) or 0 (false) \\
Is $a$ even? & {\tt zeven\_nonzero(a)} & ditto, assumes $a \neq 0$ \\
Is $a$ odd? & {\tt zodd(a)} & returns {\tt int} 1 (true) or 0 (false) \\
Is $a$ odd? & {\tt zodd\_nonzero(a)} & ditto, assumes $a \neq 0$ \\
Is $a$ zero? & {\tt zzero(a)} & returns {\tt int} 1 (true) or 0 (false) \\
$a \gets \gcd(c, b)$ & {\tt zgcd(a, b, c)} & $a < 0$ iff $b < 0 \wedge c < 0$ \\
Is $b$ a prime? & {\tt zptest(a, b, c)} & {\tt c} runs of Miller--Rabin, returns \\
{} & {} & $~~~~~$ {\tt enum zprimality} {\tt NONPRIME} (0) \\
{} & {} & $~~~~~$ (and stores the witness in {\tt a} unless \\
{} & {} & $~~~~~$ {\tt a} is {\tt NULL}),
{\tt PROBABLY\_PRIME} (1), or \\
{} & {} & $~~~~~$ {\tt PRIME} (2) \\
\textbf{Random numbers} & {} & {} \\
$a \xleftarrow{\$} \textbf{Z}_d $ & {\tt zrand(a, b, UNIFORM, d)}
& {\tt b} is a {\tt zranddev}, e.g. {\tt DEFAULT\_RANDOM} \\
\\
\end{tabular}
\end{document}
|
