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	refsheet.tex - libzahl - big integer library
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	refsheet.tex (7771B)
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	1 \documentclass[10pt]{article}
	2 \usepackage[margin=1in]{geometry}
	3 \usepackage{amsmath, amssymb, mathtools}
	4 \usepackage{microtype}
	5 \DeclarePairedDelimiter\ab{\lvert}{\rvert}
	6
	7 \newcommand{\size}{{\tt size\_t}}
	8 \newcommand{\ullong}{{\tt unsigned long long int}}
	9
	10 \newcommand{\entry}[3]{ #2 & {\tt #1} & #3 \\ }
	11 \newcommand{\cont}[1]{ & & #1 \\ }
	12
	13 \begin{document}
	14
	15
	16
	17 {\Huge libzahl}
	18 \vspace{1ex}
	19
	20 Unless specified otherwise, returns are {\tt void} and all parameters ar…
	21 \vspace{1.5em}
	22
	23
	24
	25 \hspace{-2ex}
	26 \begin{tabular}{lll}
	27
	28
	29
	30 \textbf{Initialisation} \\
	31 \entry{zsetup(env)} {Initialise libzahl} {must be called before any ot…
	32 \cont {used, {\tt env} is a {\tt jm…
	33 \cont {{\tt longjmp} to --- with va…
	34 \entry{zunsetup()} {Deinitialise libzahl} {will free any pooled memory}
	35 \entry{zinit(a)} {Initialise $a$} {call once before use in any …
	36 \entry{zfree(a)} {Deinitialise $a$} {must not be used again befor…
	37 \\
	38
	39 \textbf{Error handling} \\
	40 \entry{zerror(a)} {Get error code} {returns {\tt enum zerror},…
	41 \cont {description in {\tt const …
	42 \entry{zperror(a)} {Print error description} {behaves like {\tt perror(a…
	43 \cont {possibly {\tt NULL} or $\v…
	44 %\\
	45
	46 \textbf{Arithmetic} \\
	47 \entry{zadd(a, b, c)} {$a \gets b + c$} {}
	48 \entry{zsub(a, b, c)} {$a \gets b - c$} {}
	49 \entry{zmul(a, b, c)} {$a \gets b \cdot c$} {}
	50 \entry{zmodmul(a, b, c, d)} {$a \gets b \cdot c \mod d$} {$0 \le a~\mbo…
	51 \entry{zdiv(a, b, c)} {$a \gets b / c$} {rounded towar…
	52 \entry{zdivmod(a, b, c, d)} {$a \gets c / d$} {rounded towar…
	53 \entry{zdivmod(a, b, c, d)} {$b \gets c \mod d$} {$0 \le b~\mbo…
	54 \entry{zmod(a, b, c)} {$a \gets b \mod c$} {$0 \le a~\mbo…
	55 %\entry{zdiv\_exact(a, b, c)} {$a \gets b / c$} {assumes $c \…
	56 \entry{zsqr(a, b)} {$a \gets b^2$} {}
	57 \entry{zmodsqr(a, b, c)} {$a \gets b^2 \mod c$} {$0 \le a < \a…
	58 \entry{zsqr(a, b)} {$a \gets b^2$} {}
	59 \entry{zpow(a, b, c)} {$a \gets b^c$} {}
	60 \entry{zpowu(a, b, c)} {$a \gets b^c$} {{\tt c} is an…
	61 \entry{zmodpow(a, b, c, d)} {$a \gets b^c \mod d$} {$0 \le a~\mbo…
	62 \entry{zmodpowu(a, b, c, d)} {$a \gets b^c \mod d$} {ditto, {\tt c…
	63 \entry{zabs(a, b)} {$a \gets \ab{b}$} {}
	64 \entry{zneg(a, b)} {$a \gets -b$} {}
	65 \\
	66
	67 \textbf{Assignment} \\
	68 \entry{zset(a, b)} {$a \gets b$} {}
	69 \entry{zseti(a, b)} {$a \gets b$} {{\tt b} is an {\t…
	70 \entry{zsetu(a, b)} {$a \gets b$} {{\tt b} is a {\tt…
	71 \entry{zsets(a, b)} {$a \gets b$} {{\tt b} is a deci…
	72 %\entry{zsets\_radix(a, b, c)} {$a \gets b$} {{\tt b} is a rad…
	73 %\cont {{\tt c} is an \u…
	74 \entry{zswap(a, b)} {$a \leftrightarrow b$} {}
	75 \\
	76
	77 \textbf{Comparison} \\
	78 \entry{zcmp(a, b)} {Compare $a$ and $b$} {returns {\tt int}…
	79 \entry{zcmpi(a, b)} {Compare $a$ and $b$} {ditto, {\tt b} is…
	80 \entry{zcmpu(a, b)} {Compare $a$ and $b$} {ditto, {\tt b} is…
	81 \entry{zcmpmag(a, b)} {Compare $\ab{a}$ and $\ab{b}$} {returns {\tt int}…
	82 \\
	83
	84
	85
	86 \end{tabular}
	87 \newpage
	88 \hspace{-2ex}
	89 \begin{tabular}{lll}
	90
	91
	92
	93 \textbf{Bit operation} \\
	94 \entry{zand(a, b, c)} {$a \gets b \wedge c$} {bitwise}
	95 \entry{zor(a, b, c)} {$a \gets b \vee c$} {bitwise}
	96 \entry{zxor(a, b, c)} {$a \gets b \oplus c$} {bitwise}
	97 \entry{znot(a, b, c)} {$a \gets \lnot b$} {bitwise, cut …
	98 \entry{zlsh(a, b, c)} {$a \gets b \cdot 2^c$} {{\tt c} is a …
	99 \entry{zrsh(a, b, c)} {$a \gets b / 2^c$} {ditto, rounde…
	100 \entry{ztrunc(a, b, c)} {$a \gets b \mod 2^c$} {ditto, $a$ sh…
	101 \entry{zbits(a)} {Get number of used bits} {returns \size…
	102 \entry{zlsb(a)} {Get index of lowest set bit} {returns \size…
	103 \entry{zbtest(a, b)} {Is bit $b$ in $a$ set?} {{\tt b} is a …
	104 \entry{zbset(a, b, c, 1)} {$a \gets b$, set bit $c$} {{\tt c} is a …
	105 \entry{zbset(a, b, c, 0)} {$a \gets b$, clear bit $c$} {ditto}
	106 \entry{zbset(a, b, c, -1)} {$a \gets b$, flip bit $c$} {ditto}
	107 \entry{zsplit(a, b, c, d)} {$a \gets c / 2^d$} {{\tt d} is a …
	108 \entry{zsplit(a, b, c, d)} {$b \gets c \mod 2^d$} {ditto, $b$ sh…
	109 \\
	110
	111 \textbf{Conversion to string} \\
	112 \entry{zstr(a, b, c)} {Convert $a$ to decimal} {returns the …
	113 \cont {--- {\tt b} …
	114 {\tt NUL…
	115 \cont {either 0 or …
	116 \cont {resulting st…
	117 \cont {allocation s…
	118 %\entry{zstr\_radix(a, b, c, d)} {Convert $a$ to radix $d$} {ditto, {\tt…
	119 \entry{zstr\_length(a, b)} {Get string length of $a$} {returns \siz…
	120 \\
	121
	122 \textbf{Marshallisation} \\
	123 \entry{zsave(a, b)} {Marshal $a$ into $b$} {returns \size{} number…
	124 \cont {{\tt b} is a {\tt void…
	125 \entry{zsave(a, NULL)} {Get marshal-size of $a$} {returns \size{}}
	126 \entry{zload(a, b)} {Unmarshal $a$ from $b$} {returns \size{} number…
	127 \cont {{\tt b} is a {\tt cons…
	128 %\\
	129
	130 \textbf{Number theory} \\
	131 \entry{zsignum(a, b)} {$a \gets \mbox{sgn}~b$} {}
	132 \entry{zeven(a)} {Is $a$ even?} {returns {\tt int} 1 …
	133 \entry{zeven\_nonzero(a)} {Is $a$ even?} {ditto, assumes $a \n…
	134 \entry{zodd(a)} {Is $a$ odd?} {returns {\tt int} 1 …
	135 \entry{zodd\_nonzero(a)} {Is $a$ odd?} {ditto, assumes $a \n…
	136 \entry{zzero(a)} {Is $a$ zero?} {returns {\tt int} 1 …
	137 \entry{zgcd(a, b, c)} {$a \gets \gcd(c, b)$} {$a < 0$ if $b < 0 \w…
	138 \entry{zptest(a, b, c)} {Is $b$ a prime?} {$c$ runs of Miller--…
	139 \cont {{\tt enum zprimality…
	140 \cont {(and stores the witn…
	141 \cont {{\tt a} is {\tt NULL…
	142 \cont {{\tt PRIME} (2)}
	143 %\\
	144
	145 \textbf{Randomness} \\
	146 \entry{zrand(a, b, UNIFORM, d)} {$a \xleftarrow{\$} \textbf{Z}_d$}
	147 {{\tt b} is a {\tt enum zranddev}, e.g.}
	148 \cont {{\tt DEFAULT\_RANDOM}, {\tt FASTEST\_RANDOM}}
	149 \\
	150
	151
	152
	153 \end{tabular}
	154 \end{document}