refsheet.tex (7771B)
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 are of type {\tt z\_t}. 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 other function is} 32 \cont {used, {\tt env} is a {\tt jmp\_buf} all functions will} 33 \cont {{\tt longjmp} to --- with value 1 --- on error} 34 \entry{zunsetup()} {Deinitialise libzahl} {will free any pooled memory} 35 \entry{zinit(a)} {Initialise $a$} {call once before use in any other function} 36 \entry{zfree(a)} {Deinitialise $a$} {must not be used again before reinitialisation} 37 \\ 38 39 \textbf{Error handling} \\ 40 \entry{zerror(a)} {Get error code} {returns {\tt enum zerror}, and stores} 41 \cont {description in {\tt const char **a}} 42 \entry{zperror(a)} {Print error description} {behaves like {\tt perror(a)}, {\tt a} is a,} 43 \cont {possibly {\tt NULL} or $\varepsilon$, {\tt const char *}} 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)} {$a \gets b \cdot c \mod d$} {$0 \le a~\mbox{sgn}~bc < \ab{d}$} 51 \entry{zdiv(a, b, c)} {$a \gets b / c$} {rounded towards zero} 52 \entry{zdivmod(a, b, c, d)} {$a \gets c / d$} {rounded towards zero} 53 \entry{zdivmod(a, b, c, d)} {$b \gets c \mod d$} {$0 \le b~\mbox{sgn}~c < \ab{d}$} 54 \entry{zmod(a, b, c)} {$a \gets b \mod c$} {$0 \le a~\mbox{sgn}~b < \ab{c}$} 55 %\entry{zdiv\_exact(a, b, c)} {$a \gets b / c$} {assumes $c \vert d$} 56 \entry{zsqr(a, b)} {$a \gets b^2$} {} 57 \entry{zmodsqr(a, b, c)} {$a \gets b^2 \mod c$} {$0 \le a < \ab{c}$} 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 \ullong{}} 61 \entry{zmodpow(a, b, c, d)} {$a \gets b^c \mod d$} {$0 \le a~\mbox{sgn}~b^c < \ab{d}$} 62 \entry{zmodpowu(a, b, c, d)} {$a \gets b^c \mod d$} {ditto, {\tt c} is an \ullong{}} 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 {\tt int64\_t}} 70 \entry{zsetu(a, b)} {$a \gets b$} {{\tt b} is a {\tt uint64\_t}} 71 \entry{zsets(a, b)} {$a \gets b$} {{\tt b} is a decimal {\tt const char *}} 72 %\entry{zsets\_radix(a, b, c)} {$a \gets b$} {{\tt b} is a radix $c$ {\tt const char *},} 73 %\cont {{\tt c} is an \ullong{}} 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} $\mbox{sgn}(a - b)$} 79 \entry{zcmpi(a, b)} {Compare $a$ and $b$} {ditto, {\tt b} is an {\tt int64\_t}} 80 \entry{zcmpu(a, b)} {Compare $a$ and $b$} {ditto, {\tt b} is a {\tt uint64\_t}} 81 \entry{zcmpmag(a, b)} {Compare $\ab{a}$ and $\ab{b}$} {returns {\tt int} $\mbox{sgn}(\ab{a} - \ab{b})$} 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 at highest set bit} 98 \entry{zlsh(a, b, c)} {$a \gets b \cdot 2^c$} {{\tt c} is a \size{}} 99 \entry{zrsh(a, b, c)} {$a \gets b / 2^c$} {ditto, rounded towards zero} 100 \entry{ztrunc(a, b, c)} {$a \gets b \mod 2^c$} {ditto, $a$ shares signum with $b$} 101 \entry{zbits(a)} {Get number of used bits} {returns \size{}, 1 if $a = 0$} 102 \entry{zlsb(a)} {Get index of lowest set bit} {returns \size{}, {\tt SIZE\_MAX} if $a = 0$} 103 \entry{zbtest(a, b)} {Is bit $b$ in $a$ set?} {{\tt b} is a \size{}, returns {\tt int}} 104 \entry{zbset(a, b, c, 1)} {$a \gets b$, set bit $c$} {{\tt c} is a \size{}} 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 \size{}, rounded towards zero} 108 \entry{zsplit(a, b, c, d)} {$b \gets c \mod 2^d$} {ditto, $b$ shares signum with $c$} 109 \\ 110 111 \textbf{Conversion to string} \\ 112 \entry{zstr(a, b, c)} {Convert $a$ to decimal} {returns the resulting {\tt const char *}} 113 \cont {--- {\tt b} unless {\tt b} is 114 {\tt NULL}, --- $c$ must be} 115 \cont {either 0 or at least the length of the} 116 \cont {resulting string but at most the} 117 \cont {allocation size of {\tt b} minus 1} 118 %\entry{zstr\_radix(a, b, c, d)} {Convert $a$ to radix $d$} {ditto, {\tt d} is an \ullong{}} 119 \entry{zstr\_length(a, b)} {Get string length of $a$} {returns \size{} length of $a$ in radix $b$} 120 \\ 121 122 \textbf{Marshallisation} \\ 123 \entry{zsave(a, b)} {Marshal $a$ into $b$} {returns \size{} number of saved bytes,} 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 of read bytes,} 127 \cont {{\tt b} is a {\tt const void *}} 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 (true) or 0 (false)} 133 \entry{zeven\_nonzero(a)} {Is $a$ even?} {ditto, assumes $a \neq 0$} 134 \entry{zodd(a)} {Is $a$ odd?} {returns {\tt int} 1 (true) or 0 (false)} 135 \entry{zodd\_nonzero(a)} {Is $a$ odd?} {ditto, assumes $a \neq 0$} 136 \entry{zzero(a)} {Is $a$ zero?} {returns {\tt int} 1 (true) or 0 (false)} 137 \entry{zgcd(a, b, c)} {$a \gets \gcd(c, b)$} {$a < 0$ if $b < 0 \wedge c < 0$} 138 \entry{zptest(a, b, c)} {Is $b$ a prime?} {$c$ runs of Miller--Rabin, returns} 139 \cont {{\tt enum zprimality} {\tt NONPRIME} (0)} 140 \cont {(and stores the witness in {\tt a} unless} 141 \cont {{\tt a} is {\tt NULL}), {\tt PROBABLY\_PRIME} (1), or} 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}