diff --git a/source/numerics.tex b/source/numerics.tex index 811f7d9d90..7795ac68e2 100644 --- a/source/numerics.tex +++ b/source/numerics.tex @@ -2540,6 +2540,13 @@ and for equality and inequality operators are not shown in the synopses. +\pnum +In the descriptions of the random number engines +and random number engine adaptors +in \ref{rand.eng} and in \ref{rand.adapt}, +a constant such as $c$ takes the value of the non-type template parameter +of the same name, \tcode{c}, unless otherwise specified. + \pnum Each template specified in \ref{rand.eng} requires one or more relationships, @@ -2648,12 +2655,10 @@ \end{note} \pnum -If the template parameter -\tcode{m} is not $0$, -the following relations shall hold: - \tcode{a < m} +The following relations shall hold: + $a < m$ and - \tcode{c < m}. + $c < m$. \pnum The textual representation @@ -2668,9 +2673,9 @@ \begin{itemdescr} \pnum \effects - If $c \bmod m$ is $0$ and $\tcode{s} \bmod m$ is $0$, + If $c \bmod m$ is $0$ and $s \bmod m$ is $0$, sets the engine's state to $1$, - otherwise sets the engine's state to $\tcode{s} \bmod m$. + otherwise sets the engine's state to $s \bmod m$. \end{itemdescr} \indexlibraryctor{linear_congruential_engine}% @@ -2818,21 +2823,19 @@ \pnum The following relations shall hold: - \tcode{0 < m}, - \tcode{m <= n}, - \tcode{2u < w}, - \tcode{r <= w}, - \tcode{u <= w}, - \tcode{s <= w}, - \tcode{t <= w}, - \tcode{l <= w}, - \tcode{w <= numeric_limits::digits}, - \tcode{a <= (1u<::digits}$, + $r \leq w$, + $u \leq w$, + $s \leq w$, + $t \leq w$, + $l \leq w$, + $a \leq 2^w - 1$, + $b \leq 2^w - 1$, + $c \leq 2^w - 1$, + $d \leq 2^w - 1$, and - \tcode{f <= (1u<::digits}. + $0 < w \leq \tcode{numeric_limits::digits}$. \pnum The textual representation @@ -3026,7 +3027,7 @@ \pnum \complexity -Exactly $n \cdot \tcode{r}$ invocations +Exactly $n \cdot r$ invocations of \tcode{e}. \end{itemdescr} @@ -3196,10 +3197,8 @@ \end{codeblock} \pnum -The following relations shall hold: - \tcode{0 < r} -and - \tcode{r <= p}. +The following relation shall hold: + $0 < r \leq p$. \pnum The textual representation @@ -3342,10 +3341,8 @@ \end{codeblock}% \pnum -The following relations shall hold: - \tcode{0 < w} -and - \tcode{w <= numeric_limits::digits}. +The following relation shall hold: + $0 < w \leq \tcode{numeric_limits::digits}$. \pnum The textual representation @@ -3392,7 +3389,7 @@ \pnum The generation algorithm -yields the last value of \tcode{Y} +yields the last value of $Y$ produced while advancing \tcode{e}'s state as described above. \indexlibraryglobal{shuffle_order_engine}% @@ -3448,7 +3445,7 @@ \pnum The following relation shall hold: - \tcode{0 < k}. + $0 < k$. \pnum The textual representation pFad - Phonifier reborn

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