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[rand.eng], [rand.adapt] Use maths to describe relations between constants #4295

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[rand.eng], [rand.adapt] Use maths to describe relations between constants #4295

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175f223
[rand.eng] Blanket wording for placeholders in maths
jwakely Oct 8, 2020
be7cbe5
[rand.eng.lcong] Use maths to simplify relations
jwakely Oct 8, 2020
a66d9a7
[rand.eng.mers] Use maths to simplify relations
jwakely Oct 8, 2020
7017ffe
[rand.eng.sub] Use maths to simplify relations
jwakely Oct 8, 2020
b9c25a7
[rand.adapt.disc] Use maths to simplify relations
jwakely Oct 8, 2020
0217086
[rand.adapt.ibits] Use maths to simplify relations
jwakely Oct 8, 2020
756ce3e
[rand.adapt.shuf] Use maths to simplify relations
jwakely Oct 8, 2020
7957e0b
[rand.eng.mers], [rand.end.sub] use result_type instead of UIntType
jwakely Oct 8, 2020
bdfc8ed
[rand.eng.sub] Do not use code font for constant r
jwakely Oct 8, 2020
3cd6074
[rand.eng.lcong] Do not use code font for constant s
jwakely Oct 8, 2020
5383a93
[rand.adapt.shuf] Do not use code font for Y
jwakely Oct 8, 2020
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69 changes: 33 additions & 36 deletions source/numerics.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -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,
Expand Down Expand Up @@ -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
Expand All @@ -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}%
Expand Down Expand Up @@ -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<UIntType>::digits},
\tcode{a <= (1u<<w) - 1u},
\tcode{b <= (1u<<w) - 1u},
\tcode{c <= (1u<<w) - 1u},
\tcode{d <= (1u<<w) - 1u},
$0 < m \leq n$,
$2 < w \leq \tcode{numeric_limits<result_type>::digits}$,
$r \leq w$,
$u \leq w$,
$s \leq w$,
$t \leq w$,
$l \leq w$,
$a \leq 2^w - 1$,
$b \leq 2^w - 1$,
$c \leq 2^w - 1$,
$d \leq 2^w - 1$,
and
\tcode{f <= (1u<<w) - 1u}.
$f \leq 2^w - 1$.

\pnum
The textual representation
Expand Down Expand Up @@ -2984,11 +2987,9 @@

\pnum
The following relations shall hold:
\tcode{0u < s},
\tcode{s < r},
\tcode{0 < w},
$0 < s < r$
and
\tcode{w <= numeric_limits<UIntType>::digits}.
$0 < w \leq \tcode{numeric_limits<result_type>::digits}$.

\pnum
The textual representation
Expand Down Expand Up @@ -3026,7 +3027,7 @@

\pnum
\complexity
Exactly $n \cdot \tcode{r}$ invocations
Exactly $n \cdot r$ invocations
of \tcode{e}.
\end{itemdescr}

Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -3342,10 +3341,8 @@
\end{codeblock}%

\pnum
The following relations shall hold:
\tcode{0 < w}
and
\tcode{w <= numeric_limits<result_type>::digits}.
The following relation shall hold:
$0 < w \leq \tcode{numeric_limits<result_type>::digits}$.

\pnum
The textual representation
Expand Down Expand Up @@ -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}%
Expand Down Expand Up @@ -3448,7 +3445,7 @@

\pnum
The following relation shall hold:
\tcode{0 < k}.
$0 < k$.

\pnum
The textual representation
Expand Down