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diff --git a/docs/spec/system.html b/docs/spec/system.html index 3616425c..a7c1efab 100644 --- a/docs/spec/system.html +++ b/docs/spec/system.html @@ -474,7 +474,7 @@ <p><code><span class='Modifier'>β’_timed</span></code> returns the total time taken divided by the number of function calls (<code><span class='Value'>π¨</span></code> if provided and 1 otherwise), including the overhead required for the outer loop that counts iterations (which will typically be negligible in comparison to the BQN code).</p> <p>More accurately the modifier <code><span class='Modifier2'>β’_maxTime_</span></code> <em>may</em> fail if execution of <code><span class='Function'>π½</span></code> takes over <code><span class='Value'>π¨</span><span class='Function'>πΎ</span><span class='Value'>π©</span></code> seconds, and should fail as quickly as it is practically able to. The most likely way to implement this modifier is to interrupt execution at the given time. If <code><span class='Function'>π½</span></code> completes before the interrupt there is no need to measure the amount of time it actually took.</p> <h2 id="random-generation"><a class="header" href="#random-generation">Random generation</a></h2> -<p><code><span class='Function'>β’MakeRand</span></code> initializes a deterministic pseudorandom number generator with seed value <code><span class='Value'>π©</span></code>. <code><span class='Value'>β’rand</span></code>, if it exists, is a globally accessible generator initialized at first use; this initialization should use randomness from an outside source if available. A random generator has the following member functions:</p> +<p><code><span class='Function'>β’MakeRand</span></code> initializes a deterministic pseudorandom number generator with seed value <code><span class='Value'>π©</span></code>. <code><span class='Value'>β’rand</span></code>, if it exists, is a globally accessible generator initialized at first use; this initialization should use randomness from an outside source if available. These random generators aren't required to be cryptographically secure and should always be treated as insecure. A random generator has the following member functions:</p> <table> <thead> <tr> @@ -493,11 +493,11 @@ </tr> <tr> <td><code><span class='Function'>Subset</span></code></td> -<td>A sorted SRS of <code><span class='Value'>π¨</span></code> elements of <code><span class='Function'>β</span><span class='Value'>π©</span></code></td> +<td>A sorted SRS of <code><span class='Function'>β</span><span class='Value'>π©</span></code>, with <code><span class='Value'>π¨</span></code> elements if given</td> </tr> </tbody> </table> <p>For each of these functions, <code><span class='Value'>π©</span></code> is a natural number. For <code><span class='Function'>Range</span></code>, <code><span class='Value'>π¨</span></code> must be a valid shape if given, and for <code><span class='Function'>Deal</span></code> and <code><span class='Function'>Subset</span></code> it's a natural number less than or equal to <code><span class='Value'>π©</span></code>. All selections are made uniformly at random, that is, each possible result is equally likely. A simple random sample (SRS) of <code><span class='Value'>k</span></code> elements from list <code><span class='Value'>s</span></code> is a list of <code><span class='Value'>k</span></code> distinct elements of <code><span class='Value'>s</span></code> in any order. Both the choice of elements and their ordering must be uniformly random. <a href="../implementation/primitive/random.html#simple-random-sample">Recommended algorithms</a> for SRS selection are variants of a partial Knuth shuffle.</p> -<p>When <code><span class='Value'>π¨</span></code> isn't given, <code><span class='Function'>Deal</span></code>'s result contains all elements of <code><span class='Function'>β</span><span class='Value'>π©</span></code>, making it a random shuffle of those values, or random permutation. In <code><span class='Function'>Subset</span></code>, setting <code><span class='Value'>π¨</span></code> to <code><span class='Value'>π©</span></code> would instead always result in the list <code><span class='Function'>β</span><span class='Value'>π©</span></code>; because this is not useful, <code><span class='Value'>π¨</span></code> must be provided.</p> +<p>When <code><span class='Value'>π¨</span></code> isn't given, <code><span class='Function'>Deal</span></code>'s result contains all elements of <code><span class='Function'>β</span><span class='Value'>π©</span></code>, making it a random shuffle of those values, or random permutation. In <code><span class='Function'>Subset</span></code>, a random choice is made uniformly from the <code><span class='Number'>2</span><span class='Function'>β</span><span class='Value'>π©</span></code> subsets of <code><span class='Function'>β</span><span class='Value'>π©</span></code>, so that a subset of any length may be returned.</p> <p>In <code><span class='Function'>Range</span></code>, <code><span class='Value'>π©</span></code> may be <code><span class='Number'>0</span></code>. In this case the result consists of floating-point numbers in the unit interval from 0 to 1. The numbers should have an overall uniform distribution, but their precision and whether the endpoints 0 and 1 are possible may depend on the implementation.</p> <p>Ranges up to <code><span class='Number'>2</span><span class='Function'>β</span><span class='Number'>32</span></code> must be supported (that is, a maximum integer result of <code><span class='Paren'>(</span><span class='Number'>2</span><span class='Function'>β</span><span class='Number'>32</span><span class='Paren'>)</span><span class='Function'>-</span><span class='Number'>1</span></code>) if the number system accommodates it. In implementations based on double-precision floats it's preferable but not required to support ranges up to <code><span class='Number'>2</span><span class='Function'>β</span><span class='Number'>53</span></code>.</p> diff --git a/spec/system.md b/spec/system.md index b62db9e5..15ada7b4 100644 --- a/spec/system.md +++ b/spec/system.md @@ -210,17 +210,17 @@ More accurately the modifier `β’_maxTime_` *may* fail if execution of `π½` ta ## Random generation -`β’MakeRand` initializes a deterministic pseudorandom number generator with seed value `π©`. `β’rand`, if it exists, is a globally accessible generator initialized at first use; this initialization should use randomness from an outside source if available. A random generator has the following member functions: +`β’MakeRand` initializes a deterministic pseudorandom number generator with seed value `π©`. `β’rand`, if it exists, is a globally accessible generator initialized at first use; this initialization should use randomness from an outside source if available. These random generators aren't required to be cryptographically secure and should always be treated as insecure. A random generator has the following member functions: | Name | Summary |-----------|------------------------------ | `Range` | A number, or array of shape `π¨`, selected from `βπ©` | `Deal` | A simple random sample of `π¨β£π©` elements of `βπ©` -| `Subset` | A sorted SRS of `π¨` elements of `βπ©` +| `Subset` | A sorted SRS of `βπ©`, with `π¨` elements if given For each of these functions, `π©` is a natural number. For `Range`, `π¨` must be a valid shape if given, and for `Deal` and `Subset` it's a natural number less than or equal to `π©`. All selections are made uniformly at random, that is, each possible result is equally likely. A simple random sample (SRS) of `k` elements from list `s` is a list of `k` distinct elements of `s` in any order. Both the choice of elements and their ordering must be uniformly random. [Recommended algorithms](../implementation/primitive/random.md#simple-random-sample) for SRS selection are variants of a partial Knuth shuffle. -When `π¨` isn't given, `Deal`'s result contains all elements of `βπ©`, making it a random shuffle of those values, or random permutation. In `Subset`, setting `π¨` to `π©` would instead always result in the list `βπ©`; because this is not useful, `π¨` must be provided. +When `π¨` isn't given, `Deal`'s result contains all elements of `βπ©`, making it a random shuffle of those values, or random permutation. In `Subset`, a random choice is made uniformly from the `2βπ©` subsets of `βπ©`, so that a subset of any length may be returned. In `Range`, `π©` may be `0`. In this case the result consists of floating-point numbers in the unit interval from 0 to 1. The numbers should have an overall uniform distribution, but their precision and whether the endpoints 0 and 1 are possible may depend on the implementation. |