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authorRaimo Niskanen <[email protected]>2017-09-14 15:57:16 +0200
committerRaimo Niskanen <[email protected]>2017-10-18 12:04:24 +0200
commit0248865dea315253618e733d77177b5a80679e20 (patch)
tree5f09f35f52aa65c20f62056ee46b135325194d76 /lib/stdlib/doc/src
parent52449634868e38087d0c93a0145fcfd9d2de394b (diff)
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Implement uniform_real/0 and uniform_real_s/1
Diffstat (limited to 'lib/stdlib/doc/src')
-rw-r--r--lib/stdlib/doc/src/rand.xml118
1 files changed, 113 insertions, 5 deletions
diff --git a/lib/stdlib/doc/src/rand.xml b/lib/stdlib/doc/src/rand.xml
index 89fb858823..21f680a0ee 100644
--- a/lib/stdlib/doc/src/rand.xml
+++ b/lib/stdlib/doc/src/rand.xml
@@ -133,8 +133,9 @@
variable <c>rand_seed</c> to remember the current state.</p>
<p>If a process calls
- <seealso marker="#uniform-0"><c>uniform/0</c></seealso> or
- <seealso marker="#uniform-1"><c>uniform/1</c></seealso> without
+ <seealso marker="#uniform-0"><c>uniform/0</c></seealso>,
+ <seealso marker="#uniform-1"><c>uniform/1</c></seealso> or
+ <seealso marker="#uniform_real-0"><c>uniform_real/0</c></seealso> without
setting a seed first, <seealso marker="#seed-1"><c>seed/1</c></seealso>
is called automatically with the default algorithm and creates a
non-constant seed.</p>
@@ -168,10 +169,17 @@ R3 = rand:uniform(),</pre>
S0 = rand:seed_s(exrop),
{R4, S1} = rand:uniform_s(S0),</pre>
+ <p>Textbook basic form Box-Muller standard normal deviate</p>
+
+ <pre>
+R5 = rand:uniform_real(),
+R6 = rand:uniform(),
+SND0 = math:sqrt(-2 * math:log(R5)) * math:cos(math:pi() * R6)</pre>
+
<p>Create a standard normal deviate:</p>
<pre>
-{SND0, S2} = rand:normal_s(S1),</pre>
+{SND1, S2} = rand:normal_s(S1),</pre>
<p>Create a normal deviate with mean -3 and variance 0.5:</p>
@@ -414,7 +422,8 @@ tests. We suggest to use a sign test to extract a random Boolean value.</pre>
This function may return exactly <c>0.0</c> which can be
fatal for certain applications. If that is undesired
you can use <c>(1.0 - rand:uniform())</c> to get the
- interval <c>0.0 &lt; <anno>X</anno> =&lt; 1.0</c>.
+ interval <c>0.0 &lt; <anno>X</anno> =&lt; 1.0</c>, or instead use
+ <seealso marker="#uniform_real-0"><c>uniform_real/0</c></seealso>.
</p>
<p>
If neither endpoint is desired you can test and re-try
@@ -432,6 +441,42 @@ end.</pre>
</func>
<func>
+ <name name="uniform_real" arity="0"/>
+ <fsummary>Return a random float.</fsummary>
+ <desc><marker id="uniform_real-0"/>
+ <p>
+ Returns a random float
+ uniformly distributed in the value range
+ <c>DBL_MIN =&lt; <anno>X</anno> &lt; 1.0</c>
+ and updates the state in the process dictionary.
+ </p>
+ <p>
+ Conceptually, a random real number <c>R</c> is generated
+ from the interval <c>0 =&lt; R &lt; 1</c> and then the
+ closest rounded down normalized number
+ in the IEEE 754 Double precision format
+ is returned.
+ </p>
+ <note>
+ <p>
+ The generated numbers from this function has got better
+ granularity for small numbers than the regular
+ <seealso marker="#uniform-0"><c>uniform/0</c></seealso>
+ because all bits in the mantissa are random.
+ This property, in combination with the fact that exactly zero
+ is never returned is useful for algoritms doing for example
+ <c>1.0 / <anno>X</anno></c> or <c>math:log(<anno>X</anno>)</c>.
+ </p>
+ </note>
+ <p>
+ See
+ <seealso marker="#uniform_real_s-1"><c>uniform_real_s/1</c></seealso>
+ for more explanation.
+ </p>
+ </desc>
+ </func>
+
+ <func>
<name name="uniform" arity="1"/>
<fsummary>Return a random integer.</fsummary>
<desc><marker id="uniform-1"/>
@@ -460,7 +505,8 @@ end.</pre>
This function may return exactly <c>0.0</c> which can be
fatal for certain applications. If that is undesired
you can use <c>(1.0 - rand:uniform(State))</c> to get the
- interval <c>0.0 &lt; <anno>X</anno> =&lt; 1.0</c>.
+ interval <c>0.0 &lt; <anno>X</anno> =&lt; 1.0</c>, or instead use
+ <seealso marker="#uniform_real_s-1"><c>uniform_real_s/1</c></seealso>.
</p>
<p>
If neither endpoint is desired you can test and re-try
@@ -478,6 +524,68 @@ end.</pre>
</func>
<func>
+ <name name="uniform_real_s" arity="1"/>
+ <fsummary>Return a random float.</fsummary>
+ <desc>
+ <p>
+ Returns, for a specified state, a random float
+ uniformly distributed in the value range
+ <c>DBL_MIN =&lt; <anno>X</anno> &lt; 1.0</c>
+ and updates the state in the process dictionary.
+ </p>
+ <p>
+ Conceptually, a random real number <c>R</c> is generated
+ from the interval <c>0 =&lt; R &lt; 1</c> and then the
+ closest rounded down normalized number
+ in the IEEE 754 Double precision format
+ is returned.
+ </p>
+ <note>
+ <p>
+ The generated numbers from this function has got better
+ granularity for small numbers than the regular
+ <seealso marker="#uniform_s-1"><c>uniform_s/1</c></seealso>
+ because all bits in the mantissa are random.
+ This property, in combination with the fact that exactly zero
+ is never returned is useful for algoritms doing for example
+ <c>1.0 / <anno>X</anno></c> or <c>math:log(<anno>X</anno>)</c>.
+ </p>
+ </note>
+ <p>
+ The concept implicates that the probability to get
+ exactly zero is extremely low; so low that this function
+ is in fact guaranteed to never return zero. The smallest
+ number that it might return is <c>DBL_MIN</c>, which is
+ 2.0^(-1022).
+ </p>
+ <p>
+ The value range stated at the top of this function
+ description is technically correct, but
+ <c>0.0 =&lt; <anno>X</anno> &lt; 1.0</c>
+ is a better description of the generated numbers'
+ statistical distribution. Except that exactly 0.0
+ is never returned, which is not possible to observe
+ statistically.
+ </p>
+ <p>
+ For example; for all sub ranges
+ <c>N*2.0^(-53) =&lt; X &lt; (N+1)*2.0^(-53)</c>
+ where
+ <c>0 =&lt; integer(N) &lt; 2.0^53</c>
+ the probability is the same.
+ Compare that with the form of the numbers generated by
+ <seealso marker="#uniform_s-1"><c>uniform_s/1</c></seealso>.
+ </p>
+ <p>
+ Having to generate extra random bits for
+ small numbers costs a little performance.
+ This function is about 20% slower than the regular
+ <seealso marker="#uniform_s-1"><c>uniform_s/1</c></seealso>
+ </p>
+ </desc>
+ </func>
+
+ <func>
<name name="uniform_s" arity="2"/>
<fsummary>Return a random integer.</fsummary>
<desc>