Data update
This commit is contained in:
Ingy döt Net
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4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,53 +0,0 @@
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with Ada.Text_IO; use Ada.Text_IO;
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with Ada.Numerics.Generic_Elementary_Functions;
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with Ada.Numerics.Discrete_Random;
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procedure Avglen is
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package IIO is new Ada.Text_IO.Integer_IO (Positive); use IIO;
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package LFIO is new Ada.Text_IO.Float_IO (Long_Float); use LFIO;
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subtype FactN is Natural range 0..20;
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TESTS : constant Natural := 1_000_000;
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function Factorial (N : FactN) return Long_Float is
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Result : Long_Float := 1.0;
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begin
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for I in 2..N loop Result := Result * Long_Float(I); end loop;
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return Result;
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end Factorial;
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function Analytical (N : FactN) return Long_Float is
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Sum : Long_Float := 0.0;
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begin
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for I in 1..N loop
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Sum := Sum + Factorial(N) / Factorial(N - I) / Long_Float(N)**I;
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end loop;
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return Sum;
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end Analytical;
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function Experimental (N : FactN) return Long_Float is
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subtype RandInt is Natural range 1..N;
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package Random is new Ada.Numerics.Discrete_Random(RandInt);
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seed : Random.Generator;
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Num : RandInt;
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count : Natural := 0;
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bits : array(RandInt'Range) of Boolean;
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begin
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Random.Reset(seed);
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for run in 1..TESTS loop
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bits := (others => false);
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for I in RandInt'Range loop
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Num := Random.Random(seed); exit when bits(Num);
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bits(Num) := True; count := count + 1;
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end loop;
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end loop;
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return Long_Float(count)/Long_Float(TESTS);
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end Experimental;
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A, E, err : Long_Float;
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begin
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Put_Line(" N avg calc %diff");
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for I in 1..20 loop
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A := Analytical(I); E := Experimental(I); err := abs(E-A)/A*100.0;
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Put(I, Width=>2); Put(E ,Aft=>4, exp=>0); Put(A, Aft=>4, exp=>0);
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Put(err, Fore=>3, Aft=>3, exp=>0); New_line;
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end loop;
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end Avglen;
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@ -1,9 +1,11 @@
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func average n reps .
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fastfunc average n reps .
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len f[] n
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len seen[] n
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for r to reps
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f[] = [ ]
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for i to n : f[] &= random n
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seen[] = [ ]
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len seen[] n
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for i = 1 to n
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f[i] = random n
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seen[i] = 0
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.
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x = 1
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while seen[x] = 0
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seen[x] = 1
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@ -13,7 +15,7 @@ func average n reps .
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.
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return count / reps
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.
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func analytical n .
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fastfunc analytical n .
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s = 1
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t = 1
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for i = n - 1 downto 1
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@ -1,35 +1,31 @@
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(phixonline)-->
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<span style="color: #008080;">constant</span> <span style="color: #000000;">MAX</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">ITER</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000000</span>
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with javascript_semantics
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constant MAX = 20,
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ITER = 1000000
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<span style="color: #008080;">function</span> <span style="color: #000000;">expected</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #7060A8;">sum</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">sum</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">sum</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function expected(integer n)
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atom res = 0
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for i=1 to n do
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res += factorial(n)/power(n,i)/factorial(n-i)
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end for
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return res
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bits</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">ITER</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
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<span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<span style="color: #008080;">while</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">or_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">rand</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">/</span><span style="color: #000000;">ITER</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function test(integer n)
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integer count = 0
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for i=1 to ITER do
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integer x = 1, bits = 0
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while not and_bits(bits,x) do
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count += 1
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bits = or_bits(bits,x)
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x = power(2,rand(n)-1)
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end while
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end for
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return count/ITER
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end function
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<span style="color: #004080;">atom</span> <span style="color: #000000;">av</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ex</span>
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<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" n avg. exp. (error%)\n"</span><span style="color: #0000FF;">);</span>
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<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"== ====== ====== ========\n"</span><span style="color: #0000FF;">);</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">MAX</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">av</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">ex</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">expected</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d %8.4f %8.4f (%5.3f%%)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">av</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ex</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">av</span><span style="color: #0000FF;">/</span><span style="color: #000000;">ex</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">100</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<!--
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puts(1," n avg. exp. (error%)\n");
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puts(1,"== ====== ====== ========\n");
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for n=1 to MAX do
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atom av = test(n), ex = expected(n)
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printf(1,"%2d %8.4f %8.4f (%5.3f%%)\n", {n,av,ex,abs(1-av/ex)*100})
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end for
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@ -1,59 +0,0 @@
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function Get-AnalyticalLoopAverage ( [int]$N )
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{
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# Expected loop average = sum from i = 1 to N of N! / (N-i)! / N^(N-i+1)
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# Equivalently, Expected loop average = sum from i = 1 to N of F(i)
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# where F(N) = 1, and F(i) = F(i+1)*i/N
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$LoopAverage = $Fi = 1
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If ( $N -eq 1 ) { return $LoopAverage }
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ForEach ( $i in ($N-1)..1 )
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{
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$Fi *= $i / $N
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$LoopAverage += $Fi
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}
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return $LoopAverage
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}
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function Get-ExperimentalLoopAverage ( [int]$N, [int]$Tests = 100000 )
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{
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If ( $N -eq 1 ) { return 1 }
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# Using 0 through N-1 instead of 1 through N for speed and simplicity
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$NMO = $N - 1
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# Create array to hold mapping function
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$F = New-Object int[] ( $N )
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$Count = 0
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$Random = New-Object System.Random
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ForEach ( $Test in 1..$Tests )
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{
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# Map each number to a random number
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ForEach ( $i in 0..$NMO )
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{
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$F[$i] = $Random.Next( $N )
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}
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# For each number...
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ForEach ( $i in 0..$NMO )
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{
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# Add the number to the list
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$List = @()
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$Count++
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$List += $X = $i
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# If loop does not yet exist in list...
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While ( $F[$X] -notin $List )
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{
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# Go to the next mapped number and add it to the list
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$Count++
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$List += $X = $F[$X]
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}
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}
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}
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$LoopAvereage = $Count / $N / $Tests
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return $LoopAvereage
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}
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@ -1,12 +0,0 @@
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# Display results for N = 1 through 20
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ForEach ( $N in 1..20 )
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{
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$AnalyticalAverage = Get-AnalyticalLoopAverage $N
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$ExperimentalAverage = Get-ExperimentalLoopAverage $N
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[pscustomobject] @{
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N = $N.ToString().PadLeft( 2, ' ' )
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Analytical = $AnalyticalAverage.ToString( '0.00000000' )
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Experimental = $ExperimentalAverage.ToString( '0.00000000' )
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'Error (%)' = ( [math]::Abs( $AnalyticalAverage - $ExperimentalAverage ) / $AnalyticalAverage * 100 ).ToString( '0.00000000' )
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}
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}
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@ -1,48 +0,0 @@
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Const MAX = 20
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Const ITER = 100000
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Function expected(n)
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Dim sum
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ni=n
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For i = 1 To n
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sum = sum + fact(n) / ni / fact(n-i)
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ni=ni*n
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Next
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expected = sum
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End Function
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Function test(n )
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Dim coun,x,bits
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For i = 1 To ITER
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x = 1
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bits = 0
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Do While Not bits And x
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count = count + 1
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bits = bits Or x
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x =shift(Int(n * Rnd()))
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Loop
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Next
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test = count / ITER
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End Function
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'VBScript formats numbers but does'nt align them!
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function rf(v,n,s) rf=right(string(n,s)& v,n):end function
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'some precalculations to speed things up...
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dim fact(20),shift(20)
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fact(0)=1:shift(0)=1
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for i=1 to 20
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fact(i)=i*fact(i-1)
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shift(i)=2*shift(i-1)
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next
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Dim n
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Wscript.echo "For " & ITER &" iterations"
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Wscript.Echo " n avg. exp. (error%)"
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Wscript.Echo "== ====== ====== =========="
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For n = 1 To MAX
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av = test(n)
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ex = expected(n)
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Wscript.Echo rf(n,2," ")& " "& rf(formatnumber(av, 4),7," ") & " "& _
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rf(formatnumber(ex,4),6," ")& " ("& rf(Formatpercent(1 - av / ex,4),8," ") & ")"
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Next
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