Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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with Ada.Long_Complex_Text_IO; use Ada.Long_Complex_Text_IO;
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with Ada.Numerics; use Ada.Numerics;
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with Ada.Numerics.Long_Complex_Types; use Ada.Numerics.Long_Complex_Types;
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with Ada.Numerics.Long_Complex_Elementary_Functions; use Ada.Numerics.Long_Complex_Elementary_Functions;
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procedure Eulers_Identity is
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begin
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Put (Exp (Pi * i) + 1.0);
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end Eulers_Identity;
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@ -1,9 +1,6 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #004080;">complex</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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<span style="color: #004080;">complex</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_new</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_add</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_exp</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_mul</span><span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">both</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1e16</span><span style="color: #0000FF;">),</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1e15</span><span style="color: #0000FF;">),</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
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<!--
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with javascript_semantics
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include builtins\complex.e
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complex res = complex_add(complex_exp(complex_mul(PI,complex_new(0,1))),1)
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?complex_sprint(res,both:=true)
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?complex_sprint(complex_round(res,1e16),true)
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?complex_sprint(complex_round(res,1e15),true)
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@ -1,30 +1,29 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">rules</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #008000;">"-1+1"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">},</span>
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<span style="color: #0000FF;">{</span><span style="color: #008000;">"-1+0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-1"</span><span style="color: #0000FF;">},</span>
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<span style="color: #0000FF;">{</span><span style="color: #008000;">"i*0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">},</span>
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<span style="color: #0000FF;">{</span><span style="color: #008000;">"sin(pi)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">},</span>
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<span style="color: #0000FF;">{</span><span style="color: #008000;">"cos(pi)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-1"</span><span style="color: #0000FF;">},</span>
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<span style="color: #0000FF;">{</span><span style="color: #008000;">"exp(i*pi)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"cos(pi)+i*sin(pi)"</span><span style="color: #0000FF;">}}</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">seen</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> <span style="color: #000080;font-style:italic;">-- (be safe and avoid infinite loops)</span>
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<span style="color: #008080;">while</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- "" re-treading</span>
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<span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">10000</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- "" ever-growing</span>
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<span style="color: #000000;">seen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">bool</span> <span style="color: #000000;">found</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">string</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</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;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">found</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
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<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">substitute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">found</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">"%s = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">})</span>
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</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;">procedure</span>
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with javascript_semantics
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constant rules = {{"-1+1","0"},
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{"-1+0","-1"},
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{"i*0","0"},
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{"sin(pi)","0"},
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{"cos(pi)","-1"},
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{"exp(i*pi)","cos(pi)+i*sin(pi)"}}
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<span style="color: #000000;">reduce</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"exp(i*pi)+1"</span><span style="color: #0000FF;">)</span>
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<!--
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procedure reduce(string s)
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string t = s
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sequence seen = {} -- (be safe and avoid infinite loops)
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while not find(t,seen) -- "" re-treading
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and length(t)<10000 do -- "" ever-growing
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seen = append(seen,t)
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bool found = false
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for i=1 to length(rules) do
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string {r,e} = rules[i]
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if match(r,t) then
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found = true
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t = substitute(t,r,e)
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end if
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end for
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if not found then exit end if
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printf(1,"%s = %s\n",{s,t})
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s = repeat(' ',length(s))
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end while
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end procedure
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reduce("exp(i*pi)+1")
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