Library: verification for all floating-point types

finally I was able to come up with a rather concise test that works with float, double and long double; especially the aliasing due to rounding could be demonstrated, and the precision limit is made plausible. Interestingly, `std::fabs()` really works precise enough so that a very large positive domain can be implemented and tested with exact match
Library: investigate what could be tested with floating-point
2026-09-16 04:23:55 +02:00 · 2026-09-15 21:53:56 +02:00 · 2026-09-15 01:37:38 +02:00
4 changed files with 392 additions and 12 deletions
--- a/src/lib/util-quant.hpp
+++ b/src/lib/util-quant.hpp
@ -216,7 +216,7 @@ namespace util {
      offset += PERIOD;
    if (not (offset < PERIOD)) // can happen due to ε or non-finite values
      offset = 0;
-    F res = minVal + offset;   // could be rounded to maxVal
+    F res = minVal + offset;   // could be rounded to maxVal (or become infinite)
    return res < maxVal? res : minVal;
  }
  
@ -245,6 +245,7 @@ namespace util {
  limit_cyclicWrap (F period)
  {
    REQUIRE (std::isfinite (period));
+    REQUIRE (F(0) < period);
    F limit = period / std::numeric_limits<F>::epsilon();
    if (not std::isfinite (limit))
      limit = std::numeric_limits<F>::max();
--- a/tests/15library.tests
+++ b/tests/15library.tests
@ -53,6 +53,11 @@ return: 0
 END


+TEST "Cyclic wrapping number domain" CyclicWrap_test <<END
+return: 0
+END
+
+
 TEST "Deleter function collection" DelStash_test <<END
 return: 0
 END
--- a/tests/lib/cyclic-wrap-test.cpp
+++ b/tests/lib/cyclic-wrap-test.cpp
@ -0,0 +1,197 @@
+/*
+  CyclicWrap(Test)  -  verify cyclically wrapping number domain
+
+   Copyright (C)
+     2026,            Hermann Vosseler <Ichthyostega@web.de>
+
+  **Lumiera** is free software; you can redistribute it and/or modify it
+  under the terms of the GNU General Public License as published by the
+  Free Software Foundation; either version 2 of the License, or (at your
+  option) any later version. See the file COPYING for further details.
+
+* *****************************************************************/
+
+/** @file util-floordiv-test.cpp
+ ** unit test \ref CyclicWrap_test
+ */
+
+
+#include "test/run.hpp"
+#include "lib/util-quant.hpp"
+#include "lib/util.hpp"
+
+using ::Test;
+using util::isLimited;
+using std::floating_point;
+
+namespace util {
+namespace test {
+  
+  namespace{ // Test helpers...
+    
+    template<typename NUM>
+    constexpr NUM _MAX = std::numeric_limits<NUM>::max();
+    
+    template<typename NUM>
+    constexpr NUM _MIN = std::numeric_limits<NUM>::lowest();
+    
+    template<floating_point FLO>
+    constexpr FLO _EPS = std::numeric_limits<FLO>::epsilon();
+    
+  } // (End) Test helpers
+  
+  
+  
+  
+  /******************************************************************//**
+   * @test Demonstrate and verify a cyclic wrapping numeric domain.
+   *     - show the wrapping behaviour with simple numbers
+   *     - verify the behaviour pattern for all integer types (signed / unsigned)
+   *     - verify the computation works at the very bounds of the domain
+   *     - verify the most difficult path with a negative minVal,
+   *       and the smallest number in the domain
+   *     - show a similar simple wrapping behaviour with all float types
+   *     - demonstrate the meaning of the precision limit
+   *     - demonstrate aliasing and sanitised rounding errors
+   * @see util::cyclicWrap
+   * @see parameter-scale-test.cpp
+   */
+  class CyclicWrap_test : public Test
+    {
+      
+      virtual void
+      run (Arg)
+        {
+          simpleDemonstration();
+          
+          verifyIntegerTypes<int>();
+          verifyIntegerTypes<uint>();
+          verifyIntegerTypes<int8_t>();
+          verifyIntegerTypes<uint8_t>();
+          verifyIntegerTypes<int16_t> ();
+          verifyIntegerTypes<uint16_t>();
+          verifyIntegerTypes<int32_t> ();
+          verifyIntegerTypes<uint32_t>();
+          verifyIntegerTypes<int64_t> ();
+          verifyIntegerTypes<uint64_t>();
+          
+          verifyFloatTypes<float>();
+          verifyFloatTypes<double>();
+          verifyFloatTypes<f128>();
+        }
+      
+      
+      void
+      simpleDemonstration ()
+        {
+          CHECK (10 == cyclicWrap (10,10,15));
+          CHECK (11 == cyclicWrap (11,10,15));
+          CHECK (12 == cyclicWrap (12,10,15));
+          CHECK (13 == cyclicWrap (13,10,15));
+          CHECK (14 == cyclicWrap (14,10,15));
+          CHECK (10 == cyclicWrap (15,10,15));
+          CHECK (11 == cyclicWrap (16,10,15));
+          CHECK (12 == cyclicWrap (17,10,15));
+          CHECK (13 == cyclicWrap (18,10,15));
+          CHECK (14 == cyclicWrap (19,10,15));
+          CHECK (10 == cyclicWrap (20,10,15));
+          
+          CHECK (10 == cyclicWrap ( 0,10,15));
+          CHECK (14 == cyclicWrap (-1,10,15));
+        }
+      
+      
+      template<typename I>
+      void
+      verifyIntegerTypes ()
+        {
+          const I LOWER(-100);   // note: expected to wrap for unsigned types
+          const I UPPER(LOWER+5);
+          
+          auto cyc = [&](I val){ return cyclicWrap (val, LOWER,UPPER); };
+          
+          CHECK (LOWER   == cyc(LOWER+0) );
+          CHECK (LOWER+1 == cyc(LOWER+1) );
+          CHECK (LOWER+2 == cyc(LOWER+2) );
+          CHECK (LOWER+3 == cyc(LOWER+3) );
+          CHECK (LOWER+4 == cyc(LOWER+4) );
+          CHECK (LOWER   == cyc(LOWER+5) );
+          
+          CHECK (LOWER   == cyc(LOWER-5) );
+          CHECK (LOWER+1 == cyc(LOWER-4) );
+          CHECK (LOWER+2 == cyc(LOWER-3) );
+          CHECK (LOWER+3 == cyc(LOWER-2) );
+          CHECK (LOWER+4 == cyc(LOWER-1) );
+          
+          
+          CHECK (isLimited (LOWER, cyc(_MAX<I>), UPPER));
+          CHECK (isLimited (LOWER, cyc(_MIN<I>), UPPER));
+          
+          CHECK (isLimited (LOWER, cyc(_MAX<I>-1), UPPER));
+          CHECK (isLimited (LOWER, cyc(_MIN<I>+1), UPPER));
+          
+          //------ Demonstrate behaviour at lower domain bound
+          //
+          I dist = LOWER - _MIN<I>;  // guaranteed to be positive and representable in-domain
+          I step = (dist / 5) * 5;   // the next applicable grid point
+          I excess = dist - step;
+          I offset = 5 - excess;     // flip orientation (since the input val lies below LOWER)
+          
+          CHECK (LOWER + offset == cyc(_MIN<I>) );
+        }
+      
+      
+      template<typename F>
+      void
+      verifyFloatTypes()
+        {
+          auto cyc = [&](F val){ return cyclicWrap (val, F(-10),F(-5)); };
+
+          CHECK (almostEqual (F(-10), cyc(0))  );
+          CHECK (almostEqual (F( -9), cyc(1))  );
+          CHECK (almostEqual (F( -8), cyc(2))  );
+          CHECK (almostEqual (F( -7), cyc(3))  );
+          CHECK (almostEqual (F( -6), cyc(4))  );
+          CHECK (almostEqual (F(-10), cyc(5))  );
+          CHECK (almostEqual (F( -9), cyc(6))  );
+          CHECK (almostEqual (F( -8), cyc(7))  );
+          CHECK (almostEqual (F( -7), cyc(8))  );
+          CHECK (almostEqual (F( -6), cyc(9))  );
+          CHECK (almostEqual (F(-10), cyc(105)));
+          
+          // For each period-length, a precision limit can be computed;
+          // whenever bounds or inputs approach that limit, the rounding errors
+          // approach the order of magnitude of the period-length, and thus
+          // computing of wrapped values becomes pointless...
+          F period5 = F(5);
+          F limit5  = limit_cyclicWrap<F> (period5);
+          
+          // one ULP-Step at the limit equals already half the period-length:
+          CHECK (almostEqual (period5/2, limit5 * _EPS<F>));
+          // so small steps will alias...
+          CHECK (limit5 + 1 == limit5);
+          
+          // HOWEWER, very large periods can be handled (within numeric precision)
+          CHECK (1 == cyclicWrap<F>( 1, 1,_MAX<F>) );
+          CHECK (2 == cyclicWrap<F>( 2, 1,_MAX<F>) );   // note: these values are *exact* -- due to std::fmod()
+          CHECK (3 == cyclicWrap<F>( 3, 1,_MAX<F>) );
+          CHECK (4 == cyclicWrap<F>( 4, 1,_MAX<F>) );
+          CHECK (5 == cyclicWrap<F>( 5, 1,_MAX<F>) );
+          
+          CHECK (1 == cyclicWrap<F>(-1, 1,_MAX<F>) );   // yet this one gets aliased with the minVal
+          
+          F epsStep =  _MAX<F>*_EPS<F>;
+          // yet the following input is clearly below minVal and will wrap upwards...
+          F wrapped = cyclicWrap (-epsStep, F(1),_MAX<F>);
+          
+          CHECK (      1 < wrapped);
+          CHECK (wrapped < _MAX<F>);
+        }
+    };
+  
+  
+  
+  LAUNCHER (CyclicWrap_test, "unit common");
+  
+  
+}} // namespace util::test
--- a/wiki/thinkPad.ichthyo.mm
+++ b/wiki/thinkPad.ichthyo.mm
@ -86141,7 +86141,7 @@ class ScaleRegistry
  </body>
 </html></richcontent>
 </node>
-<node CREATED="1789313909221" ID="ID_636669321" MODIFIED="1789314360236">
+<node CREATED="1789313909221" ID="ID_636669321" MODIFIED="1789423588613">
 <richcontent TYPE="NODE"><html>
  <head/>
  <body>
@ -86158,7 +86158,8 @@ class ScaleRegistry
    </p>
  </body>
 </html></richcontent>
-<node BACKGROUND_COLOR="#accdc3" COLOR="#3f4015" CREATED="1789314198004" ID="ID_1198665569" MODIFIED="1789314547810" TEXT="Integral: Abdeckung der gesamten Dom&#xe4;ne per Unsigned...">
+<linktarget COLOR="#49a8d6" DESTINATION="ID_636669321" ENDARROW="Default" ENDINCLINATION="87;46;" ID="Arrow_ID_1613615444" SOURCE="ID_945572666" STARTARROW="None" STARTINCLINATION="260;14;"/>
+<node BACKGROUND_COLOR="#accdc3" COLOR="#3f4015" CREATED="1789314198004" FOLDED="true" ID="ID_1198665569" MODIFIED="1789423416268" TEXT="Integral: Abdeckung der gesamten Dom&#xe4;ne per Unsigned...">
 <icon BUILTIN="wizard"/>
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@ -86257,7 +86258,7 @@ class ScaleRegistry
 <icon BUILTIN="wizard"/>
 </node>
 </node>
-<node BACKGROUND_COLOR="#accdc3" COLOR="#3f4015" CREATED="1789314221349" ID="ID_63841523" MODIFIED="1789314713492" TEXT="Floatingpoint: Nicht-handhabbare Bereiche beachten...">
+<node BACKGROUND_COLOR="#accdc3" COLOR="#3f4015" CREATED="1789314221349" FOLDED="true" ID="ID_63841523" MODIFIED="1789423414551" TEXT="Floatingpoint: Nicht-handhabbare Bereiche beachten...">
 <icon BUILTIN="wizard"/>
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 <richcontent TYPE="NODE"><html>
@ -86337,7 +86338,7 @@ class ScaleRegistry
 </node>
 </node>
 </node>
-<node BACKGROUND_COLOR="#accdc3" COLOR="#3f4015" CREATED="1789314739520" ID="ID_900911623" MODIFIED="1789314802300" TEXT="Erl&#xe4;uterung der L&#xf6;ungsstrategie">
+<node BACKGROUND_COLOR="#accdc3" COLOR="#3f4015" CREATED="1789314739520" FOLDED="true" ID="ID_900911623" MODIFIED="1789423604616" TEXT="Erl&#xe4;uterung der L&#xf6;ungsstrategie">
 <richcontent TYPE="NOTE"><html>
  <head/>
  <body>
@ -86527,7 +86528,7 @@ class ScaleRegistry
    </p>
  </body>
 </html></richcontent>
-<node BACKGROUND_COLOR="#f8ecbf" CREATED="1789340923095" HGAP="104" ID="ID_921584380" MODIFIED="1789347764151" VSHIFT="56">
+<node BACKGROUND_COLOR="#f8ecbf" CREATED="1789340923095" HGAP="104" ID="ID_921584380" MODIFIED="1789423600852" VSHIFT="56">
 <richcontent TYPE="NODE"><html>
  <head/>
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@ -86769,13 +86770,14 @@ Prop.1: dist%3       1  2  0  1  2  0
    </p>
  </body>
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-<linktarget COLOR="#f8263e" DESTINATION="ID_921584380" ENDARROW="Default" ENDINCLINATION="-16;141;" ID="Arrow_ID_244758209" SOURCE="ID_380512260" STARTARROW="None" STARTINCLINATION="195;11;"/>
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+<linktarget COLOR="#f8263e" DESTINATION="ID_921584380" ENDARROW="Default" ENDINCLINATION="-16;141;" ID="Arrow_ID_244758209" SOURCE="ID_380512260" STARTARROW="None" STARTINCLINATION="198;10;"/>
+</node>
 </node>
 </node>
 <node BACKGROUND_COLOR="#aff8e9" COLOR="#338800" CREATED="1789340798664" HGAP="15" ID="ID_1175604381" MODIFIED="1789340850559" TEXT="damit k&#xf6;nnte ich implementieren..." VSHIFT="18">
 <icon BUILTIN="idea"/>
-<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1789340871908" ID="ID_380512260" MODIFIED="1789342452121" STYLE="fork" TEXT="die Erl&#xe4;uterung f&#xfc;r den Unsigned-Fall ist zu knapp">
+<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1789340871908" ID="ID_380512260" MODIFIED="1789423600852" STYLE="fork" TEXT="die Erl&#xe4;uterung f&#xfc;r den Unsigned-Fall ist zu knapp">
 <richcontent TYPE="NOTE"><html>
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@ -86784,7 +86786,7 @@ Prop.1: dist%3       1  2  0  1  2  0
    </p>
  </body>
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-<arrowlink COLOR="#f8263e" DESTINATION="ID_921584380" ENDARROW="Default" ENDINCLINATION="-16;141;" ID="Arrow_ID_244758209" STARTARROW="None" STARTINCLINATION="195;11;"/>
+<arrowlink COLOR="#f8263e" DESTINATION="ID_921584380" ENDARROW="Default" ENDINCLINATION="-16;141;" ID="Arrow_ID_244758209" STARTARROW="None" STARTINCLINATION="198;10;"/>
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@ -86806,13 +86808,14 @@ Prop.1: dist%3       1  2  0  1  2  0
 </node>
 <node CREATED="1789356710360" ID="ID_521207014" MODIFIED="1789356723054" TEXT="der -1-Verschiebe-Trick nutzt Modulus-Arithmetik"/>
 </node>
-<node CREATED="1789360000999" ID="ID_879348844" MODIFIED="1789360029799" TEXT="die Limit-Definition sollte direkt bei der cyclicWrap-Funktion selber definiert sein"/>
+<node COLOR="#435e98" CREATED="1789360000999" ID="ID_879348844" MODIFIED="1789423630533" TEXT="die Limit-Definition sollte direkt bei der cyclicWrap-Funktion selber definiert sein">
+<icon BUILTIN="yes"/>
 </node>
 </node>
 </node>
 </node>
 <node CREATED="1789258808256" ID="ID_1240046297" MODIFIED="1789258815646" TEXT="Einf&#xfc;hren der Fallunterscheidung">
-<node CREATED="1789258816860" ID="ID_1706182584" MODIFIED="1789258941151" TEXT="Policy-based Design erscheint die sauberste L&#xf6;sung">
+<node BACKGROUND_COLOR="#d2beaf" COLOR="#5c4d6e" CREATED="1789258816860" ID="ID_1706182584" MODIFIED="1789423431524" TEXT="Policy-based Design erscheint die sauberste L&#xf6;sung">
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  <body>
@ -86822,8 +86825,182 @@ Prop.1: dist%3       1  2  0  1  2  0
  </body>
 </html></richcontent>
 <icon BUILTIN="yes"/>
+<icon BUILTIN="hourglass"/>
+</node>
+<node BACKGROUND_COLOR="#c8c0b6" COLOR="#435e98" CREATED="1789313641938" ID="ID_1271083241" MODIFIED="1789423457169" TEXT="zun&#xe4;chst gen&#xfc;gt eine generische Library-funktion als Delegate">
+<icon BUILTIN="forward"/>
+</node>
+</node>
+<node COLOR="#338800" CREATED="1789423486714" ID="ID_253445206" MODIFIED="1789438207120" TEXT="neue Implementierung">
+<icon BUILTIN="button_ok"/>
+<node CREATED="1789423493685" ID="ID_1410459624" MODIFIED="1789423506223" TEXT="entwickelt ausgehend von der naiven &#xbb;modulus&#xab;-L&#xf6;sung"/>
+<node BACKGROUND_COLOR="#accdc3" COLOR="#3f4015" CREATED="1789423507714" ID="ID_945572666" MODIFIED="1789423613866" TEXT="zu einer generischen L&#xf6;sung ausgebaut &#x27f5; Claude">
+<arrowlink COLOR="#49a8d6" DESTINATION="ID_636669321" ENDARROW="Default" ENDINCLINATION="87;46;" ID="Arrow_ID_1613615444" STARTARROW="None" STARTINCLINATION="260;14;"/>
+<icon BUILTIN="wizard"/>
+</node>
+<node COLOR="#338800" CREATED="1789423635808" ID="ID_840921741" MODIFIED="1789525417179" TEXT="Testabdeckung &#x2014; Grenzf&#xe4;lle">
+<icon BUILTIN="button_ok"/>
+<node COLOR="#435e98" CREATED="1789428970477" FOLDED="true" ID="ID_1439061940" MODIFIED="1789525368840" TEXT="habe gestern schon gesehen: f&#xfc;r sich sind util::flordiv | wrap wohl &#x201e;wasserdicht&#x201c;">
+<icon BUILTIN="idea"/>
+<node CREATED="1789429005712" ID="ID_1890368766" MODIFIED="1789429031093" TEXT="die Division liefert stets einen kleineren Quotient als der Dividend"/>
+<node CREATED="1789429032161" ID="ID_1469836197" MODIFIED="1789429058156" TEXT="die Korrektur-Logik arbeitet &#xbb;gl&#xfc;cklicherweise&#xab; stets zur Dom&#xe4;ne nach innen"/>
+<node COLOR="#338800" CREATED="1789433766523" ID="ID_167005830" MODIFIED="1789433779815" TEXT="dies in UtilFloordiv_test dokumentieren">
+<icon BUILTIN="button_ok"/>
+<node COLOR="#435e98" CREATED="1789433789808" ID="ID_538605241" MODIFIED="1789433827387" TEXT="jeweils an die Domain-Ober/Untergrenze gehen"/>
+<node COLOR="#435e98" CREATED="1789433801119" ID="ID_1533251912" MODIFIED="1789433827418" TEXT="durch 1, 2 und 5 teilen"/>
+<node COLOR="#435e98" CREATED="1789433808102" ID="ID_1210053047" MODIFIED="1789433827419" TEXT="Vorzeichen wechseln"/>
+<node COLOR="#435e98" CREATED="1789433812805" ID="ID_1425318347" MODIFIED="1789433827421" TEXT="auch f&#xfc;r uint, int64_t, int8_t"/>
+</node>
+</node>
+<node COLOR="#338800" CREATED="1789437807095" ID="ID_932126209" MODIFIED="1789437907066" TEXT="zun&#xe4;chst eine einfache Demonstration (als Dokumentation)">
+<richcontent TYPE="NOTE"><html>
+  <head/>
+  <body>
+    <p>
+      .... ich k&#246;nnte mir denken, da&#223; mancher Leser das Konzept nicht gleich versteht, deshalb ist ein solches einfaches Beispiel nie verkehrt
+    </p>
+  </body>
+</html></richcontent>
+<icon BUILTIN="button_ok"/>
+</node>
+<node COLOR="#338800" CREATED="1789437908944" FOLDED="true" ID="ID_880098415" MODIFIED="1789525347778" TEXT="systematisch alle real-existierenden Integral-Typen abdecken">
+<icon BUILTIN="button_ok"/>
+<node BACKGROUND_COLOR="#c8c0b6" COLOR="#435e98" CREATED="1789437929974" ID="ID_532498668" MODIFIED="1789438198770" TEXT="die eigentliche Test-Funktion als Template">
+<icon BUILTIN="idea"/>
+</node>
+<node COLOR="#338800" CREATED="1789437943780" ID="ID_1291965296" MODIFIED="1789438178462" TEXT="konstruiere das Test-Beispiel &#xbb;trickreich&#xab;">
+<icon BUILTIN="button_ok"/>
+<node CREATED="1789437965201" ID="ID_1576393662" MODIFIED="1789437977028" TEXT="so da&#xdf; es sich f&#xfc;r Signed und Unsigned gut testen l&#xe4;&#xdf;t"/>
+<node CREATED="1789437977859" ID="ID_1376129649" MODIFIED="1789438001984" TEXT="soll aber auch den komplexeren Pfad ausleuchten"/>
+<node CREATED="1789438002860" ID="ID_1338563274" MODIFIED="1789438069296" TEXT="&#x27f9; sollte die zyklische Dom&#xe4;ne in den negativen Bereich legen">
+<node CREATED="1789438070916" ID="ID_379253711" MODIFIED="1789438081989" TEXT="f&#xfc;r Unsigned sollte das wrappen"/>
+<node CREATED="1789438082993" ID="ID_1576673426" MODIFIED="1789438091635" TEXT="aber trotzdem noch sicher in die Dom&#xe4;ne passen"/>
+<node CREATED="1789438092936" ID="ID_1900067766" MODIFIED="1789438108922" TEXT="und f&#xfc;r Signed ist dann der Offset garantiert repr&#xe4;sentierbar"/>
+<node CREATED="1789438111305" ID="ID_1260779668" MODIFIED="1789438125620" TEXT="und zwar grade f&#xfc;r den problematischen Fall unter der Untergrenze"/>
+</node>
+</node>
+<node COLOR="#338800" CREATED="1789438130012" ID="ID_1945361876" MODIFIED="1789438175874" TEXT="teste die Dom&#xe4;nen-Grenzen auf valides Ergebnis (in der zyklischen Domain)">
+<icon BUILTIN="button_ok"/>
+</node>
+<node COLOR="#338800" CREATED="1789438158204" ID="ID_527867911" MODIFIED="1789438175875" TEXT="rechne explizit den Wert f&#xfc;r die Domain-Untergrenze nach">
+<icon BUILTIN="button_ok"/>
+</node>
+</node>
+<node COLOR="#338800" CREATED="1789485850174" FOLDED="true" ID="ID_1074654514" MODIFIED="1789525408140" TEXT="systematische Testabdeckung f&#xfc;r Floatingpoint-Typen entwickeln">
+<icon BUILTIN="button_ok"/>
+<node COLOR="#435e98" CREATED="1789485871331" ID="ID_552981037" MODIFIED="1789525115154" TEXT="mu&#xdf; zun&#xe4;chst einmal herausfinden was man &#xfc;berhaupt testen k&#xf6;nnte">
+<icon BUILTIN="yes"/>
+<node CREATED="1789485882603" ID="ID_1932453860" MODIFIED="1789485901968" TEXT="geschenkt: einen einfachen cyclicWrap">
+<richcontent TYPE="NOTE"><html>
+  <head/>
+  <body>
+    <p>
+      ganz analog zum Integral-Fall
+    </p>
+  </body>
+</html></richcontent>
+</node>
+<node CREATED="1789485908054" ID="ID_1390215073" MODIFIED="1789485917984" TEXT="mit dem Verhalten am Limit experimentieren"/>
+<node CREATED="1789485919101" ID="ID_126516087" MODIFIED="1789485942979" TEXT="Limit-Werte anschauen &#x27f9; sie wachsen mit der Periodenl&#xe4;nge"/>
+<node CREATED="1789485944250" ID="ID_758296300" MODIFIED="1789485958924" TEXT="man k&#xf6;nnte also mit Input knapp unter dem Limit testen"/>
+<node CREATED="1789485959655" ID="ID_1357089333" MODIFIED="1789518269807" TEXT="oder mit einem Offset knapp unter dem Limit"/>
+<node COLOR="#5b280f" CREATED="1789485980355" ID="ID_1975112618" MODIFIED="1789525168334" TEXT="man k&#xf6;nnte zeigen da&#xdf; die Berechnung ungenau wird &#xfc;ber dem Limit">
+<icon BUILTIN="button_cancel"/>
+<node CREATED="1789486105659" ID="ID_1422733682" MODIFIED="1789486116438" TEXT="f&#xfc;r maxVal &gt; Limit"/>
+<node CREATED="1789486117635" ID="ID_1961938709" MODIFIED="1789486122240" TEXT="aber auch f&#xfc;r zu gro&#xdf;e Domain"/>
+</node>
+<node COLOR="#5b280f" CREATED="1789485994791" ID="ID_1294711924" MODIFIED="1789525135527" TEXT="man k&#xf6;nnte eine Domain-Gr&#xf6;&#xdf;e am Limit testen">
+<richcontent TYPE="NOTE"><html>
+  <head/>
+  <body>
+    <p>
+      die sollte dann aber nur f&#252;r Input-Werte unterhalb des Limits funktionieren, allerdings auch negative Werte; oberhalb des Limits w&#252;rde ich Entgleisungen vermuten
+    </p>
+  </body>
+</html></richcontent>
+<icon BUILTIN="button_cancel"/>
+<node CREATED="1789525137057" ID="ID_188158552" MODIFIED="1789525146844" TEXT="nein: l&#xe4;&#xdf;t sich nicht sinnvoll im Test demonstrieren"/>
+<node CREATED="1789525147624" ID="ID_888819868" MODIFIED="1789525160044" TEXT="(ich sehe die Entgleisungen wenn ich mir die Zahlen im Debugger anschaue)"/>
+</node>
+</node>
+<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1789486294164" ID="ID_712679325" MODIFIED="1789517587212" TEXT="Beobachtungen: genau am Limit funktioniert das einfache Beispiel noch">
+<icon BUILTIN="broken-line"/>
+<node CREATED="1789486311768" ID="ID_204301662" MODIFIED="1789486325968" TEXT="ein Epsilon drunter wird absorbiert"/>
+<node BACKGROUND_COLOR="#cab2bd" COLOR="#980009" CREATED="1789486326998" ID="ID_185831565" MODIFIED="1789517613464" TEXT="m&#xfc;&#xdf;te also tats&#xe4;chlich ein ULP daneben gehen">
+<icon BUILTIN="idea"/>
+</node>
+<node CREATED="1789517621465" ID="ID_1146256096" MODIFIED="1789517635375" TEXT="tats&#xe4;chlich: das Stepping wird unzuverl&#xe4;ssig"/>
+<node CREATED="1789517696551" ID="ID_825633898" MODIFIED="1789517744461" TEXT="limit &#xb7; &#x3b5; &#x2261; &#xbd; periode">
+<node CREATED="1789517760503" ID="ID_205743420" MODIFIED="1789517788314" TEXT="das haben wir aber genau so definiert...">
+<icon BUILTIN="messagebox_warning"/>
+</node>
+<node CREATED="1789517771893" ID="ID_624480094" MODIFIED="1789517791174" TEXT="insofern ist das kein &#xbb;Test&#xab;">
+<icon BUILTIN="stop-sign"/>
+<node CREATED="1789517806226" ID="ID_1031466232" MODIFIED="1789517811675" TEXT="ein Test sollte Verhalten zeigen"/>
+<node CREATED="1789517812425" ID="ID_1660313139" MODIFIED="1789517821515" TEXT="und nicht eine Definition replizieren"/>
+</node>
+</node>
+</node>
+<node CREATED="1789518828341" ID="ID_452450374" MODIFIED="1789525394621">
+<richcontent TYPE="NODE"><html>
+  <head/>
+  <body>
+    <p>
+      Problem ist: hier kann ich kein &#187;<b>korrekt</b>&#171; oder &#187;<b>defekt</b>&#171; zeigen
+    </p>
+  </body>
+</html></richcontent>
+<linktarget COLOR="#57fec0" DESTINATION="ID_452450374" ENDARROW="Default" ENDINCLINATION="-182;8;" ID="Arrow_ID_1586349868" SOURCE="ID_409017691" STARTARROW="None" STARTINCLINATION="87;8;"/>
+<icon BUILTIN="broken-line"/>
+<node CREATED="1789518866588" ID="ID_1949224608" MODIFIED="1789518885765" TEXT="das Verhalten wird zum Limit hin zunehmend &#xbb;unscharf&#xab;"/>
+<node CREATED="1789518886522" ID="ID_515488673" MODIFIED="1789518921574" TEXT="wie viel Unsch&#xe4;rfe tolerierbar ist l&#xe4;&#xdf;t sich nicht generisch sagen">
+<node CREATED="1789518978509" ID="ID_1991175199" MODIFIED="1789518986039" TEXT="es gibt keine &#xbb;Schrittweite&#xab;"/>
+<node CREATED="1789518987204" ID="ID_30471047" MODIFIED="1789519013068" TEXT="wann ist ein &quot;off by 0.1&#xab; noch tolerierbar??"/>
+</node>
+<node CREATED="1789518902636" ID="ID_1841879477" MODIFIED="1789518930946" TEXT="letztlich sind floating-point-numbers immer &#xbb;unscharf&#xab;"/>
+<node CREATED="1789518945761" ID="ID_1474263016" MODIFIED="1789518957882" TEXT="jedwede Demonstration w&#xfc;rde eben nur dieses darstellen"/>
+<node BACKGROUND_COLOR="#f7dba2" COLOR="#690f14" CREATED="1789522669935" ID="ID_1829288235" MODIFIED="1789522703291" TEXT="und : eine klar verst&#xe4;ndliche Demonstration ist schwer">
+<icon BUILTIN="messagebox_warning"/>
+<node COLOR="#b21478" CREATED="1789522720139" ID="ID_1872531495" MODIFIED="1789522906208" TEXT="Grenzwerte sind &#xbb;unhandlich&#xab;">
+<richcontent TYPE="NOTE"><html>
+  <head/>
+  <body>
+    <p>
+      sobald man mit &#949; und ULPs hantiert, sind die numerischen Werte nur so minuti&#246;s verschieden, da&#223; man es in der &#252;blichen, gerundeten Darstellung gar nicht sieht. Damit scheiden alle Test-Methoden aus, die &quot;einfache Zahlen&quot; verwenden und ein festes Ergebnis vorgeben. Hinzu kommt, da&#223; man auch einen &#949;-Vergleich machen mu&#223;, und dann ohne gesonderte &#220;berlegung nicht offensichtlich ist, welche &quot;Unsch&#228;rfe&quot; nun &quot;unscharf&quot; ist, und welche Teil des Test-Subjekts ist. Nicht da&#223; man das alles irgendwie &quot;hinbekommt&quot; &#8212; aber der Leser versteht nicht mehr, <i>was hier gespielt wird.</i>
+    </p>
+  </body>
+</html></richcontent>
+<font NAME="SansSerif" SIZE="11"/>
+<icon BUILTIN="smily_bad"/>
+</node>
+</node>
+</node>
+<node BACKGROUND_COLOR="#c8c0b6" COLOR="#435e98" CREATED="1789521749900" ID="ID_912513687" MODIFIED="1789525194850" TEXT="sollte aber trotzdem wesentliche Elemente demonstrieren">
+<icon BUILTIN="yes"/>
+<node CREATED="1789521771353" ID="ID_559262092" MODIFIED="1789522935600" TEXT="was das &#xbb;limit&#xab; bedeutet : n&#xe4;mlich im Verh&#xe4;ltnis zur Periode"/>
+<node CREATED="1789521783888" ID="ID_1660128606" MODIFIED="1789521817663" TEXT="da&#xdf; das Wrapping mit einem sehr gro&#xdf;en Intervall funktioniert"/>
+<node CREATED="1789521818763" ID="ID_22678032" MODIFIED="1789521843436" TEXT="da&#xdf; es nahe der Interval-Obergrenze zu einem Aliasing kommen kann"/>
+</node>
+<node BACKGROUND_COLOR="#a6fdce" COLOR="#338800" CREATED="1789521853775" ID="ID_1420946197" MODIFIED="1789525101636" TEXT="Test formulieren...">
+<icon BUILTIN="yes"/>
+<node CREATED="1789521897465" ID="ID_1330009757" MODIFIED="1789521904636" TEXT="zun&#xe4;chst alles f&#xfc;r double"/>
+<node CREATED="1789521905359" ID="ID_284924920" MODIFIED="1789521995911" TEXT="aber bereits mit Konversionen und almostEqual"/>
+<node CREATED="1789525027288" ID="ID_1906103710" MODIFIED="1789525036691" TEXT="dann auf generischen Float umstellen...">
+<node CREATED="1789525037796" ID="ID_767684162" MODIFIED="1789525039283" TEXT="float"/>
+<node CREATED="1789525040023" ID="ID_1224952753" MODIFIED="1789525041834" TEXT="double"/>
+<node CREATED="1789525042606" ID="ID_815586095" MODIFIED="1789525045834" TEXT="long double"/>
+</node>
+</node>
+</node>
+<node BACKGROUND_COLOR="#174956" COLOR="#8dfd49" CREATED="1788313090668" HGAP="15" ID="ID_904924646" MODIFIED="1789525281531" STYLE="bubble" TEXT="ufff: GR&#xdc;N" VSHIFT="2">
+<edge COLOR="#61fe5b" STYLE="bezier" WIDTH="thin"/>
+<icon BUILTIN="ksmiletris"/>
+<node COLOR="#0f3e46" CREATED="1789525285095" HGAP="36" ID="ID_409017691" MODIFIED="1789525404221" STYLE="fork" TEXT="das ist schon &#xbb;advanced stuff&#xab;...." VSHIFT="-10">
+<arrowlink COLOR="#57fec0" DESTINATION="ID_452450374" ENDARROW="Default" ENDINCLINATION="-182;8;" ID="Arrow_ID_1586349868" STARTARROW="None" STARTINCLINATION="87;8;"/>
+<font NAME="SansSerif" SIZE="10"/>
+</node>
+</node>
 </node>
-<node CREATED="1789313641938" ID="ID_1271083241" MODIFIED="1789313655675" TEXT="man k&#xf6;nnte aber auch versuchen, an eine generische Library-funktion zu delegieren"/>
 </node>
 </node>
 <node COLOR="#338800" CREATED="1789171888403" ID="ID_1422919144" MODIFIED="1789171908101" TEXT="min/max clamp">