Parameters: resolve type precision problems with scale-joinig

The selection of the intermediary working type, used for exponential
and logarithmic functions when combining values from different scales,
was implemented too simplistic.

Following the example of the `NumberJoinType`, it seems preferrable
to spell out the decision logic explicitly. This allows to pick `long doubl`
as working type especially in cases where 64bit integral parameters are
involved, either as source or destination.

With these final tweaks, the `verify_valueJoining()` test is not complete,
presumably with path coverage of the conversion functions.

The Scale descriptor and operational logic is now defined to the point
that it can be integrated into the general Parameter implementation machinery.

src/lib/par/scale.hpp

@@ -42,6 +42,7 @@ namespace lib {
 namespace par {
   namespace err = lumiera::error;
   
+  using std::abs;
   using util::_Fmt;
   using std::optional;
   
@@ -79,6 +80,7 @@ namespace par {
       bool isValid()  const;
       bool isFactor() const;
       bool isCyclic() const;
+      bool isLimited() const;
       bool isLogarithmic() const;
       
       /* ===== conforming operations ===== */
@@ -125,7 +127,8 @@ namespace par {
        and (not isCyclic()
            or (minVal and maxVal
                and *minVal < *maxVal
-               and VAL(0) < cyclicLim)
+               and VAL(0) < cyclicLim
+               and abs (*maxVal) <= cyclicLim)
            )
            ;
   }
@@ -146,6 +149,14 @@ namespace par {
     return VAL(0) != cyclicLim;
   }
   
+  template<typename VAL>
+  inline bool
+  Scale<VAL>::isLimited()  const
+  {
+    return (maxVal or minVal)
+       and not isCyclic();
+  }
+  
   template<typename VAL>
   inline bool
   Scale<VAL>::isLogarithmic()  const

src/lib/par/type-handler.hpp

@@ -154,20 +154,13 @@ _Pragma("GCC diagnostic pop")
   
   template<typename T>
   concept number = integral<T> or floating_point<T>;
-
+  
-  /**
+  
-   * the best-precision floating point type to carry out
-   * a numeric operation to combine two values
-   * @note the result type is always some floating point,
-   *       since the goal is to use the exponential / logarithm family.
-   * @todo 9/26 we _could_ go from integral to long double for 64bit,
-   *       yet it is not clear if we ever need that tiny bit of extra precision...
-   */
-  template<number V, number W>
-  using CommonComputeType = std::conditional_t<integral<V> and integral<W>, double
-                                                                          , common_type_t<V, W>>;
-
   namespace {
+    static_assert (64 <= std::numeric_limits<lflp>::digits
+                  ,"long double type can not represent uint64_t exactly");
+    
+    
     /** @internal decision logic for combining numeric parameters */
     template<typename V, typename W>
     auto
@@ -189,6 +182,22 @@ _Pragma("GCC diagnostic pop")
               // Expand to long double, which can hold 64bit without precision loss
         }
     }
+    
+    /** @internal logic to pick a suitable floating-point for intermediary computations */
+    template<typename V, typename W>
+    auto
+    selectCommonComputeType()
+    {
+      if constexpr (is_integral_v<V> and is_integral_v<W>)
+        { // ensure integral precision is retained to the degree possible...
+          if constexpr (8 > sizeof(V) and 8 > sizeof(W))
+              return std::type_identity<double>{};
+          else
+              return std::type_identity<lflp>{};
+        }
+      else
+          return std::type_identity<common_type_t<V,W>>{};
+    }
   }
   
   /**
@@ -199,8 +208,17 @@ _Pragma("GCC diagnostic pop")
    *  - in the remaining problematic case(s), long double is used, as it can accommodate
    *    the full 64bit value range without loss on platforms relevant for Lumiera.
    */
-  template<typename A, typename B>
+  template<number V, number W>
-  using NumberJoinType = typename decltype(selectNumberJoinType<A,B>())::type;
+  using NumberJoinType = typename decltype(selectNumberJoinType<V,W>())::type;
+
+  /**
+   * best-precision floating point type to carry out
+   * a numeric operation to transform and adapt value scales.
+   * @note the result type is always some floating point,
+   *       since the goal is to use the exponential / logarithm family.
+   */
+  template<number V, number W>
+  using CommonComputeType = typename decltype(selectCommonComputeType<V,W>())::type;
   
   
   

tests/16parameter.tests

@@ -17,7 +17,7 @@ return: 0
 END
 
 
-PLANNED "Parameter value scales" ParameterScale_test << END
+TEST "Parameter value scales" ParameterScale_test << END
 return: 0
 END
 

tests/lib/par/parameter-scale-test.cpp

@@ -21,13 +21,6 @@
 #include "lib/par/scale.hpp"
 #include "test/diagnostic-output.hpp"/////////////TODO
 
-//#include <utility>
-//#include <string>
-//#include <vector>
-
-//using std::string;
-//using std::vector;
-//using std::swap;
 using test::roughEQ;
 
 
@@ -35,8 +28,6 @@ namespace lib {
 namespace par {
 namespace test{
   
-//  using lumiera::error::LUMIERA_ERROR_LOGIC;
-  
   namespace {//Test helpers....
     
     template<typename NUM>
@@ -59,7 +50,13 @@ namespace test{
   
   
   /**************************************************************************//**
-   * @test cover properties of generic parameter containers.
+   * @test demonstrate features and verify behaviour of value Scale definitions.
+   *     - a par::Scale is a descriptor record with some feature configuration settings
+   *     - some combination of setting marks specific scale features to be present
+   *     - values can be _conformed_ to comply with the scale constraints
+   *     - a Scale can be configured to maintain cyclic wrapping values
+   *     - values defined on different scales can be _joined_ (numerically combined)
+   *     - scales can be defined to be logarithmic, and work together with linear scales. 
    */
   class ParameterScale_test : public Test
     {
@@ -68,6 +65,7 @@ namespace test{
       run (Arg)
         {
           simpleUsage();
+          verify_Predicate();
           verify_Conforming();
           verify_cyclicScale();
           verify_valueJoining();
@@ -88,6 +86,51 @@ namespace test{
         }
       
       
+      /** @test verify the feature detection and descriptor predicates */
+      void
+      verify_Predicate()
+        {
+          Scale<double> scale;
+          
+          CHECK (scale.isValid());
+          CHECK (not scale.isCyclic());
+          CHECK (not scale.isLimited());
+          CHECK (not scale.isLogarithmic());
+          
+          scale.minVal = -5;
+          CHECK (scale.isValid());
+          CHECK (not scale.isCyclic());
+          CHECK (    scale.isLimited());
+          
+          scale.cyclicLim = 10;
+          CHECK (not scale.isValid());
+          CHECK (    scale.isCyclic());
+          CHECK (not scale.isLimited());
+          
+          scale.maxVal = +5;
+          CHECK (    scale.isValid());
+          CHECK (    scale.isCyclic());
+          CHECK (not scale.isLimited());
+          
+          CHECK (not scale.isFactor());
+          scale.neutral = 2;
+          CHECK (not scale.isFactor());
+          scale.neutral = 1;
+          CHECK (    scale.isFactor());
+          
+          CHECK (scale.metric == LIN);
+          CHECK (not scale.isLogarithmic());
+          scale.metric = NOM;
+          CHECK (not scale.isLogarithmic());
+          scale.metric = DEC;
+          CHECK (    scale.isLogarithmic());
+          scale.metric = BIN;
+          CHECK (    scale.isLogarithmic());
+          scale.metric = NAT;
+          CHECK (    scale.isLogarithmic());
+        }
+      
+      
       /** @test accommodate values to comply with the scale
        *      - optionally a maximum and minimum can be enforced
        *      - optionally the value can be cyclically wrapped
@@ -181,7 +224,9 @@ namespace test{
        *      - applying a linear factor to a logarithmic scale is
        *        transformed into an addition in the logarithmic domain
        *      - adding a linear offset to a logarithmic scale is rejected
-       * @todo WIP 9/26 🔁 define ⟶ ✔ implement
+       *      - extended precision scales handled using `lflp` (≙`long double`)
+       *      - this allows to retain full precision of 64bit integrals
+       * @todo WIP 9/26 ✔ define ⟶ ✔ implement
        */
       void
       verify_valueJoining()
@@ -276,7 +321,7 @@ namespace test{
           CHECK (logb (_MAX<int64_t>) < logb (megaScale.cyclicLim)); // ...which the (cyclic) target scale can still handle precisely!
           
           lflp res1 = megaScale.join (-5, 1e18f, fscale);            // log10 ⟼ 18, so we add -5dB + 180dB;
-          CHECK (roughEQ (res1, -5));                                //          the cyclicWrap then computes 175 - (-10) ≡ 185 % 20 (≙5) + (minVal ≙ -10)                    
+          CHECK (roughEQ (res1, -5));                                //          the cyclicWrap then computes 175 - (-10) ≡ 185 % 20 (≙5) + (minVal ≙ -10)
           
           // but the computation is not exact...
           CHECK (0 != std::fmod (res1, 1));
@@ -295,10 +340,10 @@ namespace test{
           // compare to target scale with lesser precision...
           Scale<double> doubleTargetScale = {.metric = DEC};
           Scale<uint64_t> longTargetScale = {.metric = DEC};
-          CHECK (180 == doubleTargetScale.join (0, int64_t(1e18),   lscale));
+          CHECK (180 == doubleTargetScale.join (0, int64_t(1e18),    lscale));        // uses double for internal log10 computation
-          CHECK (180 == doubleTargetScale.join (0, int64_t(1e18)+1, lscale));
+          CHECK (180 == doubleTargetScale.join (0, int64_t(1e18)-10, lscale));        // offset chosen large enough to prevail in int64_t but not in double
-          CHECK (180 ==   longTargetScale.join (0, int64_t(1e18),   lscale));
+          CHECK (180 ==   longTargetScale.join (0, int64_t(1e18),    lscale));        // 64bit integral scales use long-double for log10 computation internally
-          CHECK (180 !=   longTargetScale.join (0, int64_t(1e18)+1, lscale));  /////////////OOO this is a Bug! we should indeed use lflp for the interim computation
+          CHECK (179 ==   longTargetScale.join (0, int64_t(1e18)-10, lscale));        // ...and thus the offset survives the log10 and is truncated down on conversion
         }
       
       

wiki/thinkPad.ichthyo.mm

@@ -86269,16 +86269,17 @@ class ScaleRegistry
 </node>
 </node>
 </node>
-<node CREATED="1789159365103" ID="ID_435108847" MODIFIED="1789159397705" TEXT="sollte dann wohl gleich eine generische Registry sein...">
+<node CREATED="1789159365103" ID="ID_435108847" MODIFIED="1790094564624" TEXT="sollte dann wohl gleich eine generische Registry sein...">
 <linktarget COLOR="#426aa5" DESTINATION="ID_435108847" ENDARROW="Default" ENDINCLINATION="28;-70;" ID="Arrow_ID_1818399541" SOURCE="ID_735608493" STARTARROW="None" STARTINCLINATION="-393;12;"/>
+<linktarget COLOR="#365ac0" DESTINATION="ID_435108847" ENDARROW="Default" ENDINCLINATION="-11;82;" ID="Arrow_ID_246372510" SOURCE="ID_438812693" STARTARROW="None" STARTINCLINATION="14;-8;"/>
 <node CREATED="1789159448086" ID="ID_1755995276" MODIFIED="1789159547368" TEXT="Feste Index-Tabelle + heap-allozierte Extents"/>
 </node>
 </node>
 </node>
 </node>
 </node>
-<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1789170321059" ID="ID_533778146" MODIFIED="1789170328666" TEXT="einfache / vorl&#xe4;ufige Implementierung">
+<node COLOR="#338800" CREATED="1789170321059" ID="ID_533778146" MODIFIED="1790094388582" TEXT="einfache / vorl&#xe4;ufige Implementierung">
-<icon BUILTIN="pencil"/>
+<icon BUILTIN="button_ok"/>
 <node CREATED="1789170329999" ID="ID_247689608" MODIFIED="1789170375860" TEXT="&#xbb;vorl&#xe4;ufig&#xab; insofern ich komplexe Themen ignorieren sollte (Nominal-Skalen, Quantisierung)">
 <icon BUILTIN="idea"/>
 </node>
@@ -87235,9 +87236,9 @@ Prop.1: dist%3       1  2  0  1  2  0
 <icon BUILTIN="button_ok"/>
 </node>
 </node>
-<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1789171911830" ID="ID_944344547" MODIFIED="1789171915156" TEXT="join">
+<node COLOR="#338800" CREATED="1789171911830" ID="ID_944344547" MODIFIED="1790094358125" TEXT="join">
-<icon BUILTIN="pencil"/>
+<icon BUILTIN="button_ok"/>
-<node COLOR="#338800" CREATED="1789171916490" ID="ID_920699877" MODIFIED="1789172001819" TEXT="einfacher Fall: gemeinsame Scale">
+<node COLOR="#338800" CREATED="1789171916490" FOLDED="true" ID="ID_920699877" MODIFIED="1790094384518" TEXT="einfacher Fall: gemeinsame Scale">
 <icon BUILTIN="button_ok"/>
 <node COLOR="#338800" CREATED="1789171933617" ID="ID_284757000" MODIFIED="1789171970154" TEXT="isFactor definieren">
 <icon BUILTIN="button_ok"/>
@@ -87251,7 +87252,7 @@ Prop.1: dist%3       1  2  0  1  2  0
 <icon BUILTIN="button_ok"/>
 </node>
 </node>
-<node COLOR="#338800" CREATED="1789172002831" ID="ID_939833813" MODIFIED="1789961933370" TEXT="gemische Scales handhaben">
+<node COLOR="#338800" CREATED="1789172002831" FOLDED="true" ID="ID_939833813" MODIFIED="1790094383113" TEXT="gemische Scales handhaben">
 <icon BUILTIN="button_ok"/>
 <node COLOR="#338800" CREATED="1789949153983" ID="ID_781783423" MODIFIED="1789949195612" TEXT="ushort-Scale mit Limits &#x27f5; kombiniert mit int64_t">
 <icon BUILTIN="button_ok"/>
@@ -87263,7 +87264,7 @@ Prop.1: dist%3       1  2  0  1  2  0
 <arrowlink COLOR="#28b55c" DESTINATION="ID_1223578931" ENDARROW="Default" ENDINCLINATION="-139;1297;" ID="Arrow_ID_225645373" STARTARROW="None" STARTINCLINATION="111;6;"/>
 <icon BUILTIN="button_ok"/>
 </node>
-<node COLOR="#338800" CREATED="1789961742643" ID="ID_949990390" MODIFIED="1789961760832" TEXT="Verbindung verschiedener log-Scales">
+<node COLOR="#338800" CREATED="1789961742643" FOLDED="true" ID="ID_949990390" MODIFIED="1790094370986" TEXT="Verbindung verschiedener log-Scales">
 <icon BUILTIN="button_ok"/>
 <node COLOR="#435e98" CREATED="1789961765581" ID="ID_1536983378" MODIFIED="1789961783683" TEXT="Umwandlung linear &#x27f7; log">
 <node CREATED="1790021597423" ID="ID_5025438" MODIFIED="1790021610941" TEXT="die Konvertierungs-Funktionen sind strukturell eigenartig">
@@ -87285,8 +87286,7 @@ Prop.1: dist%3       1  2  0  1  2  0
       </li>
     </ul>
   </body>
-</html>
+</html></richcontent>
-</richcontent>
 </node>
 <node CREATED="1790021537463" ID="ID_1193038289" MODIFIED="1790022831555" TEXT="Funktion Scale&lt;VAL&gt;::asLogarithm ist zudem gar nicht von der Quell-Skala abh&#xe4;ngig"/>
 </node>
@@ -87315,8 +87315,7 @@ Prop.1: dist%3       1  2  0  1  2  0
       &#220;berraschung: die Logarithmen-Matematik funktioniert ... aber das dumme Mensch braucht endlos um zu kapieren da&#223; die Beispielwerte stimmen
     </p>
   </body>
-</html>
+</html></richcontent>
-</richcontent>
 </node>
 <node CREATED="1789961831540" ID="ID_104579195" MODIFIED="1789961843094" TEXT="aber auf der Ergebnis-Seite mu&#xdf; er aufgeschlagen werden"/>
 </node>
@@ -87332,15 +87331,26 @@ Prop.1: dist%3       1  2  0  1  2  0
   </body>
 </html></richcontent>
 </node>
-<node BACKGROUND_COLOR="#f8f1cb" COLOR="#a50125" CREATED="1790036164854" ID="ID_229924653" MODIFIED="1790036192419" TEXT="im Besonderen die Bestimmung des Arbeits-Datentyps sollte gepr&#xfc;ft werden">
+<node BACKGROUND_COLOR="#c8c0b6" COLOR="#435e98" CREATED="1790036164854" ID="ID_229924653" MODIFIED="1790094127028" TEXT="im Besonderen die Bestimmung des Arbeits-Datentyps">
 <icon BUILTIN="messagebox_warning"/>
-<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1790037266068" ID="ID_1040329780" MODIFIED="1790037379434" TEXT="tats&#xe4;chlich: die Wahl des Rechen-Datentyps ist zu einfach implementiert">
+<node BACKGROUND_COLOR="#e0ceaa" COLOR="#400f69" CREATED="1790037266068" ID="ID_1040329780" MODIFIED="1790094099158" TEXT="tats&#xe4;chlich: die Wahl des Rechen-Datentyps ist zu einfach implementiert">
-<linktarget COLOR="#e20b48" DESTINATION="ID_1040329780" ENDARROW="Default" ENDINCLINATION="805;29;" ID="Arrow_ID_1796905346" SOURCE="ID_31887994" STARTARROW="None" STARTINCLINATION="478;26;"/>
+<linktarget COLOR="#5425ca" DESTINATION="ID_1040329780" ENDARROW="Default" ENDINCLINATION="805;29;" ID="Arrow_ID_1796905346" SOURCE="ID_31887994" STARTARROW="None" STARTINCLINATION="478;26;"/>
-<icon BUILTIN="flag-pink"/>
+<icon BUILTIN="messagebox_warning"/>
-<node BACKGROUND_COLOR="#fafe99" COLOR="#fa002a" CREATED="1790037396226" HGAP="28" ID="ID_341439483" MODIFIED="1790037416138" TEXT="wir gehen von integral &#x27f6; double" VSHIFT="-7">
+<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1790037396226" HGAP="28" ID="ID_341439483" MODIFIED="1790094090617" TEXT="wir gehen von integral &#x27f6; double" VSHIFT="-7">
 <icon BUILTIN="broken-line"/>
 </node>
 </node>
+<node COLOR="#338800" CREATED="1790090085802" ID="ID_222503371" MODIFIED="1790094103279" TEXT="auch hier umstellen auf eine explizit ausformulierte Fall-Logik">
+<richcontent TYPE="NOTE"><html>
+  <head/>
+  <body>
+    <p>
+      nicht mehr versuchen, alles in einen Typ-Ausdruck zu packen; stattdessen hier auch die Technik mit einer Constexpr-Funktion, die einen type_identity-Record liefert
+    </p>
+  </body>
+</html></richcontent>
+<icon BUILTIN="button_ok"/>
+</node>
 </node>
 </node>
 </node>
@@ -87373,6 +87383,15 @@ Prop.1: dist%3       1  2  0  1  2  0
 </node>
 </node>
 </node>
+<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1790094428926" ID="ID_1432141408" MODIFIED="1790094455904" TEXT="mu&#xdf; nun die Scale (Descriptor) sinnvoll in die Parameter-Implementierung integrieren">
+<icon BUILTIN="yes"/>
+<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1790094459596" ID="ID_184861465" MODIFIED="1790094482634" TEXT="brauche dazu eine Registrierung und Scale-IDs">
+<icon BUILTIN="forward"/>
+<node CREATED="1790094501963" ID="ID_438812693" MODIFIED="1790094572153" TEXT="und diese Registry sollte generisch angelegt sein">
+<arrowlink COLOR="#365ac0" DESTINATION="ID_435108847" ENDARROW="Default" ENDINCLINATION="-11;82;" ID="Arrow_ID_246372510" STARTARROW="None" STARTINCLINATION="14;-8;"/>
+</node>
+</node>
+</node>
 </node>
 <node CREATED="1788134884746" ID="ID_195532610" MODIFIED="1788134888546" TEXT="Builder-Notation">
 <node CREATED="1788134893182" ID="ID_1219540786" MODIFIED="1788134948392" TEXT="naheliegend: statischer Einsteieg vom Parameter-Frontend">
@@ -87442,8 +87461,8 @@ Prop.1: dist%3       1  2  0  1  2  0
 </html></richcontent>
 </node>
 </node>
-<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1788896830329" ID="ID_355463973" MODIFIED="1788896840672" TEXT="Scale-Konfiguration erm&#xf6;glichen">
+<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1788896830329" ID="ID_355463973" MODIFIED="1790094404823" TEXT="Scale-Konfiguration erm&#xf6;glichen">
-<icon BUILTIN="flag-yellow"/>
+<icon BUILTIN="pencil"/>
 </node>
 </node>
 <node CREATED="1788654131472" ID="ID_1807734347" MODIFIED="1788654185033" TEXT="Prototyp-Builder">
@@ -87520,7 +87539,7 @@ Prop.1: dist%3       1  2  0  1  2  0
 <node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1788203400185" ID="ID_900611719" MODIFIED="1788307794257" TEXT="Builder-Notation schaffen">
 <icon BUILTIN="full-2"/>
 </node>
-<node COLOR="#435e98" CREATED="1788203422590" ID="ID_1249325546" MODIFIED="1788570267353" TEXT="Valure-Konversionen einbinden">
+<node COLOR="#435e98" CREATED="1788203422590" ID="ID_1249325546" MODIFIED="1788570267353" TEXT="Value-Konversionen einbinden">
 <icon BUILTIN="full-3"/>
 <node COLOR="#338800" CREATED="1788313016806" ID="ID_1966722816" MODIFIED="1788403892705" TEXT="generisch per Indirektion">
 <icon BUILTIN="button_ok"/>
@@ -87576,8 +87595,8 @@ Prop.1: dist%3       1  2  0  1  2  0
 <icon BUILTIN="hourglass"/>
 </node>
 </node>
-<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1789159639409" ID="ID_654373559" MODIFIED="1789607860036" TEXT="Scale-Eigenschaften abstecken per ParameterScale_test">
+<node COLOR="#338800" CREATED="1789159639409" ID="ID_654373559" MODIFIED="1790094342453" TEXT="Scale-Eigenschaften abstecken per ParameterScale_test">
-<icon BUILTIN="pencil"/>
+<icon BUILTIN="button_ok"/>
 <node CREATED="1789159687318" ID="ID_1480074646" MODIFIED="1789160197623" TEXT="Hier nur rein die Scale-Descriptoren und das intendierte Verhalten">
 <richcontent TYPE="NOTE"><html>
   <head/>
@@ -87605,6 +87624,11 @@ Prop.1: dist%3       1  2  0  1  2  0
 <icon BUILTIN="button_ok"/>
 </node>
 </node>
+<node COLOR="#338800" CREATED="1790094258921" ID="ID_1942061887" MODIFIED="1790094261651" TEXT="verify_Predicate">
+<icon BUILTIN="button_ok"/>
+<node CREATED="1790094263246" ID="ID_1388987426" MODIFIED="1790094274333" TEXT="demonstriert die wichtigsten Informations-Funktionen"/>
+<node COLOR="#310088" CREATED="1790094276841" ID="ID_783774183" MODIFIED="1790094312786" TEXT="(isValid() wird i.d.R. mit dem jeweilgen Feature zusammen abgedeckt)"/>
+</node>
 <node COLOR="#338800" CREATED="1789607293094" ID="ID_734632281" MODIFIED="1789607296849" TEXT="verify_Conforming">
 <icon BUILTIN="button_ok"/>
 <node CREATED="1789607298013" ID="ID_452068382" MODIFIED="1789607555871" TEXT="im Grunde offensichtlich und redundant">
@@ -87640,17 +87664,17 @@ Prop.1: dist%3       1  2  0  1  2  0
 <icon BUILTIN="yes"/>
 </node>
 </node>
-<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1789675604211" ID="ID_201071963" MODIFIED="1789676070358" TEXT="verify_valueJoining">
+<node COLOR="#338800" CREATED="1789675604211" ID="ID_201071963" MODIFIED="1790094240877" TEXT="verify_valueJoining">
-<icon BUILTIN="pencil"/>
+<icon BUILTIN="button_ok"/>
 <node COLOR="#338800" CREATED="1790015115678" ID="ID_1510723485" MODIFIED="1790015142255" TEXT="Schritt-1 : teste Typ-Konvertierung und Zusammenspiel mit conform()">
 <icon BUILTIN="button_ok"/>
 </node>
 <node COLOR="#338800" CREATED="1790015143816" ID="ID_1173177816" MODIFIED="1790015164942" TEXT="Schritt-2 : kl&#xe4;re und repariere das noch bestehende signed/unsigned-Problem">
 <icon BUILTIN="button_ok"/>
 </node>
-<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1790015165677" ID="ID_1207373600" MODIFIED="1790021319393" TEXT="Schritt-2 : Pfadabdeckung der Logarithmus-Skalen-Behandlung">
+<node COLOR="#338800" CREATED="1790015165677" ID="ID_1207373600" MODIFIED="1790094237018" TEXT="Schritt-2 : Pfadabdeckung der Logarithmus-Skalen-Behandlung">
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-<icon BUILTIN="flag-pink"/>
+<icon BUILTIN="button_ok"/>
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@@ -87659,12 +87683,12 @@ Prop.1: dist%3       1  2  0  1  2  0
       jaja ... oft wei&#223; man nicht ob es um &quot;overengieering&quot; geht, oder man selber einfach <i>faul</i>&#160;ist
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+</html></richcontent>
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-<node CREATED="1790028975682" HGAP="66" ID="ID_228688702" LINK="#ID_1208653097" MODIFIED="1790036783775" TEXT="auch noch einen log-double-Fall" VSHIFT="-1">
+<node COLOR="#338800" CREATED="1790028975682" FOLDED="true" HGAP="66" ID="ID_228688702" LINK="#ID_1208653097" MODIFIED="1790094232863" TEXT="auch noch einen log-double-Fall" VSHIFT="-1">
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+<icon BUILTIN="button_ok"/>
+<node COLOR="#435e98" CREATED="1790036164854" ID="ID_585649034" MODIFIED="1790094228089" TEXT="Augenmerk auf Arbeits-Datentyp legen">
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@@ -87693,13 +87717,12 @@ Prop.1: dist%3       1  2  0  1  2  0
       Tats&#228;chlich ist der ganze Zweig mit dem Genauigkeits-Limit nur f&#252;r floating-point-Typen notwendig; und diesen Branch-Guard kann man tats&#228;chlich schon zur compile-time machen!
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-</html>
+</html></richcontent>
-</richcontent>
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-<node CREATED="1790036598900" ID="ID_246190994" MODIFIED="1790036617586" TEXT="ein echter Logarithmus ist am &#xbb;intereessantesten&#xab;">
+<node BACKGROUND_COLOR="#b7d8bb" COLOR="#338800" CREATED="1790036598900" ID="ID_246190994" MODIFIED="1790094211855" TEXT="ein echter Logarithmus ist am &#xbb;intereessantesten&#xab;">
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@@ -87738,8 +87761,7 @@ Prop.1: dist%3       1  2  0  1  2  0
       das ist die gr&#246;&#223;tm&#246;gliche 10-er-Potenz, die noch in 63bit reinpa&#223;t
     </p>
   </body>
-</html>
+</html></richcontent>
-</richcontent>
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 <node CREATED="1790037016669" ID="ID_1010388251" MODIFIED="1790037055912" TEXT="dann ist der Rechenfehler am Ende &#x2248; 10^10"/>
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@@ -87756,8 +87778,8 @@ Prop.1: dist%3       1  2  0  1  2  0
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-<node BACKGROUND_COLOR="#fafe99" COLOR="#fa002a" CREATED="1790037238039" ID="ID_31887994" MODIFIED="1790037379434" TEXT="uint64_t &#x27f9; auch nicht &#x27f5; das ist nicht plausibel">
+<node COLOR="#435e98" CREATED="1790037238039" ID="ID_31887994" MODIFIED="1790094163676" TEXT="uint64_t &#x27f9; auch nicht &#x27f5; das ist nicht plausibel">
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+<arrowlink COLOR="#5425ca" DESTINATION="ID_1040329780" ENDARROW="Default" ENDINCLINATION="805;29;" ID="Arrow_ID_1796905346" STARTARROW="None" STARTINCLINATION="478;26;"/>
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@@ -87765,6 +87787,9 @@ Prop.1: dist%3       1  2  0  1  2  0
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+<node BACKGROUND_COLOR="#d2beaf" COLOR="#5c4d6e" CREATED="1790094336075" ID="ID_814063222" MODIFIED="1790094337810" TEXT="verify_NominalScale">
+<icon BUILTIN="hourglass"/>
+</node>
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