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Timeline: demonstrate safeguards against reversed and toxic input

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This commit is contained in:
Fischlurch 2022-11-18 02:55:28 +01:00
parent cfe3a6618f
commit 90aba4df09
6 changed files with 328 additions and 61 deletions
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4
src/lib/time/timevalue.hpp
View file

@ -475,6 +475,10 @@ namespace time {
Duration (TimeSpan const& interval);
Duration (FrameCnt count, FrameRate const& fps);
Duration (Duration const& o)
: Duration{Offset(o)}
{ }
static const Duration NIL;
void accept (Mutation const&);

56
src/stage/model/zoom-window.hpp
View file

@ -168,6 +168,22 @@ namespace model {
const uint MAX_PX_WIDTH{1000000};
const FSecs MAX_TIMESPAN{_FSecs(Time::MAX-Time::MIN)};
const FSecs MICRO_TICK{1_r/Time::SCALE};
/** Maximum quantiser to be handled in fractional arithmetics without hazard.
* @remark due to the common divisor normalisation, and the typical time computations,
* DENOMINATOR * Time::Scale has to stay below INT_MAX, with some safety margin
*/
const int64_t LIM_HAZARD{int64_t{1} << 40 };
inline int
toxicDegree (Rat poison)
{
const int64_t HAZARD_DEGREE{util::ilog2(LIM_HAZARD)};
int64_t magNum = util::ilog2(abs(poison.numerator()));
int64_t magDen = util::ilog2(abs(poison.denominator()));
int64_t degree = max (magNum, magDen);
return max (0, degree - HAZARD_DEGREE);
}
}
@ -461,14 +477,34 @@ namespace model {
*/
static TimeValue
ensureNonEmpty (TimeVar& startRef, TimeValue endPoint)
ensureNonEmpty (Time start, TimeValue endPoint)
{
if (startRef < endPoint)
return endPoint;
if (startRef <= Time::MAX - Time{DEFAULT_CANVAS})
return startRef + Time{DEFAULT_CANVAS};
startRef = Time::MAX - Time{DEFAULT_CANVAS};
return Time::MAX;
return (start < endPoint)? endPoint
: start + Time{DEFAULT_CANVAS};
}
/**
* Check and possibly sanitise a rational number to avoid internal numeric overflow.
* Fractional arithmetics can be insidious, due to the frequent re-normalisation;
* seemingly "harmless" numbers with a large denominator can cause numeric wrap-around.
* As safeguard, by introducing a tiny error, problematic numbers can be re-quantised
* to smaller denominators; moreover, large numbers must be limit checked.
* @remark Both the denominator and the numerator must be kept below a toxic limit,
* which is defined by the ability to multiply with Time::Scale without wrap-around.
* This heuristic is based on the actual computations done with the zoom factor and
* is thus specific to the ZoomWindow implementation. To sanitise, the denominator
* is reduced logarithmically (bit-shift) sufficiently and then used as new quantiser,
* thus ensuring that both denominator (=quantiser) and numerator are below limit.
* @note the check is based on the 2-logarithm of numerator and denominator, which is
* pretty much the fastest possibility (even a simple comparison would have
* to do the same). Values below threshold are simply passed-through.
*/
static Rat
detox (Rat poison)
{
int toxicity = toxicDegree (poison);
return toxicity ? util::reQuant(poison, poison.denominator() >> toxicity)
: poison;
}
static Rat
@ -493,7 +529,7 @@ namespace model {
FSecs dur{afterWin_-startWin_};
Rat adjMetric = Rat(pxWidth) / dur;
ENSURE (pxWidth == rational_cast<uint> (adjMetric*dur));
return adjMetric;
return detox (adjMetric);
}
void
@ -503,7 +539,7 @@ namespace model {
REQUIRE (afterWin_> startWin_);
FSecs dur{afterWin_-startWin_};
uint pxWidth = rational_cast<uint> (px_per_sec_*dur);
dur = Rat(pxWidth) / changedMetric;
dur = Rat(pxWidth) / detox (changedMetric);
dur = min (dur, MAX_TIMESPAN);
dur = max (dur, MICRO_TICK); // prevent window going void
TimeVar timeDur{dur};
@ -782,7 +818,7 @@ namespace model {
posFactor = posFactor*posFactor*posFactor; // -1 ... +1 but accelerating towards boundaries
posFactor = (posFactor + 1) / 2; // 0 ... 1
posFactor = util::limited (0, posFactor, 1);
return posFactor;
return detox (posFactor);
}
};

5
tests/15library.tests
View file

@ -508,6 +508,11 @@ return: 0
END
TEST "fractional arithmetics" Rational_test <<END
return: 0
END
TEST "RefArray_test" RefArray_test <<END
return: 0
END

5
tests/51-gui-model.tests
View file

@ -40,3 +40,8 @@ END
PLANNED "Concept demonstration: retrieve session contents" SessionStructureMapping_test <<END
return: 0
END
TEST "zoom timespan handling" ZoomWindow_test <<END
return: 0
END

129
tests/stage/model/zoom-window-test.cpp
View file

@ -35,7 +35,7 @@
#define SHOW_TYPE(_TY_) \
cout << "typeof( " << STRINGIFY(_TY_) << " )= " << lib::meta::typeStr<_TY_>() <<endl;
#define SHOW_EXPR(_XX_) \
cout << "#Probe# " << STRINGIFY(_XX_) << " ? = " << _XX_ <<endl;
cout << "#--◆--# " << STRINGIFY(_XX_) << " ? = " << _XX_ <<endl;
//////////////////////////////////////////////////////////////////////////////TODO
@ -87,7 +87,9 @@ namespace test {
verify_changeNotification();
toxic_corner_cases();
safeguard_zero_init();
safeguard_reversed_intervals();
safeguard_toxic_zoomFactor();
}
@ -486,47 +488,91 @@ namespace test {
}
/** @test verify safeguards when used in extreme corner cases */
/** @test verify safeguards against empty initialisation interval */
void
toxic_corner_cases()
safeguard_zero_init()
{
{
ZoomWindow win{0, TimeSpan{_t(0), FSecs(0)}};
CHECK (win.visible() == TimeSpan(_t(0), _t(23))); // uses DEFAULT_CANVAS instead of empty TimeSpan
CHECK (win.px_per_sec() == 25); // falls back on default initial zoom factor
CHECK (win.pxWidth() == 575); // allocates pixels in accordance to default
win.setOverallDuration(Duration{FSecs(50)});
win.setVisibleDuration(Duration{FSecs(0)});
CHECK (win.overallSpan() == TimeSpan(_t(0), _t(50)));
CHECK (win.visible() == TimeSpan(_t(0), _t(23))); // falls back to DEFAULT_CANVAS size
CHECK (win.pxWidth() == 575); // allocates pixels in accordance to default
win.calibrateExtension(0);
CHECK (win.px_per_sec() == 25); // stays at default zoom factor
CHECK (win.pxWidth() == 1); // retains 1px window size
CHECK (win.visible().duration() == _t(1,25)); // visible window has thus 1/25s duration
win.setOverallRange(TimeSpan(_t(10), _t(0)));
SHOW_EXPR (win.overallSpan());
SHOW_EXPR (win.visible());
SHOW_EXPR (_raw(win.visible().duration()));
SHOW_EXPR (win.px_per_sec());
SHOW_EXPR (win.pxWidth());
CHECK (TimeSpan(_t(10), _t(0)).duration() == Duration(FSecs(10))); // TimeSpan is always properly oriented by construction
Duration evilReversed = static_cast<Duration> (_t(-10));
SHOW_EXPR (evilReversed);
SHOW_EXPR (TimeSpan(_t(20), evilReversed));
}
{
Rat poison{_raw(Time::MAX)-101010101010101010, _raw(Time::MAX)+23};
SHOW_EXPR(poison);
Rat sane = util::reQuant (poison, _raw(Time::MAX) / Time::SCALE);
SHOW_EXPR(sane);
SHOW_EXPR(rational_cast<double>(poison));
SHOW_EXPR(rational_cast<double>(sane));
ZoomWindow win{0, TimeSpan{_t(0), FSecs(0)}};
CHECK (win.visible() == TimeSpan(_t(0), _t(23))); // uses DEFAULT_CANVAS instead of empty TimeSpan
CHECK (win.px_per_sec() == 25); // falls back on default initial zoom factor
CHECK (win.pxWidth() == 575); // allocates pixels in accordance to default
win.setOverallDuration(Duration{FSecs(50)});
win.setVisibleDuration(Duration{FSecs(0)});
CHECK (win.overallSpan() == TimeSpan(_t(0), _t(50)));
CHECK (win.visible() == TimeSpan(_t(0), _t(23))); // falls back to DEFAULT_CANVAS size
CHECK (win.pxWidth() == 575); // allocates pixels in accordance to default
win.calibrateExtension(0);
CHECK (win.px_per_sec() == 25); // stays at default zoom factor
CHECK (win.pxWidth() == 1); // retains 1px window size
CHECK (win.visible().duration() == _t(1,25)); // visible window has thus 1/25s duration
}
/** @test verify safeguards against reversed time intervals */
void
safeguard_reversed_intervals()
{
ZoomWindow win{1};
win.setVisibleDuration(Duration{FSecs(1,25)});
win.setOverallRange(TimeSpan(_t(10), _t(0))); // set an "reversed" overall time range
CHECK (win.overallSpan() == TimeSpan(_t(10), _t(20))); // range has been flipped forward
CHECK (win.visible().duration() == Time(40,0));
CHECK (win.px_per_sec() == 25);
CHECK (win.pxWidth() == 1);
CHECK (TimeSpan(_t(10), _t(0)).duration() == Duration(FSecs(10))); // TimeSpan is always properly oriented by construction
Time negaTime = _t(-10);
CHECK (negaTime < Time::ZERO);
Duration& evilDuration = reinterpret_cast<Duration&> (negaTime); // attempt fabricate a subverted TimeSpan
CHECK (evilDuration < Time::ZERO); // ...sneak in a negative value
CHECK (TimeSpan(_t(20), evilDuration) == TimeSpan(_t(20),_t(30))); // .....yet won't make it get past Duration copy ctor!
}
/** @test demonstrate sanitising of "poisonous" fractional zoom factor
* - construct an example factor of roughly 2/3, but using extremely large
* numerator and denominator close to total time axis dimensions.
* - even simple calculations with this poison value will fail
* - construct a new quantiser, based on the number to be sanitised
* - re-quantise the toxic number into this new quantiser
* - the sanitised number is almost identical to the toxic original
* - yet all the simple calculations can be carried out flawlessly
* - both toxic and sanitised number lead to the same zoom timespan
*/
void
safeguard_toxic_zoomFactor()
{
Rat poison{_raw(Time::MAX)-101010101010101010, _raw(Time::MAX)+23};
CHECK (poison == 206435633551724850_r/307445734561825883);
CHECK (poison + Time::SCALE < 0); // simple calculations fail due to numeric overflow
CHECK (Time(FSecs(poison)) < Time::ZERO); // conversion to µ-ticks also leads to overflow
CHECK (-6 == _raw(Time(FSecs(poison))));
using util::ilog2;
CHECK (40 == ilog2 (LIM_HAZARD)); // LIM_HAZARD is based on MAX_INT / Time::Scale
CHECK (57 == ilog2 (poison.numerator())); // use the leading bit position as size indicator
CHECK (58 == ilog2 (poison.denominator())); // use the maximum of numerator or denominator bit position
CHECK (58-40 == 18); // everything beyond LIM_HAZARD counts as "toxic"
int toxicity = toxicDegree (poison);
CHECK (toxicity == 18);
int64_t quant = poison.denominator() >> toxicity; // shift away the excess toxic LSB
CHECK (quant == 1172812402961);
CHECK (ilog2 (quant) == ilog2 (LIM_HAZARD));
Rat detoxed = util::reQuant(poison, quant); // and use this "shortened" denominator for re-quantisation
CHECK (detoxed == 787489446837_r/1172812402961); // the resulting fraction uses way smaller numbers
CHECK (0.671453834f == rational_cast<float> (poison)); // but yields approximately the same effective value
CHECK (0.671453834f == rational_cast<float> (detoxed));
CHECK (detoxed+Time::SCALE == 1172813190450446837_r/1172812402961); // result: we can calculate without failure
CHECK (Time(FSecs(detoxed)) > Time::ZERO); // can convert re-quantised number to µ-ticks
CHECK (671453 == _raw(Time(FSecs(detoxed))));
// and resulting µ-ticks will be effectively the same
CHECK (1906 == _raw(TimeValue(1280 / rational_cast<long double>(poison))));
CHECK (1906 == _raw(TimeValue(1280 / rational_cast<long double>(detoxed))));
ZoomWindow win{};
// SHOW_EXPR(win.overallSpan());
// SHOW_EXPR(_raw(win.visible().duration()));
@ -535,7 +581,6 @@ namespace test {
// CHECK (win.visible() == TimeSpan(_t(0), _t(23)));
// CHECK (win.px_per_sec() == 25);
// CHECK (win.pxWidth() == 575);
}
}
};

190
wiki/thinkPad.ichthyo.mm
View file

@ -39555,6 +39555,9 @@
</node>
</node>
<node CREATED="1668262940706" ID="ID_1639008148" MODIFIED="1668262957124" TEXT="&#x27f9; Eingangs-Checks vereinfachen"/>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668554856002" ID="ID_1728331882" MODIFIED="1668554864730" TEXT="potentiell sch&#xe4;dliche Eingabedaten">
<icon BUILTIN="flag-yellow"/>
<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1668262961151" ID="ID_1262854527" MODIFIED="1668270708694" TEXT="alle Eing&#xe4;nge daraufhin pr&#xfc;fen">
<icon BUILTIN="pencil"/>
<node CREATED="1668263281549" ID="ID_1653448250" MODIFIED="1668263292760" TEXT="potentiell gef&#xe4;hrlich">
@ -39615,11 +39618,53 @@
<icon BUILTIN="help"/>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668263473958" ID="ID_1175951405" MODIFIED="1668270354481" TEXT="conformWindowToMetric (Rat changedMetric)">
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<node BACKGROUND_COLOR="#fefc4e" COLOR="#351d75" CREATED="1668555596031" HGAP="151" ID="ID_1196389964" MODIFIED="1668555795593" TEXT="&#xd83e;&#xdc46; die zentrale Gelenkstelle" VSHIFT="4">
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<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1668555725214" ID="ID_1632657793" MODIFIED="1668555774726" TEXT="alle potentiell gef&#xe4;hrlichen Wirkpfade kommen hier vorbei"/>
<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1668555737844" ID="ID_625503483" MODIFIED="1668555774726" TEXT="hier verwandeln sich Eingabedaten in Parameterdaten"/>
</node>
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<icon BUILTIN="info"/>
<node CREATED="1668701689231" ID="ID_1495743277" MODIFIED="1668701701766" TEXT="changedMetric &#x27f6; dur">
<node CREATED="1668701735972" ID="ID_1362411868" MODIFIED="1668701746854" TEXT="metric.num &#x27f6; dur.denom"/>
<node CREATED="1668701831578" ID="ID_364333659" MODIFIED="1668701864041" TEXT="Lim: metric.denom * pixWidth &lt; MAX_INT">
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<node CREATED="1668701935616" ID="ID_1861389254" MODIFIED="1668701941971" TEXT="wegen isGridAligned()"/>
</node>
<node CREATED="1668701946449" ID="ID_296260515" MODIFIED="1668701964086" TEXT="anschlie&#xdf;end wird dur -&gt; Time gerundet">
<icon BUILTIN="idea"/>
</node>
</node>
<node CREATED="1668702760034" ID="ID_868876168" MODIFIED="1668703402758" TEXT="placeWindowRelativeToAnchor (dur)">
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</node>
</node>
<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1668703282413" HGAP="-88" ID="ID_1113812536" MODIFIED="1668703442612" TEXT="Input (changedMetric) mu&#xdf; entgiftet werden" VSHIFT="23">
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<icon BUILTIN="clanbomber"/>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668703200176" ID="ID_1915595988" MODIFIED="1668703230862" TEXT="conformMetricToWindow()">
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<icon BUILTIN="flag-yellow"/>
<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1668703282413" ID="ID_1976673029" MODIFIED="1668703442613" TEXT="Output mu&#xdf; entgiftet werden">
<edge COLOR="#f74141" STYLE="linear"/>
<icon BUILTIN="clanbomber"/>
</node>
<node CREATED="1668703253721" ID="ID_562775888" MODIFIED="1668703454748" TEXT="output &#x27f6; finaler Metrik-Faktor">
<icon BUILTIN="messagebox_warning"/>
</node>
</node>
<node COLOR="#435e98" CREATED="1668263585452" ID="ID_195681721" MODIFIED="1668270219934" TEXT="conformWindowToCanvas(&lt;current-settings&gt;)">
<node CREATED="1668270193562" ID="ID_918641802" MODIFIED="1668270440632" TEXT="nur additive arithmetik">
@ -39690,6 +39735,7 @@
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<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1668270677518" HGAP="31" ID="ID_51247840" MODIFIED="1668293080653" STYLE="fork" TEXT="Berechnung kann wild entgleisen" VSHIFT="2">
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@ -39707,13 +39753,35 @@
<node CREATED="1668292982369" ID="ID_1496719180" MODIFIED="1668293079087" TEXT="Assignment an eine TimeVar macht einen Guard-check">
<icon BUILTIN="idea"/>
</node>
<node CREATED="1668292909179" ID="ID_944892675" MODIFIED="1668293079087" TEXT="sofern der duration-Parameter auch sauber ist...."/>
<node CREATED="1668292909179" ID="ID_944892675" MODIFIED="1668703468960" TEXT="sofern der duration-Parameter auch sauber ist....">
<icon BUILTIN="yes"/>
</node>
</node>
<node CREATED="1668270662235" ID="ID_238899324" MODIFIED="1668293024213" TEXT="kein wirklicher Schaden m&#xf6;glich">
<node CREATED="1668293046153" ID="ID_1545859602" MODIFIED="1668293053428" TEXT="danach haben wir wieder einen TimeValue"/>
<node CREATED="1668293054279" ID="ID_202153481" MODIFIED="1668293059275" TEXT="und dieser liegt im Limit"/>
<node CREATED="1668293062334" ID="ID_1382128860" MODIFIED="1668293074089" TEXT="nachfolgende Normalisierung erledigt den Rest"/>
</node>
<node CREATED="1668703609105" ID="ID_1557527906" MODIFIED="1668703662246">
<richcontent TYPE="NODE"><html>
<head>
</head>
<body>
<p>
&#10233; <u><b>Fazit</b></u>:
</p>
<ul>
<li>
erh&#228;lt Invariante
</li>
<li>
Ergebnis kann aber <i>inhaltlich falsch</i>&#160;sein
</li>
</ul>
</body>
</html></richcontent>
</node>
</node>
<node COLOR="#435e98" CREATED="1668263721530" ID="ID_829406482" MODIFIED="1668270430868" TEXT="establishWindowDuration (TimeVar duration)">
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@ -39723,19 +39791,41 @@
<icon BUILTIN="button_ok"/>
</node>
</node>
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<icon BUILTIN="messagebox_warning"/>
<node CREATED="1668267470317" ID="ID_409576187" MODIFIED="1668267475864" TEXT="kann entgleisen"/>
<node CREATED="1668269162412" ID="ID_983739705" MODIFIED="1668269175422" TEXT="Fehlfunktion ist aber letztlich harmlos"/>
<node CREATED="1668269178282" ID="ID_697782687" MODIFIED="1668269188827" TEXT="die nachgelagerte Normalisierung f&#xe4;ngt die Konsequenzen auf"/>
<node COLOR="#338800" CREATED="1668269189680" ID="ID_1612606864" MODIFIED="1668269410626" TEXT="aber: Limitierung am Ausgang fehlt &#x27f9; nachr&#xfc;sten">
<icon BUILTIN="button_ok"/>
</node>
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<richcontent TYPE="NODE"><html>
<head>
</head>
<body>
<p>
Vorsicht: Ergebnis-Faktor kann trotzdem <i><font color="#f41bbc">giftig sein</font></i>
</p>
</body>
</html></richcontent>
<icon BUILTIN="clanbomber"/>
</node>
<node COLOR="#338800" CREATED="1668703745543" ID="ID_660082790" MODIFIED="1668736277567" TEXT="Ergebnis auch noch entgiften!">
<icon BUILTIN="button_ok"/>
</node>
</node>
</node>
</node>
<node CREATED="1668554900067" ID="ID_1302892550" MODIFIED="1668554974542" TEXT="kritische Wirkpfade">
<node CREATED="1668555028046" ID="ID_660534369" MODIFIED="1668555056498" TEXT="sehr kleine Metrix (&#x2259; exterm zoom-out)"/>
<node CREATED="1668555072594" ID="ID_742229180" MODIFIED="1668555089126" TEXT="Ansteuern exterm gro&#xdf;er Zeit-Positionen"/>
<node CREATED="1668555157385" ID="ID_1157546672" MODIFIED="1668555164702" TEXT="Time-wrap nach extremem Offset"/>
<node CREATED="1668555183502" ID="ID_1287974241" MODIFIED="1668555191961" TEXT="Einspeisen giftiger Metrik"/>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668180030777" ID="ID_1319796356" MODIFIED="1668180136077" TEXT="1 &#xb5;-Tick">
<icon BUILTIN="flag-yellow"/>
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@ -39748,11 +39838,11 @@
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<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1668270062492" ID="ID_1671513743" MODIFIED="1668270626473" TEXT="entgiftungs-Methode schaffen">
<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1668270062492" ID="ID_1671513743" MODIFIED="1668736241536" TEXT="entgiftungs-Methode schaffen">
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<node COLOR="#435e98" CREATED="1668292035888" HGAP="50" ID="ID_511660460" MODIFIED="1668295679206" TEXT="ist das &#xfc;berhaupt m&#xf6;glich" VSHIFT="9">
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<icon BUILTIN="button_cancel"/>
@ -39808,8 +39898,8 @@
<linktarget COLOR="#c6476e" DESTINATION="ID_91804756" ENDARROW="Default" ENDINCLINATION="220;-12;" ID="Arrow_ID_1385445807" SOURCE="ID_199183662" STARTARROW="None" STARTINCLINATION="721;42;"/>
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<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668294526618" ID="ID_603305402" MODIFIED="1668294542704" TEXT="maximale Gefahr...">
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<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1668294526618" ID="ID_603305402" MODIFIED="1668736269643" TEXT="maximale Gefahr...">
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<node CREATED="1668294547631" ID="ID_1464756735" MODIFIED="1668294561849" TEXT="Nenner der bestehenden Metrik ist nahe Time::MAX"/>
<node CREATED="1668294577579" ID="ID_1456441768" MODIFIED="1668294606739" TEXT="Z&#xe4;hler der neuen Metrik ist knapp unter ZOOM_MAX_RESOLUTION"/>
<node CREATED="1668294624158" ID="ID_1703677216" MODIFIED="1668294635105" TEXT="dann kann die neue Duration entgleisen">
@ -40067,7 +40157,89 @@
</node>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668295799991" ID="ID_192811111" MODIFIED="1668474435369" TEXT="Z&#xe4;hler gegen Limit pr&#xfc;fen und ggfs kappen">
<node COLOR="#990000" CREATED="1668295799991" ID="ID_192811111" MODIFIED="1668736212375" TEXT="Z&#xe4;hler gegen Limit pr&#xfc;fen und ggfs kappen">
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<node CREATED="1668561130068" ID="ID_1984177447" MODIFIED="1668561136326" TEXT="gef&#xe4;llt mir gar nicht..."/>
<node CREATED="1668703798232" ID="ID_661092441" MODIFIED="1668703817686" TEXT="Ergebnis sollte stets n&#xe4;herungsweise korrekt sein!">
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</node>
<node COLOR="#435e98" CREATED="1668561137011" ID="ID_1372010715" MODIFIED="1668736186079" TEXT="bessere Idee als &quot;kappen&quot;?">
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<node CREATED="1668561156200" ID="ID_646114106" MODIFIED="1668561196159" TEXT="man k&#xf6;nnte nochmal reQuantisieren">
<node CREATED="1668699891224" ID="ID_420975014" MODIFIED="1668699935567" TEXT="reduzieren um Z&#xe4;hler - LIM_HAZARD"/>
<node CREATED="1668699947962" ID="ID_307211451" MODIFIED="1668700039253" TEXT="das erste Quansitieren bewirkt n&#xe4;mlich u.U fast gar nix">
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<head>
</head>
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<p>
...und zwar in dem Fall, in dem der Nenner nur knapp &#252;ber der Schwelle LIM_HAZARD liegt; dann findet n&#228;mlich fast keine Reduktion der Gr&#246;&#223;enordnung statt
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</node>
<node CREATED="1668561196884" ID="ID_1903032995" MODIFIED="1668736191824" TEXT="oder gleich gegen einen kleineren Divisor...">
<icon BUILTIN="forward"/>
<node CREATED="1668703944877" ID="ID_676279711" MODIFIED="1668704058851" TEXT="auf Effekt der re-Quantisierung abstellen">
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<ul>
<li>
der Nenner wird garantiert gleich dem vorgegebenen Quantisierer sein
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<li>
aber der Z&#228;hler ist ggfs um das Verh&#228;ltnis Z&#228;hler / Nenner gr&#246;&#223;er als der Quantisierer
</li>
</ul>
</body>
</html></richcontent>
<icon BUILTIN="yes"/>
</node>
<node CREATED="1668705598237" ID="ID_434566365" MODIFIED="1668705615391" TEXT="&#x27f9; es sind zwei Vorgaben umzusetzen">
<node CREATED="1668705616466" ID="ID_1803292875" MODIFIED="1668705683542" TEXT="Quant &lt; LIM_HAZARD"/>
<node CREATED="1668705658797" ID="ID_1607621699" MODIFIED="1668705687757" TEXT="Quant so viel kleiner da&#xdf; Z&#xe4;hler &lt; LIM_HAZARD"/>
</node>
<node COLOR="#435e98" CREATED="1668705712605" ID="ID_801769631" MODIFIED="1668736224441" TEXT="das ist am effizientesten &#xfc;ber den 2-er-Logarithmus umsetzbar">
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<node CREATED="1668705828544" ID="ID_27322947" MODIFIED="1668705883187" TEXT="lb(z&#xe4;hler) - lb(nenner) &#x27fc; zusatz-Faktor"/>
<node CREATED="1668705906923" ID="ID_21115436" MODIFIED="1668705925067" TEXT="bei &#xdc;berschu&#xdf; den Quantiser entsprechend reduzieren"/>
</node>
</node>
</node>
</node>
<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1668705939639" ID="ID_393310295" MODIFIED="1668736180984" TEXT="Implementierung">
<icon BUILTIN="pencil"/>
<node COLOR="#338800" CREATED="1668705949188" ID="ID_510681740" MODIFIED="1668707393273" TEXT="2-er-Logarithmen berechnen">
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<node CREATED="1668705960324" ID="ID_1999378206" MODIFIED="1668705972646" TEXT="ist die effizientest m&#xf6;gliche L&#xf6;sung">
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<node CREATED="1668705973302" ID="ID_1516053648" MODIFIED="1668705991661" TEXT="auch ein einfacher Gr&#xf6;&#xdf;envergleich mu&#xdf; n&#xe4;mlich das gr&#xf6;&#xdf;te gesetze Bit finden"/>
</node>
<node COLOR="#338800" CREATED="1668706081924" ID="ID_1548560727" MODIFIED="1668707394524" TEXT="daraus Reduktions-Faktor ermitteln">
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<node CREATED="1668706195686" ID="ID_894705182" MODIFIED="1668706204807" TEXT="der &#xdc;berschu&#xdf; gegen&#xfc;ber LIM_HAZARD"/>
<node CREATED="1668706205651" ID="ID_1995535678" MODIFIED="1668706221245" TEXT="und zwar das Maximum von Z&#xe4;hler und Nenner"/>
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<node COLOR="#338800" CREATED="1668706244774" ID="ID_972239326" MODIFIED="1668707396226" TEXT="Bitshift auf den Nenner um den Reduktoins-Faktor &#x27fc; neuer Quantiser">
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<node COLOR="#338800" CREATED="1668706302918" ID="ID_319812477" MODIFIED="1668707397496" TEXT="reQuant falls notwendig, sonst unver&#xe4;ndert durchreichen">
<icon BUILTIN="button_ok"/>
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</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668707398858" ID="ID_1529383789" MODIFIED="1668707464339" TEXT="Test">
<icon BUILTIN="flag-yellow"/>
<node COLOR="#338800" CREATED="1668707465449" ID="ID_1678870601" MODIFIED="1668736173820" TEXT="toxicDegree mit einigen Beispielen demonstrieren">
<icon BUILTIN="button_ok"/>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668707479892" ID="ID_1964644327" MODIFIED="1668707490200" TEXT="ansonsten durch Ausreizen der Extremwerte testen">
<icon BUILTIN="flag-yellow"/>
</node>
</node>