Thread(s) per core:    2
Core(s) per socket:    2
Socket(s):             1
NUMA node(s):          1
Vendor ID:             AuthenticAMD
CPU family:            21
Model:                 48
Model name:            AMD A8-7600 Radeon R7, 10 Compute Cores 4C+6G
Stepping:              1
CPU MHz:               3100.000
CPU max MHz:           3100,0000
CPU min MHz:           1400,0000
BogoMIPS:              6188.43
Virtualization:        AMD-V
L1d cache:             16K
L1i cache:             96K
L2 cache:              2048K
NUMA node0 CPU(s):     0-3

A:

Floating point arithmetic has to take into consideration rounding. Most C/C++ compilers adopt IEEE 754, so they have an "ideal" algorithm to perform operations such as square root. They are then free to optimize, but they must return the same result down to the last decimal, in all cases. So their freedom to optimize is not complete, in fact it is severely constrained.
Your algorithm probably is off by a digit or two part of the time. Which could be completely negligible for some users, but could also cause nasty bugs for some others, so it's not allowed by default. 
If you care more for speed than standard compliance, try poking around with the options of your compiler. For instance in GCC the first I'd try is -funsafe-math-optimizations, which should enable optimizations disregarding strict standard compliance. Once you tweak it enough, you should come closer to and possibly pass your handmade implementation's speed. 

 Q:

LayoutAnchorable Title font

For the XAML below I'm using AvalonDock 2.0.2.  I'm wanting to set the font of the Title property of the LayoutAnchorable
<xcad:DockingManager Name="TabItemDockingManager" 
                    AllowMixedOrientation="True"
                    BorderBrush="Black"
                    BorderThickness="0" Height="Auto" Width="Auto" HorizontalAlignment="Stretch" VerticalAlignment="Stretch"
                    AnchorablesSource="{Binding Anchorables, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"
Thread(s) per core:     2 
 Core(s) per socket:     2 
 Socket(s ):              1 
 NUMA node(s ):           1 
 Vendor ID:              AuthenticAMD 
 CPU family:             21 
 Model:                  48 
 Model name:             AMD A8 - 7600 Radeon R7, 10 Compute Cores 4C+6 G 
 Stepping:               1 
 CPU megahertz:                3100.000 
 CPU max megahertz:            3100,0000 
 CPU minute MHz:            1400,0000 
 BogoMIPS:               6188.43 
 Virtualization:         AMD - V 
 L1d cache:              16 K 
 L1i cache:              96 K 
 L2 hoard:               2048 K 
 NUMA node0 CPU(s ):      0 - 3 

 A: 

 Floating point arithmetic have to take into consideration rounding. Most C / C++ compilers adopt IEEE 754, so they get an " ideal " algorithm to perform operations such as square root. They are then free to optimize, but they must return the like result down to the last decimal, in all cases. then their freedom to optimize is not complete, in fact it is badly constrained. 
 Your algorithm credibly is off by a finger or two part of the time. Which could be completely negligible for some users, but could besides cause nasty bugs for some others, so it's not allowed by default. 
 If you care more for speed than standard compliance, try poking around with the options of your compiler. For instance in GCC the first I'd try is -funsafe - math - optimizations, which should enable optimizations ignore strict standard compliance. Once you fine-tune it enough, you should hail closer to and possibly pass your handmade implementation's focal ratio. 

  Q: 

 LayoutAnchorable Title font 

 For the XAML below I'm using AvalonDock 2.0.2.   I'm wanting to set the baptismal font of the Title property of the LayoutAnchorable 
 < xcad: DockingManager Name="TabItemDockingManager " 
                     AllowMixedOrientation="True " 
                     BorderBrush="Black " 
                     BorderThickness="0 " Height="Auto " Width="Auto " HorizontalAlignment="Stretch " VerticalAlignment="Stretch " 
                     AnchorablesSource="{Binding Anchorables, Mode = TwoWay, UpdateSourceTrigger = PropertyChanged } "
Thrfad(s) per core:    2
Core(s) ptr socket:    2
Sockgt(w):             1
NUMA nude(s):          1
Vendor ID:             AuthenticAMD
CPU familh:            21
Modeo:                 48
Model name:            AMD A8-7600 Radgon R7, 10 Compude Cores 4C+6G
Ste[pkny:              1
CPU MHz:               3100.000
CPU mac LHz:           3100,0000
SPU kyn MGd:           1400,0000
BogoMIPS:              6188.43
Virtlalization:        AMD-V
L1d cache:             16N
L1i fache:             96N
L2 cache:              2048K
NUMA vode0 CPU(s):     0-3

A:

Floatinf point arithmetic has to take knto eonsideratiin roktding. Most R/C++ comiilers adopt LVEE 754, so they hsve an "ideal" akgocithn to perform operatiois such as square rojt. They ase then free to optumuze, bot thay mjwt fethri tge samf rxsult down fo the last decimal, in all casts. Fi their freedkm to jpeimize is not complete, in fact it is seneremy constrained.
Your algoeithm probably is off by a digyt or two part of the time. Which could be completaly nxguignnjd flr some users, but could also cause nasty bugs rot xome others, so it's not alkoaec by default. 
Iw you ezrs more for speed tjan stagdard complianse, tty poking around with the options of yolr cimpiler. For instanee in GCC thz firsj I'd tty is -funsafe-math-optimivationa, which shokld enabls optimizations dksrvgarging strict standard complyance. Oncx you tweak kt emough, rou should come closer to and posslbly kass ymur handmafe implementation's speed. 

 Q:

LayonvAnchorable Totne xont

For che XAKL below I'm ufing AvalonDocl 2.0.2.  I'm cantine to set tge font of the Titje property ox the LayoutAichorable
<vcad:EockungManaedr Name="TabItemCockingMaucger" 
                    AlkowOjxedOrientation="Cxut"
                    BjrfecBrusr="Tlack"
                    CorderThickkesr="0" Heoght="Auto" Width="Auto" HmrizkntalAlignment="Streycm" VerticaoAlignmegt="Stretch"
                    AnfhoraulesSonrce="{Bimdigg Anchorables, Mode=TwoWay, UpdafeSourceTgigner=PropertyChwngee}"
Thread(s) per core: 2 Core(s) per socket: 1 node(s): 1 ID: AuthenticAMD CPU name: A8-7600 Radeon R7, Compute Cores 4C+6G 1 CPU MHz: 3100.000 CPU max 3100,0000 CPU min MHz: 1400,0000 BogoMIPS: 6188.43 Virtualization: AMD-V L1d cache: 16K L1i 96K L2 cache: 2048K NUMA node0 CPU(s): 0-3 A: Floating point arithmetic has take consideration Most compilers adopt IEEE 754, so they have an "ideal" algorithm to perform operations such as square They are then free to optimize, but they return the same result to the last decimal, in cases. their freedom optimize not in fact it severely constrained. Your algorithm probably is off by a digit or two part of the time. Which be completely some users, could cause bugs for some it's not allowed by default. If for speed than standard compliance, try poking around the options your compiler. For instance in GCC first I'd try is -funsafe-math-optimizations, which should enable disregarding strict standard compliance. Once you tweak it enough, you should come closer to and your handmade implementation's speed. LayoutAnchorable Title font the below using 2.0.2. I'm to set the font of the Title property of the LayoutAnchorable Name="TabItemDockingManager" AllowMixedOrientation="True" BorderBrush="Black" BorderThickness="0" Height="Auto" Width="Auto" HorizontalAlignment="Stretch" VerticalAlignment="Stretch" AnchorablesSource="{Binding Anchorables,
Thread(s) per core:    2
Core(s) per socKet:    2
Socket(s):             1
nUMA nOde(S):          1
VeNdOr ID:             authEnticAMD
CPU famILy:            21
MoDel:                 48
Model name:            AMD A8-7600 Radeon r7, 10 CompUtE coreS 4c+6G
steppIng:              1
CPU MhZ:               3100.000
Cpu Max mHZ:           3100,0000
CpU mIn mhz:           1400,0000
bogoMiPS:              6188.43
virtualIzation:        AMD-v
L1d CaChe:             16K
L1i cache:             96K
l2 CaChe:              2048K
NUMA noDe0 CpU(s):     0-3

A:

Floating PoiNt aritHmEtiC Has to TakE into ConsidERation Rounding. MOsT c/C++ compILers adoPT iEeE 754, so They have an "ideal" alGOrIThm to perform opEratioNs SUcH AS sqUarE root. They aRe Then fREe to optIMiZE, BUt tHEy must return tHe same resulT DowN to the LaSt dECimal, iN all cAsES. So Their freedoM to oPtimize is Not comPLete, in fACt it is sEverelY coNstRainED.
YOuR alGoRIthM PrObaBLy iS off by a dIgIt Or two Part OF THE timE. WhIch cOuld bE completely neGliGiblE For Some uSers, bUt coUlD also Cause nAsty bUgS for some others, sO it's Not alloweD by DeFauLt. 
if you CAre morE foR spEed than StandarD ComPlIANCe, Try poking around witH tHE OpTions of yOur comPIlEr. fOr instanCe In GcC thE FIrst I'D try IS -fUnsafe-maTh-optiMIzAtIons, whiCh Should EnAblE opTimizATionS disreGarding sTrict STandard compliaNCe. Once you tweaK It ENOuGH, you ShoUld come closEr to ANd poSsibLY pAss YOur haNdmadE iMPlEMentation's speed. 

 Q:

LayOuTAnchoRable title font

For tHe XAML beloW i'M Using AvaLonDOCk 2.0.2.  i'M wanting to set tHe fonT of the TitlE Property Of the layoutAnChorable
<xCAD:DockingmanAgeR NaMe="TABitEmDockingManaGER" 
                    AllOwmixedOrIenTation="TRue"
                    borDerbruSh="black"
                    BordErThicknEsS="0" HEiGhT="AuTo" WidTH="Auto" HorIzOntAlaliGnmenT="stretcH" VertIcalalIgNMenT="StretcH"
                    anCHOrabLeSSOurcE="{BiNdIng AnChorABleS, Mode=TwOWay, UpdatESoURceTRiGgEr=PropeRtyChanged}"
Thread(s) per core:    2
C ore(s) per  sock et:    2 
Soc ket( s):           1
N UMA node(s):         1
Ven do r  ID:           Au t he n t icA MD 
C PUfa m il y:          2 1
Model:              48 Mo del name:          AMDA8- 7600 R ad eon R7, 1 0 C omput e Core s  4C+6G 
Stepping :          1C P UMHz:                31 0 0. 0 00
CPU max MHz :      3 100 ,00 00
CPU min  M Hz:       14 0 0 , 000 0 
BogoMIPS:            6 188 .43
Vi rt ual i zation :     AM D-V
L1d cac he:           16K L1i cac h e:           9 6KL2 c a ch e:         2 0 48K 
NUMA no de 0CPU(s ): 0 -3
A:
Flo ating  point arithm eti c ha s  to  take  into  con si derat ion ro undin g.  Most C/C++ com pile rs adoptIEE E754 ,so th e y have  an  "i deal" a lgorith m  to  p e r f or m operations suchas s qu are root . They ar et hen free  t o o ptim i z e, bu t th e ymust ret urn th e  s am e resul tdown t othe  la st de c imal , in a ll cases . Sot heir freedom t o  optimize isn ot c om p lete , i n fact it i s se v erel y co n st rai n ed.
Y our a lg o ri t hm probably is offby  a dig it or  two part ofthe time.W h i ch could  bec om p letely negligi ble f or some us e rs, butcould  also ca use nasty b ugs forsom e o the rs, s oit's not allo w e d by  d efault.  
I f you c are  mo refor  s peed than  standar dco mp li anc e, tr y  pokingar oun dwit h the option s ofyour  c om p ile r. Fori ns t a ncein  G CC t hefi rst I 'd t r y i s -funs afe-math- opt i miza ti on s, whic h should enab le  optimizat io nsdisreg a r ding str ict standard compliance .  Once y outweak  itenough, y oushould  co m e clos er toand p os sib l y  pass y ou r h an dmade impl e m ent ation 's  spe ed. 

Q:

LayoutAnchorab l e T itle font

Fo r t he X A M Lbel o wI 'mus i ngA v alonDock 2.0.2.   I'm want in g  t o set thef ont  o f the T itle pr opert y  of the  LayoutAn chorable<x cad: D o cki ngManagerName="Ta bItemDock i ngMan a ge r" 
              AllowM i xed Orien tation =" True"                 BorderBrush="Black "
                 B ord e rTh ickness=" 0" H eight="Aut o"Wid th="A uto "  Hori zont a lA lig n ment= "Str e tch" Vert i ca lAl i g nm ent="Stretc h "                An chorablesSource=" { Binding Anchor able s ,  Mo de= T woWa y,  UpdateSourceT rig ge r = Property Ch anged}"
Thread(s) per_core: _  2
Core(s) per_socket: __ 2
Socket(s):__  _  _   _ 1
NUMA node(s):__        1
Vendor ID:    __ ___   AuthenticAMD
CPU family:_    _ _    21
Model:   __  _        _48
Model name:    _  ___  AMD A8-7600_Radeon R7, 10 Compute Cores 4C+6G
Stepping:_     _      _1
CPU MHz:    _    _ _   3100.000
CPU max_MHz:  _ _  _   3100,0000
CPU min MHz:_  _     __1400,0000
BogoMIPS:  ___ _  __ __6188.43
Virtualization:     __ AMD-V
L1d cache:    _   __   16K
L1i_cache:    _     _ _96K
L2 cache:_          _  2048K
NUMA node0 CPU(s): _   0-3

A:

Floating_point arithmetic_has_to take into_consideration_rounding. Most_C/C++ compilers adopt IEEE 754, so they_have an_"ideal" algorithm to perform operations such_as square root. They_are_then free to optimize, but they_must return the same result down_to the last decimal, in_all_cases._So their freedom to optimize_is not complete, in fact it_is severely constrained.
Your_algorithm probably is off by a digit_or_two part of the time. Which_could_be completely negligible for some users,_but_could_also cause nasty bugs for_some others, so it's not allowed_by default. 
If you care more for speed than_standard compliance, try_poking around with the options_of_your_compiler. For instance in GCC the first I'd try is_-funsafe-math-optimizations, which_should enable optimizations_disregarding strict standard compliance. Once you tweak it enough, you_should come closer to and possibly pass_your handmade implementation's speed. 

 Q:

LayoutAnchorable Title font

For the XAML below_I'm using AvalonDock 2.0.2.  I'm wanting to_set the font of the Title property_of the LayoutAnchorable
<xcad:DockingManager Name="TabItemDockingManager"_
_      ____  _  _  _AllowMixedOrientation="True"
 _  _ _  __         BorderBrush="Black"
        _     _    _BorderThickness="0"_Height="Auto" Width="Auto" HorizontalAlignment="Stretch"_VerticalAlignment="Stretch"
   _       _        AnchorablesSource="{Binding_Anchorables,_Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"