}; class B2 { public: virtual void f2(); virtual void f3(int); virtual void f4(); }; 60 vptr other stuff… &B1::f1 &B1::f2 vtbl for B1 B1 object vptr other stuff… &B2::f2 &B2::f3 vtbl vtbl for B2 B2 object &B2::f4 Copyright © 2020 by Stephen C. Dewhurst and Daniel Saks Derived Class Layout Under Multiple Inheritance  Under multiple inheritance, an object may have more than one vptr vptr. class D: public B1, public B2 { public: void f2() override; // overrides B1::f2 and B2::f2 void f3(int) override; // overrides B2::f3 virtual void f5(); }; 61 other stuff… &B1::f1 &D::f2 vtbl

partitioningMemory 29 B0 B1 B2 • One row open per bank • Logical partitioningMemory 30 B0 B1 B2 B3 • One row open per bank • Logical partitioningMemory 31 B0 B1 B2 B3 BG0 • Bank group – a grouping B1 B2 B3 BG0 B0 B1 B2 B3 BG1 • Bank group – a grouping of logically addressable banks • Multiple open rows per bank group • Multiple outstanding commands in progressMemory 33 B0 B1 B2 B3 B1 B2 B3 BG1 B0 B1 B2 B3 BG2 • Bank group – a grouping of logically addressable banks • Multiple open rows per bank group • Multiple outstanding commands in progressMemory 34 B0 B1 B2 B3

+ $b; } function calc($a1, $b2) { //$a1: [ANY], $b2: [ANY] $T3 = $a1 * 2; //$T3: [LONG, DOUBLE] $a4 = $T3 % 1000; //$a4: [LONG] $T5 = $b2 * 3; //$T5: [LONG OPCODE HANDLER function calc($a1, $b2) { //$a1: [ANY], $b2: [ANY] $T3 = $a1 * 2; //$T3: [LONG, DOUBLE] $a4 = $T3 % 1000; //$a4: [LONG] $T5 = $b2 * 3; //$T5: [LONG, DOUBLE] AVOIDING function calc($a1, $b2) { //$a1: [ANY], $b2: [ANY] $T3 = $a1 * 2; //$T3: [LONG, DOUBLE] $a4 = $T3 % 1000; //$a4: [LONG] $T5 = $b2 * 3; //$T5: [LONG,

a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 a0 a1 b2 b3 a4 a5 b6 b7 a8 a9 a10 a11 b12 b13 b14 b15 mask a a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 b0 b1 b2 b3 <4> b aCopyright © 2020 Bob Steagall K E W B } a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 <3> a13 a14 a15 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b aCopyright © 2020 Bob Steagall

what is the size of the given struct Widget? struct Widget { bool b1; float f; bool b2; }; std::cout << sizeof(Widget) << '\n'; // prints 12Order of Member Data 35 Task, Step 1: Assuming what is the size of the given struct Widget? struct Widget { bool b1; float f; bool b2; }; std::cout << sizeof(Widget) << '\n'; // prints 12 // Needs to be 4-byte aligned on x64 char what is the size of the given struct Widget? struct Widget { bool b1; double d; bool b2; }; std::cout << sizeof(Widget) << '\n'; // prints 24Order of Member Data 37 Task, Step 2: Assuming

constants b1 b2 : bool -- declare two constants at once /- check their types -/ #check m -- output: nat #check n #check n + 0 -- nat #check m * (n + 0) -- nat #check b1 -- bool #check b1 && b2 -- "&&" "&&" is boolean and #check b1 || b2 -- boolean or #check tt -- boolean "true" -- Try some examples of your own. Any text between the /- and -/ constitutes a comment that is ignored by Lean. Similarly, + 5 Here are some more abstract examples: constants α β : Type constants a1 a2 : α constants b1 b2 : β constant f : α → α constant g : α → β constant h : α → β → α constant p : α → α → bool #check

... ... ... ... cs−1 as−1,1 as−1,2 as−1,3 . . . as−1,s−1 0 cs as,1 as,2 as,3 . . . as,s−1 as,s b1 b2 b3 . . . bs−1 bs ai,j: coefficients (A: Runge-Kutta matrix) bj: weights ci: nodes s: number of .. cs−1 as−1,1 as−1,2 as−1,3 . . . as−1,s−1 0 cs as,1 as,2 as,3 . . . as,s−1 as,s b1 b2 b3 . . . bs−1 bs ˜b1 ˜b2 ˜b3 . . . ˜bs−1 ˜bs ˜yn+1 = yn + h s � i=1 ˜biki en+1 = ˜yn+1 − yn+1 = h s � i=1 cs−1 as−1,1 as−1,2 as−1,3 . . . as−1,s−1 as−1,s cs as,1 as,2 as,3 . . . as,s−1 as,s b1 b2 b3 . . . bs−1 bs ˜b1 ˜b2 ˜b3 . . . ˜bs−1 ˜bs yn+1 = yn + h s � i=1 biki ki = f � tn + cih, yn + h s � j=1

параметра в значение 1 (без группировки) @startuml skinparam groupInheritance 1 A1 <|-- B1 A2 <|-- B2 A2 <|-- C2 A3 <|-- B3 A3 <|-- C3 A3 <|-- D3 A4 <|-- B4 A4 <|-- C4 A4 <|-- D4 A4 <|-- E4 @enduml значение 2 (группировка если 2 и более) @startuml skinparam groupInheritance 2 A1 <|-- B1 A2 <|-- B2 A2 <|-- C2 A3 <|-- B3 A3 <|-- C3 A3 <|-- D3 A4 <|-- B4 A4 <|-- C4 A4 <|-- D4 A4 <|-- E4 @enduml значение 3 (группировка если 3 и более) @startuml skinparam groupInheritance 3 A1 <|-- B1 A2 <|-- B2 A2 <|-- C2 A3 <|-- B3 A3 <|-- C3 A3 <|-- D3 A4 <|-- B4 A4 <|-- C4 A4 <|-- D4 A4 <|-- E4 @enduml