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Last modified on 18 Apr 2019

Comp 520

Course Website

Acronyms

   
AOT Ahead Of Time compilation
AST Abstract Syntax Tree
CST Concrete Syntax Tree
GC Garbage Collection
IL Intermediate Language
IR Intermediate Representation
JIT Just In Time compilation
JVM Java Virtual Machine
LALR Look Ahead Left-to-right Right derivation
LL Left-to-right Left derivation
LR Left-to-right Right derivation
LSP Local Stack Pointer
PC Program Counter
SP Stack Pointer
VM Virtual Machine

Intro

  • A compiler transforms source files (eg in Java, C) into target code (eg x86)
  • A scanner transforms source file characters into more meaningful tokens
    • Keyword - eg if
    • Variable identifiers - eg var0
    • Syntax/structural elements - eg {
    • Note that keywords take precedence over any other rules
    • Whitespace is typically ignored
  • Language (Comp 330 Review)
    • Σ - alphabet, set of symbols, typically finite
    • Word - finite sequence of symbols from alphabet
    • Σ* - set of all possible words in Σ
    • Language - subset of Σ*
  • Regular languages - languages that can be accepted by a DFA, and for which regular expressions exist
  • At its core, a regular expression contains
    • ∅ - language with no strings
    • ε - empty string
    • α for α ∈ Σ
    • - alternation
    • · - concatenation
    • * - zero or more occurrences

Scanners

  • Scanners
    • First phase of compiler
    • List of regular expressions; one per token type
    • Internally, transforms regular expressions to DFAs
  • Algorithm is to match all DFAs against input
    • Find the longest match
      • If not empty, remove input and return a matching token
      • Otherwise, return input as output
    • If max length is the same for multiple DFAs, first one is typically used
  • Rules can use look-aheads to increase match length, even though token length remains unchanged
    • Eg FORTRAN 363.EQ.363; avoids mattching 363. as float
  • Context-sensitive grammars
    • Eg in C, (a) * b is either a type cast or a multiplication if a is a type or variable respectively
    • Solution is to either feed semantic language to the scanner, or run multiple passes
  • Scanners should have a . rule at the end to match any unexpected character if no other rules match
  • Line numbers in flex
    • Manually counting by matching against \n
    • Use %option yylineno to get the updated variable
  • Scanner actions
    • Do nothing
    • Perform arbitrary computation
    • Return a token
  • Scanner efficiency
    • Reduce number of regular expressions; note that keywords are already valid identifiers
  • Scanner error handler
    • Eg if positive ints cannot start with 0
    • Parser error - check for two consecutive int tokens and fail on match
    • Lexical error - create a new rule capturing all integers (allowing 0 prefix), and throw if rule matches
  • Parsers
    • Second phase of compiler
    • Aka syntactic analysis
    • Takes tokens from scanner and generates a parse tree using CFG
    • Pushdown automata - FSM + unbounded stack
      • Used ot recognize CFG
    • CFG - Context-free grammar
      • V - set of variables
      • Σ - set of terminals where V ∩ Σ = ∅
      • R - set of rules, where LHS ∈ V & RHS ∈ V ∪ Σ
      • S - start variable where S ∈ V
      • While DFAs and NFAs are equally powerful, DPDAs do not recognize all CFGs
      • BNF - backus-naur form
      • EBNF

Parsing

  • Parse tree - aka concrete syntax tree
    • Built exactly from CFG rules
    • Parent nodes form LHS of readwrite rule
    • Child nodes form RHS of readwrite rules
    • Leaves form parsed input sentence
  • Ambiguous grammar
    • Multiple parse tree results
    • Precedence - order of operations
    • Associativity - grouping of operations with same precedence
    • Rewriting grammar
      • Operands must not expand to other operations of lower precedence
      • If left associative, only LHS may expand; if right associative, only RHS may expand
    • Dangling else problem - ambiguous if statements without terminating token; solution in C is to match each else with the closest unmatched if
    • Look Ahead Left-to-right Rightmost derivation parser (LALR)
      • Bottom up
      • Eg yacc + bison (LALR(1)), SableCC
    • Left-to-right Leftmost-derivation parser (LL)
      • Top down
      • For LL(k), look k tokens ahead and determine when to reduce
      • Note that not all grammars are LL(k) for any fixed k
      • Some rules require unbounded lookahead
      • Recursive Descent Parsers
        • Repeatedly expand left non-terminal
          • If one occurrence, use rule
          • If multiple, there’s a conflict
          • If none, there’s an error
        • Problematic when rules have same prefixes of length greater than the lookahead count
          • Resolved by factoring the grammar
          • Eg if then end, if then else end becomes if then ifend, where ifendend | else end
        • Left recursion also a problem. A → A β ε expands to ε A A β A β β …

Shift-Reduce Bottom-Up Parsing

  • Two token collections, one for input stream and one for stack representation
  • Shift - place token from stream to stack; more symbols are needed before applying rule
  • Reduce - replace multiple symbols on stack with single symbol according to grammar
  • Accept - when start symbol (S') is on the stack
  • Using a table, effectively like LR parsing but in reverse
  • Deciding between shift and reduce
    • Implemented as stack of states; represents top content without caring about sub contents

Abstract Syntax Tree

  • Parsing conflicts
  • Resolving conflicts
    • For operations with same precedence & left associativity, prefer reducing
    • When reduction contains operation of lower precedence than lookahead token, prefer shifting
  • Compiler architecture
    • One-pass compiler - scans only once
      • Prevents modularity and limits optimization
      • Historically good as it’s fast and space efficient
    • Multi-pass compiler - 5-15 phases
      • Requires intermediate representation (IR) of program
  • Abstract syntax tree (AST)
    • Only important terminals kept
    • Tree is not language dependent
  • Building IRs
    • Extend parser & execute semantic actions
    • Semantic actions - arbitrary actions executed during parser execution
    • Semantic values
      • Terminals - provided by scanner
      • Non-terminal - created by parser
  • Building IRs
    • Extends parser
    • Executes semantic actions during process
    • Values are terminal (provided by scanner) or non-terminal (created by parser)
  • LALR(1)
    • Left recursion, for efficiency

JOOS

  • Subset of Java
  • Types - boolean, int, char, external (Object, Boolean, Integer, String, etc)
  • Expressions - evaluate to a value
    • Constants, variables, binary op, unary op, class creation, expression cast, method invocation
  • Statements - no associated values
    • Expression statements, blocks, control (if, while), return

Weeding

  • If we wish to create certain constraints (ie avoid division by 0), updating the parser will double the code
  • Instead, we can weed out exceptions by parsing invalid code and running pass-throughs afterwards
  • Can also be used in more complicated cases, like distinguishing casting or parentheses around expressions.

Symbol Table

  • Semantic analysis - analyzes meaning of program
    • Symbol table - analyzes variable definitions & uses
      • Maps identifier to meanings
  • Used in JOOS for
    • Class hierarchy - what classes, inheritance
    • Class members - what fields, what methods, signatures
    • Identifier - when defined, when used
    • Type checking - analyzes expression types & uses
  • Previously, var declarations were done in one pass. In this case, we wouldn’t be able to use elements in the global scope until they were defined
  • Identifiers in the same scope can be unique, but can shadow parent scopes
  • Dynamic scoping - uses program state to resolve symbols
  • Mutual recursion
    • Requires two traversals, one to collect definitions and another to collect uses

Type Checking

  • Type annotations are invariant about the run-time behaviour
  • Rules
    • Declaration - introduce variables
    • Propagation - expression type determines enclosing expression type
    • Restrictions - expression type constrained by usage context
    • Logical rules
      • (Γ ⊢ P) / ( Γ ⊢ C) - if P is provable under context Γ, then C is provable under context Γ
      • Γ ⊢ E : T - under context Γ, it is provable that E is well typed with type T
      • (Γ [x ↦ T] ⊢ S) / (Γ ⊢ x; S) - modify context
        • x maps to T within context Γ, and S typechecks with x added to the symbol table
      • (Γ(x) = T) / (Γ ⊢ x : T) - access context
      • x := T - x is assignable to a value oof type T
      • a ∨ b - or conditions
    • L - class library
    • C - current class
    • M - current method
    • V - variables
  • Type proof
    • Internal nodes are inferences
    • Leaves are axioms or true predicates
    • Program is statically type correct iff it is root of some type proof

Virtual Machines

  • Ahead of time compilation (AOT) - source code to machine code before execution
    • Advantages
      • Fast execution
      • Allows optimization
      • Intermediate languages facilitate code generation for target architectures
    • Disadvantages
      • Runtime information ignored
      • Code generator must be built
    • Virtual machines
      • Not tied to any architecture
      • Delays generating native code until execution time
  • Interpreted - instructions read one at a time; not compiled
    • Advantages
      • Easy to generate virtual machine code
      • Code is architecture independent
      • Bytecode can be more compact
    • Disadvantages
      • Poor performance
  • Just in time (JIT) - generate native code during program execution
    • Advantages
      • Target specific architectural details
      • Observe program properties at runtime
      • Efficiently allocate optimization time towards important methods
    • Disadvantages
      • Program performance depends on compile time
  • Abstract machine - intermediate language

Java Virtual Machine

  • .class files
    • Magic number (0xCAFEBABE)
    • Minor version/major version
    • Constant pool
    • Access flags
    • This class
    • Super class
    • Interfaces
    • Fields
    • Methods
    • Attributes
  • Java class loaders
    • Extend java.lang.ClassLoader
    • Allow for loading classes from other sources & transforming classes during loading
  • Consists of
    • Memory
      • Stack (function call frames)
        • Call stack (function call frames)
          • Reference to constant pool
          • Reference to current object (this) if any
          • Method arguments
          • Local variables
          • Local stack for intermediate results (baby stack)
        • Baby/operand/local stack - operands & results from instructions
      • Heap (dynamically allocated memory)
      • Constant pool (shared constant data)
      • Code segment (JVM instructions of currently loaded class files)
    • Registers
      • No general purpose registers
      • Stack pointer (sp) pointing to top of stack
      • Local stack pointer (lsp) points to location in current stack frame
      • Program counter (pc) points to current instruction
    • Condition codes
    • Execution unit
  • Data Types
    • Primitives - boolean, integral (byte, short, int, …), floating, internal
    • Reference - class, array, interface
  • Jasmin Code
    • Z - boolean
    • F - float
    • I - int
    • J - long
    • V - void
    • Reference types represented by fully qualified names
    • Methods
      • Signature - .method <modifiers> <name>(<parameter types>) <return type>
      • Stack limits .limit stack <limit>, .limit locals <limit>
      • Method body
      • Termination line .end method
  • JVM contains 256 instructions for arithmetic ops, constant loading, local operations, branch operations, stack operations, class operations, and method operations
    • Unary arithmetic ops
      • ineg - negate
      • i2c - to char, % 65536
    • Binary arithmetic ops
      • iadd
      • isub
      • irem
    • Direct ops
      • iinc k a - local[k] += a
    • Constant loading
      • iconst_0 - load 0
      • aconst_null -load null
      • ldc_int i - load int
    • Local ops
      • iload k - add local[k] to stack
      • istore k - pop stack and store to local[k]
      • aload, astore, counterparts for references
    • Field ops
      • getfield f sig, putfield f sig, modify fields of objects using value from stack.
    • Branch ops
      • goto L
      • ifeq L, ifgt L, ifnonnull L - reads first stack value
      • if_icmpeq_L - compares top two elements
    • Stack ops
      • dup - repeat stack value
      • pop
      • swap
      • nop - does nothing
    • Class ops
      • new C - allocate space
      • invokespecial C/<init>()V - execute constructor
      • instance_of C - puts 0 or 1 on stack
      • checkcast
    • Method ops
      • invokevirtual m sig - calls method taking in o (self) plus all args
      • ireturn, return
  • Java Class Loading
    • ClassLoader finds class and checks that method exists
    • If method not loaded, it is verified
    • Method body is interpreted
    • If executed multiple times, bytecode is translated to native code
    • If method becomes hot, native code is optimized
  • Bytecode verification syntax
    • First 4 bytes should be 0xCAFEBABE
    • Bytecodes should be syntactically correct
      • All instructions complete
      • Branch targets within code segment
      • Only legal offsets referenced
      • Constants have appropriate types
      • Execution must return
    • Stack (Important)
      • Should be same size along all execution paths
      • Should have the same types along
  • Resource offsets
    • For variables that can never exist together (same scope level), we can reuse offsets and lower our limit
    • Extra slot required for non-static method
  • Labels
    • if - 1 label
    • ifelse - 2 labels
    • while - 2 labels
    • || and && - 1 label (short circuit)
    • == ,<, >, <=, >=, and != - 2 labels (like ifelse branching, as we are not saving a value in the stack)
    • !: - 2 labels
    • toString coercion - 2 labels

{Bite}Code Generation

  • Code templates allow code generation from AST, without worrying about surrounding context
    • Simple, recursive strategy
Template Jasmin
if (E) S E
ifeq stop
S
stop:
if (E) S_1 else S_2 E
ifeq else
S_1
goto stop
else:
S_2
stop:

Optimization

  • Focus on
    • Reducing execution time
    • Reducing code size
    • Reducing power consumption
  • Duff’s Device - For loop unrolling for any count
    register count;
    {
        register n = (count + 7) / 8;
        switch (count % 8) {
          case 0: do { *to = *from++;
          case 7:      *to = *from++;
          case 6:      *to = *from++;
          case 5:      *to = *from++;
          case 4:      *to = *from++;
          case 3:      *to = *from++;
          case 2:      *to = *from++;
          case 1:      *to = *from++;
          } while (--n > 0);
        }
    }
    
  • Peephole optimization focuses on a small window at a time, without program context
    • We can look at the instruction at the current and following positions
    • We can check if a label is alive
    • We can modify the current instruction, or delete a label
  • When writing peephole patterns, ensure that it is sound
    • Local variables have same values
    • Stack height changes by same amount
    • All paths yield same outcome

Midterm Review

  • Compiler phases
    • Scan - chars to tokens
    • Parse - tokens to syntax tree
    • Weed - rejects invalid trees (syntax)
    • Symbol - tracks context
    • Type - AST to AST + types; rejects programs that are semantically correct but syntactically wrong
    • Resource
    • Code
    • Optimize
    • Emit
  • Type checking definitions
    • a / b - if a then b
    • a ⊢ b - if under the assumptions of a, then b is provable
    • a : b - a has type b

Garbage Collection

  • Memory allocation
    • In stack
      • Function call info, local variables, return values
      • Allocated & deallocated at beginning & end of function
      • Contains fixed size data
      • Contains constant pool, local vars, baby stack
      • Memory allocation is easy
    • In heap
      • Dynamic - unknown size & time
      • Requires runtime support for managing heap space
    • Data never point from stack to heap
    • Heap deallocation
      • Manual - user code
        • Advantages
          • Reduces runtime complexity
          • Programmer has full control
          • May be more efficient
        • Disadvantages
          • Requires extensive effort
          • Error prone
          • Often less efficient
            • Can free larger blocks at once
      • Continuous - determined on the spot
      • Periodic - interval checks
  • When are records dead?
    • Ideally, when they are never accessed again, but this is undecidable
    • Conservative assumption - if they are no longer used within stacks; dead records may still be referenced from other dead records

Reference Counting

  • Continuous GC
  • Extra field to track pointers
  • Increment on creation, decrement on destruction
  • Dead when reference count is 0
  • Disadvantage
    • Cyclic references don’t get GC’d
    • Incremental; continuous slow down
  • Automatic Reference Counting (ARC)
    • For objective-C & Swift
    • retain and release inserted at compile time
    • Unnecessary updates are optimized

Mark & Sweep

  • Periodic GC
  • Mark - starting from root (eg stack), if not marked, mark and apply dfs
  • Sweep - go through all records and reclaim unmarked once
    • Unmark all marked records as we go
  • Assumes that
    • We know the size of each record
    • We know which fields are pointers
  • Can run in parallel
  • Disadvantage
    • Scanning can be expensive
    • Heap may become fragmented
      • Can be resolved using compaction, where we collect all live objects and reorganize them to be contiguous

Stop & Copy

  • Periodic GC
  • Divides heap into two, only uses one at a time
  • Runs fully copy of live record to other allocation, then switches roles of two parts
  • Copy is done using BFS, and invokes Forward to ensure that all reference go to the to-space (before the switch)
  • Avoids fragmentation
  • Avoids stack & pointer reversal
  • Disadvantage
    • Wastes half the memory

Further Optimization

  • Generational Collection
    • The young die quickly; those that remain live for a long time will likely continue to remain live
    • Divide heap into generations, and check GC more frequently for younger generations; promote if record survives several collections
  • Incremental collection
    • Interweave GC with program execution, to reduce undesirable pauses
  • Two-player access
    • Use mutator and collector

Virtual Machines (VirtualRISC)

  • Register-based IR
    • Stack - for function call frames
    • Heap - for dynamically allocated memory
    • Global pool - for global variables
    • Code segment - for VirtualRISC instructions
  • Registers
    • Ri - unbounded general purpose registers
    • sp - stack pointer to top of stack
    • fp - frame pointer to current stack frame
    • pc - program counter to current instruction
      • Automatically incremented per instruction execution
      • May also be changed by function calls & branches
  • Instructions
    • Movement
      • [..] indicates memory location store in register
      • Store - st <src>, <dst>
        • st Ri, [Rj]; [Rj] := Ri
      • Load - ld <src>, <dst>
        • ld [Ri + C], Rj; Rj := [Ri + C]
      • Move - mov <src>, <dst>
        • mov Ri, Rj; Rj := Ri
    • Math Ops
      • op <src1>, <src2>, <dst>
      • add Ri, Rj, Rk; Rk := Ri + Rj; (sub, mul, div)
    • Branching
      • b L; (bg, bge, bl, ble, bne)
      • if R1 <= 0 goto L1cmp R1, 0; ble L1
    • Special
      • call L; R15 := pc; pc := L
      • save sp, -C, sp; save registers, allocating C bytes on stack
      • restore; restore registers
      • ret; pc := R15 + 8
      • nop; do nothing
  • Stack Frame
    • Created by function call; push fp; fp := sp; sp := sp + C
    • Popped by function return sp := fp; fp = pop
    • Local variables stored relative to fp
  • Calling
    • Function starts by save sp, -C, sp, where C is arbitrarily large (eg 112; multiple of 4)
    • Function ends by restore, then ret, where the value is R0
    • Parameters
      • Passed in registers R0, R1, etc
      • If in memory, convention is fp = 68 + 4k, where k is a non-negative integer; this is stored in the callers frame
    • Local variables
      • Use any general purpose register
      • May use memory; convention is fp = 4k, where k is a non-negative integer (in class, starts at [fp = 12])

Native Code Generation

  • JOOS Code executes through
    • Interpreter
    • Ahead-of-time compiler
      • Translate directly to native code
      • Not as useful for Java/JOOS
        • Method code fetched as needed
        • Needs to allow code across internet
        • Should support different native code sets
    • Just-in-time compiler
      • Merge interpreters with traditional compilation techniques
      • When method is invoked for the first time
        • Bytecode fetched
        • Translated into native code
        • Control given to generated code
      • Needs to be fast to be useful
  • Important problems
    • Instruction selection - choose correct instructions from native code instruction set
    • Memory modelling - decide where to store variables & allocate registers
    • Method calling - determine calling conventions
    • Branch handling - allocate branch targets
  • Map locals/stacks to frame
    • Stack memory can be arbitrarily large, but is limited by hardware ulimit -a
    • Registers are very limited, usually much less than number of program variables
    • Want to allocate as many variables in register as possible
    • Liveness analysis
      • Variable is live if it can be read in the future
      • Undecidable, but can be approximated

Naïve Allocation

  • No assumptions between instructions; each must load respective contents to proper register
    • Eg: loading and adding requires loading to registers, storing to stack, then loading from stack (to registers) and adding; optimal is to use registers directly

Fixed Register Allocation

  • m registers to first m locals
  • n registers to first n stack locations
  • k scratch registers
  • Spill remaining locals & locations into memory
  • Registers allocated once, and does not change
  • No difficult control flow paths
  • Wastes registers, and assumes first locals/stack locations are more important

Basic Block Register Allocation

  • Registers allocated on demand
  • Slots kept in registers within basic block
  • Registers not wasted
  • Less spill code
  • Much more complex
  • Spill occurs at end of basic block

Branching

  • When branching forward in native code, target address is not yet known
  • Unresolved branches are kept in a table, then patched when the code is generated

Web Assembly

  • ASM - LLVM to JS static compiler (2011)
  • Load store consistently - ensuring that stored value and loaded value are of the same size
    • For instance, setting an int and loading as a char breaks the consistency
    • ASM assumes the program respects it, and does not make verification; can therefore store single int in one value of the stack
  • Still no parallelism, and no garbage collection
  • To support more features, JS must also grow

  • WebAssembly aims to bridge the gap in performance
    • Supports integers & float types natively
    • Increased loading speed via binary decoding
    • Parallelism via SIMD
    • Garbage collector for main memory
    • Code validation
    • Hardware-independent
  • Pipeline - decode → validate → instantiate & invoke
  • Decoding/encoding
    • Bytes as is
    • Type map; eg 0x7Fi32
  • Validation
    • Decoded values must be within limit (no overflow)

GPU

  • Optimized for throughput
    • Slow cores
    • Larger number of hardware threads
  • SIMT - Single Instruction, Multiple Thread
    • Program specifies behaviour of single thread
  • SIMD - Single Instruction, Multiple Data
    • Program specifies behaviour of all threads in width
  • Thread groups
    • Collection of threads
    • May work together
    • Can be synchronized and share data
  • Thread hierarchy
    • Thread identifier - unique per thread
    • Group identifier - unique per thread group
  • Memory hierarchy
    • Each thread has private memory
    • Each thread group has shared memory
      • Requires synchronization
      • Cannot be accessed by other groups
  • Coalescing - based on transaction size, we can minimize the number of accesses by retrieving a larger contiguous block of values

Final Exam

  • Scanner & Parser
    • How to implement scanner in flex or SableCC
    • DFA’s/NFA’s, CFGs
    • Parser ambiguity
    • No precedence directives
    • Scanner tokens
      • Keywords
      • Syntax elements
      • Literals
      • Identifier
      • Comments
      • Errors (.)
    • Parsing
      • Lists (empty, nonempty)
      • Recursion
      • Expressions
  • Typechecking
    • Can specify multiple rules
  • Bytecode Generation
    • Review both midterm and final
    • Jasmin syntax
      • dup, swap, putfield Class