Memory Management for Self-Adjusting Computation Matthew Hammer - PowerPoint PPT Presentation

Memory Management for Self-Adjusting Computation Matthew Hammer Umut Acar Toyota Technological Institute at Chicago International Symposium on Memory Management, 2008

Overview of Talk • Previous frameworks written in SML • We implement a framework for C In this talk, we • Briefly review self-adjusting computation • Discuss memory management issues • Introduce and evaluate our approach • Compare to previous SML framework Matthew Hammer Memory Management for Self-Adjusting Computation 2 / 42

Self-Adjusting Computation Motivation : Incremental change is pervasive. Many applications encounter data that changes slowly or incrementally over time. • Applications that interact with a physical environment. E.g., Robots. • Applications that interact with a user. E.g., Games, Editors, Compilers, etc. • Application that rely on modeling or simulation. E.g., Scientific Computing, Computational Biology, Motion Simulation. Matthew Hammer Memory Management for Self-Adjusting Computation 3 / 42

Self-Adjusting Computation Ordinary Program Runs Input 1 Program Output 1 • Ordinary programs often run repeatedly on Input 2 Program Output 2 changing input. • What if input and output change by only small increments? Input N Program Output N Matthew Hammer Memory Management for Self-Adjusting Computation 4 / 42

Self-Adjusting Computation Ordinary Program Runs Input 1 Program Output 1 small small change • Ordinary programs often change run repeatedly on Input 2 Program Output 2 changing input. • What if input and output change by only small increments? Input N Program Output N Matthew Hammer Memory Management for Self-Adjusting Computation 4 / 42

Self-Adjusting Computation Ordinary Program Runs Self-Adjusting Program Runs Self-Adj. Input 1 Program Output 1 Input 1 Output 1 Program small small small small Trace 1 change change change change Self-Adj. Input 2 Program Output 2 Input 2 Output 2 Program Trace 2 Trace N-1 Self-Adj. Input N Program Output N Input N Output N Program Matthew Hammer Memory Management for Self-Adjusting Computation 4 / 42

Self-Adjusting Computation Self-Adjusting Program Runs • Record execution in a Self-Adj. Input 1 Output 1 Program program trace small small • When input changes, a Trace 1 change change change propagation Self-Adj. algorithm updates the Input 2 Output 2 Program output and trace as if the program was run Trace 2 “from-scratch”. • Tries to reuse past computation when Trace N-1 possible Self-Adj. Input N Output N Program Matthew Hammer Memory Management for Self-Adjusting Computation 4 / 42

Self-Adjusting Computation Previous work has shown effectiveness for many applications: O ( 1 ) List primitives (map, reverse, . . . ) Sorting: mergesort, quicksort O ( log n ) 2D Convex hulls O ( log n ) [ESA ’06] Tree contraction [Miller, Reif ’85] O ( log n ) [SODA ’04]. 3D Convex Hulls O ( log n ) [SCG ’07] Meshing in 2D and 3D O ( log n ) [FWCG ’07] Bayesian Inference on Trees O ( log n ) [NIPS ’07] O ( s d log n ) Bayesian Inference on Graphs [UAI ’08] All bounds are randomized (expected time) and are within an expected constant factor of optimal or best known-bounds. Matthew Hammer Memory Management for Self-Adjusting Computation 5 / 42

Writing Self-Adjusting Programs Program Transformation Trace In Self-Adj. Input Program Output Input Output Program Trace Out Ordinary programs may be transformed into self-adjusting ones • Special operations added to create/update program trace • Done either by hand, or via compiler support Previous work focused on supporting SML programs Matthew Hammer Memory Management for Self-Adjusting Computation 6 / 42

Motivation for this Work Want to write self-adjusting computations in C. Benefits • Performance (both time and space). • Large user base • Broad hardware support (e.g., robots) • Interoperability with other libraries/software Challenges • Memory management • Ensuring Safety & Correct-usage Matthew Hammer Memory Management for Self-Adjusting Computation 7 / 42

Motivation for this Work Want to write self-adjusting computations in C. Benefits • Performance (both time and space). • Large user base • Broad hardware support (e.g., robots) • Interoperability with other libraries/software Challenges • Memory management • Ensuring Safety & Correct-usage This talk will focus on memory management. Matthew Hammer Memory Management for Self-Adjusting Computation 7 / 42

Motivation for this Work Want to write self-adjusting computations in C. Some Memory Management Options • Leave it to the programmer? — breaks abstractions of framework • Use an existing collector? — previous work suggests performance problems Our Approach Couples memory management with the existing change propagation algorithm. • Memory allocation recorded in program trace • Dead objects are identified during change propagation • Dead objects are reclaimed automatically Matthew Hammer Memory Management for Self-Adjusting Computation 7 / 42

Motivation for this Work Want to write self-adjusting computations in C. Some Memory Management Options • Leave it to the programmer? — breaks abstractions of framework • Use an existing collector? — previous work suggests performance problems Our Approach Couples memory management with the existing change propagation algorithm. • Memory allocation recorded in program trace • Dead objects are identified during change propagation • Dead objects are reclaimed automatically Matthew Hammer Memory Management for Self-Adjusting Computation 7 / 42

Examples Matthew Hammer Memory Management for Self-Adjusting Computation 8 / 42

Self-Adjusting Primitives modref • A modifiable reference ( modref ) is a (input) memory cell that stores changeable f 3 data . read • The input, output and intermediate data call of the program is instrumented with g modrefs. • To access its contents, a modref is read write during a function invocation. • To set its contents, a modref is written 9 • The program trace stores the program’s modref (output) callgraph and modref dependencies. Matthew Hammer Memory Management for Self-Adjusting Computation 9 / 42

Example: Mapping a List Input List ? Let’s map a list in a self-adjusting way. • The input is stored in a modref • We have to read it to see a list cell • We are given an empty modref to write the output E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List ? Let’s map a list in a self-adjusting way. read • The input is stored in a modref • We have to read it to map see a list cell • We are given an empty modref to write the output E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List a ? Cons Case read read • Read input cell value • Map a �→ a’ map • Allocate output cell • Write output cell • Recurse on tails E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List a ? Cons Case read read • Read input cell value • Map a �→ a’ map • Allocate output cell • Write output cell • Recurse on tails E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List a ? Cons Case read read • Read input cell value • Map a �→ a’ map • Allocate output cell • Write output cell allocate • Recurse on tails a' E E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List a ? Cons Case read read • Read input cell value • Map a �→ a’ map • Allocate output cell • Write output cell allocate • Recurse on tails write a' E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input Input List List a ? Cons Case read read • Read input cell value • Map a �→ a’ map call map • Allocate output cell • Write output cell allocate • Recurse on tails write a' E Output Output Dest Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List ? Nil Case • Read nil input • Write nil output E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List ? read Nil Case • Read nil input map • Write nil output E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List nil nil read read value Nil Case • Read nil input map • Write nil output E Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42

Example: Mapping a List Input List nil nil read read value Nil Case • Read nil input map • Write nil output write nil Output Dest Matthew Hammer Memory Management for Self-Adjusting Computation 10 / 42