CS Component of the ASCI Center for Computational Modeling at ...

CS Component of the ASCI Center for Computational Modeling at ...

Global Address Space Programming in Titanium Kathy Yelick CS267 CS267 Lecture 8 Titanium 1 Titanium Goals Performance close to C/FORTRAN + MPI or better Safety as safe as Java, extended to parallel framework Expressiveness close to usability of threads add minimal set of features Compatibility, interoperability, etc. no gratuitous departures from Java standard

CS267 Lecture 8 Titanium 2 Titanium Take the best features of threads and MPI global address space like threads (ease programming) SPMD parallelism like MPI (for performance) local/global distinction, i.e., layout matters (for performance) Based on Java, a cleaner C++ classes, memory management Language is extensible through classes domain-specific language extensions current support for grid-based computations, including AMR Optimizing compiler communication and memory optimizations synchronization analysis cache and other uniprocessor optimizations

CS267 Lecture 8 Titanium 3 New Language Features Scalable parallelism SPMD model of execution with global address space Multidimensional arrays points and index sets as first-class values to simplify programs iterators for performance Checked Synchronization single-valued variables and globally executed methods Global Communication Library Immutable classes user-definable non-reference types for performance Operator overloading

by demand from our user community Semi-automated zone-based memory management as safe as a garbage-collected language better parallel performance and scalability CS267 Lecture 8 Titanium 4 Lecture Outline Linguistic support for uniprocessor performance Immutable classes Multidimensional Arrays foreach Parallelism Support

SPMD execution Global and local references Communication Barriers and single Synchronized (not yet implemented) Example: Sharks and Fish Java introduction interspersed Compiler status CS267 Lecture 8 Titanium 5 Java: A Cleaner C++ Java is an object-oriented language classes (no standalone functions) with methods inheritance between classes; multiple interface inheritance only Documentation on web at java.sun.com Syntax similar to C++ class Hello { public static void main (String [] argv) {

System.out.println(Hello, world!); } } Safe Strongly typed: checked at compile time, no unsafe casts Automatic memory management Titanium is (almost) strict superset CS267 Lecture 8 Titanium 6 Java Objects Primitive scalar types: boolean, double, int, etc. implementations will store these on the program stack access is fast -- comparable to other languages Objects: user-defined and from the standard library passed by pointer value (object sharing) into functions has level of indirection (pointer to) implicit simple model, but inefficient for small objects

2.6 r: 7.1 3 true CS267 Lecture 8 i: 4.3 Titanium 7 Java Object Example class Complex { private double real; private double imag; public Complex(double r, double i) { real = r; imag = i; } public Complex add(Complex c) { return new Complex(c.real + real, c.imag + imag); public double getReal {return real; } public double getImag {return imag;} } Complex c = new Complex(7.1, 4.3);

c = c.add(c); class VisComplex extends Complex { ... } CS267 Lecture 8 Titanium 8 Immutable Classes in Titanium For small objects, would sometimes prefer to avoid level of indirection pass by value (copying of entire object) especially when objects are immutable -- fields are unchangable extends the idea of primitive values (1, 4.2, etc.) to userdefined values Titanium introduces immutable classes all fields are final (implicitly) cannot inherit from (extend) or be inherited by other classes needs to have 0-argument constructor, e.g., Complex () immutable class Complex { ... } Complex c = new Complex(7.1, 4.3); CS267 Lecture 8

Titanium 9 Arrays, Points, Domains Fast, expressive arrays multidimensional lower bound, upper bound, stride concise indexing: A[p] instead of A(i, j, k) Points tuple of integers as primitive type Domains rectangular sets of points (bounds and stride) arbitrary sets of points Multidimensional iterators CS267 Lecture 8

Titanium 10 Arrays in Java Arrays in Java are objects Only 1D arrays are directly supported Array bounds are checked (as in Fortran) Multidimensional arrays as arrays-of-arrays are slow CS267 Lecture 8 Titanium 11 Multidimensional Arrays in Titanium New kind of multidimensional array added

Two arrays may overlap (unlike Java arrays) Indexed by Points (tuple of ints) Constructed over a set of Points, called Domains RectDomains are special case of domains Points, Domains and RectDomains are built-in immutable classes Support for adaptive meshes and other mesh/grid operations RectDomain<2> d = [0:n,0:n]; Point<2> p = [1, 2]; double [2d] a = new double [d]; a[0,0] = a[9,9]; CS267 Lecture 8 Titanium 12 Nave MatMul with Titanium Arrays public static void matMul(double [2d] a, double [2d] b,

double [2d] c) { int n = c.domain().max()[1]; // assumes square for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { for (int k = 0; k < n; k++) { c[i,j] += a[i,k] * b[k,j]; } } } } CS267 Lecture 8 Titanium 13 Unordered iteration As seen in matmul, we need to reorder iterations Compilers can (in principle) do this for matrix multiply, but hard in general Titanium adds unordered iteration on rectangular domains foreach (p within r) { }

p is a Point new point, scoped only within the foreach body r is a previously-declared RectDomain Foreach simplifies bounds checking as well note: current optimizer does not include bounds checks Additional operations on domains and arrays to subset and transform CS267 Lecture 8 Titanium 14 Better MatMul with Titanium Arrays public static void matMul(double [2d] a, double [2d] b, double [2d] c) { foreach (ij within c.domain()) { double [1d] aRowi = a.slice(1, ij[1]); double [1d] bColj = a.slice(2, ij[2]); foreach (k within aRowi.domain()) { c[ij] += aRowi[k] + bColj[k]; } }

} Note that code is still unblocked. CS267 Lecture 8 Titanium 15 Point, RectDomain, Arrays in General Points specified by a tuple of ints RectDomains given by: lower bound point upper bound point stride point Array given by RectDomain and element type Point<2> lb = [1, 1]; Point<2> ub = [10, 20]; RectDomain<2> R = [lb : ub : [2, 2]]; double [2d] A = new double[r]; ... foreach (p in A.domain()) {

A[p] = B[2 * p + [1, 1]]; } CS267 Lecture 8 Titanium 16 Example: Domain Domains in general are not rectangular Built using set operations union, + intersection, * difference, - [0, 0]; [6, 4]; r = [lb : ub : [2, 2]]; (6, 4) (0, 0)

r + [1, 1] Example is red-black algorithm Point<2> lb = Point<2> ub = RectDomain<2> Domain<2> red foreach (p in ... } r (7, 5) (1, 1) = r + (r + [1, 1]); red) { red

(7, 5) (0, 0) CS267 Lecture 8 Titanium 17 Example using Domains and foreach Gauss-Seidel red-black computation in multigrid void gsrb() { boundary (phi); for (domain<2> d = res; d != null; d = (d == red ? black : null)) { foreach (q in d) unordered iteration res[q] = ((phi[n(q)] + phi[s(q)] + phi[e(q)] + phi[w(q)])*4 + (phi[ne(q) + phi[nw(q)] + phi[se(q)] + phi[sw(q)]) - 20.0*phi[q] - k*rhs[q]) * 0.05; foreach (q in d) phi[q] += res[q];

} } CS267 Lecture 8 Titanium 18 SPMD Execution Model Java programs can be run as Titanium, but the result will be that all processors do all the work E.g., parallel hello world class HelloWorld { public static void main (String [] argv) { System.out.println(Hello from proc Ti.thisProc()); } } Any non-trivial program will have communication and synchronization between processors CS267 Lecture 8 Titanium 19

SPMD Execution Model A common style is compute/communicate E.g., in each timestep within fish simulation with gravitation attraction read all fish and compute forces on mine Ti.barrier(); write to my fish using new forces Ti.barrier(); CS267 Lecture 8 Titanium 20 SPMD Model All processor start together and execute same code, but not in lock-step Sometimes they take different branches if (Ti.thisProc() == 0) { do setup } for(all data I own) { compute on data } Common source of bugs is barriers or other global

operations inside branches or loops barrier, broadcast, reduction, exchange A single method is one called by all procs public single static void allStep() A single variable has the same value on all procs int single timestep = 0; CS267 Lecture 8 Titanium 21 SPMD Execution Model Barriers and single in FishSimulation class FishSim { public static single void main (String [] argv) { int single allTimestep = 0; int single allEndTime = 100; for (; allTimestep < allEndTime; allTimestep++){ read all fish and compute forces on mine Ti.barrier(); write to my fish using new forces

Ti.barrier(); } } } Single on methods may be inferred by compiler CS267 Lecture 8 Titanium 22 Global Address Space Processes allocate locally References can be passed to other processes Class C { int val; } C gv; // global pointer C local lv; // local pointer if (thisProc() lv = new } gv = broadcast

gv.val = ; // = gv.val; // CS267 Lecture 8 == 0) { C(); lv from 0; full functionality Process 0 lv gv LOCAL HEAP Other processes lv gv

lv gv lv gv lv gv lv gv LOCAL HEAP Titanium 23 Use of Global / Local Default is global opposite of Split-C easier to port shared-memory programs harder to use sequential kernels

Use local declarations in critical sections same trade-off as Split-C (same implementation as Split-C) shared memory: no performance implications distributed memory: save overhead of a few instructions when using a global reference to access a local object CS267 Lecture 8 Titanium 24 Distributed Data Structures Build distributed data structures: broadcast or exchange

RectDomain <1> single allProcs = [0:Ti.numProcs-1]; RectDomain <1> myFishDomain = [0:myFishCount-1]; Fish [1d] single [1d] allFish = new Fish [allProcs][1d]; Fish [1d] myFish = new Fish [myFishDomain]; allFish.exchage(myFish); Now each processor has an array of global pointers, one to each processors chunk of fish CS267 Lecture 8 Titanium 25 Consistency Model Titanium adopts the Java memory consistency model Roughly: Access to shared variables that are not synchronized have undefined behavior. Use synchronization to control access to shared variables. barriers synchronized methods and blocks

CS267 Lecture 8 Titanium 26 Other Language Extensions Java extensions for expressiveness & performance Operator overloading Zone-based memory management The following are not yet implemented in the compiler Parameterized types (aka templates) watching for standard Foreign function interface CS267 Lecture 8 Titanium 27 Implementation Strategy

compile Titanium into C Solaris or Posix threads for SMPs Active Messages (Split-C library) for communication MPI (*) Status runs on SUN Enterprise 8-way SMP runs on Berkeley NOW T3E port may be available by end of semester (*) Clump port may be available by end of semester (*) tuning for performance (*)

(*) Indicates area for possible term projects CS267 Lecture 8 Titanium 28 Applications Three-D AMR Poisson Solver (AMR3D) block-structured grids 2000 line program algorithm not yet fully implemented in other languages tests performance and effectiveness of language features Other 2D Poisson Solvers (under development) infinite domains based on method of local corrections Three-D Electromagnetic Waves (EM3D)

unstructured grids Several smaller benchmarks CS267 Lecture 8 Titanium 29 Current Sequential Performance Taken on Ultrasparc Roughly 10x faster than JDK version of Java Compare codes written using Java arrays and Titanium arrays DAXPY 3D multigrid 2D multigrid EM3D C/C++/ Java Titanium Overhead FORTRAN Arrays Arrays

1.4s 6.8s 1.5s 7% 12s 26s 117% 5.4s 6.2s 15% 0.7s 1.8s 1.0s 42% More work to do here CS267 Lecture 8 Titanium 30 Parallel performance Speedup on Ultrasparc SMP

AMR largely limited by current algorithm problem size 2 levels, with top one serial Not yet optimized with local for distributed memory 8 7 6 5 em3d amr 4 3 2 1 0

CS267 Lecture 8 1 2 4 8 Titanium 31 How to use Titanium Documentation on http://www.cs.berkeley.edu/projects/titanium Includes: Reference manual (terse), tutorial (incomplete), compiler documentation; To run compiler: use path /disks/srs/titanium/sparc-sun-solaris2.6/bin/ use tcbuild Myprog.ti Myprog.ti is the titanium file containing class Myprog class Myprog has main method

creates executable Myprog tcbuild --backend smp-narrow for smp code tcbuild --backend split-c for NOW code tcbuild --help for more information Debugger also exist (sequential code only) CS267 Lecture 8 Titanium 32 Recommended Use If writing from scratch, may start by writing Java code (faster compiler, not faster code) Next use sequential Titanium may omit data layout and problem partitioning Next use smp Titanium need to partition work, but not data Finally, optimize for NOW Any code the runs on an SMP should run correctly (if slowly) without modifications on the NOW.

Only exceptions: your code contains race conditions our compiler contains bugs (please report) CS267 Lecture 8 Titanium 33 Caveats Performance on the NOW is still being optimized (report egregious problems to us) Garbage collection does not work on NOW -- need to use regions Static has MPI-like meaning, not threads one copy of a static per processor Bounds checking is not on by default CS267 Lecture 8 Titanium 34

Titanium Status Titanium language definition complete. Titanium compiler running. Compiles for uniprocessors, NOW; others soon. Application developments ongoing. Lots of research opportunities. CS267 Lecture 8 Titanium 35

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