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![Connectivity: Operator objects
• Operator private members
– Operator’s edges are sub-vectors of g.vecIn, g.vecOut
– Start of EdgeIn objects: EdgeInIndex baseIn_;
– Start of EdgeOut objects: EdgeOutIndex baseOut_;
• Number of connections
– Inputs: vecOp[x+1].baseIn_ - vecOp[x].baseIn_
– Outputs: vecOp[x+1].baseOut_ - vecOp[x].baseOut_](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/85/MathWorks-Interview-Lecture-29-320.jpg)
![Connectivity: EdgeIn objects
• EdgeIn private members
– Sink Operator: OperatorIndex dstOp_;
– Source EdgeOut: EdgeOutIndex src_;
• EdgeIn connection position
– Use pointer arithmetic:
this - (vecIn + vecOp[dstOp_].baseIn_);](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/85/MathWorks-Interview-Lecture-30-320.jpg)
![Connectivity: EdgeOut objects
• EdgeOut private members
– Source Operator: OperatorIndex srcOp_;
– Sink EdgeIn: EdgeInXIndex dst_;
• EdgeOut connection position
– Use pointer arithmetic
this - (vecOut + vecOp[srcOp_].baseOut_);](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/85/MathWorks-Interview-Lecture-31-320.jpg)
![Thin graph construction
Method Effect
graph.add(BreadCrumb, Op, Locus, Expansion,
unsigned nVarIn =0, unsigned nVarOut =0);
Add an Operator and its
Edge resources
graph.connect(OperatorIndex srcOp, unsigned srcPos,
OperatorIndex dstOp, unsigned dstPos);
Guarantee a srcOp[srcPos] to
dstOp[dstPos] edge exists](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/85/MathWorks-Interview-Lecture-33-320.jpg)
![Graph overlay
• Template object publically derived from Graph
• Macro hides lots of template boilerplate
• User supplied types for parallel vectors
– MyOperator ovOp[OperatorIndex]
– MyEdgeIn ovIn[EdgeInIndex]
– MyEdgeOut ovOut[EdgeOutIndex]
• Constructor shares vectors and LiteralTable](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/85/MathWorks-Interview-Lecture-36-320.jpg)
![Connectivity: Operator objects
• Operator private members
– Operator’s edges are sub-vectors of g.vecIn, g.vecOut
– Start of EdgeIn objects: EdgeInIndex baseIn_;
– Start of EdgeOut objects: EdgeOutIndex baseOut_;
• Number of connections
– Inputs: vecOp[x+1].baseIn_ - vecOp[x].baseIn_
– Outputs: vecOp[x+1].baseOut_ - vecOp[x].baseOut_](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/75/MathWorks-Interview-Lecture-29-2048.jpg)
![Connectivity: EdgeIn objects
• EdgeIn private members
– Sink Operator: OperatorIndex dstOp_;
– Source EdgeOut: EdgeOutIndex src_;
• EdgeIn connection position
– Use pointer arithmetic:
this - (vecIn + vecOp[dstOp_].baseIn_);](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/75/MathWorks-Interview-Lecture-30-2048.jpg)
![Connectivity: EdgeOut objects
• EdgeOut private members
– Source Operator: OperatorIndex srcOp_;
– Sink EdgeIn: EdgeInXIndex dst_;
• EdgeOut connection position
– Use pointer arithmetic
this - (vecOut + vecOp[srcOp_].baseOut_);](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/75/MathWorks-Interview-Lecture-31-2048.jpg)
![Thin graph construction
Method Effect
graph.add(BreadCrumb, Op, Locus, Expansion,
unsigned nVarIn =0, unsigned nVarOut =0);
Add an Operator and its
Edge resources
graph.connect(OperatorIndex srcOp, unsigned srcPos,
OperatorIndex dstOp, unsigned dstPos);
Guarantee a srcOp[srcPos] to
dstOp[dstPos] edge exists](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/75/MathWorks-Interview-Lecture-33-2048.jpg)
![Graph overlay
• Template object publically derived from Graph
• Macro hides lots of template boilerplate
• User supplied types for parallel vectors
– MyOperator ovOp[OperatorIndex]
– MyEdgeIn ovIn[EdgeInIndex]
– MyEdgeOut ovOut[EdgeOutIndex]
• Constructor shares vectors and LiteralTable](https://image.slidesharecdn.com/c67eb25a-2046-4ebf-9d6f-749fa4c8e517-160502211949/75/MathWorks-Interview-Lecture-36-2048.jpg)
MathWorks Interview Lecture
- 1. Selling an executable dataflow graph based IR John Yates
- 2. Order of presentation •Who am I and why am I here? • 2010: Netezza needs a new architecture • A family of statically typed acyclic DFG IRs • (Time permitting: Some engineering details) • Q&A
- 3. “Who am Iand why am I here?” (with apologies to Adm. Stockdale)
- 4. 1970: Maybe I’llbe a programmer • NYC hippie, ponytail, curled handlebar mustache • Liberal arts high school, lousy student • Wanted to build things, real things • Computers seemed interesting and intuitive • Luckily in 1970 programmers were scarce
- 5. 40 years… – 1970:learning the craft, various jobs (all in assembler) – 1978: Digital Equipment Corp • Pascal frontend, dynamic programming code selector – 1983: Apollo Computer • Designed RISC ISP w/ explicit parallel dispatch (pre-VLIW) • Lead architect for RISC backend optimizer; built team • 1st commercial: SSA IR, SW pipeliner, lattice const prop – 1992: Binary translation: DEC (sw), Chromatic (hw-support) • More SSA IR, lowering; built teams; lot of patents (many hw) – 1999: Everfile - NFS-like Win32 internet file system – 2002: Netezza, badge #26 • Storage: compression, indices, access methods, txns, CBTs 20+years
- 6. 2010: Netezza needs anew architecture
- 7. Data parallel analyticsengine • Data partitioned across a cluster of nodes – Multiple “slices” per node to exploit multi-core • Execution model: – Leader accepts query, produces an execution plan – Leader broadcasts plan’s parallel components – Cluster performs data parallel work – Leader performs work requiring a single locus • Competition: Teradata, Green Plum, DB2, …
- 8.
- 9. Latency Netezza’s problems PG Plan Split1 Split2 Gen FPGA Gen C++ Gen C++ CompileCompile Load DLL Bcast Load DLL Load FPGA ExecuteExecute Very simplisticcode generator: -Lowering across an enormous semantic gulf - No intermediate representation - Very complex, very fragile - Difficult to implement much more than general case code patterns Hardware development time scales N workers
- 10. Garth’s incomplete Marlinvision • What is the real input to the interpreter? • How do we get from query plan to that form? PG Plan Split Bcast Interpret (faster?) Interpret (faster?) N workers Unspecified miracle Multi- core?
- 11. A family ofstatically typed acyclic data flow graph IRs
- 12. Working backwards • Graph •Dataflow • Acyclic • Statically typed • A family of … IRs
- 13. Graph • Operators – Labelnames a function – Edge connections in and out • Edges – Directed (“dataflow”)
- 14. Dataflow • Dataflow machines –Apply history, wisdom, insights to the interpreter • Value semantics – All edges carry data – No other kinds of edges (i.e. no anti-dependence) – No updatable shared state (i.e. no store) • Expose all opportunities for concurrency
- 15. Acyclic • No backedges≡ no cycles J • Can exploit topological ordering – Fact propagation: rDFS (forward) or DFS (reverse) – No iteration, guaranteed termination – Linear algorithms, O(graph)
- 16. Statically typed • Edgesinitially have unknown type • A well-formed graph can be statically typed – Linear pass over topologically ordered Operators – Assign edge types per Operator descriptors – Inconsistencies can be diagnosed and reported
- 17. • Well-nested subsetsof edge type vocabularies • Constraining edge types constrains operators A family of … IRs PG Plan Split Bcast Interpret N workers Lower andOpt Lower andOpt Lower andOpt Interpret Tree patterns Graph1 patterns Graph2 patterns High level tree - tuples High level graph - tuples Mid level graph - nullable values Low level graph - values Common pattern notation Topo expand, insert CLONEs Topo expand, insert CLONEs ≈
- 18. Nothing convinces likeworking code • First delivery – Table drive operator semantics – Utilities: build, edit & expand – Topologically sort – Type check & report errors Split Bcast Interpret N workers Interpret Topo expand, insert CLONEs Topo expand, insert CLONEs Graph assembler Graph assembly program
- 19. Sold! • Working coderendered my successive lowerings idea credible • Overall Marlin added ~10 engineers; I got 3 • My team got itsfirst end-to-end test case working PG Plan Split Bcast Interpret N workers Lower andOpt Lower andOpt Lower andOpt Interpret Tree patterns Graph1 patterns Graph2 patterns Topo expand, insert CLONEs Topo expand, insert CLONEs
- 20. IBM killed theMarlin program… • Marlin was a clean up project promising… – Performance and shorter development cycles – But no new features nor functionality • It is always hard to fund significant clean up – Especially if not legitimately tied to a coveted feature • Harder if your company is under duress • Harder still if DB2 is gunning for your headcount
- 21.
- 22.
- 23. Why clone? • Afterexpansion all edges are point-to-point – No output is multiply-consumed • Chunk handoff along an edge becomes trivial – Think C++11’s new move semantics • So only clones implement reference counting
- 24. Broadcast • Serialize /deserialize • On network size matters • Graph object – Small number of scalar members – Handful of C++ vector (some ephemeral) – Position independent (no pointers in vectors)
- 25. No pointers • Pointersindex the linear address space – Implicit context (there is only one address space) • Unsigned as vector index – User must provide explicit context (vector base) – 32 bit indices are ½ the size of 64 bit pointers – Position independence simplifies serialization
- 26. The graph object •Exposed read-only data – Vector of Operator objects – Vector of EdgeIn objects – Vector of EdgeOut objects – Literal table and pool • Private data (may be missing or elided) – Vector of EdgeIn next links – Vector of Operator BreadCrumbs
- 27. Discardable elements • vecBc:BreadCrumbs vector • vecNxt: EdgeIn sibling links • LiteralPool hash table array
- 28. Graph vector details VectorIndex Type Element Type Element Size g.vecOp OperatorIndex Operator 16 bytes g.vecOut EdgeOutIndex EdgeOut 8 bytes g.vecIn EdgeInIndex EdgeIn 8 bytes g.lit LiteralKey Literal multiple of 8 bytes g.vecNxt EdgeInIndex EdgeInIndex 4 bytes g.vecBc OperatorIndex BreadCrumb 4 bytes
- 29. Connectivity: Operator objects •Operator private members – Operator’s edges are sub-vectors of g.vecIn, g.vecOut – Start of EdgeIn objects: EdgeInIndex baseIn_; – Start of EdgeOut objects: EdgeOutIndex baseOut_; • Number of connections – Inputs: vecOp[x+1].baseIn_ - vecOp[x].baseIn_ – Outputs: vecOp[x+1].baseOut_ - vecOp[x].baseOut_
- 30. Connectivity: EdgeIn objects •EdgeIn private members – Sink Operator: OperatorIndex dstOp_; – Source EdgeOut: EdgeOutIndex src_; • EdgeIn connection position – Use pointer arithmetic: this - (vecIn + vecOp[dstOp_].baseIn_);
- 31. Connectivity: EdgeOut objects •EdgeOut private members – Source Operator: OperatorIndex srcOp_; – Sink EdgeIn: EdgeInXIndex dst_; • EdgeOut connection position – Use pointer arithmetic this - (vecOut + vecOp[srcOp_].baseOut_);
- 32.
- 33. Thin graph construction MethodEffect graph.add(BreadCrumb, Op, Locus, Expansion, unsigned nVarIn =0, unsigned nVarOut =0); Add an Operator and its Edge resources graph.connect(OperatorIndex srcOp, unsigned srcPos, OperatorIndex dstOp, unsigned dstPos); Guarantee a srcOp[srcPos] to dstOp[dstPos] edge exists
- 34. Whole graph operations OperationEffect Graph(); Construct an empty Graph void done(); Topo sort and type check Graph(Graph const thinGraph&, bool forSpu); Partitioning constructor BinStream& operator << (BinStream&, Graph const&); Put to a BinStream (cheap) BinStream& operator >> (BinStream&, Graph&); Get from a BinStream (cheap) void expand(bool forSpu, Environment const& env); Expand, insert clones, etc.
- 35. Graph states andconversions • Start with a “thin” graph • Leader plus one representative node and dataslice • Operators tagged with a locus and expansion rule • Outputs can have multiple consumers • Partition into leader-side & node-side subsets • Expand based on loci and system topology • Duplicate operators, adjust in and out arities, add sites • Expand edges: fan-in, fan-out, parallel • Introduce clones as needed
- 36. Graph overlay • Templateobject publically derived from Graph • Macro hides lots of template boilerplate • User supplied types for parallel vectors – MyOperator ovOp[OperatorIndex] – MyEdgeIn ovIn[EdgeInIndex] – MyEdgeOut ovOut[EdgeOutIndex] • Constructor shares vectors and LiteralTable
- 37. 1973: Began 2-axiscontroller I wrote every line of code (in assembler)
- 38. 1975: First installation 0.5MegaWatt torch cutting up to ¾” steel plate at Marion Power Shovel
- 39. 1975: Torch on…I was hooked!