Download as PDF, PPTX
Uploaded byJiahao Chen
Julia: Multimethods for abstraction and performance
This document discusses Julia's use of multimethod dispatch and generic functions to provide both data abstraction and high performance. Julia bridges the divide between computer science and computational science by allowing users to write generic code that can also achieve native machine performance when applicable. Its type system and multimethods allow methods to be specialized for different argument types, enabling both abstraction and optimized implementations.
More Related Content
Similar to Julia: Multimethods for abstraction and performance
![Coded Agents – with UiPath SDK + LangGraph [Virtual Hands-on Workshop]](https://cdn.slidesharecdn.com/ss_thumbnails/codedagentsdeck-251215155422-5497c599-thumbnail.jpg?width=640&height=640&fit=bounds)
Julia: Multimethods for abstraction and performance
- 1. Multimethods for abstractionand performance Jiahao Chen Research Scientist MIT CSAIL jiahao.github.io GitHub: @jiahao
- 2. People like toreinvent programming languages
- 4. Alan Edelman AndreasNoack Xianyi Zhang Jarrett Revels Oscar BlumbergDavid Sanders The Julia Lab at MIT Simon Danisch Jiahao Chen Weijian Zhang U. Manchester Jake Bolewski USAP Shashi GowdaAmit Murthy Tanmay Mohapatra Eka Palamadai Collaborators Joey Huchette Isaac Virshup Steven Johnson MIT Mathematics Yes Sian Ng Miles Lubin Iain Dunning Jon Malmaud Simon Kornblith Yichao Yu Harvard Jeremy Kepner Lincoln Labs Stavros Papadopoulos Intel Labs Nikos Patsopoulos Brigham Woman’s Hospital Pete Szolovits CSAIL Alex Townsend MIT Mathematics Jack Poulson Stanford
- 5. Mike Innes Julia Computing Summerof Code alums Keno Fischer Julia Computing Jameson Nash Julia Computing Simon Danisch Julia Lab Shashi Gowda Julia Lab Leah Hanson Stripe John Myles White Facebook Jarrett Revels Julia Lab 2013 2014 2015 Jacob Quinn Domo Kenta Sato U. Tokyo Rohit Varkey Thankachan Nat’l Inst. Tech. Karnataka Simon Danish Julia Lab David Gold U. Washington Keno FischerJameson NashStefan KarpinskiJeff Bezanson Viral B. Shah Alums at Mike Innes
- 6. 445 contributors toJulia 726 package authors as of 2016-03-15
- 7. https://github.com/jiahao/ijulia-notebooks The world of 808packages, 726 authors 445 contributors to julia repo 6,841 stargazers 549 watchers
- 8. What’s the bigdeal about Julia ? A high level language with C-like speed julialang.org/benchmarks
- 9. What’s the bigdeal about Julia ? Normalized average lines of code (shortest = 0, longest = 1) Execution time (C = 1) https://groups.google.com/d/msg/julia-users/BYRAeQJuvTw/O7VK7-vp1EEJ fast and expressive
- 10.
- 11. It bridges thedivide between computer science and computational science What’s the big deal about Julia ?
- 12. It bridges thedivide between computer science and computational science What’s the big deal about Julia ? data abstraction performance
- 13. It bridges thedivide between computer science and computational science What’s the big deal about Julia ? data abstraction performance What if you didn’t have to choose between data abstraction and performance?
- 14. Thesis: Users want towrite generic code. Users also want native machine performance (when available). Julia’s generic function system with multimethods (multiple dispatch) lets you have both.
- 15. Is Julia objectoriented? Yes, but maybe not in a way you’re familiar with.* Generic functions** like in CLOS, unlike C++ classes. *G. Castagna, Object Oriented Programming: A Unified Foundation, http://link.springer.com/book/10.1007/978-1-4612-4138-6 **L. G. DeMichiel and R. P. Gabriel, §3.2 of The Common Lisp Object System: An Overview, http://www.dreamsongs.com/Files/ECOOP.pdf
- 16. Object-oriented programming withclasses What can I do with/to a thing?
- 17. methods objects Object-oriented programmingwith classes What can I do with/to a thing?
- 18. methods objects Object-oriented programmingwith classes What can I do with/to a thing?
- 19. methods objects Object-oriented programmingwith classes What can I do with/to a thing? top up pay fare lose buy
- 20. methods objects Object-oriented programmingwith classes What can I do with/to a thing? top up pay fare lose buy top up pay fare lose buy
- 21. methods objects Object-oriented programmingwith classes What can I do with/to a thing? top up pay fare lose buy top up pay fare lose buy
- 22. methods objects Object-oriented programmingwith classes What can I do with/to a thing? top up pay fare lose buy top up pay fare lose buy pay fare lose buy
- 23. methods objects Object-oriented programmingwith classes What can I do with/to a thing? top up pay fare lose buy classes are more fundamental than methods top up pay fare lose buy pay fare lose buy
- 24. OOP with classesmultimethods What can I do with/to a thing? top up pay fare lose buy generic function objectsmethods multimethods relationships between objects and functions
- 25. Multimethods for linearalgebra What can I do with/to a thing? compute spectral factorization compute singular values compute singular values and vectors compute eigenvalues generic function objectsmethods Methods can take advantage of special matrix structures eigvals eigfact svdvals svdfact Matrix SymTridiagonal Bidiagonal
- 26. Data types asa lattice D. Scott, “Data types as lattices”, SIAM J. Comput. 5: 522-87, 1976, doi:10.1137/0205037 Real Number FloatingPoint Rational Complex Float64 BigFloat… … Integer is a parameter of is a subtype of Signed BigInt Any Int64… …
- 27. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… …
- 28. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… …
- 29. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… …
- 30. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… … no method here try supertype super(Int64) = Signed
- 31. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… … no method here try supertype super(Int64) = Signed no method here either super(Signed) = Integer
- 32. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… … no method here try supertype super(Int64) = Signed no method here either super(Signed) = Integer found a method
- 33. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… …
- 34. Signed Multimethods with typelattice traversal Real Number FloatingPoint Rational Float64 BigFloat… Integer is a parameter of is a subtype of BigInt Any Int64… …
- 42. easy to callexternal C functions, e.g. CLAPACK sstev, dstev…
- 43. So how doesthis help us with linear algebra? Multi-method dispatch with generic fallbacks Matrix operations on general rings
- 44. So how doesthis help us with linear algebra? Multi-method dispatch with generic fallbacks Matrix operations on general rings textbook algorithm
- 45. So how doesthis help us with linear algebra? Multi-method dispatch with generic fallbacks Matrix operations on general rings
- 46.
- 47.
- 48.
- 49. JuMP: a domainspecific language Iain Dunning Miles Lubin MIT Operations Research Joey HuchetteYes Sian Ng
- 50.
- 52. In summary, Types helpsusers express scientific computations and helps the compiler specialize code for performance Other advanced features for genericness and performance: metaprogramming with macros and generated functions, parametric polymorphism, native parallel computing, … try Julia today! juliabox.org JuliaCon - June 21-25 at MIT CSAIL juliacon.org
- 53. Other references B. Liskov,The Power of Abstraction, Turing Award lecture, OOPSLA’09. https://www.youtube.com/watch? v=qAKrMdUycb8 J. Sammet, Programming Languages: History and Fundamentals, Prentice-Hall, 1969.
- 54. Are classes reallythat bad? Yes, when you break their abstraction. http://okmij.org/ftp/Computation/Subtyping/
- 55. The circle-ellipse problem(aka the square-rectangle problem)
- 56. The circle-ellipse problem(aka the square-rectangle problem) Is a circle an ellipse?
- 57. The circle-ellipse problem(aka the square-rectangle problem) Is a circle an ellipse? Yes: it is a special case of an ellipse with degenerate foci zero eccentricity etc.
- 58. The circle-ellipse problem(aka the square-rectangle problem) Is a circle an ellipse? Yes: it is a special case of an ellipse with degenerate foci zero eccentricity etc. No: it makes no sense to change the second focus of a circle.
- 59. The circle-ellipse problem #ProgramA foo = Ellipse(r1 = 0.5, r2 = 1.0) get_r2(foo)
- 60. The circle-ellipse problem #ProgramA foo = Ellipse(r1 = 0.5, r2 = 1.0) get_r2(foo) Circle(r = 0.5)
- 61. The circle-ellipse problem #ProgramA foo = Ellipse(r1 = 0.5, r2 = 1.0) get_r2(foo) Circle(r = 0.5) You can make this program work: define get_r2(x::Circle) = x.r
- 62. #Program B foo =Ellipse() set_r1(foo, 0.5) set_r2(foo, 1.0) get_r1(foo)*get_r2(foo) == 0.5 The circle-ellipse problem #Program A foo = Ellipse(r1 = 0.5, r2 = 1.0) get_r2(foo) Circle(r = 0.5) You can make this program work: define get_r2(x::Circle) = x.r
- 63. #Program B foo =Ellipse() set_r1(foo, 0.5) set_r2(foo, 1.0) get_r1(foo)*get_r2(foo) == 0.5 The circle-ellipse problem #Program A foo = Ellipse(r1 = 0.5, r2 = 1.0) get_r2(foo) Circle() Circle(r = 0.5) You can make this program work: define get_r2(x::Circle) = x.r
- 64. #Program B foo =Ellipse() set_r1(foo, 0.5) set_r2(foo, 1.0) get_r1(foo)*get_r2(foo) == 0.5 The circle-ellipse problem #Program A foo = Ellipse(r1 = 0.5, r2 = 1.0) get_r2(foo) Circle() Circle(r = 0.5) You can’t substitute a Circle for an Ellipse in this program. You can make this program work: define get_r2(x::Circle) = x.r
- 65. #Program B foo =Ellipse() set_r1(foo, 0.5) set_r2(foo, 1.0) get_r1(foo)*get_r2(foo) == 0.5 The circle-ellipse problem #Program A foo = Ellipse(r1 = 0.5, r2 = 1.0) get_r2(foo) Circle() Circle(r = 0.5) You can’t substitute a Circle for an Ellipse in this program. You can make this program work: define get_r2(x::Circle) = x.r If you can mutate objects (“covariant context”)*, then circles are not ellipses because of the Liskov substitution principle** (one of the SOLID principles). *G. Castagna, Covariance and contravariance : conflict without a cause. In Object Oriented Programming: A Unified Foundation, http://link.springer.com/book/10.1007/978-1-4612-4138-6 **B. Liskov, Keynote address - data abstraction and hierarchy, OOPSLA '87 Proceedings Addendum, 17-34. B. Liskov and J. M. Wing. "A Behavioral Notion of Subtyping," ACM Trans. Programming Languages and Systems 16(6):1811-1841, Nov 1994.
- 66. n-ary operations mylist =ListOfNumbers(); mylist.push!(1.0);
- 67. n-ary operations Methods areassociated with classes. mylist = ListOfNumbers(); mylist.push!(1.0);
- 68. n-ary operations Methods areassociated with classes. mylist = ListOfNumbers(); mylist.push!(1.0); A unary operation on a class can be implemented as a method of that class. The abstraction of classes can break down for functions involving multiple classes.
- 69. n-ary operations Neither. Matrix+ DiagonalMatrix needs to access private fields, thus breaking encapsulation*. *A loaded term; see D. J. Armstrong, The quarks of object-oriented development, Commun. ACM 49 (2): 123-8, Feb 2006, doi:10.1145/1113034.1113040
- 70. n-ary operations Adding adiagonal matrix and an ordinary (dense) matrix: is it a method of Matrix or DiagonalMatrix? Neither. Matrix + DiagonalMatrix needs to access private fields, thus breaking encapsulation*. *A loaded term; see D. J. Armstrong, The quarks of object-oriented development, Commun. ACM 49 (2): 123-8, Feb 2006, doi:10.1145/1113034.1113040
- 71. n-ary operations Adding adiagonal matrix and an ordinary (dense) matrix: is it a method of Matrix or DiagonalMatrix? class Matrix { private: int m, n; float *data; // … friend Matrix operator+(Matrix M, DiagonalMatrix D); //non-member function }; class DiagonalMatrix{ private: int n; //store only the diagonals float *diagonaldata; // … friend Matrix operator+(Matrix M, DiagonalMatrix D); //non-member function }; Neither. Matrix + DiagonalMatrix needs to access private fields, thus breaking encapsulation*. *A loaded term; see D. J. Armstrong, The quarks of object-oriented development, Commun. ACM 49 (2): 123-8, Feb 2006, doi:10.1145/1113034.1113040