typing the numeric tower
play

Typing the Numeric Tower Vincent St-Amour, Sam Tobin-Hochstadt, - PowerPoint PPT Presentation

Jul 31, 2023 •321 likes •1.16k views

Typing the Numeric Tower Vincent St-Amour, Sam Tobin-Hochstadt, Matthew Flatt, Matthias Felleisen PLT PADL 2012 - January 24th, 2012 Approaches to numerics Traditional Java, C(++), Fortran, ... Type Classes Haskell, Clean, ...

  1. Typing the Numeric Tower Vincent St-Amour, Sam Tobin-Hochstadt, Matthew Flatt, Matthias Felleisen PLT PADL 2012 - January 24th, 2012

  3. Approaches to numerics • Traditional Java, C(++), Fortran, ... • Type Classes Haskell, Clean, ... • Numeric Tower Racket, Scheme, Smalltalk, ...

  4. Approaches to numerics • Traditional Java, C(++), Fortran, ... • Type Classes Haskell, Clean, ... • Numeric Tower Racket, Scheme, Smalltalk, ...

  5. Approaches to numerics • Traditional Java, C(++), Fortran, ... • Type Classes Racket, Scheme, Smalltalk, ... } Haskell, Clean, ... Typed Numeric Tower Typed Racket • Numeric Tower

  6. Our criteria • Ease of expression • Domain fidelity • Static checking • Performance

  7. Our benchmarks

  8. Type Classes p = (2^31) - 1 a = 7^5 x = unsafePerformIO $ newIORef 42 genRandom min max = do old <- readIORef x writeIORef x (mod (a * old) p) new <- readIORef x return $ min + (((max-min) * (fromInteger new)) / (fromInteger p))

  9. Type Classes p = (2^31) - 1 a = 7^5 x = unsafePerformIO $ newIORef 42 genRandom min max = do old <- readIORef x writeIORef x (mod (a * old) p) new <- readIORef x return $ min + (((max-min) * (fromInteger new)) / (fromInteger p)) genRandom 2.3 7.4 -- => 2.3016764082953687

  10. Type Classes p = (2^31) - 1 a = 7^5 x = unsafePerformIO $ newIORef 42 genRandom min max = do old <- readIORef x writeIORef x (mod (a * old) p) new <- readIORef x return $ min + (((max-min) * (fromInteger new)) / (fromInteger p)) genRandom 2.3 7.4 -- => 2.3016764082953687 genRandom (toRational 2) (toRational 7) -- => 9927678409 % 2147483647

  11. Type Classes Ease of expression p = (2^31) - 1 a = 7^5 x = unsafePerformIO $ newIORef 42 genRandom min max = do old <- readIORef x writeIORef x (mod (a * old) p) new <- readIORef x return $ min + (((max-min) * (fromInteger new)) / (fromInteger p)) genRandom 2.3 7.4 -- => 2.3016764082953687 genRandom (toRational 2) (toRational 7) -- => 9927678409 % 2147483647

  12. Type Classes Ease of expression Domain fidelity p = (2^31) - 1 a = 7^5 x = unsafePerformIO $ newIORef 42 genRandom min max = do old <- readIORef x writeIORef x (mod (a * old) p) new <- readIORef x return $ min + (((max-min) * (fromInteger new)) / (fromInteger p)) genRandom 2.3 7.4 -- => 2.3016764082953687 genRandom (toRational 2) (toRational 7) -- => 9927678409 % 2147483647

  13. Type Classes Ease of expression Domain fidelity Static checking p = (2^31) - 1 a = 7^5 x = unsafePerformIO $ newIORef 42 genRandom min max = do old <- readIORef x writeIORef x (mod (a * old) p) new <- readIORef x return $ min + (((max-min) * (fromInteger new)) / (fromInteger p)) genRandom 2.3 7.4 -- => 2.3016764082953687 genRandom (toRational 2) (toRational 7) -- => 9927678409 % 2147483647

  14. Type Classes Ease of expression Domain fidelity Static checking Performance p = (2^31) - 1 a = 7^5 x = unsafePerformIO $ newIORef 42 genRandom min max = do old <- readIORef x writeIORef x (mod (a * old) p) new <- readIORef x return $ min + (((max-min) * (fromInteger new)) / (fromInteger p)) genRandom 2.3 7.4 -- => 2.3016764082953687 genRandom (toRational 2) (toRational 7) -- => 9927678409 % 2147483647

  15. Numeric Tower (define p (- (expt 2 31) 1)) (define A (expt 7 5)) (define x 42) ; state of the PRNG (define (gen-random min max) (set! x (modulo (* A x) p)) (+ min (/ (* (- max min) x) p)))

  16. Numeric Tower (define p (- (expt 2 31) 1)) (define A (expt 7 5)) (define x 42) ; state of the PRNG (define (gen-random min max) (set! x (modulo (* A x) p)) (+ min (/ (* (- max min) x) p))) (gen-random 2.3 7.4) ; => 2.3016764082953687

  17. Numeric Tower (define p (- (expt 2 31) 1)) (define A (expt 7 5)) (define x 42) ; state of the PRNG (define (gen-random min max) (set! x (modulo (* A x) p)) (+ min (/ (* (- max min) x) p))) (gen-random 2.3 7.4) ; => 2.3016764082953687 (gen-random 2 7) ; => 9927678409/2147483647

  18. Numeric Tower Ease of expression (define p (- (expt 2 31) 1)) (define A (expt 7 5)) (define x 42) ; state of the PRNG (define (gen-random min max) (set! x (modulo (* A x) p)) (+ min (/ (* (- max min) x) p))) (gen-random 2.3 7.4) ; => 2.3016764082953687 (gen-random 2 7) ; => 9927678409/2147483647

  19. Numeric Tower Ease of expression Domain fidelity (define p (- (expt 2 31) 1)) (define A (expt 7 5)) (define x 42) ; state of the PRNG (define (gen-random min max) (set! x (modulo (* A x) p)) (+ min (/ (* (- max min) x) p))) (gen-random 2.3 7.4) ; => 2.3016764082953687 (gen-random 2 7) ; => 9927678409/2147483647

  20. Numeric Tower Ease of expression Domain fidelity Static checking (define p (- (expt 2 31) 1)) (define A (expt 7 5)) (define x 42) ; state of the PRNG (define (gen-random min max) (set! x (modulo (* A x) p)) (+ min (/ (* (- max min) x) p))) (gen-random 2.3 7.4) ; => 2.3016764082953687 (gen-random 2 7) ; => 9927678409/2147483647

  21. Numeric Tower Ease of expression Domain fidelity Static checking Performance (define p (- (expt 2 31) 1)) (define A (expt 7 5)) (define x 42) ; state of the PRNG (define (gen-random min max) (set! x (modulo (* A x) p)) (+ min (/ (* (- max min) x) p))) (gen-random 2.3 7.4) ; => 2.3016764082953687 (gen-random 2 7) ; => 9927678409/2147483647

  22. Type Classes q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a)

  23. Type Classes q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a) q 2.4 36.2 (-7.5) -- => 0.20441209042786124

  24. Type Classes q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a) q 2.4 36.2 (-7.5) -- => 0.20441209042786124 q (fromInteger 1) (fromInteger 3) (fromInteger (-4)) -- => 1.0

  25. Type Classes q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a) q 2.4 36.2 (-7.5) -- => 0.20441209042786124 q (fromInteger 1) (fromInteger 3) (fromInteger (-4)) -- => 1.0 q (fromInteger 1) (fromInteger 3) (fromInteger 3) -- => NaN

  26. Type Classes Ease of expression q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a) q 2.4 36.2 (-7.5) -- => 0.20441209042786124 q (fromInteger 1) (fromInteger 3) (fromInteger (-4)) -- => 1.0 q (fromInteger 1) (fromInteger 3) (fromInteger 3) -- => NaN

  27. Type Classes Ease of expression Domain fidelity q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a) q 2.4 36.2 (-7.5) -- => 0.20441209042786124 q (fromInteger 1) (fromInteger 3) (fromInteger (-4)) -- => 1.0 q (fromInteger 1) (fromInteger 3) (fromInteger 3) -- => NaN

  28. Type Classes Ease of expression Domain fidelity Static checking q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a) q 2.4 36.2 (-7.5) -- => 0.20441209042786124 q (fromInteger 1) (fromInteger 3) (fromInteger (-4)) -- => 1.0 q (fromInteger 1) (fromInteger 3) (fromInteger 3) -- => NaN

  29. Type Classes Ease of expression Domain fidelity Static checking Performance q :: (Floating a) => a -> a -> a -> a q a b c = (-b + sqrt (b**2 - 4*a*c)) / (2*a) q 2.4 36.2 (-7.5) -- => 0.20441209042786124 q (fromInteger 1) (fromInteger 3) (fromInteger (-4)) -- => 1.0 q (fromInteger 1) (fromInteger 3) (fromInteger 3) -- => NaN

  30. Numeric Tower (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a)))

  31. Numeric Tower (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a))) (q 2.4 36.2 -7.5) ; => 0.20441209042786124

  32. Numeric Tower (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a))) (q 2.4 36.2 -7.5) ; => 0.20441209042786124 (q 1 3 -4) ; => 1 ; =>

  33. Numeric Tower (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a))) (q 2.4 36.2 -7.5) ; => 0.20441209042786124 (q 1 3 -4) ; => 1 ; => (q 1 3 3) ; => -1.5+0.8660254037844386i ; =>

  34. Numeric Tower Ease of expression (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a))) (q 2.4 36.2 -7.5) ; => 0.20441209042786124 (q 1 3 -4) ; => 1 ; => (q 1 3 3) ; => -1.5+0.8660254037844386i ; =>

  35. Numeric Tower Ease of expression Domain fidelity (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a))) (q 2.4 36.2 -7.5) ; => 0.20441209042786124 (q 1 3 -4) ; => 1 ; => (q 1 3 3) ; => -1.5+0.8660254037844386i ; =>

  36. Numeric Tower Ease of expression Domain fidelity Static checking (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a))) (q 2.4 36.2 -7.5) ; => 0.20441209042786124 (q 1 3 -4) ; => 1 ; => (q 1 3 3) ; => -1.5+0.8660254037844386i ; =>

  37. Numeric Tower Ease of expression Domain fidelity Static checking Performance (define (q a b c) (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c)))) (* 2 a))) (q 2.4 36.2 -7.5) ; => 0.20441209042786124 (q 1 3 -4) ; => 1 ; => (q 1 3 3) ; => -1.5+0.8660254037844386i ; =>

  38. Type Classes Numeric Tower PRNG Quad PRNG Quad Ease of expression Domain fidelity Static checking Performance

Recommend

Typing and ML Typing and ML A name for a set of values and some operations which can be

Typing and ML Typing and ML A name for a set of values and some operations which can be

Typing Typing Typing and ML Typing and ML A name for a set of values and some operations which can be performed on that set of values. CSC324 A collection of computational entities that share some common property. Winter 2007

412 views • 9 slides
Tower &amp; Tower &amp; Tower &amp; Tower &amp; Ashbourne Ashbourne Ashbourne Ashbourne

Tower &amp; Tower &amp; Tower &amp; Tower &amp; Ashbourne Ashbourne Ashbourne Ashbourne

Tower &amp; Tower &amp; Tower &amp; Tower &amp; Ashbourne Ashbourne Ashbourne Ashbourne Cabinet Presentation Fire Safety: UK Building Regulations Comparison Slough Borough Council England Scotland Wales Tower &amp; Ashbourne

497 views • 23 slides
Typing and ML Typing and ML Definition Program organization and documentation A name for a

Typing and ML Typing and ML Definition Program organization and documentation A name for a

Typing Typing Uses/Merits Uses/Merits Type errors Type errors Typing and ML Typing and ML Definition Program organization and documentation A name for a set of values and some operations A type error occurs when execution of

725 views • 5 slides
Tower Operation Management System TOMS Hu Yuming, China Background Tower control is one of

Tower Operation Management System TOMS Hu Yuming, China Background Tower control is one of

Tower Operation Management System TOMS Hu Yuming, China Background Tower control is one of the most complex parts in ATC service. A typical tower control consists of many particular procedures and steps . ACC Tower Tower Cruise TMA

543 views • 17 slides
PRIMARILY RESIDENTIAL DEVELOPMENT Approved office development New offices in the mixed- use

PRIMARILY RESIDENTIAL DEVELOPMENT Approved office development New offices in the mixed- use

TOWER 4 TOWER 2 RESIDENTIAL RESIDENTIAL 120,000 sq. ft. 275,000 sq. ft. TOWER 1 TOWER 5 RESIDENTIAL RESIDENTIAL 165,000 sq. ft. 130,000 sq. ft. HOTEL 150,000 sq.ft PROJECT VISION The proposed redevelopment of Eau Claire Market is a

258 views • 10 slides
numpy : Numerical Python &quot;Duck'' typing makes Python slow Duck Typing If it looks like a

numpy : Numerical Python &quot;Duck'' typing makes Python slow Duck Typing If it looks like a

numpy : Numerical Python &quot;Duck'' typing makes Python slow Duck Typing If it looks like a duck, then it is a duck. a.k.a. dynamic typing Dynamic typing requires lots of metadata around a variable. Solution: numpy data structures Data

230 views • 8 slides
Typing and ML Typing and ML CSC324 Fall 2004 Sheila McIlraith Acknowledgement: The material

Typing and ML Typing and ML CSC324 Fall 2004 Sheila McIlraith Acknowledgement: The material

Typing and ML Typing and ML CSC324 Fall 2004 Sheila McIlraith Acknowledgement: The material in these notes is derived from a variety of sources, including: Elements of ML Programming (Ullman), Concepts in Programming Languages (Mitchell)

647 views • 26 slides
Typing and ML Typing and ML CSC324 Fall 2004 Sheila McIlraith Acknowledgement: The material

Typing and ML Typing and ML CSC324 Fall 2004 Sheila McIlraith Acknowledgement: The material

Typing and ML Typing and ML CSC324 Fall 2004 Sheila McIlraith Acknowledgement: The material in these notes is derived from a variety of sources, including: Elements of ML Programming (Ullman), Concepts in Programming Languages (Mitchell)

595 views • 36 slides
Recognize people by the way they type Typing Biometrics Authentication Cybercrime &amp; identity

Recognize people by the way they type Typing Biometrics Authentication Cybercrime &amp; identity

Typing Biometrics Authentication Recognize people by the way they type Typing Biometrics Authentication Cybercrime &amp; identity theft 17 million victims $30 billion / year Typing Biometrics Authentication The way you type is unique Typing

143 views • 10 slides
Performance Evaluation for Gradual Typing Asumu Takikawa Daniel Feltey *Ben Greenman Max S.

Performance Evaluation for Gradual Typing Asumu Takikawa Daniel Feltey *Ben Greenman Max S.

Performance Evaluation for Gradual Typing Asumu Takikawa Daniel Feltey *Ben Greenman Max S. New Jan Vitek Matthias Felleisen 9 years of sound gradual typing Gradual Typing for Functional Languages, Jeremy Siek &amp; Walid Taha. SFP '06

829 views • 41 slides
Decision Trees with Numeric Tests Industrial-strength algorithms For an algorithm to be useful

Decision Trees with Numeric Tests Industrial-strength algorithms For an algorithm to be useful

Decision Trees with Numeric Tests Industrial-strength algorithms For an algorithm to be useful in a wide range of real- world applications it must: Permit numeric attributes Allow missing values Be robust in the presence of

297 views • 16 slides
Tower Hamlets Together: Discovery Phase Findings and next steps Tower Hamlets Vanguard Outcomes

Tower Hamlets Together: Discovery Phase Findings and next steps Tower Hamlets Vanguard Outcomes

Tower Hamlets Together: Discovery Phase Findings and next steps Tower Hamlets Vanguard Outcomes Framework Articulates our ambition to improve health and social care outcomes and experience for Tower Hamlets citizens Is co-produced

251 views • 12 slides
Condition Numbers of Numeric and Algebraic Problems Stephen Vavasis 1 1 Department of

Condition Numbers of Numeric and Algebraic Problems Stephen Vavasis 1 1 Department of

Condition Numbers of Numeric and Algebraic Problems Stephen Vavasis 1 1 Department of Combinatorics &amp; Optimization University of Waterloo 2011-Nov-16 / Fields Inst. Workshop on Hybrid Symbolic-Numeric Computation 1/ 76 Outline Condition

1.12k views • 81 slides
Presentation Outline Numeric Targets Allocations Other Items Path to Completion

Presentation Outline Numeric Targets Allocations Other Items Path to Completion

Presentation Outline Numeric Targets Allocations Other Items Path to Completion Numeric Targets Canyon Lake Chlorophyll- a ELCOM-CAEDYM reference scenario runs extended Draft report based on 2007-11 Final targets

225 views • 20 slides
PAUL PARFITT BAE/MAE Structural Option Senior Thesis Tower 333 May 4 th 2007 Tower 333

PAUL PARFITT BAE/MAE Structural Option Senior Thesis Tower 333 May 4 th 2007 Tower 333

PAUL PARFITT BAE/MAE Structural Option Senior Thesis Tower 333 May 4 th 2007 Tower 333 Introduction Proposal Lateral System Redesign Elimination of Moment Frames Core-Only Solution Cost Analysis &amp; Schedule Reduction

814 views • 43 slides
Proposed Telecommunications Tower 7 Harlech Court, Markham Ontario Why is the tower needed?

Proposed Telecommunications Tower 7 Harlech Court, Markham Ontario Why is the tower needed?

Proposed Telecommunications Tower 7 Harlech Court, Markham Ontario Why is the tower needed? Maintain the current wireless infrastructure presently located within the community Voice (phone) Data (email, SMS) Internet service (web)

316 views • 12 slides
To Type or Not to Type: Quantifying Detectable Bugs in JavaScript Zheng Gao , Christian Bird

To Type or Not to Type: Quantifying Detectable Bugs in JavaScript Zheng Gao , Christian Bird

To Type or Not to Type: Quantifying Detectable Bugs in JavaScript Zheng Gao , Christian Bird , Earl Barr University College London, Microsoft Research Static Typing vs. Dynamic Typing Static Typing vs. Dynamic Typing

807 views • 68 slides
Programming Languages Lecture 4 Benefits of dynamic typing Not adapted from Dan Grossman's PL

Programming Languages Lecture 4 Benefits of dynamic typing Not adapted from Dan Grossman's PL

Programming Languages Lecture 4 Benefits of dynamic typing Not adapted from Dan Grossman's PL class, U. of Washington Declaring functions in C++ vs Python C++ uses static typing : most code can be checked at compile-time to make sure rules

593 views • 10 slides
Estuarine Nutrient Numeric Endpoint San Francisco Bay Stakeholder Advisory Group (SF Bay SAG)

Estuarine Nutrient Numeric Endpoint San Francisco Bay Stakeholder Advisory Group (SF Bay SAG)

Estuarine Nutrient Numeric Endpoint San Francisco Bay Stakeholder Advisory Group (SF Bay SAG) Meeting October 4, 2010, 1- 3:30 pm Meeting Goals Provide overview of approach and near-term steps to develop nutrient numeric endpoints (NNE)

579 views • 36 slides
Lets do some Computer Algebra and Combinatorics! SYMBOLIC-NUMERIC TOOLS FOR ANALYTIC

Lets do some Computer Algebra and Combinatorics! SYMBOLIC-NUMERIC TOOLS FOR ANALYTIC

SYMBOLIC-NUMERIC TOOLS FOR ANALYTIC COMBINATORICS IN SEVERAL VARIABLES Stephen Melczer ENS Lyon / Inria &amp; University of Waterloo Joint work with Bruno Salvy Lets do some Computer Algebra and Combinatorics! SYMBOLIC-NUMERIC TOOLS

489 views • 38 slides
Introduction to Data Science: Principles ordered categorical data do not have magnitude

Introduction to Data Science: Principles ordered categorical data do not have magnitude

Measurements and Data Types Categorical attributes Discrete numeric attributes Getting data Continuous Numeric Attributes Other examples Units Getting data Categorical attributes Categorical attributes Continuous Numeric Attributes

897 views • 47 slides
pump tower function tests Shuoxing Wu WA105-3x1x1 bi-weekly meeting 27.07.2016 LAr pump tower

pump tower function tests Shuoxing Wu WA105-3x1x1 bi-weekly meeting 27.07.2016 LAr pump tower

pump tower function tests Shuoxing Wu WA105-3x1x1 bi-weekly meeting 27.07.2016 LAr pump tower Shuoxing Wu ETHZ 2 LAr pump tower function test self-recirculation to simulate outer LAr bath real operation condition h valves open pump

57 views • 5 slides
TYPICAL FLOOR PLAN CLUB HOUSE DEVELOPMENT MAIN ENTRANCE 3 BHK TOWER - C 3 BHK TOWER - B 4 BHK

TYPICAL FLOOR PLAN CLUB HOUSE DEVELOPMENT MAIN ENTRANCE 3 BHK TOWER - C 3 BHK TOWER - B 4 BHK

TYPICAL FLOOR PLAN CLUB HOUSE DEVELOPMENT MAIN ENTRANCE 3 BHK TOWER - C 3 BHK TOWER - B 4 BHK TOWER - A SITE LAYOUT MAIN ENTRANCE 3 BHK UNIT PLAN 4 BHK UNIT PLAN FACTSHEET : Rs. 100/sft for Garden Facing Units in advance at the time of

98 views • 5 slides
Analysis of Hope Point Tower Proposal 7-18-17 DRAFT 1 Hope Point Tower q Parcel 42, west

Analysis of Hope Point Tower Proposal 7-18-17 DRAFT 1 Hope Point Tower q Parcel 42, west

Analysis of Hope Point Tower Proposal 7-18-17 DRAFT 1 Hope Point Tower q Parcel 42, west bank of Providence River, north of I-195, south of downtown. q A mixed-use project with residential, retail &amp; parking to be built in a single phase.

528 views • 9 slides

More recommend