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Where are you going with those types? Vincent St-Amour, Sam - PowerPoint PPT Presentation

Mar 17, 2024 •128 likes •839 views

Where are you going with those types? Vincent St-Amour, Sam Tobin-Hochstadt, Matthew Flatt, Matthias Felleisen PLT / Northeastern University Boston, MA, USA PLT / University of Utah Salt Lake City, UT, USA IFL 2010 - September 3rd, 2010

  1. Where are you going with those types? Vincent St-Amour, Sam Tobin-Hochstadt, Matthew Flatt, Matthias Felleisen PLT / Northeastern University Boston, MA, USA PLT / University of Utah Salt Lake City, UT, USA IFL 2010 - September 3rd, 2010

  2. Generating fast code in the presence of ad-hoc polymorphism is hard.

  3. Case study: generic arithmetic (+ 2 2)

  4. Case study: generic arithmetic (+ 2 2) (+ 2.3 2.4)

  5. Case study: generic arithmetic (+ 2 2) (+ 2.3 2.4) (+ 2.3 2)

  6. Case study: generic arithmetic (+ 2 2) (+ 2.3 2.4) (+ 2.3 2) (+ 2+3i 2+4i)

  7. Case study: generic arithmetic (+ 2 2) (+ 2.3 2.4) (+ 2.3 2) (+ 2+3i 2+4i) Types of arguments are not known statically.

  8. Case study: generic arithmetic #lang racket (+ 2.3 2.4)

  9. Case study: generic arithmetic #lang racket (+ 2.3 2.4) (define (add x y) (cond ((and (float? x) (float? y)) (let* ([val-x (strip-type-tag x)] [val-y (strip-type-tag y)] [result (add-floats val-x val-y)]) (tag-as-float result))) ((and (integer? x) (integer? y)) ...) ((and (complex? x) (complex? y)) ...) (else (error))))

  10. Case study: generic arithmetic #lang racket (+ 2.3 2.4) (define (add x y) (cond ((and (float? x) (float? y)) (let* ([val-x (strip-type-tag x)] [val-y (strip-type-tag y)] [result (add-floats val-x val-y)]) (tag-as-float result))) ((and (integer? x) (integer? y)) ...) ((and (complex? x) (complex? y)) ...) (else (error))))

  11. Our solution • Type-specialized primitives • Composition of: • Type-driven rewriting • Primitives drive optimization Typechecker τ Rewriting Primitives Compiler

  12. Implementation • Typed Racket • Higher-order functional language • Generic arithmetic (and complexes)

  13. Implementation • Typed Racket • Higher-order functional language • Generic arithmetic (and complexes) Applicable to other languages

  14. Type-specialized primitives

  15. #lang racket (fl+ x y)

  16. #lang racket (fl+ 2.3 2.4)

  17. #lang racket (fl+ 2.3 2.4) 4.7

  18. #lang racket (fl+ 2 2)

  19. #lang racket (fl+ 2 2) segmentation fault

  20. #lang typed/racket (let: ([x : Float 2.3] [y : Float 2.4]) (fl+ x y))

  21. #lang typed/racket (let: ([x : Float 2.3] [y : Float 2.4]) (fl+ x y))

  22. #lang typed/racket (let: ([x : Float 2.3] [y : Float 2.4]) (fl+ x y)) 4.7

  23. #lang typed/racket (let: ([x : Integer 2] [y : Integer 2]) (fl+ x y))

  24. #lang typed/racket (let: ([x : Integer 2] [y : Integer 2]) (fl+ x y))

  25. #lang typed/racket (let: ([x : Integer 2] [y : Integer 2]) (fl+ x y)) Type Checker: No function domains matched in function application: Domains: Float Float Arguments: Integer Integer in: (fl+ x y)

  26. Type-driven rewriting

  27. #lang typed/racket (let: ([x : Float 2.3] [y : Float 2.4]) (+ x y))

  28. #lang typed/racket (let: ([x : Float 2.3] [y : Float 2.4]) (+ x y))

  29. #lang typed/racket (let: ([x : Float 2.3] [y : Float 2.4]) (fl+ x y))

  30. #lang typed/racket (let: ([x : Float 2.3] [y : Float 2.4]) (fl+ x y)) 4.7

  31. Primitives drive optimization

  32. #lang typed/racket (* (+ x y) (+ z w))

  33. load $x $r1 load $y $r2 ... fadd $r1 $r2 $r3 ... sto $r3 $tmp1 #lang typed/racket load $z $r4 (* (+ x y) load $w $r5 (+ z w)) ... fadd $r4 $r5 $r6 ... sto $r6 $tmp2 load $tmp1 $r7 load $tmp2 $r8 ... fmul $r7 $r8 $r9 ... sto $r9 $tmp3

  34. load $x $r1 load $y $r2 ... fadd $r1 $r2 $r3 ... sto $r3 $tmp1 #lang typed/racket load $z $r4 (* (+ x y) load $w $r5 (+ z w)) ... fadd $r4 $r5 $r6 ... sto $r6 $tmp2 load $tmp1 $r7 load $tmp2 $r8 ... fmul $r3 $r6 $r9 ... sto $r9 $tmp3

  35. load $x $r1 load $y $r2 ... fadd $r1 $r2 $r3 ... sto $r3 $tmp1 #lang typed/racket load $z $r4 (* (+ x y) load $w $r5 (+ z w)) ... fadd $r4 $r5 $r6 #lang typed/racket ... (fl* (fl+ x y) sto $r6 $tmp2 (fl+ z w)) load $tmp1 $r7 load $tmp2 $r8 ... fmul $r3 $r6 $r9 ... sto $r9 $tmp3

  36. load $x $r1 load $y $r2 ... fadd $r1 $r2 $r3 ... sto $r3 $tmp1 #lang typed/racket load $z $r4 (* (+ x y) load $w $r5 (+ z w)) ... fadd $r4 $r5 $r6 #lang typed/racket ... (fl* (fl+ x y) sto $r6 $tmp2 (fl+ z w)) load $tmp1 $r7 load $tmp2 $r8 ... fmul $r3 $r6 $r9 ... sto $r9 $tmp3

  37. #lang typed/racket (let ([a (+ x y)]) (* a (- z a)))

  38. load $x $r1 load $y $r2 ... fadd $r1 $r2 $r3 ... sto $r3 $a #lang typed/racket load $z $r4 (let ([a (+ x y)]) load $a $r5 (* a (- z a))) ... fsub $r4 $r5 $r6 ... sto $r6 $tmp1 load $a $r7 load $tmp1 $r8 ... fmul $r7 $r8 $r9 ... sto $r9 $tmp2

  39. load $x $r1 load $y $r2 ... fadd $r1 $r2 $r3 ... sto $r3 $a #lang typed/racket load $z $r4 (let ([a (+ x y)]) load $a $r5 (* a (- z a))) ... fsub $r4 $r3 $r6 ... sto $r6 $tmp1 load $a $r7 load $tmp1 $r8 ... fmul $r3 $r6 $r9 ... sto $r9 $tmp2

  40. load $x $r1 load $y $r2 ... fadd $r1 $r2 $r3 ... sto $r3 $a #lang typed/racket load $z $r4 (let ([a (+ x y)]) load $a $r5 (* a (- z a))) ... fsub $r4 $r3 $r6 #lang typed/racket ... (let ([a (fl+ x y)]) sto $r6 $tmp1 (fl* a (fl- z a))) load $a $r7 load $tmp1 $r8 ... fmul $r3 $r6 $r9 ... sto $r9 $tmp2

  41. #lang typed/racket (let loop ([acc 0.0]) (if (> acc x) acc (loop (+ y acc))))

  42. mov 0.0 $r1 ... sto $r1 $acc #lang typed/racket (let loop ([acc 0.0]) loop: (if (> acc x) load $acc $r2 acc load $x $r3 ... (loop (+ y acc)))) flcmp $r2 $r3 jgt end load $y $r4 load $acc $r5 ... fadd $r4 $r5 $r6 ... sto $r6 $acc jmp loop end:

  43. mov 0.0 $r1 ... sto $r1 $acc #lang typed/racket (let loop ([acc 0.0]) loop: (if (> acc x) load $acc $r2 acc load $x $r3 ... (loop (+ y acc)))) flcmp $r2 $r3 jgt end load $y $r4 load $acc $r5 ... fadd $r4 $r5 $r6 ... sto $r6 $acc jmp loop end:

  44. mov 0.0 $r1 ... sto $r1 $acc #lang typed/racket (let loop ([acc 0.0]) loop: (if (> acc x) load $acc $r2 acc load $x $r3 ... (loop (+ y acc)))) flcmp $r1 $r3 jgt end #lang typed/racket load $y $r4 (let loop ([acc 0.0]) load $acc $r5 ... (if (fl> acc x) fadd $r4 $r1 $r6 acc ... (loop (fl+ y acc)))) sto $r6 $acc jmp loop end: sto $r1 $acc

  45. mov 0.0 $r1 ... sto $r1 $acc #lang typed/racket (let loop ([acc 0.0]) loop: (if (> acc x) load $acc $r2 acc load $x $r3 ... (loop (+ y acc)))) flcmp $r1 $r3 jgt end #lang typed/racket load $y $r4 (let loop ([acc 0.0]) load $acc $r5 ... (if (fl> acc x) fadd $r4 $r1 $r6 acc ... (loop (fl+ y acc)))) sto $r6 $acc jmp loop end: sto $r1 $acc

  46. mov 0.0 $r1 ... sto $r1 $acc load $x $r3 #lang typed/racket load $y $r4 (let loop ([acc 0.0]) loop: (if (> acc x) load $acc $r2 acc load $x $r3 ... (loop (+ y acc)))) flcmp $r1 $r3 jgt end #lang typed/racket load $y $r4 (let loop ([acc 0.0]) load $acc $r5 ... (if (fl> acc x) fadd $r4 $r1 $r6 acc ... (loop (fl+ y acc)))) sto $r6 $acc jmp loop end: sto $r1 $acc

  47. Results

  48. Speedup 2.50 benchmarks pseudoknot 15.72 mandelbrot 2.16 nbody 1.24 takl 15.91 FFT 1.60 data structures banker's queue 1.34 leftist heap 2.78 industrial application FFT Bigger is better Average of 5 runs on x86

  49. In-depth look: Industrial FFT

  50. #lang racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i]) (- (+ x y) z))

  51. #lang racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i] [x-real (real-part x)] [x-imag (imag-part x)] [y-real (real-part y)] [y-imag (imag-part y)] [z-real (real-part z)] [z-imag (imag-part z)]) (make-rectangular (- (+ x-real y-real) z-real) (- (+ x-imag y-imag) z-imag)))

  52. #lang racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i] [x-real (real-part x)] [x-imag (imag-part x)] [y-real (real-part y)] [y-imag (imag-part y)] [z-real (real-part z)] [z-imag (imag-part z)]) (make-rectangular (fl- (fl+ x-real y-real) z-real) (fl- (fl+ x-imag y-imag) z-imag)))

  53. #lang racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i] [x-real (real-part x)] [x-imag (imag-part x)] [y-real (real-part y)] [y-imag (imag-part y)] [z-real (real-part z)] [z-imag (imag-part z)]) (make-rectangular (fl- (fl+ x-real y-real) z-real) (fl- (fl+ x-imag y-imag) z-imag))) Significant manual labor

  54. #lang racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i] [x-real (real-part x)] [x-imag (imag-part x)] [y-real (real-part y)] [y-imag (imag-part y)] [z-real (real-part z)] [z-imag (imag-part z)]) (make-rectangular (fl- (fl+ x-real y-real) z-real) (fl- (fl+ x-imag y-imag) z-imag))) Significant manual labor Error prone

  55. #lang typed/racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i]) (- (+ x y) z))

  56. #lang typed/racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i]) (- (+ x y) z)) Unboxed intermediate results

  57. #lang typed/racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i]) (- (+ x y) z)) Unboxed intermediate results Unboxed let bindings

  58. #lang typed/racket (let* ([x 2.3+2.4i] [y 2.5+2.6i] [z 2.7+2.8i]) (- (+ x y) z)) Unboxed intermediate results Unboxed let bindings Unboxed loop variables

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