How to memoize - Speaker Deck

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PRESENTATION TITLE: [REDACTED] AUTHOR: DENIS DEFREYNE (@DDFREYNE) OCCASION: RUG45B, 2018-03-01    AUDIENCE: INHABITANTS OF EARTH

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What do you do when you have an expensive function, and you need to use its return value multiple times?

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def total_price vat = calc_base_price * VAT_RATE calc_base_price + vat end 

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def total_price base_price = calc_base_price vat = base_price * VAT_RATE base_price + vat end

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0 LOCAL VARIABLES

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A B C D E F G H B1 B2

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children

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children.map(&:depth)

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children.map(&:depth).max

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children.map(&:depth).max || 0

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(children.map(&:depth).max || 0) + 1

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def depth (children.map(&:depth).max || 0) + 1 end

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A B C D E F G H B1 B2

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a.depth = b.depth + 1 A B C D E F G H B1 B2

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a.depth = b.depth + 1 b.depth = [b1.depth, c.depth].max + 1 A B C D E F G H B1 B2

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a.depth = b.depth + 1 b.depth = [b1.depth, c.depth].max + 1 … A B C D E F G H B1 B2

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a.depth = b.depth + 1 b.depth = [b1.depth, c.depth].max + 1 … b2.depth = f.depth + 1 A B C D E F G H B1 B2

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a.depth = b.depth + 1 b.depth = [b1.depth, c.depth].max + 1 … b2.depth = f.depth + 1 e.depth = f.depth + 1 A B C D E F G H B1 B2

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a.depth = b.depth + 1 b.depth = [b1.depth, c.depth].max + 1 … b2.depth = f.depth + 1 e.depth = f.depth + 1 … A B C D E F G H B1 B2

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def depth (children.map(&:depth).max || 0) + 1 end

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def depth @_depth ||= (children.map(&:depth).max || 0) + 1 end

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1 MEMOIZATION USING ||=

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def fib(n) case n when 0 0 when 1 1 else fib(n - 1) + fib(n - 2) end end

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def fib(n) case n when 0 0 when 1 1 else fib(n - 1) + fib(n - 2) end end fib(0) = 0 fib(1) = 1 fib(2) = 1 fib(3) = 2 fib(4) = 3 fib(5) = 5 fib(6) = 8 fib(7) = 13 fib(8) = 21 fib(9) = 34

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fib(40)

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fib(40) = fib(38) + fib(39)

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fib(40) = fib(38) + fib(39) = fib(38) + fib(37) + fib(38)

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fib(40) = fib(38) + fib(39) = fib(38) + fib(37) + fib(38) = fib(36) + fib(37) + fib(37) + fib(38)

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fib(40) = fib(38) + fib(39) = fib(38) + fib(37) + fib(38) = fib(36) + fib(37) + fib(37) + fib(38) = fib(36) + fib(37) + fib(37) + fib(36) + fib(37)

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fib(40) = fib(38) + fib(39) = fib(38) + fib(37) + fib(38) = fib(36) + fib(37) + fib(37) + fib(38) = fib(36) + fib(37) + fib(37) + fib(36) + fib(37) = …

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fib(40) takes 15 seconds  on my 3.1 GHz machine!

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def fib(n) init = [0, 1] while init.size <= n init << init.last(2).sum end init[n] end

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def fib(n) @fib ||= {} @fib[n] ||= case n when 0 0 when 1 1 else fib(n - 1) + fib(n - 2) end end

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2 ARGUMENT-AWARE MEMOIZATION USING ||=

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def fib(n) … end memoize :fib

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def memoize(method_name) end

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def memoize(method_name) end

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def memoize(method_name) nonmemoized_method_name = '__nonmemoized_' + method_name.to_s alias_method nonmemoized_method_name, method_name end

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def memoize(method_name) nonmemoized_method_name = '__nonmemoized_' + method_name.to_s alias_method nonmemoized_method_name, method_name define_method(method_name) do |*args| @cache ||= {} method_cache = (@cache[method_name] ||= {}) send(nonmemoized_method_name, *args) end end

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3 GENERIC MEMOIZATION USING #MEMOIZE

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class Node def depth (children.map(&:depth).max || 0) + 1 end memoize :depth end

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h = Node.new g = Node.new(h) f = Node.new(g) e = Node.new(f) d = Node.new(e) c = Node.new(d) b2 = Node.new(f) b1 = Node.new(b2) b = Node.new(c, b1) a = Node.new(b)    p a.depth  B C D E F G B1 B2 B C D E B1 B2

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h = Node.new g = Node.new(h) f = Node.new(g) e = Node.new(f) d = Node.new(e) c = Node.new(d) b2 = Node.new(f) b1 = Node.new(b2) b = Node.new(c, b1) a = Node.new(b)    a.freeze  p a.depth B C D E F G B1 B2 B C D E B1 B2

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node.rb:123:in `depth': can't modify frozen Node (FrozenError)

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def memoize(method_name) nonmemoized_method_name = '__nonmemoized_' + method_name.to_s alias_method nonmemoized_method_name, method_name method_cache = {} define_method(method_name) do |*args| instance_cache = (method_cache[self] ||= {}) if instance_cache.key?(args) instance_cache[args] else instance_cache[args] = send(nonmemoized_method_name, *args) end end end

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4 GENERIC MEMOIZATION SUPPORTING #FREEZE

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We’re running out of memory!

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require 'weakref'    ref = WeakRef.new("hi")  ref.upcase

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require 'weakref'    ref = WeakRef.new("hi")  ref.upcase # a> HI 

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require 'weakref'    ref = WeakRef.new("hi")  ref.upcase # a> HI  GC.start  ref.upcase

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require 'weakref'    ref = WeakRef.new("hi")  ref.upcase # a> HI  GC.start  ref.upcase # WeakRef45RefError (Invalid Reference - probably recycled)

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require 'ref' ref = RefnoSoftReference.new("hello")  ref.object.upcase # a> HI

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define_method(method_name) do |*args| instance_cache = (method_cache[self] ||= {}) value = instance_cache[args]&.object if value value else instance_cache[args] = Ref45SoftReference.new( send(original_method_name, *args) ) end end

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RefnoSoftReference.new(123) # a> ArgumentError (cannot define finalizer for Integer)

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class ValueWrapper attr_reader :value def initialize(value) @value = value end end

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define_method(method_name) do |*args| instance_cache = (method_cache[self] ||= {}) value = instance_cache[args]&.object if wrapper wrapper.value else value = send(original_method_name, *args) wrapper = ValueWrapper.new(value) instance_cache[args] = RefnoSoftReference.new(wrapper) value end end

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5 GENERIC MEMORY-EFFICIENT MEMOIZATION

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Thread safety? Nöpe.

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(I’ll get around to that, eventually.)

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EXECUTIVE SUMMARY TIME

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We now have a memoization mechanism that… * … has a nice API * … supports multiple arguments * … supports frozen objects * … is memory-efficient * … and soon will be thread-safe

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I love immutability.

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You don’t have to implement this yourself, ever. Give ddmemoize a try: github.com/ddfreyne/ddmemoize

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require 'ddmemoize' class FibFast DDMemoize.activate(self) memoized def run(n) if n == 0 0 elsif n == 1 1 else run(n - 1) + run(n - 2) end end end

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DDMemoize.print_metrics memoization │ hit miss % ────────────┼─────────────────── FibFast#fib │ 998 1001 49.9%

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Q&A