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Experiments with memoization, using ECMAScript 2015 (ES6) fat arrow function syntax. fix is a variant of the applicative order fix point combinator (Y), memo is a memoization function for functions of a single argument that recurse using an external name, and fixmemo is a merging of the two into a memoizing fix point combinator for functions of …
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| /* Some experiments for memoization functions on Fibonacci sequence. */ | |
| /* This uses the SpiderMonkey JS Shell functions print and dateNow for its output. */ | |
| let | |
| fix= | |
| f=>( | |
| (f=>f(f)) | |
| (g=>f((...a)=>g(g)(...a)))), | |
| memo= | |
| f=>( | |
| (map=>a=>( | |
| map.has(a) | |
| ?map.get(a) | |
| :map.set(a,f(a)).get(a))) | |
| (new Map)), | |
| fixmemo = | |
| f=>( | |
| (map=>fix( | |
| z=>a=>( | |
| map.has(a) | |
| ?map.get(a) | |
| :map.set(a,f(b=>z(b))(a)).get(a)))) | |
| (new Map)), | |
| memocurried= | |
| ((m=>fix( | |
| z=>f=>l=>( | |
| m((0<l?z(f)(l-1):f))))) | |
| (memo)), | |
| time= | |
| f=>( | |
| (n=>[f(),dateNow()-n]) | |
| (dateNow())), | |
| memfib= | |
| memo( | |
| n=>( | |
| n===0 | |
| ?0 | |
| :n===1 | |
| ?1 | |
| :memfib(n-1)+memfib(n-2))), | |
| memofib=( | |
| memocurried( | |
| n=>( | |
| n===0 | |
| ?0 | |
| :n===1 | |
| ?1 | |
| :(memofib(n-1)+memofib(n-2)))) | |
| (1)), | |
| fmfib= | |
| fixmemo( | |
| fib=>n=>( | |
| n===0 | |
| ?0 | |
| :n===1 | |
| ?1 | |
| :fib(n-1)+fib(n-2))), | |
| Fibonacci= | |
| fix( | |
| fib=>n=>( | |
| n===0 | |
| ?0 | |
| :n===1 | |
| ?1 | |
| :fib(n-1)+fib(n-2))), | |
| recfromcorec=( | |
| (f,...a) => fix( | |
| z => n => ( | |
| a.length > n | |
| ? a[n] | |
| : (a[a.length]=f(),z(n))))), | |
| cofibs= | |
| (m=0,n=1,o)=>( | |
| ()=>( | |
| [m,n,o]=[n,m+n,m], | |
| o)), | |
| fibco=recfromcorec(cofibs()), | |
| fdfib=( | |
| (f=>n=>( | |
| n<0 | |
| ?(()=>{throw 'Fibonacci takes a positive integral argument.'})() | |
| :f(n)[0])) | |
| (fix( | |
| z=>n=>( | |
| n===0 | |
| ?[0,1] | |
| :( | |
| (([a,b])=>( | |
| ((c,d)=>( | |
| n%2===0 | |
| ?[c,d] | |
| :[d,c+d])) | |
| (a*(b*2-a),a*a+b*b))) | |
| (z(Math.floor(n/2)))))))) | |
| ; | |
| print( | |
| 'Unmemoized: fib(0x20):\n\t', | |
| time(()=>Fibonacci(0x20)),'\n\t', | |
| time(()=>Fibonacci(0x20))); | |
| print( | |
| 'Memoized: fib(0x20):\n\t', | |
| time(()=>memfib(0x20)),'\n\t', | |
| time(()=>memfib(0x20))); | |
| print( | |
| 'Curry memoized: fib(0x20):\n\t', | |
| time(()=>memofib(0x20)),'\n\t', | |
| time(()=>memofib(0x20))); | |
| print( | |
| 'Fixmemoized: fib(0x20):\n\t', | |
| time(()=>fmfib(0x20)),'\n\t', | |
| time(()=>fmfib(0x20))); | |
| print( | |
| 'Corecursion: fib(0x20):\n\t', | |
| time(()=>fibco(0x20)),'\n\t', | |
| time(()=>fibco(0x20))); | |
| print( | |
| 'Fast Doubling Fibbonacci algorithm: fib(0x20):\n\t', | |
| time(()=>fdfib(0x20)),'\n\t', | |
| time(()=>fdfib(0x20))); | |
| print( | |
| 'Memoized: fib(0x40):\n\t', | |
| time(()=>memfib(0x40)),'\n\t', | |
| time(()=>memfib(0x40))); | |
| print( | |
| 'Curry memoized: fib(0x40):\n\t', | |
| time(()=>memofib(0x40)),'\n\t', | |
| time(()=>memofib(0x40))); | |
| print( | |
| 'Fixmemoized: fib(0x40):\n\t', | |
| time(()=>fmfib(0x40)),'\n\t', | |
| time(()=>fmfib(0x40))); | |
| print( | |
| 'Corecursion: fib(0x40):\n\t', | |
| time(()=>fibco(0x40)),'\n\t', | |
| time(()=>fibco(0x40))); | |
| print( | |
| 'Fast Doubling Fibbonacci algorithm: fib(0x40):\n\t', | |
| time(()=>fdfib(0x40)),'\n\t', | |
| time(()=>fdfib(0x40))); | |
| print( | |
| 'Memoized: fib(0x400):\n\t', | |
| time(()=>memfib(0x400)),'\n\t', | |
| time(()=>memfib(0x400))); | |
| print( | |
| 'Curry memoized: fib(0x400):\n\t', | |
| time(()=>memofib(0x400)),'\n\t', | |
| time(()=>memofib(0x400))); | |
| print( | |
| 'Fixmemoized: fib(0x400):\n\t', | |
| time(()=>fmfib(0x400)),'\n\t', | |
| time(()=>fmfib(0x400))); | |
| print( | |
| 'Corecursion: fib(0x400):\n\t', | |
| time(()=>fibco(0x400)),'\n\t', | |
| time(()=>fibco(0x400))); | |
| print( | |
| 'Fast Doubling Fibbonacci algorithm: fib(0x400):\n\t', | |
| time(()=>fdfib(0x400)),'\n\t', | |
| time(()=>fdfib(0x400))); | |
| print( | |
| 'Memoized: fib(0x800):\n\t', | |
| time(()=>memfib(0x800)),'\n\t', | |
| time(()=>memfib(0x800))); | |
| print( | |
| 'Curry memoized: fib(0x800):\n\t', | |
| time(()=>memofib(0x800)),'\n\t', | |
| time(()=>memofib(0x800))); | |
| print( | |
| 'Fixmemoized: fib(0x800):\n\t', | |
| time(()=>fmfib(0x800)),'\n\t', | |
| time(()=>fmfib(0x800))); | |
| print( | |
| 'Corecursion: fib(0x800):\n\t', | |
| time(()=>fibco(0x800)),'\n\t', | |
| time(()=>fibco(0x800))); | |
| print( | |
| 'Fast Doubling Fibbonacci algorithm: fib(0x800):\n\t', | |
| time(()=>fdfib(0x800)),'\n\t', | |
| time(()=>fdfib(0x800))); | |
| print( | |
| 'Memoized: fib(0x1000):\n\t', | |
| time(()=>memfib(0x1000)),'\n\t', | |
| time(()=>memfib(0x1000))); | |
| print( | |
| 'Curry memoized: fib(0x1000):\n\t', | |
| time(()=>memofib(0x1000)),'\n\t', | |
| time(()=>memofib(0x1000))) | |
| print( | |
| 'Fixmemoized: fib(0x1000):\n\t', | |
| time(()=>fmfib(0x1000)),'\n\t', | |
| time(()=>fmfib(0x1000))); | |
| print( | |
| 'Corecursion: fib(0x1000):\n\t', | |
| time(()=>fibco(0x1000)),'\n\t', | |
| time(()=>fibco(0x1000))); | |
| print( | |
| 'Fast Doubling Fibbonacci algorithm: fib(0x1000):\n\t', | |
| time(()=>fdfib(0x1000)),'\n\t', | |
| time(()=>fdfib(0x1000))); | |
| /* RESULTS: | |
| Unmemoized: fib(0x20): | |
| 2178309,13702.607177734375 | |
| 2178309,14864.7529296875 | |
| Memoized: fib(0x20): | |
| 2178309,0.52783203125 | |
| 2178309,0.008056640625 | |
| Curry memoized: fib(0x20): | |
| 2178309,0.2958984375 | |
| 2178309,0.0048828125 | |
| Fixmemoized: fib(0x20): | |
| 2178309,36.14892578125 | |
| 2178309,0.0048828125 | |
| Corecursion: fib(0x20): | |
| 2178309,0.6240234375 | |
| 2178309,0.0048828125 | |
| Fast Doubling Fibbonacci algorithm: fib(0x20): | |
| 2178309,0.281982421875 | |
| 2178309,0.575927734375 | |
| Memoized: fib(0x40): | |
| 10610209857723,0.310791015625 | |
| 10610209857723,0.005859375 | |
| Curry memoized: fib(0x40): | |
| 10610209857723,0.154052734375 | |
| 10610209857723,0.0048828125 | |
| Fixmemoized: fib(0x40): | |
| 10610209857723,0.380126953125 | |
| 10610209857723,0.076171875 | |
| Corecursion: fib(0x40): | |
| 10610209857723,0.27685546875 | |
| 10610209857723,0.006103515625 | |
| Fast Doubling Fibbonacci algorithm: fib(0x40): | |
| 10610209857723,0.14306640625 | |
| 10610209857723,0.078125 | |
| Memoized: fib(0x400): | |
| 4.506699633677816e+213,2.569091796875 | |
| 4.506699633677816e+213,0.015869140625 | |
| Curry memoized: fib(0x400): | |
| 4.506699633677816e+213,0.67919921875 | |
| 4.506699633677816e+213,0.008056640625 | |
| Fixmemoized: fib(0x400): | |
| 4.506699633677816e+213,12.121826171875 | |
| 4.506699633677816e+213,0.01611328125 | |
| Corecursion: fib(0x400): | |
| 4.506699633677816e+213,12.364990234375 | |
| 4.506699633677816e+213,0.010986328125 | |
| Fast Doubling Fibbonacci algorithm: fib(0x400): | |
| 4.506699633677817e+213,0.1259765625 | |
| 4.506699633677817e+213,0.136962890625 | |
| Memoized: fib(0x800): | |
| Infinity,0.322998046875 | |
| Infinity,0.00390625 | |
| Curry memoized: fib(0x800): | |
| Infinity,0.906982421875 | |
| Infinity,0.01318359375 | |
| Fixmemoized: fib(0x800): | |
| Infinity,6.6689453125 | |
| Infinity,0.011962890625 | |
| Corecursion: fib(0x800): | |
| Infinity,1.593994140625 | |
| Infinity,0.0068359375 | |
| Fast Doubling Fibbonacci algorithm: fib(0x800): | |
| Infinity,0.0869140625 | |
| Infinity,0.06689453125 | |
| Memoized: fib(0x1000): | |
| Infinity,0.658935546875 | |
| Infinity,0.006103515625 | |
| Curry memoized: fib(0x1000): | |
| Infinity,1.137939453125 | |
| Infinity,0.006103515625 | |
| Fixmemoized: fib(0x1000): | |
| Infinity,11.991943359375 | |
| Infinity,0.012939453125 | |
| Corecursion: fib(0x1000): | |
| Infinity,3.60107421875 | |
| Infinity,0.012939453125 | |
| Fast Doubling Fibbonacci algorithm: fib(0x1000): | |
| NaN,0.10205078125 | |
| NaN,0.0791015625 | |
| */ |
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