I have a system that generates decision trees and converts them into nested Common Lisp if statements with predicates that check if a variable value is >= or <= a given integer e.g.
(LAMBDA (V1 V2)
(IF (>= V1 2)
(IF (<= V1 3)
(IF (<= V2 3)
(IF (>= V2 2) 16 (IF (>= V2 1) 6 0))
(IF (<= V2 4) 10 0))
(IF (<= V1 4)
(IF (>= V2 1) (IF (<= V2 3) 6 0) 0)
0))
(IF (>= V1 1)
(IF (>= V2 2) (IF (<= V2 4) 10 0) 0)
0)))
I then use eval to compile the Lisp code, producing functions that run much faster than interpreting the original decision tree. This compilation step takes surprisingly long, though: a function with 5000 nested ifs takes over a minute to compile (in Clozure Common Lisp on a powerbook), even though generating the if statement took about 100 milliseconds. Why does such a simple structure take so long? Is there anything I can do to substantially speed it up, some declaration maybe? I'd greatly appreciate any pointers you can offer.
The actual portable function to compile functions is called COMPILE.
You can tell the Common Lisp compiler to invest less work via low optimize qualities for speed, space, debug and compilation-speed - whether this has any influence depends on the implementation.
The Clozure CL compiler is usually not the brightest one, but relatively fast. Generally I think the compiler maintainer might be able to give you more hints how to speed up compilation. Generally I would look for three
tell the compiler to do less work: no type inference, no code optimization, no generation of debug information, no space saving effort, ...
if it is necessary tell the compiler things which it would have to infer - like instead of type inference by the compiler, declare all the types during code generation. But that would mean that you actually need some advantage from type declarations like increased runtime safety or code optimizations.
the compiler itself may have speed penalties which may depend on the size of the source code. For example if that is quadratic, the compile time would increase by four if we double the code size. Only the compiler maintainers may know what to do in those cases - maybe they would need to implement more efficient data structures or similar....
The next option is to use a Lisp interpreter. They usually have very little definition time overhead - but the code usually runs much slower at runtime. In some problem domains it may be possible to follow a mixed approach: compile code which changes not very often and interpret code which changes often.
You could certainly (declare (optimize (compilation-speed 3))), and maybe reduce other qualities (see http://clhs.lisp.se/Body/d_optimi.htm#optimize).
However, I'd guess that the slow compilation is caused by the optimizations the compiler makes, so the result seems likely to be not so fast at execution time. But maybe not, you'd have to experiment.
I'd also think about what optimizations you could make yourself using your domain knowledge. Hints for that might also come from analyzing the output of disassemble on your generated functions.
Finally, maybe you can translate your decision trees into lookup tables, if the number of distinct values is not too big.
I've looked through On Lisp, Practical Common Lisp and the SO archives in order to answer this on my own, but those attempts were frustrated by my inability to name the concept I'm interested in. I would be grateful if anyone could just tell me the canonical term for this sort of thing.
This question is probably best explained by an example. Let's say I want to implement Python-style list comprehensions in Common Lisp. In Python I would write:
[x*2 for x in range(1,10) if x > 3]
So I begin by writing down:
(listc (* 2 x) x (range 1 10) (> x 3))
and then defining a macro that transforms the above into the correct comprehension. So far so good.
The interpretation of that expression, however, would be opaque to a reader not already familiar with Python list comprehensions. What I'd really like to be able to write is the following:
(listc (* 2 x) for x in (range 1 10) if (> x 3))
but I haven't been able to track down the Common Lisp terminology for this. It seems that the loop macro does exactly this sort of thing. What is it called, and how can I implement it? I tried macro-expanding a sample loop expression to see how it's put together, but the resulting code was unintelligible. Could anyone guide me in the right direction?
Thanks in advance.
Well, what for does is essentially, that it parses the forms supplied as its body. For example:
(defmacro listc (expr &rest forms)
;;
;;
;; (listc EXP for VAR in GENERATOR [if CONDITION])
;;
;;
(labels ((keyword-p (thing name)
(and (symbolp thing)
(string= name thing))))
(destructuring-bind (for* variable in* generator &rest tail) forms
(unless (and (keyword-p for* "FOR") (keyword-p in* "IN"))
(error "malformed comprehension"))
(let ((guard (if (null tail) 't
(destructuring-bind (if* condition) tail
(unless (keyword-p if* "IF") (error "malformed comprehension"))
condition))))
`(loop
:for ,variable :in ,generator
:when ,guard
:collecting ,expr)))))
(defun range (start end &optional (by 1))
(loop
:for k :upfrom start :below end :by by
:collecting k))
Apart from the hackish "parser" I used, this solution has a disadvantage, which is not easily solved in common lisp, namely the construction of the intermediate lists, if you want to chain your comprehensions:
(listc x for x in (listc ...) if (evenp x))
Since there is no moral equivalent of yield in common lisp, it is hard to create a facility, which does not require intermediate results to be fully materialized. One way out of this might be to encode the knowledge of possible "generator" forms in the expander of listc, so the expander can optimize/inline the generation of the base sequence without having to construct the entire intermediate list at run-time.
Another way might be to introduce "lazy lists" (link points to scheme, since there is no equivalent facility in common lisp -- you had to build that first, though it's not particularily hard).
Also, you can always have a look at other people's code, in particular, if they tries to solve the same or a similar problem, for example:
Iterate
Loop in SBCL
Pipes (which does the lazy list thing)
Macros are code transformers.
There are several ways of implementing the syntax of a macro:
destructuring
Common Lisp provides a macro argument list which also provides a form of destructuring. When a macro is used, the source form is destructured according to the argument list.
This limits how macro syntax looks like, but for many uses of Macros provides enough machinery.
See Macro Lambda Lists in Common Lisp.
parsing
Common Lisp also gives the macro the access to the whole macro call form. The macro then is responsible for parsing the form. The parser needs to be provided by the macro author or is part of the macro implementation done by the author.
An example would be an INFIX macro:
(infix (2 + x) * (3 + sin (y)))
The macro implementation needs to implement an infix parser and return a prefix expression:
(* (+ 2 x) (+ 3 (sin y)))
rule-based
Some Lisps provide syntax rules, which are matched against the macro call form. For a matching syntax rule the corresponding transformer will be used to create the new source form. One can easily implement this in Common Lisp, but by default it is not a provided mechanism in Common Lisp.
See syntax case in Scheme.
LOOP
For the implementation of a LOOP-like syntax one needs to write a parser which is called in the macro to parse the source expression. Note that the parser does not work on text, but on interned Lisp data.
In the past (1970s) this has been used in Interlisp in the so-called 'Conversational Lisp', which is a Lisp syntax with a more natural language like surface. Iteration was a part of this and the iteration idea has then brought to other Lisps (like Maclisp's LOOP, from where it then was brought to Common Lisp).
See the PDF on 'Conversational Lisp' by Warren Teitelmann from the 1970s.
The syntax for the LOOP macro is a bit complicated and it is not easy to see the boundaries between individual sub-statements.
See the extended syntax for LOOP in Common Lisp.
(loop for i from 0 when (oddp i) collect i)
same as:
(loop
for i from 0
when (oddp i)
collect i)
One problem that the LOOP macro has is that the symbols like FOR, FROM, WHEN and COLLECT are not the same from the "COMMON-LISP" package (a namespace). When I'm now using LOOP in source code using a different package (namespace), then this will lead to new symbols in this source namespace. For that reason some like to write:
(loop
:for i :from 0
:when (oddp i)
:collect i)
In above code the identifiers for the LOOP relevant symbols are in the KEYWORD namespace.
To make both parsing and reading easier it has been proposed to bring parentheses back.
An example for such a macro usage might look like this:
(iter (for i from 0) (when (oddp i) (collect i)))
same as:
(iter
(for i from 0)
(when (oddp i)
(collect i)))
In above version it is easier to find the sub-expressions and to traverse them.
The ITERATE macro for Common Lisp uses this approach.
But in both examples, one needs to traverse the source code with custom code.
To complement Dirk's answer a little:
Writing your own macros for this is entirely doable, and perhaps a nice exercise.
However there are several facilities for this kind of thing (albeit in a lisp-idiomatic way) out there of high quality, such as
Loop
Iterate
Series
Loop is very expressive, but has a syntax not resembling the rest of common lisp. Some editors don't like it and will indent poorly. However loop is defined in the standard. Usually it's not possible to write extentions to loop.
Iterate is even more expressive, and has a familiar lispy syntax. This doesn't require any special indentation rules, so all editors indenting lisp properly will also indent iterate nicely. Iterate isn't in the standard, so you'll have to get it yourself (use quicklisp).
Series is a framework for working on sequences. In most cases series will make it possible not to store intermediate values.
In one of my first attempts to create functional code, I ran into a performance issue.
I started with a common task - multiply the elements of two arrays and sum up the results:
var first:Array[Float] ...
var second:Array[Float] ...
var sum=0f;
for (ix<-0 until first.length)
sum += first(ix) * second(ix);
Here is how I reformed the work:
sum = first.zip(second).map{ case (a,b) => a*b }.reduceLeft(_+_)
When I benchmarked the two approaches, the second method takes 40 times as long to complete!
Why does the second method take so much longer? How can I reform the work to be both speed efficient and use functional programming style?
The main reasons why these two examples are so different in speed are:
the faster one doesn't use any generics, so it doesn't face boxing/unboxing.
the faster one doesn't create temporary collections and, thus, avoids extra memory copies.
Let's consider the slower one by parts. First:
first.zip(second)
That creates a new array, an array of Tuple2. It will copy all elements from both arrays into Tuple2 objects, and then copy a reference to each of these objects into a third array. Now, notice that Tuple2 is parameterized, so it can't store Float directly. Instead, new instances of java.lang.Float are created for each number, the numbers are stored in them, and then a reference for each of them is stored into the Tuple2.
map{ case (a,b) => a*b }
Now a fourth array is created. To compute the values of these elements, it needs to read the reference to the tuple from the third array, read the reference to the java.lang.Float stored in them, read the numbers, multiply, create a new java.lang.Float to store the result, and then pass this reference back, which will be de-referenced again to be stored in the array (arrays are not type-erased).
We are not finished, though. Here's the next part:
reduceLeft(_+_)
That one is relatively harmless, except that it still do boxing/unboxing and java.lang.Float creation at iteration, since reduceLeft receives a Function2, which is parameterized.
Scala 2.8 introduces a feature called specialization which will get rid of a lot of these boxing/unboxing. But let's consider alternative faster versions. We could, for instance, do map and reduceLeft in a single step:
sum = first.zip(second).foldLeft(0f) { case (a, (b, c)) => a + b * c }
We could use view (Scala 2.8) or projection (Scala 2.7) to avoid creating intermediary collections altogether:
sum = first.view.zip(second).map{ case (a,b) => a*b }.reduceLeft(_+_)
This last one doesn't save much, actually, so I think the non-strictness if being "lost" pretty fast (ie, one of these methods is strict even in a view). There's also an alternative way of zipping that is non-strict (ie, avoids some intermediary results) by default:
sum = (first,second).zipped.map{ case (a,b) => a*b }.reduceLeft(_+_)
This gives much better result that the former. Better than the foldLeft one, though not by much. Unfortunately, we can't combined zipped with foldLeft because the former doesn't support the latter.
The last one is the fastest I could get. Faster than that, only with specialization. Now, Function2 happens to be specialized, but for Int, Long and Double. The other primitives were left out, as specialization increases code size rather dramatically for each primitive. On my tests, though Double is actually taking longer. That might be a result of it being twice the size, or it might be something I'm doing wrong.
So, in the end, the problem is a combination of factors, including producing intermediary copies of elements, and the way Java (JVM) handles primitives and generics. A similar code in Haskell using supercompilation would be equal to anything short of assembler. On the JVM, you have to be aware of the trade-offs and be prepared to optimize critical code.
I did some variations of this with Scala 2.8. The loop version is as you write but the
functional version is slightly different:
(xs, ys).zipped map (_ * _) reduceLeft(_ + _)
I ran with Double instead of Float, because currently specialization only kicks in for Double. I then tested with arrays and vectors as the carrier type. Furthermore, I tested Boxed variants which work on java.lang.Double's instead of primitive Doubles to measure
the effect of primitive type boxing and unboxing. Here is what I got (running Java 1.6_10 server VM, Scala 2.8 RC1, 5 runs per test).
loopArray 461 437 436 437 435
reduceArray 6573 6544 6718 6828 6554
loopVector 5877 5773 5775 5791 5657
reduceVector 5064 4880 4844 4828 4926
loopArrayBoxed 2627 2551 2569 2537 2546
reduceArrayBoxed 4809 4434 4496 4434 4365
loopVectorBoxed 7577 7450 7456 7463 7432
reduceVectorBoxed 5116 4903 5006 4957 5122
The first thing to notice is that by far the biggest difference is between primitive array loops and primitive array functional reduce. It's about a factor of 15 instead of the 40 you have seen, which reflects improvements in Scala 2.8 over 2.7. Still, primitive array loops are the fastest of all tests whereas primitive array reduces are the slowest. The reason is that primitive Java arrays and generic operations are just not a very good fit. Accessing elements of primitive Java arrays from generic functions requires a lot of boxing/unboxing and sometimes even requires reflection. Future versions of Scala will specialize the Array class and then we should see some improvement. But right now that's what it is.
If you go from arrays to vectors, you notice several things. First, the reduce version is now faster than the imperative loop! This is because vector reduce can make use of efficient bulk operations. Second, vector reduce is faster than array reduce, which illustrates the inherent overhead that arrays of primitive types pose for generic higher-order functions.
If you eliminate the overhead of boxing/unboxing by working only with boxed java.lang.Double values, the picture changes. Now reduce over arrays is a bit less than 2 times slower than looping, instead of the 15 times difference before. That more closely approximates the inherent overhead of the three loops with intermediate data structures instead of the fused loop of the imperative version. Looping over vectors is now by far the slowest solution, whereas reducing over vectors is a little bit slower than reducing over arrays.
So the overall answer is: it depends. If you have tight loops over arrays of primitive values, nothing beats an imperative loop. And there's no problem writing the loops because they are neither longer nor less comprehensible than the functional versions. In all other situations, the FP solution looks competitive.
This is a microbenchmark, and it depends on how the compiler optimizes you code. You have 3 loops composed here,
zip . map . fold
Now, I'm fairly sure the Scala compiler cannot fuse those three loops into a single loop, and the underlying data type is strict, so each (.) corresponds to an intermediate array being created. The imperative/mutable solution would reuse the buffer each time, avoiding copies.
Now, an understanding of what composing those three functions means is key to understanding performance in a functional programming language -- and indeed, in Haskell, those three loops will be optimized into a single loop that reuses an underlying buffer -- but Scala cannot do that.
There are benefits to sticking to the combinator approach, however -- by distinguishing those three functions, it will be easier to parallelize the code (replace map with parMap etc). In fact, given the right array type, (such as a parallel array) a sufficiently smart compiler will be able to automatically parallelize your code, yielding more performance wins.
So, in summary:
naive translations may have unexpected copies and inefficiences
clever FP compilers remove this overhead (but Scala can't yet)
sticking to the high level approach pays off if you want to retarget your code, e.g. to parallelize it
Don Stewart has a fine answer, but it might not be obvious how going from one loop to three creates a factor of 40 slowdown. I'll add to his answer that Scala compiles to JVM bytecodes, and not only does the Scala compiler not fuse the three loops into one, but the Scala compiler is almost certainly allocating all the intermediate arrays. Notoriously, implementations of the JVM are not designed to handle the allocation rates required by functional languages. Allocation is a significant cost in functional programs, and that's one the loop-fusion transformations that Don Stewart and his colleagues have implemented for Haskell are so powerful: they eliminate lots of allocations. When you don't have those transformations, plus you're using an expensive allocator such as is found on a typical JVM, that's where the big slowdown comes from.
Scala is a great vehicle for experimenting with the expressive power of an unusual mix of language ideas: classes, mixins, modules, functions, and so on. But it's a relatively young research language, and it runs on the JVM, so it's unreasonable to expect great performance except on the kind of code that JVMs are good at. If you want to experiment with the mix of language ideas that Scala offers, great—it's a really interesting design—but don't expect the same performance on pure functional code that you'd get with a mature compiler for a functional language, like GHC or MLton.
Is scala functional programming slower than traditional coding?
Not necessarily. Stuff to do with first-class functions, pattern matching, and currying need not be especially slow. But with Scala, more than with other implementations of other functional languages, you really have to watch out for allocations—they can be very expensive.
The Scala collections library is fully generic, and the operations provided are chosen for maximum capability, not maximum speed. So, yes, if you use a functional paradigm with Scala without paying attention (especially if you are using primitive data types), your code will take longer to run (in most cases) than if you use an imperative/iterative paradigm without paying attention.
That said, you can easily create non-generic functional operations that perform quickly for your desired task. In the case of working with pairs of floats, we might do the following:
class FastFloatOps(a: Array[Float]) {
def fastMapOnto(f: Float => Float) = {
var i = 0
while (i < a.length) { a(i) = f(a(i)); i += 1 }
this
}
def fastMapWith(b: Array[Float])(f: (Float,Float) => Float) = {
val len = a.length min b.length
val c = new Array[Float](len)
var i = 0
while (i < len) { c(i) = f(a(i),b(i)); i += 1 }
c
}
def fastReduce(f: (Float,Float) => Float) = {
if (a.length==0) Float.NaN
else {
var r = a(0)
var i = 1
while (i < a.length) { r = f(r,a(i)); i += 1 }
r
}
}
}
implicit def farray2fastfarray(a: Array[Float]) = new FastFloatOps(a)
and then these operations will be much faster. (Faster still if you use Double and 2.8.RC1, because then the functions (Double,Double)=>Double will be specialized, not generic; if you're using something earlier, you can create your own abstract class F { def f(a: Float) : Float } and then call with new F { def f(a: Float) = a*a } instead of (a: Float) => a*a.)
Anyway, the point is that it's not the functional style that makes functional coding in Scala slow, it's that the library is designed with maximum power/flexibility in mind, not maximum speed. This is sensible, since each person's speed requirements are typically subtly different, so it's hard to cover everyone supremely well. But if it's something you're doing more than just a little, you can write your own stuff where the performance penalty for a functional style is extremely small.
I am not an expert Scala programmer, so there is probably a more efficient method, but what about something like this. This can be tail call optimized, so performance should be OK.
def multiply_and_sum(l1:List[Int], l2:List[Int], sum:Int):Int = {
if (l1 != Nil && l2 != Nil) {
multiply_and_sum(l1.tail, l2.tail, sum + (l1.head * l2.head))
}
else {
sum
}
}
val first = Array(1,2,3,4,5)
val second = Array(6,7,8,9,10)
multiply_and_sum(first.toList, second.toList, 0) //Returns: 130
To answer the question in the title: Simple functional constructs may be slower than imperative on the JVM.
But, if we consider only simple constructs, then we might as well throw out all modern languages and stick with C or assembler. If you look a the programming language shootout, C always wins.
So why choose a modern language? Because it lets you express a cleaner design. Cleaner design leads to performance gains in the overall operation of the application. Even if some low-level methods can be slower. One of my favorite examples is the performance of BuildR vs. Maven. BuildR is written in Ruby, an interpreted, slow, language. Maven is written in Java. A build in BuildR is twice as fast as Maven. This is due mostly to the design of BuildR which is lightweight compared with that of Maven.
Your functional solution is slow because it is generating unnecessary temporary data structures. Removing these is known as deforesting and it is easily done in strict functional languages by rolling your anonymous functions into a single anonymous function and using a single aggregator. For example, your solution written in F# using zip, map and reduce:
let dot xs ys = Array.zip xs ys |> Array.map (fun (x, y) -> x * y) -> Array.reduce ( * )
may be rewritten using fold2 so as to avoid all temporary data structures:
let dot xs ys = Array.fold2 (fun t x y -> t + x * y) 0.0 xs ys
This is a lot faster and the same transformation can be done in Scala and other strict functional languages. In F#, you can also define the fold2 as inline in order to have the higher-order function inlined with its functional argument whereupon you recover the optimal performance of the imperative loop.
Here is dbyrnes solution with arrays (assuming Arrays are to be used) and just iterating over the index:
def multiplyAndSum (l1: Array[Int], l2: Array[Int]) : Int =
{
def productSum (idx: Int, sum: Int) : Int =
if (idx < l1.length)
productSum (idx + 1, sum + (l1(idx) * l2(idx))) else
sum
if (l2.length == l1.length)
productSum (0, 0) else
error ("lengths don't fit " + l1.length + " != " + l2.length)
}
val first = (1 to 500).map (_ * 1.1) toArray
val second = (11 to 510).map (_ * 1.2) toArray
def loopi (n: Int) = (1 to n).foreach (dummy => multiplyAndSum (first, second))
println (timed (loopi (100*1000)))
That needs about 1/40 of the time of the list-approach. I don't have 2.8 installed, so you have to test #tailrec yourself. :)
I have a function that takes a parameter and produces a result. Unfortunately, it takes quite long for the function to produce the result. The function is being called quite often with the same input, that's why it would be convenient if I could cache the results. Something like
let cachedFunction = createCache slowFunction
in (cachedFunction 3.1) + (cachedFunction 4.2) + (cachedFunction 3.1)
I was looking into Data.Array and although the array is lazy, I need to initialize it with a list of pairs (using listArray) - which is impractical . If the 'key' is e.g. the 'Double' type, I cannot initialize it at all, and even if I can theoretically assign an Integer to every possible input, I have several tens of thousands possible inputs and I only actually use a handful. I would need to initialize the array (or, preferably a hash table, as only a handful of resutls will be used) using a function instead of a list.
Update: I am reading the memoization articles and as far as I understand it the MemoTrie could work the way I want. Maybe. Could somebody try to produce the 'cachedFunction'? Prefereably for a slow function that takes 2 Double arguments? Or, alternatively, that takes one Int argument in a domain of ~ [0..1 billion] that wouldn't eat all memory?
Well, there's Data.HashTable. Hash tables don't tend to play nicely with immutable data and referential transparency, though, so I don't think it sees a lot of use.
For a small number of values, stashing them in a search tree (such as Data.Map) would probably be fast enough. If you can put up with doing some mangling of your Doubles, a more robust solution would be to use a trie-like structure, such as Data.IntMap; these have lookup times proportional primarily to key length, and roughly constant in collection size. If Int is too limiting, you can dig around on Hackage to find trie libraries that are more flexible in the type of key used.
As for how to cache the results, I think what you want is usually called "memoization". If you want to compute and memoize results on demand, the gist of the technique is to define an indexed data structure containing all possible results, in such a way that when you ask for a specific result it forces only the computations needed to get the answer you want. Common examples usually involve indexing into a list, but the same principle should apply for any non-strict data structure. As a rule of thumb, non-function values (including infinite recursive data structures) will often be cached by the runtime, but not function results, so the trick is to wrap all of your computations inside a top-level definition that doesn't depend on any arguments.
Edit: MemoTrie example ahoy!
This is a quick and dirty proof of concept; better approaches may exist.
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
import Data.MemoTrie
import Data.Binary
import Data.ByteString.Lazy hiding (map)
mangle :: Double -> [Int]
mangle = map fromIntegral . unpack . encode
unmangle :: [Int] -> Double
unmangle = decode . pack . map fromIntegral
instance HasTrie Double where
data Double :->: a = DoubleTrie ([Int] :->: a)
trie f = DoubleTrie $ trie $ f . unmangle
untrie (DoubleTrie t) = untrie t . mangle
slow x
| x < 1 = 1
| otherwise = slow (x / 2) + slow (x / 3)
memoSlow :: Double -> Integer
memoSlow = memo slow
Do note the GHC extensions used by the MemoTrie package; hopefully that isn't a problem. Load it up in GHCi and try calling slow vs. memoSlow with something like (10^6) or (10^7) to see it in action.
Generalizing this to functions taking multiple arguments or whatnot should be fairly straightforward. For further details on using MemoTrie, you might find this blog post by its author helpful.
See memoization
There are a number of tools in GHC's runtime system explicitly to support memoization.
Unfortunately, memoization isn't really a one-size fits all affair, so there are several different approaches that we need to support in order to cope with different user needs.
You may find the original 1999 writeup useful as it includes several implementations as examples:
Stretching the Storage Manager: Weak Pointers and Stable Names in Haskell by Simon Peyton Jones, Simon Marlow, and Conal Elliott
I will add my own solution, which seems to be quite slow as well. First parameter is a function that returns Int32 - which is unique identifier of the parameter. If you want to uniquely identify it by different means (e.g. by 'id'), you have to change the second parameter in H.new to a different hash function. I will try to find out how to use Data.Map and test if I get faster results.
import qualified Data.HashTable as H
import Data.Int
import System.IO.Unsafe
cache :: (a -> Int32) -> (a -> b) -> (a -> b)
cache ident f = unsafePerformIO $ createfunc
where
createfunc = do
storage <- H.new (==) id
return (doit storage)
doit storage = unsafePerformIO . comp
where
comp x = do
look <- H.lookup storage (ident x)
case look of
Just res -> return res
Nothing -> do
result <- return (f x)
H.insert storage (ident x) result
return result
You can write the slow function as a higher order function, returning a function itself. Thus you can do all the preprocessing inside the slow function and the part that is different in each computation in the returned (hopefully fast) function. An example could look like this:
(SML code, but the idea should be clear)
fun computeComplicatedThing (x:float) (y:float) = (* ... some very complicated computation *)
fun computeComplicatedThingFast = computeComplicatedThing 3.14 (* provide x, do computation that needs only x *)
val result1 = computeComplicatedThingFast 2.71 (* provide y, do computation that needs x and y *)
val result2 = computeComplicatedThingFast 2.81
val result3 = computeComplicatedThingFast 2.91
I have several tens of thousands possible inputs and I only actually use a handful. I would need to initialize the array ... using a function instead of a list.
I'd go with listArray (start, end) (map func [start..end])
func doesn't really get called above. Haskell is lazy and creates thunks which will be evaluated when the value is actually required.
When using a normal array you always need to initialize its values. So the work required for creating these thunks is necessary anyhow.
Several tens of thousands is far from a lot. If you'd have trillions then I would suggest to use a hash table yada yada
I don't know haskell specifically, but how about keeping existing answers in some hashed datastructure (might be called a dictionary, or hashmap)? You can wrap your slow function in another function that first check the map and only calls the slow function if it hasn't found an answer.
You could make it fancy by limiting the size of the map to a certain size and when it reaches that, throwing out the least recently used entry. For this you would additionally need to keep a map of key-to-timestamp mappings.
I'm fairly new to Scheme and am attempting to learn it on my own from scratch. I'm stuck on the syntax of this problem. I know that if I want to find out if a number is a power of 2, in C for instance, I would simply do:
return (x & (x - 1)) == 0;
which would return true or false. How would I be able to convert this into a couple simple lines in Scheme?
I'll give you a hint since you're trying to learn the language.
Scheme has a function called (bitwise-and ...) which is equivalent to the & operator in C (there is also (bitwise-xor ...), (bitwise-not ..), etc., which do the expected thing).
(Here is the documentation of the (bitwise-and ...) function)
Given that, would you be able to translate what you've written in your question into Scheme code?
N.B: For a problem like this, you really don't need to resort to bitwise operations when using Scheme. Realistically, you should be writing a (possibly probably tail) recursive function that will compute this for you.
You can do this using a built in bitwise operator.
(define (pow2? x)
(= (bitwise-and x (- x 1))
0))
Scheme also has biwise operators.
But if you really want to develop your scheme skills, you should write a function that decides if an integer is a power of 2 by recursively dividing it by 2 until you are left with either 2 or with an odd number. This would be very inefficient, but really cool nonetheless.