I was running my code through Clippy and it suggested changing the following:
const SPECIAL_VALUE: u8 = 0; // May change eventually.
pub fn version1(value: u8) -> bool {
(value >= 1 && value <= 9) || value == SPECIAL_VALUE
}
Into
pub fn version2(value: u8) -> bool {
(1..=9).contains(&value) || value == SPECIAL_VALUE
}
Since it is more readable. Unfortunately the resulting assembly output is twice as long, even with optimization level 3. Manually inlining it (2-nestings down), gives almost the same code as version1 and is as efficient.
pub fn manually_inlined(value: u8) -> bool {
(1 <= value && value <= 9) || value == SPECIAL_VALUE
}
If I remove the || value == SPECIAL_VALUE they all resolve with the same (though with 1 more instruction added to decrement the parameter value before a compare). Also if I change SPECIAL_VALUE to something not adjacent to the range they all resolve to same assembly code as version2, which is the reason why I kept it 0 unless I eventually have to change it.
I have a link to Godbolt with the code here: https://rust.godbolt.org/z/bMYzfcYob
Why is the compiler failing to properly inline/optimize version2? Is it an "optimization bug"? Or am I misunderstanding some semantics of Rust, maybe something with the borrowing prevents the optimization, but can't the compiler assume no mutation of value due to the aliasing and referencing rules?
Trying to do the same in C++ suggest, yields the worse option in both cases (https://godbolt.org/z/zahfz65W3)
Edit: Changing the compiler for my C++ version to GCC makes it optimized in both cases.
This was indeed a missed optimization opportunity that has now been corrected in LLVM. https://github.com/rust-lang/rust/issues/90609#issuecomment-1046037263 .
Taking this simple comparison loopValue == "Firstname", is the following statement true?
If the internal operand inspecting the first char does not match the compared string, it will early abort
So taking the rawer form loopValue and "Firstname" are both []byte. And it would walk the array kind of like so as callback loop for truth:
someInspectionFunc(loopValue, "Firstname", func(charA, charB) {
return charA == charB
})
... making it keep on going until it bumps false and checks if the number of iterations was equal to both their lengths. Also does it check length first?
if len(loopValue) != len("Firstname") {
return false
}
I can't really find an explanation in the go source-code on GitHub as it's a bit above me.
The reason I'm asking this is because I'm doing big data processing and am benchmarking and doing cpu, memory and allocation pprof to squeeze some more juice out of the process. From that process it kind of made me think how Go (but also just C in general) would do this under the hood. Is this fully on an assembly level or does the comparison already happen in native Go code (kind of like sketched in the snippets above)?
Please let me know if I'm being too vague or if I missed something. Thank you
Update
When I did a firstCharater match in big strings of json, before really comparing I got about 3.7% benchmarking gain on 100k heavy entries:
<some irrelevant inspection code>.. v[0] == firstChar && v == lookFor {
// Match found when it reaches here
}
the code above (especially on long strings) is faster than just going for v == lookFor.
The function is handled in assembly. The amd64 version is:
TEXT runtime·eqstring(SB),NOSPLIT,$0-33
MOVQ s1str+0(FP), SI
MOVQ s2str+16(FP), DI
CMPQ SI, DI
JEQ eq
MOVQ s1len+8(FP), BX
LEAQ v+32(FP), AX
JMP runtime·memeqbody(SB)
eq:
MOVB $1, v+32(FP)
RET
And it's the compiler's job to ensure that the strings are of equal length before that is called. (The runtime·memeqbody function is actually where the optimized memory comparisons happen, but there's probably no need to post the full text here)
The equivalent Go code would be:
func eqstring_generic(s1, s2 string) bool {
if len(s1) != len(s2) {
return false
}
for i := 0; i < len(s1); i++ {
if s1[i] != s2[i] {
return false
}
}
return true
}
When normally using a for-in-loop, the counter (in this case number) is a constant in each iteration:
for number in 1...10 {
// do something
}
This means I cannot change number in the loop:
for number in 1...10 {
if number == 5 {
++number
}
}
// doesn't compile, since the prefix operator '++' can't be performed on the constant 'number'
Is there a way to declare number as a variable, without declaring it before the loop, or using a normal for-loop (with initialization, condition and increment)?
To understand why i can’t be mutable involves knowing what for…in is shorthand for. for i in 0..<10 is expanded by the compiler to the following:
var g = (0..<10).generate()
while let i = g.next() {
// use i
}
Every time around the loop, i is a freshly declared variable, the value of unwrapping the next result from calling next on the generator.
Now, that while can be written like this:
while var i = g.next() {
// here you _can_ increment i:
if i == 5 { ++i }
}
but of course, it wouldn’t help – g.next() is still going to generate a 5 next time around the loop. The increment in the body was pointless.
Presumably for this reason, for…in doesn’t support the same var syntax for declaring it’s loop counter – it would be very confusing if you didn’t realize how it worked.
(unlike with where, where you can see what is going on – the var functionality is occasionally useful, similarly to how func f(var i) can be).
If what you want is to skip certain iterations of the loop, your better bet (without resorting to C-style for or while) is to use a generator that skips the relevant values:
// iterate over every other integer
for i in 0.stride(to: 10, by: 2) { print(i) }
// skip a specific number
for i in (0..<10).filter({ $0 != 5 }) { print(i) }
let a = ["one","two","three","four"]
// ok so this one’s a bit convoluted...
let everyOther = a.enumerate().filter { $0.0 % 2 == 0 }.map { $0.1 }.lazy
for s in everyOther {
print(s)
}
The answer is "no", and that's a good thing. Otherwise, a grossly confusing behavior like this would be possible:
for number in 1...10 {
if number == 5 {
// This does not work
number = 5000
}
println(number)
}
Imagine the confusion of someone looking at the number 5000 in the output of a loop that is supposedly bound to a range of 1 though 10, inclusive.
Moreover, what would Swift pick as the next value of 5000? Should it stop? Should it continue to the next number in the range before the assignment? Should it throw an exception on out-of-range assignment? All three choices have some validity to them, so there is no clear winner.
To avoid situations like that, Swift designers made loop variables in range loops immutable.
Update Swift 5
for var i in 0...10 {
print(i)
i+=1
}
I'm a newbie to this site, so if I mess up any question-asking etiquette here I apologize in advance... Thanks!
This is extremely simplified example code, but I think it shows what I'm talking about: I have a C++ method that makes a call into another method to test a value...
char m_array[MAX]; // class member, MAX is a #define
foo(unsigned int n)
{
if (validNumber(n)) //test n
{
// do stuff
m_array[n-1] = 0;
}
}
where: validNumber(unsigned int val) { return ((val > 0) && (val <= MAX)); }
The irritation I'm having is that PC Lint's Value Tracking seems to ignore the validNumber() call and gives a warning 661 possible access of out-of-bounds pointer (1 beyond end of data) by operator '['
However if I do it like this, Lint is happy:
if ((n > 0) && (n <= MAX)) //test n
...
So, does Lint's Value Tracking just not work if the test is a method call?
Thanks again,
HF
I'd guess that validNumber is defined after foo, but in any case, PC Lint normally makes one pass over the code, and in such cases it doesn't see validNumber as a check for the boundaries for n.
You could try the option -passes(2) or even 3, and see what Lint makes out of it. I think (but didn't try) that Lint would then correctly note that the value for n is within the correct bounds.
I'm writing a function to find triangle numbers and the natural way to write it is recursively:
function triangle (x)
if x == 0 then return 0 end
return x+triangle(x-1)
end
But attempting to calculate the first 100,000 triangle numbers fails with a stack overflow after a while. This is an ideal function to memoize, but I want a solution that will memoize any function I pass to it.
Mathematica has a particularly slick way to do memoization, relying on the fact that hashes and function calls use the same syntax:
triangle[0] = 0;
triangle[x_] := triangle[x] = x + triangle[x-1]
That's it. It works because the rules for pattern-matching function calls are such that it always uses a more specific definition before a more general definition.
Of course, as has been pointed out, this example has a closed-form solution: triangle[x_] := x*(x+1)/2. Fibonacci numbers are the classic example of how adding memoization gives a drastic speedup:
fib[0] = 1;
fib[1] = 1;
fib[n_] := fib[n] = fib[n-1] + fib[n-2]
Although that too has a closed-form equivalent, albeit messier: http://mathworld.wolfram.com/FibonacciNumber.html
I disagree with the person who suggested this was inappropriate for memoization because you could "just use a loop". The point of memoization is that any repeat function calls are O(1) time. That's a lot better than O(n). In fact, you could even concoct a scenario where the memoized implementation has better performance than the closed-form implementation!
You're also asking the wrong question for your original problem ;)
This is a better way for that case:
triangle(n) = n * (n - 1) / 2
Furthermore, supposing the formula didn't have such a neat solution, memoisation would still be a poor approach here. You'd be better off just writing a simple loop in this case. See this answer for a fuller discussion.
I bet something like this should work with variable argument lists in Lua:
local function varg_tostring(...)
local s = select(1, ...)
for n = 2, select('#', ...) do
s = s..","..select(n,...)
end
return s
end
local function memoize(f)
local cache = {}
return function (...)
local al = varg_tostring(...)
if cache[al] then
return cache[al]
else
local y = f(...)
cache[al] = y
return y
end
end
end
You could probably also do something clever with a metatables with __tostring so that the argument list could just be converted with a tostring(). Oh the possibilities.
In C# 3.0 - for recursive functions, you can do something like:
public static class Helpers
{
public static Func<A, R> Memoize<A, R>(this Func<A, Func<A,R>, R> f)
{
var map = new Dictionary<A, R>();
Func<A, R> self = null;
self = (a) =>
{
R value;
if (map.TryGetValue(a, out value))
return value;
value = f(a, self);
map.Add(a, value);
return value;
};
return self;
}
}
Then you can create a memoized Fibonacci function like this:
var memoized_fib = Helpers.Memoize<int, int>((n,fib) => n > 1 ? fib(n - 1) + fib(n - 2) : n);
Console.WriteLine(memoized_fib(40));
In Scala (untested):
def memoize[A, B](f: (A)=>B) = {
var cache = Map[A, B]()
{ x: A =>
if (cache contains x) cache(x) else {
val back = f(x)
cache += (x -> back)
back
}
}
}
Note that this only works for functions of arity 1, but with currying you could make it work. The more subtle problem is that memoize(f) != memoize(f) for any function f. One very sneaky way to fix this would be something like the following:
val correctMem = memoize(memoize _)
I don't think that this will compile, but it does illustrate the idea.
Update: Commenters have pointed out that memoization is a good way to optimize recursion. Admittedly, I hadn't considered this before, since I generally work in a language (C#) where generalized memoization isn't so trivial to build. Take the post below with that grain of salt in mind.
I think Luke likely has the most appropriate solution to this problem, but memoization is not generally the solution to any issue of stack overflow.
Stack overflow usually is caused by recursion going deeper than the platform can handle. Languages sometimes support "tail recursion", which re-uses the context of the current call, rather than creating a new context for the recursive call. But a lot of mainstream languages/platforms don't support this. C# has no inherent support for tail-recursion, for example. The 64-bit version of the .NET JITter can apply it as an optimization at the IL level, which is all but useless if you need to support 32-bit platforms.
If your language doesn't support tail recursion, your best option for avoiding stack overflows is either to convert to an explicit loop (much less elegant, but sometimes necessary), or find a non-iterative algorithm such as Luke provided for this problem.
function memoize (f)
local cache = {}
return function (x)
if cache[x] then
return cache[x]
else
local y = f(x)
cache[x] = y
return y
end
end
end
triangle = memoize(triangle);
Note that to avoid a stack overflow, triangle would still need to be seeded.
Here's something that works without converting the arguments to strings.
The only caveat is that it can't handle a nil argument. But the accepted solution can't distinguish the value nil from the string "nil", so that's probably OK.
local function m(f)
local t = { }
local function mf(x, ...) -- memoized f
assert(x ~= nil, 'nil passed to memoized function')
if select('#', ...) > 0 then
t[x] = t[x] or m(function(...) return f(x, ...) end)
return t[x](...)
else
t[x] = t[x] or f(x)
assert(t[x] ~= nil, 'memoized function returns nil')
return t[x]
end
end
return mf
end
I've been inspired by this question to implement (yet another) flexible memoize function in Lua.
https://github.com/kikito/memoize.lua
Main advantages:
Accepts a variable number of arguments
Doesn't use tostring; instead, it organizes the cache in a tree structure, using the parameters to traverse it.
Works just fine with functions that return multiple values.
Pasting the code here as reference:
local globalCache = {}
local function getFromCache(cache, args)
local node = cache
for i=1, #args do
if not node.children then return {} end
node = node.children[args[i]]
if not node then return {} end
end
return node.results
end
local function insertInCache(cache, args, results)
local arg
local node = cache
for i=1, #args do
arg = args[i]
node.children = node.children or {}
node.children[arg] = node.children[arg] or {}
node = node.children[arg]
end
node.results = results
end
-- public function
local function memoize(f)
globalCache[f] = { results = {} }
return function (...)
local results = getFromCache( globalCache[f], {...} )
if #results == 0 then
results = { f(...) }
insertInCache(globalCache[f], {...}, results)
end
return unpack(results)
end
end
return memoize
Here is a generic C# 3.0 implementation, if it could help :
public static class Memoization
{
public static Func<T, TResult> Memoize<T, TResult>(this Func<T, TResult> function)
{
var cache = new Dictionary<T, TResult>();
var nullCache = default(TResult);
var isNullCacheSet = false;
return parameter =>
{
TResult value;
if (parameter == null && isNullCacheSet)
{
return nullCache;
}
if (parameter == null)
{
nullCache = function(parameter);
isNullCacheSet = true;
return nullCache;
}
if (cache.TryGetValue(parameter, out value))
{
return value;
}
value = function(parameter);
cache.Add(parameter, value);
return value;
};
}
}
(Quoted from a french blog article)
In the vein of posting memoization in different languages, i'd like to respond to #onebyone.livejournal.com with a non-language-changing C++ example.
First, a memoizer for single arg functions:
template <class Result, class Arg, class ResultStore = std::map<Arg, Result> >
class memoizer1{
public:
template <class F>
const Result& operator()(F f, const Arg& a){
typename ResultStore::const_iterator it = memo_.find(a);
if(it == memo_.end()) {
it = memo_.insert(make_pair(a, f(a))).first;
}
return it->second;
}
private:
ResultStore memo_;
};
Just create an instance of the memoizer, feed it your function and argument. Just make sure not to share the same memo between two different functions (but you can share it between different implementations of the same function).
Next, a driver functon, and an implementation. only the driver function need be public
int fib(int); // driver
int fib_(int); // implementation
Implemented:
int fib_(int n){
++total_ops;
if(n == 0 || n == 1)
return 1;
else
return fib(n-1) + fib(n-2);
}
And the driver, to memoize
int fib(int n) {
static memoizer1<int,int> memo;
return memo(fib_, n);
}
Permalink showing output on codepad.org. Number of calls is measured to verify correctness. (insert unit test here...)
This only memoizes one input functions. Generalizing for multiple args or varying arguments left as an exercise for the reader.
In Perl generic memoization is easy to get. The Memoize module is part of the perl core and is highly reliable, flexible, and easy-to-use.
The example from it's manpage:
# This is the documentation for Memoize 1.01
use Memoize;
memoize('slow_function');
slow_function(arguments); # Is faster than it was before
You can add, remove, and customize memoization of functions at run time! You can provide callbacks for custom memento computation.
Memoize.pm even has facilities for making the memento cache persistent, so it does not need to be re-filled on each invocation of your program!
Here's the documentation: http://perldoc.perl.org/5.8.8/Memoize.html
Extending the idea, it's also possible to memoize functions with two input parameters:
function memoize2 (f)
local cache = {}
return function (x, y)
if cache[x..','..y] then
return cache[x..','..y]
else
local z = f(x,y)
cache[x..','..y] = z
return z
end
end
end
Notice that parameter order matters in the caching algorithm, so if parameter order doesn't matter in the functions to be memoized the odds of getting a cache hit would be increased by sorting the parameters before checking the cache.
But it's important to note that some functions can't be profitably memoized. I wrote memoize2 to see if the recursive Euclidean algorithm for finding the greatest common divisor could be sped up.
function gcd (a, b)
if b == 0 then return a end
return gcd(b, a%b)
end
As it turns out, gcd doesn't respond well to memoization. The calculation it does is far less expensive than the caching algorithm. Ever for large numbers, it terminates fairly quickly. After a while, the cache grows very large. This algorithm is probably as fast as it can be.
Recursion isn't necessary. The nth triangle number is n(n-1)/2, so...
public int triangle(final int n){
return n * (n - 1) / 2;
}
Please don't recurse this. Either use the x*(x+1)/2 formula or simply iterate the values and memoize as you go.
int[] memo = new int[n+1];
int sum = 0;
for(int i = 0; i <= n; ++i)
{
sum+=i;
memo[i] = sum;
}
return memo[n];