I'm thinking more about how much system memory my programs will use nowadays. I'm currently doing A level Computing at college and I know that in most programs the difference will be negligible but I'm wondering if the following actually makes any difference, in any language.
Say I wanted to output "True" or "False" depending on whether a condition is true. Personally, I prefer to do something like this:
Dim result As String
If condition Then
Result = "True"
Else
Result = "False"
EndIf
Console.WriteLine(result)
However, I'm wondering if the following would consume less memory, etc.:
If condition Then
Console.WriteLine("True")
Else
Console.WriteLine("False")
EndIf
Obviously this is a very much simplified example and in most of my cases there is much more to be outputted, and I realise that in most commercial programs these kind of statements are rare, but hopefully you get the principle.
I'm focusing on VB.NET here because that is the language used for the course, but really I would be interested to know how this differs in different programming languages.
The main issue making if's fast or slow is predictability.
Modern CPU's (anything after 2000) use a mechanism called branch prediction.
Read the above link first, then read on below...
Which is faster?
The if statement constitutes a branch, because the CPU needs to decide whether to follow or skip the if part.
If it guesses the branch correctly the jump will execute in 0 or 1 cycle (1 nanosecond on a 1Ghz computer).
If it does not guess the branch correctly the jump will take 50 cycles (give or take) (1/200th of a microsecord).
Therefore to even feel these differences as a human, you'd need to execute the if statement many millions of times.
The two statements above are likely to execute in exactly the same amount of time, because:
assigning a value to a variable takes negligible time; on average less than a single cpu cycle on a multiscalar CPU*.
calling a function with a constant parameter requires the use of an invisible temporary variable; so in all likelihood code A compiles to almost the exact same object code as code B.
*) All current CPU's are multiscalar.
Which consumes less memory
As stated above, both versions need to put the boolean into a variable.
Version A uses an explicit one, declared by you; version B uses an implicit one declared by the compiler.
However version A is guaranteed to only have one call to the function WriteLine.
Whilst version B may (or may not) have two calls to the function WriteLine.
If the optimizer in the compiler is good, code B will be transformed into code A, if it's not it will remain with the redundant calls.
How bad is the waste
The call takes about 10 bytes for the assignment of the string (Unicode 2 bytes per char).
But so does the other version, so that's the same.
That leaves 5 bytes for a call. Plus maybe a few extra bytes to set up a stackframe.
So lets say due to your totally horrible coding you have now wasted 10 bytes.
Not much to worry about.
From a maintainability point of view
Computer code is written for humans, not machines.
So from that point of view code A is clearly superior.
Imagine not choosing between 2 options -true or false- but 20.
You only call the function once.
If you decide to change the WriteLine for another function you only have to change it in one place, not two or 20.
How to speed this up?
With 2 values it's pretty much impossible, but if you had 20 values you could use a lookup table.
Obviously that optimization is not worth it unless code gets executed many times.
If you need to know the precise amount of memory the instructions are going to take, you can use ildasm on your code, and see for yourself. However, the amount of memory consumed by your code is much less relevant today, when the memory is so cheap and abundant, and compilers are smart enough to see common patterns and reduce the amount of code that they generate.
A much greater concern is readability of your code: if a complex chain of conditions always leads to printing a conditionally set result, your first code block expresses this idea in a cleaner way than the second one does. Everything else being equal, you should prefer whatever form of code that you find the most readable, and let the compiler worry about optimization.
P.S. It goes without saying that Console.WriteLine(condition) would produce the same result, but that is of course not the point of your question.
Related
I am pretty new to Raku and I have a questions to functional methods, in particular with reduce.
I originally had the method:
sub standardab{
my $mittel = mittel(#_);
my $foo = 0;
for #_ {
$foo += ($_ - $mittel)**2;
}
$foo = sqrt($foo/(#_.elems));
}
and it worked fine. Then I started to use reduce:
sub standardab{
my $mittel = mittel(#_);
my $foo = 0;
$foo = #_.reduce({$^a + ($^b-$mittel)**2});
$foo = sqrt($foo/(#_.elems));
}
my execution time doubled (I am applying this to roughly 1000 elements) and the solution differed by 0.004 (i guess rounding error).
If I am using
.race.reduce(...)
my execution time is 4 times higher than with the original sequential code.
Can someone tell me the reason for this?
I thought about parallelism initialization time, but - as I said - i am applying this to 1000 elements and if i change other for loops in my code to reduce it gets even slower!
Thanks for your help
Summary
In general, reduce and for do different things, and they are doing different things in your code. For example, compared with your for code, your reduce code involves twice as many arguments being passed and is doing one less iteration. I think that's likely at the root of the 0.004 difference.
Even if your for and reduce code did the same thing, an optimized version of such reduce code would never be faster than an equally optimized version of equivalent for code.
I thought that race didn't automatically parallelize reduce due to reduce's nature. (Though I see per your and #user0721090601's comment I'm wrong.) But it will incur overhead -- currently a lot.
You could use race to parallelize your for loop instead, if it's slightly rewritten. That might speed it up.
On the difference between your for and reduce code
Here's the difference I meant:
say do for <a b c d> { $^a } # (a b c d) (4 iterations)
say do reduce <a b c d>: { $^a, $^b } # (((a b) c) d) (3 iterations)
For more details of their operation, see their respective doc (for, reduce).
You haven't shared your data, but I will presume that the for and/or reduce computations involve Nums (floats). Addition of floats isn't commutative, so you may well get (typically small) discrepancies if the additions end up happening in a different order.
I presume that explains the 0.004 difference.
On your sequential reduce being 2X slower than your for
my execution time doubled (I am applying this to roughly 1000 elements)
First, your reduce code is different, as explained above. There are general abstract differences (eg taking two arguments per call instead of your for block's one) and perhaps your specific data leads to fundamental numeric computation differences (perhaps your for loop computation is primarily integer or float math while your reduce is primarily rational?). That might explain the execution time difference, or some of it.
Another part of it may be the difference between, on the one hand, a reduce, which will by default compile into calls of a closure, with call overhead, and two arguments per call, and temporary memory storing intermediate results, and, on the other, a for which will by default compile into direct iteration, with the {...} being just inlined code rather than a call of a closure. (That said, it's possible a reduce will sometimes compile to inlined code; and it may even already be that way for your code.)
More generally, Rakudo optimization effort is still in its relatively early days. Most of it has been generic, speeding up all code. Where effort has been applied to particular constructs, the most widely used constructs have gotten the attention so far, and for is widely used and reduce less so. So some or all the difference may just be that reduce is poorly optimized.
On reduce with race
my execution time [for .race.reduce(...)] is 4 times higher than with the original sequential code
I didn't think reduce would be automatically parallelizable with race. Per its doc, reduce works by "iteratively applying a function which knows how to combine two values", and one argument in each iteration is the result of the previous iteration. So it seemed to me it must be done sequentially.
(I see in the comments that I'm misunderstanding what could be done by a compiler with a reduction. Perhaps this is if it's a commutative operation?)
In summary, your code is incurring raceing's overhead without gaining any benefit.
On race in general
Let's say you're using some operation that is parallelizable with race.
First, as you noted, race incurs overhead. There'll be an initialization and teardown cost, at least some of which is paid repeatedly for each evaluation of an overall statement/expression that's being raced.
Second, at least for now, race means use of threads running on CPU cores. For some payloads that can yield a useful benefit despite any initialization and teardown costs. But it will, at best, be a speed up equal to the number of cores.
(One day it should be possible for compiler implementors to spot that a raced for loop is simple enough to be run on a GPU rather than a CPU, and go ahead and send it to a GPU to achieve a spectacular speed up.)
Third, if you literally write .race.foo... you'll get default settings for some tunable aspects of the racing. The defaults are almost certainly not optimal and may be way off.
The currently tunable settings are :batch and :degree. See their doc for more details.
More generally, whether parallelization speeds up code depends on the details of a specific use case such as the data and hardware in use.
On using race with for
If you rewrite your code a bit you can race your for:
$foo = sum do race for #_ { ($_ - $mittel)**2 }
To apply tuning you must repeat the race as a method, for example:
$foo = sum do race for #_.race(:degree(8)) { ($_ - $mittel)**2 }
This is a question popped into my mind while reading the halting problem, collatz conjecture and Kolmogorov complexity. I have tried to search for something similar but I was unable to find a particular topic maybe because it is not of great value or it could just be a trivial question.
For the sake of simplicity I will give three examples of programs/functions.
function one(s):
return s
function two(s):
while (True):
print s
function three(s):
for i from 0 to 10^10:
print(s)
So my questions is, if there is a way to formalize the length of a program (like the bits used to describe it) and also the internal memory used by the program, to determine the minimum/maximum number of time/steps needed to decide whether the program will terminate or run forever.
For example, in the first function the program doesn't alter its internal memory and halts after some time steps.
In the second example, the program runs forever but the program also doesn't alter its internal memory. For example, if we considered all the programs with the same length as with the program two that do not alter their state, couldn't we determine an upper bound of steps, which if surpassed we could conclude that this program will never terminate ? (If not why ?)
On the last example, the program alters its state (variable i). So, at each step the upper bound may change.
[In short]
Kolmogorov complexity suggests a way of finding the (descriptive) complexity of an object such as a piece of text. I would like to know, given a formal way of describing the memory-space used by a program (computed in runtime), if we could compute a maximum number of steps, which if surpassed would allow us to know whether this program will terminate or run forever.
Finally, I would like to suggest me any source that I might find useful and help me figure out what I am exactly looking for.
Thank you. (sorry for my English, not my native language. I hope I was clear)
If a deterministic Turing machine enters precisely the same configuration twice (which we can detect b keeping a trace of configurations seen so far), then we immediately know the TM will loop forever.
If it known in advance that a deterministic Turing machine cannot possibly use more than some fixed constant amount of its input tape, then the TM must explicitly halt or eventually enter some configuration it has already visited. Suppose the TM can use at most k tape cells, the tape alphabet is T and the set of states is Q. Then there are (|T|+1)^k * |Q| unique configurations (the number of strings over (T union blank) of length k times the number of states) and by the pigeonhole principle we know that a TM that takes that many steps must enter some configuration it has already been to before.
one: because we are given that this function does not use internal memory, we know that it either halts or loops forever.
two: because we are given that this function does not use internal memory, we know that it either halts or loops forever.
three: because we are given that this function only uses a fixed amount of internal memory (like 34 bits) we can tell in fewer than 2^34 iterations of the loop whether the TM will halt or not for any given input s, guaranteed.
Now, knowing how much tape a TM is going to use, or how much memory a program is going to use, is not a problem a TM can solve. But if you have an oracle (like a person who was able to do a proof) that tells you a correct fixed upper bound on memory, then the halting problem is solvable.
If my code is calling a function, and one of the function's arguments will vary based on a certain condition, is it more efficient to have the conditional statement as an argument of the function, or to call the function multiple times in the conditional statement.
Example:
(if condition (+ 4 3) (+ 5 3))
(+ (if condition 4 5) 3)
Obiously this is just an example: in the real scenario the numbers would be replaced by long, complex expressions, full of variables. The if might instead be a long cond statement.
Which would be more efficient in terms of speed, space etc?
Don't
What you care about is not performance (in this case the difference will be trivial) but code readability.
Remember,
"... a computer language is not just a way of getting a computer to
perform operations, but rather ... it is a novel formal medium for
expressing ideas about methodology"
Abelson/Sussman "Structure and
Interpretation of Computer Programs".
You are writing code primarily for others (and you yourself next year!) to read. The fact that the computer can execute it is a welcome fringe benefit.
(I am exaggerating, of course, but much less than you think).
Okay...
Now that you skipped the harangue (if you claim you did not, close your eyes and tell me which specific language I mention above), let me try to answer your question.
If you profiled your program and found that this place is the bottleneck, you should first make sure that you are using the right algorithm.
E.g., using a linearithmic sort (merge/heap) instead of quadratic (bubble/insertion) sort will make much bigger difference than micro-optimizations like you are contemplating.
Then you should disassemble both versions of your code; the shorter version is (ceteris paribus) likely to be marginally faster.
Finally, you can waste a couple of hours of machine time repeatedly running both versions on the same output on an otherwise idle box to discover that there is no statistically significant difference between the two approaches.
I agree with everything in sds's answer (except using a trick question -_-), but I think it might be nice to add an example. The code you've given doesn't have enough context to be transparent. Why 5? Why 4? Why 3? When should each be used? Should there always be only two options? The code you've got now is sort of like:
(defun compute-cost (fixed-cost transaction-type)
(+ fixed-cost
(if (eq transaction-type 'discount) ; hardcoded magic numbers
3 ; and conditions are brittle
4)))
Remember, if you need these magic numbers (3 and 4) here, you might need them elsewhere. If you ever have to change them, you'll have to hope you don't miss any cases. It's not fun. Instead, you might do something like this:
(defun compute-cost (fixed-cost transaction-type)
(+ fixed-cost
(variable-cost transaction-type)))
(defun variable-cost (transaction-type)
(case transaction-type
((employee) 2) ; oh, an extra case we'd forgotten about!
((discount) 3)
(t 4)))
Now there's an extra function call, it's true, but computation of the magic addend is pulled out into its own component, and can be reused by anything that needs it, and can be updated without changing any other code.
I've got an algorithm using a single (positive integer) number as an input to produce an output. And I've got the reverse function which should do the exact opposite, going back from the output to the same integer number. This should be a unique one-to-one reversible mapping.
I've tested this for some integers, but I want to be 100% sure that it works for all of them, up to a known limit.
The problem is that if I just test every integer, it takes an unreasonably long time to run. If I use 64-bit integers, that's a lot of numbers to check if I want to check them all. On the other hand, if I only test every 10th or 100th number, I'm not going to be 100% sure at the end. There might be some awkward weird constellation in one of the 90% or 99% which I didn't test.
Are there any general ways to identify edge cases so that just those "interesting" or "risky" numbers are checked? Or should I just pick numbers at random? Or test in increasing increments?
Or to put the question another way, how can I approach this so that I gain 100% confidence that every case will be properly handled?
The approach for this is generally checking every step of the computation for potential flaws. Concerning integer math, that is overflows, underflows and rounding errors from division, basically that the mathematical result can't be represented accurately. In addition, all operations derived from this suffer similar problems.
The process of auditing then looks at single steps in turn. For example, if you want to allocate memory for N integers, you need N times the size of an integer in bytes and this multiplication can overflow. You now determine those values where the multiplication overflows and create according tests that exercise these. Note that for the example of allocating memory, proper handling typically means that the function does not allocate memory but fail.
The principle behind this is that you determine the ranges for every operation where the outcome is somehow different (like e.g. where it overflows) and then make sure via tests that both variants work. This reduces the number of tests from all possible input values to just those where you expect a significant difference.
I have a shader where I want to move half of the vertices in the vertex shader. I'm trying to decide the best way to do this from a performance standpoint, because we're dealing with well over 100,000 verts, so speed is critical. I've looked at 3 different methods: (pseudo-code, but enough to give you the idea. The <complex formula> I can't give out, but I can say that it involves a sin() function, as well as a function call (just returns a number, but still a function call), as well as a bunch of basic arithmetic on floating point numbers).
if (y < 0.5)
{
x += <complex formula>;
}
This has the advantage that the <complex formula> is only executed half the time, but the downside is that it definitely causes a branch, which may actually be slower than the formula. It is the most readable, but we care more about speed than readability in this context.
x += step(y, 0.5) * <complex formula>;
Using HLSL's step() function (which returns 0 if the first param is greater and 1 if less), you can eliminate the branch, but now the <complex formula> is being called every time, and its results are being multiplied by 0 (thus wasted effort) half of the time.
x += (y < 0.5) ? <complex formula> : 0;
This I don't know about. Does the ?: cause a branch? And if not, are both sides of the equation evaluated or only the one that is relevant?
The final possibility is that the <complex formula> could be offloaded back to the CPU instead of the GPU, but I worry that it will be slower in calculating sin() and other operations, which might result in a net loss. Also, it means one more number has to be passed to the shader, and that could cause overhead as well. Anyone have any insight as to which would be the best course of action?
Addendum:
According to http://msdn.microsoft.com/en-us/library/windows/desktop/bb509665%28v=vs.85%29.aspx
the step() function uses a ?: internally, so it's probably no better than my 3rd solution, and potentially worse since <complex formula> is definitely called every time, whereas it may be only called half the time with a straight ?:. (Nobody's answered that part of the question yet.) Though avoiding both and using:
x += (1.0 - y) * <complex formula>;
may well be better than any of them, since there's no comparison being made anywhere. (And y is always either 0 or 1.) Still executes the <complex formula> needlessly half the time, but might be worth it to avoid branches altogether.
Perhaps look at this answer.
My guess (this is a performance question: measure it!) is that you are best off keeping the if statement.
Reason number one: The shader compiler, in theory (and if invoked correctly), should be clever enough to make the best choice between a branch instruction, and something similar to the step function, when it compiles your if statement. The only way to improve on it is to profile[1]. Note that it's probably hardware-dependent at this level of granularity.
[1] Or if you have specific knowledge about how your data is laid out, read on...
Reason number two is the way shader units work: If even one fragment or vertex in the unit takes a different branch to the others, then the shader unit must take both branches. But if they all take the same branch - the other branch is ignored. So while it is per-unit, rather than per-vertex - it is still possible for the expensive branch to be skipped.
For fragments, the shader units have on-screen locality - meaning you get best performance with groups of nearby pixels all taking the same branch (see the illustration in my linked answer). To be honest, I don't know how vertices are grouped into units - but if your data is grouped appropriately - you should get the desired performance benefit.
Finally: It's worth pointing out that your <complex formula> - if you're saying that you can hoist it out of your HLSL manually - it may well get hoisted into a CPU-based pre-shader anyway (on PC at least, from memory Xbox 360 doesn't support this, no idea about PS3). You can check this by decompiling the shader. If it is something that you only need to calculate once per-draw (rather than per-vertex/fragment) it probably is best for performance to do it on the CPU.
I got tired of my conditionals being ignored so I just made a another kernel and did an override in c execution.
If you need it to be accurate all the time I suggest this fix.