Any algorithm you can implement in a HLL you can implement in assembly. On the other hand, there are many algorithms you can implement in assembly which you cannot implement in a HLL. - Randall Hyde
I found this statement in the forward to a book on assembly. The book is here: https://courses.engr.illinois.edu/ece390/books/artofasm/fwd/fwd.html#109
Does anyone know an example of this type of algorithm?
It's plain wrong.
You can implement any algorithm (in the CS sense of the word) in any turing complete programming language.
On the other hand, if he would have said something a like: "Some algorithms can be implemented very efficiently, and with ease in assembly, much more so than what is possible in most high level programming languages", then his statement would have made sense...
Interesting text though....
There is a sense in which it is trivially false: in the worst case, you could write an emulator in the HLL and then run the algorithm in there. But that's cheating a bit because now the HLL does not directly implement the algorithm.
A concrete example of what many HLL's can't do (or maybe they can in practice, but it is not guaranteed that they can do it), is directly implementing a XOR linked list. In many languages you just cannot XOR pointers, and/or it wouldn't make sense even if you could (consider garbage collection). Of course you can refer to every node by an integer ID and XOR those, but that's a workaround, not a direct implementation.
HLL's often have trouble implementing unstructured control flow, though many (particularly older) languages offer a goto. That means you may have to jump through hoops to implement a state machine (using a switch in a loop or whatever), instead of letting the state be implied by the program counter.
There are also many algorithms and data structures that rely on operations that don't exist in typical HLL's, for example popcnt or lzcnt, which can again be emulated, but then so can everything.
In case you have strict limitations in terms of memory and/or execution time, you might be forced to use assembly language.
High level languages typically require a run-time library which might be too big to fit into your program memory.
Think of a time-critical driver routine. An interrupt service routine for example. If there are only a few nanoseconds available for the routine, assembly language might be the only viable option.
How about this? You need to write some assembly code in order to access system registers and tables. But onces the setup is done, no CPU instructions are executed (everything's done by the complex CPU exception handling mechanisms) and yet the thing is Turing-complete and can "run" programs.
Related
This is mostly out of curiosity.
One fragment from some VHDL code that I've been working on recently resembles the following:
led_q <= (pwm_d and ch_ena) when pwm_ena = '1' else ch_ena;
This is a mux-style expression, of course. But it's also equivalent to the following basic logic expression (at least when ignoring non-binary states):
led_q <= ch_ena and (pwm_d or not pwm_ena);
Is one "better" than the other in terms of logic utilisation or efficiency when actually implemented in an FPGA? Is it preferable to use one over the other, or is the compiler smart enough to pick the "best" on its own?
(For the curious, the purpose of the expression is to define the state of an LED -- if ch_ena is false it should always be off as the channel is disabled, otherwise it should either be on solidly or flashing according to pwm_d, according to pwm_ena (PWM enable). I think the first form describes this more obviously than the second, although it's not too hard to realise how the second behaves.)
For a simple logical expression, like the one shown, where the synthesis tool can easily create a complete truth table, the expression is likely to be converted to an internal truth table, which is then directly mapped to the available FPGA LUT resources. Since the truth table is identical for the two equivalent expressions, the hardware will also be the same.
However, for complex expressions where a complete truth table can't be generated, e.g. when using arithmetic operations, and/or where dedicated resources are available, the synthesis tool may choose to hold an internal representation that is more closely related to the original VHDL code, and in this case the VHDL coding style can have a great impact on the resulting logic, even for equivalent expressions.
In the end, the implementation is tool specific, so the best way to find out what logic is generated is to try it with the specific tool, in special for large or timing critical parts of the design, where the implementation is critical.
In general it depends on the target architecture. For Xilinx FPGAs the logic is mostly mapped into LUTs with sporadic use of the hard logic resources where the mapper can make use of them. Every possible LUT configuration has essentially equal performance so there's little benefit to scrutinizing the mapper's work unless you're really pushing the speed limits of the device where you'd be forced into manually instantiating hand-mapped LUTs.
Non-LUT based architectures like the Actel/Microsemi device families use 2-input muxes as the main logic primitive and everything is mapped down to them. You can't generalize what is best across all types of FPGAs and CPLDs but nowadays you can mostly trust that the mapper will do a decent enough job using timing constraints to push it toward the results you need.
With regards to the question I think it is best to avoid obscure Boolean expressions where possible. They tend to be hard to decipher months later when you forgot what you meant them to do. I would lean toward the when-else simply from a code maintenance point of view. Even for this trivial example you have to think closely about what behavior it describes whereas the when-else describes the intended behavior directly in human level syntax.
HDLs work best when you use the highest abstraction possible and avoid wallowing around with low-level bit twiddling. This is a place where VHDL truly shines if you leverage the more advanced features of the language and move away from describing raw logic everywhere. Let the synthesizer do the work. Introductory learning materials focus on the low level structural gate descriptions and logic expressions because that is easiest for beginners to get a start on but it is not the best way to use VHDL for complex designs in the long run.
Of course there are situations where Booleans are better, particularly when doing bitwise operations across vectors in parallel which requires messy loops to do the same imperatively. It all depends on the context.
One of the promises of side-effect free, referentially transparent functional programming is that such code can be extensively optimized.
To quote Wikipedia:
Immutability of data can, in many cases, lead to execution efficiency, by allowing the compiler to make assumptions that are unsafe in an imperative language, thus increasing opportunities for inline expansion.
I'd like to see examples where a functional language compiler outperforms an imperative one by producing a better optimized code.
Edit: I tried to give a specific scenario, but apparently it wasn't a good idea. So I'll try to explain it in a different way.
Programmers translate ideas (algorithms) into languages that machines can understand. At the same time, one of the most important aspects of the translation is that also humans can understand the resulting code. Unfortunately, in many cases there is a trade-off: A concise, readable code suffers from slow performance and needs to be manually optimized. This is error-prone, time consuming, and it makes the code less readable (up to totally unreadable).
The foundations of functional languages, such as immutability and referential transparency, allow compilers to perform extensive optimizations, which could replace manual optimization of code and free programmers from this trade-off. I'm looking for examples of ideas (algorithms) and their implementations, such that:
the (functional) implementation is close to the original idea and is easy to understand,
it is extensively optimized by the compiler of the language, and
it is hard (or impossible) to write similarly efficient code in an imperative language without manual optimizations that reduce its conciseness and readability.
I apologize if it is a bit vague, but I hope the idea is clear. I don't want to give unnecessary restrictions on the answers. I'm open to suggestions if someone knows how to express it better.
My interest isn't just theoretical. I'd like to use such examples (among other things) to motivate students to get interested in functional programming.
At first, I wasn't satisfied by a few examples suggested in the comments. On second thoughts I take my objections back, those are good examples. Please feel free to expand them to full answers so that people can comment and vote for them.
(One class of such examples will be most likely parallelized code, which can take advantage of multiple CPU cores. Often in functional languages this can be done easily without sacrificing code simplicity (like in Haskell by adding par or pseq in appropriate places). I' be interested in such examples too, but also in other, non-parallel ones.)
There are cases where the same algorithm will optimize better in a pure context. Specifically, stream fusion allows an algorithm that consists of a sequence of loops that may be of widely varying form: maps, filters, folds, unfolds, to be composed into a single loop.
The equivalent optimization in a conventional imperative setting, with mutable data in loops, would have to achieve a full effect analysis, which no one does.
So at least for the class of algorithms that are implemented as pipelines of ana- and catamorphisms on sequences, you can guarantee optimization results that are not possible in an imperative setting.
A very recent paper Haskell beats C using generalised stream fusion by Geoff Mainland, Simon Peyton Jones, Simon Marlow, Roman Leshchinskiy (submitted to ICFP 2013) describes such an example. Abstract (with the interesting part in bold):
Stream fusion [6] is a powerful technique for automatically transforming
high-level sequence-processing functions into efficient implementations.
It has been used to great effect in Haskell libraries
for manipulating byte arrays, Unicode text, and unboxed vectors.
However, some operations, like vector append, still do not perform
well within the standard stream fusion framework. Others,
like SIMD computation using the SSE and AVX instructions available
on modern x86 chips, do not seem to fit in the framework at
all.
In this paper we introduce generalized stream fusion, which
solves these issues. The key insight is to bundle together multiple
stream representations, each tuned for a particular class of stream
consumer. We also describe a stream representation suited for efficient
computation with SSE instructions. Our ideas are implemented
in modified versions of the GHC compiler and vector library.
Benchmarks show that high-level Haskell code written using
our compiler and libraries can produce code that is faster than both
compiler- and hand-vectorized C.
This is just a note, not an answer: the gcc has a pure attribute suggesting it can take account of purity; the obvious reasons are remarked on in the manual here.
I would think that 'static single assignment' imposes a form of purity -- see the links at http://lambda-the-ultimate.org/node/2860 or the wikipedia article.
make and various build systems perform better for large projects by assuming that various build steps are referentially transparent; as such, they only need to rerun steps that have had their inputs change.
For small to medium sized changes, this can be a lot faster than building from scratch.
Let's say you have to implement a tool to efficiently solve an NP-hard problem, with unavoidable possible explosion of memory usage (the output size in some cases exponential to the input size) and you are particularly concerned about the performances of this tool at running time. The source code has also to be readable and understandable once the underlying theory is known, and this requirement is as important as the efficiency of the tool itself.
I personally think that 3 languages could be suitable for these three requirements: c++, scala, java.
They all provide the right abstraction on data types that makes it possible to compare different structures or apply the same algorithms (which is also important) to different data types.
C++ has the advantage of being statically compiled and optimized, and with function inlining (if the data structures and algorithms are designed carefully) and other optimisation techniques it's possible to achieve a performance close to that of pure C while maintaining a fairly good readability.
If you also put a lot of care in data representation you can optimise the cache performance, which can gain orders of magnitude in speed when the cache miss rate is low.
Java is instead JIT compiled, which allows to apply optimisations during runtime, and in this category of algorithms that could have different behaviours between different runs, that may be a plus. I fear instead that such an approach could suffer from garbage collector, however in the case of this algorithm it's common to continuously allocate memory and java heap performance is notoriously better than C/C++ and if you implement your own memory manager inside the language you could even achieve good efficiency.
This approach instead is not able to inline method invocation (which induces a huge performance penalty) and doesn't give you control over the cache performance. Among the pros there's a better and cleaner syntax than C++.
My concerns about scala are more or less the same as Java, plus the fact that I can't control how the language is optimised unless I have a deep knowledge on the compiler and the standard library. But well: I get a very clean syntax :)
What's your take on the subject? Have you had to deal with this already? Would you implement an algorithm with such properties and requirements in any of these languages or would you suggest something else? How would you compare them?
Usually I’d say “C++” in a heartbeat. The secret being that C++ simply produces less (memory) garbage that needs managing.
On the other hand, your observation that
however in the case of this algorithm it's common to continuously allocate memory
is a hint that Java / Scala may actually be more suited. But then you could use a small object heap in C++ as well. Boost has one that uses the standard allocator interface, if memory serves.
Another advantage of C++ is obviously the use of abstraction without penalty through templates – i.e. that you can easily create generic algorithmic components that can interact without incurring a runtime overhead due to abstraction. In fact, you noted that
it's possible to achieve a performance close to that of pure C while maintaining a fairly good readability
– this is looking at things the wrong way: Templates allow C++ to achieve performance superior to that of C while still maintaining high abstraction.
D might be worth a look, seeing as how it tries to be a better C++.
From a superficial glance, it has better source code readability than C++ does, so that's one of your points covered.
It also has memory management, which makes playing with algorithms a bit easier.
And templates
Here is a stackoverflow discussion comparing the performance of C++ and D
The languages you noticed were my first guesses as well.
Each language has a different take on how to handle specific issues like compilation, memory management and source code, but in theory, any of them should be fitting to your problem.
It is impossible to tell which is best, and there is likely no major difference if you are familiar enough with all of them to work around their respective quirks.
And obviously, if you actually find the need to optimize (I'm not sure if that's a given), that's possible in each language. Lower level languages obviously offer more options, but are also (far) more complex to actually improve.
A single note about C++ vs Java: This is really a holy war, and if you've followed the recent development you'll probably have your own opinion. I, for one, think Java offers enough good aspects to make up for its flaws, usually.
And a final note on C++ vs C: According to my knowledge, the difference usually amounts to a sufficiently low percentage to ignore this. It it doesn't make a difference for the source code, it's fine to go with C, if C++ could make for easier-to-read source code, go with C++. In any case, the choice is kind of negligible.
In the end, remember that money spent on a few hours of programming/optimizing this could as well go into slightly superior hardware to make up for missed tiny details.
It all boils down to: Any of your options is fine as long as you do it right (domain knowledge).
I would use a language which makes it very easy to work on the algorithm. Get the algorithm right and it could very easily outweigh any advantage from fine-tuning the wrong algorithm. Don't be scared to play around in a language normally thought of as slow in execution speed if that language makes it easier to express algorithmic ideas. It is usually much easier to transcribe the right algorithm into another language than it is to eek-out the last dregs of speed from the wrong algorithm in the fastest executing language.
So do it in a language you are comfortable with and which is expressive. You might surprise yourself and find that what is produced is fast enough!
I'm searching for an algorithm (or an argument of such an algorithm) in functional style which is faster than an imperative one.
I like functional code because it's expressive and mostly easier to read than it's imperative pendants. But I also know that this expressiveness can cost runtime overhead. Not always due to techniques like tail recursion - but often they are slower.
While programming I don't think about runtime costs of functional code because nowadays PCs are very fast and development time is more expensive than runtime. Furthermore for me readability is more important than performance. Nevertheless my programs are fast enough so I rarely need to solve a problem in an imperative way.
There are some algorithms which in practice should be implemented in an imperative style (like sorting algorithms) otherwise in most cases they are too slow or requires lots of memory.
In contrast due to techniques like pattern matching a whole program like a parser written in an functional language may be much faster than one written in an imperative language because of the possibility of compilers to optimize the code.
But are there any algorithms which are faster in a functional style or are there possibilities to setting up arguments of such an algorithm?
A simple reasoning. I don't vouch for terminology, but it seems to make sense.
A functional program, to be executed, will need to be transformed into some set of machine instructions.
All machines (I've heard of) are imperative.
Thus, for every functional program, there's an imperative program (roughly speaking, in assembler language), equivalent to it.
So, you'll probably have to be satisfied with 'expressiveness', until we get 'functional computers'.
The short answer:
Anything that can be easily made parallel because it's free of side-effects will be quicker on a multi-core processor.
QuickSort, for example, scales up quite nicely when used with immutable collections: http://en.wikipedia.org/wiki/Quicksort#Parallelization
All else being equal, if you have two algorithms that can reasonably be described as equivalent, except that one uses pure functions on immutable data, while the second relies on in-place mutations, then the first algorithm will scale up to multiple cores with ease.
It may even be the case that your programming language can perform this optimization for you, as with the scalaCL plugin that will compile code to run on your GPU. (I'm wondering now if SIMD instructions make this a "functional" processor)
So given parallel hardware, the first algorithm will perform better, and the more cores you have, the bigger the difference will be.
FWIW there are Purely functional data structures, which benefit from functional programming.
There's also a nice book on Purely Functional Data Structures by Chris Okasaki, which presents data structures from the point of view of functional languages.
Another interesting article Announcing Intel Concurrent Collections for Haskell 0.1, about parallel programming, they note:
Well, it happens that the CnC notion
of a step is a pure function. A step
does nothing but read its inputs and
produce tags and items as output. This
design was chosen to bring CnC to that
elusive but wonderful place called
deterministic parallelism. The
decision had nothing to do with
language preferences. (And indeed, the
primary CnC implementations are for
C++ and Java.)
Yet what a great match Haskell and CnC
would make! Haskell is the only major
language where we can (1) enforce that
steps be pure, and (2) directly
recognize (and leverage!) the fact
that both steps and graph executions
are pure.
Add to that the fact that Haskell is
wonderfully extensible and thus the
CnC "library" can feel almost like a
domain-specific language.
It doesn't say about performance – they promise to discuss some of the implementation details and performance in future posts, – but Haskell with its "pureness" fits nicely into parallel programming.
One could argue that all programs boil down to machine code.
So, if I dis-assemble the machine code (of an imperative program) and tweak the assembler, I could perhaps end up with a faster program. Or I could come up with an "assembler algorithm" that exploits some specific CPU feature, and therefor it really is faster than the imperative language version.
Does this situation lead to the conclusion that we should use assembler everywhere? No, we decided to use imperative languages because they are less cumbersome. We write pieces in assembler because we really need to.
Ideally we should also use FP algorithms because they are less cumbersome to code, and use imperative code when we really need to.
Well, I guess you meant to ask if there is an implementation of an algorithm in functional programming language that is faster than another implementation of the same algorithm but in an imperative language. By "faster" I mean that it performs better in terms of execution time or memory footprint on some inputs according to some measurement that we deem trustworthy.
I do not exclude this possibility. :)
To elaborate on Yasir Arsanukaev's answer, purely functional data structures can be faster than mutable data structures in some situations becuase they share pieces of their structure. Thus in places where you might have to copy a whole array or list in an imperative language, where you can get away with a fraction of the copying because you can change (and copy) only a small part of the data structure. Lists in functional languages are like this -- multiple lists can share the same tail since nothing can be modified. (This can be done in imperative languages, but usually isn't, because within the imperative paradigm, people aren't usually used to talking about immutable data.)
Also, lazy evaluation in functional languages (particularly Haskell which is lazy by default) can also be very advantageous because it can eliminate code execution when the code's results won't actually be used. (One can be very careful not to run this code in the first place in imperative languages, however.)
Isn't every language compiled into low-level computer language?
If so, shouldn't all languages have the same performance?
Just wondering...
As pointed out by others, not every language is translated into machine language; some are translated into some form (bytecode, reverse Polish, AST) that is interpreted.
But even among languages that are translated to machine code,
Some translators are better than others
Some language features are easier to translate to high-performance code than others
An example of a translator that is better than some others is the GCC C compiler. It has had many years' work invested in producing good code, and its translations outperform those of the simpler compilers lcc and tcc, for example.
An example of a feature that is hard to translate to high-performance code is C's ability to do pointer arithmetic and to dereference pointers: when a program stores through a pointer, it is very difficult for the compiler to know what memory locations are affected. Similarly, when an unknown function is called, the compiler must make very pessimistic assumptions about what might happen to the contents of objects allocated on the heap. In a language like Java, the compiler can do a better job translating because the type system enforces greater separation between pointers of different types. In a language like ML or Haskell, the compiler can do better still, because in these languages, most data allocated in memory cannot be changed by a function call. But of course object-oriented languages and functional languages present their own translation challenges.
Finally, translation of a Turing-complete language is itself a hard problem: in general, finding the best translation of a program is an NP-hard problem, which means that the only solutions known potentially take time exponential in the size of the program. This would be unacceptable in a compiler (can't wait forever to compile a mere few thousand lines), and so compilers use heuristics. There is always room for improvement in these heuristics.
It is easier and more efficient to map some languages into machine language than others. There is no easy analogy that I can think of for this. The closest I can come to is translating Italian to Spanish vs. translating a Khoisan language into Hawaiian.
Another analogy is saying "Well, the laws of physics are what govern how every animal moves, so why do some animals move so much faster than others? Shouldn't they all just move at the same speed?".
No, some languages are simply interpreted. They never actually get turned into machine code. So those languages will generally run slower than low-level languages like C.
Even for the languages which are compiled into machine code, sometimes what comes out of the compiler is not the most efficient possible way to write that given program. So it's often possible to write programs in, say, assembly language that run faster than their C equivalents, and C programs that run faster than their JIT-compiled Java equivalents, etc. (Modern compilers are pretty good, though, so that's not so much of an issue these days)
Yes, all programs get eventually translated into machine code. BUT:
Some programs get translated during compilation, while others are translated on-the-fly by an interpreter (e.g. Perl) or a virtual machine (e.g. original Java)
Obviously, the latter is MUCH slower as you spend time on translation during running.
Different languages can be translated into DIFFERENT machine code. Even when the same programming task is done. So that machine code might be faster or slower depending on the language.
You should understand the difference between compiling (which is translating) and interpreting (which is simulating). You should also understand the concept of a universal basis for computation.
A language or instruction set is universal if it can be used to write an interpreter (or simulator) for any other language or instruction set. Most computers are electronic, but they can be made in many other ways, such as by fluidics, or mechanical parts, or even by people following directions. A good teaching exercise is to write a small program in BASIC and then have a classroom of students "execute" the program by following its steps. Since BASIC is universal (to a first approximation) you can use it to write a program that simulates the instruction set for any other computer.
So you could take a program in your favorite language, compile (translate) it into machine language for your favorite machine, have an interpreter for that machine written in BASIC, and then (in principle) have a class full of students "execute" it. In this way, it is first being reduced to an instruction set for a "fast" machine, and then being executed by a very very very slow "computer". It will still get the same answer, only about a trillion times slower.
Point being, the concept of universality makes all computers equivalent to each other, even though some are very fast and others are very slow.
No, some languages are run by a 'software interpreter' as byte code.
Also, it depends on what the language does in the background as well, so 2 identically functioning programs in different languages may have different mechanics behind the scenes and hence be actually running different instructions resulting in differing performance.