Thread safety while sharing a reference between POSIX threads in OCaml - thread-safety

A primitive way to have two threads share a state with type int ref in OCaml is:
let add i x =
x := !x + i;
Printf.printf "add %d: x is now %d\n" i !x;
flush stdout
let rec run f x d =
f x;
Thread.delay d;
run f x d
let _ =
let x = ref 0 in
ignore(Thread.create (run (add 1) x) 0.2);
run (add 10) x 0.1
Function add just adds i to the integer in the reference x. Function run simply keeps applying f to the same argument x with delays of d between each application. The main function starts with 0 as the integer in the reference and invokes the run function in parallel with different arguments: (1) adding 1 and delaying 0.2s between calls; (2) adding 10 and delaying 0.1s between calls.
The output of running this program was:
add 10: x is now 10
add 1: x is now 11
add 10: x is now 21
add 10: x is now 31
add 1: x is now 32
add 10: x is now 42
add 10: x is now 52
add 1: x is now 53
add 10: x is now 63
add 10: x is now 73
add 1: x is now 74
add 10: x is now 84
add 10: x is now 94
add 1: x is now 95
[...]
It's easy to see that the contents of the reference are shared between threads.
I have used this construction in a case where the first run function was performing numerical calculations and the other run function was plotting the numbers calculated in the first thread. It worked well. In that case one of the threads was writing to the state but the other one was only reading. In the example coded above both threads write to the state which I think can be problematic, but I don't exactly know why.
My Question
My questions about this are:
(1) Is this construction unsafe? If so, do you have an example where it can go wrong?
(2) Do you know of a better construction to achieve the same goal? Should I use some kind of locks or signals?
Thanks in advance for any help!
All the best,
Surikator.

It's not safe. You have a race condition, the code works because of your particular timings and because the add function relies on the way the scheduler is implemented (which is subject to change).
What you need to remember is that conceptually your thread can be suspended at any time. Suppose the thread is suspended after the access to !x, or after the computation (!x+1) or between the assignment and the printf. If the other thread chimes in and executes the whole function before the suspended one is allowed to proceed, the result will be wrong.
One way to show the problem is to replace the add function by :
let add i x =
x := !x + i;
for i = 1 to Random.int 1000 do ignore (Unix.getaddrinfo "localhost" "" []) done;
Printf.printf "add %d: x is now %d\n" i !x;
flush stdout
(A simpler way is to insert a random Thread.delay between the assignement and the printf, but with the above you can see that a "regular" computation can bring in the problem)
Here's the result on my machine :
> ./test.native
add 10: x is now 11
add 1: x is now 11
add 10: x is now 21
add 1: x is now 32
add 10: x is now 32
add 1: x is now 43
You need to ensure that the addition, the assignement and the printf are executed "atomically" by a thread ("atomically" in the sense that if a thread in suspended in this body of code no one should be allowed to enter it). One way of doing
that is to use a mutex :
let add =
let m = Mutex.create () in
fun i x ->
Mutex.lock m;
try
x := !x + i;
for i = 1 to Random.int 1000 do ignore (Unix.getaddrinfo "localhost" "" []) done;
Printf.printf "add %d: x is now %d\n" i !x;
flush stdout;
Mutex.unlock m;
with e -> Mutex.unlock m; raise e
Note that this works for the example you give but it assumes that only add modifies x. For more on the subject I recommend you to read :
http://ocamlunix.forge.ocamlcore.org/threads.html
and in particular :
http://ocamlunix.forge.ocamlcore.org/threads.html#htoc64

Related

Logitech Gaming Software lua script code for pure random numbers

I've been trying for days to try find a way to make random numbers in the logitech gaming software (LGS) scripts. I know there is the
math.random()
math.randomseed()
but the thing is i need a changing value for the seed and the solutions from others are to add a os.time or tick() or GetRunningTime stuff which is NOT supported in the LGS scripts.
I was hoping some kind soul could help me by showing me a piece of code that makes pure random numbers. Because i don't want the pseudo random numbers because they are only random once. I need it to be random every time It runs the command. Like if i loop the math.randomI() one hundred times it will show a different number every time.
Thanks in advance!
Having a different seed won't guaratee you having a different number every time.
It will only ensure that you don't have the same random sequence every time you run your code.
A simple and most likely sufficient solution would be to use the mouse position as a random seed.
On a 4K screen that's over 8 Million different possible random seeds and it very unlikely that you hit the same coordinates within a reasonable time. Unless your game demands to click the same position over and over while you run that script.
This RNG receives entropy from all events.
Initial RNG state will be different on every run.
Just use random instead of math.random in your code.
local mix
do
local K53 = 0
local byte, tostring, GetMousePosition, GetRunningTime = string.byte, tostring, GetMousePosition, GetRunningTime
function mix(data1, data2)
local x, y = GetMousePosition()
local tm = GetRunningTime()
local s = tostring(data1)..tostring(data2)..tostring(tm)..tostring(x * 2^16 + y).."#"
for j = 2, #s, 2 do
local A8, B8 = byte(s, j - 1, j)
local L36 = K53 % 2^36
local H17 = (K53 - L36) / 2^36
K53 = L36 * 126611 + H17 * 505231 + A8 + B8 * 3083
end
return K53
end
mix(GetDate())
end
local function random(m, n) -- replacement for math.random
local h = mix()
if m then
if not n then
m, n = 1, m
end
return m + h % (n - m + 1)
else
return h * 2^-53
end
end
EnablePrimaryMouseButtonEvents(true)
function OnEvent(event, arg)
mix(event, arg) -- this line adds entropy to RNG
-- insert your code here:
-- if event == "MOUSE_BUTTON_PRESSED" and arg == 3 then
-- local k = random(5, 10)
-- ....
-- end
end

Code not working with bigger values of for loops

I am implementing a Szudik's pairing function in Matlab, where i pair 2 values coming from 2 different matrices X and Y, into a unique value given by the function 'CantorPairing2D(X,Y), After this i reverse the process to check for it's invertibility given by the function 'InverseCantorPairing2( X )'. But I seem to get an unusual problem, when i check this function for small matrices of size say 10*10, it works fine, but the for my code i have to use a 256 *256 matrices A and B, and then the code goes wrong, actually what it gives is a bit strange, because when i invert the process, the values in the matrix A, are same as cvalues of B in some places, for instance A(1,1)=B(1,1), and A(1,2)=B(1,2). Can somebody help.
VRNEW=CantorPairing2D(VRPRO,BLOCK3);
function [ Z ] = CantorPairing2D( X,Y )
[a,~] =(size(X));
Z=zeros(a,a);
for i=1:a
for j=1:a
if( X(i,j)~= (max(X(i,j),Y(i,j))) )
Z(i,j)= X(i,j)+(Y(i,j))^2;
else
Z(i,j)= (X(i,j))^2+X(i,j)+Y(i,j);
end
end
end
Z=Z./1000;
end
function [ A,B ] = InverseCantorPairing2( X )
[a, ~] =(size(X));
Rfinal=X.*1000;
A=zeros(a,a);
B=zeros(a,a);
for i=1:a
for j=1:a
if( ( Rfinal(i,j)- (floor( sqrt(Rfinal(i,j))))^2) < floor(sqrt(Rfinal(i,j))) )
T=floor(sqrt(Rfinal(i,j)));
B(i,j)=T;
A(i,j)=Rfinal(i,j)-T^2;
else
T=floor( (-1+sqrt(1+4*Rfinal(i,j)))/2 );
A(i,j)=T;
B(i,j)=Rfinal(i,j)-T^2-T;
end
end
end
end
Example if A= 45 16 7 17
7 22 11 25
11 12 9 17
2 11 3 5
B= 0 0 0 1
0 0 0 1
1 1 1 1
1 3 0 0
Then after pairing i get
C =2.0700 0.2720 0.0560 0.3070
1.4060 0.5060 0.1320 0.6510
0.1330 0.1570 0.0910 0.3070
0.0070 0.1350 0.0120 0.0300
after the inverse pairing i should get the same A and same B. But for bigger matrices it is giving unusual behaviour, because some elements of A are same as B.
If possible it would help immensely a counter example where your code does fail.
I got to reproduce your code behaviour and I have rewritten your code in a vectorised fashion. You should get the bug, but hopefully it is a first step to uncover the underlying logic and find the bug itself.
I am not familiar with the specific algorithm, but I observe a discrepancy in the CantorPairing definition.
for elements where Y = X your if statement would be false, since X = max(X,X); so for those elements your Z would be X^2+X+Y, but for hypothesis X =Y, therefore your would have:
X^2+X+X = X^2+2*X;
now, if we perturb slightly the equation and suppose Y = X + 10*eps, your if statement would be true (since Y > X) and your Z would be X + Y ^2; since X ~=Y we can approximate to X + X^2
therefore your equation is very temperamental to numerical approximation ( and you definitely have a discontinuity in Z). Again, I am not familiar with the algorithm and it may very well be the behaviour you want, but it is unlikely: so I am pointing this out.
Following is my version of your code, I report it also because I hope it will be pedagogical in getting you acquainted with logical indexing and vectorized code (which is the idiomatic form for MATLAB, let alone much faster than nested for loops).
function [ Z ] = CantorPairing2D( X,Y )
[a,~] =(size(X));
Z=zeros(a,a);
firstConditionIndeces = Y > X; % if Y > X then X is not the max between Y and X
% update elements on which to apply first equation
Z(firstConditionIndeces) = X(firstConditionIndeces) + Y(firstConditionIndeces).^2;
% update elements on the remaining elements
Z(~firstConditionIndeces) = X(~firstConditionIndeces).^2 + X(~firstConditionIndeces) + Y(~firstConditionIndeces) ;
Z=Z./1000;
end
function [ A,B ] = InverseCantorPairing2( X )
[a, ~] =(size(X));
Rfinal=X.*1000;
A=zeros(a,a);
B=zeros(a,a);
T = zeros(a,a) ;
% condition deciding which updates to be applied
indecesToWhichApplyFstFcn = Rfinal- (floor( sqrt(Rfinal )))^2 < floor(sqrt(Rfinal)) ;
% elements on which to apply the first update
T(indecesToWhichApplyFstFcn) = floor(sqrt(Rfinal )) ;
B(indecesToWhichApplyFstFcn) = floor(Rfinal(indecesToWhichApplyFstFcn)) ;
A(indecesToWhichApplyFstFcn) = Rfinal(indecesToWhichApplyFstFcn) - T(indecesToWhichApplyFstFcn).^2;
% updates on which to apply the remaining elements
A(~indecesToWhichApplyFstFcn) = floor( (-1+sqrt(1+4*Rfinal(~indecesToWhichApplyFstFcn )))/2 ) ;
B(~indecesToWhichApplyFstFcn) = Rfinal(~indecesToWhichApplyFstFcn) - T(~indecesToWhichApplyFstFcn).^2 - T(~indecesToWhichApplyFstFcn) ;
end

Does VBScript have increment operator?

For y = 1 to 10
y = y+1
print(y)
Next
For the above code the output which I get is 2,4,6,8,10. Shouldn't the o/p be 2,3,4,5,6,7,8,9,10
Can I consider y = y+1 as y++
The default step increment for a vbscript for loop is 1. By adding in y=y+1, you are effectively increasing your increment by 2 each cycle:
For y = 2 to 10 step 2
Wscript.echo y
Next
There is no "increment operator" as such; However you could consider step an increment operator in this context (both positive and negative).
y = y + 1 is similar as the intended concept y++.
You would probably be best using that type of operation inside a do/while loop where there are no auto increments eg:
y = 0
do while y < 10
y = y + 1
wscript.echo y
Loop
See this previous post:
Does VBScript have Increment Operators
in a For...Next loop, you won'T need to increase the counter value manualy.
You are increasing the value that is increased by the For loop:
For y = 1 to 10 ' starts at 1, next is 3
y = y+1 ' but you increase it to 2, increased to 4
print(y) ' prints 2, 4
Next ' Increases to 3, 5, up to 11, then stops because it's greater than 10
No, VB Script doesn't have an increment operator. VB script is based on BASIC which is a language meant for learning and the increment operator is considered to be confusing by many so it was never added on purpose.
As for your second question, to get the output you want remove y = y+1 line and change loop to For y = 2 to 10. Also, yes, y=y+1 is the same as y++ in most languages.

Set::write error when using For loop

Solving a complicated formula f(u,v)==0, where
I assign some constant value to u and then solve v.
I can solve it without for-loop, but encounter errors by adding For[] enclosing the codes,
where saying
Set::write: Tag Times in "Solve[] with exact coefficients solns is Protected.
A simple example to illustrate my idea:
For[ i = 1, i < 5, i++,
f = x^2 + y^2 - 10;
x = i;
eqn = (f == 0);
soln = Solve[eqn, y]
]
will get error:
Set::write: "Tag Times in (-9+y^2) is Protected."
Only when I add For[ ] at the outside of the code
(inner 4-line code works fine without for loop)
So it seems that there is an variable assignment permission issue in the for loop
How can I avoid it?
I no longer have Mathematica 7 installed, and your code runs (although with no printed output...) on Mathematica 10. Based on the error message, it sounds like you need to Clear[f] before trying to reassign it.
For[i = 1, i < 5, i++,
Clear[f];
f = x^2 + y^2 - 10;
x = i;
eqn = (f == 0);
soln = Solve[eqn, y];
Print[soln]
]
However, you're still really mixing things up. Consider what happens with your code as the loop executes. First it starts with i=1 and says:
Clear[f] -- or don't, this isn't the only issue
f = x^2 + y^2 - 10 -- This gives me an expression with symbols x and y
x=i -- This sets x=1 since i=1 already
At this point, the expression for f has become y^2 - 9`. Next time it comes around, it will repeat:
f = x^2 + y^2 - 10 -- But x is no longer a symbol!! So now it still treats x=1...
This becomes a nightmare. I could try to hack your code into working with the fewest changes (e.g. make it Clear[f,x] or something), but that's not really the best advice I can give.
A better overall construction would be something like:
Eqn[x_,y_]=(x^2+y^2-10==0);
For[i=1,i<5,i++,
Print[Solve[Eqn[i,y],y]];
];
Your function f is a function, so you should make it a function like f[x_,y_]=something. Better yet, just make the entire equation into a function as above. That way, you never actually modify the values of x or y and don't get caught with issues in your loop.
And before you use this new code I've given you, clear everything or just quit the Kernel.

Code Golf: Fractran

Locked. This question and its answers are locked because the question is off-topic but has historical significance. It is not currently accepting new answers or interactions.
The Challenge
Write a program that acts as a Fractran interpreter. The shortest interpreter by character count, in any language, is the winner. Your program must take two inputs: The fractran program to be executed, and the input integer n. The program may be in any form that is convenient for your program - for example, a list of 2-tuples, or a flat list. The output must be a single integer, being the value of the register at the end of execution.
Fractran
Fractran is a trivial esoteric language invented by John Conway. A fractran program consists of a list of positive fractions and an initial state n. The interpreter maintains a program counter, initially pointing to the first fraction in the list. Fractran programs are executed in the following fashion:
Check if the product of the current state and the fraction currently under the program counter is an integer. If it is, multiply the current state by the current fraction and reset the program counter to the beginning of the list.
Advance the program counter. If the end of the list is reached, halt, otherwise return to step 1.
For details on how and why Fractran works, see the esolang entry and this entry on good math/bad math.
Test Vectors
Program: [(3, 2)]
Input: 72 (2332)
Output: 243 (35)
Program: [(3, 2)]
Input: 1296 (2434)
Output: 6561 (38)
Program: [(455, 33), (11, 13), (1, 11), (3, 7), (11, 2), (1, 3)]
Input: 72 (2332)
Output: 15625 (56)
Bonus test vector:
Your submission does not need to execute this last program correctly to be an acceptable answer. But kudos if it does!
Program: [(455, 33), (11, 13), (1, 11), (3, 7), (11, 2), (1, 3)]
Input: 60466176 (210310)
Output: 7888609052210118054117285652827862296732064351090230047702789306640625 (5100)
Submissions & Scoring
Programs are ranked strictly by length in characters - shortest is best. Feel free to submit both a nicely laid out and documented and a 'minified' version of your code, so people can see what's going on.
The language 'J' is not admissible. This is because there's already a well-known solution in J on one of the linked pages. If you're a J fan, sorry!
As an extra bonus, however, anyone who can provide a working fractran interpreter in fractran will receive a 500 reputation point bonus. In the unlikely event of multiple self-hosting interpreters, the one with the shortest number of fractions will receive the bounty.
Winners
The official winner, after submitting a self-hosting fractran solution comprising 1779 fractions, is Jesse Beder's solution. Practically speaking, the solution is too slow to execute even 1+1, however.
Incredibly, this has since been beaten by another fractran solution - Amadaeus's solution in only 84 fractions! It is capable of executing the first two test cases in a matter of seconds when running on my reference Python solution. It uses a novel encoding method for the fractions, which is also worth a close look.
Honorable mentions to:
Stephen Canon's solution, in 165 characters of x86 assembly (28 bytes of machine code)
Jordan's solution in 52 characters of ruby - which handles long integers
Useless's solution in 87 characters of Python, which, although not the shortest Python solution, is one of the few solutions that isn't recursive, and hence handles harder programs with ease. It's also very readable.
Fractran - 1779 fractions
(Edit: fixed)
(I hope people are still following this thread, because this took a while!)
It appears SO won't let me post something as long as this, so I posted the Fractran source here.
Input is specified as follows:
First, we encode a fraction m/n = p_0^a0... p_k^ak by:
Start with 1. Then, for each ai:
Multiply by p_2i^ai if ai > 0
Multiply by p_2i+1^{-ai} if a_i < 0
This way, we encode any fraction as a positive integer. Now, given a progoram (sequence of encoded fractions F0, F1, ...), we encode that by
p_0^F0 p1^F1 ...
Finally, input to the interpreter is given by:
2^(program) 3^(input) 5
where program and input are encoded as above. For example, in the first test problem, 3/2 gets encoded to 15, so the program gets encoded to 2^15; and 108 gets encoded to 500. So, we pass
2^{2^15} 3^500 5
to the program. The output, then is of the form
2^(program) 3^(output)
so in the first example, it'll be
2^{2^15} 3^3125
How does it work?
I wrote a meta-language that compiles down to Fractran. It allows for functions (simple Fractran and sequences of other functions), and a while loop and if statement (for convenience!). The code for that can be found here.
If you want to compile that code down to Fractran yourself, my (C++) program can be found here [tar.gz]. In a stunning display of dogfooding (and showing off), I used my C++ YAML parser yaml-cpp, so you'd have to download and link with that. For both yaml-cpp and the "compiler", you'll need CMake for cross-platform makefile generating.
The usage of this program is:
./fracc interpreter.frp
The it reads the name of a function from standard input, and writes the corresponding "pseudo-Fraction" (I'll explain that in a second) to standard output. So to compile the interpreter (the Interpret function), you could run
echo "Interpret" | ./fracc interpreter.frp > interpret
The output ("pseudo-Fractran") will be a sequence of lines, each with a string of space-separated digits. A line corresponds to a fraction: if the nth digit in the line is an, then the fraction is the product of p_n^an.
It's very easy to convert this to Fractran, but if you're lazy, you can use to-fractions.py. [Note: earlier I had a C++ program, and I had carelessly ignored integer overflow. I translated it to Python to avoid this.]
Note about input: if you want to test out a different function this way, the convention is always the same. It has a number of parameters (usually the comment above the function explains this) in pseudo-Fractran, so give it what it wants, plus a 1 on the very next slot (so in ordinary Fractran, multiply once by the first prime that it won't use). This is a "signal" bit to the function to start going.
However,
I don't recommend actually trying to run the Fractran interpreter (alas). I tested many of its components, and, for example, the function IncrementPrimes, which takes a pair of primes and returns the next two primes, takes about 8 minutes to run, using my silly C++ interpreter (no need to post that :). Plus, it goes (at least) quadratically in the number of function calls - doubling the number of function calls makes it take at least four times as long (more if there are while loops or if statements). So I'm guessing that running the interpreter will take at least days, if not years :(
So how do I know it works? Well, of course I'm not 100% certain, but I'm pretty close. First of all, I tested many, many of its components, and in particular, I tested all of the elements of the meta-language (sequences of functions and if and while statements) very thoroughly.
Also, the meta-language is easy to translate into your favorite language, and even easier to translate to C++, since all parameters of functions are passed by reference. If you're feeling lazy again, you can download my translation here [tar.gz] (there's no makefile; it's just two .cpp files, so directly calling gcc is fine).
So you can compare the two interpreters, run the C++ version (it also takes input/output in pseudo-Fractran), check that that works, and then convince yourself that the meta-language works too.
Or!
If you're feeling inspired, and really want to see this interpreter interpreted, you can write a "clever" Fractran interpreter based around the type of Fractran output that we get. The output is very structured - sequences of functions are implemented using signals, so if you somehow cache where the interpreter was, you could jump there immediately if nothing important changed. This, I think, would dramatically speed up the program (perhaps cutting down running time by one or more powers).
But, I'm not really sure how to do this, and I'm happy with what's done, so I'll leave it as an exercise for the reader.
Fractran: 84 fractions
FTEVAL = [197*103/(2^11*101), 101/103, 103*127/(2*101), 101/103, 109/101,
2*23/(197*109), 109/23, 29/109,197*41*47/(31*59), 11^10*53/(127*197), 197/53,
37/197, 7^10*43/(11^10*37), 37/43, 59/(37*47), 59/47, 41*61/59, 31*67/(41*61),
61/67, 7*67/(127*61), 61/67,101/71, 73/(127^9*29), 79/(127^2*73),
83/(127*73), 89/(2*29), 163/29, 127^11*89/79, 337/83, 2*59/89, 71/61,
7*173/(127*163), 163/173, 337*167/163, 347/(31*337), 337/347, 151/337,
1/71,19*179/(3*7*193), 193/179, 157/(7*193), 17*181/193, 7*211/(19*181),
181/211, 193/181, 157/193, 223/(7*157), 157/223, 281*283/239,
3*257*269/(7*241), 241/269, 263/241, 7*271/(257*263), 263/271, 281/263,
241/(17*281), 1/281, 307/(7*283), 283/307, 293/283, 71*131/107, 193/(131*151),
227/(19*157), 71*311/227, 233/(151*167*311), 151*311/229, 7*317/(19*229),
229/317, 239*331/217, 71*313/157, 239*251/(151*167*313), 239*251/(151*313),
149/(251*293), 107/(293*331), 137/199, 2^100*13^100*353/(5^100*137),
2*13*353/(5*137), 137/353, 349/137, 107/349, 5^100*359/(13^100*149),
5*359/(13*149), 149/359, 199/149]
This is written entirely by hand. I did make up a pseudo language to be able to express things more clearly, but I did not write a compiler and opted to write optimized Fractran code directly.
FTEVAL takes input 3^initial_state * 5^encoded_program * 199, produces intermediate results 3^interpreted_program_state * 199, and completely halts at a number divisible by 233.
The interpreted program is embeded as a list of base 10 digits inside a single base 11 number, using the digit "a" to mark the boundary except at the very end. The addition program [3/2] is encoded as
int("3a2", 11) = 475.
The multiplication program [455/33, 11/13, 1/11, 3/7, 11/2, 1/3] is encoded as
int("1a3a11a2a3a7a1a11a11a13a455a33", 11) = 3079784207925154324249736405657
which is a truly large number.
The first test vector finished in less than one second, produced the desired result after 4545 iterations and halted after 6172 iterations. Here is the complete output.
Unfortunately, sage segfaulted when I tried the second test vector (but I think it'll work under Nick's implementation using prime exponent vectors).
The space here is really too small to explain everything. But here is my pseudocode. I will write up my process in a couple of days, hopefully.
# Notations:
# %p
# designates the exponent of prime factor p that divides the
# current state.
# mov x y
# directly translates to the fraction y/x; its meaning: test if x divides
# the current state, if so divide the current state by x and multiply it by
# y. In effect, the prime exponents of x and y are exchanged. A Fractran
# program only comprises of these instructions; when one is executable, the
# program continues from the beginning.
# dec x => mov x, 1
# wipes out all factors of x
# inc x => mov 1, x
# this form is here for the sake of clarity, it usually appears in a
# loop's entry statement and is merged as such when compiled
# sub n ret m {...}
# conceptually represents a Fractran sub-program, which will execute just
# like a normal Fractran program, that is, the sub-program's statements
# execute when triggered and loop back. The sub-program only exits when none of
# its statement is executable, in which occasion we multiply the program's
# state by m. We can also explicitly break out early on some conditions.
# It is also possible to enter a sub-prorgram via multiple entry points and
# we must take care to avoiding this kind of behavior (except in case where
# it is desirable).
# entry point 101: return 29
# Divide %2 modulo 11:
# - quotient is modified in-place
# - remainder goes to %127
sub 101 ret 101 { mov 2^11, 197 }
sub 101 ret 109 { mov 2, 127 }
sub 109 ret 29 { mov 197, 2 }
# entry point 59: return 61
# Multiply %127 by 10^%31 then add result to %7,
# also multiply %31 by 10 in-place.
sub 59 ret 41*61 {
mov 31, 197*41
sub 197 ret 37 { mov 127, 11^10 }
sub 37 { mov 11^10, 7^10 }
}
sub 61 ret 61 { mov 41, 31 }
sub 61 ret 61 { mov 127, 7 } # the case where %31==0
# entry point 71: return 151 if success, 151*167 if reached last value
# Pop the interpreted program stack (at %2) to %7.
sub 71 {
# call sub 101
inc 101
# if remainder >= 9:
mov 29*127^9, 73
# if remainder == 11, goto 79
mov 73*127^2, 79
# else:
# if remainder == 10, goto 83
mov 73*127, 83
# else:
# if quotient >= 1: goto 89
mov 29*2, 89
# else: goto 163
mov 29, 163
# 79: restore remainder to original value, then goto 89
mov 79, 127^11*89
# 83: reached a border marker, ret
mov 83, 337
# 89: the default loop branch
# restore quotient to original value, call 59 and loop when that rets
mov 2*89, 59
mov 61, 71
# 163: reached stack bottom,
# ret with the halt signal
sub 163 ret 337*167 { mov 127, 7 }
# 337: clean up %31 before ret
sub 337 ret 151 { dec 31 }
}
# entry point 193, return 157
# Divide %3 modulo %7:
# - quotient goes to %17
# - remainder goes to %19
sub 193 ret 17*181 {
mov 3*7, 19
}
mov 7*193, 157
sub 181 ret 193 { mov 19, 7 }
mov 193, 157
sub 157 ret 157 { dec 7 }
# entry point 239: return 293
# Multiply %17 by %7, result goes to %3
mov 239, 281*283
sub 241 { mov 7, 3*257 }
sub 263 ret 281 { mov 257, 7 }
mov 281*17, 241
sub 283 ret 293 { dec 7 }
# entry point 107: return 149 if success, 233 if stack empty
# Pop the stack to try execute each fraction
sub 107 {
# pop the stack
inc 71*131
# 151: popped a value
# call divmod %3 %7
mov 131*151, 193
# if remainder > 0:
mov 19*157, 227
# pop and throw away the numerator
mov 227, 71*311
# if stack is empty: halt!
mov 151*167*311, 233
# else: call 239 to multiply back the program state and gave loop signal
mov 151*311, 229
sub 229 ret 239*331 { mov 19, 7 }
# else: (remainder == 0)
# pop the numerator
mov 157, 71*313
# clear the stack empty signal if present
# call 239 to update program state and gave ret signal
mov 151*167*313, 239*251
mov 151*313, 239*251
# after program state is updated
# 313: ret
mov 293*251, 149
# 331: loop
mov 293*331, 107
}
# main
sub 199 {
# copy the stack from %5 to %2 and %13
sub 137 ret 137 { mov 5^100, 2^100*13^100 }
sub 137 ret 349 { mov 5, 2*13 }
# call sub 107
mov 349, 107
# if a statement executed, restore stack and loop
sub 149 ret 149 { mov 13^100, 5^100 }
sub 149 ret 199 { mov 13, 5 }
}
x86_64 assembly, 165 characters (28 bytes of machine code).
State is passed in %rdi, Program (pointer to null-terminated array of fractions) is in %rsi. Results are returned in %rax per the usual C-style calling conventions. Using non-standard calling conventions or Intel syntax (this is AT&T syntax) would drop a few more characters, but I'm lazy; someone else can do that. An instruction or two can almost certainly be saved by re-arranging the control flow, if someone wants to do that, feel free.
Intermediate computations (state*numerator) can be up to 128 bits wide, but only 64 bit state is supported.
_fractran:
0: mov %rsi, %rcx // set aside pointer to beginning of list
1: mov (%rcx), %rax // load numerator
test %rax, %rax // check for null-termination of array
jz 9f // if zero, exit
mul %rdi
mov 8(%rcx), %r8 // load denominator
div %r8
test %rdx, %rdx // check remainder of division
cmovz %rax, %rdi // if zero, keep result
jz 0b // and jump back to program start
add $16, %rcx // otherwise, advance to next instruction
jmp 1b
9: mov %rdi, %rax // copy result for return
ret
Delete comments, extraneous whitespace, and the verbose label _fractran for minimized version.
Ruby, 58 57 56 53 52 characters
This is my first-ever code golf entry, so please be gentle.
def f(n,c)d,e=c.find{|i,j|n%j<1};d ?f(n*d/e,c):n end
Usage:
irb> f 108, [[455, 33], [11, 13], [1,11], [3,7], [11,2], [1,3]]
=> 15625
irb> f 60466176, [[455, 33], [11, 13], [1, 11], [3, 7], [11, 2], [1, 3]]
=> 7888609052210118054117285652827862296732064351090230047702789306640625
Pretty version (252):
def fractran(instruction, program)
numerator, denominator = program.find do |numerator, denominator|
instruction % denominator < 1
end
if numerator
fractran(instruction * numerator / denominator, program)
else
instruction
end
end
Ruby, 53 52 using Rational
Inspired by gnibbler's solution I was able to get a solution using Rational down to 53 52 characters. Still one longer than the (less elegant) solution above.
def f(n,c)c.map{|i|return f(n*i,c)if i*n%1==0};n end
Usage:
irb> require 'rational'
irb> f 60466176, [Rational(455, 33), Rational(11, 13), Rational(1, 11), Rational(3, 7), Rational(11, 2), Rational(1, 3)]
=> Rational(7888609052210118054117285652827862296732064351090230047702789306640625, 1)
(A to_i call for prettier output would add 5 more characters.)
Golfscript - 32
{:^{1=1$\%!}?.1={~#\/*^f}{}if}:f
; 108 [[3 2]] f p
# 243
; 1296 [[3 2]] f p
# 6561
; 108 [[455 33][11 13][1 11][3 7][11 2][1 3]] f p
# 15625
; 60466176 [[455 33][11 13][1 11][3 7][11 2][1 3]] f p
# 7888609052210118054117285652827862296732064351090230047702789306640625
Haskell, 102 characters
import List
import Ratio
l&n=maybe n((&)l.numerator.(n%1*).(!!)l)$findIndex((==)1.denominator.(n%1*))l
$ ghci
Prelude> :m List Ratio
Prelude List Ratio> let l&n=maybe n((&)l.numerator.(n%1*).(!!)l)$findIndex((==)1.denominator.(n%1*))l
Prelude List Ratio> [3%2]&108
243
Prelude List Ratio> [3%2]&1296
6561
Prelude List Ratio> [455%33,11%13,1%11,3%7,11%2,1%3]&108
15625
88 with relaxed restrictions on the input/output format.
import List
import Ratio
l&n=maybe n((&)l.(*)n.(!!)l)$findIndex((==)1.denominator.(*)n)l
Prelude List Ratio> let l&n=maybe n((&)l.(*)n.(!!)l)$findIndex((==)1.denominator
Prelude List Ratio> [455%33,11%13,1%11,3%7,11%2,1%3]&108
15625 % 1
Python, 83 82 81 72 70 characters.
It's convenient to have input as fractions.Fraction objects. Same idea as in Ruby solution.
def f(n,c):d=[x for x in c if x*n%1==0];return d and f(n*d[0],c) or n
# Test code:
from fractions import Fraction as fr
assert f(108, [fr(3, 2)]) == 243
assert f(1296, [fr(3, 2)]) == 6561
assert f(108, [fr(455, 33), fr(11, 13), fr(1, 11), fr(3, 7), fr(11, 2), fr(1, 3)]) == 15625
assert f(60466176, [fr(455, 33), fr(11, 13), fr(1, 11), fr(3, 7), fr(11, 2), fr(1, 3)]) == 7888609052210118054117285652827862296732064351090230047702789306640625
C, 159 153 151 131 111 110 characters
v[99],c,d;main(){for(;scanf("%d",v+c++););while(d++,v[++d])
*v%v[d]?0:(*v=*v/v[d]*v[d-1],d=0);printf("%d",*v);}
$ cc f.c
$ echo 108 3 2 . | ./a.out; echo
243
$ echo 1296 3 2 . | ./a.out; echo
6561
$ echo 108 455 33 11 13 1 11 3 7 11 2 1 3 . | ./a.out; echo
15625
Python - 53
Improvement thanks to Paul
f=lambda n,c:next((f(n*x,c)for x in c if x*n%1==0),n)
testcases
from fractions import Fraction as fr
assert f(108, [fr(3, 2)]) == 243
assert f(1296, [fr(3, 2)]) == 6561
assert f(108, [fr(455, 33), fr(11, 13), fr(1, 11), fr(3, 7), fr(11, 2), fr(1, 3)]) == 15625
assert f(60466176, [fr(455, 33), fr(11, 13), fr(1, 11), fr(3, 7), fr(11, 2), fr(1, 3)]) == 7888609052210118054117285652827862296732064351090230047702789306640625
Python - 54 Without using Fraction
f=lambda n,c:next((f(n*i/j,c)for i,j in c if n%j<1),n)
Python - 55
This one is somewhat theoretical. The first two cases run ok, but the other two fail from recursion depth. Maybe someone can get it to work with a generator expression
f=lambda n,c:([f(n*i/j,c)for i,j in c if n%j<1]+[n])[0]
Here's one possibility, but grows to 65 even without including the import
from itertools import chain
f=lambda n,c:(chain((f(n*i/j,c)for i,j in c if n%j<1),[n])).next()
F#: 80 chars
let rec f p=function|x,(e,d)::t->f p (if e*x%d=0I then(e*x/d,p)else(x,t))|x,_->x
Here's an expanded version using match pattern with |cases instead of function:
//program' is the current remainder of the program
//program is the full program
let rec run program (input,remainingProgram) =
match input, remainingProgram with
| x, (e,d)::rest ->
if e*x%d = 0I then //suffix I --> bigint
run program (e*x/d, program) //reset the program counter
else
run program (x, rest) //advance the program
| x, _ -> x //no more program left -> output the state
Test code:
let runtests() =
[ f p1 (108I,p1) = 243I
f p1 (1296I,p1) = 6561I
f p2 (108I,p2) = 15625I
f p2 (60466176I,p2) = pown 5I 100]
And result (tested in F# interactive):
> runtests();;
val it : bool list = [true; true; true; true]
Edit let's have some more fun with this, and calculate some primes (see linked page in the starting post). I've written a new function g that yields the intermediate values of the state.
//calculate the first n primes with fractran
let primes n =
let ispow2 n =
let rec aux p = function
| n when n = 1I -> Some p
| n when n%2I = 0I -> aux (p+1) (n/2I)
| _ -> None
aux 0 n
let pp = [(17I,91I);(78I,85I);(19I,51I);(23I,38I);(29I,33I);(77I,29I);(95I,23I);
(77I,19I);(1I,17I);(11I,13I);(13I,11I);(15I,14I);(15I,2I);(55I,1I)]
let rec g p (x,pp) =
seq { match x,pp with
|x,(e,d)::t -> yield x
yield! g p (if e*x%d=0I then (e*x/d,p) else (x,t))
|x,_ -> yield x }
g pp (2I,pp)
|> Seq.choose ispow2
|> Seq.distinct
|> Seq.skip 1 //1 is not prime
|> Seq.take n
|> Seq.to_list
Takes a whopping 4.7 seconds to cough up the first 10 prime numbers:
> primes 10;;
Real: 00:00:04.741, CPU: 00:00:04.005, GC gen0: 334, gen1: 0, gen2: 0
val it : int list = [2; 3; 5; 7; 11; 13; 17; 19; 23; 29]
This is, without doubt, the most bizarre and slow prime number generator I've ever written. I'm not sure whether that's a good thing or a bad thing.
A Javascript one: 99 characters. No bonus vector :(
function g(n,p,q,i,c){i=0;while(q=p[i],c=n*q[0],(c%q[1]?++i:(n=c/q[1],i=0))<p.length){};return n;};
Input is in the format [[a,b],[c,d]]. I took advantage of Javascript's lenience: instead of doing var x=0, y=0;, you can add as many parameters as you like. It doesn't matter whether you actually pass them or not, since they default to null.
Pretty version:
function g(n,p) {
var q, c, i=0;
while(i < p.length) {
q = p[i];
c = n * q[0];
if(c % q[1] != 0) {
++i;
} else {
n = c % q[1];
i = 0;
}
}
return n;
};
Python, 110 103 95 87 characters
frc.py
def f(n,c):
d=c
while len(d):
if n%d[1]:d=d[2:]
else:n=d[0]*n/d[1];d=c
return n
test.py
(shows how to drive it)
from frc import f
def test():
"""
>>> f(108, [3,2])
243
>>> f(1296, [3,2])
6561
>>> f(108, [455,33,11,13,1,11,3,7,11,2,1,3])
15625
>>> f(60466176, [455, 33,11, 13,1, 11,3, 7,11, 2,1, 3])
7888609052210118054117285652827862296732064351090230047702789306640625L
"""
pass
import doctest
doctest.testmod()
C#:
Tidy version:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace Test
{
class Program
{
static void Main(string[] args)
{
int ip = 1;
decimal reg = Convert.ToInt32(args[0]);
while (true)
{
if (ip+1 > args.Length)
{
break;
}
decimal curfrac = Convert.ToDecimal(args[ip]) / Convert.ToDecimal(args[ip+1]);
if ((curfrac * reg) % 1 == 0)
{
ip = 1;
reg = curfrac * reg;
}
else
{
ip += 2;
}
}
Console.WriteLine(reg);
Console.ReadKey(true);
}
}
}
Cut down version weighing in at 201 chars (without the namespace declarations or any of that, just the single using statement (not system) and the Main function):
using System;namespace T{using b=Convert;static class P{static void Main(string[] a){int i=1;var c=b.ToDecimal(a[0]);while(i+1<=a.Length){var f=b.ToDecimal(a[i])/b.ToDecimal(a[i+1]);if((f*c)%1==0){i=1;c*=f;}else{i+=2;}}Console.Write(c);}}}
Examples (input is through command line arguments):
input: 108 3 2
output: 243.00
input: 1296 3 2
output: 6561.0000
input: 108 455 33 11 13 1 11 3 7 11 2 1 3
output: 45045.000000000000000000000000
Groovy, 136 117 107 characters.
Call as groovy fractal.groovy [input state] [program vector as list of numbers]
a=args.collect{it as int}
int c=a[0]
for(i=1;i<a.size;i+=2) if(c%a[i+1]==0){c=c/a[i+1]*a[i];i=-1}
println c
Sample
bash$ groovy fractal.groovy 108 455 33 11 13 1 11 3 7 11 2 1 3
Output: 15625
Perl, 84 82 char
Uses standard input.
#P=<>=~/\d+/g;$_=<>;
($a,$%)=#P[$i++,$i++],$_*$a%$%or$i=0,$_*=$a/$%while$i<#P;
print
Takes 110 chars to pass the bonus test:
use Math'BigInt blcm;#P=<>=~/\d+/g;$_=blcm<>;
($%,$=)=#P[$i++,$i++],$_*$%%$=or$i=0,($_*=$%)/=$=while$i<#P;print
Haskell: 116 109 characters
f p x[]=x
f p x((n,d):b)|x*n`mod`d==0=f p(x*n`div`d)p|True=f p x b
main=do{p<-readLn;x<-readLn;print$f p x p}
This ended up as somewhat of a knockoff of Dario's entry.
Scheme: 326
I thought a Scheme submission was needed, for parity. I also just wanted the excuse to play with it. (Excuse my rudimentary knowledge, I'm sure this could be optimized, and I am open to suggestions!)
#lang scheme
(define fractran_interpreter
(lambda (state pc program)
(cond
((eq? pc (length program))
(print state))
((integer? (* state (list-ref program pc)))
(fractran_interpreter (* state (list-ref program pc)) 0 program))
(else
(fractran_interpreter state (+ pc 1) program)))))
Tests:
(fractran_interpreter 108 0 '(3/2))
(fractran_interpreter 60466176 0 '(455/33 11/13 1/11 3/7 11/2 1/3))
I get the bonus vector! (using Dr. Scheme, allocating 256 mb)
Lua:
Tidy code:
a=arg;
ip=2;
reg=a[1];
while a[ip] do
curfrac = a[ip] / a[ip+1];
if (curfrac * reg) % 1 == 0 then
ip=2;
reg = curfrac * reg
else
ip=ip+2
end
end
print(reg)
Compact code weighing in at 98 chars (reduction suggested by Scoregraphic on my other answer, and more suggested by gwell):
a=arg i=2 r=a[1]while a[i]do c=a[i]/a[i+1]v=c*r if v%1==0 then i=2 r=v else i=i+2 end end print(r)
Run from the command line, supplying the base number first then the series of fractions presented as numbers with space separation, like the following:
C:\Users\--------\Desktop>fractran.lua 108 3 2
243
C:\Users\--------\Desktop>fractran.lua 1296 3 2
6561
C:\Users\--------\Desktop>fractran.lua 108 455 33 11 13 1 11 3 7 11 2 1 3
15625
(manually typed some of that in because it's a pain to get stuff out of the command line, though that is the results returned)
Does NOT handle the bonus vector sadly :(
Reference implementation in Python
This implementation operates on prime factorizations.
First, it decodes a list of fraction tuples by encoding the numerator and denominator as a list of (idx, value) tuples, where idx is the number of the prime (2 is prime 0, 3 is prime 1, and so forth).
The current state is a list of exponents for each prime, by index. Executing an instruction requires first iterating over the denominator, checking if the indexed state element is at least the specified value, then, if it matches, decrementing state elements specified in the denominator, and incrementing those specified in the numerator.
This approach is about 5 times the speed of doing arithmetic operations on large integers in Python, and is a lot easier to debug!
A further optimisation is provided by constructing an array mapping each prime index (variable) to the first time it is checked for in the denominator of a fraction, then using that to construct a 'jump_map', consisting of the next instruction to execute for each instruction in the program.
def primes():
"""Generates an infinite sequence of primes using the Sieve of Erathsones."""
D = {}
q = 2
idx = 0
while True:
if q not in D:
yield idx, q
idx += 1
D[q * q] = [q]
else:
for p in D[q]:
D.setdefault(p + q, []).append(p)
del D[q]
q += 1
def factorize(num, sign = 1):
"""Factorizes a number, returning a list of (prime index, exponent) tuples."""
ret = []
for idx, p in primes():
count = 0
while num % p == 0:
num //= p
count += 1
if count > 0:
ret.append((idx, count * sign))
if num == 1:
return tuple(ret)
def decode(program):
"""Decodes a program expressed as a list of fractions by factorizing it."""
return [(factorize(n), factorize(d)) for n, d in program]
def check(state, denom):
"""Checks if the program has at least the specified exponents for each prime."""
for p, val in denom:
if state[p] < val:
return False
return True
def update_state(state, num, denom):
"""Checks the program's state and updates it according to an instruction."""
if check(state, denom):
for p, val in denom:
state[p] -= val
for p, val in num:
state[p] += val
return True
else:
return False
def format_state(state):
return dict((i, v) for i, v in enumerate(state) if v != 0)
def make_usage_map(program, maxidx):
firstref = [len(program)] * maxidx
for i, (num, denom) in enumerate(program):
for idx, value in denom:
if firstref[idx] == len(program):
firstref[idx] = i
return firstref
def make_jump_map(program, firstref):
jump_map = []
for i, (num, denom) in enumerate(program):
if num:
jump_map.append(min(min(firstref[idx] for idx, val in num), i))
else:
jump_map.append(i)
return jump_map
def fractran(program, input, debug_when=None):
"""Executes a Fractran program and returns the state at the end."""
maxidx = max(z[0] for instr in program for part in instr for z in part) + 1
state = [0]*maxidx
if isinstance(input, (int, long)):
input = factorize(input)
for prime, val in input:
state[prime] = val
firstref = make_usage_map(program, maxidx)
jump_map = make_jump_map(program, firstref)
pc = 0
length = len(program)
while pc < length:
num, denom = program[pc]
if update_state(state, num, denom):
if num:
pc = jump_map[pc]
if debug_when and debug_when(state):
print format_state(state)
else:
pc += 1
return format_state(state)
Perl 6: 77 Characters (experimental)
sub f(#p,$n is copy){
loop {my$s=first {!($n%(1/$_))},#p or return $n;$n*=$s}}
Newline is optional. Call as:
say f([3/2], 1296).Int;
say f([455/33, 11/13, 1/11, 3/7, 11/2, 1/3], 60466176).Int;
Readable version:
sub Fractran (#program, $state is copy) {
loop {
if my $instruction = first #program:
-> $inst { $state % (1 / $inst) == 0 } {
$state *= $instruction;
} else {
return $state.Int;
}
}
}
Notes:
The colon notation first #program: pointy-sub doesn't work on current implementations; first BLOCK, #program has to be used instead.
Rakudo appears to have a buggy Rat giving incorrect results. Current Niecza runs all of the test programs correctly and quickly, including the "bonus" fraction.
Haskell, 142 characters
Without any additional libraries and full I/O.
t n f=case f of{(a,b):f'->if mod n b == 0then(\r->r:(t r f))$a*n`div`b else t n f';_->[]}
main=readLn>>=(\f->readLn>>=(\n->print$last$t n f))
Java, 200 192 179 characters
I think everyone knows that Java would not have the shortest implementation, but I wanted to see how it would compare. It solves the trivial examples, but not the bonus one.
Here is the minimized version:
class F{public static void main(String[]a){long p=new Long(a[0]);for(int i=1;i<a.length;){long n=p*new Long(a[i++]),d=new Long(a[i++]);if(n%d<1){p=n/d;i=1;}}System.out.print(p);}}
java -cp . F 108 455 33 11 13 1 11 3 7 11 2 1 3
15625
java -cp . F 1296 3 2
6561
Here is the cleaned-up version:
public class Fractran {
public static void main(String[] args) {
long product = new Long(args[0]);
for (int index = 1; index < args.length;) {
long numerator = product * new Long(args[index++]);
long denominator = new Long(args[index++]);
if (numerator % denominator < 1) {
product = numerator / denominator;
index = 1;
} // if
} // for
System.out.print(product);
}
}
Scheme 73 characters
My first attempt, at doing this with completely standard R5RS Scheme, came in at 104 characters:
(define(f p n)(let l((q p)(n n))(if(null? q)n(let((a(* n(car q))))(if(integer?
a)(l p a)(l(cdr q)n))))))
Running against a few items in the test vector:
> (f '(3/2) 1296)
6561
> (f '(455/33 11/13 1/11 3/7 11/2 1/3) 60466176)
7888609052210118054117285652827862296732064351090230047702789306640625
If you assume that λ is bound to lambda and let/cc is defined (as they are in PLT Scheme; see below for definitions for running this in Schemes that don't define those), then I can adapt Jordan's second Ruby solution to Scheme, which comes out to 73 characters (note that the argument order is the reverse of my first solution, but the same as Jordan's; in this version, that saves one character).:
(define(f n p)(let/cc r(map(λ(i)(if(integer?(* n i))(r(f(* n i)p))))p)n))
If I don't have λ and let/cc predefined, then this one comes in at 111 characters (88 if the fairly common call/cc abbreviation is defined):
(define(f n p)(call-with-current-continuation(lambda(r)(map(lambda(i)(if(integer?(*
n i))(r(f(* n i)p))))p)n)))
Definitions of λ and let/cc:
(define-syntax λ
(syntax-rules ()
((_ . body) (lambda . body)))
(define-syntax let/cc
(syntax-rules ()
((_ var . body) (call-with-current-continuation (lambda (var) . body)))))
A bit late... dc 84 chars
Just for fun a dc solution (OpenBSD)
[ss1sp]s1[Rlp1+sp]s2?l1xz2/sz[z2/ds_:bl_:az0<L]dsLx
1[;als*lp;b~0=1e2lpdlz!<L]dsLxlsp
It handles all the cases:
$ dc fractran.dc
455 33 11 13 1 11 3 7 11 2 1 3 60466176
7888609052210118054117285652827862296732064351090230047702789306640625
I can't leave comments yet but here's a "slightly" shorter version of RCIX's C# version (i believe it's 7 chars shorter)
using System;namespace T{static class P{static void Main(string[] a){int i=1;Func<string,decimal> d=Convert.ToDecimal;var c=d(a[0]);while(i+1<=a.Length){var f=d(a[i])/d(a[++i]);if((f*c)%1==0){i=1;c*=f;}else i++;}Console.Write(c);}}}
which uses
Func<string,decimal> d=Convert.ToDecimal
and calls d(); instead of
using b=Convert;
and repeatedly calling b.ToDecimal();.
I also removed an unnecessary pair of curly braces around the else statement to gain 1 char :).
I also replaced the a[i+1] with a[++i] and in the following else body i replaced i+=2 with i++ to gain another char :P

Resources