I have a program that often has the boolean algorithm pattern of: (f(a) && g(b)) || (f(b) && g(a)).
For example,
if ((isA(event[1]) && isTens(event[3])) || (isA(event[3]) && isTens(event[1])))
cnt += 1
end
How can I use a macro, #pmacro, to do the same, so to be called as such:
if (#pmacro(isA(), isTens(), event[1], event[3]))
cnt += 1
end
So far, I tried something like this
function isCombination(f, g, e1, e2)
if (f(e1) && g(e2)) || (f(e2) && g(e1))
true
else
false
end
end
And,
julia> isCombination(BJcore.isA, BJcore.isTens, event[1], event[3])
Works but, should I use meta-programming here?
You don't need a macro for that. Since Julia supports higher order programming, you can define a function - I'll call it predicate here - that accepts the functions f and g as arguments and performs the required check.
julia> predicate(f, g, a, b) = (f(a) && g(b) || f(b) && g(a))
predicate (generic function with 1 method)
julia> predicate(iseven, isodd, 4, 3)
true
julia> predicate(iseven, isodd, 3, 3)
false
julia> predicate(iseven, isodd, 3, 4)
true
Edit: The edit to the question happened while I was writing the answer, but you've hit upon the solution. isCombination and predicate are pretty much the same function.
As for metaprogramming: when there's a non-metaprogramming solution to a problem, the answer to "should I use metaprogramming" is almost always no. Metaprogramming is a powerful tool, but can make your code harder to read and maintain unless applied judiciously and with care.
Related
For illustration, let us say I have the following macros computing rows in a truth table:
macro bool_to_lit(a)
eval(a) ? (x -> x) : (x -> !x)
end
macro make_clause(xs, bools, res)
lits = map((x -> #eval #bool_to_lit $x), bools.args)
clause_elements = map.(lits, xs.args)
and_res = all(push!(clause_elements, res))
return and_res
end
##make_clause((false, false), (false, false), true) returns true
#bool_to_lit returns a closure depending on the value of its argument, and #make_clause uses the result to compute values of its own. However, since #make_clause uses #eval, my understanding is that it actually runs #bool_to_lit (and therefore does not just perform a syntactic transformation).
Would it be better (as in faster and generating cleaner code) to avoid use of nested #eval in cases such as this, such that the entire result of the whole macro tree is evaluated only once at rutime?
Is it a tradeoff between easier coding (i.e. treating nested macros as functions when #eval is used) vs. correctness (i.e. only compile-time syntactic transformations when avoiding nested #eval)?
(Disclaimer: I shortened the logic of your code a bit. Maybe there's an error I made doing that, but the general point is the same.)
In most cases, no, you shouldn't use eval in a macro. There are two possible alternatives to what you gave. First, if you require the macro only to work on literal booleans (ie., the values true and false), then these are stored right in the AST, and you can do normal computations directly at compile time:
julia> macro make_clause_literal(xs, bools, res)
clause_elements = map((lit, arg) -> lit == arg, bools.args, xs.args)
res && all(clause_elements)
end
#make_clause_literal (macro with 1 method)
julia> #macroexpand #make_clause_literal((false, false), (false, false), true)
true
There should be some checking added if the inputs really are literal booleans.
On the other hand, if you want to put in other expressions at well, transform the code to something efficient that does the same thing, and leave evaluation to runtime:
julia> macro make_clause(xs, bools, res)
clause_elements = map((lit, arg) -> :($lit == $arg), bools.args, xs.args)
esc(:($res && $(foldr((e,f) -> :($e && $f), clause_elements))))
end
#make_clause (macro with 1 method)
julia> #macroexpand #make_clause((false, false), (false, false), true)
:(true && (false == false && false == false))
julia> #macroexpand #make_clause((false, false), (false, x), y)
:(y && (false == false && x == false))
Constructing a sequence of && should be as good as it gets in terms of avoiding intermediate arrays and short circuiting.
A third option, which I would recommend, is to write a normal runtime function doing the clause evaluation, and rewriting either of the above macros in terms of a call to that. I leave that as an exercise. You could also do a combination of both approaches and evaluate the expression at compile time as far as possible, but I guess the compiler will already do that to some extent.
I would like to inject code into a function. For concreteness, consider a simple simulater:
function simulation(A, x)
for t in 1:1000
z = randn(3)
x = A*x + z
end
end
Sometimes I would like to record the values of x every ten time-steps, sometimes the values of z every 20 time-steps, and sometimes I don't want to record any values. I could, of course, put some flags as arguments to the function, and have some if-else statements. But I would like to rather keep the simulation code clean, and only inject a piece of code like
if t%10 == 0
append!(rec_z, z)
end
into particular places of the function whenever I need it. For that, I'd like to write a macro such that monitoring a particular value becomes
#monitor(:z, 10)
simulation(A, x)
Is that possible with Julia's Metaprogramming capabilities?
No, you cannot use metaprogramming to inject code into an already-written function. Metaprogramming can only do things that you could directly write yourself at precisely the location where the macro itself is written. That means that a statement like:
#monitor(:z, 10); simulation(A, x)
cannot even modify the simulation(A, x) function call. It can only expand out to some normal Julia code that runs before simulation is called. You could, perhaps, include the simulation function call as an argument to the macro, e.g., #monitor(:z, 10, simulation(A, x)), but now all the macro can do is change the function call itself. It still cannot "go back" and add new code to a function that was already written.
You could, however, carefully and meticulously craft a macro that takes the function definition body and modifies it to add your debug code, e.g.,
#monitor(:z, 10, function simulation(A, x)
for t in 1:1000
# ...
end
end)
But now you must write code in the macro that traverses the code in the function body, and injects your debug statement at the correct place. This is not an easy task. And it's even harder to write in a robust manner that wouldn't break the moment you modified your actual simulation code.
Traversing code and inserting it is a much easier task for you to do yourself with an editor. A common idiom for debugging statements is to use a one-liner, like this:
const debug = false
function simulation (A, x)
for t in 1:1000
z = rand(3)
x = A*x + z
debug && t%10==0 && append!(rec_z, z)
end
end
What's really cool here is that by marking debug as constant, Julia is able to completely optimize away the debugging code when it's false — it doesn't even appear in the generated code! So there is no overhead when you're not debugging. It does mean, however, that you have to restart Julia (or reload the module it's in) for you to change the debug flag. Even when debug isn't marked as const, I cannot measure any overhead for this simple loop. And chances are, your loop will be more complicated than this one. So don't worry about performance here until you actually double-check that it's having an effect.
You might be interested in this which i just whipped up. It doesn't QUITE do what you are doing, but it's close. Generally safe and consistent places to add code are the beginning and end of code blocks. These macros allow you to inject some code in those location (and even pass code parameters!)
Should be useful for say toggle-able input checking.
#cleaninject.jl
#cleanly injects some code into the AST of a function.
function code_to_inject()
println("this code is injected")
end
function code_to_inject(a,b)
println("injected code handles $a and $b")
end
macro inject_code_prepend(f)
#make sure this macro precedes a function definition.
isa(f, Expr) || error("checkable macro must precede a function definition")
(f.head == :function) || error("checkable macro must precede a function definition")
#be lazy and let the parser do the hard work.
b2 = parse("code_to_inject()")
#inject the generated code into the AST.
unshift!(f.args[2].args, b2)
#return the escaped function to the parser so that it generates the new function.
return Expr(:escape, f)
end
macro inject_code_append(f)
#make sure this macro precedes a function definition.
isa(f, Expr) || error("checkable macro must precede a function definition")
(f.head == :function) || error("checkable macro must precede a function definition")
#be lazy and let the parser do the hard work.
b2 = parse("code_to_inject()")
#inject the generated code into the AST.
push!(f.args[2].args, b2)
#return the escaped function to the parser so that it generates the new function.
return Expr(:escape, f)
end
macro inject_code_with_args(f)
#make sure this macro precedes a function definition.
isa(f, Expr) || error("checkable macro must precede a function definition")
(f.head == :function) || error("checkable macro must precede a function definition")
#be lazy and let the parser do the hard work.
b2 = parse(string("code_to_inject(", join(f.args[1].args[2:end], ","), ")"))
#inject the generated code into the AST.
unshift!(f.args[2].args, b2)
#return the escaped function to the parser so that it generates the new function.
return Expr(:escape, f)
end
################################################################################
# RESULTS
#=
julia> #inject_code_prepend function p()
println("victim function")
end
p (generic function with 1 method)
julia> p()
this code is injected
victim function
julia> #inject_code_append function p()
println("victim function")
end
p (generic function with 1 method)
julia> p()
victim function
this code is injected
julia> #inject_code_with_args function p(a, b)
println("victim called with $a and $b")
end
p (generic function with 2 methods)
julia> p(1, 2)
injected code handles 1 and 2
victim called with 1 and 2
=#
MATLAB operators usually translate into a function form as in the following examples:
~A => not(A)
A + B => plus(A,B)
A(...) => subsref(...)
A(...) = ... => subsasgn(...)
etc.
Now please consider the operators && and ||.
The various documentation (1-doc for or, 2-doc for and, 3-the MATLAB Programming Fundamentals ebook), does not shed any light on this, and nor do help and, help or, help relop.
This also didn't help: profile('on','-detail','builtin').
What I can say is that | seems to be redirected to or() judging by the following example:
>> 1 || [0,0]
ans =
1
>> 1 | [0,0]
ans =
1 1
>> or(1,[0,0])
ans =
1 1
>> 1 && [0,0]
Operands to the || and && operators must be convertible to logical scalar values.
So my question is: assuming it's possible - how can one explicitly call the underlying function of && and ||?
(note: this question deals with the aspect of "how", not "why")
There can't be a function implementing the underlying functionality. Assume there is a function scor which implements this operator, then calling scor(true,B) would evaluate B before calling scor, but the operator does not evaluate B.
Obviously scor could be defined scor=#(x,y)(x||y), but it will evaluate B in the upper case.
/Regarding the comment using function handles, this might be a workaround:
%not printing a:
true||fprintf('a')
%printing a:
scor=#(x,y)(x||y)
scor(true,fprintf('a'))
%not printing a:
scor(true,#()(fprintf('a')))
Given an arbitrary list of booleans, what is the most elegant way of determining that exactly one of them is true?
The most obvious hack is type conversion: converting them to 0 for false and 1 for true and then summing them, and returning sum == 1.
I'd like to know if there is a way to do this without converting them to ints, actually using boolean logic.
(This seems like it should be trivial, idk, long week)
Edit: In case it wasn't obvious, this is more of a code-golf / theoretical question. I'm not fussed about using type conversion / int addition in PROD code, I'm just interested if there is way of doing it without that.
Edit2: Sorry folks it's a long week and I'm not explaining myself well. Let me try this:
In boolean logic, ANDing a collection of booleans is true if all of the booleans are true, ORing the collection is true if least one of them is true. Is there a logical construct that will be true if exactly one boolean is true? XOR is this for a collection of two booleans for example, but any more than that and it falls over.
You can actually accomplish this using only boolean logic, although there's perhaps no practical value of that in your example. The boolean version is much more involved than simply counting the number of true values.
Anyway, for the sake of satisfying intellectual curiosity, here goes. First, the idea of using a series of XORs is good, but it only gets us half way. For any two variables x and y,
x ⊻ y
is true whenever exactly one of them is true. However, this does not continue to be true if you add a third variable z,
x ⊻ y ⊻ z
The first part, x ⊻ y, is still true if exactly one of x and y is true. If either x or y is true, then z needs to be false for the whole expression to be true, which is what we want. But consider what happens if both x and y are true. Then x ⊻ y is false, yet the whole expression can become true if z is true as well. So either one variable or all three must be true. In general, if you have a statement that is a chain of XORs, it will be true if an uneven number of variables are true.
Since one is an uneven number, this might prove useful. Of course, checking for an uneven number of truths is not enough. We additionally need to ensure that no more than one variable is true. This can be done in a pairwise fashion by taking all pairs of two variables and checking that they are not both true. Taken together these two conditions ensure that exactly one if the variables are true.
Below is a small Python script to illustrate the approach.
from itertools import product
print("x|y|z|only_one_is_true")
print("======================")
for x, y, z in product([True, False], repeat=3):
uneven_number_is_true = x ^ y ^ z
max_one_is_true = (not (x and y)) and (not (x and z)) and (not (y and z))
only_one_is_true = uneven_number_is_true and max_one_is_true
print(int(x), int(y), int(z), only_one_is_true)
And here's the output.
x|y|z|only_one_is_true
======================
1 1 1 False
1 1 0 False
1 0 1 False
1 0 0 True
0 1 1 False
0 1 0 True
0 0 1 True
0 0 0 False
Sure, you could do something like this (pseudocode, since you didn't mention language):
found = false;
alreadyFound = false;
for (boolean in booleans):
if (boolean):
found = true;
if (alreadyFound):
found = false;
break;
else:
alreadyFound = true;
return found;
After your clarification, here it is with no integers.
bool IsExactlyOneBooleanTrue( bool *boolAry, int size )
{
bool areAnyTrue = false;
bool areTwoTrue = false;
for(int i = 0; (!areTwoTrue) && (i < size); i++) {
areTwoTrue = (areAnyTrue && boolAry[i]);
areAnyTrue |= boolAry[i];
}
return ((areAnyTrue) && (!areTwoTrue));
}
No-one mentioned that this "operation" we're looking for is shortcut-able similarly to boolean AND and OR in most languages. Here's an implementation in Java:
public static boolean exactlyOneOf(boolean... inputs) {
boolean foundAtLeastOne = false;
for (boolean bool : inputs) {
if (bool) {
if (foundAtLeastOne) {
// found a second one that's also true, shortcut like && and ||
return false;
}
foundAtLeastOne = true;
}
}
// we're happy if we found one, but if none found that's less than one
return foundAtLeastOne;
}
With plain boolean logic, it may not be possible to achieve what you want. Because what you are asking for is a truth evaluation not just based on the truth values but also on additional information(count in this case). But boolean evaluation is binary logic, it cannot depend on anything else but on the operands themselves. And there is no way to reverse engineer to find the operands given a truth value because there can be four possible combinations of operands but only two results. Given a false, can you tell if it is because of F ^ F or T ^ T in your case, so that the next evaluation can be determined based on that?.
booleanList.Where(y => y).Count() == 1;
Due to the large number of reads by now, here comes a quick clean up and additional information.
Option 1:
Ask if only the first variable is true, or only the second one, ..., or only the n-th variable.
x1 & !x2 & ... & !xn |
!x1 & x2 & ... & !xn |
...
!x1 & !x2 & ... & xn
This approach scales in O(n^2), the evaluation stops after the first positive match is found. Hence, preferred if it is likely that there is a positive match.
Option 2:
Ask if there is at least one variable true in total. Additionally check every pair to contain at most one true variable (Anders Johannsen's answer)
(x1 | x2 | ... | xn) &
(!x1 | !x2) &
...
(!x1 | !xn) &
(!x2 | !x3) &
...
(!x2 | !xn) &
...
This option also scales in O(n^2) due to the number of possible pairs. Lazy evaluation stops the formula after the first counter example. Hence, it is preferred if its likely there is a negative match.
(Option 3):
This option involves a subtraction and is thus no valid answer for the restricted setting. Nevertheless, it argues how looping the values might not be the most beneficial solution in an unrestricted stetting.
Treat x1 ... xn as a binary number x. Subtract one, then AND the results. The output is zero <=> x1 ... xn contains at most one true value. (the old "check power of two" algorithm)
x 00010000
x-1 00001111
AND 00000000
If the bits are already stored in such a bitboard, this might be beneficial over looping. Though, keep in mind this kills the readability and is limited by the available board length.
A last note to raise awareness: by now there exists a stack exchange called computer science which is exactly intended for this type of algorithmic questions
It can be done quite nicely with recursion, e.g. in Haskell
-- there isn't exactly one true element in the empty list
oneTrue [] = False
-- if the list starts with False, discard it
oneTrue (False : xs) = oneTrue xs
-- if the list starts with True, all other elements must be False
oneTrue (True : xs) = not (or xs)
// Javascript
Use .filter() on array and check the length of the new array.
// Example using array
isExactly1BooleanTrue(boolean:boolean[]) {
return booleans.filter(value => value === true).length === 1;
}
// Example using ...booleans
isExactly1BooleanTrue(...booleans) {
return booleans.filter(value => value === true).length === 1;
}
One way to do it is to perform pairwise AND and then check if any of the pairwise comparisons returned true with chained OR. In python I would implement it using
from itertools import combinations
def one_true(bools):
pairwise_comp = [comb[0] and comb[1] for comb in combinations(bools, 2)]
return not any(pairwise_comp)
This approach easily generalizes to lists of arbitrary length, although for very long lists, the number of possible pairs grows very quickly.
Python:
boolean_list.count(True) == 1
OK, another try. Call the different booleans b[i], and call a slice of them (a range of the array) b[i .. j]. Define functions none(b[i .. j]) and just_one(b[i .. j]) (can substitute the recursive definitions to get explicit formulas if required). We have, using C notation for logical operations (&& is and, || is or, ^ for xor (not really in C), ! is not):
none(b[i .. i + 1]) ~~> !b[i] && !b[i + 1]
just_one(b[i .. i + 1]) ~~> b[i] ^ b[i + 1]
And then recursively:
none(b[i .. j + 1]) ~~> none(b[i .. j]) && !b[j + 1]
just_one(b[i .. j + 1] ~~> (just_one(b[i .. j]) && !b[j + 1]) ^ (none(b[i .. j]) && b[j + 1])
And you are interested in just_one(b[1 .. n]).
The expressions will turn out horrible.
Have fun!
That python script does the job nicely. Here's the one-liner it uses:
((x ∨ (y ∨ z)) ∧ (¬(x ∧ y) ∧ (¬(z ∧ x) ∧ ¬(y ∧ z))))
Retracted for Privacy and Anders Johannsen provided already correct and simple answers. But both solutions do not scale very well (O(n^2)). If performance is important you can stick to the following solution, which performs in O(n):
def exact_one_of(array_of_bool):
exact_one = more_than_one = False
for array_elem in array_of_bool:
more_than_one = (exact_one and array_elem) or more_than_one
exact_one = (exact_one ^ array_elem) and (not more_than_one)
return exact_one
(I used python and a for loop for simplicity. But of course this loop could be unrolled to a sequence of NOT, AND, OR and XOR operations)
It works by tracking two states per boolean variable/list entry:
is there exactly one "True" from the beginning of the list until this entry?
are there more than one "True" from the beginning of the list until this entry?
The states of a list entry can be simply derived from the previous states and corresponding list entry/boolean variable.
Python:
let see using example...
steps:
below function exactly_one_topping takes three parameter
stores their values in the list as True, False
Check whether there exists only one true value by checking the count to be exact 1.
def exactly_one_topping(ketchup, mustard, onion):
args = [ketchup,mustard,onion]
if args.count(True) == 1: # check if Exactly one value is True
return True
else:
return False
How do you want to count how many are true without, you know, counting? Sure, you could do something messy like (C syntax, my Python is horrible):
for(i = 0; i < last && !booleans[i]; i++)
;
if(i == last)
return 0; /* No true one found */
/* We have a true one, check there isn't another */
for(i++; i < last && !booleans[i]; i++)
;
if(i == last)
return 1; /* No more true ones */
else
return 0; /* Found another true */
I'm sure you'll agree that the win (if any) is slight, and the readability is bad.
It is not possible without looping. Check BitSet cardinality() in java implementation.
http://fuseyism.com/classpath/doc/java/util/BitSet-source.html
We can do it this way:-
if (A=true or B=true)and(not(A=true and B=true)) then
<enter statements>
end if
What is the difference between the | and || logical operators in MATLAB?
I'm sure you've read the documentation for the short-circuiting operators, and for the element-wise operators.
One important difference is that element-wise operators can operate on arrays whereas the short-circuiting operators apply only to scalar logical operands.
But probably the key difference is the issue of short-circuiting. For the short-circuiting operators, the expression is evaluated from left to right and as soon as the final result can be determined for sure, then remaining terms are not evaluated.
For example, consider
x = a && b
If a evaluates to false, then we know that a && b evaluates to false irrespective of what b evaluates to. So there is no need to evaluate b.
Now consider this expression:
NeedToMakeExpensiveFunctionCall && ExpensiveFunctionCall
where we imagine that ExpensiveFunctionCall takes a long time to evaluate. If we can perform some other, cheap, test that allows us to skip the call to ExpensiveFunctionCall, then we can avoid calling ExpensiveFunctionCall.
So, suppose that NeedToMakeExpensiveFunctionCall evaluates to false. In that case, because we have used short-circuiting operators, ExpensiveFunctionCall will not be called.
In contrast, if we used the element-wise operator and wrote the function like this:
NeedToMakeExpensiveFunctionCall & ExpensiveFunctionCall
then the call to ExpensiveFunctionCall would never be skipped.
In fact the MATLAB documentation, which I do hope you have read, includes an excellent example that illustrates the point very well:
x = (b ~= 0) && (a/b > 18.5)
In this case we cannot perform a/b if b is zero. Hence the test for b ~= 0. The use of the short-circuiting operator means that we avoid calculating a/b when b is zero and so avoid the run-time error that would arise. Clearly the element-wise logical operator would not be able to avoid the run-time error.
For a longer discussion of short-circuit evaluation, refer to the Wikipedia article on the subject.
Logical Operators
MATLAB offers three types of logical operators and functions:
| is Element-wise — operate on corresponding elements of logical arrays.
Example:
vector inputs A and B
A = [0 1 1 0 1];
B = [1 1 0 0 1];
A | B = 11101
|| is Short-circuit — operate on scalar, logical expressions
Example:
|| : Returns logical 1 (true) if either input, or both, evaluate to true, and logical 0 (false) if they do not.
Operand: logical expressions containing scalar values.
A || B (B is only evaluated if A is false)
A = 1;
B = 0;
C =(A || (B = 1));
B is 0 after this expression and C is 1.
Other is, Bit-wise — operate on corresponding bits of integer values or arrays.
reference link
|| is used for scalar inputs
| takes array input in if/while statements
From the source:-
Always use the && and || operators when short-circuiting is required.
Using the elementwise operators (& and |) for short-circuiting can
yield unexpected results.
Short-circuit || means, that parameters will be evaluated only if necessarily in expression.
In our example expr1 || expr2 if expr1 evaluates to TRUE, than there is no need to evaluate second operand - the result will be always TRUE. If you have a long chain of Short-circuit operators A || B || C || D and your first evaluates to true, then others won't be evaluated.
If you substitute Element-wise logical | to A | B | C | D then all elements will be evaluated regardless of previous operands.
| represents OR as a logical operator. || is also a logical operator called a short-circuit OR
The most important advantage of short-circuit operators is that you can use them to evaluate an expression only when certain conditions are satisfied. For example, you want to execute a function only if the function file resides on the current MATLAB path. Short-circuiting keeps the following code from generating an error when the file, myfun.m, cannot be found:
comp = (exist('myfun.m') == 2) && (myfun(x) >= y)
Similarly, this statement avoids attempting to divide by zero:
x = (b ~= 0) && (a/b > 18.5)
You can also use the && and || operators in if and while statements to take advantage of their short-circuiting behavior:
if (nargin >= 3) && (ischar(varargin{3}))