I have the following bitwise expression and was wondering if it could be simplified or if there is a general way of interpreting the output.
(x & y) | (~x & ~y)
The only "simpler" version is ~(x^y) (where ^ is the XOR operator).
However, It's not going to make a significant difference computationally, and is harder to read for most people (XOR is not as natural as AND and OR). There's not a simpler version using just AND and OR operators, so I would suggest you just leave it as-is.
if there is a general way of interpreting the output.
"Either both are true or both are false" is a natural interpretation.
Related
I am writing an algorithm in a limited language where the bitwise operators at my disposal are
AND: &
OR: |
XOR: ^
SRL: << (shift left)
SLL: >> (shift right)
I realized I need to be able to take the bitwise complement of an integer, commonly denoted ~x in other languages.
Could I somehow express ~x, using only the {&, |, ^, <<, >>} operators?
I would try to just implement this operator in the language’s compiler, but it seems like a very challenging task. I would much rather do some dirty hack to express NOT x without ~.
I've been asked to compute !x without using !.
Examples:
bang(3) = 0
bang(0) = 1
The legal operations: ~, $, |, ^, +, <<, >>
I don't understand what a bang does? I thought it was a factorial.
If in C, your "!" is a boolean inverse of its argument. So, !0 yields 1 and 1(anything else) yields 0. The "~" is the bitwise version of it, essentially flipping each bit in the (following) number - much easier to understand if you constrain yourself to unsigned numbers.
!x can be emulated with things like (x?1:0) - which isn't in your list - and the && and || operators - which also aren't in your list. "$" isn't an operator in C, so I'm a bit puzzled by that one - what language are you in? You might have some luck using the | and looping through all the bits to figure out if any are set, after that point using the bitwise operators on just your resulting 1 bit make it pretty easy to emulate "!".
I could just lay it out, but if you're taking a class, the struggle is where most of the gain is for this particular problem.
! is the logical negation operator. Your favorite search engine will tell you more.
I'm not looking for an implementation, just pseudo-code, or at least an algorithm to handle this effectively. I need to process statements like these:
(a) # if(a)
(a,b) # if(a || b)
(a+b) # if(a && b)
(a+b,c) # same as ((a+b),c) or if((a&&b) || c)
(a,b+c) # same as (a,(b|c)) or if(a || (b&&c))
So the + operator takes precedence over the , operator. (so my + is like mathematical multiplication with , being mathematical addition, but that is just confusing).
I think a recursive function would be best, so I can handle nested parentheses nice and easy by a recursive call. I'll also take care of error handling once the function returns, so no worries there. The problems I'm having:
I just don't know how to tackle the precedence thing. I could return true as soon as I see a , and the previous value was true. Otherwise, I'll rerun the same routine. A plus would effectively be a bool multiplication (ie true*true=true, true*false=false etc...).
Error detection: I've thought up several schemes to handle the input, but there are a lot of ugly bad things I want to detect and print an error to the user. None of the schemes I thought of handle errors in a unified (read: centralized) place in the code, which would be nice for maintainability and readability:
()
(,...
(+...
(a,,...
(a,+...
(a+,...
(a++...
Detecting these in my "routine" above should take care of bad input. Of course I'll check end-of-input each time I read a token.
Of course I'll have the problem of maybe having o read the full text file if there are unmatched parenthesis, but hey, people should avoid such tension.
EDIT: Ah, yes, I forgot the ! which should also be usable like the classic not operator:
(!a+b,c,!d)
Tiny update for those interested: I had an uninformed wild go at this, and wrote my own implementation from scratch. It may not be pretty enough for the die-hards, so hence this question on codereview.
The shunting-yard algorithm is easily implementable in a relatively short amount of code. It can be used to convert an infix expression like those in your examples into postfix expressions, and evaluation of a postfix expression is Easy-with-a-capital-E (you don't strictly need to complete the infix-to-postfix conversion; you can evaluate the postfix output of the shunting yard directly and just accumulate the result as you go along).
It handles operator precedence, parentheses, and both unary and binary operators (and with a little effort can be modified to handle infix ternary operators, like the conditional operator in many languages).
Write it in yacc (bison) it becomes trivial.
/* Yeacc Code */
%token IDENTIFIER
%token LITERAL
%%
Expression: OrExpression
OrExpression: AndExpression
| OrExpression ',' AndExpression
AndExpression: NotExpression
| AndExpression '+' NotExpression
NotExpression: PrimaryExpression
| '!' NotExpression
PrimaryExpression: Identifier
| Literal
| '(' Expression ')'
Literal: LITERAL
Identifier: IDENTIFIER
%%
There's probably a better (there's definitely a more concise) description of this, but I learned how to do this from this tutorial many years ago:
http://compilers.iecc.com/crenshaw/
It's a very easy read for non-programmers too (like me). You'll need only the first few chapters.
I have a code like
A = B|C|D|E;
Throwing the warning "suggest parentheses around arithmetic in operand of |"
Expecting that expression needs high priority paranthesis for operators, tried the following ways:
A=(B|C)|(D|E);
one more as :
A=(((B|C)|D)|E);
Still the same warning persists.
Please help me in resolving this.
Thanks,
Sujatha
B, C,D are enums and E is an integer.
You have some arithmetic operator in your expression that isn't really simply B, or that isn't really simply C, etc. The compiler is suggesting that you parenthesize whichever expression so that readers will see that you wrote what you meant. If you don't parenthesize, everyone has to remember exactly what the priorities are, and they have to figure out if you remembered when you wrote it.
Try this: (B)|(C)|(D)|(E).
This is a weird warning. You only really need to pay attention to precedence when you're using different operators and those operators have different precedences. For instance, in arithmetic multiplication has higher precedence than addition.
But in this case you're using only one operator multiple times. Bitwise or is associative and commutative ((A | B) | C == A | (B | C) and A | B == B | A) so there's really no reason for the warning.
Or are we all sticking to our taught "&&, ||, !" way?
Any thoughts in why we should use one or the other?
I'm just wondering because several answers state thate code should be as natural as possible, but I haven't seen a lot of code with "and, or, not" while this is more natural.
I like the idea of the not operator because it is more visible than the ! operator. For example:
if (!foo.bar()) { ... }
if (not foo.bar()) { ... }
I suggest that the second one is more visible and readable. I don't think the same argument necessarily applies to the and and or forms, though.
"What's in a name? That which we call &&, || or !
By any other name would smell as sweet."
In other words, natural depends on what you are used to.
Those were not supported in the old days. And even now you need to give a special switch to some compilers to enable these keywords. That's probably because old code base may have had some functions || variables named "and" "or" "not".
One problem with using them (for me anyway) is that in MSVC you have to include iso646.h or use the (mostly unusable) /Za switch.
The main problem I have with them is the Catch-22 that they're not commonly used, so they require my brain to actively process the meaning, where the old-fashioned operators are more or less ingrained (kind of like the difference between reading a learned language vs. your native language).
Though I'm sure I'd overcome that issue if their use became more universal. If that happened, then I'd have the problem that some boolean operators have keywords while others don't, so if alternate keywords were used, you might see expressions like:
if ((x not_eq y) and (y == z) or (z <= something)) {...}
when it seems to me they should have alternate tokens for all the (at least comparison) operators:
if ((x not_eq y) and (y eq z) or (z lt_eq something)) {...}
This is because the reason the alternate keywords (and digraphs and trigraphs) were provided was not to make the expressions more readable - it was because historically there have been (and maybe still are) keyboards and/or codepages in some localities that do not have certain punctuation characters. For example, the invariant part of the ISO 646 codepage (surprise) is missing the '|', '^' and '~' characters among others.
Although I've been programming C++ from quite some time, I did not know that the keywords "and" "or" and "not" were allowed, and I've never seen it used.
I searched through my C++ book, and I found a small section mentioning alternative representation for the normal operators "&&", "||" and "!", where it explains those are available for people with non-standard keyboards that do not have the "&!|" symbols.
A bit like trigraphs in C.
Basically, I would be confused by their use, and I think I would not be the only one.
Using a representation which is non-standard, should really have a good reason to be used.
And if used, it should be used consistently in the code, and described in the coding standard.
The digraph and trigraph operators were actually designed more for systems that didn't carry the standard ASCII character set - such as IBM mainframes (which use EBCDIC). In the olden days of mechanical printers, there was this thing called a "48-character print chain" which, as its name implied, only carried 48 characters. A-Z (uppercase), 0-9 and a handful of symbols. Since one of the missing symbols was an underscore (which rendered as a space), this could make working with languages like C and PL/1 a real fun activity (is this 2 words or one word with an underscore???).
Conventional C/C++ is coded with the symbols and not the digraphs. Although I have been known to #define "NOT", since it makes the meaning of a boolean expression more obvious, and it's visually harder to miss than a skinny little "!".
I wish I could use || and && in normal speech. People try very hard to misunderstand when I say "and" or "or"...
I personally like operators to look like operators. It's all maths, and unless you start using "add" and "subtract" operators too it starts to look a little inconsistent.
I think some languages suit the word-style and some suit the symbols if only because it's what people are used to and it works. If it ain't broke, don't fix it.
There is also the question of precedence, which seems to be one of the reasons for introducing the new operators, but who can be bothered to learn more rules than they need to?
In cases where I program with names directly mapped to the real world, I tend to use 'and' and 'or', for example:
if(isMale or isBoy and age < 40){}
It's nice to use 'em in Eclipse+gcc, as they are highlighted. But then, the code doesn't compile with some compilers :-(
Using these operators is harmful. Notice that and and or are logical operators whereas the similar-looking xor is a bitwise operator. Thus, arguments to and and or are normalized to 0 and 1, whereas those to xor aren't.
Imagine something like
char *p, *q; // Set somehow
if(p and q) { ... } // Both non-NULL
if(p or q) { ... } // At least one non-NULL
if(p xor q) { ... } // Exactly one non-NULL
Bzzzt, you have a bug. In the last case you're testing whether at least one of the bits in the pointers is different, which probably isn't what you thought you were doing because then you would have written p != q.
This example is not hypothetical. I was working together with a student one time and he was fond of these literate operators. His code failed every now and then for reasons that he couldn't explain. When he asked me, I could zero in on the problem because I knew that C++ doesn't have a logical xor operator, and that line struck me as very odd.
BTW the way to write a logical xor in C++ is
!a != !b
I like the idea, but don't use them. I'm so used to the old way that it provides no advantage to me doing it either way. Same holds true for the rest of our group, however, I do have concerns that we might want to switch to help avoid future programmers from stumbling over the old symbols.
So to summarize: it's not used a lot because of following combination
old code where it was not used
habit (more standard)
taste (more math-like)
Thanks for your thoughts