Thread overview
D Compilers Disprove Fermat’s Last Theorem
May 17
user1234
May 18
Dukc
May 20
deadalnix
May 17

I accidentally found an old funny article about the undefined behavior in C / C++:
C Compilers Disprove Fermat’s Last Theorem

After a little testing, I can confidently state that D compilers disprove Fermat’s Last Theorem too!

// fermat.d
import std.stdio;

bool fermat() {
  const max = 1000;
  int a = 1, b = 1, c = 1;
  while(true) {
    if(((a * a * a) == ((b * b * b) + (c * c * c)))) return true;
    a++;
    if(a > max) { a=1; b++; }
    if(b > max) { b=1; c++; }
    if(c > max) { c=1; }
  }
  return false;
}

void main() {
  if(fermat()) writeln("Fermat's Last Theorem has been disproved.");
  else writeln("Fermat's Last Theorem has not been disproved.");
}
$ ldc2 -O2 --run fermat.d
Fermat's Last Theorem has been disproved.

Check it out on run.dlang.io

May 17

On Monday, 17 May 2021 at 07:53:56 UTC, Jack Applegame wrote:

>

I accidentally found an old funny article about the undefined behavior in C / C++:
C Compilers Disprove Fermat’s Last Theorem

After a little testing, I can confidently state that D compilers disprove Fermat’s Last Theorem too!
...
Fermat's Last Theorem has been disproved.

Check it out on [run.dlang.io](https://run.dlang.io/is/TrO2aH)

intersting but dmd -O does not disprove.
Alos it's not about D, it's about backend optimizations, as expalined in the article.

May 17
On Mon, May 17, 2021 at 07:53:56AM +0000, Jack Applegame via Digitalmars-d wrote:
> I accidentally found an old funny article about the undefined behavior
> in C / C++:
> [C Compilers Disprove Fermat’s Last
> Theorem](https://blog.regehr.org/archives/140)
> 
> After a little testing, I can confidently state that D compilers disprove Fermat’s Last Theorem too!

This reminds me of this thread:

	https://forum.dlang.org/post/mailman.3657.1591403118.31109.digitalmars-d@puremagic.com

in which DMD-compiled code is able to perceive quantum superimposition directly, as opposed to LDC-produced code that can only perceive one of the collapsed states at a time.

:-D


T

-- 
Shin: (n.) A device for finding furniture in the dark.
May 18

On Monday, 17 May 2021 at 08:24:22 UTC, user1234 wrote:

>

intersting but dmd -O does not disprove.
Alos it's not about D, it's about backend optimizations, as expalined in the article.

To be more accurate, dmd-compiled code enters infinite loop, just as it should. Printing "fermat's theorem has not been disproven" would be just as wrong as LDC behaviour.

It's surprising how so many backends can have the same optimizing bug even in 2021. Kudos for DMD doing the right thing.

May 20

On Tuesday, 18 May 2021 at 07:17:50 UTC, Dukc wrote:

>

On Monday, 17 May 2021 at 08:24:22 UTC, user1234 wrote:

>

intersting but dmd -O does not disprove.
Alos it's not about D, it's about backend optimizations, as expalined in the article.

To be more accurate, dmd-compiled code enters infinite loop, just as it should. Printing "fermat's theorem has not been disproven" would be just as wrong as LDC behaviour.

It's surprising how so many backends can have the same optimizing bug even in 2021. Kudos for DMD doing the right thing.

Believe it or not, it is not a bug, at least not in C++. Consider the transforms as follow.

1/ What's after the loop is unreachable, therefore it can be removed.
2/ An analysis of the function shows that it has no side effects.
3/ Now the function must return true, granted that it returns at all.
4/ At the call site, we got a function with no side effect that can only return true, therefore we can constant fold the call to true.

You will note that all the transformation are trivially correct, except 3, because we don't know if the function will return or not. This is where precise legalese of the language definition comes into play, as it turns out, in C++ - and C++ is by far the language people working on optimizer have focused the most - it is not mandatory to prove that the function will terminate.

In a way, it does make sense, because providing that the function will terminate is equivalent to proving the halting problem, or, in this specific case, Fermat's last theorem, which is not something reasonable to expect from the optimizer.

If the language asks you to prove this terminates, then the cost you pay is that many function that will terminate will not be optimized, because it is too difficult to prove it.