Finding if a number is perfect square

Asked Jan 03 '21 at 14:40

Active Jan 03 '21 at 14:57

Viewed 56 times

I used the following code to found if a specific number is a perfect square:

Clear["Global`*"];
ParallelTable[
  If[IntegerQ[Sqrt[ ...]], ..., Nothing], {..., ..., ...}] //. {} -> 
  Nothing

Mathematice can do this for numbers up to:

$MaxMachineNumber

1.79769*10^308

But my code is way, way too slow. Is there an other way to write the code in Mathematica that will be much faster?

I would accept a recommendation to use another programming language to find if a number is a perfect square for large values (like $10^{12}$ and bigger)? I know that ULLONG_MAX in C++ can handle values up to $18446744073709551615$. But code in C++ is slow for larger values. I also thought about using properties of square numbers in my program, but that means that I also need to compute the values.

edited Jan 03 '21 at 14:57

m_goldberg

107,779
16
103
257

asked Jan 03 '21 at 14:40

Jan Eerland

2,001
10
17

Have you seen this? – J. M.'s missing motivation Jan 03 '21 at 14:44
@J.M.'sennui Yes I saw, but I am using Mathematica 12.0. What program is the fastest? And are they faster than using a pure C++ pogram that can parallize a lot of calculations? – Jan Eerland Jan 03 '21 at 14:48
@m_goldberg No it does not. See my comment above. – Jan Eerland Jan 03 '21 at 15:03
You may also be interested in the internal function NumberTheory`PowersRepresentationsDump`ProbablePerfectSquareQ. – MarcoB Jan 03 '21 at 15:17
@Derik if the missing link is “what approach is the fastest”, then you should benchmark each approach on your computer to see. – MarcoB Jan 03 '21 at 15:19
1

In this answer I use a C function isqrt that computes integer square roots and that will return -1 if a number is not a perfect square. It's quite fast and may work for you too. Depending on your use case you can set myint to be 64-bits instead of 128-bits (using typedef int64_t myint; at the beginning of the code), which will make the code still much faster. – Roman Jan 03 '21 at 18:14
Here are some more ideas for a fast C code. – Roman Jan 03 '21 at 18:19

Finding if a number is perfect square

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