Answered in comments.

I find the built-in function IntegerReverse[n] is roughly an order of magnitude slower than the simple alternative FromDigits[Reverse[IntegerDigits[n]]].

Tests were made with the following code:

testnumbers = Range[10^4];
(IntegerReverse /@ testnumbers;) // Timing
((FromDigits[Reverse[IntegerDigits[#]]]&) /@ testnumbers;) // Timing

Version 11 gives:

{0.140625, Null}
{0.015625, Null}

Version 10 (on a different machine) gives:

{0.0625, Null}
{0.015625, Null}

This is a huge difference. I'm wondering if I'm missing a slowing feature of IntegerReverse or something like that.

Can anyone confirm this result? Should we report this to wolfram?

  • 1
    $\begingroup$ You may be interested in evaluating <<GeneralUtilities`; PrintDefinitions[IntegerReverse] to see the features and spot the differences. $\endgroup$
    – user31159
    Sep 15, 2016 at 12:06
  • $\begingroup$ Thanks. This answers the question. I did not thought, that this small overhead produces such a delay in evaluation. $\endgroup$ Sep 15, 2016 at 12:14

1 Answer 1


A substantial part of the timing difference in this example is due to the automatic compilation used by Map. Note the crossover setting

SystemOptions["CompileOptions" -> "MapCompileLength"]

(* {"CompileOptions" -> {"MapCompileLength" -> 100}} *)

and compare

testnumbers = Range[10^4];
AbsoluteTiming[Map[FromDigits[Reverse[IntegerDigits[#]]] &, testnumbers];]

(* {0.006648, Null} *)


SetSystemOptions["CompileOptions" -> "MapCompileLength" -> Infinity];   
AbsoluteTiming[Map[FromDigits[Reverse[IntegerDigits[#]]] &, testnumbers];]

(* {0.015754, Null} *)

The relevant part of the implementation of IntegerReverse, while straightforward and seemingly similar

Attributes[IntegerReverse] := {Listable, Protected, ReadProtected};
IntegerReverse[n_Integer] := With[{digits = Quiet @ IntegerDigits @ n},
     FromDigits[Reverse[digits]] /; ListQ[digits]];

is not compilation-friendly. This weakness may be addressed by a future version of the compiler.


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