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I coined Integers Of Unusual Size to mean "bignum" using GMP, the underpinning of Mathematica's ability to craft very big numbers.

I have these functions from this question:

ascendingQ[x_] := 3 == Mod[x, 4]
uniqueQ[x_] := 0 != Mod[2 x - 1, 3]
uniqueRank[n_, m_] := Block[{a = If[1 != n && OddQ[n], n - 1, n]},
   (n + IntegerExponent[a, 2]) 2^m - 1]  

The first two need "bignum" inputs and the third needs "bignum" output

And I have this variation of countOrbit which we will use for our research:

totalOrbit[x_] := 
 Block[{h = x, t, c = 0, m, n, mt = 0, nt = 0},
  While[1 != h,
   h = (t = -1 + (3/2)^(m = IntegerExponent[h + 1, 2]) (h + 1))/
     2^(n = IntegerExponent[t, 2]);
   mt += m;
   nt += n;
  c = 2 mt + nt

This needs "bignum" everywhere. When we get a sufficiently frisky totalOrbit I will recast countOrbit.

After I execute the compiled totalOrbit, I get error messages about exceeding machine precision,

cto = Compile[{x}, totalOrbit[x]]

so, I need a way to indicate that all numbers are "bignums."

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Unfortunately Compile supports only machine-size integers, ruling out bignums. – kirma Aug 5 '13 at 10:54
@kirma, make that an answer and I will accept it. – Fred Kline Aug 5 '13 at 11:48

2 Answers 2

up vote 3 down vote accepted

Unfortunately Compile supports only machine-size integers, ruling out bignums.

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As pointed out in the comments, Compile uses machine numbers only. Also note that IntegerExponent is not a compilable function as can be seen from this example:

f = Compile[{{in, _Integer, 0}}, IntegerExponent[in]];

Note the call to MainEvaluate in the output. This indicates that the function can not be compiled.

Concerning your top level functions, the switch between bignum and machine integer is opaque in Mathematica. If a calculation needs big integers it will internally switch to such a representation. No action on your part is required for that.

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