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MathGroup Archive 2007

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Re: Next representable number

  • To: mathgroup at
  • Subject: [mg73627] Re: [mg73542] Next representable number
  • From: Daniel Lichtblau <danl at>
  • Date: Fri, 23 Feb 2007 04:38:41 -0500 (EST)
  • References: <>

Andrew Moylan wrote:
> What's a neat way to determine the next (higher) representable number
> (at a given precision)? That is, I want f[x] to be the smallest
> representable number (at precision Precision[x]) that's larger than x.

I'm not sure this is quite correct but here goes.

(1) Convert to binary using RealDigits.

(2) Add one to the last "bit" in the mantissa. No matter if it 
"overflows"; the reverse conversion won't mind. This feature caused 
remarkable controversy in-house a few months ago.

(3) Convert from {mantissa,exponent} to a rational using FromDigits.

(4) Numericize to the original precision.

nextRepresentable[x_Real] := Module[
   {mant, expon, prec=Precision[x]},
   {mant,expon} = RealDigits[x];
   N[FromDigits[{Append[Most[mant],Last[mant]+1],expon}], prec]

In[40]:= ee = N[7/4,22]
Out[40]= 1.750000000000000000000

In[41]:= ff = nextRepresentable[ee]
Out[41]= 1.750000000000000000001

In[42]:= InputForm[ff-ee]
Out[42]//InputForm= 1.`0.45593195564972433*^-21

Daniel Lichtblau
Wolfram Research

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