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Re: avoiding non-machine numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115581] Re: avoiding non-machine numbers
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sat, 15 Jan 2011 04:46:03 -0500 (EST)
  • References: <igpbd4$fae$1@smc.vnet.net>

On 14.01.2011 12:17, wpb wrote:
> By default, Mathematica switches to non-machine numbers when needed,
> eg,
>
> In[4334]:= Exp[-50.^2]
>
> Out[4334]= 1.835672669162*10^-1086
>
> But this has a severe possible drawback in terms of computational
> speed. For example, the following is very quick
>
> In[4420]:= t = RandomReal[NormalDistribution[0, .1], 400000];
> Exp[-t^2]; // Timing
>
> Out[4421]= {0., Null}
>
> but in the following computation non-machine numbers are generated,
> and we get an enormous decrease in speed:
>
> In[4422]:= t = RandomReal[NormalDistribution[0, 20], 400000];
> Exp[-t^2]; // Timing
>
> Out[4423]= {1.25, Null}
>
> So is it possible to get a computation such as Exp[-50.^2] to evaluate
> to zero in a very fast way? That is, that small numbers outside
> machine-precision range evaluate to zero automatically?
>
> Thanks, Wicher
>

-$MachinePrecision Log[10] gives -36.7368. So all values less than this 
value should be ignored:

mExp[x_] := 0. /; x < -36.7368;
mExp[x_] := Exp[x];
SetAttributes[mExp, {Listable, NumericFunction}];

t=-RandomReal[NormalDistribution[0, 20], 400000]^2;
{t0, r0} = Timing[Exp[t]];
{t1, r1} = Timing[mExp[t]];
Union[r1 - r0 // Chop]
1 - t1 / t0
returns {0} as (chopped) differences and an improvement in speed of ~ 30%

Peter


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