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Re: Numerical accuracy/precision - this is a bug or a feature?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120162] Re: Numerical accuracy/precision - this is a bug or a feature?
  • From: FranD <seacrofter001 at yahoo.com>
  • Date: Sun, 10 Jul 2011 05:02:57 -0400 (EDT)

Is using "`" an acceptable work-around?

a = 2.`30; b = Sqrt[2]; c = a b;
check[x_] := {x, Precision[x]} 

check[a]    {2.00000000000000000000000000000, 30.}
check[b]    {Sqrt[2], \[Infinity]}
check[c]    {2.82842712474619009760337744842, 30.}

-FranD


Slawek wrote:

> Let Mathematica (6.x, 7.x) compute quite a simple
> product
> 
> In[1]:= N[N[2.0, 20] * N[Sqrt[2] , 20], 20]
> 
> Out[1]= 2.82843
> 
> This is a bug.
> 
> Why?
> 
> Now we analyze it in details:
> 
> 1. N[2.0,20] should give 2 with
> accuracy/precision/whatsever about 20 
> decimal digits, i.e. 2.00000000000000000000
> 
> 2. Sqrt[2] should give... Sqrt[2]
> 
> 3. N[Sqrt[2]] should give 1.4142135623730950488 (this
> is copy-paste from 
> Mathematica output to N[Sqrt[2]] )
> 
> 4. The product 2.00000000000000000000 *
> 1.4142135623730950488 is 
> 2.8284271247461900976 (again copy-paste)
> 
> 5. BUT THE RESULT OF  N[2.0, 20] * N[Sqrt[2] , 20]
>  "truncated to 20 digits" 
> is Out[1]= 2.82843
> 
> Where are missing digits?!
> 
> slawek


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