Re: How do twice Working Precision in square operation

• To: mathgroup at smc.vnet.net
• Subject: [mg86125] Re: [mg86002] How do twice Working Precision in square operation
• From: danl at wolfram.com
• Date: Sun, 2 Mar 2008 13:58:16 -0500 (EST)
• References: <200802291122.GAA19237@smc.vnet.net>

```> Who know how  forced  double numerical precision in operation ^2 or
> triple in ^3
> e.g. we have number with precision 300 digits after comma and we do
> square of this number
>
> N[-23.83242089169940112293636352304345516242356370829658528533245578869781207629749826968513219545485106785646817025052324254382671446440221122018213525849182937524917564915820784936033688847601879751439448736954164351572578669610243156800163244111408628195484090841094436992490050778`263.90219946983575^2,600]
>
>
> How do that on Mathematica ?
>
> BEST WISHES
> ARTUR

Call the input nn. You could do

nn2 = SetPrecision[nn^2, 600]

but the digits added will be garbage. Well, actually what gets appended
are zeros in base 2 (which, numerically, are garbage, but not random
garbage). You can see this by looking at RealDigits[nn2, 2].

If you question involves wanting to see justifiable digits, you cannot
because, mathematically, they do not exist. Mathematica is showing all
digits that are justified (up to a fairly reliable first order
approximation of error, if you want to get a bit technical).

Daniel Lichtblau
Wolfram Research

```

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