Re: How do twice Working Precision in square operation

• To: mathgroup at smc.vnet.net
• Subject: [mg86154] Re: How do twice Working Precision in square operation
• From: Steven Siew <siewsk at bp.com>
• Date: Mon, 3 Mar 2008 04:43:09 -0500 (EST)
• References: <200802291122.GAA19237@smc.vnet.net> <fqb8rc\$n3f\$1@smc.vnet.net>

```In[3]:=
n=12.34
n2=n*n

Out[3]= 12.34
Out[4]= 152.276

At fist glance, it seems like you can get 6 digits of precision if you
square a number with 4 digits of precision.

But, if you assume the number 12.34 has a lower bound of 12.341 and a
higher bound of 12.349 then you can see

In[5]:=
low=12.341
low2=low*low

Out[5]= 12.341
Out[6]= 152.3

In[7]:=
high=12.349
high2=high*high

Out[7]= 12.349
Out[8]= 152.498

You can see that low2=152.3 and high2=152.49 , so you only get at most
"3 to 4" digits of precision after you have square the number. You do
not get 6 digits of precision. As Daniel Lichtblau from Wolfram has
mentioned, increasing the precision artificially is nothing but self-
deception.

On Mar 1, 8:49 pm, Artur <gra... at csl.pl> wrote:
> 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]
>