Re: String-to-Number Conversion Precision
- To: mathgroup at smc.vnet.net
- Subject: [mg112359] Re: String-to-Number Conversion Precision
- From: Peter Breitfeld <phbrf at t-online.de>
- Date: Fri, 10 Sep 2010 06:13:34 -0400 (EDT)
- References: <i6crfo$sa1$1@smc.vnet.net>
Ben wrote:
> I'm reading real numbers from a file and I'm trying to convert them
> from string format (with arbitrary precision) to real values with the
> same precision as given in the strings.
>
> For example, when I convert "1.867524468", I want the result to be set
> to precision 10. Instead, I get the following.
>
> In[1]:= string = "1.867524468"
> Out[1]:= "1.867524468"
>
> In[2]:= x = ToExpression[string]
> Out[2]:= 1.86752
>
> The last 4-digits get cut off. This is fine for when I do math with
> the number because the extra digits are still stored, but not when I
> want to rewrite the number to a different file. When I convert the
> number back to a string for file output, the last 4-digits remain
> lost.
>
> In[3]:= ToString[x]
> Out[3]:= "1.86752"
>
> Is there a function or formula I can use to automatically set the
> precision of these numbers to their precision in the string? Thanks.
>
Mathematica treats numbers with less then $MachinePrecision digits
always as having MachinePrecision. It _displays_ them with 6 digits
after the decimal point, but knows all the digits. You can display them
using NumberForm or better (in this case) using InputForm. So
In[3]:= ToString[InputForm[x]]
will give you all the original digits.
To set the precision for longer numbers according to the length of the
input string you may use something like this:
string = "1.867524468121212771299123312";
x = ToExpression[string]
SetPrecision[x, StringLength[string] - 1]
{Precision[x], Accuracy[x]}
InputForm[x]
--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de