Re: How Computers Represent Floats

[colinr(at)toliman.uio.no (Colin Rosenthal)]

On Thu, 30 Nov 2000 13:23:41 -0700, 
William B. Clodius <wclodius@lanl.gov> wrote:
>
>
>"William B. Clodius" wrote:
>> <snip> IEEE 754 requires that all intermediate calculations
>> be performed a higher precision so
>Ignore the above incomplete sentence. What I originally attempted to
>write was covered later.
>> 
>> <snip>
>
>Some other surprises. 
>
>The definition of the IEEE 754 mantisa, an integer with values from
>2^n_mant to 2*2^n_mant-1, where n_mant is the number of bits available
>for the mantisa, is termed a normalized number. This is error prone for
>very small numbers. IEEE 754 mandates that there be available for such
>small numbers what are termed denorms where the mantissa is  interpreted
>as an integer from 0 to 2^n_mant, so that accuracy degrades gradually
>for such values. However, this complicates the implementation of the
>floating point, so some processors, e.g., the DEC Alpha make this
>available only in software at a greatly reduced performance.

This sounds like it relates to my most recent problem - generating
real input files with IDL for a DEC Alpha fortran program. The
fortran program had big problems manipulating small numbers
generated by the IDL and I had to pepper the IDL code with WHERE
statements to set all very small numbers to zero. Has anyone else
seen stuff like this? 

-- 
Colin Rosenthal
Astrophysics Institute
University of Oslo