[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: How Computers Represent Floats

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