Floating Point toolbox
Purpose
The goal of this toolbox is to provide a collection of
algorithms for floating point number management.
This is more a learning tool than an operationnal component,
although it might complement some features which are not
provided by Scilab.
The flps_systemgui function allows to see the distribution
of floating point numbers graphically.
By varying the rounding mode, the precision and the logscale,
we can actually the distribution of a toy floating
point number. Adding or suppressing the denormals can be
instructive too.
The functions allow to compute automatically the
properties of the current Scilab system with
respect to the doubles. It is similar in spirit
to the number_properties functions, except that
our functions are based on macros and that
the returned values are made consistent
with the references cited in the bibliography.
Moreover, the flps_radix function returns
the current radix and allows to check that the
current rounding mode is round-to-nearest (which
is IEEE's default).
The functions allow to create virtual floating point
systems, which allows to see their discrete nature
in simplified examples. The rounding mode of
such a virtual floating point system can be configured
to one of the four mode from the IEEE standard.
This feature allows to see the effect of the rounding mode
on the distribution of floating point numbers. This is
not easy to see with a straightforward Scilab, since the
rounding mode is round-to-nearest, most of the time.
The following is a list of the current functions :
flps_IEEEdouble : Returns the floating point system for a IEEE double.
flps_IEEEdoubleext : Returns an IEEE double extended floating point system.
flps_IEEEsingle : Returns the floating point system for a IEEE single.
flps_chop : Round matrix elements to t significant binary places.
flps_emax : Returns the maximum exponent and value before overflow.
flps_emin : Returns the minimum exponent and value before underflow.
flps_eps : Returns the machine epsilon and the precision for Scilab doubles.
flps_format2system : Returns the floating point system of the given format.
flps_frexp : Returns the exponent and fraction.
flps_frombary : Returns the floating point number given its b-ary
decomposition.
flps_isIEEE : Returns true if the current system satisfies basic IEEE
requirements.
flps_numbereval : Returns the value of the current floating point number.
flps_numberformat : Returns the floating point number of the given double.
flps_numbernew : Returns a new floating point number.
flps_radix : Compute the radix used for Scilab doubles.
flps_systemall : Returns the list of floating point numbers of the given
floating point system.
flps_systemgui : Plots all the numbers in the current floating point system
flps_systemnew : Returns a new floating point system.
flps_tobary : Returns the digits of the b-ary decomposition.
See DLAMCH for a comparison with Lapack's algorithms:
http://www.netlib.org/misc/dlamch.f
See number_properties in Scilab for a comparison :
modules/elementary_functions/sci_gateway/fortran/sci_f_number_properties.f
Author
Michael Baudin
Licence
This toolbox is released under the CeCILL_V2 licence :
http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt