Floating Point

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.

Features

The following is a list of the current functions :

• Convert
• flps_Me2sm : Returns the (s,m) representation given (M,e).
• flps_double2hex : Converts a double into a hexadecimal string.
• flps_frombary : Returns the floating point number given its b-ary decomposition.
• flps_hex2double : Converts a hexadecimal string into its double.
• flps_sme2M : Returns the integral significand from (s,m,e).
• flps_tobary : Returns the digits of the b-ary decomposition.
• Functions
• flps_chop : Round matrix elements to t significant binary places.
• flps_frexp : Returns the exponent and fraction.
• flps_minimumdecimalstr : Returns the minimum string for equality.
• flps_signbit : Returns the sign bit of x
• Number
• flps_number2hex : Converts a floating point number into a hexadecimal string.
• flps_numbereval : Returns the value of the current floating point number.
• flps_numbergetclass : Returns the class of the number;
• flps_numberisfinite : Returns true if the number is finite.
• flps_numberisinf : Returns true if the number is an infinity.
• flps_numberisnan : Returns true if the number is a nan.
• flps_numberisnormal : Returns true if the number is bnormal.
• flps_numberissubnormal : Returns true if the number is subnormal.
• flps_numberiszero : Returns true if the number is zero.
• flps_numbernew : Returns a new floating point number.
• Properties
• 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_isIEEE : Returns true if the current system satisfies basic IEEE requirements.
• System
• 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.

Bibliography

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

ATOMS

http://atoms.scilab.org/toolboxes/floatingpoint

Author

Copyright (C) 2010 - DIGITEO - Michael Baudin

Acknowledgements

• Samuel Gougeon
• Calixte Denizet

Licence

This toolbox is released under the CeCILL_V2 licence :

http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt

Development Team