YourOwnPersonnalRemez

Simple tool for playing around polynomial approximation for numerical functions.

Dependencies

• numpy
• matplotlib
• bigfloat
• json
• fpylll https://github.com/fplll/fpylll

All dependencies can be installed with pip using the provided requirements.txt file (assuming your setup already has their dependencies, such as a recent version of fplll for example https://github.com/fplll/fplll)

pip3 install -r requirements.txt

Usage

Command line

yopr can be called from the command line

python3 yopr.py --method remez --function "bigfloat.exp" --interval 0,0.125 --epsilon 1e-7 --degree 8 --plot

A list of possible options can be displayed: python3 yopr.py --help

Dumping axf-compatible output

By using --dump-axf-approx <filename> yopr can output the approximation in the AXF format (see https://github.com/metalibm/axf for more information on AXF, the Approximation eXchange Format).

python3 yopr.py --method remez --function "bigfloat.exp" --interval 0,0.125 --epsilon 1e-7 --degree 8 --dump-axf-approx exp-fp32.json.axf 

Examples

Various example scripts are available and can be adapted to your needs:

Internal

CVP based approximation

Using Euclidean Lattices and the Closest Vector Problem, this method tries to find a good approximation for a given function.

Remez approximation

Polynomial conditionner

References

-- N. Brisebarre, S. Chevillard "Efficient polynomial L-inf approximation" (https://hal.archives-ouvertes.fr/inria-00119513v1)