lakshayg
Sollya - library for safe floating-point code development
I discovered Sollya today when trying to find a good polynomial approximation to ArcTan in [0, 1]. This tool provides an implementation of the Remez Algorithm which I used to compute the polynomial approximation.
Installation
Installation of this tool is straightforward on Ubuntu. It depends on the following libraries:
- libxml2-dev
- libmpfi-dev
- libmpfr-dev
- libgmp-dev
- libfplll-dev
All of these can be installed on Ubuntu by running apt-get install {lib}.
Building the tool: ./configure && make
Usage
The documentation of Sollya has a good page with various examples
The tool provides a number of functions. To compute the approximation, we
can use the remez function. Here is an example of approximating sin(x)
in the range [-pi/2, pi/2].
remez(sin(x),[|1,3,5,7|],[-pi/2,pi/2],1,1e-10);
This yields a polynomial with the following coefficients
| N | coefficient |
|---|---|
| 1 | 0.9999966159080027758584108080842308779136959066439 |
| 3 | -0.16664828381895057659620411447060988814996627242661 |
| 5 | 8.3063252271598984923167323097762502541923865405786e-3 |
| 7 | -1.8363653976946848392387223432528423431195832560898e-4 |
Here’s a plot of the approximation error
