A Remez algorithm implementation to approximate functions using polynomials.
A tutorial is available in the wiki section.
Build instructions are available below.
Approximate atan(sqrt(3+x³)-exp(1+x))
over the range [sqrt(2),pi²]
with a 5th degree polynomial for double
floats:
lolremez --double -d 5 -r "sqrt(2):pi²" "atan(sqrt(3+x³)-exp(1+x))"
Result:
/* Approximation of f(x) = atan(sqrt(3+x³)-exp(1+x))
* on interval [ sqrt(2), pi² ]
* with a polynomial of degree 5. */
double f(double x)
{
double u = -3.9557569330471555e-5;
u = u * x + 1.2947712130833294e-3;
u = u * x + -1.6541397035559147e-2;
u = u * x + 1.0351664953941214e-1;
u = u * x + -3.2051562487328135e-1;
return u * x + -1.1703528319321961;
}
Binary functions/operators:
Exponent shortcuts:
Constants:
Math functions:
Parsing rules:
As of now, the erf()
family of function is inaccurate in the [7,19] range.
See this issue
If you got the source code from Git, make sure the submodules are properly initialised:
git submodule update --init --recursive
On Windows, just open lolremez.sln
in Visual Studio.
On Linux, make sure the following packages are installed:
automake autoconf libtool pkg-config
On Windows, just build the solution in Visual Studio.
On Linux, bootstrap the project and configure it:
./bootstrap
./configure
Finally, build the project:
make
The resulting executable is lolremez
. You can manually copy it to any
installation location, or run the following:
sudo make install
A docker image can easily be built using the provided Dockerfile
docker build -t lolremez .
This command will create a local Docker image "lolremez", you can the invoke lolremez
as follows:
docker run --rm lolremez --double -d 5 -r "sqrt(2):pi²" "atan(sqrt(3+x³)-exp(1+x))"
// Approximation of f(x) = atan(sqrt(3+x³)-exp(1+x))
// on interval [ sqrt(2), pi² ]
// with a polynomial of degree 5.
// p(x)=((((-3.9557569330471555e-5*x+1.2947712130833294e-3)*x-1.6541397035559147e-2)*x+1.0351664953941214e-1)*x-3.2051562487328135e-1)*x-1.1703528319321961
double f(double x)
{
double u = -3.9557569330471555e-5;
u = u * x + 1.2947712130833294e-3;
u = u * x + -1.6541397035559147e-2;
u = u * x + 1.0351664953941214e-1;
u = u * x + -3.2051562487328135e-1;
return u * x + -1.1703528319321961;
}
-r -pi/4:pi/4
is now valid.0x1.999999999999999ap-4
.--float
, --double
and --long-double
options to choose precision.