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:
- + - * / %
- atan2(y, x), pow(x, y)
- min(x, y), max(x, y)
- fmod(x, y)
Exponent shortcuts:
- x², x³…
Constants:
- e,
- pi, π
- tau, τ (Tau is great for trolling)
Math functions:
- abs() (absolute value)
- sqrt() (square root), cbrt() (cubic root)
- exp(), exp2(), erf(), log(), log2(), log10()
- sin(), cos(), tan()
- asin(), acos(), atan()
- sinh(), cosh(), tanh()
Parsing rules:
- -a^b is -(a^b)
- a^b^c is (a^b)^c
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
- Fix a grave problem with extrema finding when using a weight function; results were suboptimal.
- Switch to a header-only big float implementation that tremendously improves build times.
- Print gnuplot-friendly formulas.
- Fix a severe bug in cbrt().
- Implement erf().
- Implement % and fmod().
- Make the executable size even smaller.
- lolremez can now also act as a simple command line calculator.
- Allow expressions in the range specification:
-r -pi/4:pi/4is now valid. - Allow using “pi” and “e” in expressions, as well as “π”.
- Bugfixes in the expression parser.
- Support for hexadecimal floats, e.g.
0x1.999999999999999ap-4. - New
--float,--doubleand--long-doubleoptions to choose precision. - Trim down DLL dependencies to allow for lighter binaries.
- implemented an expression parser so that the user does not have to recompile the software before each use.
- C/C++ function output.
- use threading to find zeros and extrema.
- use successive parabolic interpolation to find extrema.
- significant performance and accuracy improvements thanks to various bugfixes and a better extrema finder for the error function.
- user can now define accuracy of the final result.
- exp(), sin(), cos() and tan() are now about 20% faster.
- multiplying a real number by an integer power of two is now a virtually free operation.
- fixed a rounding bug in the real number printing routine.