A Remez algorithm toolkit to approximate functions using polynomials.

A tutorial is available in the wiki section.

Approximate atan(sqrt(3+x)-exp(1+x)) over the range [-1,1] with a 5th degree polynomial:

lolremez -d 5 -r -1:1 "atan(sqrt(3+x)-exp(1+x))"

Result:

/* Approximation of f(x) = atan(sqrt(3+x)-exp(1+x))
 * on interval [ -1.0000000000000000000, 1.0000000000000000000 ]
 * with a polynomial of degree 5. */
float f(float x)
{
    float u = -1.1514600677101831554e-1f;
    u = u * x + -3.1404157365765952659e-1f;
    u = u * x + 4.7315508009637667259e-1f;
    u = u * x + 5.7678822318891844828e-1f;
    u = u * x + -1.2480195820255797595f;
    return u * x + -7.6941172112944451609e-1f;
}

Binary functions/operators:

• + - * /
• atan2(y, x), pow(x, y)
• min(x, y), max(x, y)

Math functions:

• abs() (absolute value)
• sqrt() (square root), cbrt() (cubic root)
• exp(), exp2(), log(), log2(), log10()
• sin(), cos(), tan()
• asin(), acos(), atan()
• sinh(), cosh(), tanh()

• 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.