Fast INverse Exponentiation

Compute x^(1/n) and x^n faster than standard methods

Make sure you are using at least C++20 standard for this library

Just clone, compile and run using

g++ -std=c++2a -O2 -Wall -pedantic test.cpp && ./test.out

The following program illustrates a basic example

#include "FINE.h"
#include "FINEd.h"
#include <cmath>
#include <cstdio>

int main(int argc, char *argv[]) {

    float a = 19.2f;
    int n = 2;

    printf("FINE Value: %f\n", Q_exp(a, n));
    printf("FINEd Value: %f\n", Q_exp_double(a, n));
    printf("C value: %f\n", pow(a, n));
    printf("\n");
    printf("FINE Value: %f\n", Q_nroot(a, n));
    printf("FINEd Value: %f\n", Q_nroot_double(a, n));
    printf("Quake 3 Value: %f\n", Quake(a));
    printf("C value: %f\n", pow(a, -1./n));
    
    return 0;
}

For a trial run with the above program,

Exponent
FINE Value: 369.421783
FINEd Value: 369.421772
C value: 368.640029


Inverse-Root
FINE Value: 0.226177
FINEd Value: 0.226177
Quake 3 Value: 0.228213
C value: 0.228218

When the computations were repeated with different values for N=50,000 times (in microseconds)

Exponent
Times (float, double, C): 390, 387, 2306

Inverse-Root
Times (float, double, Quake, C): 1291, 1629, 658, 2069

The Quake method supports only inverse square roots

This work takes inspiration from the Fast Inverse Square Root from the Quake 3 Engine (although sources mention it is older) and generalizes it to both 32-bit and 64-bit floating-point values.

Note that fast computation of inverse n-th root requires fast exponentiation (x^n) as well and is included.

Please direct your queries to gpavanb1 for any questions.