#version 450

#include "glu_head.comp"

// based on Abramowitz and Stegun formula 7.1.26 or similar Hastings' approximation
// ref: https://www.johndcook.com/blog/python_erf/
const float p_erf  = 0.3275911f;
const float a1_erf = 0.254829592f;
const float a2_erf = -0.284496736f;
const float a3_erf = 1.421413741f;
const float a4_erf = -1.453152027f;
const float a5_erf = 1.061405429f;

const float SQRT_2_INV = 0.70710678118654752440084436210484f;

float op(float a, float b) {
    const float a_div_sqr2 = a * SQRT_2_INV;
    const float sign_x = sign(a_div_sqr2);
    const float x = abs(a_div_sqr2);
    const float t = 1.0f / (1.0f + p_erf * x);
    const float y = 1.0f - (((((a5_erf * t + a4_erf) * t) + a3_erf) * t + a2_erf) * t + a1_erf) * t * exp(-x * x);
    const float erf_approx = sign_x * y;

    return 0.5f * a * (1.0f + erf_approx) * b;
}

#include "glu_main.comp"