// SPDX-License-Identifier: Apache-2.0
// Copyright Contributors to the ACES Project.

// <ACEStransformID>urn:ampas:aces:transformId:v2.0:Lib.Academy.Tonescale.a2.v1</ACEStransformID>
// <ACESuserName>Tonescale Functions</ACESuserName>

// 
// Library File with functions used for pre-calculating the tonescale parameters and 
// applying the fwd/inv tonescale function
//



struct TSParams 
{
	float n;
	float n_r;
	float g;
	float t_1;
	float c_t; 
	float s_2;
	float u_2;
	float m_2;
	float forward_limit;
    float inverse_limit;
    float log_peak;
};

// Tonescale pre-calculations
TSParams init_TSParams(float peakLuminance)
{

	// Preset constants that set the desired behavior for the curve
	const float n = peakLuminance;

	const float n_r = 100.0;	  // normalized white in nits (what 1.0 should be)
	const float g = 1.15;		  // surround / contrast
	const float c = 0.18;		  // anchor for 18% grey
	const float c_d = 10.013;	  // output luminance of 18% grey (in nits)
	const float w_g = 0.14;		  // change in grey between different peak luminance
	const float t_1 = 0.04;		  // shadow toe or flare/glare compensation
	const float r_hit_min = 128.; // scene-referred value "hitting the roof" for SDR (e.g. when n = 100 nits)
	const float r_hit_max = 896.; // scene-referred value "hitting the roof" for when n = 10000 nits

	// Calculate output constants
	const float r_hit = r_hit_min + (r_hit_max - r_hit_min) * (log(n / n_r) / log(10000. / 100.));
	const float m_0 = (n / n_r);
	const float m_1 = 0.5 * (m_0 + sqrt(m_0 * (m_0 + 4. * t_1)));
	const float u = pow((r_hit / m_1) / ((r_hit / m_1) + 1), g);
	const float m = m_1 / u;
	const float w_i = log(n / 100.) / log(2.);
	const float c_t = c_d / n_r * (1. + w_i * w_g);
	const float g_ip = 0.5 * (c_t + sqrt(c_t * (c_t + 4. * t_1)));
	const float g_ipp2 = -(m_1 * pow((g_ip / m), (1. / g))) / (pow(g_ip / m, 1. / g) - 1.);
	const float w_2 = c / g_ipp2;
	const float s_2 = w_2 * m_1;
	const float u_2 = pow((r_hit / m_1) / ((r_hit / m_1) + w_2), g);
	const float m_2 = m_1 / u_2;

	TSParams p;
	p.n = n;
	p.n_r = n_r;
	p.g = g;
	p.t_1 = t_1;
	p.c_t = c_t;
	p.s_2 = s_2;
	p.u_2 = u_2;
	p.m_2 = m_2;
	p.forward_limit = 8.0 * r_hit;
	p.inverse_limit = n / (u_2 * n_r);
	p.log_peak = log10(n / n_r);

	return p;
}

/* --- Tone scale math --- */
float tonescale_fwd(float x,		// scene-referred input (i.e. linear ACES2065-1)
					TSParams params // struct of type TSParams
)
{
	// forward MM tone scale
	float f = params.m_2 * pow(max(0.0, x) / (x + params.s_2), params.g);
	float h = max(0., f * f / (f + params.t_1)); // forward flare

	return h * params.n_r; // output is luminance in cd/m^2
}

float tonescale_inv(float Y,		// luminance in cd/m^2
					TSParams params // struct of type TSParams
)
{
	float Z = max(0., min(params.n / (params.u_2 * params.n_r), Y));
	float h = (Z + sqrt(Z * (4. * params.t_1 + Z))) / 2.;
	float f = params.s_2 / (pow((params.m_2 / h), (1. / params.g)) - 1.);

	return f; // output is scene-referred input
}