#ifndef UNITY_LEFTOVER_INCLUDED
#define UNITY_LEFTOVER_INCLUDED

//-------------------------------------------------------------------------------------

inline half Pow4 (half x)
{
    return x*x*x*x;
}

inline float2 Pow4 (float2 x)
{
    return x*x*x*x;
}

inline half3 Pow4 (half3 x)
{
    return x*x*x*x;
}

inline half4 Pow4 (half4 x)
{
    return x*x*x*x;
}

// Pow5 uses the same amount of instructions as generic pow(), but has 2 advantages:
// 1) better instruction pipelining
// 2) no need to worry about NaNs
inline half Pow5 (half x)
{
    return x*x * x*x * x;
}

inline half2 Pow5 (half2 x)
{
    return x*x * x*x * x;
}

inline half3 Pow5 (half3 x)
{
    return x*x * x*x * x;
}

inline half4 Pow5 (half4 x)
{
    return x*x * x*x * x;
}

inline half3 FresnelTerm (half3 F0, half cosA)
{
    half t = Pow5 (1 - cosA);   // ala Schlick interpoliation
    return F0 + (1-F0) * t;
}
inline half3 FresnelLerp (half3 F0, half3 F90, half cosA)
{
    half t = Pow5 (1 - cosA);   // ala Schlick interpoliation
    return lerp (F0, F90, t);
}
// approximage Schlick with ^4 instead of ^5
inline half3 FresnelLerpFast (half3 F0, half3 F90, half cosA)
{
    half t = Pow4 (1 - cosA);
    return lerp (F0, F90, t);
}

// Note: Disney diffuse must be multiply by diffuseAlbedo / PI. This is done outside of this function.
half DisneyDiffuse(half NdotV, half NdotL, half LdotH, half perceptualRoughness)
{
    half fd90 = 0.5 + 2 * LdotH * LdotH * perceptualRoughness;
    // Two schlick fresnel term
    half lightScatter   = (1 + (fd90 - 1) * Pow5(1 - NdotL));
    half viewScatter    = (1 + (fd90 - 1) * Pow5(1 - NdotV));

    return lightScatter * viewScatter;
}

// NOTE: Visibility term here is the full form from Torrance-Sparrow model, it includes Geometric term: V = G / (N.L * N.V)
// This way it is easier to swap Geometric terms and more room for optimizations (except maybe in case of CookTorrance geom term)

// Generic Smith-Schlick visibility term
inline half SmithVisibilityTerm (half NdotL, half NdotV, half k)
{
    half gL = NdotL * (1-k) + k;
    half gV = NdotV * (1-k) + k;
    return 1.0 / (gL * gV + 1e-5f); // This function is not intended to be running on Mobile,
                                    // therefore epsilon is smaller than can be represented by half
}

// Smith-Schlick derived for Beckmann
inline half SmithBeckmannVisibilityTerm (half NdotL, half NdotV, half roughness)
{
    half c = 0.797884560802865h; // c = sqrt(2 / Pi)
    half k = roughness * c;
    return SmithVisibilityTerm (NdotL, NdotV, k) * 0.25f; // * 0.25 is the 1/4 of the visibility term
}

// Ref: http://jcgt.org/published/0003/02/03/paper.pdf
inline float SmithJointGGXVisibilityTerm (float NdotL, float NdotV, float roughness)
{
#if 0
    // Original formulation:
    //  lambda_v    = (-1 + sqrt(a2 * (1 - NdotL2) / NdotL2 + 1)) * 0.5f;
    //  lambda_l    = (-1 + sqrt(a2 * (1 - NdotV2) / NdotV2 + 1)) * 0.5f;
    //  G           = 1 / (1 + lambda_v + lambda_l);

    // Reorder code to be more optimal
    half a          = roughness;
    half a2         = a * a;

    half lambdaV    = NdotL * sqrt((-NdotV * a2 + NdotV) * NdotV + a2);
    half lambdaL    = NdotV * sqrt((-NdotL * a2 + NdotL) * NdotL + a2);

    // Simplify visibility term: (2.0f * NdotL * NdotV) /  ((4.0f * NdotL * NdotV) * (lambda_v + lambda_l + 1e-5f));
    return 0.5f / (lambdaV + lambdaL + 1e-5f);  // This function is not intended to be running on Mobile,
                                                // therefore epsilon is smaller than can be represented by half
#else
    // Approximation of the above formulation (simplify the sqrt, not mathematically correct but close enough)
    float a = roughness;
    float lambdaV = NdotL * (NdotV * (1 - a) + a);
    float lambdaL = NdotV * (NdotL * (1 - a) + a);

#if defined(SHADER_API_SWITCH)
    return 0.5f / (lambdaV + lambdaL + 1e-4f); // work-around against hlslcc rounding error
#else
    return 0.5f / (lambdaV + lambdaL + 1e-5f);
#endif

#endif
}

inline float GGXTerm (float NdotH, float roughness)
{
    float a2 = roughness * roughness;
    float d = (NdotH * a2 - NdotH) * NdotH + 1.0f; // 2 mad
    return UNITY_INV_PI * a2 / (d * d + 1e-7f); // This function is not intended to be running on Mobile,
                                            // therefore epsilon is smaller than what can be represented by half
}

inline half PerceptualRoughnessToSpecPower (half perceptualRoughness)
{
    half m = PerceptualRoughnessToRoughness(perceptualRoughness);   // m is the true academic roughness.
    half sq = max(1e-4f, m*m);
    half n = (2.0 / sq) - 2.0;                          // https://dl.dropboxusercontent.com/u/55891920/papers/mm_brdf.pdf
    n = max(n, 1e-4f);                                  // prevent possible cases of pow(0,0), which could happen when roughness is 1.0 and NdotH is zero
    return n;
}

// BlinnPhong normalized as normal distribution function (NDF)
// for use in micro-facet model: spec=D*G*F
// eq. 19 in https://dl.dropboxusercontent.com/u/55891920/papers/mm_brdf.pdf
inline half NDFBlinnPhongNormalizedTerm (half NdotH, half n)
{
    // norm = (n+2)/(2*pi)
    half normTerm = (n + 2.0) * (0.5/UNITY_PI);

    half specTerm = pow (NdotH, n);
    return specTerm * normTerm;
}

//-------------------------------------------------------------------------------------


#endif // UNITY_LEFTOVER_INCLUDED