CAM_DRT_v053_pex2.blink

kernel DRT_CAM_Kernel : ImageComputationKernel<ePixelWise>
{
  Image<eRead, eAccessPoint, eEdgeClamped> src; // the input image
  Image<eWrite> dst; // the output image

  param:
    //
    // Input Parameters
    //

    // Encoding of the Input Image
    // 0: Linear
    // 1: ACEScct
    // 2: sRGB
    // 3: BT.1886 (Gamma 2.4)
    // 4: Gamma 2.6
    // 5: ST2084
    int encodingIn;

    // Primaries of the Input Image
    // 0: AP0-ACES
    // 1: AP1-ACES
    // 2: sRGB/Rec.709-D65
    // 3: Rec.2020-D65
    // 4: P3-D65
    // 5: P3-DCI
    int primariesIn;

    // Tonescale mode
    // 0: Linear
    // 1: Daniele Evo Curve
    int toneScaleMode;

    // Disable Degree of Adaptation Model for Zhai2018 CAT
    // This is only effective if the limit primaries have a non-D65 white point
    // since the input conversion is assumed to be fully adapted
    // and the output conversion does not apply a CAT
    bool discountIlluminant_in;
    bool discountIlluminant_mid;
    bool discountIlluminant_out;

    // Toggles for Hellwig 2022 specific params
    bool HK_mode_in;
    bool HK_mode_mid;
    bool HK_mode_out;
    int compressMode;

    // Reference Luminance in Cd/sqm
    float referenceLuminance;

    // Viewing Conditions (for output)
    // 0: Dark
    // 1: Dim
    // 2: Average
    int viewingConditions;
    int outputViewingConditions;

    // Toggle  Tone Mapping
    bool applyTonecurve;
    
    // Target Peak Luminance
    float peakLuminance;

    // Toggle chroma compression
    bool applyChromaCompression;
    bool applyInGamutExpansion;
    bool applyInGamutCompression;
    bool applyReachClamp;
    bool monochrome;

    // Chroma compression params (limit, k1, k2)
    float chroma_compress;
    float chroma_expand;
    float chroma_expand_thr;
    int cc_et;
    int ccReach;
    // xy coordintes for chroma compression gamut
    float2 crxy;
    float2 cgxy;
    float2 cbxy;
    float2 cwxy;

    //
    // Gamut Mapping Parameters
    //

    // Primaries of the Target Gamut
    // 0: AP0-ACES
    // 1: AP1-ACES
    // 2: sRGB/Rec.709-D65 # now just Rec.709
    // 3: Rec.2020-D65 # now just Rec.2020
    // 4: P3-D65 # now just P3
    // 5: P3-DCI # no longer included
    int primariesLimit;
    
    // White point of the limiting gamut
    // effectively the "creative white"
    // 0: ACES white
    // 1: D65
    // Could add others, or user white point
    int whiteLimit;

    // Primaries of the Gamut reached by the gamut compressor
    // 0: AP0-ACES
    // 1: AP1-ACES
    // 2: sRGB/Rec.709-D65
    // 3: Rec.2020-D65
    // 4: P3-D65
    // 5: P3-DCI
    // 6: Spectral Locus
    // 7: Chroma Compression Space
    int primariesReach;


    // Toggle Gamut Compression
    bool applyGamutCompression;

    // the 1D LUT used for quickly findig the approximate limiting gamut cusp JMh coordinates
    // the samples are spaced by HSV hue increments of the limiting RGB gamut
    // so to find the correct entry for a given CAM hue (h) value 
    // one must search the table entries for the matching entry.z component
    int gamutCuspTableSize;

    // Blend Between Compressing towards
    // Target Gamut Cusp Luminance (0.0)
    // and Mid Luminance (1.0)
    float cuspMidBlend;

    // Focus distance of the compression focal point from the achromatic axis
    float focusDistance;
    float focusAdjustGain;
    float focusAdjustPeakGain;
    bool disableFocusGain;

    // Gamut Compression Fuction Parameters
    // Threshold / min Limit / max Limit / Power
    float4 compressionFuncParams;
    bool sixAxisCompressionMode;
    float4 compressionFuncParamsR;
    float4 compressionFuncParamsY;
    float4 compressionFuncParamsG;
    float4 compressionFuncParamsC;
    float4 compressionFuncParamsB;
    float4 compressionFuncParamsM;
    bool Reachcompressmode;
    bool reachNick;
    bool Locuscompressmode;

    int boundryIntersectionMethod;
    // 36 gamut parameters
    // float upperHullGamma[36];
    bool disableUpperHullGamma;
    bool disableLowerHullGamma;
    float lowerHullGamma;
    float upperHullGamma;

    // How much the edges of the target RGB cube are smoothed when finding the gamut boundary 
    // in order to reduce visible contours at the gamut cusps
    float smoothCusps;

    //
    // Output Parameters
    //

    // Encoding of the Output Image
    // 0: Linear
    // 1: ACEScct
    // 2: sRGB
    // 3: BT.1886 (Gamma 2.4)
    // 4: Gamma 2.6
    // 5: ST2084
    int encodingOut;

    // Primaries of the Output Image
    // 0: AP0-ACES
    // 1: AP1-ACES
    // 2: sRGB/Rec.709-D65
    // 3: Rec.2020-D65
    // 4: P3-D65
    // 5: P3-DCI
    int primariesOut;

    // Clamp output values to 0.0 - 1.0
    bool fitWhite;
    bool clampOutput;
    bool softclampOutput;
    float clamp_thr;
    float clamp_dist;

    //
    // Extra Parameters
    //

    // Toggle Inverse Transform
    bool invert;
    // Diagnostic path modes
    int diagnosticMode;

    // DanieleEvoCurve (ACES2 candidate) parameters
    float mmScaleFactor;
    float daniele_n; // peak white  
    float daniele_n_r;    // Normalized white in nits (what 1.0 should be)
    float daniele_g;      // surround / contrast
    float daniele_c;      // scene-referred grey
    float daniele_c_d;    // display-referred grey (in nits)
    float daniele_w_g;    // grey change between different peak luminance
    float daniele_t_1;     // shadow toe, flare/glare compensation - how ever you want to call it
    float daniele_r_hit_min;  // Scene-referred value "hitting the roof" at 100 nits
    float daniele_r_hit_max;  // Scene-referred value "hitting the roof" at 10,000 nits

    // Hellwig 2022 CAM params
    // the kernel parameters

    // 0 = Stock CAT16
    // 1 = Thomas's custom primaries
    // 2 = live from params below
    int catDataSelection; // original vs modified CAT16 matrix
    // xy coordintes for custom CAT matrix
    float2 rxy;
    float2 gxy;
    float2 bxy;
    float2 wxy;
    float ra;
    float ba;
 
    // Input vars
    float3 XYZ_w;
    float XYZ_w_scaler;
    float L_A;
    float Y_b;
    float3 L_B;
    float3 userSurround;
    bool discount_illuminant;
    // Output vars
    float L_A_out;
    float Y_b_out;


  local:

    // constants
    float HALF_MINIMUM;
    float HALF_MAXIMUM;

    // Hellwig 2022 constants
    float3x3 CAT_CAT16;
    float3x3 panlrcm;

    float daniele_r_hit;
    float daniele_m_0;
    float daniele_m_1;
    float daniele_u;
    float daniele_m;
    float daniele_w_i;
    float daniele_c_t;
    float daniele_g_ip;
    float daniele_g_ipp2;
    float daniele_w_2;
    float daniele_s_2;
    float daniele_u_2;
    float daniele_m_2;

    // Chroma compression pre-calculated constants
    float compr;      // Compression
    float sat;        // Saturation
    float sat_thr;    // Threshold to start expanding saturation

    // ST2084 vars
    float st2084_m_1;
    float st2084_m_2;
    float st2084_c_1;
    float st2084_c_2;
    float st2084_c_3;
    float st2084_m_1_d;
    float st2084_m_2_d;
    float st2084_L_p;

    // using the float3x3 type to store the array of 6 coefficients
    // because Blink does not support generic array assignments

    // matrix vars
    float3x3 identity_matrix;

    float3x3 XYZ_to_RGB_input;
    float3x3 XYZ_to_RGB_limit;
    float3x3 XYZ_to_RGB_reach;
    float3x3 XYZ_to_RGB_output;

    float3x3 RGB_to_XYZ_input;
    float3x3 RGB_to_XYZ_limit;
    float3x3 RGB_to_XYZ_reach;
    float3x3 RGB_to_XYZ_output;

    float3x3 AP1_to_XYZ;
    float3x3 XYZ_to_AP1;

    // white points
    float3 inWhite;
    float3 outWhite;
    float3 refWhite;
    float3 limitWhite;

    // the maximum RGB value of the limiting gamut
    float boundaryRGB;

    // the maximum lightness value of the limiting gamut
    float limitJmax;

    // the maximum colorfulness value of the limiting gamut
    float limitMmax;

    // Middle gray J
    float midJ;

    // Hellwig model's gamma (1 / cz)
    float model_gamma;

    // the 'gamutCuspTableUnsorted' table is populated
    // in increments of H of the limiting gamut HSV space starting at H=0.0
    // since it is unlikely that HSV.H=0 and JMh.h=0 line up
    // the entries are then wrap-around shifted
    // so that the 'gamutCuspTable' starts with the lowest JMh.h value
    // both tables need to be declared here since temporary array variables
    // in the init() fuction seem to crash Nuke on some systems
    float3 gamutCuspTableUnsorted[360*8];
    float3 gamutCuspTable[360*8];
    float3 gamutCuspTableUnsortedAP1[360*8];
    float3 gamutCuspTableAP1[360*8];
    float3 gamutCuspTableReach[360*8];
    float3 cgamutCuspTable[360*8];
    float3 cgamutReachTable[360*8];
    float gamutTopGamma[360*8];
    float gamutBottomGamma[360*8];
    float LocusLimitMTable[360*8];

  void define()
  {

  }

// Functions used in ACES 2.0 candidate CAM DRT
// Derived from v49


  // multiplies a 3D vector with a 3x3 matrix
  float3 vector_dot( float3x3 m, float3 v)
  {
    float3 r = 1.0f;
    for(int c = 0; c<3; c++)
    {
      r[c] = m[c][0]*v.x + m[c][1]*v.y + m[c][2]*v.z;
    }

    return r;
  }

  // linear interpolation between two values a & b with the bias t
  float lerp(float a, float b, float t)
  {
    return a + t * (b - a);
  }

  // linear interpolation between two float4 values a & b with the bias t
  float4 lerp4(float4 a, float4 b, float t)
  {
    return a + t * (b - a);
  }

  // "safe" power function to avoid NANs or INFs when taking a fractional power of a negative base
  // this one initially returned -pow(abs(b), e) for negative b
  // but this ended up producing undesirable results in some cases
  // so now it just returns 0.0 instead
  float spow( float base, float exponent )
  {
    // a = np.atleast_1d(a)
    float a = base;
    float b = exponent;
    // // p = as_float_array(p)

    // float a_p = sign(a) * pow(  fabs(a) ,p)  ; 

    // // a_p[np.isnan(a_p)] = 0

    // return a_p;

    // np.sign(a) * pow(np.abs(a) , b) 

    // float a_p =  sign(a) * pow(fabs(a) , b) ;
    // if ( isnan(a_p) )
    // {
    //     a_p = a_p;
    // }
    // else 
    // {
    //     a_p = 0.0;
    // }
    // return a_p;

    if(base < 0.0f && exponent != floor(exponent) )
    {
      return 0.0f;
    }
    else
    {
     return pow(base, exponent); 
    }
  }


  // clamp the components of a 3D vector between a min & max value
  float3 clamp3(float3 v, float min, float max)
  {
    v.x = clamp(v.x, min, max);
    v.y = clamp(v.y, min, max);
    v.z = clamp(v.z, min, max);
    return v;
  }


  float3 float3spow( float3 base, float exponent )
  {
      return float3(spow(base.x, exponent), spow(base.y, exponent), spow(base.z, exponent));
  }

  float3 float3sign( float3 v )
  {
      return float3(sign(v.x), sign(v.y), sign(v.z));
  }


  float3 float3abs( float3 a )
  {
    return fabs(a);
  }

    // "safe" div
    float sdiv( float a, float b )
    {
        if(b == 0.0f)
        {
        return 0.0f;
        }
        return a / b;
        }
    
  float clip(float x, float a, float b)
  {
    return max(a, min(x, b));
  }

  float mod(float a, float N)
  {
    return a - N*floor(a/N);
  } 

  float degree_of_adaptation(float  F, float L_A )
  {
    float D = F * (1 - (1 / 3.6) * exp((-L_A - 42) / 92));

    return D;
  }

  // convert radians to degrees
  float degrees( float radians )
  {
    return radians * 180.0f / PI;
  }

  // convert degrees to radians
  float radians( float degrees )
  {
    return degrees / 180.0f * PI;
  }

  // "PowerP" compression function (also used in the ACES Reference Gamut Compression transform)
  // values of v above  'treshold' are compressed by a 'power' function
  // so that an input value of 'limit' results in an output of 1.0
  float compressPowerP( float v, float threshold, float limit, float power, int inverse )
  {
    float s = (limit-threshold)/pow(pow((1.0f-threshold)/(limit-threshold),-power)-1.0f,1.0f/power);

    float vCompressed;

    if( inverse )
    {
      vCompressed = (v<threshold||limit<1.0001f||v>threshold+s)?v:threshold+s*pow(-(pow((v-threshold)/s,power)/(pow((v-threshold)/s,power)-1.0f)),1.0f/power);
    }
    else
    {
      vCompressed = (v<threshold||limit<1.0001f)?v:threshold+s*((v-threshold)/s)/(pow(1.0f+pow((v-threshold)/s,power),1.0f/power));
    }

    return vCompressed;
  }

  float3 compress_aces(float3 rgb, float3 c, float3 m, float3 y, int invert)
  {
    float ach = max(rgb.x, max(rgb.y, rgb.z));
    float3 d = 0.0f;

    if (ach)
    {
      d.x = (ach - rgb.x) / fabs(ach);
      d.y = (ach - rgb.y) / fabs(ach);
      d.z = (ach - rgb.z) / fabs(ach);
    }

    rgb.x = compressPowerP(d.x, c.x, c.y, c.z, invert);
    rgb.y = compressPowerP(d.y, m.x, m.y, m.z, invert);
    rgb.z = compressPowerP(d.z, y.x, y.y, y.z, invert);

    rgb = ach - rgb * fabs(ach);

    return rgb;
  }

  // basic 3D hypotenuse function, does not deal with under/overflow
  float hypot_float3(float3 xyz)
  {
    return sqrt(xyz.x*xyz.x + xyz.y*xyz.y + xyz.z*xyz.z);
  }

  float3 compress_bjorn(float3 xyz)
  {
    float C = (xyz.x+xyz.y+xyz.z)/3;

    float3 xyz_temp = xyz - C;
    float R = hypot_float3(xyz_temp);

    if (R == 0.0f || C == 0.0f)
      return xyz;

    R = R * 0.816496580927726;     // sqrt(2/3)

    xyz_temp = xyz_temp / R;

    float r = R/C ;
    r = r*r ;
    r = sqrt(4.0f / r + 1.0f) - 1.0f;

    float s = -min(xyz_temp.x, min(xyz_temp.y, xyz_temp.z));
    s = s -0.5f;

    float t = 0.5f + sqrt(s*s + r*r / 4.0f);
    t = C / t;                                 // t is always >= 0.5f

    xyz_temp = xyz_temp * t + C;

    return xyz_temp;
  }

float3 uncompress_bjorn(float3 xyz)
{
    float C = (xyz.x+xyz.y+xyz.z)/3;

    float3 xyz_temp = xyz - C;
    float R = hypot_float3(xyz_temp);

    if (R == 0.0f || C == 0.0f)
    return xyz;

    R = R * 0.816496580927726;     // sqrt(2/3)

    xyz_temp = xyz_temp / R;

    float t = C/R;
    t = t -0.5f;

    float s = -min(xyz_temp.x, min(xyz_temp.y, xyz_temp.z));
    s = s -0.5f;

    float r = 2 * sqrt(fabs(t*t - s*s)) + 1;
    r = sqrt(fabs(r*r - 1));
    if (r == 0.0)
      return xyz;
    r = C * 2/r;

    xyz_temp = xyz_temp * r + C;

    return xyz_temp;
}


  float hue_angle_dependency_Hellwig2022(float hr)
  {
    return
     -0.160 * cos(hr)
    + 0.132 * cos(2 * hr)
    - 0.405 * sin(hr)
    + 0.080 * sin(2 * hr)
    + 0.792;
    }


  float3x3  RGBPrimsToXYZMatrix(float2 rxy, float2 gxy, float2 bxy, float2 wxy,float Y, bool direction)
  {
    // # given r g b chromaticities and whitepoint, convert RGB colors to XYZ
    // # based on CtlColorSpace.cpp from the CTL source code : 77
    // # param: xy - dict of chromaticity xy coordinates: rxy: float2(x, y) etc
    // # param: Y - luminance of "white" - defaults to 1.0
    // # param: inverse - calculate XYZ to RGB instead

    float2 r = rxy;
    float2 g = gxy;
    float2 b = bxy;
    float2 w = wxy;

    float X = w.x * Y / w.y;
    float Z = (1 - w.x - w.y) * Y / w.y;

    // # Scale factors for matrix rows
    float d = r.x * (b.y - g.y) + b.x * (g.y - r.y) + g.x * (r.y - b.y);

    float Sr =    (X * (b.y - g.y) -      \
            g.x * (Y * (b.y - 1.0f) +  \
            b.y  * (X + Z)) +       \
            b.x  * (Y * (g.y - 1.0f) + \
            g.y * (X + Z))) / d ;
    
    float Sg =    (X * (r.y - b.y) +      \
            r.x * (Y * (b.y - 1.0f) +  \
            b.y * (X + Z)) -        \
            b.x * (Y * (r.y - 1.0f) +  \
            r.y * (X + Z))) / d ;

    float Sb =    (X * (g.y - r.y) -      \
            r.x * (Y * (g.y - 1.0f) +  \
            g.y * (X + Z)) +        \
            g.x * (Y * (r.y - 1.0f) +  \
            r.y * (X + Z))) / d ;

    // # Assemble the matrix
    float Mdata[] =
    {
            Sr * r.x, Sr * r.y, Sr * (1.0f - r.x - r.y),
            Sg * g.x, Sg * g.y, Sg * (1.0f - g.x - g.y),
            Sb * b.x, Sb * b.y, Sb * (1.0f - b.x - b.y),
    };

    float MdataNukeOrder[] = {
      Mdata[0], Mdata[3], Mdata[6],
      Mdata[1], Mdata[4], Mdata[7],
      Mdata[2], Mdata[5], Mdata[8],
    };

    float3x3 newMatrix;
    newMatrix.setArray(MdataNukeOrder);

    // create inverse matrix
    float3x3 newMatrixInverse = newMatrix.invert();

    // return forward or inverse matrix
    if (direction == 0)
    {
      return newMatrix;
    }
    else if (direction == 1)
    {
      return newMatrixInverse;
    }
  }

  // convert ACEScct encoded values to linear
  float ACEScct_to_linear( float v )
  {
    return v > 0.155251141552511f ? spow( 2.0f, v * 17.52f - 9.72f) : (v - 0.0729055341958355f) / 10.5402377416545f;
  }

  // encode linear values as ACEScct
  float linear_to_ACEScct( float v )
  {
    return v > 0.0078125f ? (log2(v) + 9.72f) / 17.52f : 10.5402377416545f * v + 0.0729055341958355f;
  }


  // convert sRGB gamma encoded values to linear
  float sRGB_to_linear( float v )
  {
    return v < 0.04045f ? v / 12.92f : spow((v + 0.055f) / 1.055f, 2.4f);
  }

  // encode linear values as sRGB gamma
  float linear_to_sRGB( float v )
  {
    return v <= 0.0031308f ? 12.92f * v : 1.055 * (spow(v, 1.0f / 2.4f)) - 0.055f;
  }

  float3 post_adaptation_non_linear_response_compression_forward(float3 RGB, float F_L)
  {
      float3 F_L_RGB = float3spow(F_L * float3abs(RGB) / 100.0f, 0.42f);
      float3 RGB_c = (400.0f * sign(RGB) * F_L_RGB) / (27.13f + F_L_RGB);
      return RGB_c;
  }

  float3 post_adaptation_non_linear_response_compression_inverse(float3 RGB,float F_L)
  {
      float3 RGB_p =  (float3sign(RGB) * 100.0f / F_L * float3spow((27.13f * float3abs(RGB)) / (400.0f - float3abs(RGB)), 1.0f / 0.42f) );
      return RGB_p;
  }

  // convert HSV cylindrical projection values to RGB
  float3 HSV_to_RGB( float3 HSV )
  {
    float C = HSV.z*HSV.y;
    float X = C*(1.0f-fabs(fmod(HSV.x*6.0f,2.0f)-1.0f));
    float m = HSV.z-C;

    float3 RGB;
    RGB.x = (HSV.x<1.0f/6.0f?  C :HSV.x<2.0f/6.0f?  X :HSV.x<3.0f/6.0f?0.0f:HSV.x<4.0f/6.0f?0.0f:HSV.x<5.0f/6.0f?  X :  C )+m;
    RGB.y = (HSV.x<1.0f/6.0f?  X :HSV.x<2.0f/6.0f?  C :HSV.x<3.0f/6.0f?  C :HSV.x<4.0f/6.0f?  X :HSV.x<5.0f/6.0f?0.0f:0.0f)+m;
    RGB.z = (HSV.x<1.0f/6.0f?0.0f:HSV.x<2.0f/6.0f?0.0f:HSV.x<3.0f/6.0f?  X :HSV.x<4.0f/6.0f?  C :HSV.x<5.0f/6.0f?  C :  X )+m;
    return RGB;
  }


  // convert RGB to HSV cylindrical projection values
  float3 RGB_to_HSV( float3 RGB )
  {
    float cmax = max(RGB.x,max(RGB.y,RGB.z));
    float cmin = min(RGB.x,min(RGB.y,RGB.z));
    float delta = cmax-cmin;

    float3 HSV;
    HSV.x = delta==0.0f?0.0f:cmax==RGB.x?(fmod((RGB.y-RGB.z)/delta+6.0f,6.0f))/6.0f:cmax==RGB.y?(((RGB.z-RGB.x)/delta+2.0f)/6.0f):(((RGB.x-RGB.y)/delta+4.0f)/6.0f);
    HSV.y = cmax == 0.0f ? 0.0f : delta / cmax;
    HSV.z = cmax;
    return HSV;
  }

  // Smooth minimum of a and b
  float smin(float a, float b, float s)
  {
    float h = max(s - fabs(a - b), 0.0) / s;
    return min(a, b) - h * h * h * s * (1.0f / 6.0f);
  }

  // reimplemented from https://github.com/nick-shaw/aces-ot-vwg-experiments/blob/master/python/intersection_approx.py
  float solve_J_intersect(float2 JM, float focusJ, float maxJ, float slope_gain)
  {
    float a = JM.y / (focusJ * slope_gain);
    float b = 0.0f;
    float c = 0.0f;
    float intersectJ = 0.0f;
    
    if (JM.x < focusJ)
    {
        b = 1.0f - JM.y / slope_gain;
    } 
    else
    {
        b= -(1.0f + JM.y / slope_gain + maxJ * JM.y / (focusJ * slope_gain));
    } 

    if (JM.x < focusJ)
    {
        c = -JM.x;
    } 
    else
    {
        c = maxJ * JM.y / slope_gain + JM.x;
    }

    float root = sqrt(b*b - 4.0f * a * c);

    if (JM.x < focusJ)
    {
        intersectJ = 2.0f * c / (-b - root);
    } 
    else
    {
        intersectJ = 2.0f * c / (-b + root);
    } 

    return intersectJ;
  }

    // check if the 3D point 'v' is inside a cube with the dimensions cubeSize x cubeSize x cubeSize 
  // the 'smoothing' parameter rounds off the edges and corners of the cube with the exception of the 0,0,0 and cubeSize x cubeSize x cubeSize corners
  // a smoothing value of 0.0 applies no smoothing and 1.0 the maximum amount (smoothing values > 1.0 result in undefined behavior )
  int isInsideCube( float3 v, float cubeSize, float smoothing)
  {
    float3 normv = v / cubeSize;

    float minv = min(normv.x, min(normv.y, normv.z));
    float maxv = max(normv.x, max(normv.y, normv.z));

    if( smoothing <= 0.0f )
    {
      // when not smoothing we can use a much simpler test
      if(minv < 0.0f || maxv > 1.0f)
      {
        return 0;
      }

      return 1;
    }

    float3 clamped = normv;

    float radius = smoothing/2.0f;

    radius = clamp(radius*maxv*(1.0f-minv), 0.0f, radius);

    clamped.x = clamp(normv.x, radius, 1.0f-radius);
    clamped.y = clamp(normv.y, radius, 1.0f-radius);
    clamped.z = clamp(normv.z, radius, 1.0f-radius);


    if( length(normv - clamped ) > radius)
    {
      return 0;
    }

    return 1;
  }

  float3 viewingConditionsToSurround(int viewingConditions)
  {
      float3 newSurround;
      // hack to turn incoming int value into surround coeffs
      if (viewingConditions == 0)
      {
          // "Dark": InductionFactors_CIECAM02(0.8, 0.525, 0.8),
          newSurround = float3(0.8, 0.525, 0.8);
      }
      else if (viewingConditions == 1)
      {
          // "Dim": InductionFactors_CIECAM02(0.9, 0.59, 0.9),
          newSurround = float3(0.9, 0.59, 0.9);
      }
      else if (viewingConditions == 2)
      {
          // "Average": InductionFactors_CIECAM02(1, 0.69, 1),
          newSurround = float3(1.0, 0.69, 1.0);
      }
      else if (viewingConditions == 3)
      {
          // Pull from external input
          newSurround = userSurround;
      }
      return newSurround;
  }


  // convert XYZ tristimulus values to the CAM J (lightness), M (colorfulness) and h (hue) correlates
  // needs XYZ tristimulus values for the reference white and the viewing conditions as parameters
  float3 XYZ_to_JMh( float3 XYZ, float3 referenceWhite, int viewingConditions , float L_A, float Y_b, bool discountIlluminant, bool HK_mode)
  {
    return XYZ_to_Hellwig2022_JMh(XYZ, referenceWhite, L_A, Y_b,viewingConditionsToSurround(viewingConditions),discountIlluminant,HK_mode);
  }

  // convert the CAM J (lightness), M (colorfulness) and h (hue) correlates to XYZ tristimulus values
  // needs XYZ tristimulus values for the reference white and the viewing conditions as parameters
  float3 JMh_to_XYZ( float3 JMh, float3 referenceWhite, int viewingConditions , float L_A, float Y_b, bool discountIlluminant, bool HK_mode)
  {
    return Hellwig2022_JMh_to_XYZ(JMh, referenceWhite, L_A, Y_b, viewingConditionsToSurround(viewingConditions), discountIlluminant,HK_mode);
  }

  // convert ST2084 PQ encoded values to linear
  float ST2084_to_linear( float v )
  {
    float V_p = spow(v, st2084_m_2_d);
    return spow((max(0.0f, V_p - st2084_c_1) / (st2084_c_2 - st2084_c_3 * V_p)), st2084_m_1_d)*st2084_L_p;
  }

  // encode linear values as ST2084 PQ
  float linear_to_ST2084( float v )
  {
    float Y_p = spow(max(0.0f, v) / st2084_L_p, st2084_m_1);

    return spow((st2084_c_1 + st2084_c_2 * Y_p) / (st2084_c_3 * Y_p + 1.0f), st2084_m_2);
  }

  // decode value 'v' with the inverse of the selected encoding fuction to luminance
  float encodingToLuminance(int encoding, float v)
  {
    if( encoding == 1 )
    {
      // ACEScct
      return ACEScct_to_linear(v) * referenceLuminance;
    }
    else if( encoding == 2 )
    {
      // sRGB
      return sRGB_to_linear(v) * referenceLuminance;
    }
    else if( encoding == 3 )
    {
      // BT.1886 (Gamma 2.4)
      return spow(v, 2.4f) * referenceLuminance;
    }
    else if( encoding == 4 )
    {
      // Gamma 2.6
      return spow(v, 2.6f) * referenceLuminance;
    }
    else if( encoding == 5 )
    {
      // ST2084
      return ST2084_to_linear(v);
    }
    else
    {
      // Linear
      // default
      return v * referenceLuminance;
    }
  }

  // decode the components of a 3D vector 'v' with the inverse of the selected encoding fuction to luminance
  float3 encodingToLuminance3(int encoding, float3 v)
  {
    float3 lin;
    lin.x = encodingToLuminance(encoding, v.x);
    lin.y = encodingToLuminance(encoding, v.y);
    lin.z = encodingToLuminance(encoding, v.z);

    return lin;
  }

  // encode the linear luminance value 'v' with the encoding fuction selected by 'encoding'
  float luminanceToEncoding(int encoding, float v)
  {
    if( encoding == 1 )
    {
      // ACEScct
      return linear_to_ACEScct(v / referenceLuminance);
    }
    else if( encoding == 2 )
    {
      // sRGB
      return linear_to_sRGB(v / referenceLuminance);
    }
    else if( encoding == 3 )
    {
      // BT.1886 (Gamma 2.4)
      return spow(v / referenceLuminance, 1.0f/2.4f);
    }
    else if( encoding == 4 )
    {
      // Gamma 2.6
      return spow(v / referenceLuminance, 1.0f/2.6f);
    }
    else if( encoding == 5 )
    {
      // ST2084
      return linear_to_ST2084(v);
    }
    else
    {
      // Linear
      // default
      return v / referenceLuminance;
    }
  }

  // encode the linear luminance value components of a 3D vector 'v' with the encoding fuction selected by 'encoding'
  float3 luminanceToEncoding3(int encoding, float3 v)
  {
    float3 enc;
    enc.x = luminanceToEncoding(encoding, v.x);
    enc.y = luminanceToEncoding(encoding, v.y);
    enc.z = luminanceToEncoding(encoding, v.z);

    return enc;
  }

  // convert RGB values in the output colorspace to the CAM J (lightness), M (colorfulness) and h (hue) correlates
  float3 output_RGB_to_JMh(float3 RGB)
  {
    float3 luminanceRGB = encodingToLuminance3(encodingOut, RGB);
    float3 XYZ = vector_dot(RGB_to_XYZ_output, luminanceRGB);
    float3 JMh = XYZ_to_JMh(XYZ, limitWhite, viewingConditions, L_A_out, Y_b_out, discountIlluminant_out,HK_mode_out);
    return JMh;
  }

  // convert RGB values in the output colorspace to the CAM J (lightness), M (colorfulness) and h (hue) correlates
  float3 luminance_RGB_to_JMh(float3 luminanceRGB)
  {
    float3 XYZ = vector_dot(RGB_to_XYZ_output, luminanceRGB);
    float3 JMh = XYZ_to_JMh(XYZ, refWhite, outputViewingConditions, L_A, Y_b, discountIlluminant_mid, HK_mode_mid);
    return JMh;
  }

  // convert CAM J (lightness), M (colorfulness) and h (hue) correlates to  RGB values in the output colorspace
  float3 JMh_to_output_RGB(float3 JMh)
  {
    float3 luminanceXYZ = JMh_to_XYZ( JMh, limitWhite, outputViewingConditions , L_A_out, Y_b_out, discountIlluminant_out, HK_mode_out);

    // switch to treat incoming data as luminanceXYZ when in breakout mode
    if (diagnosticMode == 105)
    {
      luminanceXYZ = JMh;
    }

    // First matrix to limiting gamut for clamping
    float3 luminanceRGB = vector_dot(XYZ_to_RGB_limit, luminanceXYZ);

    if( fitWhite)
    {
      // Scale to fit maximum creative white channel value
      float3 creativeWhiteXYZ = vector_dot(RGB_to_XYZ_limit, float3(1.0f, 1.0f, 1.0f));
      float3 creativeWhiteRGB = vector_dot(XYZ_to_RGB_output, creativeWhiteXYZ);
      luminanceRGB  *= 1.0f / max(creativeWhiteRGB.x, max(creativeWhiteRGB.y, creativeWhiteRGB.z));
    }

    if( softclampOutput )
    {
      // Soft clamp by compressing negative display linear values
      float3 compr = float3(clamp_thr, clamp_dist, 1.2f);
      luminanceRGB = compress_aces(luminanceRGB, compr, compr, compr, 0);
    }

    if( clampOutput )
    {
      // Clamp to between zero and peak luminance 
      luminanceRGB = clamp3(luminanceRGB, 0.0f, peakLuminance);
    }

    // Matrix to output (encoding) gamut (eventually concatenate to a single matrix)
    luminanceRGB = vector_dot(RGB_to_XYZ_limit, luminanceRGB);
    luminanceRGB = vector_dot(XYZ_to_RGB_output, luminanceRGB);

    // return luminanceRGB when in breakout mode
    if (diagnosticMode == 105)
    {
      return luminanceRGB;
    }

    float3 outputRGB = luminanceToEncoding3( encodingOut, luminanceRGB);

    return outputRGB;
  }

  // convert CAM J (lightness), M (colorfulness) and h (hue) correlates to  RGB values in the output colorspace
  float3 JMh_to_luminance_RGB(float3 JMh)
  {
      float3 luminanceXYZ = JMh_to_XYZ( JMh, refWhite, outputViewingConditions , L_A, Y_b, discountIlluminant_mid, HK_mode_mid);
      float3 luminanceRGB = vector_dot(XYZ_to_RGB_output, luminanceXYZ);

      return luminanceRGB;
  }


  // convert linear RGB values with the limiting primaries to CAM J (lightness), M (colorfulness) and h (hue) correlates
  float3 limit_RGB_to_JMh(float3 RGB)
  {
    float3 luminanceRGB = RGB * boundaryRGB *referenceLuminance;
    float3 XYZ = vector_dot(RGB_to_XYZ_limit, luminanceRGB);
    float3 JMh = XYZ_to_JMh(XYZ, refWhite, viewingConditions, L_A, Y_b, discountIlluminant_mid, HK_mode_mid);
    return JMh;
  }

    // convert linear RGB values with the limiting primaries to CAM J (lightness), M (colorfulness) and h (hue) correlates
    float3 reach_RGB_to_JMh(float3 RGB)
    {
      float3 luminanceRGB = RGB * boundaryRGB *referenceLuminance;
      float3 XYZ = vector_dot(RGB_to_XYZ_reach, luminanceRGB);
      float3 JMh = XYZ_to_JMh(XYZ, refWhite, viewingConditions, L_A, Y_b, discountIlluminant_mid, HK_mode_mid);
      return JMh;
    }

  // convert linear RGB values with the AP1 primaries to CAM J (lightness), M (colorfulness) and h (hue) correlates
  float3 AP1_RGB_to_JMh(float3 RGB)
  {
    float3 luminanceRGB = RGB * boundaryRGB *referenceLuminance;
    float3 XYZ = vector_dot(AP1_to_XYZ, luminanceRGB);
    float3 JMh = XYZ_to_JMh(XYZ, refWhite, viewingConditions, L_A, Y_b, discountIlluminant_mid, HK_mode_mid);
    return JMh;
  }


  // convert CAM J (lightness), M (colorfulness) and h (hue) correlates to linear RGB values with the limiting primaries
  float3 JMh_to_limit_RGB(float3 JMh)
  {
    float3 luminanceXYZ = JMh_to_XYZ( JMh, refWhite, viewingConditions, L_A, Y_b, discountIlluminant_mid, HK_mode_mid );
    float3 luminanceRGB = vector_dot(XYZ_to_RGB_limit, luminanceXYZ);
    float3 RGB = luminanceRGB / boundaryRGB / referenceLuminance;
    return RGB;
  }

    // convert CAM J (lightness), M (colorfulness) and h (hue) correlates to linear RGB values with the reach primaries
    float3 JMh_to_reach_RGB(float3 JMh)
    {
        float3 luminanceXYZ = JMh_to_XYZ( JMh, refWhite, viewingConditions, L_A, Y_b, discountIlluminant_mid, HK_mode_mid );
        float3 luminanceRGB = vector_dot(XYZ_to_RGB_reach, luminanceXYZ);
        float3 RGB = luminanceRGB / boundaryRGB / referenceLuminance;
        return RGB;
    }

  // XYZ to Hellwig2020 JMh
  //
  //     XYZ
  //         *CIE XYZ* tristimulus values of test sample / stimulus.
  //     XYZ_w
  //         *CIE XYZ* tristimulus values of reference white.
  //     L_A
  //         Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
  //         to be 20% of the luminance of a white object in the scene).
  //     Y_b
  //         Luminous factor of background :math:`Y_b` such as
  //         :math:`Y_b = 100 x L_b / L_w` where :math:`L_w` is the luminance of the
  //         light source and :math:`L_b` is the luminance of the background. For
  //         viewing images, :math:`Y_b` can be the average :math:`Y` value for the
  //         pixels in the entire image, or frequently, a :math:`Y` value of 20,
  //         approximate an :math:`L^*` of 50 is used.
  //     surround
  //         Surround viewing conditions induction factors.
  //         Truth value indicating if the illuminant should be discounted.
  //     discount_illuminant
  //
  // NOTE: Following modifications have been made to stock Hellwig2022 model for this DRT:
  //
  // - Custom primaries
  // - Eccentriticty factor has been removed
  // - Compress mode
  //
  float3 XYZ_to_Hellwig2022_JMh( float3 XYZ, float3 XYZ_w, float L_A, float Y_b, float3 surround, bool discountIlluminant, bool HK_mode)
    {
        XYZ_w = XYZ_w * XYZ_w_scaler;

        // # Step 0
        // # Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
        float3x3 MATRIX_16 = CAT_CAT16;
        float3 RGB_w = vector_dot(MATRIX_16, XYZ_w);

        // # Computing degree of adaptation :math:`D`.
        float D = clip(degree_of_adaptation(surround.x, L_A), 0, 1);
        if(discountIlluminant)
        {
            D = 1.0f;
        }

        // # Viewing conditions dependent parameters
        float k = 1 / (5 * L_A + 1);
        float k4 = pow(k,4);
        float F_L = 0.2f * k4 * (5.0f * L_A) + 0.1f * pow((1.0f - k4), 2.0f) * spow(5.0f * L_A, 1.0f / 3.0f) ;
        float n = sdiv(Y_b, XYZ_w.y);
        float z = 1.48 + sqrt(n);

        float3 D_RGB = D * XYZ_w.y / RGB_w + 1 - D;
        float3 RGB_wc = D_RGB * RGB_w;
        float3 RGB_aw = post_adaptation_non_linear_response_compression_forward(RGB_wc, F_L);

        // # Computing achromatic responses for the whitepoint.
        float R_aw = RGB_aw.x ;
        float G_aw = RGB_aw.y ;
        float B_aw = RGB_aw.z ;

        float A_w = ra * R_aw + G_aw + ba * B_aw;

        // # Step 1
        // # Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
        float3 RGB = vector_dot(MATRIX_16, XYZ);

        // # Step 2
        float3 RGB_c = D_RGB * RGB;

        // # Step 3
        // # Applying forward post-adaptation non-linear response compression.

        if (compressMode)
        {
          RGB_c = compress_bjorn(RGB_c);
        }

        float3 RGB_a = post_adaptation_non_linear_response_compression_forward(RGB_c, F_L);

        if (compressMode)
        {
          RGB_a = uncompress_bjorn(RGB_a);
        }

        // # Step 4
        // # Converting to preliminary cartesian coordinates.
        float R_a = RGB_a.x ;
        float G_a = RGB_a.y ;
        float B_a = RGB_a.z ;
        float a = R_a - 12.0f * G_a / 11.0f + B_a / 11.0f;
        float b = (R_a + G_a - 2.0f * B_a) / 9.0f;

        // # Computing the *hue* angle :math:`h`.
        // Unclear why this isnt matching the python version.
        float hr = atan2(b, a);
        float h = mod(degrees(hr), 360.0f);

        // # Step 6
        // # Computing achromatic responses for the stimulus.
        float R_a2 = RGB_a.x ;
        float G_a2 = RGB_a.y ;
        float B_a2 = RGB_a.z ;

        float A = ra * R_a2 + G_a2 + ba * B_a2;

        // # Step 7
        // # Computing the correlate of *Lightness* :math:`J`.
        float J = 100.0f * spow(sdiv(A, A_w), surround.y * z);

        // # Step 8
        // # Computing the correlate of *brightness* :math:`Q`.
        float Q = (2.0f / float(surround.y)) * (J / 100.0f) * A_w;

        // # Step 9
        // # Computing the correlate of *colourfulness* :math:`M`.
        float M = 43.0f * surround.z * sqrt(a * a + b * b);

        // # Computing the correlate of *chroma* :math:`C`.
        float C = 35.0f * sdiv(M, A_w);

        // # Computing the correlate of *saturation* :math:`s`.
        float s = 100.0f * sdiv(M, Q);

        // # *Helmholtz–Kohlrausch* Effect Extension.
        float J_HK = J + hue_angle_dependency_Hellwig2022(hr) * spow(C, 0.587f);
        float Q_HK = (2.0f / surround.y) * (J_HK / 100.0f) * A_w ;

        if (HK_mode)
        {
          return {J_HK,M,h};
        }
        else
        {
          if (J == 0.0f)
            M = 0.0f;
          return {J,M,h};
        }
    }

    float3 Hellwig2022_JMh_to_XYZ( float3 JMh, float3 XYZ_w, float L_A, float Y_b, float3 surround, bool discountIlluminant, bool HK_mode)
    {
        float J = JMh.x;
        float M = JMh.y;
        float h = JMh.z;
        XYZ_w  = XYZ_w  * XYZ_w_scaler;
  
        // # Step 0
        // # Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
        float3x3 MATRIX_16 = CAT_CAT16;
        float3 RGB_w = vector_dot(MATRIX_16, XYZ_w);

        // # Computing degree of adaptation :math:`D`.
        float D = clip(degree_of_adaptation(surround.x, L_A), 0, 1);
        if(discountIlluminant)
        {
            D = 1.0f;
        }

        // # Viewing conditions dependent parameters
        float k = 1 / (5 * L_A + 1);
        float k4 = pow(k,4);
        float F_L = 0.2f * k4 * (5.0f * L_A) + 0.1f * pow((1.0f - k4), 2.0f) * spow(5.0f * L_A, 1.0f / 3.0f) ;
        float n = sdiv(Y_b, XYZ_w.y);
        float z = 1.48 + sqrt(n);

        float3 D_RGB = D * XYZ_w.y / RGB_w + 1 - D;
        float3 RGB_wc = D_RGB * RGB_w;
        float3 RGB_aw = post_adaptation_non_linear_response_compression_forward(RGB_wc, F_L);

        // # Computing achromatic responses for the whitepoint.
        float R_aw = RGB_aw.x ;
        float G_aw = RGB_aw.y ;
        float B_aw = RGB_aw.z ;
        float A_w = ra * R_aw + G_aw + ba * B_aw;

        float hr = radians(h);

        // # *Helmholtz–Kohlrausch* Effect Extension.
        float C = (M * 35) / A_w;
        if (HK_mode)
        {
          J = J - hue_angle_dependency_Hellwig2022(hr) * spow(C, 0.587f);
        }

        // # Computing achromatic response :math:`A` for the stimulus.
        float A = A_w * spow(J / 100.0f, 1.0f / (surround.y * z));

        // # Computing *P_p_1* to *P_p_2*.
        float P_p_1 = 43.0f * surround.z;
        float P_p_2 = A;

        // # Step 3
        // # Computing opponent colour dimensions :math:`a` and :math:`b`.
        float gamma = M / P_p_1;
        float a = gamma * cos(hr);
        float b = gamma * sin(hr);

        // # Step 4
        // # Applying post-adaptation non-linear response compression matrix.
        float3 RGB_a = vector_dot(panlrcm, float3(P_p_2, a, b)) / 1403.0f;

        // # Step 5
        // # Applying inverse post-adaptation non-linear response compression.
        if (compressMode)
        {
          RGB_a = compress_bjorn(RGB_a);
        }

        float3 RGB_c = post_adaptation_non_linear_response_compression_inverse(RGB_a, F_L);

        if (compressMode)
        {
          RGB_c = uncompress_bjorn(RGB_c);
        }

        // # Step 6
        float3 RGB = RGB_c / D_RGB;
        
        // # Step 7
        float3x3 MATRIX_INVERSE_16 = CAT_CAT16.invert();
        float3 XYZ = vector_dot(MATRIX_INVERSE_16, RGB);

        return XYZ;
    }


  // retrieve the JM coordinates of the limiting gamut cusp at the hue slice 'h'
  // cusps are very expensive to compute
  // and the DRT is only using them for lightness mapping
  // which does not require a high degree of accuracy
  // so instead we use a pre-computed table of cusp points
  // sampled at 1 degree hue intervals of the the RGB target gamut
  // and lerp between them to get the approximate J & M values
  float2 cuspFromTable(float h)
  {

    float3 lo;
    float3 hi;

    if( h <= gamutCuspTable[0].z )
    {
      lo = gamutCuspTable[gamutCuspTableSize-1];
      lo.z = lo.z-360.0f;
      hi = gamutCuspTable[0];
    }
    else if( h >= gamutCuspTable[gamutCuspTableSize-1].z )
    {
      lo = gamutCuspTable[gamutCuspTableSize-1];
      hi = gamutCuspTable[0];
      hi.z = hi.z+360.f;
    }
    else
    {
      for(int i = 1; i < gamutCuspTableSize; ++i)
      {
        if( h <= gamutCuspTable[i].z )
        {
          lo = gamutCuspTable[i-1];
          hi = gamutCuspTable[i];
          break;
        }
      }
    }

    float t = (h - lo.z) / (hi.z - lo.z);

    float cuspJ = lerp(lo.x, hi.x, t);
    float cuspM = lerp(lo.y, hi.y, t);

    return float2(cuspJ,cuspM);
  }

    float2 cuspFromTableAP1(float h)
  {

    float3 lo;
    float3 hi;

    if( h <= gamutCuspTableAP1[0].z )
    {
      lo = gamutCuspTableAP1[gamutCuspTableSize-1];
      lo.z = lo.z-360.0f;
      hi = gamutCuspTableAP1[0];
    }
    else if( h >= gamutCuspTableAP1[gamutCuspTableSize-1].z )
    {
      lo = gamutCuspTableAP1[gamutCuspTableSize-1];
      hi = gamutCuspTableAP1[0];
      hi.z = hi.z+360.f;
    }
    else
    {
      for(int i = 1; i < gamutCuspTableSize; ++i)
      {
        if( h <= gamutCuspTableAP1[i].z )
        {
          lo = gamutCuspTableAP1[i-1];
          hi = gamutCuspTableAP1[i];
          break;
        }
      }
    }

    float t = (h - lo.z) / (hi.z - lo.z);

    float cuspJ = lerp(lo.x, hi.x, t);
    float cuspM = lerp(lo.y, hi.y, t);

    return float2(cuspJ,cuspM);
  }


  float2 cuspFromTableLocus(float h)
  {

    float cuspJ = 69;
    float cuspM = LocusLimitMTable[int(h)];
    return float2(cuspJ,cuspM);
  }

  float2 ccuspFromTable(float h)
  {

    float3 lo;
    float3 hi;

    if( h <= cgamutCuspTable[0].z )
    {
      lo = cgamutCuspTable[gamutCuspTableSize-1];
      lo.z = lo.z-360.0f;
      hi = cgamutCuspTable[0];
    }
    else if( h >= cgamutCuspTable[gamutCuspTableSize-1].z )
    {
      lo = cgamutCuspTable[gamutCuspTableSize-1];
      hi = cgamutCuspTable[0];
      hi.z = hi.z+360.f;
    }
    else
    {
      for(int i = 1; i < gamutCuspTableSize; ++i)
      {
        if( h <= cgamutCuspTable[i].z )
        {
          lo = cgamutCuspTable[i-1];
          hi = cgamutCuspTable[i];
          break;
        }
      }
    }

    float t = (h - lo.z) / (hi.z - lo.z);

    float cuspJ = lerp(lo.x, hi.x, t);
    float cuspM = lerp(lo.y, hi.y, t);

    return float2(cuspJ,cuspM);
  }

  float cReachFromTable(float h)
  {
    float3 lo;
    float3 hi;

    if( h <= cgamutReachTable[0].z )
    {
      lo = cgamutReachTable[gamutCuspTableSize-1];
      lo.z = lo.z-360.0f;
      hi = cgamutReachTable[0];
    }
    else if( h >= cgamutReachTable[gamutCuspTableSize-1].z )
    {
      lo = cgamutReachTable[gamutCuspTableSize-1];
      hi = cgamutReachTable[0];
      hi.z = hi.z+360.f;
    }
    else
    {
      for(int i = 1; i < gamutCuspTableSize; ++i)
      {
        if( h <= cgamutReachTable[i].z )
        {
          lo = cgamutReachTable[i-1];
          hi = cgamutReachTable[i];
          break;
        }
      }
    }

    float t = (h - lo.z) / (hi.z - lo.z);
    return lerp(lo.y, hi.y, t);
  }

  float daniele_evo_fwd(float Y)
  {
     float f = daniele_m_2 * pow(max(0.0f, Y) / (Y + daniele_s_2), daniele_g);
     float h = max(0.0f, f * f / (f + daniele_t_1));
     return h;
  }

  float daniele_evo_rev(float Y)
  {
    Y = max(0.0f, min(daniele_n / (daniele_u_2 * daniele_n_r), Y));
    float h = (Y + sqrt(Y * (4.0f * daniele_t_1 + Y))) / 2.0f;
    float f = daniele_s_2 / (pow((daniele_m_2 / h), (1.0f / daniele_g)) - 1.0f);
    return f;
  }

  // Return compression gamut cusp M scaled with an eccentricity factor
  float cusp_with_eccentricity_factor(float h)
  {
    float2 JMcusp = ccuspFromTable(h);
    float hr = radians(h);

    float e_t = 1.0f;

    // CAM16
    if (cc_et == 0)
    {
      // NOTE: custom scaler 0.275 instead of 0.25 in CAM16
      e_t = 0.275f * (cos(2.0f + hr) + 3.8f);
    }
    // Hellwig2022
    // CAM16 vs Hellwig2022: https://onlinelibrary.wiley.com/cms/asset/60788dfc-6bae-4949-bf8d-bd8c3467aef8/col22792-fig-0005-m.jpg
    else if (cc_et == 1)
    {
      float _h = hr;
      float _2_h = 2 * hr;
      float _3_h = 3 * hr;
      float _4_h = 4 * hr;
      e_t = (
        -0.0582f * cos(_h)
        - 0.0258f * cos(_2_h)
        - 0.1347f * cos(_3_h)
        + 0.0289f * cos(_4_h)
        - 0.1475f * sin(_h)
        - 0.0308f * sin(_2_h)
        + 0.0385f * sin(_3_h)
        + 0.0096f * sin(_4_h)
        + 1.0f
      );
    }
    // Custom https://www.desmos.com/calculator/vukgp6rtos
    else if (cc_et == 2)
    {
      float hr2 = hr * 2;
      float hr3 = hr * 3;
      e_t = (-0.47f * cos(hr) +
              0.07f * cos(hr2) +
             -0.11f * cos(hr3) +
             -0.33f * sin(hr) +
              0.19f * sin(hr2) +
              0.00f * sin(hr3) +
              1.86f) * 0.58f;
    }
    return JMcusp.y * e_t;
  }

  // A "toe" function that remaps the given value x between 0 and limit.
  // The k1 and k2 parameters change the size and shape of the toe.
  // https://www.desmos.com/calculator/6vplvw14ti
  float toe(float x, float limit, float k1, float k2, int inverse)
  {
    if (x > limit)
      return x;

    k2 = max(k2, 0.001f);
    k1 = sqrt(k1 * k1 + k2 * k2);
    float k3 = (limit + k1) / (limit + k2);

    if (!inverse)
      return 0.5f * (k3 * x - k1 + sqrt((k3 * x - k1) * (k3 * x - k1) + 4 * k2 * k3 * x));
    else
      return (x * x + k1 * x) / (k3 * (x + k2));
  }

  // Chroma compression
  //
  // Compresses colors inside the gamut with the aim for colorfulness to have an
  // appropriate rate of change from display black to display white, and from
  // achromatic outward to purer colors.
  //
  float chromaCompression(float3 JMh, float origJ, float linear, int invert)
  {
    float M = JMh.y;
    if (M == 0.0f)
      return M;

    float nJ = JMh.x / limitJmax;
    float snJ = max(0.0f, 1.0f - nJ);
    float Mnorm = cusp_with_eccentricity_factor(JMh.z);
    float limit = pow(nJ, 1.0f / lowerHullGamma) * cReachFromTable(JMh.z) / Mnorm;

    if (!invert)
    {
      //
      // Rescaling of M with the tonescaled J to get the M to the same range as
      // J after the tonescale.  The rescaling uses the Hellwig2022 model gamma to
      // keep the M/J ratio correct (keeping the chromaticities constant).
      //
      M *= pow(JMh.x / origJ, model_gamma);

      if (applyInGamutCompression)
      {
        // Normalize M with the rendering space cusp M
        M /= Mnorm;

        //
        // Expand the colorfulness by running the toe function in reverse.  The goal is to
        // expand less saturated colors less and more saturated colors more.  The expansion
        // increases saturation in the shadows and mid-tones but not in the highlights.
        // The 0.001 offset starts the expansions slightly above zero.  The sat_thr makes
        // the toe less aggressive near black to reduce the expansion of noise.
        //
        if (applyInGamutExpansion)
          M = limit - toe(limit - M, limit - 0.001f, snJ * sat, sqrt(nJ * nJ + sat_thr), 0);

        //
        // Compress the colorfulness.  The goal is to compress less saturated colors more and
        // more saturated colors less, especially in the highlights.  This step creates the
        // saturation roll-off in the highlights, but attemps to preserve pure colors.  This
        // mostly affects highlights and mid-tones, and does not compress shadows.
        //
        M = toe(M, limit, nJ * compr, snJ, 0);

        // Clamp M to the rendering space
        if (applyReachClamp)
          M = min(limit, M);

        // Denormalize
        M *= Mnorm;
      }
    }
    else
    {
      if (applyInGamutCompression)
      {
        M /= Mnorm;
        M = toe(M, limit, nJ * compr, snJ, 1);
        if (applyInGamutExpansion)
          M = limit - toe(limit - M, limit - 0.001f, snJ * sat, sqrt(nJ * nJ + sat_thr), 1);
        M *= Mnorm;
      }

      M *= pow(JMh.x / origJ, -model_gamma);
    }

    return M;
  }

  float3 input_RGB_to_JMh(float3 inputRGB)
  {
    // clamp input to +/- HALF_MAXIMUM range (to remove inf values, etc.)
    inputRGB = clamp3(inputRGB, -HALF_MAXIMUM, HALF_MAXIMUM);

    // convert to linear XYZ luminance values
    float3 luminanceRGB = encodingToLuminance3( encodingIn, inputRGB);
    float3 luminanceXYZ = vector_dot(RGB_to_XYZ_input, luminanceRGB);
    float3 JMh = XYZ_to_JMh(luminanceXYZ, inWhite, viewingConditions, L_A, Y_b, discountIlluminant_in, HK_mode_in);

    if (diagnosticMode == 6 || diagnosticMode == 100)
    {
      return luminanceXYZ;
    }
   else
    {
      return JMh;
    }
  }


  float3 JMh_to_input_RGB(float3 JMh)
  {
    float3 luminanceXYZ = JMh_to_XYZ( JMh, inWhite, viewingConditions , L_A, Y_b, discountIlluminant_in, HK_mode_in);
    float3 luminanceRGB = vector_dot(XYZ_to_RGB_input, luminanceXYZ);
    float3 inputRGB = luminanceToEncoding3( encodingIn, luminanceRGB);

    return inputRGB;
  }


  float3 forwardTonescale( float3 inputJMh )
  {
    float3 outputJMh;
    float3 monoJMh = float3(inputJMh.x,0.0f,0.0f);
    float3 linearJMh = JMh_to_luminance_RGB(monoJMh);
    float linear = linearJMh.x/referenceLuminance;

    float2 luminanceTS = linear;

    // switch for applying the different tonescale compression functions
    if ( toneScaleMode == 0 )
    {
      luminanceTS =  linear;
    }
    else if( toneScaleMode == 1 )
    {
      luminanceTS = daniele_evo_fwd(linear) * mmScaleFactor;
    }

    float3 tonemappedmonoJMh = luminance_RGB_to_JMh(float3(luminanceTS.x,luminanceTS.x,luminanceTS.x));
    float3 tonemappedJMh = float3(tonemappedmonoJMh.x,inputJMh.y,inputJMh.z);

    if( applyTonecurve )
    {
        outputJMh = tonemappedJMh;
    }
    else
    {
        outputJMh = inputJMh;
    }

    if (applyChromaCompression)
    {
      outputJMh.y = chromaCompression(tonemappedJMh, inputJMh.x, linear, 0);
    }

    if (monochrome)
    {
      outputJMh.y = 0.0f;
    }

    return outputJMh;
  }


  float3 inverseTonescale( float3 JMh )
  {
    float3 tonemappedJMh = JMh;

    if( ! applyTonecurve && !applyChromaCompression )
    {
      // nothing else to do here
      return tonemappedJMh;
    }

    float3 untonemappedColourJMh = tonemappedJMh;
    
    float3 monoTonemappedJMh = float3(tonemappedJMh.x,0.0f,0.0f);
    float3 monoTonemappedRGB = JMh_to_luminance_RGB(monoTonemappedJMh);
    float luminance = monoTonemappedRGB.x;

    // Dummy value to init the var
    float linear = 0.0f;
    if( toneScaleMode == 1 )
    {
        linear = daniele_evo_rev(luminance / mmScaleFactor);
    }
    else
    {
        linear = luminance;
    }

    linear = linear*referenceLuminance;
  
    if( applyTonecurve )
    {
      float3 untonemappedMonoJMh = luminance_RGB_to_JMh(float3(linear,linear,linear));
      untonemappedColourJMh = float3(untonemappedMonoJMh.x,tonemappedJMh.y,tonemappedJMh.z);
    } 

    if (applyChromaCompression)
    {
      untonemappedColourJMh.y = chromaCompression(tonemappedJMh, untonemappedColourJMh.x, linear, 1);
    }

    return  untonemappedColourJMh;
  }

  float hueDependantUpperHullGamma(float h)
  {
    if (disableUpperHullGamma)
      return upperHullGamma;

    // take float h, divide by 10, and lerp between index values from upperHullGamma_0
    int index = int(h);
    float t = (h - index);
    float gamma = 1.0f;
    if (index < gamutCuspTableSize-1)
    {
        gamma = lerp(gamutTopGamma[index], gamutTopGamma[index+1], t);
    }
    else
    {
        gamma = lerp(gamutTopGamma[gamutCuspTableSize-1], gamutTopGamma[0], t);
    }

    return gamma;
    // return gamutTopGamma[0];
    // debugPrint(&gamma,1,1); 
  }

  float hueDependantLowerHullGamma(float h)
  {
    if (disableLowerHullGamma)
      return lowerHullGamma;

    // take float h, divide by 10, and lerp between index values from upperHullGamma_0
    int index = int(h);
    float t = (h - index);
    float gamma = 1.0f;
    if (index < gamutCuspTableSize-1)
    {
        gamma = lerp(gamutBottomGamma[index], gamutBottomGamma[index+1], t);
    }
    else
    {
        gamma = lerp(gamutBottomGamma[gamutCuspTableSize-1], gamutBottomGamma[0], t);
    }

    return gamma;
  }


  // reimplemented from https://github.com/nick-shaw/aces-ot-vwg-experiments/blob/master/python/intersection_approx.py
  float3 findGamutBoundaryIntersection(float3 JMh_s, float2 JM_cusp, float J_focus, float J_max, float slope_gain, float smoothness, float gamma_top, float gamma_bottom)
  {
    float2 JM_source = float2(JMh_s.x, JMh_s.y);
    // float gamma_top = hueDependantUpperHullGamma(JMh_s.z);
    // float gamma_bottom = lowerHullGamma;

    float slope = 0.0f;

    float s = max(0.000001f, smoothness);
    JM_cusp.x *= 1.0f + 0.06f * s;   // J
    JM_cusp.y *= 1.0f + 0.18f * s;   // M

    float J_intersect_source = solve_J_intersect(JM_source, J_focus, J_max, slope_gain);
    float J_intersect_cusp = solve_J_intersect(JM_cusp, J_focus, J_max, slope_gain);


    //   print("J-axis intersection: J = {:.3f}".format(J_intersect_source))

    if (J_intersect_source < J_focus)
    {
        slope = J_intersect_source * (J_intersect_source - J_focus) / (J_focus * slope_gain);
    }
    else
    {
        slope = (J_max - J_intersect_source) * (J_intersect_source - J_focus) / (J_focus * slope_gain);

    } 

    float M_boundary_lower = J_intersect_cusp * pow(J_intersect_source / J_intersect_cusp, 1 / gamma_bottom) / (JM_cusp.x / JM_cusp.y - slope);

    float M_boundary_upper = JM_cusp.y * (J_max - J_intersect_cusp) * pow((J_max - J_intersect_source) / (J_max - J_intersect_cusp), 1.0f / gamma_top) / (slope * JM_cusp.y + J_max - JM_cusp.x);

//     float M_boundary = smin(M_boundary_lower, M_boundary_upper, smoothness);
    float M_boundary = JM_cusp.y * smin(M_boundary_lower / JM_cusp.y, M_boundary_upper / JM_cusp.y, s);

    // J_boundary is not actually needed, but the calculation would be as follows
    float J_boundary = J_intersect_source + slope * M_boundary;

    // print("Gamut boundary intersection: JM = [{:.3f}, {:.3f}]".format(J_boundary, M_boundary))


    return float3(J_boundary, M_boundary,J_intersect_source);

    // return float2(1.0f, 2.0f);
      
  }

  // Approximation of the gamut intersection to a curved and smoothened triangle
  // along the projection line 'from -> to'. 
  float2 find_gamut_intersection(float2 cusp, float2 from, float2 to, float smoothing)
  {
    float t0, t1;

    // Scale the cusp outward when smoothing to avoid reducing the gamut.  Reduce
    // smoothing for high cusps because smin() will bias it too much for the longer line.
    float s = max(lerp(smoothing, smoothing * 0.05f, cusp.x / limitJmax), 0.0001f);
    cusp.y *= 1.0f + 0.18f * s;
    cusp.x *= 1.0f + 0.07f * s;

    // Line below the cusp is curved with model_gamma
    float toJ_gamma = cusp.x * spow(to.x / cusp.x, model_gamma);
    float fromJ_gamma = cusp.x * spow(from.x / cusp.x, model_gamma);
    t0 = cusp.y * toJ_gamma / (from.y * cusp.x + cusp.y * (toJ_gamma - fromJ_gamma));

    // Line above the cusp
    t1 = cusp.y * (to.x - limitJmax) / (from.y * (cusp.x - limitJmax) + cusp.y * (to.x - from.x));

    // Smooth minimum to smooth the cusp
    t1 = smin(fabs(t0), fabs(t1), s);

    return float2(to.x * (1.0f - t1) + t1 * from.x, t1 * from.y);
  }

  float2 findCurveIntersection(float c,float2 cusp,float m,float h)
  {
    // based on this desmos plot https://www.desmos.com/calculator/pcsovzirqa
    float xc = cusp.y;
    float yc = cusp.x;
    float f = 1.0;
    float mf = m * f;
    float xi = 1.0f;
    float g1 = 1.0f/model_gamma;
    // float g2 = 1.273f;


    float g2 = hueDependantUpperHullGamma(h);
    // float g2 = upperHullGamma[0];


    if ( m*xc + c < yc)
    {
        //    below cusp
        xi = spow((1-mf) , (g1 - 1 ))  * ((yc*spow((c/yc) , (1.0/g1))) / (yc/xc-m));
        // xi = cusp.x;
    }    
    else
    {
        //    above cusp
        xi =    spow((1+mf) , ((g2-1)))    *    (   xc * (limitJmax - yc) * spow(((limitJmax-c)/(limitJmax-yc)) , (1/g2))   / (m * xc + limitJmax - yc));
        // xi = cusp.x;
    }
    float yi = (m * xi) +c;
    if (yi > limitJmax)
    {
        yi = limitJmax;
        xi = 0.0f;
    }
    return float2(yi,xi);
    // return float2(cusp.x,c);
    // return float2(0.5f,0.5f);
  }
        

  float3 getLocusBoundry(float3 Jmh)
  {
    float h = Jmh.z;

    float2 cuspLocus = cuspFromTableLocus(h);
    float cuspTarget100 = cuspLocus.y;
    float cuspTarget = cuspTarget100 * pow((Jmh.x/100.0f), model_gamma);
    float difference =  cuspLocus.y / cuspTarget;
    return float3(Jmh.x,cuspTarget,Jmh.z);
  }

  float3 getReachBoundry(float3 Jmh)
  {
    float h = Jmh.z;
    float3 lo;
    float3 hi;

    if( h <= gamutCuspTableReach[0].z )
    {
      lo = gamutCuspTableReach[gamutCuspTableSize-1];
      lo.z = lo.z-360.0f;
      hi = gamutCuspTableReach[0];
    }
    else if( h >= gamutCuspTableReach[gamutCuspTableSize-1].z )
    {
      lo = gamutCuspTableReach[gamutCuspTableSize-1];
      hi = gamutCuspTableReach[0];
      hi.z = hi.z+360.f;
    }
    else
    {
      for(int i = 1; i < gamutCuspTableSize; ++i)
      {
        if( h <= gamutCuspTableReach[i].z )
        {
          lo = gamutCuspTableReach[i-1];
          hi = gamutCuspTableReach[i];
          break;
        }
      }
    }

    float t = (h - lo.z) / (hi.z - lo.z);

    float reachMaxM = lerp(lo.x, hi.x, t);
    if( reachNick)
    {
      float2 JMcusp = cuspFromTable(Jmh.z);
      float focusJ = lerp(JMcusp.x, midJ, min(1.0f, cuspMidBlend - (JMcusp.x / limitJmax)));
      float slope_gain = limitJmax * focusDistance * getFocusGain(Jmh.x, JMcusp.x);
      float intersectJ = solve_J_intersect(float2(Jmh.x,Jmh.y), focusJ, limitJmax, slope_gain);
      float slope;
      if (intersectJ < focusJ)
	  {
			slope = intersectJ * (intersectJ - focusJ) / (focusJ * slope_gain);
	  }
	  else
	  {
			slope = (limitJmax - intersectJ) * (intersectJ - focusJ) / (focusJ * slope_gain);
	  } 
      float boundaryNick = limitJmax * pow(intersectJ/limitJmax, 1.0f / lowerHullGamma) * reachMaxM / (limitJmax - slope * reachMaxM);
      return float3(Jmh.x,boundaryNick,Jmh.z);
    }
    float cuspTarget = reachMaxM * pow((Jmh.x/limitJmax), model_gamma);
    return float3(Jmh.x,cuspTarget,Jmh.z);
  }


  float4 getCompressionFuncParams(float3 Jmh)
  {
    float h = Jmh.z;

    float angleR = 20.0f;
    float angleY = 102.0f;
    float angleG = 146.0f;
    float angleC = 193.0f;
    float angleB = 259.0f;
    float angleM = 342.0f;

    float lerpVal = 0.0f;

    if(Reachcompressmode)
    { 
        if(primariesReach != 6) // All of the primary based reach values
        {
            // use primary based reach
            float locusMax = getReachBoundry(Jmh).y;
            float difference = max(1.0001f, locusMax / Jmh.y);
            float threshold = max(compressionFuncParams.x, 1.0f / difference);
            return float4(threshold,difference,difference,compressionFuncParams.w);
        }
        else
        {
            // use locus based reach
            float locusMax = getLocusBoundry(Jmh).y;
            float difference =  locusMax / Jmh.y;
            return float4(compressionFuncParams.x,difference,difference,compressionFuncParams.w);
        }
    }
        
    if (!sixAxisCompressionMode)
      return compressionFuncParams;
    else
    {
      if (h>=angleR && h<angleY)
      {
        lerpVal = (h-angleR)/(angleY-angleR);
        return lerp4(compressionFuncParamsR, compressionFuncParamsY, lerpVal);
      }
      if (h>=angleY && h<angleG)
      {
        lerpVal = (h-angleY)/(angleG-angleY);
        return lerp4(compressionFuncParamsY, compressionFuncParamsG, lerpVal);
      }
      if (h>=angleG && h<angleC)
      {
          lerpVal = (h-angleG)/(angleC-angleG);
          return lerp4(compressionFuncParamsG, compressionFuncParamsC, lerpVal);
      }
      if (h>=angleC && h<angleB)
      {
          lerpVal = (h-angleC)/(angleB-angleC);
          return lerp4(compressionFuncParamsC, compressionFuncParamsB, lerpVal);
      }
      if (h>=angleB && h<angleM)
      {
          lerpVal = (h-angleB)/(angleM-angleB);
          return lerp4(compressionFuncParamsB, compressionFuncParamsM, lerpVal);
      }
      if (h>=angleM && h<angleR+360.0f)
      {
          lerpVal = (h-angleM)/(angleR+360.0f-angleM);
          return lerp4(compressionFuncParamsM, compressionFuncParamsR, lerpVal);
      }
      if (h<angleR)
      {
          lerpVal = (h+360.0f-angleM)/(angleR+360.0f-angleM);
          return lerp4(compressionFuncParamsM, compressionFuncParamsR, lerpVal);
      }
      else
      {
        return compressionFuncParams;
      }
    }
    
  }


   float getFocusGain(float J, float cuspJ)
   {
     if (disableFocusGain)
       return 1.0f;
     if (J > cuspJ)
     {
       // Approximate inverse required above cusp
       return pow(pow(log10((limitJmax - cuspJ) / max(0.0001f, (limitJmax - min(limitJmax, J)))), 1.0f / focusAdjustGain) + 1.0f, focusAdjustPeakGain);
     }
     else
     {
       // Analytic inverse possible below cusp
       return 1.0f;
     }
   }

  float3 compressGamut(float3 JMh, int invert)
  {
    if (disableFocusGain)
      return compressGamut2(JMh, invert, JMh.x);

    if (!invert)
    {
      return compressGamut2(JMh, 0, JMh.x);
    }
    else
    {
      float2 JMcusp = cuspFromTable(JMh.z);
      float Jx = JMh.x;

      // Analytic inverse below cusp
      if (Jx <= JMcusp.x)
        return compressGamut2(JMh, 1, Jx);

      // Approximation above cusp
      Jx = compressGamut2(JMh, 1, Jx).x;
      return compressGamut2(JMh, 1, Jx);
    }
  }

  float3 compressGamut2(float3 JMh, int invert, float Jx)
  {
    float2 project_from = float2(JMh.x, JMh.y);
    float2 JMcusp = cuspFromTable(JMh.z);

    if (!applyGamutCompression)
      return JMh;
    if (project_from.y == 0.0f)
      return JMh;

    // Calculate where the out of gamut color is projected to
    float focusJ = lerp(JMcusp.x, midJ, min(1.0f, cuspMidBlend - (JMcusp.x / limitJmax)));

    // https://www.desmos.com/calculator/9u0wiiz9ys
    float Mratio = project_from.y / (focusDistance * JMcusp.y);
    float a = max(0.001f, Mratio / focusJ);
    float b0 = 1.0f - Mratio;
    float b1 = -(1.0f + Mratio + (a * limitJmax));
    float b = project_from.x < focusJ ? b0 : b1;
    float c0 = -project_from.x;
    float c1 = project_from.x + limitJmax * Mratio;
    float c = project_from.x < focusJ ? c0 : c1;

    // XXX this sqrt can cause NaNs (subtraction goes negative)
    float J0 = sqrt(b * b - 4 * a * c);
    float J1 = (-b - J0) / (2 * a);
          J0 = (-b + J0) / (2 * a);
    float projectJ = project_from.x < focusJ ? J0 : J1;

    float slope_gain = limitJmax * focusDistance * getFocusGain(Jx, JMcusp.x);

    // Find gamut intersection
    float2 project_to = float2(projectJ, 0.0f);
    float2 JMboundary = float2(1.0f,1.0f);
    if (boundryIntersectionMethod == 0)
    {
        // Original method implemented by Pekka
        JMboundary = find_gamut_intersection(JMcusp, project_from, project_to, smoothCusps);
    }
    else if (boundryIntersectionMethod == 1)
    {
        // Alternate method shown in Oct 19 meeting
        float m = (JMh.x - projectJ) / JMh.y;
        JMboundary = findCurveIntersection(JMh.x,JMcusp,0.0f,JMh.z);
        // JMboundary = find_gamut_intersection(JMcusp, project_from, project_to, smoothCusps, JMh.z);
    }
    else if (boundryIntersectionMethod == 2)
    {
        // findGamutBoundaryIntersection(float2      JM_source, float2 JM_cusp, float J_focus, float J_max, float slope_gain, float smoothness)
        float gamma_top    = hueDependantUpperHullGamma(JMh.z);
        float gamma_bottom = hueDependantLowerHullGamma(JMh.z);
        float3 nickBoundryReturn =  findGamutBoundaryIntersection(        JMh,         JMcusp,        focusJ,   limitJmax,       slope_gain, smoothCusps,gamma_top, gamma_bottom);
        JMboundary = float2(nickBoundryReturn.x,nickBoundryReturn.y);
        project_to = float2(nickBoundryReturn.z,0.0f);
        projectJ = nickBoundryReturn.z;
    }

    // Get hue dependent compression parameters
    float4 interpolatedCompressionFuncParams;
    if( reachNick )
    {
//       interpolatedCompressionFuncParams = getCompressionFuncParams(JMh);
      interpolatedCompressionFuncParams = getCompressionFuncParams(float3(JMboundary.x,JMboundary.y,JMh.z));
    }
    else
    {
      interpolatedCompressionFuncParams = getCompressionFuncParams(float3(JMh.x,JMboundary.y,JMh.z));
    }

    if (!Reachcompressmode)
      interpolatedCompressionFuncParams.x = 1.0f / lerp(interpolatedCompressionFuncParams.z, interpolatedCompressionFuncParams.y, projectJ / limitJmax);

    // Compress the out of gamut color along the projection line
    float2 JMcompressed = project_from;

    float lowerMlimit = 0.0001f; // Testing a small value here
    if (JMh.x < limitJmax && JMh.y > lowerMlimit) // using a small value to test against here rather than 0.0, and I was getting Nans on inversion.
    {
        float v = project_from.y / JMboundary.y;
        v = compressPowerP(v, interpolatedCompressionFuncParams.x,
                           lerp(interpolatedCompressionFuncParams.z, interpolatedCompressionFuncParams.y, projectJ / limitJmax),
                           interpolatedCompressionFuncParams.w, invert);
        JMcompressed = project_to + v * (JMboundary - project_to);
    }
    else
    {
        JMcompressed = float2(JMh.x, 0.0f);
    }

    // Diagnostic outputs
    if (diagnosticMode == 5)
    {
      return float3(focusJ, Mratio, projectJ);
    }
    if (diagnosticMode == 12)
    {
      return float3(JMboundary.x, JMboundary.y, JMh.z);
    }
    if (diagnosticMode == 18)
    {
      // return float3(interpolatedCompressionFuncParams.y, interpolatedCompressionFuncParams.z, JMh.z);
      return float3(JMh.x, JMboundary.y, JMh.z);
    }
    if (diagnosticMode == 20)
    {
      // return focus point
      return float3(project_to.x, project_to.y, JMh.z);
    }
    // actual output
    else
    {
      return float3(JMcompressed.x, JMcompressed.y, JMh.z);
    }
  }

  // Generate the Hellwig2022 post adaptation non-linear compression matrix
  // that is used in the inverse of the model (JMh-to-XYZ).
  //
  // Original:
  //  460.0f, 451.0f, 288.0f,
  //  460.0f, -891.0f, -261.0f,
  //  460.0f, -220.0f, -6300.0f
  void generate_panlrcm()
  {
    float panlrcm_data[]=
    {
      // original values: 2.0f, 1.0f, 0.05f,
      ra, 1.0f, ba,
      1.0f, -12.0f / 11.0f, 1.0f / 11.0f,
      1.0f / 9.0f, 1.0f / 9.0f, -2.0f / 9.0f
    };
    panlrcm.setArray(panlrcm_data);
    panlrcm = panlrcm.invert();

    // Normalize rows so that first column is 460
    for (int i = 0; i < 3; i++)
    {
      float n = 460.0f / panlrcm[i][0];
      panlrcm[i][0] *= n;
      panlrcm[i][1] *= n;
      panlrcm[i][2] *= n;
    }
  }


  void init()
  {
    HALF_MINIMUM = 0.0000000596046448f;
    HALF_MAXIMUM = 65504.0f;

    st2084_m_1=2610.0f / 4096.0f * (1.0f / 4.0f);
    st2084_m_2=2523.0f / 4096.0f * 128.0f;
    st2084_c_1=3424.0f / 4096.0f;
    st2084_c_2=2413.0f / 4096.0f * 32.0f;
    st2084_c_3=2392.0f / 4096.0f * 32.0f;
    st2084_m_1_d = 1.0f / st2084_m_1;
    st2084_m_2_d = 1.0f / st2084_m_2;
    st2084_L_p = 10000.0f;

    // pre-calculate Daniele Evo constants
    daniele_r_hit = daniele_r_hit_min + (daniele_r_hit_max - daniele_r_hit_min) * (log(daniele_n / daniele_n_r) / log(10000.0f / 100.0f));
    daniele_m_0 = daniele_n / daniele_n_r;
    daniele_m_1 = 0.5f * (daniele_m_0 + sqrt(daniele_m_0 * (daniele_m_0 + 4.0f * daniele_t_1)));
    daniele_u = pow((daniele_r_hit / daniele_m_1) / ((daniele_r_hit / daniele_m_1) + 1.0f), daniele_g);
    daniele_m = daniele_m_1 / daniele_u;
    daniele_w_i = log(daniele_n / 100.0f) / log(2.0f);
    daniele_c_t = daniele_c_d * (1.0f + daniele_w_i * daniele_w_g) / daniele_n_r;
    daniele_g_ip = 0.5f * (daniele_c_t + sqrt(daniele_c_t * (daniele_c_t + 4.0f * daniele_t_1)));
    daniele_g_ipp2 = -daniele_m_1 * pow(daniele_g_ip / daniele_m, 1.0f / daniele_g) / (pow(daniele_g_ip / daniele_m, 1.0f / daniele_g) - 1.0f);
    daniele_w_2 = daniele_c / daniele_g_ipp2;
    daniele_s_2 = daniele_w_2 * daniele_m_1;
    daniele_u_2 = pow((daniele_r_hit / daniele_m_1) / ((daniele_r_hit / daniele_m_1) + daniele_w_2), daniele_g);
    daniele_m_2 = daniele_m_1 / daniele_u_2;

    // 1.0f / (c * z)
    model_gamma = 1.0f / (viewingConditionsToSurround(outputViewingConditions).y * (1.48f + sqrt(Y_b_out / L_A_out)));

    // Chroma compression scaling for HDR/SDR appearance match
    float log_peak = log10(daniele_n / daniele_n_r);
    compr = chroma_compress + (chroma_compress * 5.0f) * log_peak;
    sat = max(0.15f, chroma_expand - (chroma_expand * 0.82f) * log_peak);
    sat_thr = chroma_expand_thr / daniele_n;

    float identity_matrix_data[]={ 1.0f, 0.0f, 0.0f,
                                   0.0f, 1.0f, 0.0f,
                                   0.0f, 0.0f, 1.0f };
    identity_matrix.setArray(identity_matrix_data);

    // Blink does not seem to support initialising multidimensional arrays
    // So instead of being able to index the matrix data directly from one
    // we need to use long if/else statements to populate the
    // input, limit & output primary matrices
    // (maybe there is a better way?)

    float XYZ_to_AP0_ACES_matrix_data[]=
    {
       1.0498110175f,  0.0000000000f, -0.0000974845f,
      -0.4959030231f,  1.3733130458f,  0.0982400361f,
       0.0000000000f,  0.0000000000f,  0.9912520182f
    };

    float XYZ_to_AP1_ACES_matrix_data[]=
    {
       1.6410233797f, -0.3248032942f, -0.2364246952f,
      -0.6636628587f,  1.6153315917f,  0.0167563477f,
       0.0117218943f, -0.0082844420f,  0.9883948585f,
    };

    float XYZ_to_Rec709_D65_matrix_data[]=
    {
       3.2409699419f, -1.5373831776f, -0.4986107603f,
      -0.9692436363f,  1.8759675015f,  0.0415550574f,
       0.0556300797f, -0.2039769589f,  1.0569715142f,
    };

    float XYZ_to_Rec2020_D65_matrix_data[]=
    {
       1.7166511880f, -0.3556707838f, -0.2533662814f,
      -0.6666843518f,  1.6164812366f,  0.0157685458f,
       0.0176398574f, -0.0427706133f,  0.9421031212f,
    };

    float XYZ_to_P3_D65_matrix_data[]=
    {
       2.4934969119f, -0.9313836179f, -0.4027107845f,
      -0.8294889696f,  1.7626640603f,  0.0236246858f,
       0.0358458302f, -0.0761723893f,  0.9568845240f,
    };

    float XYZ_to_P3_DCI_matrix_data[]=
    {
       2.7253940305f, -1.0180030062f, -0.4401631952f,
      -0.7951680258f,  1.6897320548f,  0.0226471906f,
       0.0412418914f, -0.0876390192f,  1.1009293786f
    };

    float CAT_CAT16_data[]=
    {
      0.401288, 0.650173, -0.051461,
      -0.250268, 1.204414, 0.045854,
      -0.002079, 0.048952, 0.953127,
    };

    float Modified_CAT16_data[]=
    {
      0.656619, 0.342071, 0.00131062,
      -0.222571, 1.10658, 0.115987,
      -0.000634146, 0.05855, 0.942084,
    };

    // M Max data generated via an external Nukescript at a J value of 100
    float LocusLimitMTable_data[]=
    {
      244.8230133, 245.4952393, 246.4431458, 247.1381531, 247.2368927, 246.8459778, 245.7083588, 244.2591095, 242.5463409, 240.4208374, 238.0180511, 235.4039917, 233.010849, 230.4004669, 227.8723602, 225.2279968, 222.7197876, 214.8562622, 206.1778564, 198.0664215, 190.9799347, 184.005127, 177.7472992, 172.2332611, 166.6447754, 161.64534, 156.9872284, 152.6203003, 148.3236084, 144.2987976, 140.8540192, 137.4315033, 134.3281555, 131.2306366, 128.3477631, 125.8098145, 123.1305542, 120.5120163, 118.3302231, 116.127861, 114.0526428, 112.1633072, 110.2943344, 108.4250336, 106.711853, 105.188797, 103.6860809, 102.2319641, 100.8348923, 99.51873779, 98.26163483, 97.04810333, 95.90451813, 94.84623718, 93.86389923, 92.9352951, 92.03639984, 91.15013885, 90.27630615, 89.43255615, 88.63536072, 87.8986969, 87.23329163, 86.63896942, 86.09989166, 85.60071564, 85.12715912, 84.66781616, 84.21458435, 83.76491547, 83.30849457, 82.86478424, 82.46378326, 82.11483002, 81.82078552, 81.58016968, 81.37005615, 81.18525696, 81.01979065, 80.86772156, 80.72546387, 80.59381104, 80.48122406, 80.40287018, 80.33755493, 80.30010986, 80.28891754, 80.28807831, 80.33933258, 80.44513702, 80.57379913, 80.71469879, 80.86810303, 81.03874207, 81.23072052, 81.44044495, 81.6555481, 81.901474, 82.20778656, 82.67211151, 83.1408844, 83.62628174, 84.0898056, 84.53721619, 84.99518585, 85.49137878, 86.03423309, 86.58794403, 87.16802979, 87.72124481, 88.51965332, 89.35781097, 90.16739655, 90.94639587, 91.75927734, 92.65882111, 93.6033783, 94.64561462, 95.68405914, 96.84765625, 97.98625183, 99.09587097, 100.2806396, 101.5832748, 103.0694122, 104.6378632, 106.2420197, 107.8503952, 109.5214844, 111.3000031, 113.1901169, 115.1414337, 117.1432114, 119.3193054, 121.7141724, 124.2319031, 126.4584961, 128.9876556, 131.6906891, 134.7160034, 137.8343048, 140.7224121, 143.7820892, 147.23909, 150.6812439, 154.0381317, 157.1765747, 160.5133972, 164.2957306, 168.1366272, 171.8247986, 175.4206543, 179.2828827, 182.0374146, 185.0783844, 188.2106171, 190.9611206, 193.3639221, 195.5132294, 197.58255, 199.4234161, 201.3786011, 203.1474609, 205.016037, 206.6236725, 208.1813812, 209.8205719, 211.2774353, 212.8192749, 214.4571686, 215.6442261, 216.4818726, 217.1617279, 217.7372131, 218.2023926, 218.4073486, 218.4278564, 217.6643677, 216.4666748, 215.1212463, 213.8158264, 212.5012817, 210.8331757, 208.8956146, 206.9006958, 204.9239197, 203.0310059, 201.2084045, 199.3484344, 197.3464355, 195.217453, 193.0449677, 190.9578705, 188.9528656, 187.0009918, 185.0068817, 182.9402924, 180.8367767, 178.7057037, 176.5325165, 174.445282, 172.4908905, 170.5744934, 168.5490723, 166.459259, 164.4333649, 162.5092621, 160.4579468, 158.491806, 156.6880035, 155.0045624, 153.295166, 151.4545441, 149.5910492, 147.7821808, 146.4078522, 144.8022614, 143.2662506, 141.8236542, 140.5029602, 139.225174, 137.8959045, 136.4792175, 135.0780334, 133.7389374, 132.7613525, 131.6787109, 130.6356354, 129.64328, 128.7269897, 127.8450623, 126.9439697, 126.0015182, 125.0760727, 124.1718826, 123.4704056, 122.8062363, 122.1408768, 121.501358, 120.9004822, 120.3225555, 119.7514191, 119.2011871, 118.7055511, 118.2950592, 117.9416199, 117.5793762, 117.2029953, 116.8356552, 116.4874039, 116.1693954, 115.9030762, 115.6935577, 115.5213852, 115.3659363, 115.2032318, 115.0445251, 114.9317932, 114.8815384, 114.8605118, 114.8510284, 114.8482819, 114.848465, 114.8521805, 114.8999329, 115.0081787, 115.1483612, 115.2983322, 115.511528, 115.7195816, 115.9448853, 116.2098999, 116.5264893, 116.8126144, 117.1579666, 117.5379944, 117.9048004, 118.3263168, 118.8006821, 119.2988586, 119.8310318, 120.3776703, 121.0383987, 121.6810684, 122.4489899, 123.207077, 124.071022, 124.9082108, 125.74823, 126.6865311, 127.4425888, 127.8552094, 128.1067963, 128.3630676, 128.6606598, 128.9203491, 129.2632141, 129.708252, 130.1131287, 130.5647278, 130.9923553, 131.5979462, 132.2623444, 132.8651428, 133.4651947, 134.1470337, 134.8683624, 135.683609, 136.6136017, 137.5203552, 138.3826599, 139.2931976, 140.2762299, 141.2150574, 142.3930054, 143.7060547, 145.0472565, 146.3404083, 147.6144257, 148.9406586, 150.3545532, 151.8509674, 153.4246826, 155.0567017, 156.7265472, 158.4546509, 160.2428131, 162.1348267, 164.1415863, 166.2302551, 168.4024506, 170.5583649, 172.6457672, 174.9460449, 177.2792664, 179.6472473, 182.1867218, 184.5882721, 187.3068848, 189.8807373, 192.5116577, 195.5551453, 198.5196381, 201.3429413, 203.941452, 206.8439484, 209.5599213, 212.4866943, 215.0750885, 217.929306, 220.6668701, 223.364151, 226.2115479, 228.9524536, 231.5583954, 234.405304, 237.0275879, 239.5091705, 242.0047455, 242.0177155
    };


    // populate the input primaries matrix
    if( primariesIn == 0 )
    {
      XYZ_to_RGB_input.setArray(XYZ_to_AP0_ACES_matrix_data);
    }
    else if( primariesIn == 1 )
    {
      XYZ_to_RGB_input.setArray(XYZ_to_AP1_ACES_matrix_data);
    }
    else if( primariesIn == 2 )
    {
      XYZ_to_RGB_input.setArray(XYZ_to_Rec709_D65_matrix_data);
    }
    else if( primariesIn == 3 )
    {
      XYZ_to_RGB_input.setArray(XYZ_to_Rec2020_D65_matrix_data);
    }
    else if( primariesIn == 4 )
    {
      XYZ_to_RGB_input.setArray(XYZ_to_P3_D65_matrix_data);
    }
    else if( primariesIn == 5 )
    {
      XYZ_to_RGB_input.setArray(XYZ_to_P3_DCI_matrix_data);
    }
    else
    {
      XYZ_to_RGB_input.setArray(identity_matrix_data);
    }

    // populate the limiting primaries matrix
    // RGBPrimsToXYZMatrix
    float2 limitWhiteForMatrix;
    float2 limitRedForMatrix;
    float2 limitGreenForMatrix;
    float2 limitBlueForMatrix;
    if( whiteLimit == 0)
    {
      limitWhiteForMatrix = float2(0.32168f, 0.33767f);
    }
    else if( whiteLimit == 1)
    {
      limitWhiteForMatrix = float2(0.3127f, 0.3290f);
    }
    else
    {
      limitWhiteForMatrix = float2(0.333333f, 0.333333f);
    }

    if( primariesLimit == 0 )
    {
//       XYZ_to_RGB_limit.setArray(XYZ_to_AP0_ACES_matrix_data);
      limitRedForMatrix = float2(0.7347f, 0.2653);
      limitGreenForMatrix = float2(0.0f, 1.0f);
      limitBlueForMatrix = float2(0.0001, -0.077);
    }
    else if( primariesLimit == 1 )
    {
//       XYZ_to_RGB_limit.setArray(XYZ_to_AP1_ACES_matrix_data);
      limitRedForMatrix = float2(0.713f, 0.293f);
      limitGreenForMatrix = float2(0.165f, 0.830f);
      limitBlueForMatrix = float2(0.128f, 0.044f);
    }
    else if( primariesLimit == 2 )
    {
//       XYZ_to_RGB_limit.setArray(XYZ_to_Rec709_D65_matrix_data);
      limitRedForMatrix = float2(0.64f, 0.33f);
      limitGreenForMatrix = float2(0.3f, 0.6f);
      limitBlueForMatrix = float2(0.15f, 0.06f);
    }
    else if( primariesLimit == 3 )
    {
//       XYZ_to_RGB_limit.setArray(XYZ_to_Rec2020_D65_matrix_data);
      limitRedForMatrix = float2(0.708f, 0.292f);
      limitGreenForMatrix = float2(0.170f, 0.797f);
      limitBlueForMatrix = float2(0.131f, 0.046f);
    }
    else if( primariesLimit == 4 )
    {
//       XYZ_to_RGB_limit.setArray(XYZ_to_P3_D65_matrix_data);
      limitRedForMatrix = float2(0.680f, 0.320f);
      limitGreenForMatrix = float2(0.265f, 0.690f);
      limitBlueForMatrix = float2(0.150f, 0.060f);
    }
    else
    {
//       XYZ_to_RGB_limit.setArray(identity_matrix_data);
      limitRedForMatrix = float2(1.0f, 0.0f);
      limitGreenForMatrix = float2(0.0f, 1.0f);
      limitBlueForMatrix = float2(0.0f, 0.0f);
    }

    XYZ_to_RGB_limit = RGBPrimsToXYZMatrix(limitRedForMatrix, limitGreenForMatrix, limitBlueForMatrix, limitWhiteForMatrix, 1.0f, 1);

    // populate the reach primaries matrix
    if( primariesReach == 0 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_AP0_ACES_matrix_data);
    }
    else if( primariesReach == 1 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_AP1_ACES_matrix_data);
    }
    else if( primariesReach == 2 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_Rec709_D65_matrix_data);
    }
    else if( primariesReach == 3 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_Rec2020_D65_matrix_data);
    }
    else if( primariesReach == 4 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_P3_D65_matrix_data);
    }
    else if( primariesReach == 5 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_P3_DCI_matrix_data);
    }
    else
    {
        XYZ_to_RGB_reach.setArray(identity_matrix_data);
    }

    // populate the output primaries matrix
    if( primariesOut == 0 )
    {
      XYZ_to_RGB_output.setArray(XYZ_to_AP0_ACES_matrix_data);
    }
    else if( primariesOut == 1 )
    {
      XYZ_to_RGB_output.setArray(XYZ_to_AP1_ACES_matrix_data);
    }
    else if( primariesOut == 2 )
    {
      XYZ_to_RGB_output.setArray(XYZ_to_Rec709_D65_matrix_data);
    }
    else if( primariesOut == 3 )
    {
      XYZ_to_RGB_output.setArray(XYZ_to_Rec2020_D65_matrix_data);
    }
    else if( primariesOut == 4 )
    {
      XYZ_to_RGB_output.setArray(XYZ_to_P3_D65_matrix_data);
    }
    else if( primariesOut == 5 )
    {
      XYZ_to_RGB_output.setArray(XYZ_to_P3_DCI_matrix_data);
    }
    else
    {
      XYZ_to_RGB_output.setArray(identity_matrix_data);
    }

    RGB_to_XYZ_input  = XYZ_to_RGB_input.invert();
    RGB_to_XYZ_limit  = XYZ_to_RGB_limit.invert();
    RGB_to_XYZ_reach = XYZ_to_RGB_reach.invert();
    RGB_to_XYZ_output = XYZ_to_RGB_output.invert();

    XYZ_to_AP1.setArray(XYZ_to_AP1_ACES_matrix_data);
    AP1_to_XYZ = XYZ_to_AP1.invert();

    float3x3 XYZ_to_RGB_sRGB;
    XYZ_to_RGB_sRGB.setArray(XYZ_to_Rec709_D65_matrix_data);
    float3 white(1.0f, 1.0f, 1.0f);

    inWhite = vector_dot(RGB_to_XYZ_input, white);
    outWhite = vector_dot(RGB_to_XYZ_output, white);
    refWhite = vector_dot(RGB_to_XYZ_limit, white);
    limitWhite = vector_dot(RGB_to_XYZ_limit, white);

    boundaryRGB = peakLuminance / referenceLuminance;

    if (catDataSelection == 0)
    {
        CAT_CAT16.setArray(CAT_CAT16_data);
    }
    else if (catDataSelection == 1)
    {
        CAT_CAT16.setArray(Modified_CAT16_data);
    }
    else if (catDataSelection == 2)
    {
        CAT_CAT16 = RGBPrimsToXYZMatrix(rxy,gxy,bxy,wxy,1.0f,1);
    }

    generate_panlrcm();

    //
    // solving the RGB cusp from JMh is very expensive
    // instead we go the other way and start with a RGB cusp sweep
    // which is easily calculated by converting via HSV (Hue, 1.0, 1.0)
    // we then convert each cusp to JMh and add them to a table 
    //

    // LocusLimitMTable = LocusLimitMTable_data;
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      LocusLimitMTable[i] = LocusLimitMTable_data[i];
    }

    // calculate the maximum expected J & M values for the given limit gamut
    // these are used as limiting values for the gamut boundary searches
    // limitJmax (asumed to match limitRGB white)
    limitJmax = limit_RGB_to_JMh(float3(1.0f)).x;

    // limitMmax (assumed to coincide with one of the RGBCMY corners of the limitRGB cube)
    float3 gamutCornersTable[6];
    gamutCornersTable[0] = limit_RGB_to_JMh(float3(1.0f, 0.0f, 0.0f));
    gamutCornersTable[1] = limit_RGB_to_JMh(float3(1.0f, 1.0f, 0.0f));
    gamutCornersTable[2] = limit_RGB_to_JMh(float3(0.0f, 1.0f, 0.0f));
    gamutCornersTable[3] = limit_RGB_to_JMh(float3(0.0f, 1.0f, 1.0f));
    gamutCornersTable[4] = limit_RGB_to_JMh(float3(0.0f, 0.0f, 1.0f));
    gamutCornersTable[5] = limit_RGB_to_JMh(float3(1.0f, 0.0f, 1.0f));

    limitMmax = 0.0f;
    for( int i = 0; i < 6; ++i )
    {
        limitMmax = max(limitMmax, gamutCornersTable[i].y);
    }
    // add a little bit of margin to deal with some reddish pinks having a higher M than pure Red
    limitMmax = limitMmax * 1.2f;

  // Cusp table for chroma compression gamut
  {
    float3x3 tmpx = XYZ_to_RGB_limit;
    float3x3 tmpr = RGB_to_XYZ_limit;
    float3x3 tmpR = XYZ_to_RGB_reach;

    if( ccReach == 0 ) // Chroma Compression Space (primaries defined in kernel params)
    {
        XYZ_to_RGB_limit = RGBPrimsToXYZMatrix(crxy, cgxy, cbxy, cwxy, 1.0f, 1);
        XYZ_to_RGB_reach = XYZ_to_RGB_limit;
    }
    else if( ccReach == 1 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_AP0_ACES_matrix_data);
    }
    else if( ccReach == 2 )
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_AP1_ACES_matrix_data);
    }
    else
    {
        XYZ_to_RGB_reach.setArray(XYZ_to_Rec2020_D65_matrix_data);
    }
    RGB_to_XYZ_limit = XYZ_to_RGB_reach.invert();

    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      float hNorm = float(i) / (gamutCuspTableSize);
      float3 RGB = HSV_to_RGB(float3(hNorm, 1.0f, 1.0f));
      gamutCuspTableUnsorted[i] = limit_RGB_to_JMh(RGB);
    }
    int minhIndex = 0;
    for( int i = 1; i < gamutCuspTableSize; ++i )
    {
      if( gamutCuspTableUnsorted[i].z <  gamutCuspTableUnsorted[minhIndex].z)
      {
        minhIndex = i;
      }
    }
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      cgamutCuspTable[i] = gamutCuspTableUnsorted[(minhIndex+i)%gamutCuspTableSize];
    }
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      cgamutReachTable[i].z = i;
      for( int M = 0; M < 1300; ++M )
      {
        float sampleM = float(M);
        float3 newLimitRGB = JMh_to_reach_RGB(float3(limitJmax,sampleM,i));
        if (newLimitRGB.x < 0.0f || newLimitRGB.y < 0.0f || newLimitRGB.z < 0.0f)
        {
          cgamutReachTable[i].y = sampleM;
          break;
        }
      }
    }

    XYZ_to_RGB_limit = tmpx;
    RGB_to_XYZ_limit = tmpr;

    // With gamut mapper reach mode 7, use the chroma compression reach space with the
    // gamut mapper.
    if (primariesReach != 7)
      XYZ_to_RGB_reach = tmpR;
  }
 
  // Cusp table for limiting gamut
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      float hNorm = float(i) / (gamutCuspTableSize);
      float3 RGB = HSV_to_RGB(float3(hNorm, 1.0f, 1.0f));
      gamutCuspTableUnsorted[i] = limit_RGB_to_JMh(RGB);
    }

    int minhIndex = 0;
    for( int i = 1; i < gamutCuspTableSize; ++i )
    {
      if( gamutCuspTableUnsorted[i].z <  gamutCuspTableUnsorted[minhIndex].z)
      {
        minhIndex = i;
      }
    }

    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      gamutCuspTable[i] = gamutCuspTableUnsorted[(minhIndex+i)%gamutCuspTableSize];
    }

    // Cusp table for limiting reach gamut, values at a J of 100.  Covers M values
    // up to 10000 nits.
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
     gamutCuspTableReach[i].z = i;
     for( int M = 0; M < 1300; ++M )
      {
        float sampleM = float(M);
        float3 newLimitRGB = JMh_to_reach_RGB(float3(limitJmax,sampleM,i));
        if (newLimitRGB.x < 0.0f || newLimitRGB.y < 0.0f || newLimitRGB.z < 0.0f)
        {
          gamutCuspTableReach[i].x = sampleM;
          break;
        }
      }
    }

    midJ = XYZ_to_JMh(refWhite * daniele_c_t * mmScaleFactor, refWhite, outputViewingConditions, L_A_out, Y_b_out, discountIlluminant_mid, HK_mode_mid).x;


    // Find upper hull gamma values for the gamut mapper
    // start by taking a h angle
    // get the cusp J value for that angle
    // find a J value halfway to the Jmax
    // iterate through gamma values until the approxilate max M is negative through the actual boundry
 
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
    //  default value. This will get overridden as we loop, but can be a good diagnostic to make sure things are working
     gamutTopGamma[i] = 0.5f;
      // get cusp from cusp table at hue position
     float2 JMcusp = cuspFromTable(float(i));
     // create test value halfway betwen the cusp and the Jmax
    // positions between the cusp and Jmax we will check
     float testPositions[] = {0.01f,0.5f,0.99f};
    // variables that get set as we iterate through, once all 3 are set to true we break the loop
     bool gammaFound[3] = {false};
     // limit value, once we cross this value, we are outside of the top gamut shell 
     float maxRGBtestVal = 1.0f;
     // Tg is Test Gamma. the values are shifted two decimal points to the left. Tg 70 = Gamma 0.7
     for( int Tg = 70; Tg < 170; ++Tg )
     {
        // topGamma value created from the Tg variable
        float topGamma = float(Tg) / 100.0f;
        // loop to run through each of the positions defined in the testPositions list
        for ( int testIndex = 0 ; testIndex < 3 ; ++testIndex )
        {
                  float3 testJmh = float3(JMcusp.x + ((limitJmax - JMcusp.x) * testPositions[testIndex] ), JMcusp.y , float(i));
                  float3 approxLimit  =  findGamutBoundaryIntersection(        testJmh,         JMcusp, lerp(JMcusp.x, midJ, cuspMidBlend),   limitJmax,       10000.0f,      0.0f,       topGamma, 1.0f);
                  float3 newLimitRGB = JMh_to_limit_RGB(float3(approxLimit.x, approxLimit.y, float(i)));
                  // if any channel has broken through the top gamut hull, break
                  if (newLimitRGB.x > maxRGBtestVal || newLimitRGB.y > maxRGBtestVal || newLimitRGB.z > maxRGBtestVal)
                  {
                      gamutTopGamma[i] = topGamma;
                      gammaFound[testIndex] = true;
                  }

        }
        // once all 3 of the test
        if (gammaFound[0] && gammaFound[1] && gammaFound[2])
        {
            break;
        }
      }
    }

    // Same process, for the bottom hull gamma
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
    //  default value. This will get overridden as we loop, but can be a good diagnostic to make sure things are working
     gamutBottomGamma[i] = 0.5f;
      // get cusp from cusp table at hue position
     float2 JMcusp = cuspFromTable(float(i));
     // create test value halfway betwen the cusp and the Jmax
    // positions between the cusp and Jmax we will check
     float testPositions[] = {0.01f,0.4f,0.75f};
    // variables that get set as we iterate through, once all 3 are set to true we break the loop
     bool gammaFound[3] = {false};
     // limit value, once we cross this value, we are outside of the top gamut shell 
     float maxRGBtestVal = 1.0f;
     // Tg is Test Gamma. the values are shifted two decimal points to the left. Tg 70 = Gamma 0.7
     for( int Bg = 1140; Bg < 1200; ++Bg )
     {
        // topGamma value created from the Tg variable
        float bottomGamma = float(Bg) / 1000.0f;
        // loop to run through each of the positions defined in the testPositions list
        for ( int testIndex = 0 ; testIndex < 3 ; ++testIndex )
        {
                  float3 testJmh = float3( ((JMcusp.x) * testPositions[testIndex] ) , JMcusp.y , float(i));
                  float3 approxLimit  =  findGamutBoundaryIntersection(        testJmh,         JMcusp, lerp(JMcusp.x, midJ, cuspMidBlend),   limitJmax,       10000.0f,      0.0f,       1.0f,bottomGamma);
                  float3 newLimitRGB = JMh_to_limit_RGB(float3(approxLimit.x, approxLimit.y, float(i)));
                  // if any channel has broken through the bottom gamut hull, break
                  if (newLimitRGB.x < 0.0 || newLimitRGB.y < 0.0 || newLimitRGB.z < 0.0)
                  {
                    gamutBottomGamma[i] = bottomGamma;
                      gammaFound[testIndex] = true;
                  }

        }
        // once all 3 of the test
        if (gammaFound[0] && gammaFound[1] && gammaFound[2])
        {
            break;
        }
      }
    }



    // Cusp table for AP1 gamut
    {
    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      float hNorm = float(i) / (gamutCuspTableSize);
      float3 RGB = HSV_to_RGB(float3(hNorm, 1.0f, 1.0f));
      gamutCuspTableUnsortedAP1[i] = AP1_RGB_to_JMh(RGB);
    }

    int minhIndex = 0;
    for( int i = 1; i < gamutCuspTableSize; ++i )
    {
      if( gamutCuspTableUnsortedAP1[i].z <  gamutCuspTableUnsortedAP1[minhIndex].z)
      {
        minhIndex = i;
      }
    }

    for( int i = 0; i < gamutCuspTableSize; ++i )
    {
      gamutCuspTableAP1[i] = gamutCuspTableUnsortedAP1[(minhIndex+i)%gamutCuspTableSize];
    }
    }
  }


  void process()
  {
    SampleType(src) source = src();
    // SampleType(extra) sourceExtra = src();
    float3 srcRGB(source.x, source.y, source.z);
    // float3 extraRGB(sourceExtra.x, sourceExtra.y, sourceExtra.z);
    float3 dstRGB;
    float3 compressedJMh;
    float3 tonemappedJMh;
    float3 JMh;
    float3 diagnostic;

    if( invert )
    {
      compressedJMh = output_RGB_to_JMh(srcRGB);
      tonemappedJMh = compressGamut(compressedJMh, 1);
      JMh = inverseTonescale(tonemappedJMh);
      diagnostic = JMh_to_input_RGB(JMh);
    }
    else
    {
      JMh = input_RGB_to_JMh(srcRGB);
      tonemappedJMh = forwardTonescale(JMh);
      compressedJMh = compressGamut(tonemappedJMh, 0);
      diagnostic = JMh_to_output_RGB(compressedJMh);
    }

    if ( diagnosticMode == 1 || diagnosticMode == 6 )
    {
      // Mode 6 actually returns XYZ, mode 1 returns real JMh
      if( invert )
      {
        diagnostic =  JMh_to_input_RGB(srcRGB);
      }
      else
      {
        diagnostic =  JMh;
      }

    }
    else if ( diagnosticMode == 2 || diagnosticMode == 99 )
    {
      diagnostic = tonemappedJMh;
    }
    else if ( diagnosticMode == 3 || diagnosticMode == 5 )
    {
      diagnostic =  compressedJMh;
    }
/*
    else if ( diagnosticMode == 4 || diagnosticMode == 7 )
    {
      if (diagnosticMode == 4)
        srcRGB = JMh;
      dstRGB = JMh_to_output_RGB(srcRGB);
      diagnostic =  dstRGB;
    }
    else if ( diagnosticMode == 8)
    {
      diagnostic =  inWhite;
    }
    else if ( diagnosticMode == 9)
    {
      diagnostic =  outWhite;
    }
    else if ( diagnosticMode == 10)
    {
      diagnostic =  limitWhite;
    }
    else if (diagnosticMode == 12)
    {
      // output gamut boundry
      diagnostic = compressGamut(srcRGB, 1);
    }
    else if (diagnosticMode == 13)
    {
      // output gamut boundry
      diagnostic = compressGamut(srcRGB, invert);
    }
    else if (diagnosticMode == 14)
    {
      // output gamut cusp
      diagnostic = float3(cuspFromTable(srcRGB.z).x, cuspFromTable(srcRGB.z).y, srcRGB.z);
    }
    else if (diagnosticMode == 15)
    {
      // output AP1 cusp
      diagnostic = float3(cuspFromTableAP1(srcRGB.z).x, cuspFromTableAP1(srcRGB.z).y, srcRGB.z);
    }
    else if (diagnosticMode == 16)
    {
      // output Locus cusp
      diagnostic = float3(cuspFromTableLocus(srcRGB.z).x, cuspFromTableLocus(srcRGB.z).y, srcRGB.z);
    }
    else if (diagnosticMode == 17)
    {
      // output Locus boundry
      diagnostic = getLocusBoundry(srcRGB);
    }
    else if (diagnosticMode == 18)
    {
      // output gamut boundry
      diagnostic = compressGamut(srcRGB, 0  );
    }
    else if (diagnosticMode == 19)
    {
      // output Reach boundry
      diagnostic = getReachBoundry(srcRGB);
    }
    else if (diagnosticMode == 20)
    {
      // output JMFocus
      diagnostic = compressGamut(srcRGB, 1);
    }
    else if (diagnosticMode == 21)
    {
      // output JMFocus
      diagnostic = float3(hueDependantUpperHullGamma(srcRGB.z),0.0f,0.0f);
      // diagnostic = float3(gamutTopGamma[0],LocusLimitMTable[0],limitJmax);
    }
    else if (diagnosticMode == 22)
    {
    float2 JMcusp = cuspFromTable(srcRGB.z);
    // create test value halfway betwen the cusp and the Jmax
   //  float2 JMcusp = float2(gamutCuspTable[i].x, gamutCuspTable[i].y);
    float slope_gain = limitJmax * focusDistance;
    diagnostic = float3(JMcusp.x + ((limitJmax - JMcusp.x) / 2.0f ), JMcusp.y , srcRGB.z);
    }
    else if (diagnosticMode == 23)
    {
    float2 JMcusp = cuspFromTable(srcRGB.z);
    // create test value halfway betwen the cusp and the Jmax
   //  float2 JMcusp = float2(gamutCuspTable[i].x, gamutCuspTable[i].y);
    float slope_gain = limitJmax * focusDistance;
    float3 testJmh = float3(JMcusp.x + ((limitJmax - JMcusp.x) / 2.0f ), JMcusp.y , srcRGB.z);
    float3 approxLimit  =  findGamutBoundaryIntersection(        testJmh,         JMcusp,(JMcusp.x+38.0f)/2,   limitJmax,       slope_gain,      smoothCusps,       hueDependantUpperHullGamma(srcRGB.z),hueDependantLowerHullGamma(srcRGB.z));
    diagnostic = float3(approxLimit.x, approxLimit.y, srcRGB.z);
    }

    else if (diagnosticMode == 24)
    {
    float2 JMcusp = cuspFromTable(srcRGB.z);
    // create test value halfway betwen the cusp and the Jmax
   //  float2 JMcusp = float2(gamutCuspTable[i].x, gamutCuspTable[i].y);
    float slope_gain = limitJmax * focusDistance;
    float3 testJmh = float3(JMcusp.x + ((limitJmax - JMcusp.x) / 2.0f ), JMcusp.y , srcRGB.z);
    float3 approxLimit  =  findGamutBoundaryIntersection(        testJmh,         JMcusp,(JMcusp.x+38.0f)/2,   limitJmax,       slope_gain,      smoothCusps,       hueDependantUpperHullGamma(srcRGB.z),hueDependantLowerHullGamma(srcRGB.z));
    float3 newLimitRGB = JMh_to_limit_RGB(float3(approxLimit.x, approxLimit.y, srcRGB.z));
    diagnostic = newLimitRGB;
    }

    else if (diagnosticMode == 25)
    {
      float2 JMcusp = cuspFromTable(srcRGB.z);
      float slope_gain = limitJmax * focusDistance;
      float focusJ = lerp(JMcusp.x, midJ, cuspMidBlend);
      float3 nickBoundryReturn =  findGamutBoundaryIntersection(        srcRGB,         JMcusp,        focusJ,   limitJmax,       slope_gain, smoothCusps,       hueDependantUpperHullGamma(srcRGB.z),hueDependantLowerHullGamma(srcRGB.z));
      diagnostic = float3(srcRGB.x,nickBoundryReturn.y,srcRGB.z);
    }
    else if (diagnosticMode == 26)
    {
        // XYZ back to luminance RGB
        float3 JMh = JMh_to_XYZ( srcRGB, limitWhite, outputViewingConditions , L_A_out, Y_b_out, discountIlluminant_out, HK_mode_out);
        diagnostic = vector_dot(XYZ_to_RGB_limit, JMh);
    }
    else if (diagnosticMode == 27)
    {
      // output 
      diagnostic = float3(hueDependantLowerHullGamma(srcRGB.z),0.0f,0.0f);
      // diagnostic = float3(gamutTopGamma[0],LocusLimitMTable[0],limitJmax);
    }
    else if (diagnosticMode == 28)
    {
      // output 
      float2 JMcusp = cuspFromTable(srcRGB.z);
      diagnostic = findGamutBoundaryIntersection(        srcRGB,         JMcusp, lerp(JMcusp.x, midJ, cuspMidBlend),   limitJmax,       10000.0f,      0.0f,       hueDependantUpperHullGamma(srcRGB.z),hueDependantLowerHullGamma(srcRGB.z));

      // diagnostic = float3(gamutTopGamma[0],LocusLimitMTable[0],limitJmax);
    }



 



    // extra modes to allow for easier breakout of the order of events.
    // modes starting with 100

    ////// FORWARD PATHWAY

    else if (diagnosticMode == 100)
    {
      // display encoding to display linear
      float3 inputRGB = clamp3(srcRGB, -HALF_MAXIMUM, HALF_MAXIMUM);
      diagnostic = encodingToLuminance3( encodingIn, inputRGB);
      
    }  
        else if (diagnosticMode == 101)
    {
        // convert to linear XYZ luminance values
        diagnostic = vector_dot(RGB_to_XYZ_input, srcRGB);
    }
    else if (diagnosticMode == 102)
    {
      // convert luminanceXYZ to JMh
      diagnostic = XYZ_to_JMh(srcRGB, inWhite, viewingConditions, L_A, Y_b, discountIlluminant_in, HK_mode_in);
    }
    else if (diagnosticMode == 103)
    {
      // JMh to tonemappedJMh
      diagnostic = forwardTonescale(srcRGB);
    }
    else if (diagnosticMode == 104)
    {
      // JMh to gamut compressed JMh
      diagnostic = compressGamut(srcRGB, 0);
    }
    else if (diagnosticMode == 105)
    {
      // JMh to luminance XYZ
      diagnostic = JMh_to_XYZ( srcRGB, limitWhite, outputViewingConditions , L_A_out, Y_b_out, discountIlluminant_out, HK_mode_out);
    }
    else if (diagnosticMode == 106)
    {
        // display luminance XYZ to display linear RGB
        diagnostic = vector_dot(XYZ_to_RGB_output, srcRGB);
    }
    else if (diagnosticMode == 107)
    {
        // display linear RGB to display encoded RGB
        diagnostic = luminanceToEncoding3( encodingOut, srcRGB);
    }

    ////// INVERSE PATHWAY
    
    else if (diagnosticMode == 200)
    {
        // output display encoded RGB to display linear RGB
        diagnostic = encodingToLuminance3(encodingOut, srcRGB);
    }
    else if (diagnosticMode == 201)
    {
        // output display linear RGB to output display linear XYZ
        diagnostic = vector_dot(RGB_to_XYZ_output, srcRGB);
    }
    else if (diagnosticMode == 202)
    {
        // output XYZ to JMh
        diagnostic = XYZ_to_JMh(srcRGB, limitWhite, viewingConditions, L_A_out, Y_b_out, discountIlluminant_out,HK_mode_out);
    }
    else if (diagnosticMode == 203)
    {
        // uncompress gamut
        diagnostic = compressGamut(srcRGB, 1);
    }    
    else if (diagnosticMode == 204)
    {
        // inverse tonescale in JMh
      diagnostic = inverseTonescale(srcRGB);  
    }  
    else if (diagnosticMode == 205)
    {
        // inverted JMh back to XYZ
        diagnostic = JMh_to_XYZ( srcRGB, inWhite, viewingConditions , L_A, Y_b, discountIlluminant_in, HK_mode_in);
    }
    else if (diagnosticMode == 206)
    {
        // XYZ back to luminance RGB
        diagnostic = vector_dot(XYZ_to_RGB_input, srcRGB);
    }
    else if (diagnosticMode == 207)
    {
        // luminance RGB to input encoding RGB
        diagnostic = luminanceToEncoding3( encodingIn, srcRGB);
    }
*/
    dst() = float4(diagnostic.x, diagnostic.y, diagnostic.z, source.w ); 
  }
};