illuminants.h

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/*
    This file is part of darktable,
    Copyright (C) 2020 darktable developers.
 
    darktable is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    darktable is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with darktable.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#pragma once
 
#include "common/chromatic_adaptation.h"
#include "common/image.h"
 
 
/* Standard CIE illuminants */
typedef enum dt_illuminant_t
{
  DT_ILLUMINANT_PIPE            = 0, // $DESCRIPTION: "same as pipeline (D50)"
  DT_ILLUMINANT_A               = 1, // $DESCRIPTION: "A (incandescent)"
  DT_ILLUMINANT_D               = 2, // $DESCRIPTION: "D (daylight)"
  DT_ILLUMINANT_E               = 3, // $DESCRIPTION: "E (equi-energy)" (x = y)
  DT_ILLUMINANT_F               = 4, // $DESCRIPTION: "F (fluorescent)"
  DT_ILLUMINANT_LED             = 5, // $DESCRIPTION: "LED (LED light)"
  DT_ILLUMINANT_BB              = 6, // $DESCRIPTION: "Planckian (black body)" general black body radiator - not CIE standard
  DT_ILLUMINANT_CUSTOM          = 7, // $DESCRIPTION: "custom" input x and y directly - bypass search
  DT_ILLUMINANT_DETECT_SURFACES = 8, // $DESCRIPTION: "(AI) detect from image surfaces..." auto-detection in image from grey world model
  DT_ILLUMINANT_DETECT_EDGES    = 9, // $DESCRIPTION: "(AI) detect from image edges..."auto-detection in image from grey edges model
  DT_ILLUMINANT_CAMERA          = 10,// $DESCRIPTION: "as shot in camera" read RAW EXIF for WB
  DT_ILLUMINANT_LAST
} dt_illuminant_t;
 
// CIE fluorescent standards : https://en.wikipedia.org/wiki/Standard_illuminant
typedef enum dt_illuminant_fluo_t
{
  DT_ILLUMINANT_FLUO_F1  = 0,  // $DESCRIPTION: "F1 (Daylight 6430 K) - medium CRI"
  DT_ILLUMINANT_FLUO_F2  = 1,  // $DESCRIPTION: "F2 (Cool White 4230 K) - medium CRI"
  DT_ILLUMINANT_FLUO_F3  = 2,  // $DESCRIPTION: "F3 (White 3450 K) - medium CRI"
  DT_ILLUMINANT_FLUO_F4  = 3,  // $DESCRIPTION: "F4 (Warm White 2940 K) - medium CRI"
  DT_ILLUMINANT_FLUO_F5  = 4,  // $DESCRIPTION: "F5 (Daylight 6350 K) - medium CRI"
  DT_ILLUMINANT_FLUO_F6  = 5,  // $DESCRIPTION: "F6 (Lite White 4150 K) - medium CRI"
  DT_ILLUMINANT_FLUO_F7  = 6,  // $DESCRIPTION: "F7 (D65 simulator 6500 K) - high CRI"
  DT_ILLUMINANT_FLUO_F8  = 7,  // $DESCRIPTION: "F8 (D50 simulator 5000 K) - high CRI"
  DT_ILLUMINANT_FLUO_F9  = 8,  // $DESCRIPTION: "F9 (Cool White Deluxe 4150 K) - high CRI"
  DT_ILLUMINANT_FLUO_F10 = 9,  // $DESCRIPTION: "F10 (Tuned RGB 5000 K) - low CRI" Philips TL85, Ultralume 50
  DT_ILLUMINANT_FLUO_F11 = 10, // $DESCRIPTION: "F11 (Tuned RGB 4000 K) - low CRI" Philips TL84, Ultralume 40
  DT_ILLUMINANT_FLUO_F12 = 11, // $DESCRIPTION: "F12 (Tuned RGB 3000 K) - low CRI" Philips TL83, Ultralume 30
  DT_ILLUMINANT_FLUO_LAST
} dt_illuminant_fluo_t;
 
// CIE LED standards : https://en.wikipedia.org/wiki/Standard_illuminant
typedef enum dt_illuminant_led_t
{
  DT_ILLUMINANT_LED_B1  = 0,   // $DESCRIPTION: "B1 (Blue 2733 K)" phosphor-converted blue
  DT_ILLUMINANT_LED_B2  = 1,   // $DESCRIPTION: "B2 (Blue 2998 K)" phosphor-converted blue
  DT_ILLUMINANT_LED_B3  = 2,   // $DESCRIPTION: "B3 (Blue 4103 K)" phosphor-converted blue
  DT_ILLUMINANT_LED_B4  = 3,   // $DESCRIPTION: "B4 (Blue 5109 K)" phosphor-converted blue
  DT_ILLUMINANT_LED_B5  = 4,   // $DESCRIPTION: "B5 (Blue 6598 K)" phosphor-converted blue
  DT_ILLUMINANT_LED_BH1 = 5,   // $DESCRIPTION: "BH1 (Blue-Red hybrid 2851 K)" mix of phosphor-converted blue red
  DT_ILLUMINANT_LED_RGB1= 6,   // $DESCRIPTION: "RGB1 (RGB 2840 K)" mixing of red, green, and blue LEDs
  DT_ILLUMINANT_LED_V1  = 7,   // $DESCRIPTION: "V1 (Violet 2724 K)" phosphor-converted violet
  DT_ILLUMINANT_LED_V2  = 8,   // $DESCRIPTION: "V2 (Violet 4070 K)" phosphor-converted violet
  DT_ILLUMINANT_LED_LAST
} dt_illuminant_led_t;
 
 
                                                            //   x_2  //   y_2
 static float fluorescent[DT_ILLUMINANT_FLUO_LAST][2] = { { 0.31310f, 0.33727f },   // DT_ILLUMINANT_FLUO_F1
                                                          { 0.37208f, 0.37529f },   // DT_ILLUMINANT_FLUO_F2
                                                          { 0.40910f, 0.39430f },   // DT_ILLUMINANT_FLUO_F3
                                                          { 0.44018f, 0.40329f },   // DT_ILLUMINANT_FLUO_F4
                                                          { 0.31379f, 0.34531f },   // DT_ILLUMINANT_FLUO_F5
                                                          { 0.37790f, 0.38835f },   // DT_ILLUMINANT_FLUO_F6
                                                          { 0.31292f, 0.32933f },   // DT_ILLUMINANT_FLUO_F7
                                                          { 0.34588f, 0.35875f },   // DT_ILLUMINANT_FLUO_F8
                                                          { 0.37417f, 0.37281f },   // DT_ILLUMINANT_FLUO_F9
                                                          { 0.34609f, 0.35986f },   // DT_ILLUMINANT_FLUO_F10
                                                          { 0.38052f, 0.37713f },   // DT_ILLUMINANT_FLUO_F11
                                                          { 0.43695f, 0.40441f } }; // DT_ILLUMINANT_FLUO_F12
                                                //   x_2  //   y_2
static float led[DT_ILLUMINANT_LED_LAST][2] = { { 0.4560f, 0.4078f },  // DT_ILLUMINANT_LED_B1
                                                { 0.4357f, 0.4012f },  // DT_ILLUMINANT_LED_B2
                                                { 0.3756f, 0.3723f },  // DT_ILLUMINANT_LED_B3
                                                { 0.3422f, 0.3502f },  // DT_ILLUMINANT_LED_B4
                                                { 0.3118f, 0.3236f },  // DT_ILLUMINANT_LED_B5
                                                { 0.4474f, 0.4066f },  // DT_ILLUMINANT_LED_BH1
                                                { 0.4557f, 0.4211f },  // DT_ILLUMINANT_LED_RGB1
                                                { 0.4560f, 0.4548f },  // DT_ILLUMINANT_LED_V1
                                                { 0.3781f, 0.3775f }}; // DT_ILLUMINANT_LED_V2
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline float xy_to_CCT(const float x, const float y)
{
  // Try to find correlated color temperature from chromaticity
  // Valid for 3000 K to 50000 K
  // Reference : https://www.usna.edu/Users/oceano/raylee/papers/RLee_AO_CCTpaper.pdf
  // Warning : we throw a number ever if it's grossly off. You need to check the error later.
  const float n = (x - 0.3366f)/(y - 0.1735f);
  return -949.86315f + 6253.80338f * expf(-n / 0.92159f) + 28.70599f * expf(-n / 0.20039f) + 0.00004f * expf(-n / 0.07125f);
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void CCT_to_xy_daylight(const float t, float *x, float *y)
{
  // Take correlated color temperature in K and find the closest daylight illuminant in 4000 K - 250000 K
  float x_temp = 0.f;
  float y_temp = 0.f;
 
  if(t >= 4000.f && t <= 7000.0f)
    x_temp = ((-4.6070e9f / t + 2.9678e6f) / t + 0.09911e3f) / t + 0.244063f;
  else if(t > 7000.f && t <= 25000.f)
    x_temp = ((-2.0064e9f / t + 1.9018e6f) / t + 0.24748e3f) / t + 0.237040f;
 
  y_temp = (-3.f * x_temp + 2.87f) * x_temp - 0.275f;
 
  *x = x_temp;
  *y = y_temp;
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void CCT_to_xy_blackbody(const float t, float *x, float *y)
{
  // Take correlated color temperature in K and find the closest blackbody illuminant in 1667 K - 250000 K
  float x_temp = 0.f;
  float y_temp = 0.f;
 
  if(t >= 1667.f && t <= 4000.f)
    x_temp = ((-0.2661239e9f / t - 0.2343589e6f) / t  + 0.8776956e3f) / t + 0.179910f;
  else if(t > 4000.f && t <= 25000.f)
    x_temp = ((-3.0258469e9f / t + 2.1070379e6f) / t  + 0.2226347e3f) / t + 0.240390f;
 
  if(t >= 1667.f && t <= 2222.f)
    y_temp = ((-1.1063814f * x_temp - 1.34811020f) * x_temp + 2.18555832f) * x_temp - 0.20219683f;
  else if(t > 2222.f && t <= 4000.f)
    y_temp = ((-0.9549476f * x_temp - 1.37418593f) * x_temp + 2.09137015f) * x_temp - 0.16748867f;
  else if(t > 4000.f && t <= 25000.f)
    y_temp = (( 3.0817580f * x_temp - 5.87338670f) * x_temp + 3.75112997f) * x_temp - 0.37001483f;
 
  *x = x_temp;
  *y = y_temp;
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void illuminant_xy_to_XYZ(const float x, const float y, dt_aligned_pixel_t XYZ)
{
  XYZ[0] = x / y;             // X
  XYZ[1] = 1.f;               // Y is always 1 by definition, for an illuminant
  XYZ[2] = (1.f - x - y) / y; // Z
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void illuminant_xy_to_RGB(const float x, const float y, dt_aligned_pixel_t RGB)
{
  // Get an sRGB preview of current illuminant
  dt_aligned_pixel_t XYZ;
  illuminant_xy_to_XYZ(x, y, XYZ);
 
  // Fixme : convert to RGB display space instead of sRGB but first the display profile should be global in dt,
  // not confined to colorout where it gets created/destroyed all the time.
  dt_XYZ_to_Rec709_D50(XYZ, RGB);
 
  // Handle gamut clipping
  const float max_RGB = fmaxf(fmaxf(RGB[0], RGB[1]), RGB[2]);
  for(int c = 0; c < 3; c++) RGB[c] = fmaxf(RGB[c] / max_RGB, 0.f);
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void illuminant_CCT_to_RGB(const float t, dt_aligned_pixel_t RGB)
{
  float x, y;
  if(t > 4000.f)
    CCT_to_xy_daylight(t, &x, &y);
  else
    CCT_to_xy_blackbody(t, &x, &y);
 
  illuminant_xy_to_RGB(x, y, RGB);
}
 
 
// Fetch image from pipeline and read EXIF for camera RAW WB coeffs
static inline int find_temperature_from_raw_coeffs(const dt_image_t *img, const dt_aligned_pixel_t custom_wb,
                                                   float *chroma_x, float *chroma_y);
 
 
static inline int illuminant_to_xy(const dt_illuminant_t illuminant, // primary type of illuminant
                                   const dt_image_t *img,            // image container
                                   const dt_aligned_pixel_t custom_wb, // optional user-set WB coeffs
                                   float *x_out, float *y_out,       // chromaticity output
                                   const float t,                    // temperature in K, if needed
                                   const dt_illuminant_fluo_t fluo,  // sub-type of fluorescent illuminant, if needed
                                   const dt_illuminant_led_t iled)   // sub-type of led illuminant, if needed
{
  float x = 0.f;
  float y = 0.f;
 
  switch(illuminant)
  {
    case DT_ILLUMINANT_PIPE:
    {
      // darktable default pipeline D50
      x = 0.34567f;
      y = 0.35850f;
      break;
    }
    case DT_ILLUMINANT_E:
    {
      // Equi-energy - easy-peasy
      x = y = 1.f / 3.f;
      break;
    }
    case DT_ILLUMINANT_A:
    {
      // Special case of Planckian locus for incandescent tungsten bulbs
      x = 0.44757f;
      y = 0.40745f;
      break;
    }
    case DT_ILLUMINANT_F:
    {
      // Fluorescent lighting - look up
      if(fluo >= DT_ILLUMINANT_FLUO_LAST) break;
 
      x = fluorescent[fluo][0];
      y = fluorescent[fluo][1];
      break;
    }
    case DT_ILLUMINANT_LED:
    {
      // LED lighting - look up
      if(iled >= DT_ILLUMINANT_LED_LAST) break;
 
      x = led[iled][0];
      y = led[iled][1];
      break;
    }
    case DT_ILLUMINANT_D:
    {
      // Adjusted Planckian locus for daylight interpolated by cubic splines
      // Model valid for T in [4000 ; 25000] K
      CCT_to_xy_daylight(t, &x, &y);
      if(y != 0.f && x != 0.f) break;
      // else t is out of bounds -> use black body model (next case)
    }
    case DT_ILLUMINANT_BB:
    {
      // General Planckian locus for black body radiator interpolated by cubic splines
      // Model valid for T in [1667 ; 25000] K
      CCT_to_xy_blackbody(t, &x, &y);
      if(y != 0.f && x != 0.f) break;
      // else t is out of bounds -> use custom/original values (next case)
    }
    case DT_ILLUMINANT_CAMERA:
    {
      // Detect WB from RAW EXIF
      if(img)
        if(find_temperature_from_raw_coeffs(img, custom_wb, &x, &y)) break;
    }
    case DT_ILLUMINANT_CUSTOM: // leave x and y as-is
    case DT_ILLUMINANT_DETECT_EDGES:
    case DT_ILLUMINANT_DETECT_SURFACES:
    case DT_ILLUMINANT_LAST:
    {
      return FALSE;
    }
  }
 
  if(x != 0.f && y != 0.f)
  {
    *x_out = x;
    *y_out = y;
    return TRUE;
  }
  else
    return FALSE;
}
 
 
static inline void WB_coeffs_to_illuminant_xy(const float CAM_to_XYZ[4][3], const dt_aligned_pixel_t WB,
                                              float *x, float *y)
{
  // Find the illuminant chromaticity x y from RAW WB coeffs and camera input matrice
  dt_aligned_pixel_t XYZ, LMS;
  // Simulate white point, aka convert (1, 1, 1) in camera space to XYZ
  // warning : we multiply the transpose of CAM_to_XYZ  since the pseudoinverse transposes it
  XYZ[0] = CAM_to_XYZ[0][0] / WB[0] + CAM_to_XYZ[1][0] / WB[1] + CAM_to_XYZ[2][0] / WB[2];
  XYZ[1] = CAM_to_XYZ[0][1] / WB[0] + CAM_to_XYZ[1][1] / WB[1] + CAM_to_XYZ[2][1] / WB[2];
  XYZ[2] = CAM_to_XYZ[0][2] / WB[0] + CAM_to_XYZ[1][2] / WB[1] + CAM_to_XYZ[2][2] / WB[2];
 
  // Matrices white point is D65. We need to convert it for darktable's pipe (D50)
  static const dt_aligned_pixel_t D65 = { 0.941238f, 1.040633f, 1.088932f, 0.f };
  const float p = powf(1.088932f / 0.818155f, 0.0834f);
 
  convert_XYZ_to_bradford_LMS(XYZ, LMS);
  bradford_adapt_D50(LMS, D65, p, FALSE, LMS);
  convert_bradford_LMS_to_XYZ(LMS, XYZ);
 
  // Get white point chromaticity
  XYZ[0] /= XYZ[1];
  XYZ[2] /= XYZ[1];
  XYZ[1] /= XYZ[1];
 
  *x = XYZ[0] / (XYZ[0] + XYZ[1] + XYZ[2]);
  *y = XYZ[1] / (XYZ[0] + XYZ[1] + XYZ[2]);
}
 
 
static inline void matrice_pseudoinverse(float (*in)[3], float (*out)[3], int size)
{
  float DT_ALIGNED_ARRAY work[3][6];
 
  for(int i = 0; i < 3; i++)
  {
    for(int j = 0; j < 6; j++)
      work[i][j] = j == i+3;
    for(int j = 0; j < 3; j++)
      for(int k = 0; k < size; k++)
        work[i][j] += in[k][i] * in[k][j];
  }
  for(int i = 0; i < 3; i++)
  {
    float num = work[i][i];
    for(int j = 0; j < 6; j++)
      work[i][j] /= num;
    for(int k = 0; k < 3; k++)
    {
      if(k==i) continue;
      num = work[k][i];
      for(int j = 0; j < 6; j++)
        work[k][j] -= work[i][j] * num;
    }
  }
  for(int i = 0; i < size; i++)
    for(int j = 0; j < 3; j++)
    {
      out[i][j] = 0.0f;
      for(int k = 0; k < 3; k++)
        out[i][j] += work[j][k+3] * in[i][k];
    }
}
 
 
static int find_temperature_from_raw_coeffs(const dt_image_t *img, const dt_aligned_pixel_t custom_wb,
                                            float *chroma_x, float *chroma_y)
{
  if(img == NULL) return FALSE;
  if(!dt_image_is_matrix_correction_supported(img)) return FALSE;
 
  int has_valid_coeffs = TRUE;
  const int num_coeffs = (img->flags & DT_IMAGE_4BAYER) ? 4 : 3;
 
  // Check coeffs
  for(int k = 0; has_valid_coeffs && k < num_coeffs; k++)
    if(!isnormal(img->wb_coeffs[k]) || img->wb_coeffs[k] == 0.0f) has_valid_coeffs = FALSE;
 
  if(!has_valid_coeffs) return FALSE;
 
  // Get white balance camera factors
  dt_aligned_pixel_t WB = { img->wb_coeffs[0], img->wb_coeffs[1], img->wb_coeffs[2], img->wb_coeffs[3] };
 
  // Adapt the camera coeffs with custom white balance if provided
  // this can deal with WB coeffs that don't use the input matrix reference
  if(custom_wb)
    for(size_t k = 0; k < 4; k++) WB[k] *= custom_wb[k];
 
  // Get the camera input profile (matrice of primaries)
  float XYZ_to_CAM[4][3];
  XYZ_to_CAM[0][0] = NAN;
 
  if(!isnan(img->d65_color_matrix[0]))
  {
    // keep in sync with reload_defaults from colorin.c
    // embedded matrix is used with higher priority than standard one
    XYZ_to_CAM[0][0] = img->d65_color_matrix[0];
    XYZ_to_CAM[0][1] = img->d65_color_matrix[1];
    XYZ_to_CAM[0][2] = img->d65_color_matrix[2];
 
    XYZ_to_CAM[1][0] = img->d65_color_matrix[3];
    XYZ_to_CAM[1][1] = img->d65_color_matrix[4];
    XYZ_to_CAM[1][2] = img->d65_color_matrix[5];
 
    XYZ_to_CAM[2][0] = img->d65_color_matrix[6];
    XYZ_to_CAM[2][1] = img->d65_color_matrix[7];
    XYZ_to_CAM[2][2] = img->d65_color_matrix[8];
  }
  else
  {
    for(int k=0; k<4; k++)
      for(int i=0; i<3; i++)
        XYZ_to_CAM[k][i] = img->adobe_XYZ_to_CAM[k][i];
  }
 
  if(isnan(XYZ_to_CAM[0][0])) return FALSE;
 
  // Bloody input matrices define XYZ -> CAM transform, as if we often needed camera profiles to output
  // So we need to invert them. Here go your CPU cycles again.
  float CAM_to_XYZ[4][3];
  CAM_to_XYZ[0][0] = NAN;
  matrice_pseudoinverse(XYZ_to_CAM, CAM_to_XYZ, 3);
  if(isnan(CAM_to_XYZ[0][0])) return FALSE;
 
  float x, y;
  WB_coeffs_to_illuminant_xy(CAM_to_XYZ, WB, &x, &y);
  *chroma_x = x;
  *chroma_y = y;
 
  return TRUE;
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline float planckian_normal(const float x, const float t)
{
  float n = 0.f;
 
  // Get the direction of the normal vector to the planckian locus at current temperature
  // This is derivated from CCT_to_xy_blackbody equations
  if(t >= 1667.f && t <= 2222.f)
      n = (-3.3191442f * x - 2.69622040f) * x + 2.18555832f;
  else if(t > 2222.f && t <= 4000.f)
      n = (-2.8648428f * x - 2.74837186f) * x + 2.09137015f;
  else if(t > 4000.f && t < 25000.f)
      n = (9.2452740f * x  - 11.7467734f) * x + 3.75112997f;
  return n;
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void blackbody_xy_to_tinted_xy(const float x, const float y, const float t, const float tint,
                                             float *x_out, float *y_out)
{
  // Move further away from planckian locus in the orthogonal direction, by an amount of "tint"
  const float n = planckian_normal(x, t);
  const float norm = sqrtf(1.f + n * n);
  *x_out = x + tint * n / norm;
  *y_out = y - tint / norm;
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline float get_tint_from_tinted_xy(const float x, const float y, const float t)
{
  // Find the distance between planckian locus and arbitrary x y chromaticity in the orthogonal direction
  const float n = planckian_normal(x, t);
  const float norm = sqrtf(1.f + n * n);
  float x_bb, y_bb;
  CCT_to_xy_blackbody(t, &x_bb, &y_bb);
  const float tint = -(y - y_bb) * norm;
  return tint;
}
 
 
#ifdef _OPENMP
#pragma omp declare simd
#endif
static inline void xy_to_uv(const float xy[2], float uv[2])
{
  // Convert to CIE1960 Yuv color space, usefull to compute CCT
  // https://en.wikipedia.org/wiki/CIE_1960_color_space
  const float denom = 12.f * xy[1] - 1.882f * xy[0] + 2.9088f;
  uv[0] = 5.5932f * xy[0] + 1.9116 * xy[1];
  uv[1] = 7.8972f * xy[1];
  uv[0] /= denom;
  uv[1] /= denom;
}
 
 
/*
 * The following defines a custom OpenMP reduction so the reverse-lookup can be fully parallelized without sharing.
 *
 * Reference : https://stackoverflow.com/questions/61821090/parallelization-of-a-reverse-lookup-with-openmp
 *
 * The principle is that each thread has its own private radius and temperature, and find its own local minium radius.
 * Then, at the end of the parallel loops, we fetch all the local minima from each thread, compare them and return
 * the global minimum.
 *
 * This avoids sharing temperature and radius between threads and waiting for thread locks.
 */
typedef struct pair
{
  float radius;
  float temperature;
} pair;
 
struct pair pair_min(struct pair r, struct pair n)
{
  // r is the current min value, n in the value to compare against it
  if(n.radius < r.radius) return n;
  else return r;
}
 
// Define a new reduction operation
#ifdef _OPENMP
#pragma omp declare reduction(pairmin:struct pair:omp_out=pair_min(omp_out,omp_in))    \
  initializer(omp_priv = { FLT_MAX, 0.0f })
#endif
 
static inline float CCT_reverse_lookup(const float x, const float y)
{
  // Find out the closest correlated color temperature (closest point over the planckian locus)
  // for any arbitrary x, y chromaticity, by brute-force reverse-lookup.
  // Note that the LUT computation could be defered somewhere else, and computed once
 
  static const float T_min = 1667.f;
  static const float T_max = 25000.f;
  static const float T_range = T_max - T_min;
  static const size_t LUT_samples = 1<<16;
 
  struct pair min_radius = { FLT_MAX, 0.0f };
 
#if !(defined(__apple_build_version__) && __apple_build_version__ < 11030000) //makes Xcode 11.3.1 compiler crash
#ifdef _OPENMP
#pragma omp parallel for default(none) \
  dt_omp_firstprivate(x, y, T_min, T_range, LUT_samples) reduction(pairmin:min_radius)\
  schedule(simd:static)
#endif
#endif
  for(size_t i = 0; i < LUT_samples; i++)
  {
    // we need more values for the low temperatures, so we scale the step with a power
    const float step = powf((float)i / (float)(LUT_samples - 1), 4.0f);
 
    // Current temperature in the lookup range
    const float T = T_min +  step * T_range;
 
    // Current x, y chromaticity
    float x_bb, y_bb;
 
    if(T >= 4000.f)
      CCT_to_xy_daylight(T, &x_bb, &y_bb);
    else
      CCT_to_xy_blackbody(T, &x_bb, &y_bb);
 
    // Compute distance between current planckian chromaticity and input
    const pair radius_tmp = { dt_fast_hypotf((x_bb - x), (y_bb - y)), T };
 
    // If we found a smaller radius, save it
    min_radius = pair_min(min_radius, radius_tmp);
  }
 
  return min_radius.temperature;
}
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