cmsgamma.c

//---------------------------------------------------------------------------------
//
//  Little Color Management System
//  Copyright (c) 1998-2024 Marti Maria Saguer
//
// Permission is hereby granted, free of charge, to any person obtaining
// a copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the Software
// is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO
// THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
// LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
//
//---------------------------------------------------------------------------------
//
#include "lcms2_internal.h"

// Tone curves are powerful constructs that can contain curves specified in diverse ways.
// The curve is stored in segments, where each segment can be sampled or specified by parameters.
// a 16.bit simplification of the *whole* curve is kept for optimization purposes. For float operation,
// each segment is evaluated separately. Plug-ins may be used to define new parametric schemes,
// each plug-in may define up to MAX_TYPES_IN_LCMS_PLUGIN functions types. For defining a function,
// the plug-in should provide the type id, how many parameters each type has, and a pointer to
// a procedure that evaluates the function. In the case of reverse evaluation, the evaluator will
// be called with the type id as a negative value, and a sampled version of the reversed curve
// will be built.

// ----------------------------------------------------------------- Implementation
// Maxim number of nodes
#define MAX_NODES_IN_CURVE   4097
#define MINUS_INF            (-1E22F)
#define PLUS_INF             (+1E22F)

// The list of supported parametric curves
typedef struct _cmsParametricCurvesCollection_st {

    cmsUInt32Number nFunctions;                                     // Number of supported functions in this chunk
    cmsInt32Number  FunctionTypes[MAX_TYPES_IN_LCMS_PLUGIN];        // The identification types
    cmsUInt32Number ParameterCount[MAX_TYPES_IN_LCMS_PLUGIN];       // Number of parameters for each function

    cmsParametricCurveEvaluator Evaluator;                          // The evaluator

    struct _cmsParametricCurvesCollection_st* Next; // Next in list

} _cmsParametricCurvesCollection;

// This is the default (built-in) evaluator
static cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R);

// The built-in list
static _cmsParametricCurvesCollection DefaultCurves = {
    10,                                      // # of curve types
    { 1, 2, 3, 4, 5, 6, 7, 8, 108, 109 },    // Parametric curve ID
    { 1, 3, 4, 5, 7, 4, 5, 5,   1,   1 },    // Parameters by type
    DefaultEvalParametricFn,                 // Evaluator
    NULL                                     // Next in chain
};

// Duplicates the zone of memory used by the plug-in in the new context
static
void DupPluginCurvesList(struct _cmsContext_struct* ctx, 
                                               const struct _cmsContext_struct* src)
{
   _cmsCurvesPluginChunkType newHead = { NULL };
   _cmsParametricCurvesCollection*  entry;
   _cmsParametricCurvesCollection*  Anterior = NULL;
   _cmsCurvesPluginChunkType* head = (_cmsCurvesPluginChunkType*) src->chunks[CurvesPlugin];

    _cmsAssert(head != NULL);

    // Walk the list copying all nodes
   for (entry = head->ParametricCurves;
        entry != NULL;
        entry = entry ->Next) {

            _cmsParametricCurvesCollection *newEntry = ( _cmsParametricCurvesCollection *) _cmsSubAllocDup(ctx ->MemPool, entry, sizeof(_cmsParametricCurvesCollection));
   
            if (newEntry == NULL) 
                return;

            // We want to keep the linked list order, so this is a little bit tricky
            newEntry -> Next = NULL;
            if (Anterior)
                Anterior -> Next = newEntry;
     
            Anterior = newEntry;

            if (newHead.ParametricCurves == NULL)
                newHead.ParametricCurves = newEntry;
    }

  ctx ->chunks[CurvesPlugin] = _cmsSubAllocDup(ctx->MemPool, &newHead, sizeof(_cmsCurvesPluginChunkType));
}

// The allocator have to follow the chain
void _cmsAllocCurvesPluginChunk(struct _cmsContext_struct* ctx, 
                                const struct _cmsContext_struct* src)
{
    _cmsAssert(ctx != NULL);

    if (src != NULL) {

        // Copy all linked list
       DupPluginCurvesList(ctx, src);
    }
    else {
        static _cmsCurvesPluginChunkType CurvesPluginChunk = { NULL };
        ctx ->chunks[CurvesPlugin] = _cmsSubAllocDup(ctx ->MemPool, &CurvesPluginChunk, sizeof(_cmsCurvesPluginChunkType));
    }
}


// The linked list head
_cmsCurvesPluginChunkType _cmsCurvesPluginChunk = { NULL };

// As a way to install new parametric curves
cmsBool _cmsRegisterParametricCurvesPlugin(cmsContext ContextID, cmsPluginBase* Data)
{
    _cmsCurvesPluginChunkType* ctx = ( _cmsCurvesPluginChunkType*) _cmsContextGetClientChunk(ContextID, CurvesPlugin);
    cmsPluginParametricCurves* Plugin = (cmsPluginParametricCurves*) Data;
    _cmsParametricCurvesCollection* fl;

    if (Data == NULL) {

          ctx -> ParametricCurves =  NULL;
          return TRUE;
    }

    fl = (_cmsParametricCurvesCollection*) _cmsPluginMalloc(ContextID, sizeof(_cmsParametricCurvesCollection));
    if (fl == NULL) return FALSE;

    // Copy the parameters
    fl ->Evaluator  = Plugin ->Evaluator;
    fl ->nFunctions = Plugin ->nFunctions;

    // Make sure no mem overwrites
    if (fl ->nFunctions > MAX_TYPES_IN_LCMS_PLUGIN)
        fl ->nFunctions = MAX_TYPES_IN_LCMS_PLUGIN;

    // Copy the data
    memmove(fl->FunctionTypes,  Plugin ->FunctionTypes,   fl->nFunctions * sizeof(cmsUInt32Number));
    memmove(fl->ParameterCount, Plugin ->ParameterCount,  fl->nFunctions * sizeof(cmsUInt32Number));

    // Keep linked list
    fl ->Next = ctx->ParametricCurves;
    ctx->ParametricCurves = fl;

    // All is ok
    return TRUE;
}


// Search in type list, return position or -1 if not found
static
int IsInSet(int Type, _cmsParametricCurvesCollection* c)
{
    int i;

    for (i=0; i < (int) c ->nFunctions; i++)
        if (abs(Type) == c ->FunctionTypes[i]) return i;

    return -1;
}


// Search for the collection which contains a specific type
static
_cmsParametricCurvesCollection *GetParametricCurveByType(cmsContext ContextID, int Type, int* index)
{
    _cmsParametricCurvesCollection* c;
    int Position;
    _cmsCurvesPluginChunkType* ctx = ( _cmsCurvesPluginChunkType*) _cmsContextGetClientChunk(ContextID, CurvesPlugin);

    for (c = ctx->ParametricCurves; c != NULL; c = c ->Next) {

        Position = IsInSet(Type, c);

        if (Position != -1) {
            if (index != NULL)
                *index = Position;
            return c;
        }
    }
    // If none found, revert for defaults
    for (c = &DefaultCurves; c != NULL; c = c ->Next) {

        Position = IsInSet(Type, c);

        if (Position != -1) {
            if (index != NULL)
                *index = Position;
            return c;
        }
    }

    return NULL;
}

// Low level allocate, which takes care of memory details. nEntries may be zero, and in this case
// no optimization curve is computed. nSegments may also be zero in the inverse case, where only the
// optimization curve is given. Both features simultaneously is an error
static
cmsToneCurve* AllocateToneCurveStruct(cmsContext ContextID, cmsUInt32Number nEntries,
                                      cmsUInt32Number nSegments, const cmsCurveSegment* Segments,
                                      const cmsUInt16Number* Values)
{
    cmsToneCurve* p;
    cmsUInt32Number i;

    // We allow huge tables, which are then restricted for smoothing operations
    if (nEntries > 65530) {
        cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve of more than 65530 entries");
        return NULL;
    }

    if (nEntries == 0 && nSegments == 0) {
        cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve with zero segments and no table");
        return NULL;
    }

    // Allocate all required pointers, etc.
    p = (cmsToneCurve*) _cmsMallocZero(ContextID, sizeof(cmsToneCurve));
    if (!p) return NULL;

    // In this case, there are no segments
    if (nSegments == 0) {
        p ->Segments = NULL;
        p ->Evals = NULL;
    }
    else {
        p ->Segments = (cmsCurveSegment*) _cmsCalloc(ContextID, nSegments, sizeof(cmsCurveSegment));
        if (p ->Segments == NULL) goto Error;

        p ->Evals    = (cmsParametricCurveEvaluator*) _cmsCalloc(ContextID, nSegments, sizeof(cmsParametricCurveEvaluator));
        if (p ->Evals == NULL) goto Error;
    }

    p -> nSegments = nSegments;

    // This 16-bit table contains a limited precision representation of the whole curve and is kept for
    // increasing xput on certain operations.
    if (nEntries == 0) {
        p ->Table16 = NULL;
    }
    else {
       p ->Table16 = (cmsUInt16Number*)  _cmsCalloc(ContextID, nEntries, sizeof(cmsUInt16Number));
       if (p ->Table16 == NULL) goto Error;
    }

    p -> nEntries  = nEntries;

    // Initialize members if requested
    if (Values != NULL && (nEntries > 0)) {

        for (i=0; i < nEntries; i++)
            p ->Table16[i] = Values[i];
    }

    // Initialize the segments stuff. The evaluator for each segment is located and a pointer to it
    // is placed in advance to maximize performance.
    if (Segments != NULL && (nSegments > 0)) {

        _cmsParametricCurvesCollection *c;

        p ->SegInterp = (cmsInterpParams**) _cmsCalloc(ContextID, nSegments, sizeof(cmsInterpParams*));
        if (p ->SegInterp == NULL) goto Error;

        for (i=0; i < nSegments; i++) {

            // Type 0 is a special marker for table-based curves
            if (Segments[i].Type == 0)
                p ->SegInterp[i] = _cmsComputeInterpParams(ContextID, Segments[i].nGridPoints, 1, 1, NULL, CMS_LERP_FLAGS_FLOAT);

            memmove(&p ->Segments[i], &Segments[i], sizeof(cmsCurveSegment));

            if (Segments[i].Type == 0 && Segments[i].SampledPoints != NULL)
                p ->Segments[i].SampledPoints = (cmsFloat32Number*) _cmsDupMem(ContextID, Segments[i].SampledPoints, sizeof(cmsFloat32Number) * Segments[i].nGridPoints);
            else
                p ->Segments[i].SampledPoints = NULL;


            c = GetParametricCurveByType(ContextID, Segments[i].Type, NULL);
            if (c != NULL)
                    p ->Evals[i] = c ->Evaluator;
        }
    }

    p ->InterpParams = _cmsComputeInterpParams(ContextID, p ->nEntries, 1, 1, p->Table16, CMS_LERP_FLAGS_16BITS);
    if (p->InterpParams != NULL)
        return p;

Error:
    for (i=0; i < nSegments; i++) {
        if (p ->Segments && p ->Segments[i].SampledPoints) _cmsFree(ContextID, p ->Segments[i].SampledPoints);
        if (p ->SegInterp && p ->SegInterp[i]) _cmsFree(ContextID, p ->SegInterp[i]);
    }
    if (p -> SegInterp) _cmsFree(ContextID, p -> SegInterp);
    if (p -> Segments) _cmsFree(ContextID, p -> Segments);
    if (p -> Evals) _cmsFree(ContextID, p -> Evals);
    if (p ->Table16) _cmsFree(ContextID, p ->Table16);
    _cmsFree(ContextID, p);
    return NULL;
}


// Generates a sigmoidal function with desired steepness.
cmsINLINE double sigmoid_base(double k, double t)
{
    return (1.0 / (1.0 + exp(-k * t))) - 0.5;
}

cmsINLINE double inverted_sigmoid_base(double k, double t)
{
    return -log((1.0 / (t + 0.5)) - 1.0) / k;
}

cmsINLINE double sigmoid_factory(double k, double t)
{
    double correction = 0.5 / sigmoid_base(k, 1);

    return correction * sigmoid_base(k, 2.0 * t - 1.0) + 0.5;
}

cmsINLINE double inverse_sigmoid_factory(double k, double t)
{
    double correction = 0.5 / sigmoid_base(k, 1);

    return (inverted_sigmoid_base(k, (t - 0.5) / correction) + 1.0) / 2.0;
}


// Parametric Fn using floating point
static
cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R)
{
    cmsFloat64Number e, Val, disc;

    switch (Type) {

   // X = Y ^ Gamma
    case 1:
        if (R < 0) {

            if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
                Val = R;
            else
                Val = 0;
        }
        else
            Val = pow(R, Params[0]);
        break;

    // Type 1 Reversed: X = Y ^1/gamma
    case -1:
        if (R < 0) {

            if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
                Val = R;
            else
                Val = 0;
        }
        else
        {
            if (fabs(Params[0]) < MATRIX_DET_TOLERANCE)
                Val = PLUS_INF;
            else
                Val = pow(R, 1 / Params[0]);
        }
        break;

    // CIE 122-1966
    // Y = (aX + b)^Gamma  | X >= -b/a
    // Y = 0               | else
    case 2:
    {

        if (fabs(Params[1]) < MATRIX_DET_TOLERANCE)
        {
            Val = 0;
        }
        else
        {
            disc = -Params[2] / Params[1];

            if (R >= disc) {

                e = Params[1] * R + Params[2];

                if (e > 0)
                    Val = pow(e, Params[0]);
                else
                    Val = 0;
            }
            else
                Val = 0;
        }
    }
    break;

     // Type 2 Reversed
     // X = (Y ^1/g  - b) / a
     case -2:
     {
         if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
             fabs(Params[1]) < MATRIX_DET_TOLERANCE)
         {
             Val = 0;
         }
         else
         {
             if (R < 0)
                 Val = 0;
             else
                 Val = (pow(R, 1.0 / Params[0]) - Params[2]) / Params[1];

             if (Val < 0)
                 Val = 0;
         }
     }         
     break;


    // IEC 61966-3
    // Y = (aX + b)^Gamma + c | X <= -b/a
    // Y = c                  | else
    case 3:
    {
        if (fabs(Params[1]) < MATRIX_DET_TOLERANCE)
        {
            Val = 0;
        }
        else
        {
            disc = -Params[2] / Params[1];
            if (disc < 0)
                disc = 0;

            if (R >= disc) {

                e = Params[1] * R + Params[2];

                if (e > 0)
                    Val = pow(e, Params[0]) + Params[3];
                else
                    Val = 0;
            }
            else
                Val = Params[3];
        }
    }
    break;


    // Type 3 reversed
    // X=((Y-c)^1/g - b)/a      | (Y>=c)
    // X=-b/a                   | (Y<c)
    case -3:
    {
        if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
            fabs(Params[1]) < MATRIX_DET_TOLERANCE)
        {
            Val = 0;
        }
        else
        {
            if (R >= Params[3]) {

                e = R - Params[3];

                if (e > 0)
                    Val = (pow(e, 1 / Params[0]) - Params[2]) / Params[1];
                else
                    Val = 0;
            }
            else {
                Val = -Params[2] / Params[1];
            }
        }
    }
    break;


    // IEC 61966-2.1 (sRGB)
    // Y = (aX + b)^Gamma | X >= d
    // Y = cX             | X < d
    case 4:
        if (R >= Params[4]) {

            e = Params[1]*R + Params[2];

            if (e > 0)
                Val = pow(e, Params[0]);
            else
                Val = 0;
        }
        else
            Val = R * Params[3];
        break;

    // Type 4 reversed
    // X=((Y^1/g-b)/a)    | Y >= (ad+b)^g
    // X=Y/c              | Y< (ad+b)^g
    case -4:
    {

        e = Params[1] * Params[4] + Params[2];
        if (e < 0)
            disc = 0;
        else
            disc = pow(e, Params[0]);

        if (R >= disc) {

            if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
                fabs(Params[1]) < MATRIX_DET_TOLERANCE)

                Val = 0;

            else
                Val = (pow(R, 1.0 / Params[0]) - Params[2]) / Params[1];
        }
        else {

            if (fabs(Params[3]) < MATRIX_DET_TOLERANCE)
                Val = 0;
            else
                Val = R / Params[3];
        }

    }
    break;


    // Y = (aX + b)^Gamma + e | X >= d
    // Y = cX + f             | X < d
    case 5:
        if (R >= Params[4]) {

            e = Params[1]*R + Params[2];

            if (e > 0)
                Val = pow(e, Params[0]) + Params[5];
            else
                Val = Params[5];
        }
        else
            Val = R*Params[3] + Params[6];
        break;


    // Reversed type 5
    // X=((Y-e)1/g-b)/a   | Y >=(ad+b)^g+e), cd+f
    // X=(Y-f)/c          | else
    case -5:
    {
        disc = Params[3] * Params[4] + Params[6];
        if (R >= disc) {

            e = R - Params[5];
            if (e < 0)
                Val = 0;
            else
            {
                if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
                    fabs(Params[1]) < MATRIX_DET_TOLERANCE)

                    Val = 0;
                else
                    Val = (pow(e, 1.0 / Params[0]) - Params[2]) / Params[1];
            }
        }
        else {
            if (fabs(Params[3]) < MATRIX_DET_TOLERANCE)
                Val = 0;
            else
                Val = (R - Params[6]) / Params[3];
        }

    }
    break;


    // Types 6,7,8 comes from segmented curves as described in ICCSpecRevision_02_11_06_Float.pdf
    // Type 6 is basically identical to type 5 without d

    // Y = (a * X + b) ^ Gamma + c
    case 6:
        e = Params[1]*R + Params[2];

        // On gamma 1.0, don't clamp
        if (Params[0] == 1.0) {
            Val = e + Params[3];
        }
        else {
            if (e < 0)
                Val = Params[3];
            else
                Val = pow(e, Params[0]) + Params[3];
        }
        break;

    // ((Y - c) ^1/Gamma - b) / a
    case -6:
    {
        if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
            fabs(Params[1]) < MATRIX_DET_TOLERANCE)
        {
            Val = 0;
        }
        else
        {
            e = R - Params[3];
            if (e < 0)
                Val = 0;
            else
                Val = (pow(e, 1.0 / Params[0]) - Params[2]) / Params[1];
        }
    }
    break;


    // Y = a * log (b * X^Gamma + c) + d
    case 7:

       e = Params[2] * pow(R, Params[0]) + Params[3];
       if (e <= 0)
           Val = Params[4];
       else
           Val = Params[1]*log10(e) + Params[4];
       break;

    // (Y - d) / a = log(b * X ^Gamma + c)
    // pow(10, (Y-d) / a) = b * X ^Gamma + c
    // pow((pow(10, (Y-d) / a) - c) / b, 1/g) = X
    case -7:
    {
        if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
            fabs(Params[1]) < MATRIX_DET_TOLERANCE ||
            fabs(Params[2]) < MATRIX_DET_TOLERANCE)
        {
            Val = 0;
        }
        else
        {
            Val = pow((pow(10.0, (R - Params[4]) / Params[1]) - Params[3]) / Params[2], 1.0 / Params[0]);
        }
    }
    break;


   //Y = a * b^(c*X+d) + e
   case 8:
       Val = (Params[0] * pow(Params[1], Params[2] * R + Params[3]) + Params[4]);
       break;


   // Y = (log((y-e) / a) / log(b) - d ) / c
   // a=0, b=1, c=2, d=3, e=4,
   case -8:

       disc = R - Params[4];
       if (disc < 0) Val = 0;
       else
       {
           if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
               fabs(Params[2]) < MATRIX_DET_TOLERANCE)
           {
               Val = 0;
           }
           else
           {
               Val = (log(disc / Params[0]) / log(Params[1]) - Params[3]) / Params[2];
           }
       }
       break;


   // S-Shaped: (1 - (1-x)^1/g)^1/g
   case 108:
       if (fabs(Params[0]) < MATRIX_DET_TOLERANCE)
           Val = 0;
       else
           Val = pow(1.0 - pow(1 - R, 1/Params[0]), 1/Params[0]);
      break;

    // y = (1 - (1-x)^1/g)^1/g
    // y^g = (1 - (1-x)^1/g)
    // 1 - y^g = (1-x)^1/g
    // (1 - y^g)^g = 1 - x
    // 1 - (1 - y^g)^g
    case -108:
        Val = 1 - pow(1 - pow(R, Params[0]), Params[0]);
        break;

    // Sigmoidals
    case 109:
        Val = sigmoid_factory(Params[0], R);
        break;

    case -109:
        Val = inverse_sigmoid_factory(Params[0], R);
        break;

    default:
        // Unsupported parametric curve. Should never reach here
        return 0;
    }

    return Val;
}

// Evaluate a segmented function for a single value. Return -Inf if no valid segment found .
// If fn type is 0, perform an interpolation on the table
static
cmsFloat64Number EvalSegmentedFn(const cmsToneCurve *g, cmsFloat64Number R)
{
    int i;
    cmsFloat32Number Out32;
    cmsFloat64Number Out;

    for (i = (int) g->nSegments - 1; i >= 0; --i) {

        // Check for domain
        if ((R > g->Segments[i].x0) && (R <= g->Segments[i].x1)) {

            // Type == 0 means segment is sampled
            if (g->Segments[i].Type == 0) {

                cmsFloat32Number R1 = (cmsFloat32Number)(R - g->Segments[i].x0) / (g->Segments[i].x1 - g->Segments[i].x0);

                // Setup the table (TODO: clean that)
                g->SegInterp[i]->Table = g->Segments[i].SampledPoints;

                g->SegInterp[i]->Interpolation.LerpFloat(&R1, &Out32, g->SegInterp[i]);
                Out = (cmsFloat64Number) Out32;

            }
            else {
                Out = g->Evals[i](g->Segments[i].Type, g->Segments[i].Params, R);
            }

            if (isinf(Out))
                return PLUS_INF;
            else
            {
                if (isinf(-Out))
                    return MINUS_INF;
            }

            return Out;
        }
    }

    return MINUS_INF;
}

// Access to estimated low-res table
cmsUInt32Number CMSEXPORT cmsGetToneCurveEstimatedTableEntries(const cmsToneCurve* t)
{
    _cmsAssert(t != NULL);
    return t ->nEntries;
}

const cmsUInt16Number* CMSEXPORT cmsGetToneCurveEstimatedTable(const cmsToneCurve* t)
{
    _cmsAssert(t != NULL);
    return t ->Table16;
}


// Create an empty gamma curve, by using tables. This specifies only the limited-precision part, and leaves the
// floating point description empty.
cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurve16(cmsContext ContextID, cmsUInt32Number nEntries, const cmsUInt16Number Values[])
{
    return AllocateToneCurveStruct(ContextID, nEntries, 0, NULL, Values);
}

static
cmsUInt32Number EntriesByGamma(cmsFloat64Number Gamma)
{
    if (fabs(Gamma - 1.0) < 0.001) return 2;
    return 4096;
}


// Create a segmented gamma, fill the table
cmsToneCurve* CMSEXPORT cmsBuildSegmentedToneCurve(cmsContext ContextID,
                                                   cmsUInt32Number nSegments, const cmsCurveSegment Segments[])
{
    cmsUInt32Number i;
    cmsFloat64Number R, Val;
    cmsToneCurve* g;
    cmsUInt32Number nGridPoints = 4096;

    _cmsAssert(Segments != NULL);

    // Optimizatin for identity curves.
    if (nSegments == 1 && Segments[0].Type == 1) {

        nGridPoints = EntriesByGamma(Segments[0].Params[0]);
    }

    g = AllocateToneCurveStruct(ContextID, nGridPoints, nSegments, Segments, NULL);
    if (g == NULL) return NULL;

    // Once we have the floating point version, we can approximate a 16 bit table of 4096 entries
    // for performance reasons. This table would normally not be used except on 8/16 bits transforms.
    for (i = 0; i < nGridPoints; i++) {

        R   = (cmsFloat64Number) i / (nGridPoints-1);

        Val = EvalSegmentedFn(g, R);

        // Round and saturate
        g ->Table16[i] = _cmsQuickSaturateWord(Val * 65535.0);
    }

    return g;
}

// Use a segmented curve to store the floating point table
cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurveFloat(cmsContext ContextID, cmsUInt32Number nEntries, const cmsFloat32Number values[])
{
    cmsCurveSegment Seg[3];

    // Do some housekeeping
    if (nEntries == 0 || values == NULL)
        return NULL;

    // A segmented tone curve should have function segments in the first and last positions
    // Initialize segmented curve part up to 0 to constant value = samples[0]
    Seg[0].x0 = MINUS_INF;
    Seg[0].x1 = 0;
    Seg[0].Type = 6;

    Seg[0].Params[0] = 1;
    Seg[0].Params[1] = 0;
    Seg[0].Params[2] = 0;
    Seg[0].Params[3] = values[0];
    Seg[0].Params[4] = 0;

    // From zero to 1
    Seg[1].x0 = 0;
    Seg[1].x1 = 1.0;
    Seg[1].Type = 0;

    Seg[1].nGridPoints = nEntries;
    Seg[1].SampledPoints = (cmsFloat32Number*) values;

    // Final segment is constant = lastsample
    Seg[2].x0 = 1.0;
    Seg[2].x1 = PLUS_INF;
    Seg[2].Type = 6;
    
    Seg[2].Params[0] = 1;
    Seg[2].Params[1] = 0;
    Seg[2].Params[2] = 0;
    Seg[2].Params[3] = values[nEntries-1];
    Seg[2].Params[4] = 0;
    

    return cmsBuildSegmentedToneCurve(ContextID, 3, Seg);
}

// Parametric curves
//
// Parameters goes as: Curve, a, b, c, d, e, f
// Type is the ICC type +1
// if type is negative, then the curve is analytically inverted
cmsToneCurve* CMSEXPORT cmsBuildParametricToneCurve(cmsContext ContextID, cmsInt32Number Type, const cmsFloat64Number Params[])
{
    cmsCurveSegment Seg0;
    int Pos = 0;
    cmsUInt32Number size;
    _cmsParametricCurvesCollection* c = GetParametricCurveByType(ContextID, Type, &Pos);

    _cmsAssert(Params != NULL);

    if (c == NULL) {
        cmsSignalError(ContextID, cmsERROR_UNKNOWN_EXTENSION, "Invalid parametric curve type %d", Type);
        return NULL;
    }

    memset(&Seg0, 0, sizeof(Seg0));

    Seg0.x0   = MINUS_INF;
    Seg0.x1   = PLUS_INF;
    Seg0.Type = Type;

    size = c->ParameterCount[Pos] * sizeof(cmsFloat64Number);
    memmove(Seg0.Params, Params, size);

    return cmsBuildSegmentedToneCurve(ContextID, 1, &Seg0);
}



// Build a gamma table based on gamma constant
cmsToneCurve* CMSEXPORT cmsBuildGamma(cmsContext ContextID, cmsFloat64Number Gamma)
{
    return cmsBuildParametricToneCurve(ContextID, 1, &Gamma);
}


// Free all memory taken by the gamma curve
void CMSEXPORT cmsFreeToneCurve(cmsToneCurve* Curve)
{
    cmsContext ContextID;

    if (Curve == NULL) return;

    ContextID = Curve ->InterpParams->ContextID;

    _cmsFreeInterpParams(Curve ->InterpParams);

    if (Curve -> Table16)
        _cmsFree(ContextID, Curve ->Table16);

    if (Curve ->Segments) {

        cmsUInt32Number i;

        for (i=0; i < Curve ->nSegments; i++) {

            if (Curve ->Segments[i].SampledPoints) {
                _cmsFree(ContextID, Curve ->Segments[i].SampledPoints);
            }

            if (Curve ->SegInterp[i] != 0)
                _cmsFreeInterpParams(Curve->SegInterp[i]);
        }

        _cmsFree(ContextID, Curve ->Segments);
        _cmsFree(ContextID, Curve ->SegInterp);
    }

    if (Curve -> Evals)
        _cmsFree(ContextID, Curve -> Evals);

    _cmsFree(ContextID, Curve);
}

// Utility function, free 3 gamma tables
void CMSEXPORT cmsFreeToneCurveTriple(cmsToneCurve* Curve[3])
{

    _cmsAssert(Curve != NULL);

    if (Curve[0] != NULL) cmsFreeToneCurve(Curve[0]);
    if (Curve[1] != NULL) cmsFreeToneCurve(Curve[1]);
    if (Curve[2] != NULL) cmsFreeToneCurve(Curve[2]);

    Curve[0] = Curve[1] = Curve[2] = NULL;
}


// Duplicate a gamma table
cmsToneCurve* CMSEXPORT cmsDupToneCurve(const cmsToneCurve* In)
{
    if (In == NULL) return NULL;

    return  AllocateToneCurveStruct(In ->InterpParams ->ContextID, In ->nEntries, In ->nSegments, In ->Segments, In ->Table16);
}

// Joins two curves for X and Y. Curves should be monotonic.
// We want to get
//
//      y = Y^-1(X(t))
//
cmsToneCurve* CMSEXPORT cmsJoinToneCurve(cmsContext ContextID,
                                      const cmsToneCurve* X,
                                      const cmsToneCurve* Y, cmsUInt32Number nResultingPoints)
{
    cmsToneCurve* out = NULL;
    cmsToneCurve* Yreversed = NULL;
    cmsFloat32Number t, x;
    cmsFloat32Number* Res = NULL;
    cmsUInt32Number i;


    _cmsAssert(X != NULL);
    _cmsAssert(Y != NULL);

    Yreversed = cmsReverseToneCurveEx(nResultingPoints, Y);
    if (Yreversed == NULL) goto Error;

    Res = (cmsFloat32Number*) _cmsCalloc(ContextID, nResultingPoints, sizeof(cmsFloat32Number));
    if (Res == NULL) goto Error;

    //Iterate
    for (i=0; i <  nResultingPoints; i++) {

        t = (cmsFloat32Number) i / (cmsFloat32Number)(nResultingPoints-1);
        x = cmsEvalToneCurveFloat(X,  t);
        Res[i] = cmsEvalToneCurveFloat(Yreversed, x);
    }

    // Allocate space for output
    out = cmsBuildTabulatedToneCurveFloat(ContextID, nResultingPoints, Res);

Error:

    if (Res != NULL) _cmsFree(ContextID, Res);
    if (Yreversed != NULL) cmsFreeToneCurve(Yreversed);

    return out;
}



// Get the surrounding nodes. This is tricky on non-monotonic tables
static
int GetInterval(cmsFloat64Number In, const cmsUInt16Number LutTable[], const struct _cms_interp_struc* p)
{
    int i;
    int y0, y1;

    // A 1 point table is not allowed
    if (p -> Domain[0] < 1) return -1;

    // Let's see if ascending or descending.
    if (LutTable[0] < LutTable[p ->Domain[0]]) {

        // Table is overall ascending
        for (i = (int) p->Domain[0] - 1; i >= 0; --i) {

            y0 = LutTable[i];
            y1 = LutTable[i+1];

            if (y0 <= y1) { // Increasing
                if (In >= y0 && In <= y1) return i;
            }
            else
                if (y1 < y0) { // Decreasing
                    if (In >= y1 && In <= y0) return i;
                }
        }
    }
    else {
        // Table is overall descending
        for (i=0; i < (int) p -> Domain[0]; i++) {

            y0 = LutTable[i];
            y1 = LutTable[i+1];

            if (y0 <= y1) { // Increasing
                if (In >= y0 && In <= y1) return i;
            }
            else
                if (y1 < y0) { // Decreasing
                    if (In >= y1 && In <= y0) return i;
                }
        }
    }

    return -1;
}

// Reverse a gamma table
cmsToneCurve* CMSEXPORT cmsReverseToneCurveEx(cmsUInt32Number nResultSamples, const cmsToneCurve* InCurve)
{
    cmsToneCurve *out;
    cmsFloat64Number a = 0, b = 0, y, x1, y1, x2, y2;
    int i, j;
    int Ascending;

    _cmsAssert(InCurve != NULL);

    // Try to reverse it analytically whatever possible
 
    if (InCurve ->nSegments == 1 && InCurve ->Segments[0].Type > 0 && 
        /* InCurve -> Segments[0].Type <= 5 */ 
        GetParametricCurveByType(InCurve ->InterpParams->ContextID, InCurve ->Segments[0].Type, NULL) != NULL) {

        return cmsBuildParametricToneCurve(InCurve ->InterpParams->ContextID,
                                       -(InCurve -> Segments[0].Type),
                                       InCurve -> Segments[0].Params);
    }

    // Nope, reverse the table.
    out = cmsBuildTabulatedToneCurve16(InCurve ->InterpParams->ContextID, nResultSamples, NULL);
    if (out == NULL)
        return NULL;

    // We want to know if this is an ascending or descending table
    Ascending = !cmsIsToneCurveDescending(InCurve);

    // Iterate across Y axis
    for (i=0; i < (int) nResultSamples; i++) {

        y = (cmsFloat64Number) i * 65535.0 / (nResultSamples - 1);

        // Find interval in which y is within.
        j = GetInterval(y, InCurve->Table16, InCurve->InterpParams);
        if (j >= 0) {


            // Get limits of interval
            x1 = InCurve ->Table16[j];
            x2 = InCurve ->Table16[j+1];

            y1 = (cmsFloat64Number) (j * 65535.0) / (InCurve ->nEntries - 1);
            y2 = (cmsFloat64Number) ((j+1) * 65535.0 ) / (InCurve ->nEntries - 1);

            // If collapsed, then use any
            if (x1 == x2) {

                out ->Table16[i] = _cmsQuickSaturateWord(Ascending ? y2 : y1);
                continue;

            } else {

                // Interpolate
                a = (y2 - y1) / (x2 - x1);
                b = y2 - a * x2;
            }
        }

        out ->Table16[i] = _cmsQuickSaturateWord(a* y + b);
    }


    return out;
}

// Reverse a gamma table
cmsToneCurve* CMSEXPORT cmsReverseToneCurve(const cmsToneCurve* InGamma)
{
    _cmsAssert(InGamma != NULL);

    return cmsReverseToneCurveEx(4096, InGamma);
}

// From: Eilers, P.H.C. (1994) Smoothing and interpolation with finite
// differences. in: Graphic Gems IV, Heckbert, P.S. (ed.), Academic press.
//
// Smoothing and interpolation with second differences.
//
//   Input:  weights (w), data (y): vector from 1 to m.
//   Input:  smoothing parameter (lambda), length (m).
//   Output: smoothed vector (z): vector from 1 to m.

static
cmsBool smooth2(cmsContext ContextID, cmsFloat32Number w[], cmsFloat32Number y[], 
                cmsFloat32Number z[], cmsFloat32Number lambda, int m)
{
    int i, i1, i2;
    cmsFloat32Number *c, *d, *e;
    cmsBool st;


    c = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
    d = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
    e = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));

    if (c != NULL && d != NULL && e != NULL) {


    d[1] = w[1] + lambda;
    c[1] = -2 * lambda / d[1];
    e[1] = lambda /d[1];
    z[1] = w[1] * y[1];
    d[2] = w[2] + 5 * lambda - d[1] * c[1] *  c[1];
    c[2] = (-4 * lambda - d[1] * c[1] * e[1]) / d[2];
    e[2] = lambda / d[2];
    z[2] = w[2] * y[2] - c[1] * z[1];

    for (i = 3; i < m - 1; i++) {
        i1 = i - 1; i2 = i - 2;
        d[i]= w[i] + 6 * lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
        c[i] = (-4 * lambda -d[i1] * c[i1] * e[i1])/ d[i];
        e[i] = lambda / d[i];
        z[i] = w[i] * y[i] - c[i1] * z[i1] - e[i2] * z[i2];
    }

    i1 = m - 2; i2 = m - 3;

    d[m - 1] = w[m - 1] + 5 * lambda -c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
    c[m - 1] = (-2 * lambda - d[i1] * c[i1] * e[i1]) / d[m - 1];
    z[m - 1] = w[m - 1] * y[m - 1] - c[i1] * z[i1] - e[i2] * z[i2];
    i1 = m - 1; i2 = m - 2;

    d[m] = w[m] + lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
    z[m] = (w[m] * y[m] - c[i1] * z[i1] - e[i2] * z[i2]) / d[m];
    z[m - 1] = z[m - 1] / d[m - 1] - c[m - 1] * z[m];

    for (i = m - 2; 1<= i; i--)
        z[i] = z[i] / d[i] - c[i] * z[i + 1] - e[i] * z[i + 2];

      st = TRUE;
    }
    else st = FALSE;

    if (c != NULL) _cmsFree(ContextID, c);
    if (d != NULL) _cmsFree(ContextID, d);
    if (e != NULL) _cmsFree(ContextID, e);

    return st;
}

// Smooths a curve sampled at regular intervals.
cmsBool  CMSEXPORT cmsSmoothToneCurve(cmsToneCurve* Tab, cmsFloat64Number lambda)
{
    cmsBool SuccessStatus = TRUE;
    cmsFloat32Number *w, *y, *z;
    cmsUInt32Number i, nItems, Zeros, Poles;
    cmsBool notCheck = FALSE;

    if (Tab != NULL && Tab->InterpParams != NULL)
    {
        cmsContext ContextID = Tab->InterpParams->ContextID;

        if (!cmsIsToneCurveLinear(Tab)) // Only non-linear curves need smoothing
        {
            nItems = Tab->nEntries;
            if (nItems < MAX_NODES_IN_CURVE)
            {
                // Allocate one more item than needed
                w = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
                y = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
                z = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));

                if (w != NULL && y != NULL && z != NULL) // Ensure no memory allocation failure
                {
                    memset(w, 0, (nItems + 1) * sizeof(cmsFloat32Number));
                    memset(y, 0, (nItems + 1) * sizeof(cmsFloat32Number));
                    memset(z, 0, (nItems + 1) * sizeof(cmsFloat32Number));

                    for (i = 0; i < nItems; i++)
                    {
                        y[i + 1] = (cmsFloat32Number)Tab->Table16[i];
                        w[i + 1] = 1.0;
                    }

                    if (lambda < 0)
                    {
                        notCheck = TRUE;
                        lambda = -lambda;
                    }

                    if (smooth2(ContextID, w, y, z, (cmsFloat32Number)lambda, (int)nItems))
                    {
                        // Do some reality - checking...

                        Zeros = Poles = 0;
                        for (i = nItems; i > 1; --i)
                        {
                            if (z[i] == 0.) Zeros++;
                            if (z[i] >= 65535.) Poles++;
                            if (z[i] < z[i - 1])
                            {
                                cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Non-Monotonic.");
                                SuccessStatus = notCheck;
                                break;
                            }
                        }

                        if (SuccessStatus && Zeros > (nItems / 3))
                        {
                            cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly zeros.");
                            SuccessStatus = notCheck;
                        }

                        if (SuccessStatus && Poles > (nItems / 3))
                        {
                            cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly poles.");
                            SuccessStatus = notCheck;
                        }

                        if (SuccessStatus) // Seems ok
                        {
                            for (i = 0; i < nItems; i++)
                            {
                                // Clamp to cmsUInt16Number
                                Tab->Table16[i] = _cmsQuickSaturateWord(z[i + 1]);
                            }
                        }
                    }
                    else // Could not smooth
                    {
                        cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Function smooth2 failed.");
                        SuccessStatus = FALSE;
                    }
                }
                else // One or more buffers could not be allocated
                {
                    cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Could not allocate memory.");
                    SuccessStatus = FALSE;
                }

                if (z != NULL)
                    _cmsFree(ContextID, z);

                if (y != NULL)
                    _cmsFree(ContextID, y);

                if (w != NULL)
                    _cmsFree(ContextID, w);
            }
            else // too many items in the table
            {
                cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Too many points.");
                SuccessStatus = FALSE;
            }
        }
    }
    else // Tab parameter or Tab->InterpParams is NULL
    {
        // Can't signal an error here since the ContextID is not known at this point
        SuccessStatus = FALSE;
    }

    return SuccessStatus;
}

// Is a table linear? Do not use parametric since we cannot guarantee some weird parameters resulting
// in a linear table. This way assures it is linear in 12 bits, which should be enough in most cases.
cmsBool CMSEXPORT cmsIsToneCurveLinear(const cmsToneCurve* Curve)
{
    int i;
    int diff;

    _cmsAssert(Curve != NULL);

    for (i=0; i < (int) Curve ->nEntries; i++) {

        diff = abs((int) Curve->Table16[i] - (int) _cmsQuantizeVal(i, Curve ->nEntries));
        if (diff > 0x0f)
            return FALSE;
    }

    return TRUE;
}

// Same, but for monotonicity
cmsBool  CMSEXPORT cmsIsToneCurveMonotonic(const cmsToneCurve* t)
{
    cmsUInt32Number n;
    int i, last;
    cmsBool lDescending;

    _cmsAssert(t != NULL);

    // Degenerated curves are monotonic? Ok, let's pass them
    n = t ->nEntries;
    if (n < 2) return TRUE;

    // Curve direction
    lDescending = cmsIsToneCurveDescending(t);

    if (lDescending) {

        last = t ->Table16[0];

        for (i = 1; i < (int) n; i++) {

            if (t ->Table16[i] - last > 2) // We allow some ripple
                return FALSE;
            else
                last = t ->Table16[i];

        }
    }
    else {

        last = t ->Table16[n-1];

        for (i = (int) n - 2; i >= 0; --i) {

            if (t ->Table16[i] - last > 2)
                return FALSE;
            else
                last = t ->Table16[i];

        }
    }

    return TRUE;
}

// Same, but for descending tables
cmsBool  CMSEXPORT cmsIsToneCurveDescending(const cmsToneCurve* t)
{
    _cmsAssert(t != NULL);

    return t ->Table16[0] > t ->Table16[t ->nEntries-1];
}


// Another info fn: is out gamma table multisegment?
cmsBool  CMSEXPORT cmsIsToneCurveMultisegment(const cmsToneCurve* t)
{
    _cmsAssert(t != NULL);

    return t -> nSegments > 1;
}

cmsInt32Number  CMSEXPORT cmsGetToneCurveParametricType(const cmsToneCurve* t)
{
    _cmsAssert(t != NULL);

    if (t -> nSegments != 1) return 0;
    return t ->Segments[0].Type;
}

// We need accuracy this time
cmsFloat32Number CMSEXPORT cmsEvalToneCurveFloat(const cmsToneCurve* Curve, cmsFloat32Number v)
{
    _cmsAssert(Curve != NULL);

    // Check for 16 bits table. If so, this is a limited-precision tone curve
    if (Curve ->nSegments == 0) {

        cmsUInt16Number In, Out;

        In = (cmsUInt16Number) _cmsQuickSaturateWord(v * 65535.0);
        Out = cmsEvalToneCurve16(Curve, In);

        return (cmsFloat32Number) (Out / 65535.0);
    }

    return (cmsFloat32Number) EvalSegmentedFn(Curve, v);
}

// We need xput over here
cmsUInt16Number CMSEXPORT cmsEvalToneCurve16(const cmsToneCurve* Curve, cmsUInt16Number v)
{
    cmsUInt16Number out;

    _cmsAssert(Curve != NULL);

    Curve ->InterpParams ->Interpolation.Lerp16(&v, &out, Curve ->InterpParams);
    return out;
}


// Least squares fitting.
// A mathematical procedure for finding the best-fitting curve to a given set of points by
// minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve.
// The sum of the squares of the offsets is used instead of the offset absolute values because
// this allows the residuals to be treated as a continuous differentiable quantity.
//
// y = f(x) = x ^ g
//
// R  = (yi - (xi^g))
// R2 = (yi - (xi^g))2
// SUM R2 = SUM (yi - (xi^g))2
//
// dR2/dg = -2 SUM x^g log(x)(y - x^g)
// solving for dR2/dg = 0
//
// g = 1/n * SUM(log(y) / log(x))

cmsFloat64Number CMSEXPORT cmsEstimateGamma(const cmsToneCurve* t, cmsFloat64Number Precision)
{
    cmsFloat64Number gamma, sum, sum2;
    cmsFloat64Number n, x, y, Std;
    cmsUInt32Number i;

    _cmsAssert(t != NULL);

    sum = sum2 = n = 0;

    // Excluding endpoints
    for (i=1; i < (MAX_NODES_IN_CURVE-1); i++) {

        x = (cmsFloat64Number) i / (MAX_NODES_IN_CURVE-1);
        y = (cmsFloat64Number) cmsEvalToneCurveFloat(t, (cmsFloat32Number) x);

        // Avoid 7% on lower part to prevent
        // artifacts due to linear ramps

        if (y > 0. && y < 1. && x > 0.07) {

            gamma = log(y) / log(x);
            sum  += gamma;
            sum2 += gamma * gamma;
            n++;
        }
    }

    // We need enough valid samples
    if (n <= 1) return -1.0;

    // Take a look on SD to see if gamma isn't exponential at all
    Std = sqrt((n * sum2 - sum * sum) / (n*(n-1)));

    if (Std > Precision)
        return -1.0;

    return (sum / n);   // The mean
}

// Retrieve segments on tone curves

const cmsCurveSegment* CMSEXPORT cmsGetToneCurveSegment(cmsInt32Number n, const cmsToneCurve* t)
{
    _cmsAssert(t != NULL);

    if (n < 0 || n >= (cmsInt32Number) t->nSegments) return NULL;
    return t->Segments + n;
}