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      1 //---------------------------------------------------------------------------------
      2 //
      3 //  Little Color Management System
      4 //  Copyright (c) 1998-2013 Marti Maria Saguer
      5 //
      6 // Permission is hereby granted, free of charge, to any person obtaining
      7 // a copy of this software and associated documentation files (the "Software"),
      8 // to deal in the Software without restriction, including without limitation
      9 // the rights to use, copy, modify, merge, publish, distribute, sublicense,
     10 // and/or sell copies of the Software, and to permit persons to whom the Software
     11 // is furnished to do so, subject to the following conditions:
     12 //
     13 // The above copyright notice and this permission notice shall be included in
     14 // all copies or substantial portions of the Software.
     15 //
     16 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
     17 // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO
     18 // THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
     19 // NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
     20 // LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
     21 // OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
     22 // WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
     23 //
     24 //---------------------------------------------------------------------------------
     25 //
     26 
     27 #include "lcms2_internal.h"
     28 
     29 // Tone curves are powerful constructs that can contain curves specified in diverse ways.
     30 // The curve is stored in segments, where each segment can be sampled or specified by parameters.
     31 // a 16.bit simplification of the *whole* curve is kept for optimization purposes. For float operation,
     32 // each segment is evaluated separately. Plug-ins may be used to define new parametric schemes,
     33 // each plug-in may define up to MAX_TYPES_IN_LCMS_PLUGIN functions types. For defining a function,
     34 // the plug-in should provide the type id, how many parameters each type has, and a pointer to
     35 // a procedure that evaluates the function. In the case of reverse evaluation, the evaluator will
     36 // be called with the type id as a negative value, and a sampled version of the reversed curve
     37 // will be built.
     38 
     39 // ----------------------------------------------------------------- Implementation
     40 // Maxim number of nodes
     41 #define MAX_NODES_IN_CURVE   4097
     42 #define MINUS_INF            (-1E22F)
     43 #define PLUS_INF             (+1E22F)
     44 
     45 // The list of supported parametric curves
     46 typedef struct _cmsParametricCurvesCollection_st {
     47 
     48     int nFunctions;                                     // Number of supported functions in this chunk
     49     int FunctionTypes[MAX_TYPES_IN_LCMS_PLUGIN];        // The identification types
     50     int ParameterCount[MAX_TYPES_IN_LCMS_PLUGIN];       // Number of parameters for each function
     51     cmsParametricCurveEvaluator    Evaluator;           // The evaluator
     52 
     53     struct _cmsParametricCurvesCollection_st* Next; // Next in list
     54 
     55 } _cmsParametricCurvesCollection;
     56 
     57 // This is the default (built-in) evaluator
     58 static cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R);
     59 
     60 // The built-in list
     61 static _cmsParametricCurvesCollection DefaultCurves = {
     62     9,                                  // # of curve types
     63     { 1, 2, 3, 4, 5, 6, 7, 8, 108 },    // Parametric curve ID
     64     { 1, 3, 4, 5, 7, 4, 5, 5, 1 },      // Parameters by type
     65     DefaultEvalParametricFn,            // Evaluator
     66     NULL                                // Next in chain
     67 };
     68 
     69 // Duplicates the zone of memory used by the plug-in in the new context
     70 static
     71 void DupPluginCurvesList(struct _cmsContext_struct* ctx,
     72                                                const struct _cmsContext_struct* src)
     73 {
     74    _cmsCurvesPluginChunkType newHead = { NULL };
     75    _cmsParametricCurvesCollection*  entry;
     76    _cmsParametricCurvesCollection*  Anterior = NULL;
     77    _cmsCurvesPluginChunkType* head = (_cmsCurvesPluginChunkType*) src->chunks[CurvesPlugin];
     78 
     79     _cmsAssert(head != NULL);
     80 
     81     // Walk the list copying all nodes
     82    for (entry = head->ParametricCurves;
     83         entry != NULL;
     84         entry = entry ->Next) {
     85 
     86             _cmsParametricCurvesCollection *newEntry = ( _cmsParametricCurvesCollection *) _cmsSubAllocDup(ctx ->MemPool, entry, sizeof(_cmsParametricCurvesCollection));
     87 
     88             if (newEntry == NULL)
     89                 return;
     90 
     91             // We want to keep the linked list order, so this is a little bit tricky
     92             newEntry -> Next = NULL;
     93             if (Anterior)
     94                 Anterior -> Next = newEntry;
     95 
     96             Anterior = newEntry;
     97 
     98             if (newHead.ParametricCurves == NULL)
     99                 newHead.ParametricCurves = newEntry;
    100     }
    101 
    102   ctx ->chunks[CurvesPlugin] = _cmsSubAllocDup(ctx->MemPool, &newHead, sizeof(_cmsCurvesPluginChunkType));
    103 }
    104 
    105 // The allocator have to follow the chain
    106 void _cmsAllocCurvesPluginChunk(struct _cmsContext_struct* ctx,
    107                                 const struct _cmsContext_struct* src)
    108 {
    109     _cmsAssert(ctx != NULL);
    110 
    111     if (src != NULL) {
    112 
    113         // Copy all linked list
    114        DupPluginCurvesList(ctx, src);
    115     }
    116     else {
    117         static _cmsCurvesPluginChunkType CurvesPluginChunk = { NULL };
    118         ctx ->chunks[CurvesPlugin] = _cmsSubAllocDup(ctx ->MemPool, &CurvesPluginChunk, sizeof(_cmsCurvesPluginChunkType));
    119     }
    120 }
    121 
    122 
    123 // The linked list head
    124 _cmsCurvesPluginChunkType _cmsCurvesPluginChunk = { NULL };
    125 
    126 // As a way to install new parametric curves
    127 cmsBool _cmsRegisterParametricCurvesPlugin(cmsContext ContextID, cmsPluginBase* Data)
    128 {
    129     _cmsCurvesPluginChunkType* ctx = ( _cmsCurvesPluginChunkType*) _cmsContextGetClientChunk(ContextID, CurvesPlugin);
    130     cmsPluginParametricCurves* Plugin = (cmsPluginParametricCurves*) Data;
    131     _cmsParametricCurvesCollection* fl;
    132 
    133     if (Data == NULL) {
    134 
    135           ctx -> ParametricCurves =  NULL;
    136           return TRUE;
    137     }
    138 
    139     fl = (_cmsParametricCurvesCollection*) _cmsPluginMalloc(ContextID, sizeof(_cmsParametricCurvesCollection));
    140     if (fl == NULL) return FALSE;
    141 
    142     // Copy the parameters
    143     fl ->Evaluator  = Plugin ->Evaluator;
    144     fl ->nFunctions = Plugin ->nFunctions;
    145 
    146     // Make sure no mem overwrites
    147     if (fl ->nFunctions > MAX_TYPES_IN_LCMS_PLUGIN)
    148         fl ->nFunctions = MAX_TYPES_IN_LCMS_PLUGIN;
    149 
    150     // Copy the data
    151     memmove(fl->FunctionTypes,  Plugin ->FunctionTypes,   fl->nFunctions * sizeof(cmsUInt32Number));
    152     memmove(fl->ParameterCount, Plugin ->ParameterCount,  fl->nFunctions * sizeof(cmsUInt32Number));
    153 
    154     // Keep linked list
    155     fl ->Next = ctx->ParametricCurves;
    156     ctx->ParametricCurves = fl;
    157 
    158     // All is ok
    159     return TRUE;
    160 }
    161 
    162 
    163 // Search in type list, return position or -1 if not found
    164 static
    165 int IsInSet(int Type, _cmsParametricCurvesCollection* c)
    166 {
    167     int i;
    168 
    169     for (i=0; i < c ->nFunctions; i++)
    170         if (abs(Type) == c ->FunctionTypes[i]) return i;
    171 
    172     return -1;
    173 }
    174 
    175 
    176 // Search for the collection which contains a specific type
    177 static
    178 _cmsParametricCurvesCollection *GetParametricCurveByType(cmsContext ContextID, int Type, int* index)
    179 {
    180     _cmsParametricCurvesCollection* c;
    181     int Position;
    182     _cmsCurvesPluginChunkType* ctx = ( _cmsCurvesPluginChunkType*) _cmsContextGetClientChunk(ContextID, CurvesPlugin);
    183 
    184     for (c = ctx->ParametricCurves; c != NULL; c = c ->Next) {
    185 
    186         Position = IsInSet(Type, c);
    187 
    188         if (Position != -1) {
    189             if (index != NULL)
    190                 *index = Position;
    191             return c;
    192         }
    193     }
    194     // If none found, revert for defaults
    195     for (c = &DefaultCurves; c != NULL; c = c ->Next) {
    196 
    197         Position = IsInSet(Type, c);
    198 
    199         if (Position != -1) {
    200             if (index != NULL)
    201                 *index = Position;
    202             return c;
    203         }
    204     }
    205 
    206     return NULL;
    207 }
    208 
    209 // Low level allocate, which takes care of memory details. nEntries may be zero, and in this case
    210 // no optimation curve is computed. nSegments may also be zero in the inverse case, where only the
    211 // optimization curve is given. Both features simultaneously is an error
    212 static
    213 cmsToneCurve* AllocateToneCurveStruct(cmsContext ContextID, cmsInt32Number nEntries,
    214                                       cmsInt32Number nSegments, const cmsCurveSegment* Segments,
    215                                       const cmsUInt16Number* Values)
    216 {
    217     cmsToneCurve* p;
    218     int i;
    219 
    220     // We allow huge tables, which are then restricted for smoothing operations
    221     if (nEntries > 65530 || nEntries < 0) {
    222         cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve of more than 65530 entries");
    223         return NULL;
    224     }
    225 
    226     if (nEntries <= 0 && nSegments <= 0) {
    227         cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve with zero segments and no table");
    228         return NULL;
    229     }
    230 
    231     // Allocate all required pointers, etc.
    232     p = (cmsToneCurve*) _cmsMallocZero(ContextID, sizeof(cmsToneCurve));
    233     if (!p) return NULL;
    234 
    235     // In this case, there are no segments
    236     if (nSegments <= 0) {
    237         p ->Segments = NULL;
    238         p ->Evals = NULL;
    239     }
    240     else {
    241         p ->Segments = (cmsCurveSegment*) _cmsCalloc(ContextID, nSegments, sizeof(cmsCurveSegment));
    242         if (p ->Segments == NULL) goto Error;
    243 
    244         p ->Evals    = (cmsParametricCurveEvaluator*) _cmsCalloc(ContextID, nSegments, sizeof(cmsParametricCurveEvaluator));
    245         if (p ->Evals == NULL) goto Error;
    246     }
    247 
    248     p -> nSegments = nSegments;
    249 
    250     // This 16-bit table contains a limited precision representation of the whole curve and is kept for
    251     // increasing xput on certain operations.
    252     if (nEntries <= 0) {
    253         p ->Table16 = NULL;
    254     }
    255     else {
    256        p ->Table16 = (cmsUInt16Number*)  _cmsCalloc(ContextID, nEntries, sizeof(cmsUInt16Number));
    257        if (p ->Table16 == NULL) goto Error;
    258     }
    259 
    260     p -> nEntries  = nEntries;
    261 
    262     // Initialize members if requested
    263     if (Values != NULL && (nEntries > 0)) {
    264 
    265         for (i=0; i < nEntries; i++)
    266             p ->Table16[i] = Values[i];
    267     }
    268 
    269     // Initialize the segments stuff. The evaluator for each segment is located and a pointer to it
    270     // is placed in advance to maximize performance.
    271     if (Segments != NULL && (nSegments > 0)) {
    272 
    273         _cmsParametricCurvesCollection *c;
    274 
    275         p ->SegInterp = (cmsInterpParams**) _cmsCalloc(ContextID, nSegments, sizeof(cmsInterpParams*));
    276         if (p ->SegInterp == NULL) goto Error;
    277 
    278         for (i=0; i< nSegments; i++) {
    279 
    280             // Type 0 is a special marker for table-based curves
    281             if (Segments[i].Type == 0)
    282                 p ->SegInterp[i] = _cmsComputeInterpParams(ContextID, Segments[i].nGridPoints, 1, 1, NULL, CMS_LERP_FLAGS_FLOAT);
    283 
    284             memmove(&p ->Segments[i], &Segments[i], sizeof(cmsCurveSegment));
    285 
    286             if (Segments[i].Type == 0 && Segments[i].SampledPoints != NULL)
    287                 p ->Segments[i].SampledPoints = (cmsFloat32Number*) _cmsDupMem(ContextID, Segments[i].SampledPoints, sizeof(cmsFloat32Number) * Segments[i].nGridPoints);
    288             else
    289                 p ->Segments[i].SampledPoints = NULL;
    290 
    291 
    292             c = GetParametricCurveByType(ContextID, Segments[i].Type, NULL);
    293             if (c != NULL)
    294                     p ->Evals[i] = c ->Evaluator;
    295         }
    296     }
    297 
    298     p ->InterpParams = _cmsComputeInterpParams(ContextID, p ->nEntries, 1, 1, p->Table16, CMS_LERP_FLAGS_16BITS);
    299     if (p->InterpParams != NULL)
    300         return p;
    301 
    302 Error:
    303     if (p -> Segments) _cmsFree(ContextID, p ->Segments);
    304     if (p -> Evals) _cmsFree(ContextID, p -> Evals);
    305     if (p ->Table16) _cmsFree(ContextID, p ->Table16);
    306     _cmsFree(ContextID, p);
    307     return NULL;
    308 }
    309 
    310 
    311 // Parametric Fn using floating point
    312 static
    313 cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R)
    314 {
    315     cmsFloat64Number e, Val, disc;
    316 
    317     switch (Type) {
    318 
    319    // X = Y ^ Gamma
    320     case 1:
    321         if (R < 0) {
    322 
    323             if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
    324                 Val = R;
    325             else
    326                 Val = 0;
    327         }
    328         else
    329             Val = pow(R, Params[0]);
    330         break;
    331 
    332     // Type 1 Reversed: X = Y ^1/gamma
    333     case -1:
    334          if (R < 0) {
    335 
    336             if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
    337                 Val = R;
    338             else
    339                 Val = 0;
    340         }
    341         else
    342             Val = pow(R, 1/Params[0]);
    343         break;
    344 
    345     // CIE 122-1966
    346     // Y = (aX + b)^Gamma  | X >= -b/a
    347     // Y = 0               | else
    348     case 2:
    349         disc = -Params[2] / Params[1];
    350 
    351         if (R >= disc ) {
    352 
    353             e = Params[1]*R + Params[2];
    354 
    355             if (e > 0)
    356                 Val = pow(e, Params[0]);
    357             else
    358                 Val = 0;
    359         }
    360         else
    361             Val = 0;
    362         break;
    363 
    364      // Type 2 Reversed
    365      // X = (Y ^1/g  - b) / a
    366      case -2:
    367          if (R < 0)
    368              Val = 0;
    369          else
    370              Val = (pow(R, 1.0/Params[0]) - Params[2]) / Params[1];
    371 
    372          if (Val < 0)
    373               Val = 0;
    374          break;
    375 
    376 
    377     // IEC 61966-3
    378     // Y = (aX + b)^Gamma | X <= -b/a
    379     // Y = c              | else
    380     case 3:
    381         disc = -Params[2] / Params[1];
    382         if (disc < 0)
    383             disc = 0;
    384 
    385         if (R >= disc) {
    386 
    387             e = Params[1]*R + Params[2];
    388 
    389             if (e > 0)
    390                 Val = pow(e, Params[0]) + Params[3];
    391             else
    392                 Val = 0;
    393         }
    394         else
    395             Val = Params[3];
    396         break;
    397 
    398 
    399     // Type 3 reversed
    400     // X=((Y-c)^1/g - b)/a      | (Y>=c)
    401     // X=-b/a                   | (Y<c)
    402     case -3:
    403         if (R >= Params[3])  {
    404 
    405             e = R - Params[3];
    406 
    407             if (e > 0)
    408                 Val = (pow(e, 1/Params[0]) - Params[2]) / Params[1];
    409             else
    410                 Val = 0;
    411         }
    412         else {
    413             Val = -Params[2] / Params[1];
    414         }
    415         break;
    416 
    417 
    418     // IEC 61966-2.1 (sRGB)
    419     // Y = (aX + b)^Gamma | X >= d
    420     // Y = cX             | X < d
    421     case 4:
    422         if (R >= Params[4]) {
    423 
    424             e = Params[1]*R + Params[2];
    425 
    426             if (e > 0)
    427                 Val = pow(e, Params[0]);
    428             else
    429                 Val = 0;
    430         }
    431         else
    432             Val = R * Params[3];
    433         break;
    434 
    435     // Type 4 reversed
    436     // X=((Y^1/g-b)/a)    | Y >= (ad+b)^g
    437     // X=Y/c              | Y< (ad+b)^g
    438     case -4:
    439         e = Params[1] * Params[4] + Params[2];
    440         if (e < 0)
    441             disc = 0;
    442         else
    443             disc = pow(e, Params[0]);
    444 
    445         if (R >= disc) {
    446 
    447             Val = (pow(R, 1.0/Params[0]) - Params[2]) / Params[1];
    448         }
    449         else {
    450             Val = R / Params[3];
    451         }
    452         break;
    453 
    454 
    455     // Y = (aX + b)^Gamma + e | X >= d
    456     // Y = cX + f             | X < d
    457     case 5:
    458         if (R >= Params[4]) {
    459 
    460             e = Params[1]*R + Params[2];
    461 
    462             if (e > 0)
    463                 Val = pow(e, Params[0]) + Params[5];
    464             else
    465                 Val = Params[5];
    466         }
    467         else
    468             Val = R*Params[3] + Params[6];
    469         break;
    470 
    471 
    472     // Reversed type 5
    473     // X=((Y-e)1/g-b)/a   | Y >=(ad+b)^g+e), cd+f
    474     // X=(Y-f)/c          | else
    475     case -5:
    476 
    477         disc = Params[3] * Params[4] + Params[6];
    478         if (R >= disc) {
    479 
    480             e = R - Params[5];
    481             if (e < 0)
    482                 Val = 0;
    483             else
    484                 Val = (pow(e, 1.0/Params[0]) - Params[2]) / Params[1];
    485         }
    486         else {
    487             Val = (R - Params[6]) / Params[3];
    488         }
    489         break;
    490 
    491 
    492     // Types 6,7,8 comes from segmented curves as described in ICCSpecRevision_02_11_06_Float.pdf
    493     // Type 6 is basically identical to type 5 without d
    494 
    495     // Y = (a * X + b) ^ Gamma + c
    496     case 6:
    497         e = Params[1]*R + Params[2];
    498 
    499         if (e < 0)
    500             Val = Params[3];
    501         else
    502             Val = pow(e, Params[0]) + Params[3];
    503         break;
    504 
    505     // ((Y - c) ^1/Gamma - b) / a
    506     case -6:
    507         e = R - Params[3];
    508         if (e < 0)
    509             Val = 0;
    510         else
    511         Val = (pow(e, 1.0/Params[0]) - Params[2]) / Params[1];
    512         break;
    513 
    514 
    515     // Y = a * log (b * X^Gamma + c) + d
    516     case 7:
    517 
    518        e = Params[2] * pow(R, Params[0]) + Params[3];
    519        if (e <= 0)
    520            Val = Params[4];
    521        else
    522            Val = Params[1]*log10(e) + Params[4];
    523        break;
    524 
    525     // (Y - d) / a = log(b * X ^Gamma + c)
    526     // pow(10, (Y-d) / a) = b * X ^Gamma + c
    527     // pow((pow(10, (Y-d) / a) - c) / b, 1/g) = X
    528     case -7:
    529        Val = pow((pow(10.0, (R-Params[4]) / Params[1]) - Params[3]) / Params[2], 1.0 / Params[0]);
    530        break;
    531 
    532 
    533    //Y = a * b^(c*X+d) + e
    534    case 8:
    535        Val = (Params[0] * pow(Params[1], Params[2] * R + Params[3]) + Params[4]);
    536        break;
    537 
    538 
    539    // Y = (log((y-e) / a) / log(b) - d ) / c
    540    // a=0, b=1, c=2, d=3, e=4,
    541    case -8:
    542 
    543        disc = R - Params[4];
    544        if (disc < 0) Val = 0;
    545        else
    546            Val = (log(disc / Params[0]) / log(Params[1]) - Params[3]) / Params[2];
    547        break;
    548 
    549    // S-Shaped: (1 - (1-x)^1/g)^1/g
    550    case 108:
    551       Val = pow(1.0 - pow(1 - R, 1/Params[0]), 1/Params[0]);
    552       break;
    553 
    554     // y = (1 - (1-x)^1/g)^1/g
    555     // y^g = (1 - (1-x)^1/g)
    556     // 1 - y^g = (1-x)^1/g
    557     // (1 - y^g)^g = 1 - x
    558     // 1 - (1 - y^g)^g
    559     case -108:
    560         Val = 1 - pow(1 - pow(R, Params[0]), Params[0]);
    561         break;
    562 
    563     default:
    564         // Unsupported parametric curve. Should never reach here
    565         return 0;
    566     }
    567 
    568     return Val;
    569 }
    570 
    571 // Evaluate a segmented funtion for a single value. Return -1 if no valid segment found .
    572 // If fn type is 0, perform an interpolation on the table
    573 static
    574 cmsFloat64Number EvalSegmentedFn(const cmsToneCurve *g, cmsFloat64Number R)
    575 {
    576     int i;
    577 
    578     for (i = g ->nSegments-1; i >= 0 ; --i) {
    579 
    580         // Check for domain
    581         if ((R > g ->Segments[i].x0) && (R <= g ->Segments[i].x1)) {
    582 
    583             // Type == 0 means segment is sampled
    584             if (g ->Segments[i].Type == 0) {
    585 
    586                 cmsFloat32Number R1 = (cmsFloat32Number) (R - g ->Segments[i].x0) / (g ->Segments[i].x1 - g ->Segments[i].x0);
    587                 cmsFloat32Number Out;
    588 
    589                 // Setup the table (TODO: clean that)
    590                 g ->SegInterp[i]-> Table = g ->Segments[i].SampledPoints;
    591 
    592                 g ->SegInterp[i] -> Interpolation.LerpFloat(&R1, &Out, g ->SegInterp[i]);
    593 
    594                 return Out;
    595             }
    596             else
    597                 return g ->Evals[i](g->Segments[i].Type, g ->Segments[i].Params, R);
    598         }
    599     }
    600 
    601     return MINUS_INF;
    602 }
    603 
    604 // Access to estimated low-res table
    605 cmsUInt32Number CMSEXPORT cmsGetToneCurveEstimatedTableEntries(const cmsToneCurve* t)
    606 {
    607     _cmsAssert(t != NULL);
    608     return t ->nEntries;
    609 }
    610 
    611 const cmsUInt16Number* CMSEXPORT cmsGetToneCurveEstimatedTable(const cmsToneCurve* t)
    612 {
    613     _cmsAssert(t != NULL);
    614     return t ->Table16;
    615 }
    616 
    617 
    618 // Create an empty gamma curve, by using tables. This specifies only the limited-precision part, and leaves the
    619 // floating point description empty.
    620 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurve16(cmsContext ContextID, cmsInt32Number nEntries, const cmsUInt16Number Values[])
    621 {
    622     return AllocateToneCurveStruct(ContextID, nEntries, 0, NULL, Values);
    623 }
    624 
    625 static
    626 int EntriesByGamma(cmsFloat64Number Gamma)
    627 {
    628     if (fabs(Gamma - 1.0) < 0.001) return 2;
    629     return 4096;
    630 }
    631 
    632 
    633 // Create a segmented gamma, fill the table
    634 cmsToneCurve* CMSEXPORT cmsBuildSegmentedToneCurve(cmsContext ContextID,
    635                                                    cmsInt32Number nSegments, const cmsCurveSegment Segments[])
    636 {
    637     int i;
    638     cmsFloat64Number R, Val;
    639     cmsToneCurve* g;
    640     int nGridPoints = 4096;
    641 
    642     _cmsAssert(Segments != NULL);
    643 
    644     // Optimizatin for identity curves.
    645     if (nSegments == 1 && Segments[0].Type == 1) {
    646 
    647         nGridPoints = EntriesByGamma(Segments[0].Params[0]);
    648     }
    649 
    650     g = AllocateToneCurveStruct(ContextID, nGridPoints, nSegments, Segments, NULL);
    651     if (g == NULL) return NULL;
    652 
    653     // Once we have the floating point version, we can approximate a 16 bit table of 4096 entries
    654     // for performance reasons. This table would normally not be used except on 8/16 bits transforms.
    655     for (i=0; i < nGridPoints; i++) {
    656 
    657         R   = (cmsFloat64Number) i / (nGridPoints-1);
    658 
    659         Val = EvalSegmentedFn(g, R);
    660 
    661         // Round and saturate
    662         g ->Table16[i] = _cmsQuickSaturateWord(Val * 65535.0);
    663     }
    664 
    665     return g;
    666 }
    667 
    668 // Use a segmented curve to store the floating point table
    669 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurveFloat(cmsContext ContextID, cmsUInt32Number nEntries, const cmsFloat32Number values[])
    670 {
    671     cmsCurveSegment Seg[3];
    672 
    673     // A segmented tone curve should have function segments in the first and last positions
    674     // Initialize segmented curve part up to 0 to constant value = samples[0]
    675     Seg[0].x0 = MINUS_INF;
    676     Seg[0].x1 = 0;
    677     Seg[0].Type = 6;
    678 
    679     Seg[0].Params[0] = 1;
    680     Seg[0].Params[1] = 0;
    681     Seg[0].Params[2] = 0;
    682     Seg[0].Params[3] = values[0];
    683     Seg[0].Params[4] = 0;
    684 
    685     // From zero to 1
    686     Seg[1].x0 = 0;
    687     Seg[1].x1 = 1.0;
    688     Seg[1].Type = 0;
    689 
    690     Seg[1].nGridPoints = nEntries;
    691     Seg[1].SampledPoints = (cmsFloat32Number*) values;
    692 
    693     // Final segment is constant = lastsample
    694     Seg[2].x0 = 1.0;
    695     Seg[2].x1 = PLUS_INF;
    696     Seg[2].Type = 6;
    697 
    698     Seg[2].Params[0] = 1;
    699     Seg[2].Params[1] = 0;
    700     Seg[2].Params[2] = 0;
    701     Seg[2].Params[3] = values[nEntries-1];
    702     Seg[2].Params[4] = 0;
    703 
    704 
    705     return cmsBuildSegmentedToneCurve(ContextID, 3, Seg);
    706 }
    707 
    708 // Parametric curves
    709 //
    710 // Parameters goes as: Curve, a, b, c, d, e, f
    711 // Type is the ICC type +1
    712 // if type is negative, then the curve is analyticaly inverted
    713 cmsToneCurve* CMSEXPORT cmsBuildParametricToneCurve(cmsContext ContextID, cmsInt32Number Type, const cmsFloat64Number Params[])
    714 {
    715     cmsCurveSegment Seg0;
    716     int Pos = 0;
    717     cmsUInt32Number size;
    718     _cmsParametricCurvesCollection* c = GetParametricCurveByType(ContextID, Type, &Pos);
    719 
    720     _cmsAssert(Params != NULL);
    721 
    722     if (c == NULL) {
    723         cmsSignalError(ContextID, cmsERROR_UNKNOWN_EXTENSION, "Invalid parametric curve type %d", Type);
    724         return NULL;
    725     }
    726 
    727     memset(&Seg0, 0, sizeof(Seg0));
    728 
    729     Seg0.x0   = MINUS_INF;
    730     Seg0.x1   = PLUS_INF;
    731     Seg0.Type = Type;
    732 
    733     size = c->ParameterCount[Pos] * sizeof(cmsFloat64Number);
    734     memmove(Seg0.Params, Params, size);
    735 
    736     return cmsBuildSegmentedToneCurve(ContextID, 1, &Seg0);
    737 }
    738 
    739 
    740 
    741 // Build a gamma table based on gamma constant
    742 cmsToneCurve* CMSEXPORT cmsBuildGamma(cmsContext ContextID, cmsFloat64Number Gamma)
    743 {
    744     return cmsBuildParametricToneCurve(ContextID, 1, &Gamma);
    745 }
    746 
    747 
    748 // Free all memory taken by the gamma curve
    749 void CMSEXPORT cmsFreeToneCurve(cmsToneCurve* Curve)
    750 {
    751     cmsContext ContextID;
    752 
    753 	// added by Xiaochuan Liu
    754 	// Curve->InterpParams may be null
    755     if (Curve == NULL || Curve->InterpParams == NULL) return;
    756 
    757     ContextID = Curve ->InterpParams->ContextID;
    758 
    759     _cmsFreeInterpParams(Curve ->InterpParams);
    760 	Curve ->InterpParams = NULL;
    761 
    762     if (Curve -> Table16)
    763 	{
    764         _cmsFree(ContextID, Curve ->Table16);
    765 		Curve ->Table16 = NULL;
    766 	}
    767 
    768     if (Curve ->Segments) {
    769 
    770         cmsUInt32Number i;
    771 
    772         for (i=0; i < Curve ->nSegments; i++) {
    773 
    774             if (Curve ->Segments[i].SampledPoints) {
    775                 _cmsFree(ContextID, Curve ->Segments[i].SampledPoints);
    776 				Curve ->Segments[i].SampledPoints = NULL;
    777             }
    778 
    779             if (Curve ->SegInterp[i] != 0)
    780 			{
    781                 _cmsFreeInterpParams(Curve->SegInterp[i]);
    782 				Curve->SegInterp[i] = NULL;
    783 			}
    784         }
    785 
    786         _cmsFree(ContextID, Curve ->Segments);
    787 		Curve ->Segments = NULL;
    788         _cmsFree(ContextID, Curve ->SegInterp);
    789 		Curve ->SegInterp = NULL;
    790     }
    791 
    792     if (Curve -> Evals)
    793 	{
    794         _cmsFree(ContextID, Curve -> Evals);
    795 		Curve -> Evals = NULL;
    796 	}
    797 
    798     if (Curve)
    799 	{
    800 		_cmsFree(ContextID, Curve);
    801 		Curve = NULL;
    802 	}
    803 }
    804 
    805 // Utility function, free 3 gamma tables
    806 void CMSEXPORT cmsFreeToneCurveTriple(cmsToneCurve* Curve[3])
    807 {
    808 
    809     _cmsAssert(Curve != NULL);
    810 
    811     if (Curve[0] != NULL) cmsFreeToneCurve(Curve[0]);
    812     if (Curve[1] != NULL) cmsFreeToneCurve(Curve[1]);
    813     if (Curve[2] != NULL) cmsFreeToneCurve(Curve[2]);
    814 
    815     Curve[0] = Curve[1] = Curve[2] = NULL;
    816 }
    817 
    818 
    819 // Duplicate a gamma table
    820 cmsToneCurve* CMSEXPORT cmsDupToneCurve(const cmsToneCurve* In)
    821 {
    822 	// Xiaochuan Liu
    823 	// fix openpdf bug(mantis id:0055683, google id:360198)
    824 	// the function CurveSetElemTypeFree in cmslut.c also needs to check pointer
    825     if (In == NULL || In ->InterpParams == NULL) return NULL;
    826 
    827     return  AllocateToneCurveStruct(In ->InterpParams ->ContextID, In ->nEntries, In ->nSegments, In ->Segments, In ->Table16);
    828 }
    829 
    830 // Joins two curves for X and Y. Curves should be monotonic.
    831 // We want to get
    832 //
    833 //      y = Y^-1(X(t))
    834 //
    835 cmsToneCurve* CMSEXPORT cmsJoinToneCurve(cmsContext ContextID,
    836                                       const cmsToneCurve* X,
    837                                       const cmsToneCurve* Y, cmsUInt32Number nResultingPoints)
    838 {
    839     cmsToneCurve* out = NULL;
    840     cmsToneCurve* Yreversed = NULL;
    841     cmsFloat32Number t, x;
    842     cmsFloat32Number* Res = NULL;
    843     cmsUInt32Number i;
    844 
    845 
    846     _cmsAssert(X != NULL);
    847     _cmsAssert(Y != NULL);
    848 
    849     Yreversed = cmsReverseToneCurveEx(nResultingPoints, Y);
    850     if (Yreversed == NULL) goto Error;
    851 
    852     Res = (cmsFloat32Number*) _cmsCalloc(ContextID, nResultingPoints, sizeof(cmsFloat32Number));
    853     if (Res == NULL) goto Error;
    854 
    855     //Iterate
    856     for (i=0; i <  nResultingPoints; i++) {
    857 
    858         t = (cmsFloat32Number) i / (nResultingPoints-1);
    859         x = cmsEvalToneCurveFloat(X,  t);
    860         Res[i] = cmsEvalToneCurveFloat(Yreversed, x);
    861     }
    862 
    863     // Allocate space for output
    864     out = cmsBuildTabulatedToneCurveFloat(ContextID, nResultingPoints, Res);
    865 
    866 Error:
    867 
    868     if (Res != NULL) _cmsFree(ContextID, Res);
    869     if (Yreversed != NULL) cmsFreeToneCurve(Yreversed);
    870 
    871     return out;
    872 }
    873 
    874 
    875 
    876 // Get the surrounding nodes. This is tricky on non-monotonic tables
    877 static
    878 int GetInterval(cmsFloat64Number In, const cmsUInt16Number LutTable[], const struct _cms_interp_struc* p)
    879 {
    880     int i;
    881     int y0, y1;
    882 
    883     // A 1 point table is not allowed
    884     if (p -> Domain[0] < 1) return -1;
    885 
    886     // Let's see if ascending or descending.
    887     if (LutTable[0] < LutTable[p ->Domain[0]]) {
    888 
    889         // Table is overall ascending
    890         for (i=p->Domain[0]-1; i >=0; --i) {
    891 
    892             y0 = LutTable[i];
    893             y1 = LutTable[i+1];
    894 
    895             if (y0 <= y1) { // Increasing
    896                 if (In >= y0 && In <= y1) return i;
    897             }
    898             else
    899                 if (y1 < y0) { // Decreasing
    900                     if (In >= y1 && In <= y0) return i;
    901                 }
    902         }
    903     }
    904     else {
    905         // Table is overall descending
    906         for (i=0; i < (int) p -> Domain[0]; i++) {
    907 
    908             y0 = LutTable[i];
    909             y1 = LutTable[i+1];
    910 
    911             if (y0 <= y1) { // Increasing
    912                 if (In >= y0 && In <= y1) return i;
    913             }
    914             else
    915                 if (y1 < y0) { // Decreasing
    916                     if (In >= y1 && In <= y0) return i;
    917                 }
    918         }
    919     }
    920 
    921     return -1;
    922 }
    923 
    924 // Reverse a gamma table
    925 cmsToneCurve* CMSEXPORT cmsReverseToneCurveEx(cmsInt32Number nResultSamples, const cmsToneCurve* InCurve)
    926 {
    927     cmsToneCurve *out;
    928     cmsFloat64Number a = 0, b = 0, y, x1, y1, x2, y2;
    929     int i, j;
    930     int Ascending;
    931 
    932     _cmsAssert(InCurve != NULL);
    933 
    934     // Try to reverse it analytically whatever possible
    935 
    936     if (InCurve ->nSegments == 1 && InCurve ->Segments[0].Type > 0 &&
    937         /* InCurve -> Segments[0].Type <= 5 */
    938         GetParametricCurveByType(InCurve ->InterpParams->ContextID, InCurve ->Segments[0].Type, NULL) != NULL) {
    939 
    940         return cmsBuildParametricToneCurve(InCurve ->InterpParams->ContextID,
    941                                        -(InCurve -> Segments[0].Type),
    942                                        InCurve -> Segments[0].Params);
    943     }
    944 
    945     // Nope, reverse the table.
    946     out = cmsBuildTabulatedToneCurve16(InCurve ->InterpParams->ContextID, nResultSamples, NULL);
    947     if (out == NULL)
    948         return NULL;
    949 
    950     // We want to know if this is an ascending or descending table
    951     Ascending = !cmsIsToneCurveDescending(InCurve);
    952 
    953     // Iterate across Y axis
    954     for (i=0; i <  nResultSamples; i++) {
    955 
    956         y = (cmsFloat64Number) i * 65535.0 / (nResultSamples - 1);
    957 
    958         // Find interval in which y is within.
    959         j = GetInterval(y, InCurve->Table16, InCurve->InterpParams);
    960         if (j >= 0) {
    961 
    962 
    963             // Get limits of interval
    964             x1 = InCurve ->Table16[j];
    965             x2 = InCurve ->Table16[j+1];
    966 
    967             y1 = (cmsFloat64Number) (j * 65535.0) / (InCurve ->nEntries - 1);
    968             y2 = (cmsFloat64Number) ((j+1) * 65535.0 ) / (InCurve ->nEntries - 1);
    969 
    970             // If collapsed, then use any
    971             if (x1 == x2) {
    972 
    973                 out ->Table16[i] = _cmsQuickSaturateWord(Ascending ? y2 : y1);
    974                 continue;
    975 
    976             } else {
    977 
    978                 // Interpolate
    979                 a = (y2 - y1) / (x2 - x1);
    980                 b = y2 - a * x2;
    981             }
    982         }
    983 
    984         out ->Table16[i] = _cmsQuickSaturateWord(a* y + b);
    985     }
    986 
    987 
    988     return out;
    989 }
    990 
    991 // Reverse a gamma table
    992 cmsToneCurve* CMSEXPORT cmsReverseToneCurve(const cmsToneCurve* InGamma)
    993 {
    994     _cmsAssert(InGamma != NULL);
    995 
    996     return cmsReverseToneCurveEx(4096, InGamma);
    997 }
    998 
    999 // From: Eilers, P.H.C. (1994) Smoothing and interpolation with finite
   1000 // differences. in: Graphic Gems IV, Heckbert, P.S. (ed.), Academic press.
   1001 //
   1002 // Smoothing and interpolation with second differences.
   1003 //
   1004 //   Input:  weights (w), data (y): vector from 1 to m.
   1005 //   Input:  smoothing parameter (lambda), length (m).
   1006 //   Output: smoothed vector (z): vector from 1 to m.
   1007 
   1008 static
   1009 cmsBool smooth2(cmsContext ContextID, cmsFloat32Number w[], cmsFloat32Number y[], cmsFloat32Number z[], cmsFloat32Number lambda, int m)
   1010 {
   1011     int i, i1, i2;
   1012     cmsFloat32Number *c, *d, *e;
   1013     cmsBool st;
   1014 
   1015 
   1016     c = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
   1017     d = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
   1018     e = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
   1019 
   1020     if (c != NULL && d != NULL && e != NULL) {
   1021 
   1022 
   1023     d[1] = w[1] + lambda;
   1024     c[1] = -2 * lambda / d[1];
   1025     e[1] = lambda /d[1];
   1026     z[1] = w[1] * y[1];
   1027     d[2] = w[2] + 5 * lambda - d[1] * c[1] *  c[1];
   1028     c[2] = (-4 * lambda - d[1] * c[1] * e[1]) / d[2];
   1029     e[2] = lambda / d[2];
   1030     z[2] = w[2] * y[2] - c[1] * z[1];
   1031 
   1032     for (i = 3; i < m - 1; i++) {
   1033         i1 = i - 1; i2 = i - 2;
   1034         d[i]= w[i] + 6 * lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
   1035         c[i] = (-4 * lambda -d[i1] * c[i1] * e[i1])/ d[i];
   1036         e[i] = lambda / d[i];
   1037         z[i] = w[i] * y[i] - c[i1] * z[i1] - e[i2] * z[i2];
   1038     }
   1039 
   1040     i1 = m - 2; i2 = m - 3;
   1041 
   1042     d[m - 1] = w[m - 1] + 5 * lambda -c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
   1043     c[m - 1] = (-2 * lambda - d[i1] * c[i1] * e[i1]) / d[m - 1];
   1044     z[m - 1] = w[m - 1] * y[m - 1] - c[i1] * z[i1] - e[i2] * z[i2];
   1045     i1 = m - 1; i2 = m - 2;
   1046 
   1047     d[m] = w[m] + lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
   1048     z[m] = (w[m] * y[m] - c[i1] * z[i1] - e[i2] * z[i2]) / d[m];
   1049     z[m - 1] = z[m - 1] / d[m - 1] - c[m - 1] * z[m];
   1050 
   1051     for (i = m - 2; 1<= i; i--)
   1052         z[i] = z[i] / d[i] - c[i] * z[i + 1] - e[i] * z[i + 2];
   1053 
   1054       st = TRUE;
   1055     }
   1056     else st = FALSE;
   1057 
   1058     if (c != NULL) _cmsFree(ContextID, c);
   1059     if (d != NULL) _cmsFree(ContextID, d);
   1060     if (e != NULL) _cmsFree(ContextID, e);
   1061 
   1062     return st;
   1063 }
   1064 
   1065 // Smooths a curve sampled at regular intervals.
   1066 cmsBool  CMSEXPORT cmsSmoothToneCurve(cmsToneCurve* Tab, cmsFloat64Number lambda)
   1067 {
   1068     cmsFloat32Number w[MAX_NODES_IN_CURVE], y[MAX_NODES_IN_CURVE], z[MAX_NODES_IN_CURVE];
   1069     int i, nItems, Zeros, Poles;
   1070 
   1071     if (Tab == NULL) return FALSE;
   1072 
   1073     if (cmsIsToneCurveLinear(Tab)) return TRUE; // Nothing to do
   1074 
   1075     nItems = Tab -> nEntries;
   1076 
   1077     if (nItems >= MAX_NODES_IN_CURVE) {
   1078         cmsSignalError(Tab ->InterpParams->ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: too many points.");
   1079         return FALSE;
   1080     }
   1081 
   1082     memset(w, 0, nItems * sizeof(cmsFloat32Number));
   1083     memset(y, 0, nItems * sizeof(cmsFloat32Number));
   1084     memset(z, 0, nItems * sizeof(cmsFloat32Number));
   1085 
   1086     for (i=0; i < nItems; i++)
   1087     {
   1088         y[i+1] = (cmsFloat32Number) Tab -> Table16[i];
   1089         w[i+1] = 1.0;
   1090     }
   1091 
   1092     if (!smooth2(Tab ->InterpParams->ContextID, w, y, z, (cmsFloat32Number) lambda, nItems)) return FALSE;
   1093 
   1094     // Do some reality - checking...
   1095     Zeros = Poles = 0;
   1096     for (i=nItems; i > 1; --i) {
   1097 
   1098         if (z[i] == 0.) Zeros++;
   1099         if (z[i] >= 65535.) Poles++;
   1100         if (z[i] < z[i-1]) {
   1101             cmsSignalError(Tab ->InterpParams->ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Non-Monotonic.");
   1102             return FALSE;
   1103         }
   1104     }
   1105 
   1106     if (Zeros > (nItems / 3)) {
   1107         cmsSignalError(Tab ->InterpParams->ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly zeros.");
   1108         return FALSE;
   1109     }
   1110     if (Poles > (nItems / 3)) {
   1111         cmsSignalError(Tab ->InterpParams->ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly poles.");
   1112         return FALSE;
   1113     }
   1114 
   1115     // Seems ok
   1116     for (i=0; i < nItems; i++) {
   1117 
   1118         // Clamp to cmsUInt16Number
   1119         Tab -> Table16[i] = _cmsQuickSaturateWord(z[i+1]);
   1120     }
   1121 
   1122     return TRUE;
   1123 }
   1124 
   1125 // Is a table linear? Do not use parametric since we cannot guarantee some weird parameters resulting
   1126 // in a linear table. This way assures it is linear in 12 bits, which should be enought in most cases.
   1127 cmsBool CMSEXPORT cmsIsToneCurveLinear(const cmsToneCurve* Curve)
   1128 {
   1129     cmsUInt32Number i;
   1130     int diff;
   1131 
   1132     _cmsAssert(Curve != NULL);
   1133 
   1134     for (i=0; i < Curve ->nEntries; i++) {
   1135 
   1136         diff = abs((int) Curve->Table16[i] - (int) _cmsQuantizeVal(i, Curve ->nEntries));
   1137         if (diff > 0x0f)
   1138             return FALSE;
   1139     }
   1140 
   1141     return TRUE;
   1142 }
   1143 
   1144 // Same, but for monotonicity
   1145 cmsBool  CMSEXPORT cmsIsToneCurveMonotonic(const cmsToneCurve* t)
   1146 {
   1147     int n;
   1148     int i, last;
   1149     cmsBool lDescending;
   1150 
   1151     _cmsAssert(t != NULL);
   1152 
   1153     // Degenerated curves are monotonic? Ok, let's pass them
   1154     n = t ->nEntries;
   1155     if (n < 2) return TRUE;
   1156 
   1157     // Curve direction
   1158     lDescending = cmsIsToneCurveDescending(t);
   1159 
   1160     if (lDescending) {
   1161 
   1162         last = t ->Table16[0];
   1163 
   1164         for (i = 1; i < n; i++) {
   1165 
   1166             if (t ->Table16[i] - last > 2) // We allow some ripple
   1167                 return FALSE;
   1168             else
   1169                 last = t ->Table16[i];
   1170 
   1171         }
   1172     }
   1173     else {
   1174 
   1175         last = t ->Table16[n-1];
   1176 
   1177         for (i = n-2; i >= 0; --i) {
   1178 
   1179             if (t ->Table16[i] - last > 2)
   1180                 return FALSE;
   1181             else
   1182                 last = t ->Table16[i];
   1183 
   1184         }
   1185     }
   1186 
   1187     return TRUE;
   1188 }
   1189 
   1190 // Same, but for descending tables
   1191 cmsBool  CMSEXPORT cmsIsToneCurveDescending(const cmsToneCurve* t)
   1192 {
   1193     _cmsAssert(t != NULL);
   1194 
   1195     return t ->Table16[0] > t ->Table16[t ->nEntries-1];
   1196 }
   1197 
   1198 
   1199 // Another info fn: is out gamma table multisegment?
   1200 cmsBool  CMSEXPORT cmsIsToneCurveMultisegment(const cmsToneCurve* t)
   1201 {
   1202     _cmsAssert(t != NULL);
   1203 
   1204     return t -> nSegments > 1;
   1205 }
   1206 
   1207 cmsInt32Number  CMSEXPORT cmsGetToneCurveParametricType(const cmsToneCurve* t)
   1208 {
   1209     _cmsAssert(t != NULL);
   1210 
   1211     if (t -> nSegments != 1) return 0;
   1212     return t ->Segments[0].Type;
   1213 }
   1214 
   1215 // We need accuracy this time
   1216 cmsFloat32Number CMSEXPORT cmsEvalToneCurveFloat(const cmsToneCurve* Curve, cmsFloat32Number v)
   1217 {
   1218     _cmsAssert(Curve != NULL);
   1219 
   1220     // Check for 16 bits table. If so, this is a limited-precision tone curve
   1221     if (Curve ->nSegments == 0) {
   1222 
   1223         cmsUInt16Number In, Out;
   1224 
   1225         In = (cmsUInt16Number) _cmsQuickSaturateWord(v * 65535.0);
   1226         Out = cmsEvalToneCurve16(Curve, In);
   1227 
   1228         return (cmsFloat32Number) (Out / 65535.0);
   1229     }
   1230 
   1231     return (cmsFloat32Number) EvalSegmentedFn(Curve, v);
   1232 }
   1233 
   1234 // We need xput over here
   1235 cmsUInt16Number CMSEXPORT cmsEvalToneCurve16(const cmsToneCurve* Curve, cmsUInt16Number v)
   1236 {
   1237     cmsUInt16Number out;
   1238 
   1239     _cmsAssert(Curve != NULL);
   1240 
   1241     Curve ->InterpParams ->Interpolation.Lerp16(&v, &out, Curve ->InterpParams);
   1242     return out;
   1243 }
   1244 
   1245 
   1246 // Least squares fitting.
   1247 // A mathematical procedure for finding the best-fitting curve to a given set of points by
   1248 // minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve.
   1249 // The sum of the squares of the offsets is used instead of the offset absolute values because
   1250 // this allows the residuals to be treated as a continuous differentiable quantity.
   1251 //
   1252 // y = f(x) = x ^ g
   1253 //
   1254 // R  = (yi - (xi^g))
   1255 // R2 = (yi - (xi^g))2
   1256 // SUM R2 = SUM (yi - (xi^g))2
   1257 //
   1258 // dR2/dg = -2 SUM x^g log(x)(y - x^g)
   1259 // solving for dR2/dg = 0
   1260 //
   1261 // g = 1/n * SUM(log(y) / log(x))
   1262 
   1263 cmsFloat64Number CMSEXPORT cmsEstimateGamma(const cmsToneCurve* t, cmsFloat64Number Precision)
   1264 {
   1265     cmsFloat64Number gamma, sum, sum2;
   1266     cmsFloat64Number n, x, y, Std;
   1267     cmsUInt32Number i;
   1268 
   1269     _cmsAssert(t != NULL);
   1270 
   1271     sum = sum2 = n = 0;
   1272 
   1273     // Excluding endpoints
   1274     for (i=1; i < (MAX_NODES_IN_CURVE-1); i++) {
   1275 
   1276         x = (cmsFloat64Number) i / (MAX_NODES_IN_CURVE-1);
   1277         y = (cmsFloat64Number) cmsEvalToneCurveFloat(t, (cmsFloat32Number) x);
   1278 
   1279         // Avoid 7% on lower part to prevent
   1280         // artifacts due to linear ramps
   1281 
   1282         if (y > 0. && y < 1. && x > 0.07) {
   1283 
   1284             gamma = log(y) / log(x);
   1285             sum  += gamma;
   1286             sum2 += gamma * gamma;
   1287             n++;
   1288         }
   1289     }
   1290 
   1291     // Take a look on SD to see if gamma isn't exponential at all
   1292     Std = sqrt((n * sum2 - sum * sum) / (n*(n-1)));
   1293 
   1294     if (Std > Precision)
   1295         return -1.0;
   1296 
   1297     return (sum / n);   // The mean
   1298 }
   1299