libs/lcms2/src/cmsgamma.c

   1 //---------------------------------------------------------------------------------
   2 //
   3 //  Little Color Management System
   4 //  Copyright (c) 1998-2023 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 #include "lcms2_internal.h"
  27
  28 // Tone curves are powerful constructs that can contain curves specified in diverse ways.
  29 // The curve is stored in segments, where each segment can be sampled or specified by parameters.
  30 // a 16.bit simplification of the *whole* curve is kept for optimization purposes. For float operation,
  31 // each segment is evaluated separately. Plug-ins may be used to define new parametric schemes,
  32 // each plug-in may define up to MAX_TYPES_IN_LCMS_PLUGIN functions types. For defining a function,
  33 // the plug-in should provide the type id, how many parameters each type has, and a pointer to
  34 // a procedure that evaluates the function. In the case of reverse evaluation, the evaluator will
  35 // be called with the type id as a negative value, and a sampled version of the reversed curve
  36 // will be built.
  37
  38 // ----------------------------------------------------------------- Implementation
  39 // Maxim number of nodes
  40 #define MAX_NODES_IN_CURVE   4097
  41 #define MINUS_INF            (-1E22F)
  42 #define PLUS_INF             (+1E22F)
  43
  44 // The list of supported parametric curves
  45 typedef struct _cmsParametricCurvesCollection_st {
  46
  47     cmsUInt32Number nFunctions;                                     // Number of supported functions in this chunk
  48     cmsInt32Number  FunctionTypes[MAX_TYPES_IN_LCMS_PLUGIN];        // The identification types
  49     cmsUInt32Number ParameterCount[MAX_TYPES_IN_LCMS_PLUGIN];       // Number of parameters for each function
  50
  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     10,                                      // # of curve types
  63     { 1, 2, 3, 4, 5, 6, 7, 8, 108, 109 },    // Parametric curve ID
  64     { 1, 3, 4, 5, 7, 4, 5, 5,   1,   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 < (int) 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 optimization 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, cmsUInt32Number nEntries,
 214                                       cmsUInt32Number nSegments, const cmsCurveSegment* Segments,
 215                                       const cmsUInt16Number* Values)
 216 {
 217     cmsToneCurve* p;
 218     cmsUInt32Number i;
 219
 220     // We allow huge tables, which are then restricted for smoothing operations
 221     if (nEntries > 65530) {
 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 -> SegInterp) _cmsFree(ContextID, p -> SegInterp);
 304     if (p -> Segments) _cmsFree(ContextID, p -> Segments);
 305     if (p -> Evals) _cmsFree(ContextID, p -> Evals);
 306     if (p ->Table16) _cmsFree(ContextID, p ->Table16);
 307     _cmsFree(ContextID, p);
 308     return NULL;
 309 }
 310
 311
 312 // Generates a sigmoidal function with desired steepness.
 313 cmsINLINE double sigmoid_base(double k, double t)
 314 {
 315     return (1.0 / (1.0 + exp(-k * t))) - 0.5;
 316 }
 317
 318 cmsINLINE double inverted_sigmoid_base(double k, double t)
 319 {
 320     return -log((1.0 / (t + 0.5)) - 1.0) / k;
 321 }
 322
 323 cmsINLINE double sigmoid_factory(double k, double t)
 324 {
 325     double correction = 0.5 / sigmoid_base(k, 1);
 326
 327     return correction * sigmoid_base(k, 2.0 * t - 1.0) + 0.5;
 328 }
 329
 330 cmsINLINE double inverse_sigmoid_factory(double k, double t)
 331 {
 332     double correction = 0.5 / sigmoid_base(k, 1);
 333
 334     return (inverted_sigmoid_base(k, (t - 0.5) / correction) + 1.0) / 2.0;
 335 }
 336
 337
 338 // Parametric Fn using floating point
 339 static
 340 cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R)
 341 {
 342     cmsFloat64Number e, Val, disc;
 343
 344     switch (Type) {
 345
 346    // X = Y ^ Gamma
 347     case 1:
 348         if (R < 0) {
 349
 350             if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
 351                 Val = R;
 352             else
 353                 Val = 0;
 354         }
 355         else
 356             Val = pow(R, Params[0]);
 357         break;
 358
 359     // Type 1 Reversed: X = Y ^1/gamma
 360     case -1:
 361         if (R < 0) {
 362
 363             if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
 364                 Val = R;
 365             else
 366                 Val = 0;
 367         }
 368         else
 369         {
 370             if (fabs(Params[0]) < MATRIX_DET_TOLERANCE)
 371                 Val = PLUS_INF;
 372             else
 373                 Val = pow(R, 1 / Params[0]);
 374         }
 375         break;
 376
 377     // CIE 122-1966
 378     // Y = (aX + b)^Gamma  | X >= -b/a
 379     // Y = 0               | else
 380     case 2:
 381     {
 382
 383         if (fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 384         {
 385             Val = 0;
 386         }
 387         else
 388         {
 389             disc = -Params[2] / Params[1];
 390
 391             if (R >= disc) {
 392
 393                 e = Params[1] * R + Params[2];
 394
 395                 if (e > 0)
 396                     Val = pow(e, Params[0]);
 397                 else
 398                     Val = 0;
 399             }
 400             else
 401                 Val = 0;
 402         }
 403     }
 404     break;
 405
 406      // Type 2 Reversed
 407      // X = (Y ^1/g  - b) / a
 408      case -2:
 409      {
 410          if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 411              fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 412          {
 413              Val = 0;
 414          }
 415          else
 416          {
 417              if (R < 0)
 418                  Val = 0;
 419              else
 420                  Val = (pow(R, 1.0 / Params[0]) - Params[2]) / Params[1];
 421
 422              if (Val < 0)
 423                  Val = 0;
 424          }
 425      }
 426      break;
 427
 428
 429     // IEC 61966-3
 430     // Y = (aX + b)^Gamma + c | X <= -b/a
 431     // Y = c                  | else
 432     case 3:
 433     {
 434         if (fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 435         {
 436             Val = 0;
 437         }
 438         else
 439         {
 440             disc = -Params[2] / Params[1];
 441             if (disc < 0)
 442                 disc = 0;
 443
 444             if (R >= disc) {
 445
 446                 e = Params[1] * R + Params[2];
 447
 448                 if (e > 0)
 449                     Val = pow(e, Params[0]) + Params[3];
 450                 else
 451                     Val = 0;
 452             }
 453             else
 454                 Val = Params[3];
 455         }
 456     }
 457     break;
 458
 459
 460     // Type 3 reversed
 461     // X=((Y-c)^1/g - b)/a      | (Y>=c)
 462     // X=-b/a                   | (Y<c)
 463     case -3:
 464     {
 465         if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 466             fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 467         {
 468             Val = 0;
 469         }
 470         else
 471         {
 472             if (R >= Params[3]) {
 473
 474                 e = R - Params[3];
 475
 476                 if (e > 0)
 477                     Val = (pow(e, 1 / Params[0]) - Params[2]) / Params[1];
 478                 else
 479                     Val = 0;
 480             }
 481             else {
 482                 Val = -Params[2] / Params[1];
 483             }
 484         }
 485     }
 486     break;
 487
 488
 489     // IEC 61966-2.1 (sRGB)
 490     // Y = (aX + b)^Gamma | X >= d
 491     // Y = cX             | X < d
 492     case 4:
 493         if (R >= Params[4]) {
 494
 495             e = Params[1]*R + Params[2];
 496
 497             if (e > 0)
 498                 Val = pow(e, Params[0]);
 499             else
 500                 Val = 0;
 501         }
 502         else
 503             Val = R * Params[3];
 504         break;
 505
 506     // Type 4 reversed
 507     // X=((Y^1/g-b)/a)    | Y >= (ad+b)^g
 508     // X=Y/c              | Y< (ad+b)^g
 509     case -4:
 510     {
 511
 512         e = Params[1] * Params[4] + Params[2];
 513         if (e < 0)
 514             disc = 0;
 515         else
 516             disc = pow(e, Params[0]);
 517
 518         if (R >= disc) {
 519
 520             if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 521                 fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 522
 523                 Val = 0;
 524
 525             else
 526                 Val = (pow(R, 1.0 / Params[0]) - Params[2]) / Params[1];
 527         }
 528         else {
 529
 530             if (fabs(Params[3]) < MATRIX_DET_TOLERANCE)
 531                 Val = 0;
 532             else
 533                 Val = R / Params[3];
 534         }
 535
 536     }
 537     break;
 538
 539
 540     // Y = (aX + b)^Gamma + e | X >= d
 541     // Y = cX + f             | X < d
 542     case 5:
 543         if (R >= Params[4]) {
 544
 545             e = Params[1]*R + Params[2];
 546
 547             if (e > 0)
 548                 Val = pow(e, Params[0]) + Params[5];
 549             else
 550                 Val = Params[5];
 551         }
 552         else
 553             Val = R*Params[3] + Params[6];
 554         break;
 555
 556
 557     // Reversed type 5
 558     // X=((Y-e)1/g-b)/a   | Y >=(ad+b)^g+e), cd+f
 559     // X=(Y-f)/c          | else
 560     case -5:
 561     {
 562         disc = Params[3] * Params[4] + Params[6];
 563         if (R >= disc) {
 564
 565             e = R - Params[5];
 566             if (e < 0)
 567                 Val = 0;
 568             else
 569             {
 570                 if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 571                     fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 572
 573                     Val = 0;
 574                 else
 575                     Val = (pow(e, 1.0 / Params[0]) - Params[2]) / Params[1];
 576             }
 577         }
 578         else {
 579             if (fabs(Params[3]) < MATRIX_DET_TOLERANCE)
 580                 Val = 0;
 581             else
 582                 Val = (R - Params[6]) / Params[3];
 583         }
 584
 585     }
 586     break;
 587
 588
 589     // Types 6,7,8 comes from segmented curves as described in ICCSpecRevision_02_11_06_Float.pdf
 590     // Type 6 is basically identical to type 5 without d
 591
 592     // Y = (a * X + b) ^ Gamma + c
 593     case 6:
 594         e = Params[1]*R + Params[2];
 595
 596         if (e < 0)
 597             Val = Params[3];
 598         else
 599             Val = pow(e, Params[0]) + Params[3];
 600         break;
 601
 602     // ((Y - c) ^1/Gamma - b) / a
 603     case -6:
 604     {
 605         if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 606             fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 607         {
 608             Val = 0;
 609         }
 610         else
 611         {
 612             e = R - Params[3];
 613             if (e < 0)
 614                 Val = 0;
 615             else
 616                 Val = (pow(e, 1.0 / Params[0]) - Params[2]) / Params[1];
 617         }
 618     }
 619     break;
 620
 621
 622     // Y = a * log (b * X^Gamma + c) + d
 623     case 7:
 624
 625        e = Params[2] * pow(R, Params[0]) + Params[3];
 626        if (e <= 0)
 627            Val = Params[4];
 628        else
 629            Val = Params[1]*log10(e) + Params[4];
 630        break;
 631
 632     // (Y - d) / a = log(b * X ^Gamma + c)
 633     // pow(10, (Y-d) / a) = b * X ^Gamma + c
 634     // pow((pow(10, (Y-d) / a) - c) / b, 1/g) = X
 635     case -7:
 636     {
 637         if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 638             fabs(Params[1]) < MATRIX_DET_TOLERANCE ||
 639             fabs(Params[2]) < MATRIX_DET_TOLERANCE)
 640         {
 641             Val = 0;
 642         }
 643         else
 644         {
 645             Val = pow((pow(10.0, (R - Params[4]) / Params[1]) - Params[3]) / Params[2], 1.0 / Params[0]);
 646         }
 647     }
 648     break;
 649
 650
 651    //Y = a * b^(c*X+d) + e
 652    case 8:
 653        Val = (Params[0] * pow(Params[1], Params[2] * R + Params[3]) + Params[4]);
 654        break;
 655
 656
 657    // Y = (log((y-e) / a) / log(b) - d ) / c
 658    // a=0, b=1, c=2, d=3, e=4,
 659    case -8:
 660
 661        disc = R - Params[4];
 662        if (disc < 0) Val = 0;
 663        else
 664        {
 665            if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 666                fabs(Params[2]) < MATRIX_DET_TOLERANCE)
 667            {
 668                Val = 0;
 669            }
 670            else
 671            {
 672                Val = (log(disc / Params[0]) / log(Params[1]) - Params[3]) / Params[2];
 673            }
 674        }
 675        break;
 676
 677
 678    // S-Shaped: (1 - (1-x)^1/g)^1/g
 679    case 108:
 680        if (fabs(Params[0]) < MATRIX_DET_TOLERANCE)
 681            Val = 0;
 682        else
 683            Val = pow(1.0 - pow(1 - R, 1/Params[0]), 1/Params[0]);
 684       break;
 685
 686     // y = (1 - (1-x)^1/g)^1/g
 687     // y^g = (1 - (1-x)^1/g)
 688     // 1 - y^g = (1-x)^1/g
 689     // (1 - y^g)^g = 1 - x
 690     // 1 - (1 - y^g)^g
 691     case -108:
 692         Val = 1 - pow(1 - pow(R, Params[0]), Params[0]);
 693         break;
 694
 695     // Sigmoidals
 696     case 109:
 697         Val = sigmoid_factory(Params[0], R);
 698         break;
 699
 700     case -109:
 701         Val = inverse_sigmoid_factory(Params[0], R);
 702         break;
 703
 704     default:
 705         // Unsupported parametric curve. Should never reach here
 706         return 0;
 707     }
 708
 709     return Val;
 710 }
 711
 712 // Evaluate a segmented function for a single value. Return -Inf if no valid segment found .
 713 // If fn type is 0, perform an interpolation on the table
 714 static
 715 cmsFloat64Number EvalSegmentedFn(const cmsToneCurve *g, cmsFloat64Number R)
 716 {
 717     int i;
 718     cmsFloat32Number Out32;
 719     cmsFloat64Number Out;
 720
 721     for (i = (int) g->nSegments - 1; i >= 0; --i) {
 722
 723         // Check for domain
 724         if ((R > g->Segments[i].x0) && (R <= g->Segments[i].x1)) {
 725
 726             // Type == 0 means segment is sampled
 727             if (g->Segments[i].Type == 0) {
 728
 729                 cmsFloat32Number R1 = (cmsFloat32Number)(R - g->Segments[i].x0) / (g->Segments[i].x1 - g->Segments[i].x0);
 730
 731                 // Setup the table (TODO: clean that)
 732                 g->SegInterp[i]->Table = g->Segments[i].SampledPoints;
 733
 734                 g->SegInterp[i]->Interpolation.LerpFloat(&R1, &Out32, g->SegInterp[i]);
 735                 Out = (cmsFloat64Number) Out32;
 736
 737             }
 738             else {
 739                 Out = g->Evals[i](g->Segments[i].Type, g->Segments[i].Params, R);
 740             }
 741
 742             if (isinf(Out))
 743                 return PLUS_INF;
 744             else
 745             {
 746                 if (isinf(-Out))
 747                     return MINUS_INF;
 748             }
 749
 750             return Out;
 751         }
 752     }
 753
 754     return MINUS_INF;
 755 }
 756
 757 // Access to estimated low-res table
 758 cmsUInt32Number CMSEXPORT cmsGetToneCurveEstimatedTableEntries(const cmsToneCurve* t)
 759 {
 760     _cmsAssert(t != NULL);
 761     return t ->nEntries;
 762 }
 763
 764 const cmsUInt16Number* CMSEXPORT cmsGetToneCurveEstimatedTable(const cmsToneCurve* t)
 765 {
 766     _cmsAssert(t != NULL);
 767     return t ->Table16;
 768 }
 769
 770
 771 // Create an empty gamma curve, by using tables. This specifies only the limited-precision part, and leaves the
 772 // floating point description empty.
 773 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurve16(cmsContext ContextID, cmsUInt32Number nEntries, const cmsUInt16Number Values[])
 774 {
 775     return AllocateToneCurveStruct(ContextID, nEntries, 0, NULL, Values);
 776 }
 777
 778 static
 779 cmsUInt32Number EntriesByGamma(cmsFloat64Number Gamma)
 780 {
 781     if (fabs(Gamma - 1.0) < 0.001) return 2;
 782     return 4096;
 783 }
 784
 785
 786 // Create a segmented gamma, fill the table
 787 cmsToneCurve* CMSEXPORT cmsBuildSegmentedToneCurve(cmsContext ContextID,
 788                                                    cmsUInt32Number nSegments, const cmsCurveSegment Segments[])
 789 {
 790     cmsUInt32Number i;
 791     cmsFloat64Number R, Val;
 792     cmsToneCurve* g;
 793     cmsUInt32Number nGridPoints = 4096;
 794
 795     _cmsAssert(Segments != NULL);
 796
 797     // Optimizatin for identity curves.
 798     if (nSegments == 1 && Segments[0].Type == 1) {
 799
 800         nGridPoints = EntriesByGamma(Segments[0].Params[0]);
 801     }
 802
 803     g = AllocateToneCurveStruct(ContextID, nGridPoints, nSegments, Segments, NULL);
 804     if (g == NULL) return NULL;
 805
 806     // Once we have the floating point version, we can approximate a 16 bit table of 4096 entries
 807     // for performance reasons. This table would normally not be used except on 8/16 bits transforms.
 808     for (i = 0; i < nGridPoints; i++) {
 809
 810         R   = (cmsFloat64Number) i / (nGridPoints-1);
 811
 812         Val = EvalSegmentedFn(g, R);
 813
 814         // Round and saturate
 815         g ->Table16[i] = _cmsQuickSaturateWord(Val * 65535.0);
 816     }
 817
 818     return g;
 819 }
 820
 821 // Use a segmented curve to store the floating point table
 822 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurveFloat(cmsContext ContextID, cmsUInt32Number nEntries, const cmsFloat32Number values[])
 823 {
 824     cmsCurveSegment Seg[3];
 825
 826     // Do some housekeeping
 827     if (nEntries == 0 || values == NULL)
 828         return NULL;
 829
 830     // A segmented tone curve should have function segments in the first and last positions
 831     // Initialize segmented curve part up to 0 to constant value = samples[0]
 832     Seg[0].x0 = MINUS_INF;
 833     Seg[0].x1 = 0;
 834     Seg[0].Type = 6;
 835
 836     Seg[0].Params[0] = 1;
 837     Seg[0].Params[1] = 0;
 838     Seg[0].Params[2] = 0;
 839     Seg[0].Params[3] = values[0];
 840     Seg[0].Params[4] = 0;
 841
 842     // From zero to 1
 843     Seg[1].x0 = 0;
 844     Seg[1].x1 = 1.0;
 845     Seg[1].Type = 0;
 846
 847     Seg[1].nGridPoints = nEntries;
 848     Seg[1].SampledPoints = (cmsFloat32Number*) values;
 849
 850     // Final segment is constant = lastsample
 851     Seg[2].x0 = 1.0;
 852     Seg[2].x1 = PLUS_INF;
 853     Seg[2].Type = 6;
 854
 855     Seg[2].Params[0] = 1;
 856     Seg[2].Params[1] = 0;
 857     Seg[2].Params[2] = 0;
 858     Seg[2].Params[3] = values[nEntries-1];
 859     Seg[2].Params[4] = 0;
 860
 861
 862     return cmsBuildSegmentedToneCurve(ContextID, 3, Seg);
 863 }
 864
 865 // Parametric curves
 866 //
 867 // Parameters goes as: Curve, a, b, c, d, e, f
 868 // Type is the ICC type +1
 869 // if type is negative, then the curve is analytically inverted
 870 cmsToneCurve* CMSEXPORT cmsBuildParametricToneCurve(cmsContext ContextID, cmsInt32Number Type, const cmsFloat64Number Params[])
 871 {
 872     cmsCurveSegment Seg0;
 873     int Pos = 0;
 874     cmsUInt32Number size;
 875     _cmsParametricCurvesCollection* c = GetParametricCurveByType(ContextID, Type, &Pos);
 876
 877     _cmsAssert(Params != NULL);
 878
 879     if (c == NULL) {
 880         cmsSignalError(ContextID, cmsERROR_UNKNOWN_EXTENSION, "Invalid parametric curve type %d", Type);
 881         return NULL;
 882     }
 883
 884     memset(&Seg0, 0, sizeof(Seg0));
 885
 886     Seg0.x0   = MINUS_INF;
 887     Seg0.x1   = PLUS_INF;
 888     Seg0.Type = Type;
 889
 890     size = c->ParameterCount[Pos] * sizeof(cmsFloat64Number);
 891     memmove(Seg0.Params, Params, size);
 892
 893     return cmsBuildSegmentedToneCurve(ContextID, 1, &Seg0);
 894 }
 895
 896
 897
 898 // Build a gamma table based on gamma constant
 899 cmsToneCurve* CMSEXPORT cmsBuildGamma(cmsContext ContextID, cmsFloat64Number Gamma)
 900 {
 901     return cmsBuildParametricToneCurve(ContextID, 1, &Gamma);
 902 }
 903
 904
 905 // Free all memory taken by the gamma curve
 906 void CMSEXPORT cmsFreeToneCurve(cmsToneCurve* Curve)
 907 {
 908     cmsContext ContextID;
 909
 910     if (Curve == NULL) return;
 911
 912     ContextID = Curve ->InterpParams->ContextID;
 913
 914     _cmsFreeInterpParams(Curve ->InterpParams);
 915
 916     if (Curve -> Table16)
 917         _cmsFree(ContextID, Curve ->Table16);
 918
 919     if (Curve ->Segments) {
 920
 921         cmsUInt32Number i;
 922
 923         for (i=0; i < Curve ->nSegments; i++) {
 924
 925             if (Curve ->Segments[i].SampledPoints) {
 926                 _cmsFree(ContextID, Curve ->Segments[i].SampledPoints);
 927             }
 928
 929             if (Curve ->SegInterp[i] != 0)
 930                 _cmsFreeInterpParams(Curve->SegInterp[i]);
 931         }
 932
 933         _cmsFree(ContextID, Curve ->Segments);
 934         _cmsFree(ContextID, Curve ->SegInterp);
 935     }
 936
 937     if (Curve -> Evals)
 938         _cmsFree(ContextID, Curve -> Evals);
 939
 940     _cmsFree(ContextID, Curve);
 941 }
 942
 943 // Utility function, free 3 gamma tables
 944 void CMSEXPORT cmsFreeToneCurveTriple(cmsToneCurve* Curve[3])
 945 {
 946
 947     _cmsAssert(Curve != NULL);
 948
 949     if (Curve[0] != NULL) cmsFreeToneCurve(Curve[0]);
 950     if (Curve[1] != NULL) cmsFreeToneCurve(Curve[1]);
 951     if (Curve[2] != NULL) cmsFreeToneCurve(Curve[2]);
 952
 953     Curve[0] = Curve[1] = Curve[2] = NULL;
 954 }
 955
 956
 957 // Duplicate a gamma table
 958 cmsToneCurve* CMSEXPORT cmsDupToneCurve(const cmsToneCurve* In)
 959 {
 960     if (In == NULL) return NULL;
 961
 962     return  AllocateToneCurveStruct(In ->InterpParams ->ContextID, In ->nEntries, In ->nSegments, In ->Segments, In ->Table16);
 963 }
 964
 965 // Joins two curves for X and Y. Curves should be monotonic.
 966 // We want to get
 967 //
 968 //      y = Y^-1(X(t))
 969 //
 970 cmsToneCurve* CMSEXPORT cmsJoinToneCurve(cmsContext ContextID,
 971                                       const cmsToneCurve* X,
 972                                       const cmsToneCurve* Y, cmsUInt32Number nResultingPoints)
 973 {
 974     cmsToneCurve* out = NULL;
 975     cmsToneCurve* Yreversed = NULL;
 976     cmsFloat32Number t, x;
 977     cmsFloat32Number* Res = NULL;
 978     cmsUInt32Number i;
 979
 980
 981     _cmsAssert(X != NULL);
 982     _cmsAssert(Y != NULL);
 983
 984     Yreversed = cmsReverseToneCurveEx(nResultingPoints, Y);
 985     if (Yreversed == NULL) goto Error;
 986
 987     Res = (cmsFloat32Number*) _cmsCalloc(ContextID, nResultingPoints, sizeof(cmsFloat32Number));
 988     if (Res == NULL) goto Error;
 989
 990     //Iterate
 991     for (i=0; i <  nResultingPoints; i++) {
 992
 993         t = (cmsFloat32Number) i / (cmsFloat32Number)(nResultingPoints-1);
 994         x = cmsEvalToneCurveFloat(X,  t);
 995         Res[i] = cmsEvalToneCurveFloat(Yreversed, x);
 996     }
 997
 998     // Allocate space for output
 999     out = cmsBuildTabulatedToneCurveFloat(ContextID, nResultingPoints, Res);
1000
1001 Error:
1002
1003     if (Res != NULL) _cmsFree(ContextID, Res);
1004     if (Yreversed != NULL) cmsFreeToneCurve(Yreversed);
1005
1006     return out;
1007 }
1008
1009
1010
1011 // Get the surrounding nodes. This is tricky on non-monotonic tables
1012 static
1013 int GetInterval(cmsFloat64Number In, const cmsUInt16Number LutTable[], const struct _cms_interp_struc* p)
1014 {
1015     int i;
1016     int y0, y1;
1017
1018     // A 1 point table is not allowed
1019     if (p -> Domain[0] < 1) return -1;
1020
1021     // Let's see if ascending or descending.
1022     if (LutTable[0] < LutTable[p ->Domain[0]]) {
1023
1024         // Table is overall ascending
1025         for (i = (int) p->Domain[0] - 1; i >= 0; --i) {
1026
1027             y0 = LutTable[i];
1028             y1 = LutTable[i+1];
1029
1030             if (y0 <= y1) { // Increasing
1031                 if (In >= y0 && In <= y1) return i;
1032             }
1033             else
1034                 if (y1 < y0) { // Decreasing
1035                     if (In >= y1 && In <= y0) return i;
1036                 }
1037         }
1038     }
1039     else {
1040         // Table is overall descending
1041         for (i=0; i < (int) p -> Domain[0]; i++) {
1042
1043             y0 = LutTable[i];
1044             y1 = LutTable[i+1];
1045
1046             if (y0 <= y1) { // Increasing
1047                 if (In >= y0 && In <= y1) return i;
1048             }
1049             else
1050                 if (y1 < y0) { // Decreasing
1051                     if (In >= y1 && In <= y0) return i;
1052                 }
1053         }
1054     }
1055
1056     return -1;
1057 }
1058
1059 // Reverse a gamma table
1060 cmsToneCurve* CMSEXPORT cmsReverseToneCurveEx(cmsUInt32Number nResultSamples, const cmsToneCurve* InCurve)
1061 {
1062     cmsToneCurve *out;
1063     cmsFloat64Number a = 0, b = 0, y, x1, y1, x2, y2;
1064     int i, j;
1065     int Ascending;
1066
1067     _cmsAssert(InCurve != NULL);
1068
1069     // Try to reverse it analytically whatever possible
1070
1071     if (InCurve ->nSegments == 1 && InCurve ->Segments[0].Type > 0 &&
1072         /* InCurve -> Segments[0].Type <= 5 */
1073         GetParametricCurveByType(InCurve ->InterpParams->ContextID, InCurve ->Segments[0].Type, NULL) != NULL) {
1074
1075         return cmsBuildParametricToneCurve(InCurve ->InterpParams->ContextID,
1076                                        -(InCurve -> Segments[0].Type),
1077                                        InCurve -> Segments[0].Params);
1078     }
1079
1080     // Nope, reverse the table.
1081     out = cmsBuildTabulatedToneCurve16(InCurve ->InterpParams->ContextID, nResultSamples, NULL);
1082     if (out == NULL)
1083         return NULL;
1084
1085     // We want to know if this is an ascending or descending table
1086     Ascending = !cmsIsToneCurveDescending(InCurve);
1087
1088     // Iterate across Y axis
1089     for (i=0; i < (int) nResultSamples; i++) {
1090
1091         y = (cmsFloat64Number) i * 65535.0 / (nResultSamples - 1);
1092
1093         // Find interval in which y is within.
1094         j = GetInterval(y, InCurve->Table16, InCurve->InterpParams);
1095         if (j >= 0) {
1096
1097
1098             // Get limits of interval
1099             x1 = InCurve ->Table16[j];
1100             x2 = InCurve ->Table16[j+1];
1101
1102             y1 = (cmsFloat64Number) (j * 65535.0) / (InCurve ->nEntries - 1);
1103             y2 = (cmsFloat64Number) ((j+1) * 65535.0 ) / (InCurve ->nEntries - 1);
1104
1105             // If collapsed, then use any
1106             if (x1 == x2) {
1107
1108                 out ->Table16[i] = _cmsQuickSaturateWord(Ascending ? y2 : y1);
1109                 continue;
1110
1111             } else {
1112
1113                 // Interpolate
1114                 a = (y2 - y1) / (x2 - x1);
1115                 b = y2 - a * x2;
1116             }
1117         }
1118
1119         out ->Table16[i] = _cmsQuickSaturateWord(a* y + b);
1120     }
1121
1122
1123     return out;
1124 }
1125
1126 // Reverse a gamma table
1127 cmsToneCurve* CMSEXPORT cmsReverseToneCurve(const cmsToneCurve* InGamma)
1128 {
1129     _cmsAssert(InGamma != NULL);
1130
1131     return cmsReverseToneCurveEx(4096, InGamma);
1132 }
1133
1134 // From: Eilers, P.H.C. (1994) Smoothing and interpolation with finite
1135 // differences. in: Graphic Gems IV, Heckbert, P.S. (ed.), Academic press.
1136 //
1137 // Smoothing and interpolation with second differences.
1138 //
1139 //   Input:  weights (w), data (y): vector from 1 to m.
1140 //   Input:  smoothing parameter (lambda), length (m).
1141 //   Output: smoothed vector (z): vector from 1 to m.
1142
1143 static
1144 cmsBool smooth2(cmsContext ContextID, cmsFloat32Number w[], cmsFloat32Number y[],
1145                 cmsFloat32Number z[], cmsFloat32Number lambda, int m)
1146 {
1147     int i, i1, i2;
1148     cmsFloat32Number *c, *d, *e;
1149     cmsBool st;
1150
1151
1152     c = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
1153     d = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
1154     e = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
1155
1156     if (c != NULL && d != NULL && e != NULL) {
1157
1158
1159     d[1] = w[1] + lambda;
1160     c[1] = -2 * lambda / d[1];
1161     e[1] = lambda /d[1];
1162     z[1] = w[1] * y[1];
1163     d[2] = w[2] + 5 * lambda - d[1] * c[1] *  c[1];
1164     c[2] = (-4 * lambda - d[1] * c[1] * e[1]) / d[2];
1165     e[2] = lambda / d[2];
1166     z[2] = w[2] * y[2] - c[1] * z[1];
1167
1168     for (i = 3; i < m - 1; i++) {
1169         i1 = i - 1; i2 = i - 2;
1170         d[i]= w[i] + 6 * lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
1171         c[i] = (-4 * lambda -d[i1] * c[i1] * e[i1])/ d[i];
1172         e[i] = lambda / d[i];
1173         z[i] = w[i] * y[i] - c[i1] * z[i1] - e[i2] * z[i2];
1174     }
1175
1176     i1 = m - 2; i2 = m - 3;
1177
1178     d[m - 1] = w[m - 1] + 5 * lambda -c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
1179     c[m - 1] = (-2 * lambda - d[i1] * c[i1] * e[i1]) / d[m - 1];
1180     z[m - 1] = w[m - 1] * y[m - 1] - c[i1] * z[i1] - e[i2] * z[i2];
1181     i1 = m - 1; i2 = m - 2;
1182
1183     d[m] = w[m] + lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
1184     z[m] = (w[m] * y[m] - c[i1] * z[i1] - e[i2] * z[i2]) / d[m];
1185     z[m - 1] = z[m - 1] / d[m - 1] - c[m - 1] * z[m];
1186
1187     for (i = m - 2; 1<= i; i--)
1188         z[i] = z[i] / d[i] - c[i] * z[i + 1] - e[i] * z[i + 2];
1189
1190       st = TRUE;
1191     }
1192     else st = FALSE;
1193
1194     if (c != NULL) _cmsFree(ContextID, c);
1195     if (d != NULL) _cmsFree(ContextID, d);
1196     if (e != NULL) _cmsFree(ContextID, e);
1197
1198     return st;
1199 }
1200
1201 // Smooths a curve sampled at regular intervals.
1202 cmsBool  CMSEXPORT cmsSmoothToneCurve(cmsToneCurve* Tab, cmsFloat64Number lambda)
1203 {
1204     cmsBool SuccessStatus = TRUE;
1205     cmsFloat32Number *w, *y, *z;
1206     cmsUInt32Number i, nItems, Zeros, Poles;
1207     cmsBool notCheck = FALSE;
1208
1209     if (Tab != NULL && Tab->InterpParams != NULL)
1210     {
1211         cmsContext ContextID = Tab->InterpParams->ContextID;
1212
1213         if (!cmsIsToneCurveLinear(Tab)) // Only non-linear curves need smoothing
1214         {
1215             nItems = Tab->nEntries;
1216             if (nItems < MAX_NODES_IN_CURVE)
1217             {
1218                 // Allocate one more item than needed
1219                 w = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
1220                 y = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
1221                 z = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
1222
1223                 if (w != NULL && y != NULL && z != NULL) // Ensure no memory allocation failure
1224                 {
1225                     memset(w, 0, (nItems + 1) * sizeof(cmsFloat32Number));
1226                     memset(y, 0, (nItems + 1) * sizeof(cmsFloat32Number));
1227                     memset(z, 0, (nItems + 1) * sizeof(cmsFloat32Number));
1228
1229                     for (i = 0; i < nItems; i++)
1230                     {
1231                         y[i + 1] = (cmsFloat32Number)Tab->Table16[i];
1232                         w[i + 1] = 1.0;
1233                     }
1234
1235                     if (lambda < 0)
1236                     {
1237                         notCheck = TRUE;
1238                         lambda = -lambda;
1239                     }
1240
1241                     if (smooth2(ContextID, w, y, z, (cmsFloat32Number)lambda, (int)nItems))
1242                     {
1243                         // Do some reality - checking...
1244
1245                         Zeros = Poles = 0;
1246                         for (i = nItems; i > 1; --i)
1247                         {
1248                             if (z[i] == 0.) Zeros++;
1249                             if (z[i] >= 65535.) Poles++;
1250                             if (z[i] < z[i - 1])
1251                             {
1252                                 cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Non-Monotonic.");
1253                                 SuccessStatus = notCheck;
1254                                 break;
1255                             }
1256                         }
1257
1258                         if (SuccessStatus && Zeros > (nItems / 3))
1259                         {
1260                             cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly zeros.");
1261                             SuccessStatus = notCheck;
1262                         }
1263
1264                         if (SuccessStatus && Poles > (nItems / 3))
1265                         {
1266                             cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly poles.");
1267                             SuccessStatus = notCheck;
1268                         }
1269
1270                         if (SuccessStatus) // Seems ok
1271                         {
1272                             for (i = 0; i < nItems; i++)
1273                             {
1274                                 // Clamp to cmsUInt16Number
1275                                 Tab->Table16[i] = _cmsQuickSaturateWord(z[i + 1]);
1276                             }
1277                         }
1278                     }
1279                     else // Could not smooth
1280                     {
1281                         cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Function smooth2 failed.");
1282                         SuccessStatus = FALSE;
1283                     }
1284                 }
1285                 else // One or more buffers could not be allocated
1286                 {
1287                     cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Could not allocate memory.");
1288                     SuccessStatus = FALSE;
1289                 }
1290
1291                 if (z != NULL)
1292                     _cmsFree(ContextID, z);
1293
1294                 if (y != NULL)
1295                     _cmsFree(ContextID, y);
1296
1297                 if (w != NULL)
1298                     _cmsFree(ContextID, w);
1299             }
1300             else // too many items in the table
1301             {
1302                 cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Too many points.");
1303                 SuccessStatus = FALSE;
1304             }
1305         }
1306     }
1307     else // Tab parameter or Tab->InterpParams is NULL
1308     {
1309         // Can't signal an error here since the ContextID is not known at this point
1310         SuccessStatus = FALSE;
1311     }
1312
1313     return SuccessStatus;
1314 }
1315
1316 // Is a table linear? Do not use parametric since we cannot guarantee some weird parameters resulting
1317 // in a linear table. This way assures it is linear in 12 bits, which should be enough in most cases.
1318 cmsBool CMSEXPORT cmsIsToneCurveLinear(const cmsToneCurve* Curve)
1319 {
1320     int i;
1321     int diff;
1322
1323     _cmsAssert(Curve != NULL);
1324
1325     for (i=0; i < (int) Curve ->nEntries; i++) {
1326
1327         diff = abs((int) Curve->Table16[i] - (int) _cmsQuantizeVal(i, Curve ->nEntries));
1328         if (diff > 0x0f)
1329             return FALSE;
1330     }
1331
1332     return TRUE;
1333 }
1334
1335 // Same, but for monotonicity
1336 cmsBool  CMSEXPORT cmsIsToneCurveMonotonic(const cmsToneCurve* t)
1337 {
1338     cmsUInt32Number n;
1339     int i, last;
1340     cmsBool lDescending;
1341
1342     _cmsAssert(t != NULL);
1343
1344     // Degenerated curves are monotonic? Ok, let's pass them
1345     n = t ->nEntries;
1346     if (n < 2) return TRUE;
1347
1348     // Curve direction
1349     lDescending = cmsIsToneCurveDescending(t);
1350
1351     if (lDescending) {
1352
1353         last = t ->Table16[0];
1354
1355         for (i = 1; i < (int) n; i++) {
1356
1357             if (t ->Table16[i] - last > 2) // We allow some ripple
1358                 return FALSE;
1359             else
1360                 last = t ->Table16[i];
1361
1362         }
1363     }
1364     else {
1365
1366         last = t ->Table16[n-1];
1367
1368         for (i = (int) n - 2; i >= 0; --i) {
1369
1370             if (t ->Table16[i] - last > 2)
1371                 return FALSE;
1372             else
1373                 last = t ->Table16[i];
1374
1375         }
1376     }
1377
1378     return TRUE;
1379 }
1380
1381 // Same, but for descending tables
1382 cmsBool  CMSEXPORT cmsIsToneCurveDescending(const cmsToneCurve* t)
1383 {
1384     _cmsAssert(t != NULL);
1385
1386     return t ->Table16[0] > t ->Table16[t ->nEntries-1];
1387 }
1388
1389
1390 // Another info fn: is out gamma table multisegment?
1391 cmsBool  CMSEXPORT cmsIsToneCurveMultisegment(const cmsToneCurve* t)
1392 {
1393     _cmsAssert(t != NULL);
1394
1395     return t -> nSegments > 1;
1396 }
1397
1398 cmsInt32Number  CMSEXPORT cmsGetToneCurveParametricType(const cmsToneCurve* t)
1399 {
1400     _cmsAssert(t != NULL);
1401
1402     if (t -> nSegments != 1) return 0;
1403     return t ->Segments[0].Type;
1404 }
1405
1406 // We need accuracy this time
1407 cmsFloat32Number CMSEXPORT cmsEvalToneCurveFloat(const cmsToneCurve* Curve, cmsFloat32Number v)
1408 {
1409     _cmsAssert(Curve != NULL);
1410
1411     // Check for 16 bits table. If so, this is a limited-precision tone curve
1412     if (Curve ->nSegments == 0) {
1413
1414         cmsUInt16Number In, Out;
1415
1416         In = (cmsUInt16Number) _cmsQuickSaturateWord(v * 65535.0);
1417         Out = cmsEvalToneCurve16(Curve, In);
1418
1419         return (cmsFloat32Number) (Out / 65535.0);
1420     }
1421
1422     return (cmsFloat32Number) EvalSegmentedFn(Curve, v);
1423 }
1424
1425 // We need xput over here
1426 cmsUInt16Number CMSEXPORT cmsEvalToneCurve16(const cmsToneCurve* Curve, cmsUInt16Number v)
1427 {
1428     cmsUInt16Number out;
1429
1430     _cmsAssert(Curve != NULL);
1431
1432     Curve ->InterpParams ->Interpolation.Lerp16(&v, &out, Curve ->InterpParams);
1433     return out;
1434 }
1435
1436
1437 // Least squares fitting.
1438 // A mathematical procedure for finding the best-fitting curve to a given set of points by
1439 // minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve.
1440 // The sum of the squares of the offsets is used instead of the offset absolute values because
1441 // this allows the residuals to be treated as a continuous differentiable quantity.
1442 //
1443 // y = f(x) = x ^ g
1444 //
1445 // R  = (yi - (xi^g))
1446 // R2 = (yi - (xi^g))2
1447 // SUM R2 = SUM (yi - (xi^g))2
1448 //
1449 // dR2/dg = -2 SUM x^g log(x)(y - x^g)
1450 // solving for dR2/dg = 0
1451 //
1452 // g = 1/n * SUM(log(y) / log(x))
1453
1454 cmsFloat64Number CMSEXPORT cmsEstimateGamma(const cmsToneCurve* t, cmsFloat64Number Precision)
1455 {
1456     cmsFloat64Number gamma, sum, sum2;
1457     cmsFloat64Number n, x, y, Std;
1458     cmsUInt32Number i;
1459
1460     _cmsAssert(t != NULL);
1461
1462     sum = sum2 = n = 0;
1463
1464     // Excluding endpoints
1465     for (i=1; i < (MAX_NODES_IN_CURVE-1); i++) {
1466
1467         x = (cmsFloat64Number) i / (MAX_NODES_IN_CURVE-1);
1468         y = (cmsFloat64Number) cmsEvalToneCurveFloat(t, (cmsFloat32Number) x);
1469
1470         // Avoid 7% on lower part to prevent
1471         // artifacts due to linear ramps
1472
1473         if (y > 0. && y < 1. && x > 0.07) {
1474
1475             gamma = log(y) / log(x);
1476             sum  += gamma;
1477             sum2 += gamma * gamma;
1478             n++;
1479         }
1480     }
1481
1482     // We need enough valid samples
1483     if (n <= 1) return -1.0;
1484
1485     // Take a look on SD to see if gamma isn't exponential at all
1486     Std = sqrt((n * sum2 - sum * sum) / (n*(n-1)));
1487
1488     if (Std > Precision)
1489         return -1.0;
1490
1491     return (sum / n);   // The mean
1492 }
1493
1494
1495 // Retrieve parameters on one-segment tone curves
1496
1497 cmsFloat64Number* CMSEXPORT cmsGetToneCurveParams(const cmsToneCurve* t)
1498 {
1499     _cmsAssert(t != NULL);
1500
1501     if (t->nSegments != 1) return NULL;
1502     return t->Segments[0].Params;
1503 }