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     for (i=0; i < nSegments; i++) {
 304         if (p ->Segments && p ->Segments[i].SampledPoints) _cmsFree(ContextID, p ->Segments[i].SampledPoints);
 305         if (p ->SegInterp && p ->SegInterp[i]) _cmsFree(ContextID, p ->SegInterp[i]);
 306     }
 307     if (p -> SegInterp) _cmsFree(ContextID, p -> SegInterp);
 308     if (p -> Segments) _cmsFree(ContextID, p -> Segments);
 309     if (p -> Evals) _cmsFree(ContextID, p -> Evals);
 310     if (p ->Table16) _cmsFree(ContextID, p ->Table16);
 311     _cmsFree(ContextID, p);
 312     return NULL;
 313 }
 314
 315
 316 // Generates a sigmoidal function with desired steepness.
 317 cmsINLINE double sigmoid_base(double k, double t)
 318 {
 319     return (1.0 / (1.0 + exp(-k * t))) - 0.5;
 320 }
 321
 322 cmsINLINE double inverted_sigmoid_base(double k, double t)
 323 {
 324     return -log((1.0 / (t + 0.5)) - 1.0) / k;
 325 }
 326
 327 cmsINLINE double sigmoid_factory(double k, double t)
 328 {
 329     double correction = 0.5 / sigmoid_base(k, 1);
 330
 331     return correction * sigmoid_base(k, 2.0 * t - 1.0) + 0.5;
 332 }
 333
 334 cmsINLINE double inverse_sigmoid_factory(double k, double t)
 335 {
 336     double correction = 0.5 / sigmoid_base(k, 1);
 337
 338     return (inverted_sigmoid_base(k, (t - 0.5) / correction) + 1.0) / 2.0;
 339 }
 340
 341
 342 // Parametric Fn using floating point
 343 static
 344 cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R)
 345 {
 346     cmsFloat64Number e, Val, disc;
 347
 348     switch (Type) {
 349
 350    // X = Y ^ Gamma
 351     case 1:
 352         if (R < 0) {
 353
 354             if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
 355                 Val = R;
 356             else
 357                 Val = 0;
 358         }
 359         else
 360             Val = pow(R, Params[0]);
 361         break;
 362
 363     // Type 1 Reversed: X = Y ^1/gamma
 364     case -1:
 365         if (R < 0) {
 366
 367             if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
 368                 Val = R;
 369             else
 370                 Val = 0;
 371         }
 372         else
 373         {
 374             if (fabs(Params[0]) < MATRIX_DET_TOLERANCE)
 375                 Val = PLUS_INF;
 376             else
 377                 Val = pow(R, 1 / Params[0]);
 378         }
 379         break;
 380
 381     // CIE 122-1966
 382     // Y = (aX + b)^Gamma  | X >= -b/a
 383     // Y = 0               | else
 384     case 2:
 385     {
 386
 387         if (fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 388         {
 389             Val = 0;
 390         }
 391         else
 392         {
 393             disc = -Params[2] / Params[1];
 394
 395             if (R >= disc) {
 396
 397                 e = Params[1] * R + Params[2];
 398
 399                 if (e > 0)
 400                     Val = pow(e, Params[0]);
 401                 else
 402                     Val = 0;
 403             }
 404             else
 405                 Val = 0;
 406         }
 407     }
 408     break;
 409
 410      // Type 2 Reversed
 411      // X = (Y ^1/g  - b) / a
 412      case -2:
 413      {
 414          if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 415              fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 416          {
 417              Val = 0;
 418          }
 419          else
 420          {
 421              if (R < 0)
 422                  Val = 0;
 423              else
 424                  Val = (pow(R, 1.0 / Params[0]) - Params[2]) / Params[1];
 425
 426              if (Val < 0)
 427                  Val = 0;
 428          }
 429      }
 430      break;
 431
 432
 433     // IEC 61966-3
 434     // Y = (aX + b)^Gamma + c | X <= -b/a
 435     // Y = c                  | else
 436     case 3:
 437     {
 438         if (fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 439         {
 440             Val = 0;
 441         }
 442         else
 443         {
 444             disc = -Params[2] / Params[1];
 445             if (disc < 0)
 446                 disc = 0;
 447
 448             if (R >= disc) {
 449
 450                 e = Params[1] * R + Params[2];
 451
 452                 if (e > 0)
 453                     Val = pow(e, Params[0]) + Params[3];
 454                 else
 455                     Val = 0;
 456             }
 457             else
 458                 Val = Params[3];
 459         }
 460     }
 461     break;
 462
 463
 464     // Type 3 reversed
 465     // X=((Y-c)^1/g - b)/a      | (Y>=c)
 466     // X=-b/a                   | (Y<c)
 467     case -3:
 468     {
 469         if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 470             fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 471         {
 472             Val = 0;
 473         }
 474         else
 475         {
 476             if (R >= Params[3]) {
 477
 478                 e = R - Params[3];
 479
 480                 if (e > 0)
 481                     Val = (pow(e, 1 / Params[0]) - Params[2]) / Params[1];
 482                 else
 483                     Val = 0;
 484             }
 485             else {
 486                 Val = -Params[2] / Params[1];
 487             }
 488         }
 489     }
 490     break;
 491
 492
 493     // IEC 61966-2.1 (sRGB)
 494     // Y = (aX + b)^Gamma | X >= d
 495     // Y = cX             | X < d
 496     case 4:
 497         if (R >= Params[4]) {
 498
 499             e = Params[1]*R + Params[2];
 500
 501             if (e > 0)
 502                 Val = pow(e, Params[0]);
 503             else
 504                 Val = 0;
 505         }
 506         else
 507             Val = R * Params[3];
 508         break;
 509
 510     // Type 4 reversed
 511     // X=((Y^1/g-b)/a)    | Y >= (ad+b)^g
 512     // X=Y/c              | Y< (ad+b)^g
 513     case -4:
 514     {
 515
 516         e = Params[1] * Params[4] + Params[2];
 517         if (e < 0)
 518             disc = 0;
 519         else
 520             disc = pow(e, Params[0]);
 521
 522         if (R >= disc) {
 523
 524             if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 525                 fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 526
 527                 Val = 0;
 528
 529             else
 530                 Val = (pow(R, 1.0 / Params[0]) - Params[2]) / Params[1];
 531         }
 532         else {
 533
 534             if (fabs(Params[3]) < MATRIX_DET_TOLERANCE)
 535                 Val = 0;
 536             else
 537                 Val = R / Params[3];
 538         }
 539
 540     }
 541     break;
 542
 543
 544     // Y = (aX + b)^Gamma + e | X >= d
 545     // Y = cX + f             | X < d
 546     case 5:
 547         if (R >= Params[4]) {
 548
 549             e = Params[1]*R + Params[2];
 550
 551             if (e > 0)
 552                 Val = pow(e, Params[0]) + Params[5];
 553             else
 554                 Val = Params[5];
 555         }
 556         else
 557             Val = R*Params[3] + Params[6];
 558         break;
 559
 560
 561     // Reversed type 5
 562     // X=((Y-e)1/g-b)/a   | Y >=(ad+b)^g+e), cd+f
 563     // X=(Y-f)/c          | else
 564     case -5:
 565     {
 566         disc = Params[3] * Params[4] + Params[6];
 567         if (R >= disc) {
 568
 569             e = R - Params[5];
 570             if (e < 0)
 571                 Val = 0;
 572             else
 573             {
 574                 if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 575                     fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 576
 577                     Val = 0;
 578                 else
 579                     Val = (pow(e, 1.0 / Params[0]) - Params[2]) / Params[1];
 580             }
 581         }
 582         else {
 583             if (fabs(Params[3]) < MATRIX_DET_TOLERANCE)
 584                 Val = 0;
 585             else
 586                 Val = (R - Params[6]) / Params[3];
 587         }
 588
 589     }
 590     break;
 591
 592
 593     // Types 6,7,8 comes from segmented curves as described in ICCSpecRevision_02_11_06_Float.pdf
 594     // Type 6 is basically identical to type 5 without d
 595
 596     // Y = (a * X + b) ^ Gamma + c
 597     case 6:
 598         e = Params[1]*R + Params[2];
 599
 600         // On gamma 1.0, don't clamp
 601         if (Params[0] == 1.0) {
 602             Val = e + Params[3];
 603         }
 604         else {
 605             if (e < 0)
 606                 Val = Params[3];
 607             else
 608                 Val = pow(e, Params[0]) + Params[3];
 609         }
 610         break;
 611
 612     // ((Y - c) ^1/Gamma - b) / a
 613     case -6:
 614     {
 615         if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 616             fabs(Params[1]) < MATRIX_DET_TOLERANCE)
 617         {
 618             Val = 0;
 619         }
 620         else
 621         {
 622             e = R - Params[3];
 623             if (e < 0)
 624                 Val = 0;
 625             else
 626                 Val = (pow(e, 1.0 / Params[0]) - Params[2]) / Params[1];
 627         }
 628     }
 629     break;
 630
 631
 632     // Y = a * log (b * X^Gamma + c) + d
 633     case 7:
 634
 635        e = Params[2] * pow(R, Params[0]) + Params[3];
 636        if (e <= 0)
 637            Val = Params[4];
 638        else
 639            Val = Params[1]*log10(e) + Params[4];
 640        break;
 641
 642     // (Y - d) / a = log(b * X ^Gamma + c)
 643     // pow(10, (Y-d) / a) = b * X ^Gamma + c
 644     // pow((pow(10, (Y-d) / a) - c) / b, 1/g) = X
 645     case -7:
 646     {
 647         if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 648             fabs(Params[1]) < MATRIX_DET_TOLERANCE ||
 649             fabs(Params[2]) < MATRIX_DET_TOLERANCE)
 650         {
 651             Val = 0;
 652         }
 653         else
 654         {
 655             Val = pow((pow(10.0, (R - Params[4]) / Params[1]) - Params[3]) / Params[2], 1.0 / Params[0]);
 656         }
 657     }
 658     break;
 659
 660
 661    //Y = a * b^(c*X+d) + e
 662    case 8:
 663        Val = (Params[0] * pow(Params[1], Params[2] * R + Params[3]) + Params[4]);
 664        break;
 665
 666
 667    // Y = (log((y-e) / a) / log(b) - d ) / c
 668    // a=0, b=1, c=2, d=3, e=4,
 669    case -8:
 670
 671        disc = R - Params[4];
 672        if (disc < 0) Val = 0;
 673        else
 674        {
 675            if (fabs(Params[0]) < MATRIX_DET_TOLERANCE ||
 676                fabs(Params[2]) < MATRIX_DET_TOLERANCE)
 677            {
 678                Val = 0;
 679            }
 680            else
 681            {
 682                Val = (log(disc / Params[0]) / log(Params[1]) - Params[3]) / Params[2];
 683            }
 684        }
 685        break;
 686
 687
 688    // S-Shaped: (1 - (1-x)^1/g)^1/g
 689    case 108:
 690        if (fabs(Params[0]) < MATRIX_DET_TOLERANCE)
 691            Val = 0;
 692        else
 693            Val = pow(1.0 - pow(1 - R, 1/Params[0]), 1/Params[0]);
 694       break;
 695
 696     // y = (1 - (1-x)^1/g)^1/g
 697     // y^g = (1 - (1-x)^1/g)
 698     // 1 - y^g = (1-x)^1/g
 699     // (1 - y^g)^g = 1 - x
 700     // 1 - (1 - y^g)^g
 701     case -108:
 702         Val = 1 - pow(1 - pow(R, Params[0]), Params[0]);
 703         break;
 704
 705     // Sigmoidals
 706     case 109:
 707         Val = sigmoid_factory(Params[0], R);
 708         break;
 709
 710     case -109:
 711         Val = inverse_sigmoid_factory(Params[0], R);
 712         break;
 713
 714     default:
 715         // Unsupported parametric curve. Should never reach here
 716         return 0;
 717     }
 718
 719     return Val;
 720 }
 721
 722 // Evaluate a segmented function for a single value. Return -Inf if no valid segment found .
 723 // If fn type is 0, perform an interpolation on the table
 724 static
 725 cmsFloat64Number EvalSegmentedFn(const cmsToneCurve *g, cmsFloat64Number R)
 726 {
 727     int i;
 728     cmsFloat32Number Out32;
 729     cmsFloat64Number Out;
 730
 731     for (i = (int) g->nSegments - 1; i >= 0; --i) {
 732
 733         // Check for domain
 734         if ((R > g->Segments[i].x0) && (R <= g->Segments[i].x1)) {
 735
 736             // Type == 0 means segment is sampled
 737             if (g->Segments[i].Type == 0) {
 738
 739                 cmsFloat32Number R1 = (cmsFloat32Number)(R - g->Segments[i].x0) / (g->Segments[i].x1 - g->Segments[i].x0);
 740
 741                 // Setup the table (TODO: clean that)
 742                 g->SegInterp[i]->Table = g->Segments[i].SampledPoints;
 743
 744                 g->SegInterp[i]->Interpolation.LerpFloat(&R1, &Out32, g->SegInterp[i]);
 745                 Out = (cmsFloat64Number) Out32;
 746
 747             }
 748             else {
 749                 Out = g->Evals[i](g->Segments[i].Type, g->Segments[i].Params, R);
 750             }
 751
 752             if (isinf(Out))
 753                 return PLUS_INF;
 754             else
 755             {
 756                 if (isinf(-Out))
 757                     return MINUS_INF;
 758             }
 759
 760             return Out;
 761         }
 762     }
 763
 764     return MINUS_INF;
 765 }
 766
 767 // Access to estimated low-res table
 768 cmsUInt32Number CMSEXPORT cmsGetToneCurveEstimatedTableEntries(const cmsToneCurve* t)
 769 {
 770     _cmsAssert(t != NULL);
 771     return t ->nEntries;
 772 }
 773
 774 const cmsUInt16Number* CMSEXPORT cmsGetToneCurveEstimatedTable(const cmsToneCurve* t)
 775 {
 776     _cmsAssert(t != NULL);
 777     return t ->Table16;
 778 }
 779
 780
 781 // Create an empty gamma curve, by using tables. This specifies only the limited-precision part, and leaves the
 782 // floating point description empty.
 783 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurve16(cmsContext ContextID, cmsUInt32Number nEntries, const cmsUInt16Number Values[])
 784 {
 785     return AllocateToneCurveStruct(ContextID, nEntries, 0, NULL, Values);
 786 }
 787
 788 static
 789 cmsUInt32Number EntriesByGamma(cmsFloat64Number Gamma)
 790 {
 791     if (fabs(Gamma - 1.0) < 0.001) return 2;
 792     return 4096;
 793 }
 794
 795
 796 // Create a segmented gamma, fill the table
 797 cmsToneCurve* CMSEXPORT cmsBuildSegmentedToneCurve(cmsContext ContextID,
 798                                                    cmsUInt32Number nSegments, const cmsCurveSegment Segments[])
 799 {
 800     cmsUInt32Number i;
 801     cmsFloat64Number R, Val;
 802     cmsToneCurve* g;
 803     cmsUInt32Number nGridPoints = 4096;
 804
 805     _cmsAssert(Segments != NULL);
 806
 807     // Optimizatin for identity curves.
 808     if (nSegments == 1 && Segments[0].Type == 1) {
 809
 810         nGridPoints = EntriesByGamma(Segments[0].Params[0]);
 811     }
 812
 813     g = AllocateToneCurveStruct(ContextID, nGridPoints, nSegments, Segments, NULL);
 814     if (g == NULL) return NULL;
 815
 816     // Once we have the floating point version, we can approximate a 16 bit table of 4096 entries
 817     // for performance reasons. This table would normally not be used except on 8/16 bits transforms.
 818     for (i = 0; i < nGridPoints; i++) {
 819
 820         R   = (cmsFloat64Number) i / (nGridPoints-1);
 821
 822         Val = EvalSegmentedFn(g, R);
 823
 824         // Round and saturate
 825         g ->Table16[i] = _cmsQuickSaturateWord(Val * 65535.0);
 826     }
 827
 828     return g;
 829 }
 830
 831 // Use a segmented curve to store the floating point table
 832 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurveFloat(cmsContext ContextID, cmsUInt32Number nEntries, const cmsFloat32Number values[])
 833 {
 834     cmsCurveSegment Seg[3];
 835
 836     // Do some housekeeping
 837     if (nEntries == 0 || values == NULL)
 838         return NULL;
 839
 840     // A segmented tone curve should have function segments in the first and last positions
 841     // Initialize segmented curve part up to 0 to constant value = samples[0]
 842     Seg[0].x0 = MINUS_INF;
 843     Seg[0].x1 = 0;
 844     Seg[0].Type = 6;
 845
 846     Seg[0].Params[0] = 1;
 847     Seg[0].Params[1] = 0;
 848     Seg[0].Params[2] = 0;
 849     Seg[0].Params[3] = values[0];
 850     Seg[0].Params[4] = 0;
 851
 852     // From zero to 1
 853     Seg[1].x0 = 0;
 854     Seg[1].x1 = 1.0;
 855     Seg[1].Type = 0;
 856
 857     Seg[1].nGridPoints = nEntries;
 858     Seg[1].SampledPoints = (cmsFloat32Number*) values;
 859
 860     // Final segment is constant = lastsample
 861     Seg[2].x0 = 1.0;
 862     Seg[2].x1 = PLUS_INF;
 863     Seg[2].Type = 6;
 864
 865     Seg[2].Params[0] = 1;
 866     Seg[2].Params[1] = 0;
 867     Seg[2].Params[2] = 0;
 868     Seg[2].Params[3] = values[nEntries-1];
 869     Seg[2].Params[4] = 0;
 870
 871
 872     return cmsBuildSegmentedToneCurve(ContextID, 3, Seg);
 873 }
 874
 875 // Parametric curves
 876 //
 877 // Parameters goes as: Curve, a, b, c, d, e, f
 878 // Type is the ICC type +1
 879 // if type is negative, then the curve is analytically inverted
 880 cmsToneCurve* CMSEXPORT cmsBuildParametricToneCurve(cmsContext ContextID, cmsInt32Number Type, const cmsFloat64Number Params[])
 881 {
 882     cmsCurveSegment Seg0;
 883     int Pos = 0;
 884     cmsUInt32Number size;
 885     _cmsParametricCurvesCollection* c = GetParametricCurveByType(ContextID, Type, &Pos);
 886
 887     _cmsAssert(Params != NULL);
 888
 889     if (c == NULL) {
 890         cmsSignalError(ContextID, cmsERROR_UNKNOWN_EXTENSION, "Invalid parametric curve type %d", Type);
 891         return NULL;
 892     }
 893
 894     memset(&Seg0, 0, sizeof(Seg0));
 895
 896     Seg0.x0   = MINUS_INF;
 897     Seg0.x1   = PLUS_INF;
 898     Seg0.Type = Type;
 899
 900     size = c->ParameterCount[Pos] * sizeof(cmsFloat64Number);
 901     memmove(Seg0.Params, Params, size);
 902
 903     return cmsBuildSegmentedToneCurve(ContextID, 1, &Seg0);
 904 }
 905
 906
 907
 908 // Build a gamma table based on gamma constant
 909 cmsToneCurve* CMSEXPORT cmsBuildGamma(cmsContext ContextID, cmsFloat64Number Gamma)
 910 {
 911     return cmsBuildParametricToneCurve(ContextID, 1, &Gamma);
 912 }
 913
 914
 915 // Free all memory taken by the gamma curve
 916 void CMSEXPORT cmsFreeToneCurve(cmsToneCurve* Curve)
 917 {
 918     cmsContext ContextID;
 919
 920     if (Curve == NULL) return;
 921
 922     ContextID = Curve ->InterpParams->ContextID;
 923
 924     _cmsFreeInterpParams(Curve ->InterpParams);
 925
 926     if (Curve -> Table16)
 927         _cmsFree(ContextID, Curve ->Table16);
 928
 929     if (Curve ->Segments) {
 930
 931         cmsUInt32Number i;
 932
 933         for (i=0; i < Curve ->nSegments; i++) {
 934
 935             if (Curve ->Segments[i].SampledPoints) {
 936                 _cmsFree(ContextID, Curve ->Segments[i].SampledPoints);
 937             }
 938
 939             if (Curve ->SegInterp[i] != 0)
 940                 _cmsFreeInterpParams(Curve->SegInterp[i]);
 941         }
 942
 943         _cmsFree(ContextID, Curve ->Segments);
 944         _cmsFree(ContextID, Curve ->SegInterp);
 945     }
 946
 947     if (Curve -> Evals)
 948         _cmsFree(ContextID, Curve -> Evals);
 949
 950     _cmsFree(ContextID, Curve);
 951 }
 952
 953 // Utility function, free 3 gamma tables
 954 void CMSEXPORT cmsFreeToneCurveTriple(cmsToneCurve* Curve[3])
 955 {
 956
 957     _cmsAssert(Curve != NULL);
 958
 959     if (Curve[0] != NULL) cmsFreeToneCurve(Curve[0]);
 960     if (Curve[1] != NULL) cmsFreeToneCurve(Curve[1]);
 961     if (Curve[2] != NULL) cmsFreeToneCurve(Curve[2]);
 962
 963     Curve[0] = Curve[1] = Curve[2] = NULL;
 964 }
 965
 966
 967 // Duplicate a gamma table
 968 cmsToneCurve* CMSEXPORT cmsDupToneCurve(const cmsToneCurve* In)
 969 {
 970     if (In == NULL) return NULL;
 971
 972     return  AllocateToneCurveStruct(In ->InterpParams ->ContextID, In ->nEntries, In ->nSegments, In ->Segments, In ->Table16);
 973 }
 974
 975 // Joins two curves for X and Y. Curves should be monotonic.
 976 // We want to get
 977 //
 978 //      y = Y^-1(X(t))
 979 //
 980 cmsToneCurve* CMSEXPORT cmsJoinToneCurve(cmsContext ContextID,
 981                                       const cmsToneCurve* X,
 982                                       const cmsToneCurve* Y, cmsUInt32Number nResultingPoints)
 983 {
 984     cmsToneCurve* out = NULL;
 985     cmsToneCurve* Yreversed = NULL;
 986     cmsFloat32Number t, x;
 987     cmsFloat32Number* Res = NULL;
 988     cmsUInt32Number i;
 989
 990
 991     _cmsAssert(X != NULL);
 992     _cmsAssert(Y != NULL);
 993
 994     Yreversed = cmsReverseToneCurveEx(nResultingPoints, Y);
 995     if (Yreversed == NULL) goto Error;
 996
 997     Res = (cmsFloat32Number*) _cmsCalloc(ContextID, nResultingPoints, sizeof(cmsFloat32Number));
 998     if (Res == NULL) goto Error;
 999
1000     //Iterate
1001     for (i=0; i <  nResultingPoints; i++) {
1002
1003         t = (cmsFloat32Number) i / (cmsFloat32Number)(nResultingPoints-1);
1004         x = cmsEvalToneCurveFloat(X,  t);
1005         Res[i] = cmsEvalToneCurveFloat(Yreversed, x);
1006     }
1007
1008     // Allocate space for output
1009     out = cmsBuildTabulatedToneCurveFloat(ContextID, nResultingPoints, Res);
1010
1011 Error:
1012
1013     if (Res != NULL) _cmsFree(ContextID, Res);
1014     if (Yreversed != NULL) cmsFreeToneCurve(Yreversed);
1015
1016     return out;
1017 }
1018
1019
1020
1021 // Get the surrounding nodes. This is tricky on non-monotonic tables
1022 static
1023 int GetInterval(cmsFloat64Number In, const cmsUInt16Number LutTable[], const struct _cms_interp_struc* p)
1024 {
1025     int i;
1026     int y0, y1;
1027
1028     // A 1 point table is not allowed
1029     if (p -> Domain[0] < 1) return -1;
1030
1031     // Let's see if ascending or descending.
1032     if (LutTable[0] < LutTable[p ->Domain[0]]) {
1033
1034         // Table is overall ascending
1035         for (i = (int) p->Domain[0] - 1; i >= 0; --i) {
1036
1037             y0 = LutTable[i];
1038             y1 = LutTable[i+1];
1039
1040             if (y0 <= y1) { // Increasing
1041                 if (In >= y0 && In <= y1) return i;
1042             }
1043             else
1044                 if (y1 < y0) { // Decreasing
1045                     if (In >= y1 && In <= y0) return i;
1046                 }
1047         }
1048     }
1049     else {
1050         // Table is overall descending
1051         for (i=0; i < (int) p -> Domain[0]; i++) {
1052
1053             y0 = LutTable[i];
1054             y1 = LutTable[i+1];
1055
1056             if (y0 <= y1) { // Increasing
1057                 if (In >= y0 && In <= y1) return i;
1058             }
1059             else
1060                 if (y1 < y0) { // Decreasing
1061                     if (In >= y1 && In <= y0) return i;
1062                 }
1063         }
1064     }
1065
1066     return -1;
1067 }
1068
1069 // Reverse a gamma table
1070 cmsToneCurve* CMSEXPORT cmsReverseToneCurveEx(cmsUInt32Number nResultSamples, const cmsToneCurve* InCurve)
1071 {
1072     cmsToneCurve *out;
1073     cmsFloat64Number a = 0, b = 0, y, x1, y1, x2, y2;
1074     int i, j;
1075     int Ascending;
1076
1077     _cmsAssert(InCurve != NULL);
1078
1079     // Try to reverse it analytically whatever possible
1080
1081     if (InCurve ->nSegments == 1 && InCurve ->Segments[0].Type > 0 &&
1082         /* InCurve -> Segments[0].Type <= 5 */
1083         GetParametricCurveByType(InCurve ->InterpParams->ContextID, InCurve ->Segments[0].Type, NULL) != NULL) {
1084
1085         return cmsBuildParametricToneCurve(InCurve ->InterpParams->ContextID,
1086                                        -(InCurve -> Segments[0].Type),
1087                                        InCurve -> Segments[0].Params);
1088     }
1089
1090     // Nope, reverse the table.
1091     out = cmsBuildTabulatedToneCurve16(InCurve ->InterpParams->ContextID, nResultSamples, NULL);
1092     if (out == NULL)
1093         return NULL;
1094
1095     // We want to know if this is an ascending or descending table
1096     Ascending = !cmsIsToneCurveDescending(InCurve);
1097
1098     // Iterate across Y axis
1099     for (i=0; i < (int) nResultSamples; i++) {
1100
1101         y = (cmsFloat64Number) i * 65535.0 / (nResultSamples - 1);
1102
1103         // Find interval in which y is within.
1104         j = GetInterval(y, InCurve->Table16, InCurve->InterpParams);
1105         if (j >= 0) {
1106
1107
1108             // Get limits of interval
1109             x1 = InCurve ->Table16[j];
1110             x2 = InCurve ->Table16[j+1];
1111
1112             y1 = (cmsFloat64Number) (j * 65535.0) / (InCurve ->nEntries - 1);
1113             y2 = (cmsFloat64Number) ((j+1) * 65535.0 ) / (InCurve ->nEntries - 1);
1114
1115             // If collapsed, then use any
1116             if (x1 == x2) {
1117
1118                 out ->Table16[i] = _cmsQuickSaturateWord(Ascending ? y2 : y1);
1119                 continue;
1120
1121             } else {
1122
1123                 // Interpolate
1124                 a = (y2 - y1) / (x2 - x1);
1125                 b = y2 - a * x2;
1126             }
1127         }
1128
1129         out ->Table16[i] = _cmsQuickSaturateWord(a* y + b);
1130     }
1131
1132
1133     return out;
1134 }
1135
1136 // Reverse a gamma table
1137 cmsToneCurve* CMSEXPORT cmsReverseToneCurve(const cmsToneCurve* InGamma)
1138 {
1139     _cmsAssert(InGamma != NULL);
1140
1141     return cmsReverseToneCurveEx(4096, InGamma);
1142 }
1143
1144 // From: Eilers, P.H.C. (1994) Smoothing and interpolation with finite
1145 // differences. in: Graphic Gems IV, Heckbert, P.S. (ed.), Academic press.
1146 //
1147 // Smoothing and interpolation with second differences.
1148 //
1149 //   Input:  weights (w), data (y): vector from 1 to m.
1150 //   Input:  smoothing parameter (lambda), length (m).
1151 //   Output: smoothed vector (z): vector from 1 to m.
1152
1153 static
1154 cmsBool smooth2(cmsContext ContextID, cmsFloat32Number w[], cmsFloat32Number y[],
1155                 cmsFloat32Number z[], cmsFloat32Number lambda, int m)
1156 {
1157     int i, i1, i2;
1158     cmsFloat32Number *c, *d, *e;
1159     cmsBool st;
1160
1161
1162     c = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
1163     d = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
1164     e = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
1165
1166     if (c != NULL && d != NULL && e != NULL) {
1167
1168
1169     d[1] = w[1] + lambda;
1170     c[1] = -2 * lambda / d[1];
1171     e[1] = lambda /d[1];
1172     z[1] = w[1] * y[1];
1173     d[2] = w[2] + 5 * lambda - d[1] * c[1] *  c[1];
1174     c[2] = (-4 * lambda - d[1] * c[1] * e[1]) / d[2];
1175     e[2] = lambda / d[2];
1176     z[2] = w[2] * y[2] - c[1] * z[1];
1177
1178     for (i = 3; i < m - 1; i++) {
1179         i1 = i - 1; i2 = i - 2;
1180         d[i]= w[i] + 6 * lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
1181         c[i] = (-4 * lambda -d[i1] * c[i1] * e[i1])/ d[i];
1182         e[i] = lambda / d[i];
1183         z[i] = w[i] * y[i] - c[i1] * z[i1] - e[i2] * z[i2];
1184     }
1185
1186     i1 = m - 2; i2 = m - 3;
1187
1188     d[m - 1] = w[m - 1] + 5 * lambda -c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
1189     c[m - 1] = (-2 * lambda - d[i1] * c[i1] * e[i1]) / d[m - 1];
1190     z[m - 1] = w[m - 1] * y[m - 1] - c[i1] * z[i1] - e[i2] * z[i2];
1191     i1 = m - 1; i2 = m - 2;
1192
1193     d[m] = w[m] + lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
1194     z[m] = (w[m] * y[m] - c[i1] * z[i1] - e[i2] * z[i2]) / d[m];
1195     z[m - 1] = z[m - 1] / d[m - 1] - c[m - 1] * z[m];
1196
1197     for (i = m - 2; 1<= i; i--)
1198         z[i] = z[i] / d[i] - c[i] * z[i + 1] - e[i] * z[i + 2];
1199
1200       st = TRUE;
1201     }
1202     else st = FALSE;
1203
1204     if (c != NULL) _cmsFree(ContextID, c);
1205     if (d != NULL) _cmsFree(ContextID, d);
1206     if (e != NULL) _cmsFree(ContextID, e);
1207
1208     return st;
1209 }
1210
1211 // Smooths a curve sampled at regular intervals.
1212 cmsBool  CMSEXPORT cmsSmoothToneCurve(cmsToneCurve* Tab, cmsFloat64Number lambda)
1213 {
1214     cmsBool SuccessStatus = TRUE;
1215     cmsFloat32Number *w, *y, *z;
1216     cmsUInt32Number i, nItems, Zeros, Poles;
1217     cmsBool notCheck = FALSE;
1218
1219     if (Tab != NULL && Tab->InterpParams != NULL)
1220     {
1221         cmsContext ContextID = Tab->InterpParams->ContextID;
1222
1223         if (!cmsIsToneCurveLinear(Tab)) // Only non-linear curves need smoothing
1224         {
1225             nItems = Tab->nEntries;
1226             if (nItems < MAX_NODES_IN_CURVE)
1227             {
1228                 // Allocate one more item than needed
1229                 w = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
1230                 y = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
1231                 z = (cmsFloat32Number *)_cmsCalloc(ContextID, nItems + 1, sizeof(cmsFloat32Number));
1232
1233                 if (w != NULL && y != NULL && z != NULL) // Ensure no memory allocation failure
1234                 {
1235                     memset(w, 0, (nItems + 1) * sizeof(cmsFloat32Number));
1236                     memset(y, 0, (nItems + 1) * sizeof(cmsFloat32Number));
1237                     memset(z, 0, (nItems + 1) * sizeof(cmsFloat32Number));
1238
1239                     for (i = 0; i < nItems; i++)
1240                     {
1241                         y[i + 1] = (cmsFloat32Number)Tab->Table16[i];
1242                         w[i + 1] = 1.0;
1243                     }
1244
1245                     if (lambda < 0)
1246                     {
1247                         notCheck = TRUE;
1248                         lambda = -lambda;
1249                     }
1250
1251                     if (smooth2(ContextID, w, y, z, (cmsFloat32Number)lambda, (int)nItems))
1252                     {
1253                         // Do some reality - checking...
1254
1255                         Zeros = Poles = 0;
1256                         for (i = nItems; i > 1; --i)
1257                         {
1258                             if (z[i] == 0.) Zeros++;
1259                             if (z[i] >= 65535.) Poles++;
1260                             if (z[i] < z[i - 1])
1261                             {
1262                                 cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Non-Monotonic.");
1263                                 SuccessStatus = notCheck;
1264                                 break;
1265                             }
1266                         }
1267
1268                         if (SuccessStatus && Zeros > (nItems / 3))
1269                         {
1270                             cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly zeros.");
1271                             SuccessStatus = notCheck;
1272                         }
1273
1274                         if (SuccessStatus && Poles > (nItems / 3))
1275                         {
1276                             cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Degenerated, mostly poles.");
1277                             SuccessStatus = notCheck;
1278                         }
1279
1280                         if (SuccessStatus) // Seems ok
1281                         {
1282                             for (i = 0; i < nItems; i++)
1283                             {
1284                                 // Clamp to cmsUInt16Number
1285                                 Tab->Table16[i] = _cmsQuickSaturateWord(z[i + 1]);
1286                             }
1287                         }
1288                     }
1289                     else // Could not smooth
1290                     {
1291                         cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Function smooth2 failed.");
1292                         SuccessStatus = FALSE;
1293                     }
1294                 }
1295                 else // One or more buffers could not be allocated
1296                 {
1297                     cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Could not allocate memory.");
1298                     SuccessStatus = FALSE;
1299                 }
1300
1301                 if (z != NULL)
1302                     _cmsFree(ContextID, z);
1303
1304                 if (y != NULL)
1305                     _cmsFree(ContextID, y);
1306
1307                 if (w != NULL)
1308                     _cmsFree(ContextID, w);
1309             }
1310             else // too many items in the table
1311             {
1312                 cmsSignalError(ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: Too many points.");
1313                 SuccessStatus = FALSE;
1314             }
1315         }
1316     }
1317     else // Tab parameter or Tab->InterpParams is NULL
1318     {
1319         // Can't signal an error here since the ContextID is not known at this point
1320         SuccessStatus = FALSE;
1321     }
1322
1323     return SuccessStatus;
1324 }
1325
1326 // Is a table linear? Do not use parametric since we cannot guarantee some weird parameters resulting
1327 // in a linear table. This way assures it is linear in 12 bits, which should be enough in most cases.
1328 cmsBool CMSEXPORT cmsIsToneCurveLinear(const cmsToneCurve* Curve)
1329 {
1330     int i;
1331     int diff;
1332
1333     _cmsAssert(Curve != NULL);
1334
1335     for (i=0; i < (int) Curve ->nEntries; i++) {
1336
1337         diff = abs((int) Curve->Table16[i] - (int) _cmsQuantizeVal(i, Curve ->nEntries));
1338         if (diff > 0x0f)
1339             return FALSE;
1340     }
1341
1342     return TRUE;
1343 }
1344
1345 // Same, but for monotonicity
1346 cmsBool  CMSEXPORT cmsIsToneCurveMonotonic(const cmsToneCurve* t)
1347 {
1348     cmsUInt32Number n;
1349     int i, last;
1350     cmsBool lDescending;
1351
1352     _cmsAssert(t != NULL);
1353
1354     // Degenerated curves are monotonic? Ok, let's pass them
1355     n = t ->nEntries;
1356     if (n < 2) return TRUE;
1357
1358     // Curve direction
1359     lDescending = cmsIsToneCurveDescending(t);
1360
1361     if (lDescending) {
1362
1363         last = t ->Table16[0];
1364
1365         for (i = 1; i < (int) n; i++) {
1366
1367             if (t ->Table16[i] - last > 2) // We allow some ripple
1368                 return FALSE;
1369             else
1370                 last = t ->Table16[i];
1371
1372         }
1373     }
1374     else {
1375
1376         last = t ->Table16[n-1];
1377
1378         for (i = (int) n - 2; i >= 0; --i) {
1379
1380             if (t ->Table16[i] - last > 2)
1381                 return FALSE;
1382             else
1383                 last = t ->Table16[i];
1384
1385         }
1386     }
1387
1388     return TRUE;
1389 }
1390
1391 // Same, but for descending tables
1392 cmsBool  CMSEXPORT cmsIsToneCurveDescending(const cmsToneCurve* t)
1393 {
1394     _cmsAssert(t != NULL);
1395
1396     return t ->Table16[0] > t ->Table16[t ->nEntries-1];
1397 }
1398
1399
1400 // Another info fn: is out gamma table multisegment?
1401 cmsBool  CMSEXPORT cmsIsToneCurveMultisegment(const cmsToneCurve* t)
1402 {
1403     _cmsAssert(t != NULL);
1404
1405     return t -> nSegments > 1;
1406 }
1407
1408 cmsInt32Number  CMSEXPORT cmsGetToneCurveParametricType(const cmsToneCurve* t)
1409 {
1410     _cmsAssert(t != NULL);
1411
1412     if (t -> nSegments != 1) return 0;
1413     return t ->Segments[0].Type;
1414 }
1415
1416 // We need accuracy this time
1417 cmsFloat32Number CMSEXPORT cmsEvalToneCurveFloat(const cmsToneCurve* Curve, cmsFloat32Number v)
1418 {
1419     _cmsAssert(Curve != NULL);
1420
1421     // Check for 16 bits table. If so, this is a limited-precision tone curve
1422     if (Curve ->nSegments == 0) {
1423
1424         cmsUInt16Number In, Out;
1425
1426         In = (cmsUInt16Number) _cmsQuickSaturateWord(v * 65535.0);
1427         Out = cmsEvalToneCurve16(Curve, In);
1428
1429         return (cmsFloat32Number) (Out / 65535.0);
1430     }
1431
1432     return (cmsFloat32Number) EvalSegmentedFn(Curve, v);
1433 }
1434
1435 // We need xput over here
1436 cmsUInt16Number CMSEXPORT cmsEvalToneCurve16(const cmsToneCurve* Curve, cmsUInt16Number v)
1437 {
1438     cmsUInt16Number out;
1439
1440     _cmsAssert(Curve != NULL);
1441
1442     Curve ->InterpParams ->Interpolation.Lerp16(&v, &out, Curve ->InterpParams);
1443     return out;
1444 }
1445
1446
1447 // Least squares fitting.
1448 // A mathematical procedure for finding the best-fitting curve to a given set of points by
1449 // minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve.
1450 // The sum of the squares of the offsets is used instead of the offset absolute values because
1451 // this allows the residuals to be treated as a continuous differentiable quantity.
1452 //
1453 // y = f(x) = x ^ g
1454 //
1455 // R  = (yi - (xi^g))
1456 // R2 = (yi - (xi^g))2
1457 // SUM R2 = SUM (yi - (xi^g))2
1458 //
1459 // dR2/dg = -2 SUM x^g log(x)(y - x^g)
1460 // solving for dR2/dg = 0
1461 //
1462 // g = 1/n * SUM(log(y) / log(x))
1463
1464 cmsFloat64Number CMSEXPORT cmsEstimateGamma(const cmsToneCurve* t, cmsFloat64Number Precision)
1465 {
1466     cmsFloat64Number gamma, sum, sum2;
1467     cmsFloat64Number n, x, y, Std;
1468     cmsUInt32Number i;
1469
1470     _cmsAssert(t != NULL);
1471
1472     sum = sum2 = n = 0;
1473
1474     // Excluding endpoints
1475     for (i=1; i < (MAX_NODES_IN_CURVE-1); i++) {
1476
1477         x = (cmsFloat64Number) i / (MAX_NODES_IN_CURVE-1);
1478         y = (cmsFloat64Number) cmsEvalToneCurveFloat(t, (cmsFloat32Number) x);
1479
1480         // Avoid 7% on lower part to prevent
1481         // artifacts due to linear ramps
1482
1483         if (y > 0. && y < 1. && x > 0.07) {
1484
1485             gamma = log(y) / log(x);
1486             sum  += gamma;
1487             sum2 += gamma * gamma;
1488             n++;
1489         }
1490     }
1491
1492     // We need enough valid samples
1493     if (n <= 1) return -1.0;
1494
1495     // Take a look on SD to see if gamma isn't exponential at all
1496     Std = sqrt((n * sum2 - sum * sum) / (n*(n-1)));
1497
1498     if (Std > Precision)
1499         return -1.0;
1500
1501     return (sum / n);   // The mean
1502 }
1503
1504 // Retrieve segments on tone curves
1505
1506 const cmsCurveSegment* CMSEXPORT cmsGetToneCurveSegment(cmsInt32Number n, const cmsToneCurve* t)
1507 {
1508     _cmsAssert(t != NULL);
1509
1510     if (n < 0 || n >= (cmsInt32Number) t->nSegments) return NULL;
1511     return t->Segments + n;
1512 }