1 //---------------------------------------------------------------------------------
3 // Little Color Management System
4 // Copyright (c) 1998-2010 Marti Maria Saguer
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:
13 // The above copyright notice and this permission notice shall be included in
14 // all copies or substantial portions of the Software.
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.
24 //---------------------------------------------------------------------------------
26 #include "lcms2_internal.h"
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
38 // ----------------------------------------------------------------- Implementation
39 // Maxim number of nodes
40 #define MAX_NODES_IN_CURVE 4097
41 #define MINUS_INF (-1E22F)
42 #define PLUS_INF (+1E22F)
44 // The list of supported parametric curves
45 typedef struct _cmsParametricCurvesCollection_st {
47 int nFunctions; // Number of supported functions in this chunk
48 int FunctionTypes[MAX_TYPES_IN_LCMS_PLUGIN]; // The identification types
49 int ParameterCount[MAX_TYPES_IN_LCMS_PLUGIN]; // Number of parameters for each function
50 cmsParametricCurveEvaluator Evaluator; // The evaluator
52 struct _cmsParametricCurvesCollection_st* Next; // Next in list
54 } _cmsParametricCurvesCollection;
57 // This is the default (built-in) evaluator
58 static cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R);
61 static _cmsParametricCurvesCollection DefaultCurves = {
62 9, // # of curve types
63 { 1, 2, 3, 4, 5, 6, 7, 8, 108 }, // Parametric curve ID
64 { 1, 3, 4, 5, 7, 4, 5, 5, 1 }, // Parameters by type
65 DefaultEvalParametricFn, // Evaluator
69 // The linked list head
70 static _cmsParametricCurvesCollection* ParametricCurves = &DefaultCurves;
72 // As a way to install new parametric curves
73 cmsBool _cmsRegisterParametricCurvesPlugin(cmsPluginBase* Data)
75 cmsPluginParametricCurves* Plugin = (cmsPluginParametricCurves*) Data;
76 _cmsParametricCurvesCollection* fl;
80 ParametricCurves = &DefaultCurves;
84 fl = (_cmsParametricCurvesCollection*) _cmsPluginMalloc(sizeof(_cmsParametricCurvesCollection));
85 if (fl == NULL) return FALSE;
87 // Copy the parameters
88 fl ->Evaluator = Plugin ->Evaluator;
89 fl ->nFunctions = Plugin ->nFunctions;
91 // Make sure no mem overwrites
92 if (fl ->nFunctions > MAX_TYPES_IN_LCMS_PLUGIN)
93 fl ->nFunctions = MAX_TYPES_IN_LCMS_PLUGIN;
96 memmove(fl->FunctionTypes, Plugin ->FunctionTypes, fl->nFunctions * sizeof(cmsUInt32Number));
97 memmove(fl->ParameterCount, Plugin ->ParameterCount, fl->nFunctions * sizeof(cmsUInt32Number));
100 fl ->Next = ParametricCurves;
101 ParametricCurves = fl;
108 // Search in type list, return position or -1 if not found
110 int IsInSet(int Type, _cmsParametricCurvesCollection* c)
114 for (i=0; i < c ->nFunctions; i++)
115 if (abs(Type) == c ->FunctionTypes[i]) return i;
121 // Search for the collection which contains a specific type
123 _cmsParametricCurvesCollection *GetParametricCurveByType(int Type, int* index)
125 _cmsParametricCurvesCollection* c;
128 for (c = ParametricCurves; c != NULL; c = c ->Next) {
130 Position = IsInSet(Type, c);
132 if (Position != -1) {
142 // Low level allocate, which takes care of memory details. nEntries may be zero, and in this case
143 // no optimation curve is computed. nSegments may also be zero in the inverse case, where only the
144 // optimization curve is given. Both features simultaneously is an error
146 cmsToneCurve* AllocateToneCurveStruct(cmsContext ContextID, cmsInt32Number nEntries,
147 cmsInt32Number nSegments, const cmsCurveSegment* Segments,
148 const cmsUInt16Number* Values)
153 // We allow huge tables, which are then restricted for smoothing operations
154 if (nEntries > 65530 || nEntries < 0) {
155 cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve of more than 65530 entries");
159 if (nEntries <= 0 && nSegments <= 0) {
160 cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve with zero segments and no table");
164 // Allocate all required pointers, etc.
165 p = (cmsToneCurve*) _cmsMallocZero(ContextID, sizeof(cmsToneCurve));
168 // In this case, there are no segments
169 if (nSegments <= 0) {
174 p ->Segments = (cmsCurveSegment*) _cmsCalloc(ContextID, nSegments, sizeof(cmsCurveSegment));
175 if (p ->Segments == NULL) goto Error;
177 p ->Evals = (cmsParametricCurveEvaluator*) _cmsCalloc(ContextID, nSegments, sizeof(cmsParametricCurveEvaluator));
178 if (p ->Evals == NULL) goto Error;
181 p -> nSegments = nSegments;
183 // This 16-bit table contains a limited precision representation of the whole curve and is kept for
184 // increasing xput on certain operations.
189 p ->Table16 = (cmsUInt16Number*) _cmsCalloc(ContextID, nEntries, sizeof(cmsUInt16Number));
190 if (p ->Table16 == NULL) goto Error;
193 p -> nEntries = nEntries;
195 // Initialize members if requested
196 if (Values != NULL && (nEntries > 0)) {
198 for (i=0; i < nEntries; i++)
199 p ->Table16[i] = Values[i];
202 // Initialize the segments stuff. The evaluator for each segment is located and a pointer to it
203 // is placed in advance to maximize performance.
204 if (Segments != NULL && (nSegments > 0)) {
206 _cmsParametricCurvesCollection *c;
208 p ->SegInterp = (cmsInterpParams**) _cmsCalloc(ContextID, nSegments, sizeof(cmsInterpParams*));
209 if (p ->SegInterp == NULL) goto Error;
211 for (i=0; i< nSegments; i++) {
213 // Type 0 is a special marker for table-based curves
214 if (Segments[i].Type == 0)
215 p ->SegInterp[i] = _cmsComputeInterpParams(ContextID, Segments[i].nGridPoints, 1, 1, NULL, CMS_LERP_FLAGS_FLOAT);
217 memmove(&p ->Segments[i], &Segments[i], sizeof(cmsCurveSegment));
219 if (Segments[i].Type == 0 && Segments[i].SampledPoints != NULL)
220 p ->Segments[i].SampledPoints = (cmsFloat32Number*) _cmsDupMem(ContextID, Segments[i].SampledPoints, sizeof(cmsFloat32Number) * Segments[i].nGridPoints);
222 p ->Segments[i].SampledPoints = NULL;
225 c = GetParametricCurveByType(Segments[i].Type, NULL);
227 p ->Evals[i] = c ->Evaluator;
231 p ->InterpParams = _cmsComputeInterpParams(ContextID, p ->nEntries, 1, 1, p->Table16, CMS_LERP_FLAGS_16BITS);
235 if (p -> Segments) _cmsFree(ContextID, p ->Segments);
236 if (p -> Evals) _cmsFree(ContextID, p -> Evals);
237 if (p ->Table16) _cmsFree(ContextID, p ->Table16);
238 _cmsFree(ContextID, p);
243 // Parametric Fn using floating point
245 cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R)
247 cmsFloat64Number e, Val, disc;
256 Val = pow(R, Params[0]);
259 // Type 1 Reversed: X = Y ^1/gamma
264 Val = pow(R, 1/Params[0]);
268 // Y = (aX + b)^Gamma | X >= -b/a
271 disc = -Params[2] / Params[1];
275 e = Params[1]*R + Params[2];
278 Val = pow(e, Params[0]);
287 // X = (Y ^1/g - b) / a
292 Val = (pow(R, 1.0/Params[0]) - Params[2]) / Params[1];
300 // Y = (aX + b)^Gamma | X <= -b/a
303 disc = -Params[2] / Params[1];
309 e = Params[1]*R + Params[2];
312 Val = pow(e, Params[0]) + Params[3];
322 // X=((Y-c)^1/g - b)/a | (Y>=c)
325 if (R >= Params[3]) {
330 Val = (pow(e, 1/Params[0]) - Params[2]) / Params[1];
335 Val = -Params[2] / Params[1];
340 // IEC 61966-2.1 (sRGB)
341 // Y = (aX + b)^Gamma | X >= d
344 if (R >= Params[4]) {
346 e = Params[1]*R + Params[2];
349 Val = pow(e, Params[0]);
358 // X=((Y^1/g-b)/a) | Y >= (ad+b)^g
359 // X=Y/c | Y< (ad+b)^g
361 e = Params[1] * Params[4] + Params[2];
365 disc = pow(e, Params[0]);
369 Val = (pow(R, 1.0/Params[0]) - Params[2]) / Params[1];
377 // Y = (aX + b)^Gamma + e | X >= d
378 // Y = cX + f | X < d
380 if (R >= Params[4]) {
382 e = Params[1]*R + Params[2];
385 Val = pow(e, Params[0]) + Params[5];
390 Val = R*Params[3] + Params[6];
395 // X=((Y-e)1/g-b)/a | Y >=(ad+b)^g+e), cd+f
399 disc = Params[3] * Params[4] + Params[6];
406 Val = (pow(e, 1.0/Params[0]) - Params[2]) / Params[1];
409 Val = (R - Params[6]) / Params[3];
414 // Types 6,7,8 comes from segmented curves as described in ICCSpecRevision_02_11_06_Float.pdf
415 // Type 6 is basically identical to type 5 without d
417 // Y = (a * X + b) ^ Gamma + c
419 e = Params[1]*R + Params[2];
424 Val = pow(e, Params[0]) + Params[3];
427 // ((Y - c) ^1/Gamma - b) / a
433 Val = (pow(e, 1.0/Params[0]) - Params[2]) / Params[1];
437 // Y = a * log (b * X^Gamma + c) + d
440 e = Params[2] * pow(R, Params[0]) + Params[3];
444 Val = Params[1]*log10(e) + Params[4];
447 // (Y - d) / a = log(b * X ^Gamma + c)
448 // pow(10, (Y-d) / a) = b * X ^Gamma + c
449 // pow((pow(10, (Y-d) / a) - c) / b, 1/g) = X
451 Val = pow((pow(10.0, (R-Params[4]) / Params[1]) - Params[3]) / Params[2], 1.0 / Params[0]);
455 //Y = a * b^(c*X+d) + e
457 Val = (Params[0] * pow(Params[1], Params[2] * R + Params[3]) + Params[4]);
461 // Y = (log((y-e) / a) / log(b) - d ) / c
462 // a=0, b=1, c=2, d=3, e=4,
465 disc = R - Params[4];
466 if (disc < 0) Val = 0;
468 Val = (log(disc / Params[0]) / log(Params[1]) - Params[3]) / Params[2];
471 // S-Shaped: (1 - (1-x)^1/g)^1/g
473 Val = pow(1.0 - pow(1 - R, 1/Params[0]), 1/Params[0]);
476 // y = (1 - (1-x)^1/g)^1/g
477 // y^g = (1 - (1-x)^1/g)
478 // 1 - y^g = (1-x)^1/g
479 // (1 - y^g)^g = 1 - x
482 Val = 1 - pow(1 - pow(R, Params[0]), Params[0]);
486 // Unsupported parametric curve. Should never reach here
493 // Evaluate a segmented funtion for a single value. Return -1 if no valid segment found .
494 // If fn type is 0, perform an interpolation on the table
496 cmsFloat64Number EvalSegmentedFn(const cmsToneCurve *g, cmsFloat64Number R)
500 for (i = g ->nSegments-1; i >= 0 ; --i) {
503 if ((R > g ->Segments[i].x0) && (R <= g ->Segments[i].x1)) {
505 // Type == 0 means segment is sampled
506 if (g ->Segments[i].Type == 0) {
508 cmsFloat32Number R1 = (cmsFloat32Number) (R - g ->Segments[i].x0);
509 cmsFloat32Number Out;
511 // Setup the table (TODO: clean that)
512 g ->SegInterp[i]-> Table = g ->Segments[i].SampledPoints;
514 g ->SegInterp[i] -> Interpolation.LerpFloat(&R1, &Out, g ->SegInterp[i]);
519 return g ->Evals[i](g->Segments[i].Type, g ->Segments[i].Params, R);
527 // Create an empty gamma curve, by using tables. This specifies only the limited-precision part, and leaves the
528 // floating point description empty.
529 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurve16(cmsContext ContextID, cmsInt32Number nEntries, const cmsUInt16Number Values[])
531 return AllocateToneCurveStruct(ContextID, nEntries, 0, NULL, Values);
535 int EntriesByGamma(cmsFloat64Number Gamma)
537 if (fabs(Gamma - 1.0) < 0.001) return 2;
542 // Create a segmented gamma, fill the table
543 cmsToneCurve* CMSEXPORT cmsBuildSegmentedToneCurve(cmsContext ContextID,
544 cmsInt32Number nSegments, const cmsCurveSegment Segments[])
547 cmsFloat64Number R, Val;
549 int nGridPoints = 4096;
551 _cmsAssert(Segments != NULL);
553 // Optimizatin for identity curves.
554 if (nSegments == 1 && Segments[0].Type == 1) {
556 nGridPoints = EntriesByGamma(Segments[0].Params[0]);
559 g = AllocateToneCurveStruct(ContextID, nGridPoints, nSegments, Segments, NULL);
560 if (g == NULL) return NULL;
562 // Once we have the floating point version, we can approximate a 16 bit table of 4096 entries
563 // for performance reasons. This table would normally not be used except on 8/16 bits transforms.
564 for (i=0; i < nGridPoints; i++) {
566 R = (cmsFloat64Number) i / (nGridPoints-1);
568 Val = EvalSegmentedFn(g, R);
570 // Round and saturate
571 g ->Table16[i] = _cmsQuickSaturateWord(Val * 65535.0);
577 // Use a segmented curve to store the floating point table
578 cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurveFloat(cmsContext ContextID, cmsUInt32Number nEntries, const cmsFloat32Number values[])
580 cmsCurveSegment Seg[2];
582 // Initialize segmented curve part up to 0
587 Seg[0].Params[0] = 1;
588 Seg[0].Params[1] = 0;
589 Seg[0].Params[2] = 0;
590 Seg[0].Params[3] = 0;
591 Seg[0].Params[4] = 0;
598 Seg[1].nGridPoints = nEntries;
599 Seg[1].SampledPoints = (cmsFloat32Number*) values;
601 return cmsBuildSegmentedToneCurve(ContextID, 2, Seg);
606 // Parameters goes as: Curve, a, b, c, d, e, f
607 // Type is the ICC type +1
608 // if type is negative, then the curve is analyticaly inverted
609 cmsToneCurve* CMSEXPORT cmsBuildParametricToneCurve(cmsContext ContextID, cmsInt32Number Type, const cmsFloat64Number Params[])
611 cmsCurveSegment Seg0;
613 cmsUInt32Number size;
614 _cmsParametricCurvesCollection* c = GetParametricCurveByType(Type, &Pos);
616 _cmsAssert(Params != NULL);
619 cmsSignalError(ContextID, cmsERROR_UNKNOWN_EXTENSION, "Invalid parametric curve type %d", Type);
623 memset(&Seg0, 0, sizeof(Seg0));
629 size = c->ParameterCount[Pos] * sizeof(cmsFloat64Number);
630 memmove(Seg0.Params, Params, size);
632 return cmsBuildSegmentedToneCurve(ContextID, 1, &Seg0);
637 // Build a gamma table based on gamma constant
638 cmsToneCurve* CMSEXPORT cmsBuildGamma(cmsContext ContextID, cmsFloat64Number Gamma)
640 return cmsBuildParametricToneCurve(ContextID, 1, &Gamma);
644 // Free all memory taken by the gamma curve
645 void CMSEXPORT cmsFreeToneCurve(cmsToneCurve* Curve)
647 cmsContext ContextID;
649 if (Curve == NULL) return;
651 ContextID = Curve ->InterpParams->ContextID;
653 _cmsFreeInterpParams(Curve ->InterpParams);
655 if (Curve -> Table16)
656 _cmsFree(ContextID, Curve ->Table16);
658 if (Curve ->Segments) {
662 for (i=0; i < Curve ->nSegments; i++) {
664 if (Curve ->Segments[i].SampledPoints) {
665 _cmsFree(ContextID, Curve ->Segments[i].SampledPoints);
668 if (Curve ->SegInterp[i] != 0)
669 _cmsFreeInterpParams(Curve->SegInterp[i]);
672 _cmsFree(ContextID, Curve ->Segments);
673 _cmsFree(ContextID, Curve ->SegInterp);
677 _cmsFree(ContextID, Curve -> Evals);
679 if (Curve) _cmsFree(ContextID, Curve);
682 // Utility function, free 3 gamma tables
683 void CMSEXPORT cmsFreeToneCurveTriple(cmsToneCurve* Curve[3])
686 _cmsAssert(Curve != NULL);
688 if (Curve[0] != NULL) cmsFreeToneCurve(Curve[0]);
689 if (Curve[1] != NULL) cmsFreeToneCurve(Curve[1]);
690 if (Curve[2] != NULL) cmsFreeToneCurve(Curve[2]);
692 Curve[0] = Curve[1] = Curve[2] = NULL;
696 // Duplicate a gamma table
697 cmsToneCurve* CMSEXPORT cmsDupToneCurve(const cmsToneCurve* In)
699 if (In == NULL) return NULL;
701 return AllocateToneCurveStruct(In ->InterpParams ->ContextID, In ->nEntries, In ->nSegments, In ->Segments, In ->Table16);
704 // Joins two curves for X and Y. Curves should be monotonic.
709 cmsToneCurve* CMSEXPORT cmsJoinToneCurve(cmsContext ContextID,
710 const cmsToneCurve* X,
711 const cmsToneCurve* Y, cmsUInt32Number nResultingPoints)
713 cmsToneCurve* out = NULL;
714 cmsToneCurve* Yreversed = NULL;
715 cmsFloat32Number t, x;
716 cmsFloat32Number* Res = NULL;
720 _cmsAssert(X != NULL);
721 _cmsAssert(Y != NULL);
723 Yreversed = cmsReverseToneCurveEx(nResultingPoints, Y);
724 if (Yreversed == NULL) goto Error;
726 Res = (cmsFloat32Number*) _cmsCalloc(ContextID, nResultingPoints, sizeof(cmsFloat32Number));
727 if (Res == NULL) goto Error;
730 for (i=0; i < nResultingPoints; i++) {
732 t = (cmsFloat32Number) i / (nResultingPoints-1);
733 x = cmsEvalToneCurveFloat(X, t);
734 Res[i] = cmsEvalToneCurveFloat(Yreversed, x);
737 // Allocate space for output
738 out = cmsBuildTabulatedToneCurveFloat(ContextID, nResultingPoints, Res);
742 if (Res != NULL) _cmsFree(ContextID, Res);
743 if (Yreversed != NULL) cmsFreeToneCurve(Yreversed);
750 // Get the surrounding nodes. This is tricky on non-monotonic tables
752 int GetInterval(cmsFloat64Number In, const cmsUInt16Number LutTable[], const struct _cms_interp_struc* p)
757 // A 1 point table is not allowed
758 if (p -> Domain[0] < 1) return -1;
760 // Let's see if ascending or descending.
761 if (LutTable[0] < LutTable[p ->Domain[0]]) {
763 // Table is overall ascending
764 for (i=p->Domain[0]-1; i >=0; --i) {
769 if (y0 <= y1) { // Increasing
770 if (In >= y0 && In <= y1) return i;
773 if (y1 < y0) { // Decreasing
774 if (In >= y1 && In <= y0) return i;
779 // Table is overall descending
780 for (i=0; i < (int) p -> Domain[0]; i++) {
785 if (y0 <= y1) { // Increasing
786 if (In >= y0 && In <= y1) return i;
789 if (y1 < y0) { // Decreasing
790 if (In >= y1 && In <= y0) return i;
798 // Reverse a gamma table
799 cmsToneCurve* CMSEXPORT cmsReverseToneCurveEx(cmsInt32Number nResultSamples, const cmsToneCurve* InCurve)
802 cmsFloat64Number a = 0, b = 0, y, x1, y1, x2, y2;
806 _cmsAssert(InCurve != NULL);
808 // Try to reverse it analytically whatever possible
809 if (InCurve ->nSegments == 1 && InCurve ->Segments[0].Type > 0 && InCurve -> Segments[0].Type <= 5) {
811 return cmsBuildParametricToneCurve(InCurve ->InterpParams->ContextID,
812 -(InCurve -> Segments[0].Type),
813 InCurve -> Segments[0].Params);
816 // Nope, reverse the table.
817 out = cmsBuildTabulatedToneCurve16(InCurve ->InterpParams->ContextID, nResultSamples, NULL);
821 // We want to know if this is an ascending or descending table
822 Ascending = !cmsIsToneCurveDescending(InCurve);
824 // Iterate across Y axis
825 for (i=0; i < nResultSamples; i++) {
827 y = (cmsFloat64Number) i * 65535.0 / (nResultSamples - 1);
829 // Find interval in which y is within.
830 j = GetInterval(y, InCurve->Table16, InCurve->InterpParams);
834 // Get limits of interval
835 x1 = InCurve ->Table16[j];
836 x2 = InCurve ->Table16[j+1];
838 y1 = (cmsFloat64Number) (j * 65535.0) / (InCurve ->nEntries - 1);
839 y2 = (cmsFloat64Number) ((j+1) * 65535.0 ) / (InCurve ->nEntries - 1);
841 // If collapsed, then use any
844 out ->Table16[i] = _cmsQuickSaturateWord(Ascending ? y2 : y1);
850 a = (y2 - y1) / (x2 - x1);
855 out ->Table16[i] = _cmsQuickSaturateWord(a* y + b);
862 // Reverse a gamma table
863 cmsToneCurve* CMSEXPORT cmsReverseToneCurve(const cmsToneCurve* InGamma)
865 _cmsAssert(InGamma != NULL);
867 return cmsReverseToneCurveEx(4096, InGamma);
870 // From: Eilers, P.H.C. (1994) Smoothing and interpolation with finite
871 // differences. in: Graphic Gems IV, Heckbert, P.S. (ed.), Academic press.
873 // Smoothing and interpolation with second differences.
875 // Input: weights (w), data (y): vector from 1 to m.
876 // Input: smoothing parameter (lambda), length (m).
877 // Output: smoothed vector (z): vector from 1 to m.
880 cmsBool smooth2(cmsContext ContextID, cmsFloat32Number w[], cmsFloat32Number y[], cmsFloat32Number z[], cmsFloat32Number lambda, int m)
883 cmsFloat32Number *c, *d, *e;
887 c = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
888 d = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
889 e = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
891 if (c != NULL && d != NULL && e != NULL) {
894 d[1] = w[1] + lambda;
895 c[1] = -2 * lambda / d[1];
898 d[2] = w[2] + 5 * lambda - d[1] * c[1] * c[1];
899 c[2] = (-4 * lambda - d[1] * c[1] * e[1]) / d[2];
900 e[2] = lambda / d[2];
901 z[2] = w[2] * y[2] - c[1] * z[1];
903 for (i = 3; i < m - 1; i++) {
904 i1 = i - 1; i2 = i - 2;
905 d[i]= w[i] + 6 * lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
906 c[i] = (-4 * lambda -d[i1] * c[i1] * e[i1])/ d[i];
907 e[i] = lambda / d[i];
908 z[i] = w[i] * y[i] - c[i1] * z[i1] - e[i2] * z[i2];
911 i1 = m - 2; i2 = m - 3;
913 d[m - 1] = w[m - 1] + 5 * lambda -c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
914 c[m - 1] = (-2 * lambda - d[i1] * c[i1] * e[i1]) / d[m - 1];
915 z[m - 1] = w[m - 1] * y[m - 1] - c[i1] * z[i1] - e[i2] * z[i2];
916 i1 = m - 1; i2 = m - 2;
918 d[m] = w[m] + lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
919 z[m] = (w[m] * y[m] - c[i1] * z[i1] - e[i2] * z[i2]) / d[m];
920 z[m - 1] = z[m - 1] / d[m - 1] - c[m - 1] * z[m];
922 for (i = m - 2; 1<= i; i--)
923 z[i] = z[i] / d[i] - c[i] * z[i + 1] - e[i] * z[i + 2];
929 if (c != NULL) _cmsFree(ContextID, c);
930 if (d != NULL) _cmsFree(ContextID, d);
931 if (e != NULL) _cmsFree(ContextID, e);
936 // Smooths a curve sampled at regular intervals.
937 cmsBool CMSEXPORT cmsSmoothToneCurve(cmsToneCurve* Tab, cmsFloat64Number lambda)
939 cmsFloat32Number w[MAX_NODES_IN_CURVE], y[MAX_NODES_IN_CURVE], z[MAX_NODES_IN_CURVE];
940 int i, nItems, Zeros, Poles;
942 if (Tab == NULL) return FALSE;
944 if (cmsIsToneCurveLinear(Tab)) return FALSE; // Nothing to do
946 nItems = Tab -> nEntries;
948 if (nItems >= MAX_NODES_IN_CURVE) {
949 cmsSignalError(Tab ->InterpParams->ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: too many points.");
953 memset(w, 0, nItems * sizeof(cmsFloat32Number));
954 memset(y, 0, nItems * sizeof(cmsFloat32Number));
955 memset(z, 0, nItems * sizeof(cmsFloat32Number));
957 for (i=0; i < nItems; i++)
959 y[i+1] = (cmsFloat32Number) Tab -> Table16[i];
963 if (!smooth2(Tab ->InterpParams->ContextID, w, y, z, (cmsFloat32Number) lambda, nItems)) return FALSE;
965 // Do some reality - checking...
967 for (i=nItems; i > 1; --i) {
969 if (z[i] == 0.) Zeros++;
970 if (z[i] >= 65535.) Poles++;
971 if (z[i] < z[i-1]) return FALSE; // Non-Monotonic
974 if (Zeros > (nItems / 3)) return FALSE; // Degenerated, mostly zeros
975 if (Poles > (nItems / 3)) return FALSE; // Degenerated, mostly poles
978 for (i=0; i < nItems; i++) {
980 // Clamp to cmsUInt16Number
981 Tab -> Table16[i] = _cmsQuickSaturateWord(z[i+1]);
987 // Is a table linear? Do not use parametric since we cannot guarantee some weird parameters resulting
988 // in a linear table. This way assures it is linear in 12 bits, which should be enought in most cases.
989 cmsBool CMSEXPORT cmsIsToneCurveLinear(const cmsToneCurve* Curve)
994 _cmsAssert(Curve != NULL);
996 for (i=0; i < Curve ->nEntries; i++) {
998 diff = abs((int) Curve->Table16[i] - (int) _cmsQuantizeVal(i, Curve ->nEntries));
1006 // Same, but for monotonicity
1007 cmsBool CMSEXPORT cmsIsToneCurveMonotonic(const cmsToneCurve* t)
1011 cmsBool lDescending;
1013 _cmsAssert(t != NULL);
1015 // Degenerated curves are monotonic? Ok, let's pass them
1017 if (n < 2) return TRUE;
1020 lDescending = cmsIsToneCurveDescending(t);
1024 last = t ->Table16[0];
1026 for (i = 1; i < n; i++) {
1028 if (t ->Table16[i] - last > 2) // We allow some ripple
1031 last = t ->Table16[i];
1037 last = t ->Table16[n-1];
1039 for (i = n-2; i >= 0; --i) {
1041 if (t ->Table16[i] - last > 2)
1044 last = t ->Table16[i];
1052 // Same, but for descending tables
1053 cmsBool CMSEXPORT cmsIsToneCurveDescending(const cmsToneCurve* t)
1055 _cmsAssert(t != NULL);
1057 return t ->Table16[0] > t ->Table16[t ->nEntries-1];
1061 // Another info fn: is out gamma table multisegment?
1062 cmsBool CMSEXPORT cmsIsToneCurveMultisegment(const cmsToneCurve* t)
1064 _cmsAssert(t != NULL);
1066 return t -> nSegments > 1;
1069 cmsInt32Number CMSEXPORT cmsGetToneCurveParametricType(const cmsToneCurve* t)
1071 _cmsAssert(t != NULL);
1073 if (t -> nSegments != 1) return 0;
1074 return t ->Segments[0].Type;
1077 // We need accuracy this time
1078 cmsFloat32Number CMSEXPORT cmsEvalToneCurveFloat(const cmsToneCurve* Curve, cmsFloat32Number v)
1080 _cmsAssert(Curve != NULL);
1082 // Check for 16 bits table. If so, this is a limited-precision tone curve
1083 if (Curve ->nSegments == 0) {
1085 cmsUInt16Number In, Out;
1087 In = (cmsUInt16Number) _cmsQuickSaturateWord(v * 65535.0);
1088 Out = cmsEvalToneCurve16(Curve, In);
1090 return (cmsFloat32Number) (Out / 65535.0);
1093 return (cmsFloat32Number) EvalSegmentedFn(Curve, v);
1096 // We need xput over here
1097 cmsUInt16Number CMSEXPORT cmsEvalToneCurve16(const cmsToneCurve* Curve, cmsUInt16Number v)
1099 cmsUInt16Number out;
1101 _cmsAssert(Curve != NULL);
1103 Curve ->InterpParams ->Interpolation.Lerp16(&v, &out, Curve ->InterpParams);
1108 // Least squares fitting.
1109 // A mathematical procedure for finding the best-fitting curve to a given set of points by
1110 // minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve.
1111 // The sum of the squares of the offsets is used instead of the offset absolute values because
1112 // this allows the residuals to be treated as a continuous differentiable quantity.
1116 // R = (yi - (xi^g))
1117 // R2 = (yi - (xi^g))2
1118 // SUM R2 = SUM (yi - (xi^g))2
1120 // dR2/dg = -2 SUM x^g log(x)(y - x^g)
1121 // solving for dR2/dg = 0
1123 // g = 1/n * SUM(log(y) / log(x))
1125 cmsFloat64Number CMSEXPORT cmsEstimateGamma(const cmsToneCurve* t, cmsFloat64Number Precision)
1127 cmsFloat64Number gamma, sum, sum2;
1128 cmsFloat64Number n, x, y, Std;
1131 _cmsAssert(t != NULL);
1135 // Excluding endpoints
1136 for (i=1; i < (MAX_NODES_IN_CURVE-1); i++) {
1138 x = (cmsFloat64Number) i / (MAX_NODES_IN_CURVE-1);
1139 y = (cmsFloat64Number) cmsEvalToneCurveFloat(t, (cmsFloat32Number) x);
1141 // Avoid 7% on lower part to prevent
1142 // artifacts due to linear ramps
1144 if (y > 0. && y < 1. && x > 0.07) {
1146 gamma = log(y) / log(x);
1148 sum2 += gamma * gamma;
1153 // Take a look on SD to see if gamma isn't exponential at all
1154 Std = sqrt((n * sum2 - sum * sum) / (n*(n-1)));
1156 if (Std > Precision)
1159 return (sum / n); // The mean