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/*
* Copyright 2018 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "../skcms.h"
#include "GaussNewton.h"
#include "Macros.h"
#include "PortableMath.h"
#include "TransferFunction.h"
#include <limits.h>
#include <stdlib.h>
// f(x) = skcms_PolyTF{A,B,C,D}(x) =
// Cx x < D
// A(x^3-1) + B(x^2-1) + 1 x ≥ D
//
// We'll fit C and D directly, and then hold them constant
// and fit the other part using Gauss-Newton, subject to
// the constraint that both parts meet at x=D:
//
// CD = A(D^3-1) + B(D^2-1) + 1
//
// This lets us solve for B, reducing the optimization problem
// for that part down to just a single parameter A:
//
// CD - A(D^3-1) - 1
// B = -----------------
// D^2-1
//
// x^2-1
// f(x) = A(x^3-1) + ----- [CD - A(D^3-1) - 1] + 1
// D^2-1
//
// (x^2-1) (D^3-1)
// ∂f/∂A = x^3-1 - ---------------
// D^2-1
//
// It's important to evaluate as f(x) as A(x^3-1) + B(x^2-1) + 1
// and not Ax^3 + Bx^2 + (1-A-B) to ensure that f(1.0f) == 1.0f.
static float eval_poly_tf(float x, float A, float B, float C, float D) {
return x < D ? C*x
: A*(x*x*x-1) + B*(x*x-1) + 1;
}
typedef struct {
const skcms_Curve* curve;
const skcms_PolyTF* tf;
} rg_poly_tf_arg;
static float rg_poly_tf(float x, const void* ctx, const float P[3], float dfdP[3]) {
const rg_poly_tf_arg* arg = (const rg_poly_tf_arg*)ctx;
const skcms_PolyTF* tf = arg->tf;
float A = P[0],
C = tf->C,
D = tf->D;
float B = (C*D - A*(D*D*D - 1) - 1) / (D*D - 1);
dfdP[0] = (x*x*x - 1) - (x*x-1)*(D*D*D-1)/(D*D-1);
return skcms_eval_curve(x, arg->curve)
- eval_poly_tf(x, A,B,C,D);
}
static bool fit_poly_tf(const skcms_Curve* curve, skcms_PolyTF* tf) {
if (curve->table_entries > (uint32_t)INT_MAX) {
return false;
}
const int N = curve->table_entries == 0 ? 256
: (int)curve->table_entries;
// We'll test the quality of our fit by roundtripping through a skcms_TransferFunction,
// either the inverse of the curve itself if it is parametric, or of its approximation if not.
skcms_TransferFunction baseline;
float err;
if (curve->table_entries == 0) {
baseline = curve->parametric;
} else if (!skcms_ApproximateCurve(curve, &baseline, &err)) {
return false;
}
// We'll borrow the linear section from baseline, which is either
// exactly correct, or already the approximation we'd use anyway.
tf->C = baseline.c;
tf->D = baseline.d;
if (baseline.f != 0) {
return false; // Can't fit this (rare) kind of curve here.
}
// Detect linear baseline: (ax + b)^g + e --> ax ~~> Cx
if (baseline.g == 1 && baseline.d == 0 && baseline.b + baseline.e == 0) {
tf->A = 0;
tf->B = 0;
tf->C = baseline.a;
tf->D = INFINITY_; // Always use Cx, never Ax^3+Bx^2+(1-A-B)
return true;
}
// This case is less likely, but also guards against divide by zero below.
if (tf->D == 1) {
tf->A = 0;
tf->B = 0;
return true;
}
// Number of points already fit in the linear section.
// If the curve isn't parametric and we approximated instead, this should be exact.
const int L = (int)(tf->D * (N-1)) + 1;
// TODO: handle special case of L == N-1 to avoid /0 in Gauss-Newton.
skcms_TransferFunction inv;
if (!skcms_TransferFunction_invert(&baseline, &inv)) {
return false;
}
// Start with guess A = 0, i.e. f(x) ≈ x^2.
float P[3] = {0, 0,0};
for (int i = 0; i < 3; i++) {
rg_poly_tf_arg arg = { curve, tf };
if (!skcms_gauss_newton_step(rg_poly_tf, &arg,
P,
tf->D, 1, N-L)) {
return false;
}
}
float A = tf->A = P[0],
C = tf->C,
D = tf->D,
B = tf->B = (C*D - A*(D*D*D - 1) - 1) / (D*D - 1);
for (int i = 0; i < N; i++) {
float x = i * (1.0f/(N-1));
float rt = skcms_TransferFunction_eval(&inv, eval_poly_tf(x, A,B,C,D));
if (!isfinitef_(rt)) {
return false;
}
const int tol = (i == 0 || i == N-1) ? 0
: N/256;
int ix = (int)((N-1) * rt + 0.5f);
if (abs(i - ix) > tol) {
return false;
}
}
return true;
}
void skcms_OptimizeForSpeed(skcms_ICCProfile* profile) {
for (int i = 0; profile->has_trc && i < 3; i++) {
if (!profile->has_poly_tf[i]) {
profile->has_poly_tf[i] = fit_poly_tf(&profile->trc[i], &profile->poly_tf[i]);
}
}
}
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