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// Copyright (c) the JPEG XL Project Authors. All rights reserved.
//
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Transfer functions for color encodings.
#ifndef LIB_JXL_CMS_TRANSFER_FUNCTIONS_H_
#define LIB_JXL_CMS_TRANSFER_FUNCTIONS_H_
#include <algorithm>
#include <cmath>
#include "lib/jxl/base/status.h"
namespace jxl {
// Definitions for BT.2100-2 transfer functions (used inside/outside SIMD):
// "display" is linear light (nits) normalized to [0, 1].
// "encoded" is a nonlinear encoding (e.g. PQ) in [0, 1].
// "scene" is a linear function of photon counts, normalized to [0, 1].
// Despite the stated ranges, we need unbounded transfer functions: see
// above 1 due to chromatic adaptation. To avoid severe round-trip errors caused
// by clamping, we mirror negative inputs via copysign (f(-x) = -f(x), see
// and extend the function domains above 1.
// Hybrid Log-Gamma.
class TF_HLG_Base {
public:
// EOTF. e = encoded.
static double DisplayFromEncoded(const double e) { return OOTF(InvOETF(e)); }
// Inverse EOTF. d = display.
static double EncodedFromDisplay(const double d) { return OETF(InvOOTF(d)); }
private:
// OETF (defines the HLG approach). s = scene, returns encoded.
static double OETF(double s) {
if (s == 0.0) return 0.0;
const double original_sign = s;
s = std::abs(s);
if (s <= kDiv12) return copysignf(std::sqrt(3.0 * s), original_sign);
const double e = kA * std::log(12 * s - kB) + kC;
JXL_DASSERT(e > 0.0);
return copysignf(e, original_sign);
}
// e = encoded, returns scene.
static double InvOETF(double e) {
if (e == 0.0) return 0.0;
const double original_sign = e;
e = std::abs(e);
if (e <= 0.5) return copysignf(e * e * (1.0 / 3), original_sign);
const double s = (std::exp((e - kC) * kRA) + kB) * kDiv12;
JXL_DASSERT(s >= 0);
return copysignf(s, original_sign);
}
// s = scene, returns display.
static double OOTF(const double s) {
// The actual (red channel) OOTF is RD = alpha * YS^(gamma-1) * RS, where
// YS = 0.2627 * RS + 0.6780 * GS + 0.0593 * BS. Let alpha = 1 so we return
// "display" (normalized [0, 1]) instead of nits. Our transfer function
// interface does not allow a dependency on YS. Fortunately, the system
// gamma at 334 nits is 1.0, so this reduces to RD = RS.
return s;
}
// d = display, returns scene.
static double InvOOTF(const double d) {
return d; // see OOTF().
}
protected:
static constexpr double kA = 0.17883277;
static constexpr double kRA = 1.0 / kA;
static constexpr double kB = 1 - 4 * kA;
static constexpr double kC = 0.5599107295;
static constexpr double kDiv12 = 1.0 / 12;
};
// Perceptual Quantization
class TF_PQ_Base {
public:
static double DisplayFromEncoded(float display_intensity_target, double e) {
if (e == 0.0) return 0.0;
const double original_sign = e;
e = std::abs(e);
const double xp = std::pow(e, 1.0 / kM2);
const double num = std::max(xp - kC1, 0.0);
const double den = kC2 - kC3 * xp;
JXL_DASSERT(den != 0.0);
const double d = std::pow(num / den, 1.0 / kM1);
JXL_DASSERT(d >= 0.0); // Equal for e ~= 1E-9
return copysignf(d * (10000.0f / display_intensity_target), original_sign);
}
// Inverse EOTF. d = display.
static double EncodedFromDisplay(float display_intensity_target, double d) {
if (d == 0.0) return 0.0;
const double original_sign = d;
d = std::abs(d);
const double xp =
std::pow(d * (display_intensity_target * (1.0f / 10000.0f)), kM1);
const double num = kC1 + xp * kC2;
const double den = 1.0 + xp * kC3;
const double e = std::pow(num / den, kM2);
JXL_DASSERT(e > 0.0);
return copysignf(e, original_sign);
}
protected:
static constexpr double kM1 = 2610.0 / 16384;
static constexpr double kM2 = (2523.0 / 4096) * 128;
static constexpr double kC1 = 3424.0 / 4096;
static constexpr double kC2 = (2413.0 / 4096) * 32;
static constexpr double kC3 = (2392.0 / 4096) * 32;
};
} // namespace jxl
#endif // LIB_JXL_CMS_TRANSFER_FUNCTIONS_H_