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// Copyright 2022 Google Inc. All Rights Reserved.
//
// Use of this source code is governed by a BSD-style license
// that can be found in the COPYING file in the root of the source
// tree. An additional intellectual property rights grant can be found
// in the file PATENTS. All contributing project authors may
// be found in the AUTHORS file in the root of the source tree.
// -----------------------------------------------------------------------------
//
// Gamma correction utilities.
#include "sharpyuv/sharpyuv_gamma.h"
#include <assert.h>
#include <float.h>
#include <math.h>
#include "src/webp/types.h"
// Gamma correction compensates loss of resolution during chroma subsampling.
// Size of pre-computed table for converting from gamma to linear.
#define GAMMA_TO_LINEAR_TAB_BITS 10
#define GAMMA_TO_LINEAR_TAB_SIZE (1 << GAMMA_TO_LINEAR_TAB_BITS)
static uint32_t kGammaToLinearTabS[GAMMA_TO_LINEAR_TAB_SIZE + 2];
#define LINEAR_TO_GAMMA_TAB_BITS 9
#define LINEAR_TO_GAMMA_TAB_SIZE (1 << LINEAR_TO_GAMMA_TAB_BITS)
static uint32_t kLinearToGammaTabS[LINEAR_TO_GAMMA_TAB_SIZE + 2];
static const double kGammaF = 1. / 0.45;
#define GAMMA_TO_LINEAR_BITS 16
static volatile int kGammaTablesSOk = 0;
void SharpYuvInitGammaTables(void) {
assert(GAMMA_TO_LINEAR_BITS <= 16);
if (!kGammaTablesSOk) {
int v;
const double a = 0.09929682680944;
const double thresh = 0.018053968510807;
const double final_scale = 1 << GAMMA_TO_LINEAR_BITS;
// Precompute gamma to linear table.
{
const double norm = 1. / GAMMA_TO_LINEAR_TAB_SIZE;
const double a_rec = 1. / (1. + a);
for (v = 0; v <= GAMMA_TO_LINEAR_TAB_SIZE; ++v) {
const double g = norm * v;
double value;
if (g <= thresh * 4.5) {
value = g / 4.5;
} else {
value = pow(a_rec * (g + a), kGammaF);
}
kGammaToLinearTabS[v] = (uint32_t)(value * final_scale + .5);
}
// to prevent small rounding errors to cause read-overflow:
kGammaToLinearTabS[GAMMA_TO_LINEAR_TAB_SIZE + 1] =
kGammaToLinearTabS[GAMMA_TO_LINEAR_TAB_SIZE];
}
// Precompute linear to gamma table.
{
const double scale = 1. / LINEAR_TO_GAMMA_TAB_SIZE;
for (v = 0; v <= LINEAR_TO_GAMMA_TAB_SIZE; ++v) {
const double g = scale * v;
double value;
if (g <= thresh) {
value = 4.5 * g;
} else {
value = (1. + a) * pow(g, 1. / kGammaF) - a;
}
kLinearToGammaTabS[v] =
(uint32_t)(final_scale * value + 0.5);
}
// to prevent small rounding errors to cause read-overflow:
kLinearToGammaTabS[LINEAR_TO_GAMMA_TAB_SIZE + 1] =
kLinearToGammaTabS[LINEAR_TO_GAMMA_TAB_SIZE];
}
kGammaTablesSOk = 1;
}
}
static WEBP_INLINE int Shift(int v, int shift) {
return (shift >= 0) ? (v << shift) : (v >> -shift);
}
static WEBP_INLINE uint32_t FixedPointInterpolation(int v, uint32_t* tab,
int tab_pos_shift_right,
int tab_value_shift) {
const uint32_t tab_pos = Shift(v, -tab_pos_shift_right);
// fractional part, in 'tab_pos_shift' fixed-point precision
const uint32_t x = v - (tab_pos << tab_pos_shift_right); // fractional part
// v0 / v1 are in kGammaToLinearBits fixed-point precision (range [0..1])
const uint32_t v0 = Shift(tab[tab_pos + 0], tab_value_shift);
const uint32_t v1 = Shift(tab[tab_pos + 1], tab_value_shift);
// Final interpolation.
const uint32_t v2 = (v1 - v0) * x; // note: v1 >= v0.
const int half =
(tab_pos_shift_right > 0) ? 1 << (tab_pos_shift_right - 1) : 0;
const uint32_t result = v0 + ((v2 + half) >> tab_pos_shift_right);
return result;
}
static uint32_t ToLinearSrgb(uint16_t v, int bit_depth) {
const int shift = GAMMA_TO_LINEAR_TAB_BITS - bit_depth;
if (shift > 0) {
return kGammaToLinearTabS[v << shift];
}
return FixedPointInterpolation(v, kGammaToLinearTabS, -shift, 0);
}
static uint16_t FromLinearSrgb(uint32_t value, int bit_depth) {
return FixedPointInterpolation(
value, kLinearToGammaTabS,
(GAMMA_TO_LINEAR_BITS - LINEAR_TO_GAMMA_TAB_BITS),
bit_depth - GAMMA_TO_LINEAR_BITS);
}
////////////////////////////////////////////////////////////////////////////////
#define CLAMP(x, low, high) \
(((x) < (low)) ? (low) : (((high) < (x)) ? (high) : (x)))
#define MIN(a, b) (((a) < (b)) ? (a) : (b))
#define MAX(a, b) (((a) > (b)) ? (a) : (b))
static WEBP_INLINE float Roundf(float x) {
if (x < 0)
return (float)ceil((double)(x - 0.5f));
else
return (float)floor((double)(x + 0.5f));
}
static WEBP_INLINE float Powf(float base, float exp) {
return (float)pow((double)base, (double)exp);
}
static WEBP_INLINE float Log10f(float x) { return (float)log10((double)x); }
static float ToLinear709(float gamma) {
if (gamma < 0.f) {
return 0.f;
} else if (gamma < 4.5f * 0.018053968510807f) {
return gamma / 4.5f;
} else if (gamma < 1.f) {
return Powf((gamma + 0.09929682680944f) / 1.09929682680944f, 1.f / 0.45f);
}
return 1.f;
}
static float FromLinear709(float linear) {
if (linear < 0.f) {
return 0.f;
} else if (linear < 0.018053968510807f) {
return linear * 4.5f;
} else if (linear < 1.f) {
return 1.09929682680944f * Powf(linear, 0.45f) - 0.09929682680944f;
}
return 1.f;
}
static float ToLinear470M(float gamma) {
return Powf(CLAMP(gamma, 0.f, 1.f), 2.2f);
}
static float FromLinear470M(float linear) {
return Powf(CLAMP(linear, 0.f, 1.f), 1.f / 2.2f);
}
static float ToLinear470Bg(float gamma) {
return Powf(CLAMP(gamma, 0.f, 1.f), 2.8f);
}
static float FromLinear470Bg(float linear) {
return Powf(CLAMP(linear, 0.f, 1.f), 1.f / 2.8f);
}
static float ToLinearSmpte240(float gamma) {
if (gamma < 0.f) {
return 0.f;
} else if (gamma < 4.f * 0.022821585529445f) {
return gamma / 4.f;
} else if (gamma < 1.f) {
return Powf((gamma + 0.111572195921731f) / 1.111572195921731f, 1.f / 0.45f);
}
return 1.f;
}
static float FromLinearSmpte240(float linear) {
if (linear < 0.f) {
return 0.f;
} else if (linear < 0.022821585529445f) {
return linear * 4.f;
} else if (linear < 1.f) {
return 1.111572195921731f * Powf(linear, 0.45f) - 0.111572195921731f;
}
return 1.f;
}
static float ToLinearLog100(float gamma) {
// The function is non-bijective so choose the middle of [0, 0.01].
const float mid_interval = 0.01f / 2.f;
return (gamma <= 0.0f) ? mid_interval
: Powf(10.0f, 2.f * (MIN(gamma, 1.f) - 1.0f));
}
static float FromLinearLog100(float linear) {
return (linear < 0.01f) ? 0.0f : 1.0f + Log10f(MIN(linear, 1.f)) / 2.0f;
}
static float ToLinearLog100Sqrt10(float gamma) {
// The function is non-bijective so choose the middle of [0, 0.00316227766f[.
const float mid_interval = 0.00316227766f / 2.f;
return (gamma <= 0.0f) ? mid_interval
: Powf(10.0f, 2.5f * (MIN(gamma, 1.f) - 1.0f));
}
static float FromLinearLog100Sqrt10(float linear) {
return (linear < 0.00316227766f) ? 0.0f
: 1.0f + Log10f(MIN(linear, 1.f)) / 2.5f;
}
static float ToLinearIec61966(float gamma) {
if (gamma <= -4.5f * 0.018053968510807f) {
return Powf((-gamma + 0.09929682680944f) / -1.09929682680944f, 1.f / 0.45f);
} else if (gamma < 4.5f * 0.018053968510807f) {
return gamma / 4.5f;
}
return Powf((gamma + 0.09929682680944f) / 1.09929682680944f, 1.f / 0.45f);
}
static float FromLinearIec61966(float linear) {
if (linear <= -0.018053968510807f) {
return -1.09929682680944f * Powf(-linear, 0.45f) + 0.09929682680944f;
} else if (linear < 0.018053968510807f) {
return linear * 4.5f;
}
return 1.09929682680944f * Powf(linear, 0.45f) - 0.09929682680944f;
}
static float ToLinearBt1361(float gamma) {
if (gamma < -0.25f) {
return -0.25f;
} else if (gamma < 0.f) {
return Powf((gamma - 0.02482420670236f) / -0.27482420670236f, 1.f / 0.45f) /
-4.f;
} else if (gamma < 4.5f * 0.018053968510807f) {
return gamma / 4.5f;
} else if (gamma < 1.f) {
return Powf((gamma + 0.09929682680944f) / 1.09929682680944f, 1.f / 0.45f);
}
return 1.f;
}
static float FromLinearBt1361(float linear) {
if (linear < -0.25f) {
return -0.25f;
} else if (linear < 0.f) {
return -0.27482420670236f * Powf(-4.f * linear, 0.45f) + 0.02482420670236f;
} else if (linear < 0.018053968510807f) {
return linear * 4.5f;
} else if (linear < 1.f) {
return 1.09929682680944f * Powf(linear, 0.45f) - 0.09929682680944f;
}
return 1.f;
}
static float ToLinearPq(float gamma) {
if (gamma > 0.f) {
const float pow_gamma = Powf(gamma, 32.f / 2523.f);
const float num = MAX(pow_gamma - 107.f / 128.f, 0.0f);
const float den = MAX(2413.f / 128.f - 2392.f / 128.f * pow_gamma, FLT_MIN);
return Powf(num / den, 4096.f / 653.f);
}
return 0.f;
}
static float FromLinearPq(float linear) {
if (linear > 0.f) {
const float pow_linear = Powf(linear, 653.f / 4096.f);
const float num = 107.f / 128.f + 2413.f / 128.f * pow_linear;
const float den = 1.0f + 2392.f / 128.f * pow_linear;
return Powf(num / den, 2523.f / 32.f);
}
return 0.f;
}
static float ToLinearSmpte428(float gamma) {
return Powf(MAX(gamma, 0.f), 2.6f) / 0.91655527974030934f;
}
static float FromLinearSmpte428(float linear) {
return Powf(0.91655527974030934f * MAX(linear, 0.f), 1.f / 2.6f);
}
// Conversion in BT.2100 requires RGB info. Simplify to gamma correction here.
static float ToLinearHlg(float gamma) {
if (gamma < 0.f) {
return 0.f;
} else if (gamma <= 0.5f) {
return Powf((gamma * gamma) * (1.f / 3.f), 1.2f);
}
return Powf((expf((gamma - 0.55991073f) / 0.17883277f) + 0.28466892f) / 12.0f,
1.2f);
}
static float FromLinearHlg(float linear) {
linear = Powf(linear, 1.f / 1.2f);
if (linear < 0.f) {
return 0.f;
} else if (linear <= (1.f / 12.f)) {
return sqrtf(3.f * linear);
}
return 0.17883277f * logf(12.f * linear - 0.28466892f) + 0.55991073f;
}
uint32_t SharpYuvGammaToLinear(uint16_t v, int bit_depth,
SharpYuvTransferFunctionType transfer_type) {
float v_float, linear;
if (transfer_type == kSharpYuvTransferFunctionSrgb) {
return ToLinearSrgb(v, bit_depth);
}
v_float = (float)v / ((1 << bit_depth) - 1);
switch (transfer_type) {
case kSharpYuvTransferFunctionBt709:
case kSharpYuvTransferFunctionBt601:
case kSharpYuvTransferFunctionBt2020_10Bit:
case kSharpYuvTransferFunctionBt2020_12Bit:
linear = ToLinear709(v_float);
break;
case kSharpYuvTransferFunctionBt470M:
linear = ToLinear470M(v_float);
break;
case kSharpYuvTransferFunctionBt470Bg:
linear = ToLinear470Bg(v_float);
break;
case kSharpYuvTransferFunctionSmpte240:
linear = ToLinearSmpte240(v_float);
break;
case kSharpYuvTransferFunctionLinear:
return v;
case kSharpYuvTransferFunctionLog100:
linear = ToLinearLog100(v_float);
break;
case kSharpYuvTransferFunctionLog100_Sqrt10:
linear = ToLinearLog100Sqrt10(v_float);
break;
case kSharpYuvTransferFunctionIec61966:
linear = ToLinearIec61966(v_float);
break;
case kSharpYuvTransferFunctionBt1361:
linear = ToLinearBt1361(v_float);
break;
case kSharpYuvTransferFunctionSmpte2084:
linear = ToLinearPq(v_float);
break;
case kSharpYuvTransferFunctionSmpte428:
linear = ToLinearSmpte428(v_float);
break;
case kSharpYuvTransferFunctionHlg:
linear = ToLinearHlg(v_float);
break;
default:
assert(0);
linear = 0;
break;
}
return (uint32_t)Roundf(linear * ((1 << 16) - 1));
}
uint16_t SharpYuvLinearToGamma(uint32_t v, int bit_depth,
SharpYuvTransferFunctionType transfer_type) {
float v_float, linear;
if (transfer_type == kSharpYuvTransferFunctionSrgb) {
return FromLinearSrgb(v, bit_depth);
}
v_float = (float)v / ((1 << 16) - 1);
switch (transfer_type) {
case kSharpYuvTransferFunctionBt709:
case kSharpYuvTransferFunctionBt601:
case kSharpYuvTransferFunctionBt2020_10Bit:
case kSharpYuvTransferFunctionBt2020_12Bit:
linear = FromLinear709(v_float);
break;
case kSharpYuvTransferFunctionBt470M:
linear = FromLinear470M(v_float);
break;
case kSharpYuvTransferFunctionBt470Bg:
linear = FromLinear470Bg(v_float);
break;
case kSharpYuvTransferFunctionSmpte240:
linear = FromLinearSmpte240(v_float);
break;
case kSharpYuvTransferFunctionLinear:
return v;
case kSharpYuvTransferFunctionLog100:
linear = FromLinearLog100(v_float);
break;
case kSharpYuvTransferFunctionLog100_Sqrt10:
linear = FromLinearLog100Sqrt10(v_float);
break;
case kSharpYuvTransferFunctionIec61966:
linear = FromLinearIec61966(v_float);
break;
case kSharpYuvTransferFunctionBt1361:
linear = FromLinearBt1361(v_float);
break;
case kSharpYuvTransferFunctionSmpte2084:
linear = FromLinearPq(v_float);
break;
case kSharpYuvTransferFunctionSmpte428:
linear = FromLinearSmpte428(v_float);
break;
case kSharpYuvTransferFunctionHlg:
linear = FromLinearHlg(v_float);
break;
default:
assert(0);
linear = 0;
break;
}
return (uint16_t)Roundf(linear * ((1 << bit_depth) - 1));
}