// 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. #include "lib/jpegli/adaptive_quantization.h" #include #include #include #include #include #include #include #include #undef HWY_TARGET_INCLUDE #define HWY_TARGET_INCLUDE "lib/jpegli/adaptive_quantization.cc" #include #include #include "lib/jpegli/encode_internal.h" #include "lib/jxl/base/compiler_specific.h" #include "lib/jxl/base/status.h" HWY_BEFORE_NAMESPACE(); namespace jpegli { namespace HWY_NAMESPACE { namespace { // These templates are not found via ADL. using hwy::HWY_NAMESPACE::AbsDiff; using hwy::HWY_NAMESPACE::Add; using hwy::HWY_NAMESPACE::And; using hwy::HWY_NAMESPACE::Div; using hwy::HWY_NAMESPACE::Floor; using hwy::HWY_NAMESPACE::GetLane; using hwy::HWY_NAMESPACE::Max; using hwy::HWY_NAMESPACE::Min; using hwy::HWY_NAMESPACE::Mul; using hwy::HWY_NAMESPACE::MulAdd; using hwy::HWY_NAMESPACE::NegMulAdd; using hwy::HWY_NAMESPACE::Rebind; using hwy::HWY_NAMESPACE::ShiftLeft; using hwy::HWY_NAMESPACE::ShiftRight; using hwy::HWY_NAMESPACE::Sqrt; using hwy::HWY_NAMESPACE::Sub; using hwy::HWY_NAMESPACE::ZeroIfNegative; static constexpr float kInputScaling = 1.0f / 255.0f; // Primary template: default to actual division. template struct FastDivision { HWY_INLINE V operator()(const V n, const V d) const { return n / d; } }; // Partial specialization for float vectors. template struct FastDivision { // One Newton-Raphson iteration. static HWY_INLINE V ReciprocalNR(const V x) { const auto rcp = ApproximateReciprocal(x); const auto sum = Add(rcp, rcp); const auto x_rcp = Mul(x, rcp); return NegMulAdd(x_rcp, rcp, sum); } V operator()(const V n, const V d) const { #if 1 // Faster on SKX return Div(n, d); #else return n * ReciprocalNR(d); #endif } }; // Approximates smooth functions via rational polynomials (i.e. dividing two // polynomials). Evaluates polynomials via Horner's scheme, which is faster than // Clenshaw recurrence for Chebyshev polynomials. LoadDup128 allows us to // specify constants (replicated 4x) independently of the lane count. template HWY_INLINE HWY_MAYBE_UNUSED V EvalRationalPolynomial(const D d, const V x, const T (&p)[NP], const T (&q)[NQ]) { constexpr size_t kDegP = NP / 4 - 1; constexpr size_t kDegQ = NQ / 4 - 1; auto yp = LoadDup128(d, &p[kDegP * 4]); auto yq = LoadDup128(d, &q[kDegQ * 4]); // We use pointer arithmetic to refer to &p[(kDegP - n) * 4] to avoid a // compiler warning that the index is out of bounds since we are already // checking that it is not out of bounds with (kDegP >= n) and the access // will be optimized away. Similarly with q and kDegQ. HWY_FENCE; if (kDegP >= 1) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 1) * 4))); if (kDegQ >= 1) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 1) * 4))); HWY_FENCE; if (kDegP >= 2) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 2) * 4))); if (kDegQ >= 2) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 2) * 4))); HWY_FENCE; if (kDegP >= 3) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 3) * 4))); if (kDegQ >= 3) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 3) * 4))); HWY_FENCE; if (kDegP >= 4) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 4) * 4))); if (kDegQ >= 4) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 4) * 4))); HWY_FENCE; if (kDegP >= 5) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 5) * 4))); if (kDegQ >= 5) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 5) * 4))); HWY_FENCE; if (kDegP >= 6) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 6) * 4))); if (kDegQ >= 6) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 6) * 4))); HWY_FENCE; if (kDegP >= 7) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 7) * 4))); if (kDegQ >= 7) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 7) * 4))); return FastDivision()(yp, yq); } // Computes base-2 logarithm like std::log2. Undefined if negative / NaN. // L1 error ~3.9E-6 template V FastLog2f(const DF df, V x) { // 2,2 rational polynomial approximation of std::log1p(x) / std::log(2). HWY_ALIGN const float p[4 * (2 + 1)] = {HWY_REP4(-1.8503833400518310E-06f), HWY_REP4(1.4287160470083755E+00f), HWY_REP4(7.4245873327820566E-01f)}; HWY_ALIGN const float q[4 * (2 + 1)] = {HWY_REP4(9.9032814277590719E-01f), HWY_REP4(1.0096718572241148E+00f), HWY_REP4(1.7409343003366853E-01f)}; const Rebind di; const auto x_bits = BitCast(di, x); // Range reduction to [-1/3, 1/3] - 3 integer, 2 float ops const auto exp_bits = Sub(x_bits, Set(di, 0x3f2aaaab)); // = 2/3 // Shifted exponent = log2; also used to clear mantissa. const auto exp_shifted = ShiftRight<23>(exp_bits); const auto mantissa = BitCast(df, Sub(x_bits, ShiftLeft<23>(exp_shifted))); const auto exp_val = ConvertTo(df, exp_shifted); return Add(EvalRationalPolynomial(df, Sub(mantissa, Set(df, 1.0f)), p, q), exp_val); } // max relative error ~3e-7 template V FastPow2f(const DF df, V x) { const Rebind di; auto floorx = Floor(x); auto exp = BitCast(df, ShiftLeft<23>(Add(ConvertTo(di, floorx), Set(di, 127)))); auto frac = Sub(x, floorx); auto num = Add(frac, Set(df, 1.01749063e+01)); num = MulAdd(num, frac, Set(df, 4.88687798e+01)); num = MulAdd(num, frac, Set(df, 9.85506591e+01)); num = Mul(num, exp); auto den = MulAdd(frac, Set(df, 2.10242958e-01), Set(df, -2.22328856e-02)); den = MulAdd(den, frac, Set(df, -1.94414990e+01)); den = MulAdd(den, frac, Set(df, 9.85506633e+01)); return Div(num, den); } inline float FastPow2f(float f) { HWY_CAPPED(float, 1) D; return GetLane(FastPow2f(D, Set(D, f))); } // The following functions modulate an exponent (out_val) and return the updated // value. Their descriptor is limited to 8 lanes for 8x8 blocks. template V ComputeMask(const D d, const V out_val) { const auto kBase = Set(d, -0.74174993f); const auto kMul4 = Set(d, 3.2353257320940401f); const auto kMul2 = Set(d, 12.906028311180409f); const auto kOffset2 = Set(d, 305.04035728311436f); const auto kMul3 = Set(d, 5.0220313103171232f); const auto kOffset3 = Set(d, 2.1925739705298404f); const auto kOffset4 = Mul(Set(d, 0.25f), kOffset3); const auto kMul0 = Set(d, 0.74760422233706747f); const auto k1 = Set(d, 1.0f); // Avoid division by zero. const auto v1 = Max(Mul(out_val, kMul0), Set(d, 1e-3f)); const auto v2 = Div(k1, Add(v1, kOffset2)); const auto v3 = Div(k1, MulAdd(v1, v1, kOffset3)); const auto v4 = Div(k1, MulAdd(v1, v1, kOffset4)); // TODO(jyrki): // A log or two here could make sense. In butteraugli we have effectively // log(log(x + C)) for this kind of use, as a single log is used in // saturating visual masking and here the modulation values are exponential, // another log would counter that. return Add(kBase, MulAdd(kMul4, v4, MulAdd(kMul2, v2, Mul(kMul3, v3)))); } // mul and mul2 represent a scaling difference between jxl and butteraugli. static const float kSGmul = 226.0480446705883f; static const float kSGmul2 = 1.0f / 73.377132366608819f; static const float kLog2 = 0.693147181f; // Includes correction factor for std::log -> log2. static const float kSGRetMul = kSGmul2 * 18.6580932135f * kLog2; static const float kSGVOffset = 7.14672470003f; template V RatioOfDerivativesOfCubicRootToSimpleGamma(const D d, V v) { // The opsin space in jxl is the cubic root of photons, i.e., v * v * v // is related to the number of photons. // // SimpleGamma(v * v * v) is the psychovisual space in butteraugli. // This ratio allows quantization to move from jxl's opsin space to // butteraugli's log-gamma space. static const float kEpsilon = 1e-2; static const float kNumOffset = kEpsilon / kInputScaling / kInputScaling; static const float kNumMul = kSGRetMul * 3 * kSGmul; static const float kVOffset = (kSGVOffset * kLog2 + kEpsilon) / kInputScaling; static const float kDenMul = kLog2 * kSGmul * kInputScaling * kInputScaling; v = ZeroIfNegative(v); const auto num_mul = Set(d, kNumMul); const auto num_offset = Set(d, kNumOffset); const auto den_offset = Set(d, kVOffset); const auto den_mul = Set(d, kDenMul); const auto v2 = Mul(v, v); const auto num = MulAdd(num_mul, v2, num_offset); const auto den = MulAdd(Mul(den_mul, v), v2, den_offset); return invert ? Div(num, den) : Div(den, num); } template static float RatioOfDerivativesOfCubicRootToSimpleGamma(float v) { using DScalar = HWY_CAPPED(float, 1); auto vscalar = Load(DScalar(), &v); return GetLane( RatioOfDerivativesOfCubicRootToSimpleGamma(DScalar(), vscalar)); } // TODO(veluca): this function computes an approximation of the derivative of // SimpleGamma with (f(x+eps)-f(x))/eps. Consider two-sided approximation or // exact derivatives. For reference, SimpleGamma was: /* template V SimpleGamma(const D d, V v) { // A simple HDR compatible gamma function. const auto mul = Set(d, kSGmul); const auto kRetMul = Set(d, kSGRetMul); const auto kRetAdd = Set(d, kSGmul2 * -20.2789020414f); const auto kVOffset = Set(d, kSGVOffset); v *= mul; // This should happen rarely, but may lead to a NaN, which is rather // undesirable. Since negative photons don't exist we solve the NaNs by // clamping here. // TODO(veluca): with FastLog2f, this no longer leads to NaNs. v = ZeroIfNegative(v); return kRetMul * FastLog2f(d, v + kVOffset) + kRetAdd; } */ template V GammaModulation(const D d, const size_t x, const size_t y, const RowBuffer& input, const V out_val) { static const float kBias = 0.16f / kInputScaling; static const float kScale = kInputScaling / 64.0f; auto overall_ratio = Zero(d); const auto bias = Set(d, kBias); const auto scale = Set(d, kScale); const float* const JXL_RESTRICT block_start = input.Row(y) + x; for (size_t dy = 0; dy < 8; ++dy) { const float* const JXL_RESTRICT row_in = block_start + dy * input.stride(); for (size_t dx = 0; dx < 8; dx += Lanes(d)) { const auto iny = Add(Load(d, row_in + dx), bias); const auto ratio_g = RatioOfDerivativesOfCubicRootToSimpleGamma(d, iny); overall_ratio = Add(overall_ratio, ratio_g); } } overall_ratio = Mul(SumOfLanes(d, overall_ratio), scale); // ideally -1.0, but likely optimal correction adds some entropy, so slightly // less than that. // ln(2) constant folded in because we want std::log but have FastLog2f. const auto kGam = Set(d, -0.15526878023684174f * 0.693147180559945f); return MulAdd(kGam, FastLog2f(d, overall_ratio), out_val); } // Change precision in 8x8 blocks that have high frequency content. template V HfModulation(const D d, const size_t x, const size_t y, const RowBuffer& input, const V out_val) { // Zero out the invalid differences for the rightmost value per row. const Rebind du; HWY_ALIGN constexpr uint32_t kMaskRight[8] = {~0u, ~0u, ~0u, ~0u, ~0u, ~0u, ~0u, 0}; auto sum = Zero(d); // sum of absolute differences with right and below static const float kSumCoeff = -2.0052193233688884f * kInputScaling / 112.0; auto sumcoeff = Set(d, kSumCoeff); const float* const JXL_RESTRICT block_start = input.Row(y) + x; for (size_t dy = 0; dy < 8; ++dy) { const float* JXL_RESTRICT row_in = block_start + dy * input.stride(); const float* JXL_RESTRICT row_in_next = dy == 7 ? row_in : row_in + input.stride(); for (size_t dx = 0; dx < 8; dx += Lanes(d)) { const auto p = Load(d, row_in + dx); const auto pr = LoadU(d, row_in + dx + 1); const auto mask = BitCast(d, Load(du, kMaskRight + dx)); sum = Add(sum, And(mask, AbsDiff(p, pr))); const auto pd = Load(d, row_in_next + dx); sum = Add(sum, AbsDiff(p, pd)); } } sum = SumOfLanes(d, sum); return MulAdd(sum, sumcoeff, out_val); } void PerBlockModulations(const float y_quant_01, const RowBuffer& input, const size_t yb0, const size_t yblen, RowBuffer* aq_map) { static const float kAcQuant = 0.841f; float base_level = 0.48f * kAcQuant; float kDampenRampStart = 9.0f; float kDampenRampEnd = 65.0f; float dampen = 1.0f; if (y_quant_01 >= kDampenRampStart) { dampen = 1.0f - ((y_quant_01 - kDampenRampStart) / (kDampenRampEnd - kDampenRampStart)); if (dampen < 0) { dampen = 0; } } const float mul = kAcQuant * dampen; const float add = (1.0f - dampen) * base_level; for (size_t iy = 0; iy < yblen; iy++) { const size_t yb = yb0 + iy; const size_t y = yb * 8; float* const JXL_RESTRICT row_out = aq_map->Row(yb); const HWY_CAPPED(float, 8) df; for (size_t ix = 0; ix < aq_map->xsize(); ix++) { size_t x = ix * 8; auto out_val = Set(df, row_out[ix]); out_val = ComputeMask(df, out_val); out_val = HfModulation(df, x, y, input, out_val); out_val = GammaModulation(df, x, y, input, out_val); // We want multiplicative quantization field, so everything // until this point has been modulating the exponent. row_out[ix] = FastPow2f(GetLane(out_val) * 1.442695041f) * mul + add; } } } template V MaskingSqrt(const D d, V v) { static const float kLogOffset = 28; static const float kMul = 211.50759899638012f; const auto mul_v = Set(d, kMul * 1e8); const auto offset_v = Set(d, kLogOffset); return Mul(Set(d, 0.25f), Sqrt(MulAdd(v, Sqrt(mul_v), offset_v))); } template void Sort4(V& min0, V& min1, V& min2, V& min3) { const auto tmp0 = Min(min0, min1); const auto tmp1 = Max(min0, min1); const auto tmp2 = Min(min2, min3); const auto tmp3 = Max(min2, min3); const auto tmp4 = Max(tmp0, tmp2); const auto tmp5 = Min(tmp1, tmp3); min0 = Min(tmp0, tmp2); min1 = Min(tmp4, tmp5); min2 = Max(tmp4, tmp5); min3 = Max(tmp1, tmp3); } template void UpdateMin4(const V v, V& min0, V& min1, V& min2, V& min3) { const auto tmp0 = Max(min0, v); const auto tmp1 = Max(min1, tmp0); const auto tmp2 = Max(min2, tmp1); min0 = Min(min0, v); min1 = Min(min1, tmp0); min2 = Min(min2, tmp1); min3 = Min(min3, tmp2); } // Computes a linear combination of the 4 lowest values of the 3x3 neighborhood // of each pixel. Output is downsampled 2x. void FuzzyErosion(const RowBuffer& pre_erosion, const size_t yb0, const size_t yblen, RowBuffer* tmp, RowBuffer* aq_map) { int xsize_blocks = aq_map->xsize(); int xsize = pre_erosion.xsize(); HWY_FULL(float) d; const auto mul0 = Set(d, 0.125f); const auto mul1 = Set(d, 0.075f); const auto mul2 = Set(d, 0.06f); const auto mul3 = Set(d, 0.05f); for (size_t iy = 0; iy < 2 * yblen; ++iy) { size_t y = 2 * yb0 + iy; const float* JXL_RESTRICT rowt = pre_erosion.Row(y - 1); const float* JXL_RESTRICT rowm = pre_erosion.Row(y); const float* JXL_RESTRICT rowb = pre_erosion.Row(y + 1); float* row_out = tmp->Row(y); for (int x = 0; x < xsize; x += Lanes(d)) { int xm1 = x - 1; int xp1 = x + 1; auto min0 = LoadU(d, rowm + x); auto min1 = LoadU(d, rowm + xm1); auto min2 = LoadU(d, rowm + xp1); auto min3 = LoadU(d, rowt + xm1); Sort4(min0, min1, min2, min3); UpdateMin4(LoadU(d, rowt + x), min0, min1, min2, min3); UpdateMin4(LoadU(d, rowt + xp1), min0, min1, min2, min3); UpdateMin4(LoadU(d, rowb + xm1), min0, min1, min2, min3); UpdateMin4(LoadU(d, rowb + x), min0, min1, min2, min3); UpdateMin4(LoadU(d, rowb + xp1), min0, min1, min2, min3); const auto v = Add(Add(Mul(mul0, min0), Mul(mul1, min1)), Add(Mul(mul2, min2), Mul(mul3, min3))); Store(v, d, row_out + x); } if (iy % 2 == 1) { const float* JXL_RESTRICT row_out0 = tmp->Row(y - 1); float* JXL_RESTRICT aq_out = aq_map->Row(yb0 + iy / 2); for (int bx = 0, x = 0; bx < xsize_blocks; ++bx, x += 2) { aq_out[bx] = (row_out[x] + row_out[x + 1] + row_out0[x] + row_out0[x + 1]); } } } } void ComputePreErosion(const RowBuffer& input, const size_t xsize, const size_t y0, const size_t ylen, int border, float* diff_buffer, RowBuffer* pre_erosion) { const size_t xsize_out = xsize / 4; const size_t y0_out = y0 / 4; // The XYB gamma is 3.0 to be able to decode faster with two muls. // Butteraugli's gamma is matching the gamma of human eye, around 2.6. // We approximate the gamma difference by adding one cubic root into // the adaptive quantization. This gives us a total gamma of 2.6666 // for quantization uses. static const float match_gamma_offset = 0.019 / kInputScaling; const HWY_CAPPED(float, 8) df; static const float limit = 0.2f; // Computes image (padded to multiple of 8x8) of local pixel differences. // Subsample both directions by 4. for (size_t iy = 0; iy < ylen; ++iy) { size_t y = y0 + iy; const float* row_in = input.Row(y); const float* row_in1 = input.Row(y + 1); const float* row_in2 = input.Row(y - 1); float* JXL_RESTRICT row_out = diff_buffer; const auto match_gamma_offset_v = Set(df, match_gamma_offset); const auto quarter = Set(df, 0.25f); for (size_t x = 0; x < xsize; x += Lanes(df)) { const auto in = LoadU(df, row_in + x); const auto in_r = LoadU(df, row_in + x + 1); const auto in_l = LoadU(df, row_in + x - 1); const auto in_t = LoadU(df, row_in2 + x); const auto in_b = LoadU(df, row_in1 + x); const auto base = Mul(quarter, Add(Add(in_r, in_l), Add(in_t, in_b))); const auto gammacv = RatioOfDerivativesOfCubicRootToSimpleGamma( df, Add(in, match_gamma_offset_v)); auto diff = Mul(gammacv, Sub(in, base)); diff = Mul(diff, diff); diff = Min(diff, Set(df, limit)); diff = MaskingSqrt(df, diff); if ((iy & 3) != 0) { diff = Add(diff, LoadU(df, row_out + x)); } StoreU(diff, df, row_out + x); } if (iy % 4 == 3) { size_t y_out = y0_out + iy / 4; float* row_dout = pre_erosion->Row(y_out); for (size_t x = 0; x < xsize_out; x++) { row_dout[x] = (row_out[x * 4] + row_out[x * 4 + 1] + row_out[x * 4 + 2] + row_out[x * 4 + 3]) * 0.25f; } pre_erosion->PadRow(y_out, xsize_out, border); } } } } // namespace // NOLINTNEXTLINE(google-readability-namespace-comments) } // namespace HWY_NAMESPACE } // namespace jpegli HWY_AFTER_NAMESPACE(); #if HWY_ONCE namespace jpegli { HWY_EXPORT(ComputePreErosion); HWY_EXPORT(FuzzyErosion); HWY_EXPORT(PerBlockModulations); namespace { static constexpr int kPreErosionBorder = 1; } // namespace void ComputeAdaptiveQuantField(j_compress_ptr cinfo) { jpeg_comp_master* m = cinfo->master; if (!m->use_adaptive_quantization) { return; } int y_channel = cinfo->jpeg_color_space == JCS_RGB ? 1 : 0; jpeg_component_info* y_comp = &cinfo->comp_info[y_channel]; int y_quant_01 = cinfo->quant_tbl_ptrs[y_comp->quant_tbl_no]->quantval[1]; if (m->next_iMCU_row == 0) { m->input_buffer[y_channel].CopyRow(-1, 0, 1); } if (m->next_iMCU_row + 1 == cinfo->total_iMCU_rows) { size_t last_row = m->ysize_blocks * DCTSIZE - 1; m->input_buffer[y_channel].CopyRow(last_row + 1, last_row, 1); } const RowBuffer& input = m->input_buffer[y_channel]; const size_t xsize_blocks = y_comp->width_in_blocks; const size_t xsize = xsize_blocks * DCTSIZE; const size_t yb0 = m->next_iMCU_row * cinfo->max_v_samp_factor; const size_t yblen = cinfo->max_v_samp_factor; size_t y0 = yb0 * DCTSIZE; size_t ylen = cinfo->max_v_samp_factor * DCTSIZE; if (y0 == 0) { ylen += 4; } else { y0 += 4; } if (m->next_iMCU_row + 1 == cinfo->total_iMCU_rows) { ylen -= 4; } HWY_DYNAMIC_DISPATCH(ComputePreErosion) (input, xsize, y0, ylen, kPreErosionBorder, m->diff_buffer, &m->pre_erosion); if (y0 == 0) { m->pre_erosion.CopyRow(-1, 0, kPreErosionBorder); } if (m->next_iMCU_row + 1 == cinfo->total_iMCU_rows) { size_t last_row = m->ysize_blocks * 2 - 1; m->pre_erosion.CopyRow(last_row + 1, last_row, kPreErosionBorder); } HWY_DYNAMIC_DISPATCH(FuzzyErosion) (m->pre_erosion, yb0, yblen, &m->fuzzy_erosion_tmp, &m->quant_field); HWY_DYNAMIC_DISPATCH(PerBlockModulations) (y_quant_01, input, yb0, yblen, &m->quant_field); for (int y = 0; y < cinfo->max_v_samp_factor; ++y) { float* row = m->quant_field.Row(yb0 + y); for (size_t x = 0; x < xsize_blocks; ++x) { row[x] = std::max(0.0f, (0.6f / row[x]) - 1.0f); } } } } // namespace jpegli #endif // HWY_ONCE