Source code
Revision control
Copy as Markdown
Other Tools
// 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.
// Fast SIMD floating-point (I)DCT, any power of two.
#if defined(LIB_JXL_DCT_INL_H_) == defined(HWY_TARGET_TOGGLE)
#ifdef LIB_JXL_DCT_INL_H_
#undef LIB_JXL_DCT_INL_H_
#else
#define LIB_JXL_DCT_INL_H_
#endif
#include <stddef.h>
#include <hwy/highway.h>
#include "lib/jxl/dct_block-inl.h"
#include "lib/jxl/dct_scales.h"
#include "lib/jxl/transpose-inl.h"
HWY_BEFORE_NAMESPACE();
namespace jxl {
namespace HWY_NAMESPACE {
namespace {
// These templates are not found via ADL.
using hwy::HWY_NAMESPACE::Add;
using hwy::HWY_NAMESPACE::Mul;
using hwy::HWY_NAMESPACE::MulAdd;
using hwy::HWY_NAMESPACE::NegMulAdd;
using hwy::HWY_NAMESPACE::Sub;
template <size_t SZ>
struct FVImpl {
using type = HWY_CAPPED(float, SZ);
};
template <>
struct FVImpl<0> {
using type = HWY_FULL(float);
};
template <size_t SZ>
using FV = typename FVImpl<SZ>::type;
// Implementation of Lowest Complexity Self Recursive Radix-2 DCT II/III
// Algorithms, by Siriani M. Perera and Jianhua Liu.
template <size_t N, size_t SZ>
struct CoeffBundle {
static void AddReverse(const float* JXL_RESTRICT a_in1,
const float* JXL_RESTRICT a_in2,
float* JXL_RESTRICT a_out) {
for (size_t i = 0; i < N; i++) {
auto in1 = Load(FV<SZ>(), a_in1 + i * SZ);
auto in2 = Load(FV<SZ>(), a_in2 + (N - i - 1) * SZ);
Store(Add(in1, in2), FV<SZ>(), a_out + i * SZ);
}
}
static void SubReverse(const float* JXL_RESTRICT a_in1,
const float* JXL_RESTRICT a_in2,
float* JXL_RESTRICT a_out) {
for (size_t i = 0; i < N; i++) {
auto in1 = Load(FV<SZ>(), a_in1 + i * SZ);
auto in2 = Load(FV<SZ>(), a_in2 + (N - i - 1) * SZ);
Store(Sub(in1, in2), FV<SZ>(), a_out + i * SZ);
}
}
static void B(float* JXL_RESTRICT coeff) {
auto sqrt2 = Set(FV<SZ>(), kSqrt2);
auto in1 = Load(FV<SZ>(), coeff);
auto in2 = Load(FV<SZ>(), coeff + SZ);
Store(MulAdd(in1, sqrt2, in2), FV<SZ>(), coeff);
for (size_t i = 1; i + 1 < N; i++) {
auto in1 = Load(FV<SZ>(), coeff + i * SZ);
auto in2 = Load(FV<SZ>(), coeff + (i + 1) * SZ);
Store(Add(in1, in2), FV<SZ>(), coeff + i * SZ);
}
}
static void BTranspose(float* JXL_RESTRICT coeff) {
for (size_t i = N - 1; i > 0; i--) {
auto in1 = Load(FV<SZ>(), coeff + i * SZ);
auto in2 = Load(FV<SZ>(), coeff + (i - 1) * SZ);
Store(Add(in1, in2), FV<SZ>(), coeff + i * SZ);
}
auto sqrt2 = Set(FV<SZ>(), kSqrt2);
auto in1 = Load(FV<SZ>(), coeff);
Store(Mul(in1, sqrt2), FV<SZ>(), coeff);
}
// Ideally optimized away by compiler (except the multiply).
static void InverseEvenOdd(const float* JXL_RESTRICT a_in,
float* JXL_RESTRICT a_out) {
for (size_t i = 0; i < N / 2; i++) {
auto in1 = Load(FV<SZ>(), a_in + i * SZ);
Store(in1, FV<SZ>(), a_out + 2 * i * SZ);
}
for (size_t i = N / 2; i < N; i++) {
auto in1 = Load(FV<SZ>(), a_in + i * SZ);
Store(in1, FV<SZ>(), a_out + (2 * (i - N / 2) + 1) * SZ);
}
}
// Ideally optimized away by compiler.
static void ForwardEvenOdd(const float* JXL_RESTRICT a_in, size_t a_in_stride,
float* JXL_RESTRICT a_out) {
for (size_t i = 0; i < N / 2; i++) {
auto in1 = LoadU(FV<SZ>(), a_in + 2 * i * a_in_stride);
Store(in1, FV<SZ>(), a_out + i * SZ);
}
for (size_t i = N / 2; i < N; i++) {
auto in1 = LoadU(FV<SZ>(), a_in + (2 * (i - N / 2) + 1) * a_in_stride);
Store(in1, FV<SZ>(), a_out + i * SZ);
}
}
// Invoked on full vector.
static void Multiply(float* JXL_RESTRICT coeff) {
for (size_t i = 0; i < N / 2; i++) {
auto in1 = Load(FV<SZ>(), coeff + (N / 2 + i) * SZ);
auto mul = Set(FV<SZ>(), WcMultipliers<N>::kMultipliers[i]);
Store(Mul(in1, mul), FV<SZ>(), coeff + (N / 2 + i) * SZ);
}
}
static void MultiplyAndAdd(const float* JXL_RESTRICT coeff,
float* JXL_RESTRICT out, size_t out_stride) {
for (size_t i = 0; i < N / 2; i++) {
auto mul = Set(FV<SZ>(), WcMultipliers<N>::kMultipliers[i]);
auto in1 = Load(FV<SZ>(), coeff + i * SZ);
auto in2 = Load(FV<SZ>(), coeff + (N / 2 + i) * SZ);
auto out1 = MulAdd(mul, in2, in1);
auto out2 = NegMulAdd(mul, in2, in1);
StoreU(out1, FV<SZ>(), out + i * out_stride);
StoreU(out2, FV<SZ>(), out + (N - i - 1) * out_stride);
}
}
template <typename Block>
static void LoadFromBlock(const Block& in, size_t off,
float* JXL_RESTRICT coeff) {
for (size_t i = 0; i < N; i++) {
Store(in.LoadPart(FV<SZ>(), i, off), FV<SZ>(), coeff + i * SZ);
}
}
template <typename Block>
static void StoreToBlockAndScale(const float* JXL_RESTRICT coeff,
const Block& out, size_t off) {
auto mul = Set(FV<SZ>(), 1.0f / N);
for (size_t i = 0; i < N; i++) {
out.StorePart(FV<SZ>(), Mul(mul, Load(FV<SZ>(), coeff + i * SZ)), i, off);
}
}
};
template <size_t N, size_t SZ>
struct DCT1DImpl;
template <size_t SZ>
struct DCT1DImpl<1, SZ> {
JXL_INLINE void operator()(float* JXL_RESTRICT mem, float* /* tmp */) {}
};
template <size_t SZ>
struct DCT1DImpl<2, SZ> {
JXL_INLINE void operator()(float* JXL_RESTRICT mem, float* /* tmp */) {
auto in1 = Load(FV<SZ>(), mem);
auto in2 = Load(FV<SZ>(), mem + SZ);
Store(Add(in1, in2), FV<SZ>(), mem);
Store(Sub(in1, in2), FV<SZ>(), mem + SZ);
}
};
template <size_t N, size_t SZ>
struct DCT1DImpl {
void operator()(float* JXL_RESTRICT mem, float* JXL_RESTRICT tmp) {
CoeffBundle<N / 2, SZ>::AddReverse(mem, mem + N / 2 * SZ, tmp);
DCT1DImpl<N / 2, SZ>()(tmp, tmp + N * SZ);
CoeffBundle<N / 2, SZ>::SubReverse(mem, mem + N / 2 * SZ, tmp + N / 2 * SZ);
CoeffBundle<N, SZ>::Multiply(tmp);
DCT1DImpl<N / 2, SZ>()(tmp + N / 2 * SZ, tmp + N * SZ);
CoeffBundle<N / 2, SZ>::B(tmp + N / 2 * SZ);
CoeffBundle<N, SZ>::InverseEvenOdd(tmp, mem);
}
};
template <size_t N, size_t SZ>
struct IDCT1DImpl;
template <size_t SZ>
struct IDCT1DImpl<1, SZ> {
JXL_INLINE void operator()(const float* from, size_t from_stride, float* to,
size_t to_stride, float* JXL_RESTRICT /* tmp */) {
StoreU(LoadU(FV<SZ>(), from), FV<SZ>(), to);
}
};
template <size_t SZ>
struct IDCT1DImpl<2, SZ> {
JXL_INLINE void operator()(const float* from, size_t from_stride, float* to,
size_t to_stride, float* JXL_RESTRICT /* tmp */) {
JXL_DASSERT(from_stride >= SZ);
JXL_DASSERT(to_stride >= SZ);
auto in1 = LoadU(FV<SZ>(), from);
auto in2 = LoadU(FV<SZ>(), from + from_stride);
StoreU(Add(in1, in2), FV<SZ>(), to);
StoreU(Sub(in1, in2), FV<SZ>(), to + to_stride);
}
};
template <size_t N, size_t SZ>
struct IDCT1DImpl {
void operator()(const float* from, size_t from_stride, float* to,
size_t to_stride, float* JXL_RESTRICT tmp) {
JXL_DASSERT(from_stride >= SZ);
JXL_DASSERT(to_stride >= SZ);
CoeffBundle<N, SZ>::ForwardEvenOdd(from, from_stride, tmp);
IDCT1DImpl<N / 2, SZ>()(tmp, SZ, tmp, SZ, tmp + N * SZ);
CoeffBundle<N / 2, SZ>::BTranspose(tmp + N / 2 * SZ);
IDCT1DImpl<N / 2, SZ>()(tmp + N / 2 * SZ, SZ, tmp + N / 2 * SZ, SZ,
tmp + N * SZ);
CoeffBundle<N, SZ>::MultiplyAndAdd(tmp, to, to_stride);
}
};
template <size_t N, size_t M_or_0, typename FromBlock, typename ToBlock>
void DCT1DWrapper(const FromBlock& from, const ToBlock& to, size_t Mp,
float* JXL_RESTRICT tmp) {
size_t M = M_or_0 != 0 ? M_or_0 : Mp;
constexpr size_t SZ = MaxLanes(FV<M_or_0>());
for (size_t i = 0; i < M; i += Lanes(FV<M_or_0>())) {
// TODO(veluca): consider removing the temporary memory here (as is done in
// IDCT), if it turns out that some compilers don't optimize away the loads
// and this is performance-critical.
CoeffBundle<N, SZ>::LoadFromBlock(from, i, tmp);
DCT1DImpl<N, SZ>()(tmp, tmp + N * SZ);
CoeffBundle<N, SZ>::StoreToBlockAndScale(tmp, to, i);
}
}
template <size_t N, size_t M_or_0, typename FromBlock, typename ToBlock>
void IDCT1DWrapper(const FromBlock& from, const ToBlock& to, size_t Mp,
float* JXL_RESTRICT tmp) {
size_t M = M_or_0 != 0 ? M_or_0 : Mp;
constexpr size_t SZ = MaxLanes(FV<M_or_0>());
for (size_t i = 0; i < M; i += Lanes(FV<M_or_0>())) {
IDCT1DImpl<N, SZ>()(from.Address(0, i), from.Stride(), to.Address(0, i),
to.Stride(), tmp);
}
}
template <size_t N, size_t M, typename = void>
struct DCT1D {
template <typename FromBlock, typename ToBlock>
void operator()(const FromBlock& from, const ToBlock& to,
float* JXL_RESTRICT tmp) {
return DCT1DWrapper<N, M>(from, to, M, tmp);
}
};
template <size_t N, size_t M>
struct DCT1D<N, M, typename std::enable_if<(M > MaxLanes(FV<0>()))>::type> {
template <typename FromBlock, typename ToBlock>
void operator()(const FromBlock& from, const ToBlock& to,
float* JXL_RESTRICT tmp) {
return NoInlineWrapper(DCT1DWrapper<N, 0, FromBlock, ToBlock>, from, to, M,
tmp);
}
};
template <size_t N, size_t M, typename = void>
struct IDCT1D {
template <typename FromBlock, typename ToBlock>
void operator()(const FromBlock& from, const ToBlock& to,
float* JXL_RESTRICT tmp) {
return IDCT1DWrapper<N, M>(from, to, M, tmp);
}
};
template <size_t N, size_t M>
struct IDCT1D<N, M, typename std::enable_if<(M > MaxLanes(FV<0>()))>::type> {
template <typename FromBlock, typename ToBlock>
void operator()(const FromBlock& from, const ToBlock& to,
float* JXL_RESTRICT tmp) {
return NoInlineWrapper(IDCT1DWrapper<N, 0, FromBlock, ToBlock>, from, to, M,
tmp);
}
};
// Computes the maybe-transposed, scaled DCT of a block, that needs to be
// HWY_ALIGN'ed.
template <size_t ROWS, size_t COLS>
struct ComputeScaledDCT {
// scratch_space must be aligned, and should have space for ROWS*COLS
// floats.
template <class From>
HWY_MAYBE_UNUSED void operator()(const From& from, float* to,
float* JXL_RESTRICT scratch_space) {
float* JXL_RESTRICT block = scratch_space;
float* JXL_RESTRICT tmp = scratch_space + ROWS * COLS;
if (ROWS < COLS) {
DCT1D<ROWS, COLS>()(from, DCTTo(block, COLS), tmp);
Transpose<ROWS, COLS>::Run(DCTFrom(block, COLS), DCTTo(to, ROWS));
DCT1D<COLS, ROWS>()(DCTFrom(to, ROWS), DCTTo(block, ROWS), tmp);
Transpose<COLS, ROWS>::Run(DCTFrom(block, ROWS), DCTTo(to, COLS));
} else {
DCT1D<ROWS, COLS>()(from, DCTTo(to, COLS), tmp);
Transpose<ROWS, COLS>::Run(DCTFrom(to, COLS), DCTTo(block, ROWS));
DCT1D<COLS, ROWS>()(DCTFrom(block, ROWS), DCTTo(to, ROWS), tmp);
}
}
};
// Computes the maybe-transposed, scaled IDCT of a block, that needs to be
// HWY_ALIGN'ed.
template <size_t ROWS, size_t COLS>
struct ComputeScaledIDCT {
// scratch_space must be aligned, and should have space for ROWS*COLS
// floats.
template <class To>
HWY_MAYBE_UNUSED void operator()(float* JXL_RESTRICT from, const To& to,
float* JXL_RESTRICT scratch_space) {
float* JXL_RESTRICT block = scratch_space;
float* JXL_RESTRICT tmp = scratch_space + ROWS * COLS;
// Reverse the steps done in ComputeScaledDCT.
if (ROWS < COLS) {
Transpose<ROWS, COLS>::Run(DCTFrom(from, COLS), DCTTo(block, ROWS));
IDCT1D<COLS, ROWS>()(DCTFrom(block, ROWS), DCTTo(from, ROWS), tmp);
Transpose<COLS, ROWS>::Run(DCTFrom(from, ROWS), DCTTo(block, COLS));
IDCT1D<ROWS, COLS>()(DCTFrom(block, COLS), to, tmp);
} else {
IDCT1D<COLS, ROWS>()(DCTFrom(from, ROWS), DCTTo(block, ROWS), tmp);
Transpose<COLS, ROWS>::Run(DCTFrom(block, ROWS), DCTTo(from, COLS));
IDCT1D<ROWS, COLS>()(DCTFrom(from, COLS), to, tmp);
}
}
};
} // namespace
// NOLINTNEXTLINE(google-readability-namespace-comments)
} // namespace HWY_NAMESPACE
} // namespace jxl
HWY_AFTER_NAMESPACE();
#endif // LIB_JXL_DCT_INL_H_