diff options
Diffstat (limited to 'unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h')
| -rw-r--r-- | unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h | 651 |
1 files changed, 651 insertions, 0 deletions
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h new file mode 100644 index 000000000..08eb5595a --- /dev/null +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h @@ -0,0 +1,651 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Jianwei Cui <thucjw@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CXX11_TENSOR_TENSOR_FFT_H +#define EIGEN_CXX11_TENSOR_TENSOR_FFT_H + +// This code requires the ability to initialize arrays of constant +// values directly inside a class. +#if __cplusplus >= 201103L || EIGEN_COMP_MSVC >= 1900 + +namespace Eigen { + +/** \class TensorFFT + * \ingroup CXX11_Tensor_Module + * + * \brief Tensor FFT class. + * + * TODO: + * Vectorize the Cooley Tukey and the Bluestein algorithm + * Add support for multithreaded evaluation + * Improve the performance on GPU + */ + +template <bool NeedUprade> struct MakeComplex { + template <typename T> + EIGEN_DEVICE_FUNC + T operator() (const T& val) const { return val; } +}; + +template <> struct MakeComplex<true> { + template <typename T> + EIGEN_DEVICE_FUNC + std::complex<T> operator() (const T& val) const { return std::complex<T>(val, 0); } +}; + +template <> struct MakeComplex<false> { + template <typename T> + EIGEN_DEVICE_FUNC + std::complex<T> operator() (const std::complex<T>& val) const { return val; } +}; + +template <int ResultType> struct PartOf { + template <typename T> T operator() (const T& val) const { return val; } +}; + +template <> struct PartOf<RealPart> { + template <typename T> T operator() (const std::complex<T>& val) const { return val.real(); } +}; + +template <> struct PartOf<ImagPart> { + template <typename T> T operator() (const std::complex<T>& val) const { return val.imag(); } +}; + +namespace internal { +template <typename FFT, typename XprType, int FFTResultType, int FFTDir> +struct traits<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir> > : public traits<XprType> { + typedef traits<XprType> XprTraits; + typedef typename NumTraits<typename XprTraits::Scalar>::Real RealScalar; + typedef typename std::complex<RealScalar> ComplexScalar; + typedef typename XprTraits::Scalar InputScalar; + typedef typename conditional<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>::type OutputScalar; + typedef typename XprTraits::StorageKind StorageKind; + typedef typename XprTraits::Index Index; + typedef typename XprType::Nested Nested; + typedef typename remove_reference<Nested>::type _Nested; + static const int NumDimensions = XprTraits::NumDimensions; + static const int Layout = XprTraits::Layout; +}; + +template <typename FFT, typename XprType, int FFTResultType, int FFTDirection> +struct eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, Eigen::Dense> { + typedef const TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>& type; +}; + +template <typename FFT, typename XprType, int FFTResultType, int FFTDirection> +struct nested<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, 1, typename eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> >::type> { + typedef TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> type; +}; + +} // end namespace internal + +template <typename FFT, typename XprType, int FFTResultType, int FFTDir> +class TensorFFTOp : public TensorBase<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir>, ReadOnlyAccessors> { + public: + typedef typename Eigen::internal::traits<TensorFFTOp>::Scalar Scalar; + typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; + typedef typename std::complex<RealScalar> ComplexScalar; + typedef typename internal::conditional<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>::type OutputScalar; + typedef OutputScalar CoeffReturnType; + typedef typename Eigen::internal::nested<TensorFFTOp>::type Nested; + typedef typename Eigen::internal::traits<TensorFFTOp>::StorageKind StorageKind; + typedef typename Eigen::internal::traits<TensorFFTOp>::Index Index; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorFFTOp(const XprType& expr, const FFT& fft) + : m_xpr(expr), m_fft(fft) {} + + EIGEN_DEVICE_FUNC + const FFT& fft() const { return m_fft; } + + EIGEN_DEVICE_FUNC + const typename internal::remove_all<typename XprType::Nested>::type& expression() const { + return m_xpr; + } + + protected: + typename XprType::Nested m_xpr; + const FFT m_fft; +}; + +// Eval as rvalue +template <typename FFT, typename ArgType, typename Device, int FFTResultType, int FFTDir> +struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, Device> { + typedef TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir> XprType; + typedef typename XprType::Index Index; + static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value; + typedef DSizes<Index, NumDims> Dimensions; + typedef typename XprType::Scalar Scalar; + typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; + typedef typename std::complex<RealScalar> ComplexScalar; + typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions; + typedef internal::traits<XprType> XprTraits; + typedef typename XprTraits::Scalar InputScalar; + typedef typename internal::conditional<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>::type OutputScalar; + typedef OutputScalar CoeffReturnType; + typedef typename PacketType<OutputScalar, Device>::type PacketReturnType; + static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size; + + enum { + IsAligned = false, + PacketAccess = true, + BlockAccess = false, + Layout = TensorEvaluator<ArgType, Device>::Layout, + CoordAccess = false, + RawAccess = false + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device) : m_fft(op.fft()), m_impl(op.expression(), device), m_data(NULL), m_device(device) { + const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions(); + for (int i = 0; i < NumDims; ++i) { + eigen_assert(input_dims[i] > 0); + m_dimensions[i] = input_dims[i]; + } + + if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) { + m_strides[0] = 1; + for (int i = 1; i < NumDims; ++i) { + m_strides[i] = m_strides[i - 1] * m_dimensions[i - 1]; + } + } else { + m_strides[NumDims - 1] = 1; + for (int i = NumDims - 2; i >= 0; --i) { + m_strides[i] = m_strides[i + 1] * m_dimensions[i + 1]; + } + } + m_size = m_dimensions.TotalSize(); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { + return m_dimensions; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(OutputScalar* data) { + m_impl.evalSubExprsIfNeeded(NULL); + if (data) { + evalToBuf(data); + return false; + } else { + m_data = (CoeffReturnType*)m_device.allocate(sizeof(CoeffReturnType) * m_size); + evalToBuf(m_data); + return true; + } + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() { + if (m_data) { + m_device.deallocate(m_data); + m_data = NULL; + } + m_impl.cleanup(); + } + + EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index) const { + return m_data[index]; + } + + template <int LoadMode> + EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnType + packet(Index index) const { + return internal::ploadt<PacketReturnType, LoadMode>(m_data + index); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost + costPerCoeff(bool vectorized) const { + return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize); + } + + EIGEN_DEVICE_FUNC Scalar* data() const { return m_data; } + + + private: + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalToBuf(OutputScalar* data) { + const bool write_to_out = internal::is_same<OutputScalar, ComplexScalar>::value; + ComplexScalar* buf = write_to_out ? (ComplexScalar*)data : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * m_size); + + for (Index i = 0; i < m_size; ++i) { + buf[i] = MakeComplex<internal::is_same<InputScalar, RealScalar>::value>()(m_impl.coeff(i)); + } + + for (size_t i = 0; i < m_fft.size(); ++i) { + Index dim = m_fft[i]; + eigen_assert(dim >= 0 && dim < NumDims); + Index line_len = m_dimensions[dim]; + eigen_assert(line_len >= 1); + ComplexScalar* line_buf = (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * line_len); + const bool is_power_of_two = isPowerOfTwo(line_len); + const Index good_composite = is_power_of_two ? 0 : findGoodComposite(line_len); + const Index log_len = is_power_of_two ? getLog2(line_len) : getLog2(good_composite); + + ComplexScalar* a = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite); + ComplexScalar* b = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite); + ComplexScalar* pos_j_base_powered = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * (line_len + 1)); + if (!is_power_of_two) { + // Compute twiddle factors + // t_n = exp(sqrt(-1) * pi * n^2 / line_len) + // for n = 0, 1,..., line_len-1. + // For n > 2 we use the recurrence t_n = t_{n-1}^2 / t_{n-2} * t_1^2 + pos_j_base_powered[0] = ComplexScalar(1, 0); + if (line_len > 1) { + const RealScalar pi_over_len(EIGEN_PI / line_len); + const ComplexScalar pos_j_base = ComplexScalar( + std::cos(pi_over_len), std::sin(pi_over_len)); + pos_j_base_powered[1] = pos_j_base; + if (line_len > 2) { + const ComplexScalar pos_j_base_sq = pos_j_base * pos_j_base; + for (int j = 2; j < line_len + 1; ++j) { + pos_j_base_powered[j] = pos_j_base_powered[j - 1] * + pos_j_base_powered[j - 1] / + pos_j_base_powered[j - 2] * pos_j_base_sq; + } + } + } + } + + for (Index partial_index = 0; partial_index < m_size / line_len; ++partial_index) { + const Index base_offset = getBaseOffsetFromIndex(partial_index, dim); + + // get data into line_buf + const Index stride = m_strides[dim]; + if (stride == 1) { + memcpy(line_buf, &buf[base_offset], line_len*sizeof(ComplexScalar)); + } else { + Index offset = base_offset; + for (int j = 0; j < line_len; ++j, offset += stride) { + line_buf[j] = buf[offset]; + } + } + + // processs the line + if (is_power_of_two) { + processDataLineCooleyTukey(line_buf, line_len, log_len); + } + else { + processDataLineBluestein(line_buf, line_len, good_composite, log_len, a, b, pos_j_base_powered); + } + + // write back + if (FFTDir == FFT_FORWARD && stride == 1) { + memcpy(&buf[base_offset], line_buf, line_len*sizeof(ComplexScalar)); + } else { + Index offset = base_offset; + const ComplexScalar div_factor = ComplexScalar(1.0 / line_len, 0); + for (int j = 0; j < line_len; ++j, offset += stride) { + buf[offset] = (FFTDir == FFT_FORWARD) ? line_buf[j] : line_buf[j] * div_factor; + } + } + } + m_device.deallocate(line_buf); + if (!is_power_of_two) { + m_device.deallocate(a); + m_device.deallocate(b); + m_device.deallocate(pos_j_base_powered); + } + } + + if(!write_to_out) { + for (Index i = 0; i < m_size; ++i) { + data[i] = PartOf<FFTResultType>()(buf[i]); + } + m_device.deallocate(buf); + } + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static bool isPowerOfTwo(Index x) { + eigen_assert(x > 0); + return !(x & (x - 1)); + } + + // The composite number for padding, used in Bluestein's FFT algorithm + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index findGoodComposite(Index n) { + Index i = 2; + while (i < 2 * n - 1) i *= 2; + return i; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index getLog2(Index m) { + Index log2m = 0; + while (m >>= 1) log2m++; + return log2m; + } + + // Call Cooley Tukey algorithm directly, data length must be power of 2 + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineCooleyTukey(ComplexScalar* line_buf, Index line_len, Index log_len) { + eigen_assert(isPowerOfTwo(line_len)); + scramble_FFT(line_buf, line_len); + compute_1D_Butterfly<FFTDir>(line_buf, line_len, log_len); + } + + // Call Bluestein's FFT algorithm, m is a good composite number greater than (2 * n - 1), used as the padding length + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineBluestein(ComplexScalar* line_buf, Index line_len, Index good_composite, Index log_len, ComplexScalar* a, ComplexScalar* b, const ComplexScalar* pos_j_base_powered) { + Index n = line_len; + Index m = good_composite; + ComplexScalar* data = line_buf; + + for (Index i = 0; i < n; ++i) { + if(FFTDir == FFT_FORWARD) { + a[i] = data[i] * numext::conj(pos_j_base_powered[i]); + } + else { + a[i] = data[i] * pos_j_base_powered[i]; + } + } + for (Index i = n; i < m; ++i) { + a[i] = ComplexScalar(0, 0); + } + + for (Index i = 0; i < n; ++i) { + if(FFTDir == FFT_FORWARD) { + b[i] = pos_j_base_powered[i]; + } + else { + b[i] = numext::conj(pos_j_base_powered[i]); + } + } + for (Index i = n; i < m - n; ++i) { + b[i] = ComplexScalar(0, 0); + } + for (Index i = m - n; i < m; ++i) { + if(FFTDir == FFT_FORWARD) { + b[i] = pos_j_base_powered[m-i]; + } + else { + b[i] = numext::conj(pos_j_base_powered[m-i]); + } + } + + scramble_FFT(a, m); + compute_1D_Butterfly<FFT_FORWARD>(a, m, log_len); + + scramble_FFT(b, m); + compute_1D_Butterfly<FFT_FORWARD>(b, m, log_len); + + for (Index i = 0; i < m; ++i) { + a[i] *= b[i]; + } + + scramble_FFT(a, m); + compute_1D_Butterfly<FFT_REVERSE>(a, m, log_len); + + //Do the scaling after ifft + for (Index i = 0; i < m; ++i) { + a[i] /= m; + } + + for (Index i = 0; i < n; ++i) { + if(FFTDir == FFT_FORWARD) { + data[i] = a[i] * numext::conj(pos_j_base_powered[i]); + } + else { + data[i] = a[i] * pos_j_base_powered[i]; + } + } + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static void scramble_FFT(ComplexScalar* data, Index n) { + eigen_assert(isPowerOfTwo(n)); + Index j = 1; + for (Index i = 1; i < n; ++i){ + if (j > i) { + std::swap(data[j-1], data[i-1]); + } + Index m = n >> 1; + while (m >= 2 && j > m) { + j -= m; + m >>= 1; + } + j += m; + } + } + + template <int Dir> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_2(ComplexScalar* data) { + ComplexScalar tmp = data[1]; + data[1] = data[0] - data[1]; + data[0] += tmp; + } + + template <int Dir> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_4(ComplexScalar* data) { + ComplexScalar tmp[4]; + tmp[0] = data[0] + data[1]; + tmp[1] = data[0] - data[1]; + tmp[2] = data[2] + data[3]; + if (Dir == FFT_FORWARD) { + tmp[3] = ComplexScalar(0.0, -1.0) * (data[2] - data[3]); + } else { + tmp[3] = ComplexScalar(0.0, 1.0) * (data[2] - data[3]); + } + data[0] = tmp[0] + tmp[2]; + data[1] = tmp[1] + tmp[3]; + data[2] = tmp[0] - tmp[2]; + data[3] = tmp[1] - tmp[3]; + } + + template <int Dir> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_8(ComplexScalar* data) { + ComplexScalar tmp_1[8]; + ComplexScalar tmp_2[8]; + + tmp_1[0] = data[0] + data[1]; + tmp_1[1] = data[0] - data[1]; + tmp_1[2] = data[2] + data[3]; + if (Dir == FFT_FORWARD) { + tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, -1); + } else { + tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, 1); + } + tmp_1[4] = data[4] + data[5]; + tmp_1[5] = data[4] - data[5]; + tmp_1[6] = data[6] + data[7]; + if (Dir == FFT_FORWARD) { + tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, -1); + } else { + tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, 1); + } + tmp_2[0] = tmp_1[0] + tmp_1[2]; + tmp_2[1] = tmp_1[1] + tmp_1[3]; + tmp_2[2] = tmp_1[0] - tmp_1[2]; + tmp_2[3] = tmp_1[1] - tmp_1[3]; + tmp_2[4] = tmp_1[4] + tmp_1[6]; +// SQRT2DIV2 = sqrt(2)/2 +#define SQRT2DIV2 0.7071067811865476 + if (Dir == FFT_FORWARD) { + tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, -SQRT2DIV2); + tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, -1); + tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, -SQRT2DIV2); + } else { + tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, SQRT2DIV2); + tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, 1); + tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, SQRT2DIV2); + } + data[0] = tmp_2[0] + tmp_2[4]; + data[1] = tmp_2[1] + tmp_2[5]; + data[2] = tmp_2[2] + tmp_2[6]; + data[3] = tmp_2[3] + tmp_2[7]; + data[4] = tmp_2[0] - tmp_2[4]; + data[5] = tmp_2[1] - tmp_2[5]; + data[6] = tmp_2[2] - tmp_2[6]; + data[7] = tmp_2[3] - tmp_2[7]; + } + + template <int Dir> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_1D_merge( + ComplexScalar* data, Index n, Index n_power_of_2) { + // Original code: + // RealScalar wtemp = std::sin(M_PI/n); + // RealScalar wpi = -std::sin(2 * M_PI/n); + const RealScalar wtemp = m_sin_PI_div_n_LUT[n_power_of_2]; + const RealScalar wpi = (Dir == FFT_FORWARD) + ? m_minus_sin_2_PI_div_n_LUT[n_power_of_2] + : -m_minus_sin_2_PI_div_n_LUT[n_power_of_2]; + + const ComplexScalar wp(wtemp, wpi); + const ComplexScalar wp_one = wp + ComplexScalar(1, 0); + const ComplexScalar wp_one_2 = wp_one * wp_one; + const ComplexScalar wp_one_3 = wp_one_2 * wp_one; + const ComplexScalar wp_one_4 = wp_one_3 * wp_one; + const Index n2 = n / 2; + ComplexScalar w(1.0, 0.0); + for (Index i = 0; i < n2; i += 4) { + ComplexScalar temp0(data[i + n2] * w); + ComplexScalar temp1(data[i + 1 + n2] * w * wp_one); + ComplexScalar temp2(data[i + 2 + n2] * w * wp_one_2); + ComplexScalar temp3(data[i + 3 + n2] * w * wp_one_3); + w = w * wp_one_4; + + data[i + n2] = data[i] - temp0; + data[i] += temp0; + + data[i + 1 + n2] = data[i + 1] - temp1; + data[i + 1] += temp1; + + data[i + 2 + n2] = data[i + 2] - temp2; + data[i + 2] += temp2; + + data[i + 3 + n2] = data[i + 3] - temp3; + data[i + 3] += temp3; + } + } + + template <int Dir> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_1D_Butterfly( + ComplexScalar* data, Index n, Index n_power_of_2) { + eigen_assert(isPowerOfTwo(n)); + if (n > 8) { + compute_1D_Butterfly<Dir>(data, n / 2, n_power_of_2 - 1); + compute_1D_Butterfly<Dir>(data + n / 2, n / 2, n_power_of_2 - 1); + butterfly_1D_merge<Dir>(data, n, n_power_of_2); + } else if (n == 8) { + butterfly_8<Dir>(data); + } else if (n == 4) { + butterfly_4<Dir>(data); + } else if (n == 2) { + butterfly_2<Dir>(data); + } + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getBaseOffsetFromIndex(Index index, Index omitted_dim) const { + Index result = 0; + + if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) { + for (int i = NumDims - 1; i > omitted_dim; --i) { + const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim]; + const Index idx = index / partial_m_stride; + index -= idx * partial_m_stride; + result += idx * m_strides[i]; + } + result += index; + } + else { + for (Index i = 0; i < omitted_dim; ++i) { + const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim]; + const Index idx = index / partial_m_stride; + index -= idx * partial_m_stride; + result += idx * m_strides[i]; + } + result += index; + } + // Value of index_coords[omitted_dim] is not determined to this step + return result; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getIndexFromOffset(Index base, Index omitted_dim, Index offset) const { + Index result = base + offset * m_strides[omitted_dim] ; + return result; + } + + protected: + Index m_size; + const FFT& m_fft; + Dimensions m_dimensions; + array<Index, NumDims> m_strides; + TensorEvaluator<ArgType, Device> m_impl; + CoeffReturnType* m_data; + const Device& m_device; + + // This will support a maximum FFT size of 2^32 for each dimension + // m_sin_PI_div_n_LUT[i] = (-2) * std::sin(M_PI / std::pow(2,i)) ^ 2; + const RealScalar m_sin_PI_div_n_LUT[32] = { + RealScalar(0.0), + RealScalar(-2), + RealScalar(-0.999999999999999), + RealScalar(-0.292893218813453), + RealScalar(-0.0761204674887130), + RealScalar(-0.0192147195967696), + RealScalar(-0.00481527332780311), + RealScalar(-0.00120454379482761), + RealScalar(-3.01181303795779e-04), + RealScalar(-7.52981608554592e-05), + RealScalar(-1.88247173988574e-05), + RealScalar(-4.70619042382852e-06), + RealScalar(-1.17654829809007e-06), + RealScalar(-2.94137117780840e-07), + RealScalar(-7.35342821488550e-08), + RealScalar(-1.83835707061916e-08), + RealScalar(-4.59589268710903e-09), + RealScalar(-1.14897317243732e-09), + RealScalar(-2.87243293150586e-10), + RealScalar( -7.18108232902250e-11), + RealScalar(-1.79527058227174e-11), + RealScalar(-4.48817645568941e-12), + RealScalar(-1.12204411392298e-12), + RealScalar(-2.80511028480785e-13), + RealScalar(-7.01277571201985e-14), + RealScalar(-1.75319392800498e-14), + RealScalar(-4.38298482001247e-15), + RealScalar(-1.09574620500312e-15), + RealScalar(-2.73936551250781e-16), + RealScalar(-6.84841378126949e-17), + RealScalar(-1.71210344531737e-17), + RealScalar(-4.28025861329343e-18) + }; + + // m_minus_sin_2_PI_div_n_LUT[i] = -std::sin(2 * M_PI / std::pow(2,i)); + const RealScalar m_minus_sin_2_PI_div_n_LUT[32] = { + RealScalar(0.0), + RealScalar(0.0), + RealScalar(-1.00000000000000e+00), + RealScalar(-7.07106781186547e-01), + RealScalar(-3.82683432365090e-01), + RealScalar(-1.95090322016128e-01), + RealScalar(-9.80171403295606e-02), + RealScalar(-4.90676743274180e-02), + RealScalar(-2.45412285229123e-02), + RealScalar(-1.22715382857199e-02), + RealScalar(-6.13588464915448e-03), + RealScalar(-3.06795676296598e-03), + RealScalar(-1.53398018628477e-03), + RealScalar(-7.66990318742704e-04), + RealScalar(-3.83495187571396e-04), + RealScalar(-1.91747597310703e-04), + RealScalar(-9.58737990959773e-05), + RealScalar(-4.79368996030669e-05), + RealScalar(-2.39684498084182e-05), + RealScalar(-1.19842249050697e-05), + RealScalar(-5.99211245264243e-06), + RealScalar(-2.99605622633466e-06), + RealScalar(-1.49802811316901e-06), + RealScalar(-7.49014056584716e-07), + RealScalar(-3.74507028292384e-07), + RealScalar(-1.87253514146195e-07), + RealScalar(-9.36267570730981e-08), + RealScalar(-4.68133785365491e-08), + RealScalar(-2.34066892682746e-08), + RealScalar(-1.17033446341373e-08), + RealScalar(-5.85167231706864e-09), + RealScalar(-2.92583615853432e-09) + }; +}; + +} // end namespace Eigen + +#endif // EIGEN_HAS_CONSTEXPR + + +#endif // EIGEN_CXX11_TENSOR_TENSOR_FFT_H |