devtools/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2026-04-10 11:34:33 +08:00
Code Issues Packages Projects Releases Wiki Activity

Apply clang-format

Browse Source
This commit is contained in:
Tobias Wood
2023-11-29 11:12:48 +00:00
parent 9ea520fc45
commit f38e16c193
534 changed files with 103368 additions and 116934 deletions
Download Patch File Download Diff File Expand all files Collapse all files

348
unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h
View File

@@ -16,44 +16,62 @@
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
*/
* \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 <bool NeedUprade>
struct MakeComplex {
template <typename T>
EIGEN_DEVICE_FUNC
T operator() (const T& val) const { return val; }
EIGEN_DEVICE_FUNC T operator()(const T& val) const {
return val;
}
};
template <> struct MakeComplex<true> {
template <>
struct MakeComplex<true> {
template <typename T>
EIGEN_DEVICE_FUNC
std::complex<T> operator() (const T& val) const { return std::complex<T>(val, 0); }
EIGEN_DEVICE_FUNC std::complex<T> operator()(const T& val) const {
return std::complex<T>(val, 0);
}
};
template <> struct MakeComplex<false> {
template <>
struct MakeComplex<false> {
template <typename T>
EIGEN_DEVICE_FUNC
std::complex<T> operator() (const std::complex<T>& val) const { return val; }
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 <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<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(); }
template <>
struct PartOf<ImagPart> {
template <typename T>
T operator()(const std::complex<T>& val) const {
return val.imag();
}
};
namespace internal {
@@ -63,7 +81,8 @@ struct traits<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir> > : public traits
typedef typename NumTraits<typename XprTraits::Scalar>::Real RealScalar;
typedef typename std::complex<RealScalar> ComplexScalar;
typedef typename XprTraits::Scalar InputScalar;
typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar> OutputScalar;
typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>
OutputScalar;
typedef typename XprTraits::StorageKind StorageKind;
typedef typename XprTraits::Index Index;
typedef typename XprType::Nested Nested;
@@ -79,7 +98,8 @@ struct eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, Eigen::Dense
};
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> {
struct nested<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, 1,
typename eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> >::type> {
typedef TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> type;
};
@@ -91,22 +111,18 @@ class TensorFFTOp : public TensorBase<TensorFFTOp<FFT, XprType, FFTResultType, F
typedef typename Eigen::internal::traits<TensorFFTOp>::Scalar Scalar;
typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
typedef typename std::complex<RealScalar> ComplexScalar;
typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar> OutputScalar;
typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>
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 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 FFT& fft() const { return m_fft; }
EIGEN_DEVICE_FUNC
const internal::remove_all_t<typename XprType::Nested>& expression() const {
return m_xpr;
}
EIGEN_DEVICE_FUNC const internal::remove_all_t<typename XprType::Nested>& expression() const { return m_xpr; }
protected:
typename XprType::Nested m_xpr;
@@ -126,7 +142,8 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;
typedef internal::traits<XprType> XprTraits;
typedef typename XprTraits::Scalar InputScalar;
typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar> OutputScalar;
typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>
OutputScalar;
typedef OutputScalar CoeffReturnType;
typedef typename PacketType<OutputScalar, Device>::type PacketReturnType;
static constexpr int PacketSize = internal::unpacket_traits<PacketReturnType>::size;
@@ -147,7 +164,8 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
typedef internal::TensorBlockNotImplemented TensorBlock;
//===--------------------------------------------------------------------===//
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) {
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);
@@ -168,9 +186,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
m_size = m_dimensions.TotalSize();
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
return m_dimensions;
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
m_impl.evalSubExprsIfNeeded(NULL);
@@ -178,7 +194,8 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
evalToBuf(data);
return false;
} else {
m_data = (EvaluatorPointerType)m_device.get((CoeffReturnType*)(m_device.allocate_temp(sizeof(CoeffReturnType) * m_size)));
m_data = (EvaluatorPointerType)m_device.get(
(CoeffReturnType*)(m_device.allocate_temp(sizeof(CoeffReturnType) * m_size)));
evalToBuf(m_data);
return true;
}
@@ -192,18 +209,14 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
m_impl.cleanup();
}
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index) const {
return m_data[index];
}
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 {
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 {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
}
@@ -212,7 +225,8 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
private:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalToBuf(EvaluatorPointerType 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);
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));
@@ -228,9 +242,12 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
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));
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)
@@ -271,7 +288,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
// get data into line_buf
const Index stride = m_strides[dim];
if (stride == 1) {
m_device.memcpy(line_buf, &buf[base_offset], line_len*sizeof(ComplexScalar));
m_device.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) {
@@ -282,19 +299,18 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
// process the line
if (is_power_of_two) {
processDataLineCooleyTukey(line_buf, line_len, log_len);
}
else {
} else {
processDataLineBluestein(line_buf, line_len, good_composite, log_len, a, b, pos_j_base_powered);
}
// write back
if (FFTDir == FFT_FORWARD && stride == 1) {
m_device.memcpy(&buf[base_offset], line_buf, line_len*sizeof(ComplexScalar));
m_device.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);
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;
buf[offset] = (FFTDir == FFT_FORWARD) ? line_buf[j] : line_buf[j] * div_factor;
}
}
}
@@ -306,7 +322,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
}
}
if(!write_to_out) {
if (!write_to_out) {
for (Index i = 0; i < m_size; ++i) {
data[i] = PartOf<FFTResultType>()(buf[i]);
}
@@ -333,23 +349,26 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
}
// 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_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) {
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) {
if (FFTDir == FFT_FORWARD) {
a[i] = data[i] * numext::conj(pos_j_base_powered[i]);
}
else {
} else {
a[i] = data[i] * pos_j_base_powered[i];
}
}
@@ -358,10 +377,9 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
}
for (Index i = 0; i < n; ++i) {
if(FFTDir == FFT_FORWARD) {
if (FFTDir == FFT_FORWARD) {
b[i] = pos_j_base_powered[i];
}
else {
} else {
b[i] = numext::conj(pos_j_base_powered[i]);
}
}
@@ -369,11 +387,10 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
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]);
if (FFTDir == FFT_FORWARD) {
b[i] = pos_j_base_powered[m - i];
} else {
b[i] = numext::conj(pos_j_base_powered[m - i]);
}
}
@@ -390,16 +407,15 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
scramble_FFT(a, m);
compute_1D_Butterfly<FFT_REVERSE>(a, m, log_len);
//Do the scaling after ifft
// 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) {
if (FFTDir == FFT_FORWARD) {
data[i] = a[i] * numext::conj(pos_j_base_powered[i]);
}
else {
} else {
data[i] = a[i] * pos_j_base_powered[i];
}
}
@@ -408,9 +424,9 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
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){
for (Index i = 1; i < n; ++i) {
if (j > i) {
std::swap(data[j-1], data[i-1]);
std::swap(data[j - 1], data[i - 1]);
}
Index m = n >> 1;
while (m >= 2 && j > m) {
@@ -493,15 +509,13 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
}
template <int Dir>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_1D_merge(
ComplexScalar* data, Index n, Index n_power_of_2) {
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 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);
@@ -511,29 +525,28 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
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;
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 + n2] = data[i] - temp0;
data[i] += temp0;
data[i + 1 + n2] = data[i + 1] - temp1;
data[i + 1] += temp1;
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 + 2 + n2] = data[i + 2] - temp2;
data[i + 2] += temp2;
data[i + 3 + n2] = data[i + 3] - temp3;
data[i + 3] += temp3;
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) {
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);
@@ -559,8 +572,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
result += idx * m_strides[i];
}
result += index;
}
else {
} 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;
@@ -574,7 +586,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getIndexFromOffset(Index base, Index omitted_dim, Index offset) const {
Index result = base + offset * m_strides[omitted_dim] ;
Index result = base + offset * m_strides[omitted_dim];
return result;
}
@@ -589,76 +601,72 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
// 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)
};
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)
};
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