/
vector_operations_internal.h
2660 lines (2414 loc) · 91.5 KB
/
vector_operations_internal.h
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// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2016 - 2023 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Part of the source code is dual licensed under Apache-2.0 WITH
// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
// governing the source code and code contributions can be found in
// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
//
// ------------------------------------------------------------------------
#ifndef dealii_vector_operations_internal_h
#define dealii_vector_operations_internal_h
#include <deal.II/base/config.h>
#include <deal.II/base/memory_space.h>
#include <deal.II/base/memory_space_data.h>
#include <deal.II/base/multithread_info.h>
#include <deal.II/base/parallel.h>
#include <deal.II/base/types.h>
#include <deal.II/base/vectorization.h>
#include <deal.II/lac/vector_operation.h>
#include <cstdio>
#include <cstring>
DEAL_II_NAMESPACE_OPEN
namespace internal
{
namespace VectorOperations
{
using size_type = types::global_dof_index;
template <typename T>
bool
is_non_negative(const T &t)
{
return t >= 0;
}
template <typename T>
bool
is_non_negative(const std::complex<T> &)
{
Assert(false, ExcMessage("Complex numbers do not have an ordering."));
return false;
}
// call std::copy, except for in
// the case where we want to copy
// from std::complex to a
// non-complex type
template <typename T, typename U>
void
copy(const T *begin, const T *end, U *dest)
{
std::copy(begin, end, dest);
}
template <typename T, typename U>
void
copy(const std::complex<T> *begin,
const std::complex<T> *end,
std::complex<U> *dest)
{
std::copy(begin, end, dest);
}
template <typename T, typename U>
void
copy(const std::complex<T> *, const std::complex<T> *, U *)
{
Assert(false,
ExcMessage("Can't convert a vector of complex numbers "
"into a vector of reals/doubles"));
}
#ifdef DEAL_II_WITH_TBB
/**
* This struct takes the loop range from the tbb parallel for loop and
* translates it to the actual ranges of the for loop within the vector. It
* encodes the grain size but might choose larger values of chunks than the
* minimum grain size. The minimum grain size given to tbb is then simple
* 1. For affinity reasons, the layout in this loop must be kept in sync
* with the respective class for reductions further down.
*/
template <typename Functor>
struct TBBForFunctor
{
TBBForFunctor(Functor &functor,
const size_type start,
const size_type end)
: functor(functor)
, start(start)
, end(end)
{
const size_type vec_size = end - start;
// set chunk size for sub-tasks
const unsigned int gs =
internal::VectorImplementation::minimum_parallel_grain_size;
n_chunks =
std::min(static_cast<size_type>(4 * MultithreadInfo::n_threads()),
vec_size / gs);
chunk_size = vec_size / n_chunks;
// round to next multiple of 512 (or minimum grain size if that happens
// to be smaller). this is advantageous because our accumulation
// algorithms favor lengths of a power of 2 due to pairwise summation ->
// at most one 'oddly' sized chunk
if (chunk_size > 512)
chunk_size = ((chunk_size + 511) / 512) * 512;
n_chunks = (vec_size + chunk_size - 1) / chunk_size;
AssertIndexRange((n_chunks - 1) * chunk_size, vec_size);
AssertIndexRange(vec_size, n_chunks * chunk_size + 1);
}
void
operator()(const tbb::blocked_range<size_type> &range) const
{
const size_type r_begin = start + range.begin() * chunk_size;
const size_type r_end = std::min(start + range.end() * chunk_size, end);
functor(r_begin, r_end);
}
Functor &functor;
const size_type start;
const size_type end;
unsigned int n_chunks;
size_type chunk_size;
};
#endif
template <typename Functor>
void
parallel_for(
Functor &functor,
const size_type start,
const size_type end,
const std::shared_ptr<::dealii::parallel::internal::TBBPartitioner>
&partitioner)
{
#ifdef DEAL_II_WITH_TBB
const size_type vec_size = end - start;
// only go to the parallel function in case there are at least 4 parallel
// items, otherwise the overhead is too large
if (vec_size >=
4 * internal::VectorImplementation::minimum_parallel_grain_size &&
MultithreadInfo::n_threads() > 1)
{
Assert(partitioner.get() != nullptr,
ExcInternalError(
"Unexpected initialization of Vector that does "
"not set the TBB partitioner to a usable state."));
std::shared_ptr<tbb::affinity_partitioner> tbb_partitioner =
partitioner->acquire_one_partitioner();
TBBForFunctor<Functor> generic_functor(functor, start, end);
// We use a minimum grain size of 1 here since the grains at this
// stage of dividing the work refer to the number of vector chunks
// that are processed by (possibly different) threads in the
// parallelized for loop (i.e., they do not refer to individual
// vector entries). The number of chunks here is calculated inside
// TBBForFunctor. See also GitHub issue #2496 for further discussion
// of this strategy.
::dealii::parallel::internal::parallel_for(
static_cast<size_type>(0),
static_cast<size_type>(generic_functor.n_chunks),
generic_functor,
1,
tbb_partitioner);
partitioner->release_one_partitioner(tbb_partitioner);
}
else if (vec_size > 0)
functor(start, end);
#else
functor(start, end);
(void)partitioner;
#endif
}
// Define the functors necessary to use SIMD with TBB. we also include the
// simple copy and set operations
template <typename Number>
struct Vector_set
{
Vector_set(const Number value, Number *const dst)
: value(value)
, dst(dst)
{
Assert(dst != nullptr, ExcInternalError());
}
void
operator()(const size_type begin, const size_type end) const
{
Assert(end >= begin, ExcInternalError());
if (value == Number())
{
if constexpr (std::is_trivial_v<Number>)
{
std::memset(dst + begin, 0, sizeof(Number) * (end - begin));
return;
}
}
std::fill(dst + begin, dst + end, value);
}
const Number value;
Number *const dst;
};
template <typename Number, typename OtherNumber>
struct Vector_copy
{
Vector_copy(const OtherNumber *const src, Number *const dst)
: src(src)
, dst(dst)
{
Assert(src != nullptr, ExcInternalError());
Assert(dst != nullptr, ExcInternalError());
}
void
operator()(const size_type begin, const size_type end) const
{
Assert(end >= begin, ExcInternalError());
if constexpr (std::is_trivially_copyable<Number>() &&
std::is_same_v<Number, OtherNumber>)
std::memcpy(dst + begin, src + begin, (end - begin) * sizeof(Number));
else
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
dst[i] = src[i];
}
}
const OtherNumber *const src;
Number *const dst;
};
template <typename Number>
struct Vectorization_multiply_factor
{
Vectorization_multiply_factor(Number *const val, const Number factor)
: val(val)
, stored_factor(factor)
{}
void
operator()(const size_type begin, const size_type end) const
{
// create a local copy of the variable to help the compiler with the
// aliasing analysis
const Number factor = stored_factor;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] *= factor;
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] *= factor;
}
}
Number *const val;
const Number stored_factor;
};
template <typename Number>
struct Vectorization_add_av
{
Vectorization_add_av(Number *const val,
const Number *const v_val,
const Number factor)
: val(val)
, v_val(v_val)
, stored_factor(factor)
{}
void
operator()(const size_type begin, const size_type end) const
{
// create a local copy of the variable to help the compiler with the
// aliasing analysis
const Number factor = stored_factor;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] += factor * v_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] += factor * v_val[i];
}
}
Number *const val;
const Number *const v_val;
const Number stored_factor;
};
template <typename Number>
struct Vectorization_sadd_xav
{
Vectorization_sadd_xav(Number *val,
const Number *const v_val,
const Number a,
const Number x)
: val(val)
, v_val(v_val)
, stored_a(a)
, stored_x(x)
{}
void
operator()(const size_type begin, const size_type end) const
{
// create a local copy of the variable to help the compiler with the
// aliasing analysis
const Number x = stored_x, a = stored_a;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = x * val[i] + a * v_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = x * val[i] + a * v_val[i];
}
}
Number *const val;
const Number *const v_val;
const Number stored_a;
const Number stored_x;
};
template <typename Number>
struct Vectorization_subtract_v
{
Vectorization_subtract_v(Number *val, const Number *const v_val)
: val(val)
, v_val(v_val)
{}
void
operator()(const size_type begin, const size_type end) const
{
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] -= v_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] -= v_val[i];
}
}
Number *const val;
const Number *const v_val;
};
template <typename Number>
struct Vectorization_add_factor
{
Vectorization_add_factor(Number *const val, const Number factor)
: val(val)
, stored_factor(factor)
{}
void
operator()(const size_type begin, const size_type end) const
{
const Number factor = stored_factor;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] += factor;
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] += factor;
}
}
Number *const val;
const Number stored_factor;
};
template <typename Number>
struct Vectorization_add_v
{
Vectorization_add_v(Number *const val, const Number *const v_val)
: val(val)
, v_val(v_val)
{}
void
operator()(const size_type begin, const size_type end) const
{
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] += v_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] += v_val[i];
}
}
Number *const val;
const Number *const v_val;
};
template <typename Number>
struct Vectorization_add_avpbw
{
Vectorization_add_avpbw(Number *const val,
const Number *const v_val,
const Number *const w_val,
const Number a,
const Number b)
: val(val)
, v_val(v_val)
, w_val(w_val)
, stored_a(a)
, stored_b(b)
{}
void
operator()(const size_type begin, const size_type end) const
{
const Number a = stored_a, b = stored_b;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = val[i] + a * v_val[i] + b * w_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = val[i] + a * v_val[i] + b * w_val[i];
}
}
Number *const val;
const Number *const v_val;
const Number *const w_val;
const Number stored_a;
const Number stored_b;
};
template <typename Number>
struct Vectorization_sadd_xv
{
Vectorization_sadd_xv(Number *const val,
const Number *const v_val,
const Number x)
: val(val)
, v_val(v_val)
, stored_x(x)
{}
void
operator()(const size_type begin, const size_type end) const
{
const Number x = stored_x;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = x * val[i] + v_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = x * val[i] + v_val[i];
}
}
Number *const val;
const Number *const v_val;
const Number stored_x;
};
template <typename Number>
struct Vectorization_sadd_xavbw
{
Vectorization_sadd_xavbw(Number *val,
const Number *v_val,
const Number *w_val,
Number x,
Number a,
Number b)
: val(val)
, v_val(v_val)
, w_val(w_val)
, stored_x(x)
, stored_a(a)
, stored_b(b)
{}
void
operator()(const size_type begin, const size_type end) const
{
const Number x = stored_x, a = stored_a, b = stored_b;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = x * val[i] + a * v_val[i] + b * w_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = x * val[i] + a * v_val[i] + b * w_val[i];
}
}
Number *const val;
const Number *const v_val;
const Number *const w_val;
const Number stored_x;
const Number stored_a;
const Number stored_b;
};
template <typename Number>
struct Vectorization_scale
{
Vectorization_scale(Number *const val, const Number *const v_val)
: val(val)
, v_val(v_val)
{}
void
operator()(const size_type begin, const size_type end) const
{
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] *= v_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] *= v_val[i];
}
}
Number *const val;
const Number *const v_val;
};
template <typename Number>
struct Vectorization_equ_au
{
Vectorization_equ_au(Number *const val,
const Number *const u_val,
const Number a)
: val(val)
, u_val(u_val)
, stored_a(a)
{}
void
operator()(const size_type begin, const size_type end) const
{
const Number a = stored_a;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = a * u_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = a * u_val[i];
}
}
Number *const val;
const Number *const u_val;
const Number stored_a;
};
template <typename Number>
struct Vectorization_equ_aubv
{
Vectorization_equ_aubv(Number *const val,
const Number *const u_val,
const Number *const v_val,
const Number a,
const Number b)
: val(val)
, u_val(u_val)
, v_val(v_val)
, stored_a(a)
, stored_b(b)
{}
void
operator()(const size_type begin, const size_type end) const
{
const Number a = stored_a, b = stored_b;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = a * u_val[i] + b * v_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = a * u_val[i] + b * v_val[i];
}
}
Number *const val;
const Number *const u_val;
const Number *const v_val;
const Number stored_a;
const Number stored_b;
};
template <typename Number>
struct Vectorization_equ_aubvcw
{
Vectorization_equ_aubvcw(Number *val,
const Number *u_val,
const Number *v_val,
const Number *w_val,
const Number a,
const Number b,
const Number c)
: val(val)
, u_val(u_val)
, v_val(v_val)
, w_val(w_val)
, stored_a(a)
, stored_b(b)
, stored_c(c)
{}
void
operator()(const size_type begin, const size_type end) const
{
const Number a = stored_a, b = stored_b, c = stored_c;
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = a * u_val[i] + b * v_val[i] + c * w_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = a * u_val[i] + b * v_val[i] + c * w_val[i];
}
}
Number *const val;
const Number *const u_val;
const Number *const v_val;
const Number *const w_val;
const Number stored_a;
const Number stored_b;
const Number stored_c;
};
template <typename Number>
struct Vectorization_ratio
{
Vectorization_ratio(Number *val, const Number *a_val, const Number *b_val)
: val(val)
, a_val(a_val)
, b_val(b_val)
{}
void
operator()(const size_type begin, const size_type end) const
{
if (::dealii::parallel::internal::EnableOpenMPSimdFor<Number>::value)
{
DEAL_II_OPENMP_SIMD_PRAGMA
for (size_type i = begin; i < end; ++i)
val[i] = a_val[i] / b_val[i];
}
else
{
for (size_type i = begin; i < end; ++i)
val[i] = a_val[i] / b_val[i];
}
}
Number *const val;
const Number *const a_val;
const Number *const b_val;
};
// All sums over all the vector entries (l2-norm, inner product, etc.) are
// performed with the same code, using a templated operation defined
// here. There are always two versions defined, a standard one that covers
// most cases and a vectorized one which is only for equal types and float
// and double.
template <typename Number, typename Number2>
struct Dot
{
static constexpr bool vectorizes = std::is_same_v<Number, Number2> &&
(VectorizedArray<Number>::size() > 1);
Dot(const Number *const X, const Number2 *const Y)
: X(X)
, Y(Y)
{}
Number
operator()(const size_type i) const
{
return X[i] * Number(numbers::NumberTraits<Number2>::conjugate(Y[i]));
}
VectorizedArray<Number>
do_vectorized(const size_type i) const
{
VectorizedArray<Number> x, y;
x.load(X + i);
y.load(Y + i);
// the following operation in VectorizedArray does an element-wise
// scalar product without taking into account complex values and
// the need to take the complex-conjugate of one argument. this
// may be a bug, but because all VectorizedArray classes only
// work on real scalars, it doesn't really matter very much.
// in any case, assert that we really don't get here for
// complex-valued objects
static_assert(numbers::NumberTraits<Number>::is_complex == false,
"This operation is not correctly implemented for "
"complex-valued objects.");
return x * y;
}
const Number *const X;
const Number2 *const Y;
};
template <typename Number, typename RealType>
struct Norm2
{
static const bool vectorizes = VectorizedArray<Number>::size() > 1;
Norm2(const Number *const X)
: X(X)
{}
RealType
operator()(const size_type i) const
{
return numbers::NumberTraits<Number>::abs_square(X[i]);
}
VectorizedArray<Number>
do_vectorized(const size_type i) const
{
VectorizedArray<Number> x;
x.load(X + i);
return x * x;
}
const Number *const X;
};
template <typename Number, typename RealType>
struct Norm1
{
static const bool vectorizes = VectorizedArray<Number>::size() > 1;
Norm1(const Number *X)
: X(X)
{}
RealType
operator()(const size_type i) const
{
return numbers::NumberTraits<Number>::abs(X[i]);
}
VectorizedArray<Number>
do_vectorized(const size_type i) const
{
VectorizedArray<Number> x;
x.load(X + i);
return std::abs(x);
}
const Number *X;
};
template <typename Number, typename RealType>
struct NormP
{
static const bool vectorizes = VectorizedArray<Number>::size() > 1;
NormP(const Number *X, RealType p)
: X(X)
, p(p)
{}
RealType
operator()(const size_type i) const
{
return std::pow(numbers::NumberTraits<Number>::abs(X[i]), p);
}
VectorizedArray<Number>
do_vectorized(const size_type i) const
{
VectorizedArray<Number> x;
x.load(X + i);
return std::pow(std::abs(x), p);
}
const Number *X;
const RealType p;
};
template <typename Number>
struct MeanValue
{
static const bool vectorizes = VectorizedArray<Number>::size() > 1;
MeanValue(const Number *X)
: X(X)
{}
Number
operator()(const size_type i) const
{
return X[i];
}
VectorizedArray<Number>
do_vectorized(const size_type i) const
{
VectorizedArray<Number> x;
x.load(X + i);
return x;
}
const Number *X;
};
template <typename Number>
struct AddAndDot
{
static const bool vectorizes = VectorizedArray<Number>::size() > 1;
AddAndDot(Number *const X,
const Number *const V,
const Number *const W,
const Number a)
: X(X)
, V(V)
, W(W)
, a(a)
{}
Number
operator()(const size_type i) const
{
X[i] += a * V[i];
return X[i] * Number(numbers::NumberTraits<Number>::conjugate(W[i]));
}
VectorizedArray<Number>
do_vectorized(const size_type i) const
{
VectorizedArray<Number> x, w, v;
x.load(X + i);
v.load(V + i);
x += a * v;
x.store(X + i);
// may only load from W after storing in X because the pointers might
// point to the same memory
w.load(W + i);
// the following operation in VectorizedArray does an element-wise
// scalar product without taking into account complex values and
// the need to take the complex-conjugate of one argument. this
// may be a bug, but because all VectorizedArray classes only
// work on real scalars, it doesn't really matter very much.
// in any case, assert that we really don't get here for
// complex-valued objects
static_assert(numbers::NumberTraits<Number>::is_complex == false,
"This operation is not correctly implemented for "
"complex-valued objects.");
return x * w;
}
Number *const X;
const Number *const V;
const Number *const W;
const Number a;
};
// this is the main working loop for all vector sums using the templated
// operation above. it accumulates the sums using a block-wise summation
// algorithm with post-update. this blocked algorithm has been proposed in
// a similar form by Castaldo, Whaley and Chronopoulos (SIAM
// J. Sci. Comput. 31, 1156-1174, 2008) and we use the smallest possible
// block size, 2. Sometimes it is referred to as pairwise summation. The
// worst case error made by this algorithm is on the order O(eps *
// log2(vec_size)), whereas a naive summation is O(eps * vec_size). Even
// though the Kahan summation is even more accurate with an error O(eps)
// by carrying along remainders not captured by the main sum, that involves
// additional costs which are not worthwhile. See the Wikipedia article on
// the Kahan summation algorithm.
// The algorithm implemented here has the additional benefit that it is
// easily parallelized without changing the order of how the elements are
// added (floating point addition is not associative). For the same vector
// size and minimum_parallel_grainsize, the blocks are always the
// same and added pairwise.
// The depth of recursion is controlled by the 'magic' parameter
// vector_accumulation_recursion_threshold: If the length is below
// vector_accumulation_recursion_threshold * 32 (32 is the part of code we
// unroll), a straight loop instead of recursion will be used. At the
// innermost level, eight values are added consecutively in order to better
// balance multiplications and additions.
// Loops are unrolled as follows: the range [first,last) is broken into
// @p n_chunks each of size 32 plus the @p remainder.
// accumulate_regular() does the work on 32*n_chunks elements employing SIMD
// if possible and stores the result of the operation for each chunk in @p outer_results.
// The code returns the result as the last argument in order to make
// spawning tasks simpler and use automatic template deduction.
/**
* The minimum number of chunks (each of size 32) to divide the range
* [first,last) into two (second part of the if branch in
* accumulate_recursive).
*/
const unsigned int vector_accumulation_recursion_threshold = 128;
template <typename Operation, typename ResultType>
void
accumulate_recursive(const Operation &op,
const size_type first,
const size_type last,