У меня есть приложение, в котором мне нужно переместить данные из одного массива (input) в другой массив (output), используя третий массив со списком индексов назначения (map). Упрощенно, я хочу сделать что-то вроде output[i] = input[ map[i] ].
. Я провел следующий тест, чтобы попытаться оценить, что даст мне лучшую производительность между использованием массивов в стиле C и std :: vector, и в случае std :: vector с использованием разных операторов, а также итераторов. Я знаю, что оператор std::vector::at() имеет снижение производительности, поскольку он выполняет проверку границ, и я хотел оценить, насколько сильно это снизится, чтобы решить, стоит ли это.
Я написал пример приложения, в котором я перемещаю данные, используя разные структуры и операторы. Я использовал gprof, чтобы профилировать его под Linux.
Это исходный код приложения (test.cpp):
#include <iostream>
#include <vector>
#include <assert.h>
#include <limits.h>
// Input and output vector size
const std::size_t vector_size = 4096;
// Size of the map vector. This value must be
// <= 'vector_size'
const std::size_t map_size = 2000;
// Number of iteration for each algorithm
const std::size_t num_iterations = 1000000;
// Algorithms
void __attribute__ ((noinline)) map_c_array(int *in, std::size_t *map, int *out)
{
for (std::size_t j {0}; j < map_size; j++)
out[j] = in[map[j]];
}
void __attribute__ ((noinline)) map_vector_v1(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::size_t j {0};
for (auto const& m : map)
out.at(j++) = in.at(m);
}
void __attribute__ ((noinline)) map_vector_v2(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
for (std::size_t j{0}; j < map_size; ++j)
out.at(j) = in.at(map.at(j));
}
void __attribute__ ((noinline)) map_vector_v3(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::size_t j {0};
for (auto const& m : map)
out[j++] = in[m];
}
void __attribute__ ((noinline)) map_vector_v4(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
for (std::size_t j{0}; j < map_size; ++j)
out[j] = in[map[j]];
}
void __attribute__ ((noinline)) map_vector_v5(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::vector<int>::const_iterator inIt { in.begin() };
std::vector<int>::iterator outIt { out.begin() };
for (std::vector<std::size_t>::const_iterator mapIt { map.begin() }; mapIt != map.end(); ++mapIt)
*outIt++ = *(inIt + *mapIt);
}
void __attribute__ ((noinline)) map_vector_v6(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::vector<int>::const_iterator inIt { in.begin() };
std::vector<int>::iterator outIt { out.begin() };
for (auto const& m : map)
*outIt++ = *(inIt + m);
}
// Main program
int main(int argc, char *argv[])
{
// Run the algorithm based on vectors
for (std::size_t k {0}; k < 6; ++k)
{
// Input vector. It is of size = 'vector_size'
std::vector<int> in(vector_size, 0);
// Output vector. It is of size = 'vector_size'
std::vector<int> out(vector_size, 0);
// Mask Vector. I want to do out[i] = in[ map[i] ]
// Its values are indexes of the 'in' vector, so they all need
// to be less than or equal to 'vector_size'
// It is of size = 'map_size'. To each value in this vector there will
// be a corresponding value in the 'out' vector. So, 'map_size' need to
// be less than or equal to 'vector_size'.
std::vector<std::size_t> map(map_size, 0);
// Fill input vector with random numbers
for (std::size_t i {0}; i < vector_size; ++i)
in.at(i) = static_cast<int>( static_cast<float>(rand())/RAND_MAX * INT_MIN );
// Fill the map vector with random number, not greater that the
// maximum size of the in and out vectors.
for (std::size_t i {0}; i < map_size; ++i)
map.at(i) = static_cast<std::size_t>( static_cast<float>(rand())/RAND_MAX * vector_size );
// Copy the values using each algorithm
switch (k)
{
case 0:
for (std::size_t i {0}; i < num_iterations; ++i )
{
map_vector_v1(in, map, out);
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
}
break;
case 1:
for (std::size_t i {0}; i < num_iterations; ++i )
{
map_vector_v2(in, map, out);
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
}
break;
case 2:
for (std::size_t i {0}; i < num_iterations; ++i )
{
map_vector_v3(in, map, out);
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
}
break;
case 3:
for (std::size_t i {0}; i < num_iterations; ++i )
{
map_vector_v4(in, map, out);
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
}
break;
case 4:
for (std::size_t i {0}; i < num_iterations; ++i )
{
map_vector_v5(in, map, out);
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
}
break;
case 5:
for (std::size_t i {0}; i < num_iterations; ++i )
{
map_vector_v6(in, map, out);
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
}
break;
}
}
// Finally, run the algorithm based on C arrays
{
// Input vector. It is of size = 'vector_size'
int in[vector_size];
// Output vector. It is of size = 'vector_size'
int out[vector_size];
// Mask Vector. I want to do out[i] = in[ map[i] ]
// Its values are indexes of the 'in' vector, so they all need
// to be less than or equal to 'vector_size'
// It is of size = 'map_size'. To each value in this vector there will
// be a corresponding value in the 'out' vector. So, 'map_size' need to
// be less than or equal to 'vector_size'.
std::size_t map[map_size];
// Fill input vector with random numbers
for (std::size_t i {0}; i < vector_size; ++i)
in[i] = static_cast<int>( static_cast<float>(rand())/RAND_MAX * INT_MIN );
// Fill the map vector with random number, not greater that the
// maximum size of the in and out vectors.
for (std::size_t i {0}; i < map_size; ++i)
map[i] = static_cast<std::size_t>( static_cast<float>(rand())/RAND_MAX * vector_size );
for (std::size_t i {0}; i < num_iterations; ++i)
{
map_c_array(in, map, out);
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
}
}
}
(Примечание: я использовал атрибут noinline, чтобы компилятор не встраивал мои функции, так как я хочу см. затем в gprof).
Я скомпилировал его с помощью:
g++ -o test test.cpp -Wall -g -O3 -pg
Затем я получил профиль с:
gprof test
И вот результат:
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls Ts/call Ts/call name
35.42 3.29 3.29 map_vector_v2(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
17.17 4.89 1.60 map_vector_v1(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
11.34 5.94 1.05 map_vector_v3(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
10.37 6.90 0.96 map_vector_v5(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
9.72 7.81 0.90 map_vector_v4(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
8.64 8.61 0.80 map_c_array(int*, unsigned long*, int*)
7.67 9.32 0.71 map_vector_v6(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
0.00 9.32 0.00 1 0.00 0.00 _GLOBAL__sub_I__Z11map_c_arrayPiPmS_
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2018 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.11% of 9.32 seconds
index % time self children called name
<spontaneous>
[1] 35.3 3.29 0.00 map_vector_v2(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [1]
-----------------------------------------------
<spontaneous>
[2] 17.1 1.60 0.00 map_vector_v1(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [2]
-----------------------------------------------
<spontaneous>
[3] 11.3 1.05 0.00 map_vector_v3(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [3]
-----------------------------------------------
<spontaneous>
[4] 10.3 0.96 0.00 map_vector_v5(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [4]
-----------------------------------------------
<spontaneous>
[5] 9.7 0.90 0.00 map_vector_v4(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [5]
-----------------------------------------------
<spontaneous>
[6] 8.6 0.80 0.00 map_c_array(int*, unsigned long*, int*) [6]
-----------------------------------------------
<spontaneous>
[7] 7.6 0.71 0.00 map_vector_v6(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [7]
-----------------------------------------------
0.00 0.00 1/1 __libc_csu_init [21]
[15] 0.0 0.00 0.00 1 _GLOBAL__sub_I__Z11map_c_arrayPiPmS_ [15]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2018 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[15] _GLOBAL__sub_I__Z11map_c_arrayPiPmS_ (test.cpp) [1] map_vector_v2(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [4] map_vector_v5(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
[6] map_c_array(int*, unsigned long*, int*) [3] map_vector_v3(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [7] map_vector_v6(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
[2] map_vector_v1(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&) [5] map_vector_v4(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
Я видел:
- Заметное влияние на производительность, примерно на 60% медленнее, при использовании
std::vector::at() по сравнению с std::vector:operator[] (map_vector_v1 против map_vector_v3) . - Кажется, что использование итераторов примерно на 30% быстрее, чем использование
std::vector::operator[] (map_vector_v6 против map_vector_v3). - Я был немного удивлен, что
map_vector_v6 был немного быстрее, чем с использованием массивов в стиле C (map_c_array). - Я думал, что
map_vector_v5 и map_vector_v6 эквивалентны, поэтому меня удивило, что map_vector_v6 был быстрее.
Моя первоначальная идея заключалась в использовании map_vector_v1. Но теперь я думаю, что сделаю go с map_vector_v6, убедившись, что значения моего map вектора не выходят за рамки.
Я хотел поделиться этими результатами на случай, если это может помочь кому-то другому, или в случае, если я делаю что-то не так, что влияет на мои результаты.
Примечание: я компилирую и запускаю этот код в Ubuntu 18.04 с:
$ g++ --version
g++ (Ubuntu 7.5.0-3ubuntu1~18.04) 7.5.0
Copyright (C) 2017 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
$ gprof --version
GNU gprof (GNU Binutils for Ubuntu) 2.30
Based on BSD gprof, copyright 1983 Regents of the University of California.
This program is free software. This program has absolutely no warranty.
EDIT:
Спасибо за все ваши комментарии. Я внес некоторые изменения в свой код, например, сгенерировал новую карту и входные векторы на каждой итерации, и проделал некоторые операции с выходным вектором в конце каждой итерации, чтобы избежать его оптимизации. Я также добавил вторую вторую версию в стиле C, в которой используются указатели, что оказалось быстрее.
Вот обновленный код.
#include <iostream>
#include <vector>
#include <assert.h>
#include <limits.h>
#include <math.h>
// Input and output vector size
const std::size_t vector_size = 4096;
// Size of the map vector. This value must be
// <= 'vector_size'
const std::size_t map_size = 2000;
// Number of iteration for each algorithm
const std::size_t num_iterations = 1000000;
// Algorithms
void __attribute__ ((noinline)) map_c_array(int *in, std::size_t *map, int *out)
{
for (std::size_t j {0}; j < map_size; j++)
out[j] = in[map[j]];
}
void __attribute__ ((noinline)) map_c_array_v2(int *in, std::size_t *map, int *out)
{
for (std::size_t j {0}; j < map_size; j++)
*out++ = *(in + *map++);
}
void __attribute__ ((noinline)) map_vector_v1(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::size_t j {0};
for (auto const& m : map)
out.at(j++) = in.at(m);
}
void __attribute__ ((noinline)) map_vector_v2(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
for (std::size_t j{0}; j < map_size; ++j)
out.at(j) = in.at(map.at(j));
}
void __attribute__ ((noinline)) map_vector_v3(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::size_t j {0};
for (auto const& m : map)
out[j++] = in[m];
}
void __attribute__ ((noinline)) map_vector_v4(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
for (std::size_t j{0}; j < map_size; ++j)
out[j] = in[map[j]];
}
void __attribute__ ((noinline)) map_vector_v5(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::vector<int>::const_iterator inIt { in.begin() };
std::vector<int>::iterator outIt { out.begin() };
for (std::vector<std::size_t>::const_iterator mapIt { map.begin() }; mapIt != map.end(); ++mapIt)
*outIt++ = *(inIt + *mapIt);
}
void __attribute__ ((noinline)) map_vector_v6(const std::vector<int> &in, const std::vector<std::size_t> &map, std::vector<int> &out)
{
std::vector<int>::const_iterator inIt { in.begin() };
std::vector<int>::iterator outIt { out.begin() };
for (auto const& m : map)
*outIt++ = *(inIt + m);
}
// Main program
int main(int argc, char *argv[])
{
// Run algorithms based on vectors
for (std::size_t k {0}; k < 6; ++k)
{
// Run 'num_itertions' iteration for each algorithm
for (std::size_t i {0}; i < num_iterations; ++i )
{
// Input vector. It is of size = 'vector_size'
std::vector<int> in(vector_size, 0);
// Output vector. It is of size = 'vector_size'
std::vector<int> out(vector_size, 0);
// Mask Vector. I want to do out[i] = in[ map[i] ]
// Its values are indexes of the 'in' vector, so they all need
// to be less than or equal to 'vector_size'
// It is of size = 'map_size'. To each value in this vector there will
// be a corresponding value in the 'out' vector. So, 'map_size' need to
// be less than or equalt to 'vector_size'.
std::vector<std::size_t> map(map_size, 0);
// Fill input vector with random numbers
for (std::size_t i {0}; i < vector_size; ++i)
in.at(i) = static_cast<int>( static_cast<float>(rand())/RAND_MAX * INT_MIN );
// Fill the map vector with random number, not greater that the
// maximum size of the in and out vectors.
for (std::size_t i {0}; i < map_size; ++i)
map.at(i) = static_cast<std::size_t>( static_cast<float>(rand())/RAND_MAX * ( vector_size - 1 ) );
// Copy the values using each algorithm
switch (k)
{
case 0:
map_vector_v1(in, map, out);
break;
case 1:
map_vector_v2(in, map, out);
break;
case 2:
map_vector_v3(in, map, out);
break;
case 3:
map_vector_v4(in, map, out);
break;
case 4:
map_vector_v5(in, map, out);
break;
case 5:
map_vector_v6(in, map, out);
break;
}
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
// Do some operation in the data
for (std::size_t i {0}; i < map_size; ++i)
out[i] += rand();
}
}
// Run algorithms based on C arrays
{
// Run the algorithm based on vectors
for (std::size_t k {0}; k < 2; ++k)
{
for (std::size_t i {0}; i < num_iterations; ++i)
{
// Input vector. It is of size = 'vector_size'
int in[vector_size];
// Output vector. It is of size = 'vector_size'
int out[vector_size];
// Mask Vector. I want to do out[i] = in[ map[i] ]
// Its values are indexes of the 'in' vector, so they all need
// to be less than or equal to 'vector_size'
// It is of size = 'map_size'. To each value in this vector there will
// be a corresponding value in the 'out' vector. So, 'map_size' need to
// be less than or equalt to 'vector_size'.
std::size_t map[map_size];
// Fill input vector with random numbers
for (std::size_t i {0}; i < vector_size; ++i)
in[i] = static_cast<int>( static_cast<float>(rand())/RAND_MAX * INT_MIN );
// Fill the map vector with random number, not greater that the
// maximum size of the in and out vectors.
for (std::size_t i {0}; i < map_size; ++i)
map[i] = static_cast<std::size_t>( static_cast<float>(rand())/RAND_MAX * ( vector_size - 1 ) );
// Copy the values using each algorithm
switch (k)
{
case 0:
map_c_array(in, map, out);
break;
case 1:
map_c_array_v2(in, map, out);
break;
}
// Verify that the values were copied correctly
for (std::size_t i {0}; i < map_size; ++i)
assert( out[i] == in[map[i]] );
// Do some operation in the data
for (std::size_t i {0}; i < map_size; ++i)
out[i] += rand();
}
}
}
}
И вот результат, который я вижу сейчас:
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls Ts/call Ts/call name
30.55 3.88 3.88 map_vector_v2(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
17.76 6.14 2.26 map_vector_v1(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
10.66 7.49 1.35 map_c_array(int*, unsigned long*, int*)
9.08 8.65 1.15 map_vector_v5(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
8.92 9.78 1.13 map_vector_v3(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
7.89 10.78 1.00 map_vector_v4(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
7.89 11.79 1.00 map_vector_v6(std::vector<int, std::allocator<int> > const&, std::vector<unsigned long, std::allocator<unsigned long> > const&, std::vector<int, std::allocator<int> >&)
7.58 12.75 0.96 map_c_array_v2(int*, unsigned long*, int*)
0.00 12.75 0.00 1 0.00 0.00 _GLOBAL__sub_I__Z11map_c_arrayPiPmS_