diff --git a/README.md b/README.md
index 395a780ac87943d736d97e2bd479a37b37aab52a..9c95021fa5f084af733863db917a25f54f8f5542 100644
--- a/README.md
+++ b/README.md
@@ -127,11 +127,8 @@ To remove debugging information for MATLAB MEX functions, the analogous call wou
./configure MATLAB_MEX_CFLAGS="-O3" MATLAB_MEX_CXXFLAGS="-O3"
```
-If you want to give a try to the parallelized versions of some mex files (`A_times_B_kronecker_C` and `sparse_hessian_times_B_kronecker_C` used to get the reduced form of the second order approximation of the model) you can add the `--enable-openmp` flag, for instance:
-```
-./configure --with-matlab=/usr/local/MATLAB/R2019a MATLAB_VERSION=9.6 --enable-openmp
-```
-If the configuration goes well, the script will tell you which components are correctly configured and will be built.
+If the configuration goes well, the script will tell you which components are
+correctly configured and will be built.
Note that it is possible that some MEX files cannot be compiled, due to missing
build dependencies. If you find no way of installing the missing dependencies,
diff --git a/matlab/set_dynare_threads.m b/matlab/set_dynare_threads.m
index 30dbf2febc5963e56ac702425b0b4b759e2b3231..ca761865005441604bae76f34af70eafbf6aeb0b 100644
--- a/matlab/set_dynare_threads.m
+++ b/matlab/set_dynare_threads.m
@@ -1,7 +1,6 @@
function set_dynare_threads(mexname,n)
-% This function sets the number of threads used by some MEX files when compiled
-% with OpenMP support (i.e with --enable-openmp is given to configure) or any
-% other parallel library.
+% This function sets the number of threads used by some MEX files using
+% OpenMP features or any other parallel library.
%
% INPUTS
% o mexname [string] Name of the mex file.
@@ -10,7 +9,7 @@ function set_dynare_threads(mexname,n)
% OUTPUTS
% none.
-% Copyright (C) 2009-2012 Dynare Team
+% Copyright (C) 2009-2019 Dynare Team
%
% This file is part of Dynare.
%
diff --git a/mex/build/block_kalman_filter.am b/mex/build/block_kalman_filter.am
index 381d3a874de68f85cbb2c1a90e34c6142f4d9045..9379db00603697d5957b613be3d874d1bf9b485d 100644
--- a/mex/build/block_kalman_filter.am
+++ b/mex/build/block_kalman_filter.am
@@ -3,6 +3,7 @@ mex_PROGRAMS = block_kalman_filter
TOPDIR = $(top_srcdir)/../../sources/block_kalman_filter
block_kalman_filter_CPPFLAGS = $(AM_CPPFLAGS) -I$(TOPDIR)
+block_kalman_filter_CXXFLAGS = $(AM_CXXFLAGS) -fopenmp
nodist_block_kalman_filter_SOURCES = block_kalman_filter.cc
diff --git a/mex/build/kronecker.am b/mex/build/kronecker.am
index b570bf72a8fe27ece800a2f5dcbe4c2a8bc9fb61..bb2c138bfd8fcca1be01ab9581bc7c16408ceec1 100644
--- a/mex/build/kronecker.am
+++ b/mex/build/kronecker.am
@@ -3,6 +3,8 @@ mex_PROGRAMS = sparse_hessian_times_B_kronecker_C A_times_B_kronecker_C
nodist_sparse_hessian_times_B_kronecker_C_SOURCES = sparse_hessian_times_B_kronecker_C.cc
nodist_A_times_B_kronecker_C_SOURCES = A_times_B_kronecker_C.cc
+sparse_hessian_times_B_kronecker_C_CXXFLAGS = $(AM_CXXFLAGS) -fopenmp
+
BUILT_SOURCES = $(nodist_sparse_hessian_times_B_kronecker_C_SOURCES) $(nodist_A_times_B_kronecker_C_SOURCES)
CLEANFILES = $(nodist_sparse_hessian_times_B_kronecker_C_SOURCES) $(nodist_A_times_B_kronecker_C_SOURCES)
diff --git a/mex/build/local_state_space_iterations.am b/mex/build/local_state_space_iterations.am
index 02641c8e42eaa4e1841f12ef346795d24d18e6dc..59054b76d71a3b275fd0f8626739f4b39f461f01 100644
--- a/mex/build/local_state_space_iterations.am
+++ b/mex/build/local_state_space_iterations.am
@@ -2,6 +2,8 @@ mex_PROGRAMS = local_state_space_iteration_2
nodist_local_state_space_iteration_2_SOURCES = local_state_space_iteration_2.cc
+local_state_space_iteration_2_CXXFLAGS = $(AM_CXXFLAGS) -fopenmp
+
BUILT_SOURCES = $(nodist_local_state_space_iteration_2_SOURCES)
CLEANFILES = $(nodist_local_state_space_iteration_2_SOURCES)
diff --git a/mex/build/matlab/configure.ac b/mex/build/matlab/configure.ac
index 906aeee2e7a0ddab38ec70cd2f6436a43f761546..87cd5953c26cb32cf7d5a217ea5538f9ac6e18b4 100644
--- a/mex/build/matlab/configure.ac
+++ b/mex/build/matlab/configure.ac
@@ -129,14 +129,6 @@ else
BUILD_MS_SBVAR_MEX_MATLAB="no (missing GSL)"
fi
-AC_ARG_ENABLE([openmp], AS_HELP_STRING([--enable-openmp], [use OpenMP for parallelization of some MEX files]), [
- if test "$enable_openmp" = yes; then
- CPPFLAGS="$CPPFLAGS -DUSE_OMP"
- CFLAGS="$CFLAGS -fopenmp"
- CXXFLAGS="$CXXFLAGS -fopenmp"
- fi
-])
-
AC_ARG_WITH([m2html], AS_HELP_STRING([--with-m2html=DIR], [specify installation directory of M2HTML]), [
M2HTML=$withval
BUILD_M2HTML=yes
diff --git a/mex/build/octave/configure.ac b/mex/build/octave/configure.ac
index 7bb01f7047edbbb676450a54eee64dd7de1cacf6..d13a0e83f9c3d4268a085338f319469e17e82d09 100644
--- a/mex/build/octave/configure.ac
+++ b/mex/build/octave/configure.ac
@@ -103,14 +103,6 @@ else
BUILD_MS_SBVAR_MEX_OCTAVE="no (missing GSL or MatIO library)"
fi
-AC_ARG_ENABLE([openmp], AS_HELP_STRING([--enable-openmp], [use OpenMP for parallelization of some MEX files]), [
- if test "x$enable_openmp" = "xyes"; then
- CPPFLAGS="$CPPFLAGS -DUSE_OMP"
- CFLAGS="$CFLAGS -fopenmp"
- CXXFLAGS="$CXXFLAGS -fopenmp"
- fi
-])
-
AC_MSG_NOTICE([
Dynare is now configured for building the following components...
diff --git a/mex/build/qmc_sequence.am b/mex/build/qmc_sequence.am
index d65ea1145342c0d827d2c5c9dd1d90d1d73799cd..05084ec4d071ac76d045ab106ce4bf27cd4858ba 100644
--- a/mex/build/qmc_sequence.am
+++ b/mex/build/qmc_sequence.am
@@ -3,6 +3,7 @@ mex_PROGRAMS = qmc_sequence
TOPDIR = $(top_srcdir)/../../sources/sobol
qmc_sequence_CPPFLAGS = $(AM_CPPFLAGS) -I$(TOPDIR)
+qmc_sequence_CXXFLAGS = $(AM_CXXFLAGS) -fopenmp
nodist_qmc_sequence_SOURCES = qmc_sequence.cc
diff --git a/mex/sources/block_kalman_filter/block_kalman_filter.cc b/mex/sources/block_kalman_filter/block_kalman_filter.cc
index e6a82d67301be44f11ac475b49f2c34b54e08bbb..26ddf92e26f7a040da8ebec36f05fe4dde388765 100644
--- a/mex/sources/block_kalman_filter/block_kalman_filter.cc
+++ b/mex/sources/block_kalman_filter/block_kalman_filter.cc
@@ -19,9 +19,8 @@
#include <cmath>
#include <algorithm>
-#ifdef USE_OMP
-# include <omp.h>
-#endif
+#include <omp.h>
+
#include "block_kalman_filter.hh"
#define BLAS
@@ -372,7 +371,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
//v = Y(:,t) - a(mf)
int i_i = 0;
- //#pragma omp parallel for shared(v, i_i, d_index) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
+ //#pragma omp parallel for shared(v, i_i, d_index)
for (auto i = d_index.begin(); i != d_index.end(); i++)
{
//mexPrintf("i_i=%d, omp_get_max_threads()=%d\n",i_i,omp_get_max_threads());
@@ -383,7 +382,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
//F = P(mf,mf) + H;
i_i = 0;
if (H_size == 1)
- //#pragma omp parallel for shared(iF, F, i_i) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
+ //#pragma omp parallel for shared(iF, F, i_i)
for (auto i = d_index.begin(); i != d_index.end(); i++, i_i++)
{
int j_j = 0;
@@ -391,7 +390,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
iF[i_i + j_j * size_d_index] = F[i_i + j_j * size_d_index] = P[mf[*i] + mf[*j] * n] + H[0];
}
else
- //#pragma omp parallel for shared(iF, F, P, H, mf, i_i) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
+ //#pragma omp parallel for shared(iF, F, P, H, mf, i_i)
for (auto i = d_index.begin(); i != d_index.end(); i++, i_i++)
{
int j_j = 0;
@@ -502,9 +501,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
mexPrintf("dgetri failure with error %d\n", static_cast<int>(info));
//lik(t) = log(dF)+transpose(v)*iF*v;
-#ifdef USE_OMP
-# pragma omp parallel for shared(v_pp) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-#endif
+#pragma omp parallel for shared(v_pp)
for (int i = 0; i < size_d_index; i++)
{
double res = 0.0;
@@ -522,9 +519,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
if (missing_observations)
//K = P(:,mf)*iF;
-#ifdef USE_OMP
-# pragma omp parallel for shared(P_mf) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-#endif
+#pragma omp parallel for shared(P_mf)
for (int i = 0; i < n; i++)
{
int j_j = 0;
@@ -538,9 +533,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
for (int j = 0; j < pp; j++)
P_mf[i + j * n] = P[i + mf[j] * n];
-#ifdef USE_OMP
-# pragma omp parallel for shared(K) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-#endif
+#pragma omp parallel for shared(K)
for (int i = 0; i < n; i++)
for (int j = 0; j < size_d_index; j++)
{
@@ -552,9 +545,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
}
//a = T*(a+K*v);
-#ifdef USE_OMP
-# pragma omp parallel for shared(v_n) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-#endif
+#pragma omp parallel for shared(v_n)
for (int i = pure_obs; i < n; i++)
{
double res = 0.0;
@@ -563,9 +554,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
v_n[i] = res + a[i];
}
-#ifdef USE_OMP
-# pragma omp parallel for shared(a) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-#endif
+#pragma omp parallel for shared(a)
for (int i = 0; i < n; i++)
{
double res = 0.0;
@@ -578,24 +567,20 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
{
//P = T*(P-K*P(mf,:))*transpose(T)+QQ;
int i_i = 0;
- //#pragma omp parallel for shared(P_mf) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
+ //#pragma omp parallel for shared(P_mf)
for (auto i = d_index.begin(); i != d_index.end(); i++, i_i++)
for (int j = pure_obs; j < n; j++)
P_mf[i_i + j * size_d_index] = P[mf[*i] + j * n];
}
else
//P = T*(P-K*P(mf,:))*transpose(T)+QQ;
-#ifdef USE_OMP
-# pragma omp parallel for shared(P_mf) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-#endif
+#pragma omp parallel for shared(P_mf)
for (int i = 0; i < pp; i++)
for (int j = pure_obs; j < n; j++)
P_mf[i + j * pp] = P[mf[i] + j * n];
#ifdef BLAS
-# ifdef USE_OMP
-# pragma omp parallel for shared(K_P) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-# endif
+# pragma omp parallel for shared(K_P)
for (int i = 0; i < n; i++)
for (int j = i; j < n; j++)
{
@@ -733,9 +718,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
}
# else
-# ifdef USE_OMP
-# pragma omp parallel for shared(K_P) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-# endif
+# pragma omp parallel for shared(K_P)
for (int i = pure_obs; i < n; i++)
{
unsigned int i1 = i - pure_obs;
@@ -750,9 +733,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
}
}
-# ifdef USE_OMP
-# pragma omp parallel for shared(P_t_t1) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-# endif
+# pragma omp parallel for shared(P_t_t1)
for (int i = pure_obs; i < n; i++)
{
unsigned int i1 = i - pure_obs;
@@ -766,9 +747,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
fill_n(tmp, 0, n * n_state);
-# ifdef USE_OMP
-# pragma omp parallel for shared(tmp) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-# endif
+# pragma omp parallel for shared(tmp)
for (int i = 0; i < n; i++)
{
int max_k = i_nz_state_var[i];
@@ -785,9 +764,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
fill_n(P, 0, n * n);
int n_n_obs = -n * pure_obs;
-# ifdef USE_OMP
-# pragma omp parallel for shared(P) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-# endif
+# pragma omp parallel for shared(P)
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
@@ -802,9 +779,7 @@ BlockKalmanFilter::block_kalman_filter(int nlhs, mxArray *plhs[])
}
}
-# ifdef USE_OMP
-# pragma omp parallel for shared(P) num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
-# endif
+# pragma omp parallel for shared(P)
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
diff --git a/mex/sources/bytecode/SparseMatrix.cc b/mex/sources/bytecode/SparseMatrix.cc
index 2f076615de48da4e951fd4b143191300961378e1..1f4cb7fb670d588a8e238be218899ce2505bbf19 100644
--- a/mex/sources/bytecode/SparseMatrix.cc
+++ b/mex/sources/bytecode/SparseMatrix.cc
@@ -1923,7 +1923,7 @@ dynSparseMatrix::Init_GE(int periods, int y_kmin, int y_kmax, int Size, map<pair
NbNZCol[i] = 0;
}
int nnz = 0;
- //pragma omp parallel for num_threads(atoi(getenv("DYNARE_NUM_THREADS"))) ordered private(it4, ti_y_kmin, ti_y_kmax, eq, var, lag) schedule(dynamic)
+ //pragma omp parallel for ordered private(it4, ti_y_kmin, ti_y_kmax, eq, var, lag) schedule(dynamic)
for (t = 0; t < periods; t++)
{
ti_y_kmin = -min(t, y_kmin);
@@ -2710,7 +2710,7 @@ dynSparseMatrix::Sparse_mult_SAT_B(mxArray *A_m, mxArray *B_m)
//unsigned int nze_A = 0;
unsigned int C_col = 0;
C_j[C_col] = 0;
- //#pragma omp parallel for num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
+ //#pragma omp parallel for
for (unsigned int j = 0; j < n_B; j++)
{
for (unsigned int i = 0; i < n_A; i++)
@@ -5371,7 +5371,7 @@ dynSparseMatrix::Solve_ByteCode_Sparse_GaussianElimination(int Size, int blck, i
bc[nb_eq_todo++] = first;
first = first->NZE_C_N;
}
- //pragma omp parallel for num_threads(atoi(getenv("DYNARE_NUM_THREADS")))
+ //pragma omp parallel for
for (int j = 0; j < nb_eq_todo; j++)
{
first = bc[j];
@@ -5704,7 +5704,7 @@ dynSparseMatrix::Solve_ByteCode_Symbolic_Sparse_GaussianElimination(int Size, bo
bc[nb_eq_todo++] = first;
first = first->NZE_C_N;
}
- //#pragma omp parallel for num_threads(atoi(getenv("DYNARE_NUM_THREADS"))) shared(nb_var_piva, first_piva, nopa, save_op) reduction(+:nop)
+ //#pragma omp parallel for shared(nb_var_piva, first_piva, nopa, save_op) reduction(+:nop)
for (int j = 0; j < nb_eq_todo; j++)
{
t_save_op_s *save_op_s_l;
@@ -5873,7 +5873,7 @@ dynSparseMatrix::Solve_ByteCode_Symbolic_Sparse_GaussianElimination(int Size, bo
bc[nb_eq_todo++] = first;
first = first->NZE_C_N;
}
- //#pragma omp parallel for num_threads(atoi(getenv("DYNARE_NUM_THREADS"))) shared(nb_var_piva, first_piva, nopa, save_op) reduction(+:nop)
+ //#pragma omp parallel for shared(nb_var_piva, first_piva, nopa, save_op) reduction(+:nop)
for (int j = 0; j < nb_eq_todo; j++)
{
NonZeroElem *first = bc[j];
diff --git a/mex/sources/kronecker/sparse_hessian_times_B_kronecker_C.cc b/mex/sources/kronecker/sparse_hessian_times_B_kronecker_C.cc
index 18ee522ee0c2ec93bd8087b8c05774c5a5cdf737..93265998cc32f06afd7a439677f4100a5fa13d81 100644
--- a/mex/sources/kronecker/sparse_hessian_times_B_kronecker_C.cc
+++ b/mex/sources/kronecker/sparse_hessian_times_B_kronecker_C.cc
@@ -27,9 +27,7 @@
#include <dynmex.h>
-#ifdef USE_OMP
-# include <omp.h>
-#endif
+#include <omp.h>
#define DEBUG_OMP 0
@@ -42,9 +40,7 @@ sparse_hessian_times_B_kronecker_B(const mwIndex *isparseA, const mwIndex *jspar
** This loop is splitted into two nested loops because we use the
** symmetric pattern of the hessian matrix.
*/
-#if USE_OMP
-# pragma omp parallel for num_threads(number_of_threads)
-#endif
+#pragma omp parallel for num_threads(number_of_threads)
for (mwIndex j1B = 0; j1B < static_cast<mwIndex>(nB); j1B++)
{
#if DEBUG_OMP
@@ -95,9 +91,7 @@ sparse_hessian_times_B_kronecker_C(const mwIndex *isparseA, const mwIndex *jspar
/*
** Loop over the columns of B⊗B (or of the result matrix D).
*/
-#if USE_OMP
-# pragma omp parallel for num_threads(number_of_threads)
-#endif
+#pragma omp parallel for num_threads(number_of_threads)
for (mwIndex jj = 0; jj < static_cast<mwIndex>(nB*nC); jj++) // column of B⊗C index.
{
// Uncomment the following line to check if all processors are used.
diff --git a/mex/sources/local_state_space_iterations/local_state_space_iteration_2.cc b/mex/sources/local_state_space_iterations/local_state_space_iteration_2.cc
index b700c39b176fca280ee903dcf10cb4964e69a037..2ecd1fc9f3634f2cbaad979bc3177a5e272cfeb4 100644
--- a/mex/sources/local_state_space_iterations/local_state_space_iteration_2.cc
+++ b/mex/sources/local_state_space_iterations/local_state_space_iteration_2.cc
@@ -28,9 +28,7 @@
#include <dynmex.h>
#include <dynblas.h>
-#ifdef USE_OMP
-# include <omp.h>
-#endif
+#include <omp.h>
#define FIRST_ORDER_LOOP 1// Comment out this line to use mkl-blas instead of loops when computing ghx*yhat and ghu*epsilon
@@ -67,9 +65,7 @@ ss2Iteration_pruning(double *y2, double *y1, const double *yhat2, const double *
std::vector<int> jj1, jj2, jj3;// vector indices for ghuu
set_vector_of_indices(n, m, ii1, ii2, ii3);
set_vector_of_indices(q, m, jj1, jj2, jj3);
-#ifdef USE_OMP
-# pragma omp parallel for num_threads(number_of_threads)
-#endif
+#pragma omp parallel for num_threads(number_of_threads)
for (int particle = 0; particle < s; particle++)
{
int particle_ = particle*m;
@@ -155,9 +151,7 @@ ss2Iteration(double *y, const double *yhat, const double *epsilon,
std::vector<int> jj1, jj2, jj3;// vector indices for ghuu
set_vector_of_indices(n, m, ii1, ii2, ii3);
set_vector_of_indices(q, m, jj1, jj2, jj3);
-#ifdef USE_OMP
-# pragma omp parallel for num_threads(number_of_threads)
-#endif
+#pragma omp parallel for num_threads(number_of_threads)
for (int particle = 0; particle < s; particle++)
{
int particle_ = particle*m;
diff --git a/mex/sources/sobol/gaussian.hh b/mex/sources/sobol/gaussian.hh
index ade3ef9e35255eff5f735e4c48201e061f95704e..ea5377cb95f61a293d36e9cc4d9e7ece904680b4 100644
--- a/mex/sources/sobol/gaussian.hh
+++ b/mex/sources/sobol/gaussian.hh
@@ -2,7 +2,7 @@
**
** Pseudo code of the algorithm is given at http://home.online.no/~pjacklam/notes/invnorm
**
-** Copyright © 2010-2017 Dynare Team
+** Copyright © 2010-2019 Dynare Team
**
** This file is part of Dynare.
**
@@ -26,6 +26,8 @@
#include <limits>
#include <algorithm>
+#include <omp.h>
+
#include <dynblas.h>
using namespace std;
@@ -33,11 +35,6 @@ using namespace std;
constexpr double lb = .02425;
constexpr double ub = .97575;
-#ifdef USE_OMP
-# include <omp.h>
-#endif
-#define DEBUG_OMP 0
-
template<typename T>
T
icdf(const T uniform)
@@ -125,9 +122,7 @@ template<typename T>
void
icdfm(int n, T *U)
{
-#if USE_OMP
-# pragma omp parallel for num_threads(omp_get_num_threads())
-#endif
+#pragma omp parallel for
for (int i = 0; i < n; i++)
U[i] = icdf(U[i]);
return;
@@ -152,9 +147,7 @@ void
usphere(int d, int n, T *U)
{
icdfm(n*d, U);
-#if USE_OMP
-# pragma omp parallel for num_threads(omp_get_num_threads())
-#endif
+#pragma omp parallel for
for (int j = 0; j < n; j++)// sequence index.
{
int k = j*d;
@@ -173,9 +166,7 @@ void
usphereRadius(int d, int n, double radius, T *U)
{
icdfm(n*d, U);
-#if USE_OMP
-# pragma omp parallel for num_threads(omp_get_num_threads())
-#endif
+#pragma omp parallel for
for (int j = 0; j < n; j++)// sequence index.
{
int k = j*d;