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map2alm_transpose_mpi.c
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/*
map analysis HEALPix function w/ MPI - does MPI parallel map -> alm
This is a complete rewrite in C of the HEALPix analysis function. Parts of these routines were
taken from the public HEALPix package. See copyright and GPL info below.
-Matthew R. Becker, UofC 2010
*/
/*
!-----------------------------------------------------------------------------
!
! Copyright (C) 1997-2008 Krzysztof M. Gorski, Eric Hivon,
! Benjamin D. Wandelt, Anthony J. Banday,
! Matthias Bartelmann, Hans K. Eriksen,
! Frode K. Hansen, Martin Reinecke
!
!
! This file is part of HEALPix.
!
! HEALPix is free software; you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation; either version 2 of the License, or
! (at your option) any later version.
!
! HEALPix is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with HEALPix; if not, write to the Free Software
! Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
!
! For more information about HEALPix see http://healpix.jpl.nasa.gov
!
!-----------------------------------------------------------------------------
! Written by Hans Kristian Eriksen and Snorre Boasson,
! but copying large parts from the serial HEALPix code.
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#include <fftw3.h>
#include <gsl/gsl_math.h>
#include <mpi.h>
#include <assert.h>
#include "healpix_utils.h"
#include "healpix_shtrans.h"
void map2alm_mpi(double *alm_real, double *alm_imag, float *mapvec, HEALPixSHTPlan plan)
{
int NTasks,ThisTask;
long i,m,l,nring,j,lmin,mind,lmind;
long nstartpix,ringpix,shifted;
double nsintheta,ncostheta;
double sfact,fac1;
long Nside,Npix;
long lmax;
long firstRing,lastRing,lastRingLoop;
fftwf_complex *ngm,*sgm;
double ngmval[2],sgmval[2];
double *plm;
plmgen_data *plmdata;
double plmeps;
long firstl;
double quadweight;
double *ring_weights;
double phase[2],tmp[2];
long Nrings;
long NringsThisTask;
double runTime;
#ifdef OUTPUT_SHT_LOADBALANCE
double mintm,maxtm,avgtm;
#endif
fftwf_complex *mapvec_complex;
long memTot = 0;
double transTime,fftTime,sumTime,plmTime;
double *ringTime;
runTime = -MPI_Wtime();
MPI_Comm_size(MPI_COMM_WORLD,&NTasks);
MPI_Comm_rank(MPI_COMM_WORLD,&ThisTask);
//timing
plmTime = 0.0;
fftTime = 0.0;
sumTime = 0.0;
transTime = 0.0;
//init healpix vars
Npix = order2npix(plan.order);
Nside = order2nside(plan.order);
lmax = plan.lmax;
Nrings = 2*Nside;
plmeps = 1e-30;
quadweight = 4.0*M_PI/Npix;
//get ring_weights
ring_weights = (double*)malloc(sizeof(double)*Nrings);
assert(ring_weights != NULL);
memTot += sizeof(double)*Nrings;
for(i=0;i<Nrings;++i)
{
if(plan.ring_weights != NULL)
ring_weights[i] = plan.ring_weights[i];
else
ring_weights[i] = 0.0;
ring_weights[i] += 1.0;
ring_weights[i] *= quadweight;
}
//get rings for this task
firstRing = plan.firstRingTasks[ThisTask];
lastRing = plan.lastRingTasks[ThisTask];
if(firstRing == -1 || lastRing == -1 || plan.firstMTasks[ThisTask] == -1 || plan.lastMTasks[ThisTask] == -1)
{
fprintf(stderr,"problem with assigning rings/ms to tasks! (Did you ask for more tasks than rings?)\n");
for(i=0;i<NTasks;++i)
fprintf(stderr,"\t%ld: firstRing,lastRing,Nrings = %ld|%ld,%ld, firstM,lastM,NM = %ld|%ld|%ld\n",i,
plan.firstRingTasks[i],plan.lastRingTasks[i],2*Nside,
plan.firstMTasks[i],plan.lastMTasks[i],plan.lmax+1);
MPI_Abort(MPI_COMM_WORLD,123);
}
lastRingLoop = lastRing;
NringsThisTask = lastRing - firstRing + 1;
if(lastRing == Nrings)
--lastRingLoop;
//time the rings to get load balance correct
ringTime = (double*)malloc(sizeof(double)*NringsThisTask);
memTot += sizeof(double)*NringsThisTask;
assert(ringTime != NULL);
for(i=0;i<NringsThisTask;++i)
ringTime[i] = 0.0;
//do FFT of rings in place first
fftTime -= MPI_Wtime();
mapvec_complex = (fftwf_complex*) mapvec;
for(nring=firstRing;nring<=lastRingLoop;++nring)
{
ringTime[nring-firstRing] -= MPI_Wtime();
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
mapvec = (float*) (mapvec_complex + plan.northStartIndMapvec[nring-firstRing]);
for(i=0;i<ringpix;++i)
mapvec[i] = (float) (mapvec[i]*ring_weights[nring-1]);
ring_analysis(ringpix,mapvec);
mapvec = (float*) (mapvec_complex + plan.southStartIndMapvec[nring-firstRing]);
for(i=0;i<ringpix;++i)
mapvec[i] = (float) (mapvec[i]*ring_weights[nring-1]);
ring_analysis(ringpix,mapvec);
ringTime[nring-firstRing] += MPI_Wtime();
}
if(lastRing == Nrings)
{
ringTime[lastRing-firstRing] -= MPI_Wtime();
get_ring_info2(lastRing,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
mapvec = (float*) (mapvec_complex + plan.northStartIndMapvec[lastRing-firstRing]);
for(i=0;i<ringpix;++i)
mapvec[i] = (float) (mapvec[i]*ring_weights[lastRing-1]);
ring_analysis(ringpix,mapvec);
ringTime[lastRing-firstRing] += MPI_Wtime();
}
mapvec = (float*) mapvec_complex;
free(ring_weights);
memTot -= sizeof(double)*Nrings;
fftTime += MPI_Wtime();
//pack the data and do transpose
transTime -= MPI_Wtime();
double *transDataReal,*transDataImag;
double *transDataRealRecv,*transDataImagRecv;
long NmTD,NrTD,NmTDR,NrTDR;
NmTD = lmax+1;
NrTD = 2*(lastRing - firstRing + 1);
if(lastRing == Nrings)
--NrTD;
transDataReal = (double*)malloc(sizeof(double)*NrTD*NmTD);
assert(transDataReal != NULL);
memTot += sizeof(double)*NrTD*NmTD;
transDataImag = (double*)malloc(sizeof(double)*NrTD*NmTD);
assert(transDataImag != NULL);
memTot += sizeof(double)*NrTD*NmTD;
NmTDR = plan.lastMTasks[ThisTask] - plan.firstMTasks[ThisTask] + 1;
NrTDR = 4*Nside-1;
transDataRealRecv = (double*)malloc(sizeof(double)*NrTDR*NmTDR);
assert(transDataRealRecv != NULL);
memTot += sizeof(double)*NrTDR*NmTDR;
transDataImagRecv = (double*)malloc(sizeof(double)*NrTDR*NmTDR);
assert(transDataImagRecv != NULL);
memTot += sizeof(double)*NrTDR*NmTDR;
for(i=0;i<NmTD;++i)
for(j=0;j<NrTD;++j)
{
transDataReal[i*NrTD + j] = 0.0;
transDataImag[i*NrTD + j] = 0.0;
}
long nind;
for(nring=firstRing;nring<=lastRingLoop;++nring)
{
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
ngm = mapvec_complex + plan.northStartIndMapvec[nring-firstRing];
sgm = mapvec_complex + plan.southStartIndMapvec[nring-firstRing];
nind = nring - firstRing;
for(m=0;m<=lmax;++m)
{
//get FFTed vals - only store half since map is real so need to get correct val for given m
mind = m%ringpix;
if(mind > ringpix/2)
{
mind = ringpix - mind;
ngmval[0] = ngm[mind][0];
ngmval[1] = -ngm[mind][1];
sgmval[0] = sgm[mind][0];
sgmval[1] = -sgm[mind][1];
}
else
{
ngmval[0] = ngm[mind][0];
ngmval[1] = ngm[mind][1];
sgmval[0] = sgm[mind][0];
sgmval[1] = sgm[mind][1];
}
//phase factors of shifted rings
if(shifted)
{
phase[0] = cos(m*M_PI/ringpix);
phase[1] = -sin(m*M_PI/ringpix);
tmp[0] = ngmval[0]*phase[0] - ngmval[1]*phase[1];
tmp[1] = ngmval[0]*phase[1] + ngmval[1]*phase[0];
ngmval[0] = tmp[0];
ngmval[1] = tmp[1];
tmp[0] = sgmval[0]*phase[0] - sgmval[1]*phase[1];
tmp[1] = sgmval[0]*phase[1] + sgmval[1]*phase[0];
sgmval[0] = tmp[0];
sgmval[1] = tmp[1];
}
transDataReal[m*NrTD + 2*nind] = ngmval[0];
transDataImag[m*NrTD + 2*nind] = ngmval[1];
transDataReal[m*NrTD + 2*nind + 1] = sgmval[0];
transDataImag[m*NrTD + 2*nind + 1] = sgmval[1];
}//for(m=0;m<=lmax;++m)
}//for(nring=firstRing;nring<=lastRingLoop;++nring)
if(lastRing == Nrings)
{
nring = lastRing;
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
ngm = mapvec_complex + plan.northStartIndMapvec[nring-firstRing];
nind = nring - firstRing;
for(m=0;m<=lmax;++m)
{
//get FFTed vals - only store half since map is real so need to get correct val for given m
mind = m%ringpix;
if(mind > ringpix/2)
{
mind = ringpix - mind;
ngmval[0] = ngm[mind][0];
ngmval[1] = -ngm[mind][1];
}
else
{
ngmval[0] = ngm[mind][0];
ngmval[1] = ngm[mind][1];
}
//phase factors of shifted rings
if(shifted)
{
phase[0] = cos(m*M_PI/ringpix);
phase[1] = -sin(m*M_PI/ringpix);
tmp[0] = ngmval[0]*phase[0] - ngmval[1]*phase[1];
tmp[1] = ngmval[0]*phase[1] + ngmval[1]*phase[0];
ngmval[0] = tmp[0];
ngmval[1] = tmp[1];
}
transDataReal[m*NrTD + 2*nind] = ngmval[0];
transDataImag[m*NrTD + 2*nind] = ngmval[1];
}//for(m=0;m<=lmax;++m)
}//if(lastRing == Nrings)
//now do transpose
int *sendcnts,*sdispls,*rdispls,*recvcnts;
sendcnts = (int*)malloc(sizeof(int)*NTasks);
assert(sendcnts != NULL);
sdispls = (int*)malloc(sizeof(int)*NTasks);
assert(sdispls != NULL);
recvcnts = (int*)malloc(sizeof(int)*NTasks);
assert(recvcnts != NULL);
rdispls = (int*)malloc(sizeof(int)*NTasks);
assert(rdispls != NULL);
memTot += 4*sizeof(int)*NTasks;
for(i=0;i<NTasks;++i)
{
//compute number of m vals on task i
j = plan.lastMTasks[i] - plan.firstMTasks[i] + 1;
sendcnts[i] = NrTD*j;
}
sdispls[0] = 0;
for(i=1;i<NTasks;++i)
sdispls[i] = sdispls[i-1] + sendcnts[i-1];
MPI_Alltoall(sendcnts,1,MPI_INT,recvcnts,1,MPI_INT,MPI_COMM_WORLD);
rdispls[0] = 0;
for(i=1;i<NTasks;++i)
rdispls[i] = rdispls[i-1] + recvcnts[i-1];
int log2NTasks = 0;
while(NTasks > (1 << log2NTasks))
++log2NTasks;
int level;
int sendTask,recvTask;
MPI_Status Stat;
//algorithm to loop through pairs of tasks linearly
// -lifted from Gadget-2 under GPL (http://www.gnu.org/copyleft/gpl.html)
// -see pm_periodic.c from Gadget-2 at http://www.mpa-garching.mpg.de/gadget/
//
for(level = 0; level < (1 << log2NTasks); level++) // note: for level=0, target is the same task
{
sendTask = ThisTask;
recvTask = ThisTask ^ level;
if(recvTask < NTasks)
{
if(sendTask != recvTask)
{
MPI_Sendrecv(transDataReal+sdispls[recvTask],sendcnts[recvTask],MPI_DOUBLE,recvTask,13,
transDataRealRecv+rdispls[recvTask],recvcnts[recvTask],MPI_DOUBLE,recvTask,13,
MPI_COMM_WORLD,&Stat);
MPI_Sendrecv(transDataImag+sdispls[recvTask],sendcnts[recvTask],MPI_DOUBLE,recvTask,14,
transDataImagRecv+rdispls[recvTask],recvcnts[recvTask],MPI_DOUBLE,recvTask,14,
MPI_COMM_WORLD,&Stat);
}
else // just move cells into workspace since sendTask == recvTask and Nsend == Nrecv
{
for(i=0;i<recvcnts[recvTask];++i)
transDataRealRecv[rdispls[recvTask]+i] = transDataReal[sdispls[recvTask]+i];
for(i=0;i<recvcnts[recvTask];++i)
transDataImagRecv[rdispls[recvTask]+i] = transDataImag[sdispls[recvTask]+i];
}
}
}
free(transDataReal);
memTot -= sizeof(double)*NrTD*NmTD;
free(transDataImag);
memTot -= sizeof(double)*NrTD*NmTD;
free(sendcnts);
free(sdispls);
free(recvcnts);
memTot -= 3*sizeof(int)*NTasks;
transTime += MPI_Wtime();
//now do sum over rings for all l,m w/ MPI_Reduce
sumTime -= MPI_Wtime();
//m vars
long firstM,lastM,NMThisTask;
double *mTimes;
firstM = plan.firstMTasks[ThisTask];
lastM = plan.lastMTasks[ThisTask];
NMThisTask = lastM - firstM + 1;
mTimes = (double*)malloc(sizeof(double)*NMThisTask);
assert(mTimes != NULL);
memTot += sizeof(double)*NMThisTask;
for(i=0;i<NMThisTask;++i)
mTimes[i] = 0.0;
//init plm generator
plm = (double*)malloc(sizeof(double)*(lmax+1));
memTot += sizeof(double)*(lmax+1);
assert(plm != NULL);
plmTime -= MPI_Wtime();
plmdata = plmgen_init(lmax,plmeps);
plmTime += MPI_Wtime();
//zero alms
i = 0;
for(m=firstM;m<=lastM;++m)
for(l=m;l<=lmax;++l)
{
alm_real[i] = 0.0;
alm_imag[i] = 0.0;
++i;
}
int task;
long start;
long ind;
for(task=0;task<NTasks;++task)
{
start = rdispls[task];
firstRing = plan.firstRingTasks[task];
lastRing = plan.lastRingTasks[task];
lastRingLoop = lastRing;
NrTD = 2*(lastRing - firstRing + 1);
if(lastRing == Nrings)
{
--lastRingLoop;
--NrTD;
}
lmind = 0;
for(m=firstM;m<=lastM;++m)
{
mind = m-firstM;
mTimes[mind] -= MPI_Wtime();
ind = start + mind*NrTD;
for(nring=firstRing;nring<=lastRingLoop;++nring)
{
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
nind = nring - firstRing;
//do not sum over Ylm which are too small
lmin = get_lmin_ylm(m,nsintheta);
if(lmin <= lmax)
{
//get plms for ring
plmTime -= MPI_Wtime();
plmgen(ncostheta,nsintheta,m,plm,&firstl,plmdata);
plmTime += MPI_Wtime();
//loop over l values and update all at fixed m
if(firstl <= lmax)
{
sfact = 1.0 - 2.0*((firstl+m)%2);
for(l=firstl;l<=lmax;++l)
{
//this is always true (before plm[l] factor) assert((((l+m)%2 == 0 && sfact == 1.0)) || (((l+m)%2 == 1 && sfact == -1.0)));
alm_real[lmind + l-m] += transDataRealRecv[ind + 2*nind]*plm[l];
alm_imag[lmind + l-m] += transDataImagRecv[ind + 2*nind]*plm[l];
fac1 = sfact*plm[l];
alm_real[lmind + l-m] += transDataRealRecv[ind + 2*nind + 1]*fac1;
alm_imag[lmind + l-m] += transDataImagRecv[ind + 2*nind + 1]*fac1;
sfact = -sfact;
}
/* old, slower version
sfact = 1.0 + -2.0*((firstl+m)%2);
for(l=firstl;l<=lmax;++l)
{
almloop_real[lmind + l-m] += sfact*sgmval[0]*plm[l];
almloop_imag[lmind + l-m] += sfact*sgmval[1]*plm[l];
almloop_real[lmind + l-m] += ngmval[0]*plm[l];
almloop_imag[lmind + l-m] += ngmval[1]*plm[l];
sfact = -1.0*sfact;
}
*/
}//if(firstl <= lmax)
}//if(lmin <= lmax)
}//for(nring=firstRing;nring<=lastRingLoop;++nring)
lmind += lmax-m+1;
mTimes[mind] += MPI_Wtime();
}//for(m=firstM;m<=lastM;++m)
if(lastRing == Nrings)
{
nring = lastRing;
get_ring_info2(nring,&nstartpix,&ringpix,&ncostheta,&nsintheta,&shifted,plan.order);
nind = nring - firstRing;
lmind = 0;
for(m=firstM;m<=lastM;++m)
{
mind = m-firstM;
mTimes[mind] -= MPI_Wtime();
ind = start + mind*NrTD;
//do not sum over Ylm which are too small
lmin = get_lmin_ylm(m,nsintheta);
if(lmin <= lmax)
{
//get plms for ring
plmTime -= MPI_Wtime();
plmgen(ncostheta,nsintheta,m,plm,&firstl,plmdata);
plmTime += MPI_Wtime();
//loop over l values and update all at fixed m
for(l=firstl;l<=lmax;++l)
{
//this is always true (before plm[l] factor) assert((((l+m)%2 == 0 && sfact == 1.0)) || (((l+m)%2 == 1 && sfact == -1.0)));
alm_real[lmind + l-m] += transDataRealRecv[ind + 2*nind]*plm[l];
alm_imag[lmind + l-m] += transDataImagRecv[ind + 2*nind]*plm[l];
}
}//if(lmin <= lmax)
lmind += lmax-m+1;
mTimes[mind] += MPI_Wtime();
}//for(m=firstM;m<=lastM;++m)
}//if(lastRing == Nrings)
}//for(task=0;task<NTasks;++task)
free(transDataRealRecv);
memTot -= sizeof(double)*NrTDR*NmTDR;
free(transDataImagRecv);
memTot -= sizeof(double)*NrTDR*NmTDR;
free(rdispls);
memTot -= sizeof(int)*NTasks;
free(plm);
memTot -= sizeof(double)*(lmax+1);
plmgen_destroy(plmdata);
sumTime += MPI_Wtime();
runTime += MPI_Wtime();
#ifdef OUTPUT_SHT_LOADBALANCE
MPI_Reduce(&runTime,&mintm,1,MPI_DOUBLE,MPI_MIN,0,MPI_COMM_WORLD);
MPI_Reduce(&runTime,&maxtm,1,MPI_DOUBLE,MPI_MAX,0,MPI_COMM_WORLD);
MPI_Reduce(&runTime,&avgtm,1,MPI_DOUBLE,MPI_SUM,0,MPI_COMM_WORLD);
avgtm = avgtm/NTasks;
if(ThisTask == 0)
fprintf(stderr,"map -> alm run time max,min,avg = %f|%f|%f sec (%.2f percent)\n",maxtm,mintm,avgtm,(maxtm-avgtm)/avgtm*100.0);
MPI_Reduce(&fftTime,&mintm,1,MPI_DOUBLE,MPI_MIN,0,MPI_COMM_WORLD);
MPI_Reduce(&fftTime,&maxtm,1,MPI_DOUBLE,MPI_MAX,0,MPI_COMM_WORLD);
MPI_Reduce(&fftTime,&avgtm,1,MPI_DOUBLE,MPI_SUM,0,MPI_COMM_WORLD);
avgtm = avgtm/NTasks;
if(ThisTask == 0)
fprintf(stderr,"map -> alm fft time and load balance: max,min,avg = %f|%f|%f sec (%.2f percent)\n",maxtm,mintm,avgtm,(maxtm-avgtm)/avgtm*100.0);
MPI_Reduce(&transTime,&mintm,1,MPI_DOUBLE,MPI_MIN,0,MPI_COMM_WORLD);
MPI_Reduce(&transTime,&maxtm,1,MPI_DOUBLE,MPI_MAX,0,MPI_COMM_WORLD);
MPI_Reduce(&transTime,&avgtm,1,MPI_DOUBLE,MPI_SUM,0,MPI_COMM_WORLD);
avgtm = avgtm/NTasks;
if(ThisTask == 0)
fprintf(stderr,"map -> alm trans time and load balance: max,min,avg = %f|%f|%f sec (%.2f percent)\n",maxtm,mintm,avgtm,(maxtm-avgtm)/avgtm*100.0);
MPI_Reduce(&sumTime,&mintm,1,MPI_DOUBLE,MPI_MIN,0,MPI_COMM_WORLD);
MPI_Reduce(&sumTime,&maxtm,1,MPI_DOUBLE,MPI_MAX,0,MPI_COMM_WORLD);
MPI_Reduce(&sumTime,&avgtm,1,MPI_DOUBLE,MPI_SUM,0,MPI_COMM_WORLD);
avgtm = avgtm/NTasks;
if(ThisTask == 0)
fprintf(stderr,"map -> alm sum time and load balance: max,min,avg = %f|%f|%f sec (%.2f percent)\n",maxtm,mintm,avgtm,(maxtm-avgtm)/avgtm*100.0);
MPI_Reduce(&plmTime,&mintm,1,MPI_DOUBLE,MPI_MIN,0,MPI_COMM_WORLD);
MPI_Reduce(&plmTime,&maxtm,1,MPI_DOUBLE,MPI_MAX,0,MPI_COMM_WORLD);
MPI_Reduce(&plmTime,&avgtm,1,MPI_DOUBLE,MPI_SUM,0,MPI_COMM_WORLD);
avgtm = avgtm/NTasks;
if(ThisTask == 0)
fprintf(stderr,"map -> alm plm time and load balance: max,min,avg = %f|%f|%f sec (%.2f percent)\n",maxtm,mintm,avgtm,(maxtm-avgtm)/avgtm*100.0);
#endif
//do load balance stuff
firstRing = plan.firstRingTasks[ThisTask];
lastRing = plan.lastRingTasks[ThisTask];
lastRingLoop = lastRing;
NringsThisTask = lastRing - firstRing + 1;
if(lastRing == Nrings)
--lastRingLoop;
//add in times
for(j=0;j<NringsThisTask;++j)
map2almRingTimesGlobal[j+firstRing-1] += ringTime[j];
free(ringTime);
memTot -= sizeof(double)*NringsThisTask;
for(j=0;j<NMThisTask;++j)
alm2mapMTimesGlobal[j+firstM] += mTimes[j];
free(mTimes);
memTot -= sizeof(double)*NMThisTask;
assert(memTot == 0);
#ifdef OUTPUT_SHT_LOADBALANCE
FILE *fp;
char name[1024];
double *localTimes,*globalTimes;
long NlocalTimes;
NlocalTimes = 2*Nside;
localTimes = (double*)malloc(sizeof(double)*NlocalTimes);
assert(localTimes != NULL);
globalTimes = (double*)malloc(sizeof(double)*NlocalTimes);
assert(globalTimes != NULL);
for(i=0;i<Nmap2almRingTimesGlobal;++i)
localTimes[i] = 0.0;
for(i=0;i<Nmap2almRingTimesGlobal;++i)
localTimes[i] = map2almRingTimesGlobal[i];
MPI_Allreduce(localTimes,globalTimes,(int) Nmap2almRingTimesGlobal,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD);
sprintf(name,"./map2alm_ringtimes.%ld",plan.order);
if(ThisTask == 0)
{
remove(name);
fp = fopen(name,"w");
for(i=0;i<Nmap2almRingTimesGlobal;++i)
fprintf(fp,"%ld %.20e \n",i,globalTimes[i]);
fclose(fp);
}
free(localTimes);
free(globalTimes);
#endif
}