long long dom_decomp_3d(const long long Nx, const long long Ny, const long long Nz,
const long long Np, long long *pNGx, long long *pNGy, long long *pNGz){
long long rx_min, rx_max, rx, ry, rz, I;
long long rx0 = 1;
long long ry0 = 1;
long long rz0 = 1;
long long I0 = 1;
long long init=1;
long long quotient;
long long remainder;
long long err, t, Npt;
/* Constrain the decomposition */
rx_max = Nx < Np ? Nx : Np; /* Require ry >= 1, rz >= 1 and rx <= Nx */
/* Compute a global minimum constraint on rx. */
t = (Ny < Np ? Ny : Np)*(Nz < Np ? Nz : Np); /* t = Max(ry)*Max(rz) */
if(t < Np){ /* Require rx >= 1, ry <= Ny and rz <= Nz */
quotient = Np/t;
remainder = Np%t;
/* rx_min = the smallest integer >= Np/t */
rx_min = quotient + (remainder > 0 ? 1 : 0);
}
else rx_min = 1;
/* printf("rx_min = %d, rx_max = %d\n",rx_min, rx_max); */
for(rx = rx_min; rx <= rx_max; rx++){
quotient = Np/rx;
remainder = Np%rx;
if(remainder == 0){
Npt = quotient; /* Np for transverse (y,z) decomposition */
err = dom_decomp_2d(Ny, Nz, Npt, &ry, &rz);
if(err == 0){
/* Now compute the amount of messaging */
I = (rx - 1)*Ny*Nz + (ry - 1)*Nx*Nz + (rz - 1)*Nx*Ny;
if(I < 0) continue; /* Integer Overflow */
if(init || I < I0){
rx0 = rx;
ry0 = ry;
rz0 = rz;
I0 = I;
init = 0;
/* printf("I(rx = %d, ry = %d, rz = %d) = %d\n",rx,ry,rz,I); */
}
}
}
}
if(init) return 1; /* Error locating a solution */
*pNGx = rx0;
*pNGy = ry0;
*pNGz = rz0;
return 0;
}
static int dom_decomp_3d(const int Nx, const int Ny, const int Nz,
const int Np, int *pNGx, int *pNGy, int *pNGz){
div_t dv;
int rx_min, rx_max, rx, ry, rz, I;
int rx0=1, ry0=1, rz0=1, I0=0, init=1;
int ierr, t, Npt;
/* Constrain the decomposition */
rx_max = Nx < Np ? Nx : Np; /* Require ry >= 1, rz >= 1 and rx <= Nx */
/* Compute a global minimum constraint on rx. */
t = (Ny < Np ? Ny : Np)*(Nz < Np ? Nz : Np); /* t = Max(ry)*Max(rz) */
if(t < Np){ /* Require rx >= 1, ry <= Ny and rz <= Nz */
dv = div(Np, t);
/* rx_min = the smallest integer >= Np/t */
rx_min = dv.quot + (dv.rem > 0 ? 1 : 0);
}
else rx_min = 1;
/* printf("rx_min = %d, rx_max = %d\n",rx_min, rx_max); */
for(rx = rx_min; rx <= rx_max; rx++){
dv = div(Np, rx);
if(dv.rem == 0){
Npt = dv.quot; /* Np for transverse (y,z) decomposition */
ierr = dom_decomp_2d(Ny, Nz, Npt, &ry, &rz);
if(ierr == 0){
/* Now compute the amount of messaging */
I = (rx - 1)*Ny*Nz + (ry - 1)*(Nx + 2*nghost*rx)*Nz
+ (rz - 1)*(Nx + 2*nghost*rx)*(Ny + 2*nghost*ry);
if(I < 0){ /* Integer Overflow */
/* printf("[3d new] I = %d\n",I); */
continue;
}
if(init || I < I0){
rx0 = rx;
ry0 = ry;
rz0 = rz;
I0 = I;
init = 0;
/* printf("I(rx = %d, ry = %d, rz = %d) = %d\n",rx,ry,rz,I); */
}
}
}
}
if(init) return 1; /* Error locating a solution */
*pNGx = rx0;
*pNGy = ry0;
*pNGz = rz0;
return 0;
}
static int dom_decomp(const int Nx, const int Ny, const int Nz,
const int Np, int *pNGx, int *pNGy, int *pNGz)
{
if(Nx > 1 && Ny == 1 && Nz == 1){ /* 1-D */
if(Np > Nx) return 1; /* Too many procs. */
*pNGx = Np;
*pNGy = 1;
*pNGz = 1;
return 0;
}
else if(Nx > 1 && Ny > 1 && Nz == 1){ /* 2-D */
*pNGz = 1;
return dom_decomp_2d(Nx, Ny, Np, pNGx, pNGy);
}
else if(Nx > 1 && Ny > 1 && Nz > 1){ /* 3-D */
return dom_decomp_3d(Nx, Ny, Nz, Np, pNGx, pNGy, pNGz);
}
return 1; /* Error - particular case not expected */
}
long long main(void){
long long Nx=512, Ny=1024, Nz = 256, Np = 8, NGx, NGy, NGz, Np_max;
long long rx,ry,rz,I;
long long err1, err2;
#if 0
for(Np = 1; Np <= 2048; Np++){
dom_decomp_2d(Nx, Ny, Np, &NGx, &NGy);
printf("Nx = %d, Ny = %d, Np = %d, NGx = %d, NGy = %d\n",
Nx,Ny,Np,NGx,NGy);
printf("Grids measure: Nx/NGx = nx = %e, Ny/NGy = ny = %e\n\n",
(double)Nx/(double)NGx, (double)Ny/(double)NGy);
}
#endif
#if 1
for(Nx = 1; Nx <= 48; Nx++){
for(Ny = 1; Ny <= 48; Ny++){
for(Np = 1; Np <= Nx*Ny; Np++){
err1 = dom_decomp_2d(Nx, Ny, Np, &NGx, &NGy);
err2 = dom_decomp_2d_serial(Nx, Ny, Np, &rx, &ry);
if(err1 == 0 && err2 == 0){
if(rx != NGx || ry != NGy){
printf("Nx = %d, Ny = %d, Np = %d\n",Nx,Ny,Np);
printf("[std alg]: NGx = %d, NGy = %d\n",NGx,NGy);
printf("[linear alg]: NGx = %d, NGy = %d\n",rx,ry);
}
else if(NGx > Nx || NGy > Ny){
printf("Error: Nx = %d, Ny = %d, Np = %d, NGx = %d, NGy = %d\n",
Nx,Ny,Np,NGx,NGy);
}
/* else
printf("Nx=%d, Ny=%d, Np=%d, NGx=%d, NGy=%d\n",
Nx,Ny,Np,NGx,NGy);
*/
}
else if(err1 + err2 == 1)
printf("err1 = %d, err2 = %d\n",err1, err2);
}
}
}
#endif
#if 0
for(Nx = 1; Nx <= 48; Nx++){
for(Ny = 1; Ny <= 48; Ny++){
for(Nz = 1; Nz <= 48; Nz++){
Np_max = Nx*Ny*Nz;
Np_max = Np_max < 100000 ? Np_max : 100000;
for(Np = 1; Np <= Np_max; Np++){
err1 = dom_decomp_3d(Nx, Ny, Nz, Np, &NGx, &NGy, &NGz);
err2 = dom_decomp_3d_serial(Nx, Ny, Nz, Np, &rx, &ry, &rz);
if(err1 == 0 && err2 == 0){
if(rx != NGx || ry != NGy || rz != NGz){
printf("Nx = %d, Ny = %d, Nz = %d, Np = %d\n",Nx,Ny,Nz,Np);
printf("[std alg]: NGx = %d, NGy = %d, NGz = %d\n",NGx,NGy,NGz);
printf("[linear alg]: NGx = %d, NGy = %d, NGz = %d\n",rx,ry,rz);
I = (NGx - 1)*Ny*Nz + (NGy - 1)*Nx*Nz + (NGz - 1)*Nx*Ny;
printf("[std alg]: I = %d\n",I);
I = (rx - 1)*Ny*Nz + (ry - 1)*Nx*Nz + (rz - 1)*Nx*Ny;
printf("[linear alg]: I = %d\n",I);
}
else if(NGx > Nx || NGy > Ny || NGz > Nz){
printf("Error: Nx = %d, Ny = %d, Np = %d, NGx = %d, NGy = %d\n",
Nx,Ny,Np,NGx,NGy);
}
/* else
printf("Nx=%d, Ny=%d, Nz=%d, Np=%d, NGx=%d, NGy=%d, NGz=%d\n",
Nx,Ny,Np,NGx,NGy);
*/
}
else if(err1 + err2 == 1)
printf("err1 = %d, err2 = %d\n",err1, err2);
}
}
}
}
#endif
return 0;
}
