diff --git a/presentations/pasc/code/liblbm.fut b/presentations/pasc/code/liblbm.fut
index ea3c58b752e76969ab8870c815887ceea8586254..272a2c54b9f4460e211e3d4ca4604670d1b119d2 100644
--- a/presentations/pasc/code/liblbm.fut
+++ b/presentations/pasc/code/liblbm.fut
@@ -8,6 +8,24 @@ let tabulate_4d 'a (p: i64) (n: i64) (m: i64) (o: i64) (f: i64 -> i64 -> i64 ->
let dotprod (xs: []f32) (ys: []f32): f32 =
reduce (+) 0 (map (\(x, y) -> x * y) (zip xs ys))
+let map3d 'a [nx][ny][nz]'b (f: a -> b) (xs: [nx][ny][nz]a): [nx][ny][nz]b =
+ map(\xs1 ->
+ map(\xs2 ->
+ map(\xs3 ->
+ f xs3
+ ) xs2
+ ) xs1
+ ) xs
+
+let map2_3d 'a 'c [nx][ny][nz]'b (f: a -> c -> b) (xs: [nx][ny][nz]a) (ys: [nx][ny][nz]c): [nx][ny][nz]b =
+ map2(\xs1 ys1 ->
+ map2(\xs2 ys2 ->
+ map2(\xs3 ys3 ->
+ f xs3 ys3
+ ) xs2 ys2
+ ) xs1 ys1
+ ) xs ys
+
------------------------------------
------------ CONSTANTS -------------
------------------------------------
@@ -41,49 +59,33 @@ module d3q27 = {
}
let compute_rho [nx][ny][nz][q] (f: [nx][ny][nz][q]f32): [nx][ny][nz]f32 =
- map(\fx ->
- map(\fxy ->
- map(\fxyz ->
- reduce (+) 0 fxyz
- ) fxy
- ) fx
+ map3d(\fxyz ->
+ reduce (+) 0 fxyz
) f
let compute_j [nx][ny][nz][q][d] (f: [nx][ny][nz][q]f32)(c: [q][d]f32): [nx][ny][nz][d]f32 =
- map(\fx ->
- map(\fxy ->
- map(\fxyz ->
- map(\ci ->
- dotprod ci fxyz
- ) (transpose c) -- intrinsic
- ) fxy
- ) fx
+ map3d(\fxyz ->
+ map(\ci ->
+ dotprod ci fxyz
+ ) (transpose c) -- intrinsic
) f
let compute_feq [nx][ny][nz][q][d] (w: [q]f32) (c: [q][d]f32)(rho: [nx][ny][nz]f32)(j: [nx][ny][nz][d]f32): [nx][ny][nz][q]f32 =
- map2(\rho_x j_x ->
- map2(\rho_xy j_xy ->
- map2(\rho_xyz j_xyz ->
- let u = map(\ji -> ji / rho_xyz) j_xyz
- let u_sqr = dotprod u u
-
- in map2(\wi ci ->
- let c_u = dotprod ci u
- in wi * rho_xyz* (1 + 3*c_u + 4.5 * c_u * c_u - 1.5 * u_sqr)
- ) w c
- ) rho_xy j_xy
- )rho_x j_x
+ map2_3d(\rho_xyz j_xyz ->
+ let u = map(\ji -> ji / rho_xyz) j_xyz
+ let u_sqr = dotprod u u
+
+ in map2(\wi ci ->
+ let c_u = dotprod ci u
+ in wi * rho_xyz* (1 + 3*c_u + 4.5 * c_u * c_u - 1.5 * u_sqr)
+ ) w c
) rho j
let collision [nx][ny][nz][q] (f: [nx][ny][nz][q]f32)(feq: [nx][ny][nz][q]f32) (omega: f32): [nx][ny][nz][q]f32 =
- map2 (\fx feqx ->
- map2(\fxy feqxy ->
- map2(\fxyz feqxyz ->
- map2(\fxyzi feqxyzi ->
- (1-omega) * fxyzi + omega * feqxyzi
- ) fxyz feqxyz
- ) fxy feqxy
- ) fx feqx
+ map2_3d (\f_xyz feq_xyz ->
+ map2(\f_i feq_i ->
+ (1-omega) * f_i + omega * feq_i
+ ) f_xyz feq_xyz
) f feq
let collide [nx][ny][nz][q][d] (f: [nx][ny][nz][q]f32) (omega: f32) (w: [q]f32) (c: [q][d]f32): [nx][ny][nz][q]f32 =
diff --git a/presentations/pasc/metadata.yaml b/presentations/pasc/metadata.yaml
index da49329560aa1fc5e0933c3a4ea4a02f230dd9c4..24bccb891dfacddca0b90ca3be663a6bfc5ded70 100644
--- a/presentations/pasc/metadata.yaml
+++ b/presentations/pasc/metadata.yaml
@@ -1,7 +1,7 @@
---
# used for lecture slides and homework sheets
subtitle: "PASC workshop"
-author: "Orestis Malaspinas, HEPIA"
+author: "Orestis Malaspinas and Michaël El Kharroubi, HEPIA"
# lang: fr-CH
...
diff --git a/presentations/pasc/pres.md b/presentations/pasc/pres.md
index f962ccb50a8b22a30b36546a7955f0a3d8945a82..86f79c819d411104180d2ce8fa73ee1484d06756 100644
--- a/presentations/pasc/pres.md
+++ b/presentations/pasc/pres.md
@@ -14,7 +14,7 @@
- Statically typed, data-parallel, purely functional, array language,
- with limited functionalities (no I/O for example),
-- that compiles to sequencial, multi-core, OpenCL, and Cuda backends,
+- that compiles to sequential, multi-core, OpenCL, and Cuda backends,
- very efficiently,
- without the pain of actually writing sequential, multi-code, or GPU code.
@@ -132,8 +132,6 @@ These operations are very efficiently parallelized.
. . .
-::: cdotprod
-
## `dotprod.c`
```C
@@ -145,7 +143,6 @@ int dot_prod(int xs[], int ys[], int size) {
return dot;
}
```
-:::
# An example: the dot product from `C`
@@ -177,7 +174,7 @@ int main() {
## The algorithm
-* Cellular automaton-like algorithm for fluid flow simulation.
+* *Cellular automaton*-like algorithm for fluid flow simulation.
* Cartesian grid with $q$ variables per grid point, $f_i(\bm{x}, t)$.
* Each time step is made of:
1. Collision (local operations only).
@@ -197,8 +194,51 @@ Repeat 1-2 a certain amount of times
3. Get the data and process it.
+# The LBM-CPU pseudo-code (1/2)
+
+```C
+void collision(float f[nx][ny][nz][q]) {
+ for (int x = 0; x < nx; ++x) {
+ for (int y = 0; y < ny; ++y) {
+ for (int z = 0; z < nz; ++z) {
+ float rho, j[3];
+ compute_rho_j(f[x][y][z], &rho, j);
+ for (int i = 0; i < q; ++i) {
+ float feq = compute_feq(rho, j);
+ f[x][y][z][i] *= (1-omega) * f[x][y][z][i];
+ f[x][y][z][i] += omega * feq;
+ }
+ }
+ }
+ }
+```
+
+# The LBM-CPU pseudo-code (2/2)
+
+```C
+void propagation(float f[nx][ny][nz][q],
+ float fout[nx][ny][nz][q])
+{
+ for (int x = 0; x < nx; ++x) {
+ for (int y = 0; y < ny; ++y) {
+ for (int z = 0; z < nz; ++z) {
+ for (int i = 0; i < q; ++i) {
+ int next_x = (x-(i32.f32 c[ipop,0]) + nx) % nx;
+ int next_y = (y-(i32.f32 c[ipop,1]) + ny) % ny;
+ int next_z = (z-(i32.f32 c[ipop,2]) + nz) % nz;
+
+ fout[x][y][z][i] = f[x][y][z][i];
+ }
+ }
+ }
+ }
+}
+```
+
# The LBM pseudo-code
+## One time-step
+
```ocaml
let time_step [nx][ny][nz][q] (f: [nx][ny][nz][q]f32)
-> [nx][ny][nz][q]f32 =
@@ -217,7 +257,7 @@ let time_step [nx][ny][nz][q] (f: [nx][ny][nz][q]f32)
f: [nx][ny][nz][q]f32 -- 4d array
feq: [nx][ny][nz][q]f32 -- 4d array
rho: [nx][ny][nz]f32 -- 3d array
-j: [nx][ny][nz][d]f32 -- 4d array
+j: [nx][ny][nz][d]f32 -- 4d array
```
## Functions
@@ -236,8 +276,6 @@ let map3d 'a [nx][ny][nz]'b
## LBM equations
-On **each** grid point:
-
\begin{equation}
\rho=\sum_{i=0}^{q-1}f_i, \forall\ \bm{x}.
\end{equation}
@@ -268,7 +306,7 @@ let compute_j [nx][ny][nz][q]
map3d (\fxyz ->
map(\ci ->
dotprod ci fxyz
- ) (transpose c) -- intrinsic
+ ) c
) f
```
diff --git a/presentations/unige2020/code/Makefile b/presentations/unige2020/code/Makefile
index cc6e33264955f87c888fefc6cc0938a5b46a51a5..87f2a5b997dd94eb03a53aecea248b8e60b7a1c5 100644
--- a/presentations/unige2020/code/Makefile
+++ b/presentations/unige2020/code/Makefile
@@ -1,7 +1,9 @@
-TARGET=c
+TARGET=multicore
ifeq ($(TARGET),cuda)
CUDALIBS=-lcudart -lcuda -lnvrtc
+else ifeq ($(TARGET), multicore)
+ MULTICORELIBS=-lpthread
else ifeq ($(TARGET), opencl)
OPENCLIBS=-lOpenCL
endif
@@ -9,9 +11,9 @@ endif
CC=gcc
FC=futhark
OPTS=-Wall -Wextra -g -std=gnu11
-SANITIZERS=-fsanitize=address
+# SANITIZERS=-fsanitize=address
OPTIM=-O3
-LIBS=-lm $(SDLLIBS) $(CUDALIBS) $(OPENCLIBS) $(SANITIZERS)
+LIBS=-lm $(SDLLIBS) $(CUDALIBS) $(OPENCLIBS) $(SANITIZERS) $(MULTICORELIBS)
all: lbm3d