Prelude to halide_public

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[1] J.Ragan-Kelley, et al, Halide: A Language and Compiler for Optimizing Parallelism, Locality, and Recomputation in Image Processing Pipelines, PLDI 2013

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2
7 2 02102 0 .. 2 2 2
Func conv3x3(Func in)
{
Func f;
Var x, y;
RDom r(-1, 3, -1, 3);
Func clamped = BoudnaryConditions::constant_exterior(in, 0);
f(x, y) = sum(clamped(x+r.x, y+r.y));
return f;
}

2
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{
Func f;
Var x, y;
RDom r(-1, 3, -1, 3);
return f;
}
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{
Func f;
Var x, y;
RDom r(-1, 3, -1, 3);
return f;
}
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{
Func f;
Var x, y;
RDom r(-1, 3, -1, 3);
return f;
}
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2 02102 0 .. 2 2 2
{
Func f;
Var x, y;
RDom r(-1, 3, -1, 3);
return f;
}
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0 2 . 8C ( C C 6 G 16 8 , 8 8 A 68 8 8 (). 1 0( ,

3 23 02102 0 .. 2 3 2 3 2
Func blur_x, blur_y;
Var x, y;
blur_x(x, y) = in(x, y) + in(x+1, y);
blur_y(x, y) = (blur_x(x, y) + blur_x(x, y+1)) / 4;
for (int y=0; y<height; y++) {
for (int x=0; x<width; x++) {
blur_x[y][x] = in[y][x] + in[y][x+1];
}
}
blur_y[y][x] =
(blur_x[y][x] + blur_x[y+1][x]) / 4;
}
}
blur_x[0][x] = in[y][x] + in[y][x+1];
blur_x[1][x] =
in[y+1][x] + in[y+1][x+1];
}
blur_y[y][x] =
(blur_x[0][x] + blur_x[1][x]) / 4;
}
}
blur_y[y][x] = (in[x][y] + in[x+1][y] +
in[x][y+1] + in[x+1][y+1]) / 4;
}
}8

0 4 0 2 11 0. 8
Func box_filter_3x3(Func in) {
Func blurx, blury;
Var x, y;
blurx(x, y) = (in(x-1, y) + in(x, y) + in(x+1, y))/3;
blury(x, y) = (blurx(x, y-1) + blurx(x, y) + blurx(x, y+1))/3;
if (get_target().has_gpu_feature()) {
blury.gpu_tile(x, y, xi, yi, 32, 8);
blurx.compute_at(blury, x);
} else {
blury.tile(x, y, xi, yi, 256, 32).vectorize(xi, 8).parallel(y);
blurx.compute_at(blury, x).store_at(blury, x).vectorize(x, 8);
}
return blury;
}
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f(x, y) = in(x, y) + 1;
produce f$1 {
let f.y.loop_max = f.y.max
let f.y.loop_min = f.y.min
let f.y.loop_extent = ((f.y.max + 1) - f.y.min)
let f.x.loop_max = f.x.max
let f.x.loop_min = f.x.min
let f.x.loop_extent = ((f.x.max + 1) - f.x.min)
for (f.y, f.y.loop_min, f.y.loop_extent) {
for (f.x, f.x.loop_min, f.x.loop_extent) {
f(f.x, f.x) = in(f.x, f.y) + 1
}
}
}
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èIRVisitor IRGraphVisitor
– R a 0 0
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– n ol s C i V
èIRMutator
– C rt FV 0 0
– vh V A i V
è p VA I gx V
0 0 2 11 0./ 8

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2 12 10 1 . 1 2 1 2 1
class PrintLoops : public IRVisitor {
using IRVisitor::visit;
void visit(const For *op) {
std::cout << op->name << std::endl;
IRVisitor::visit(op);
}
};
void print_loops(Stmt s) {
PrintLoops v;
s.accept(v);
}

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}
};
PrintLoops v;
s.accept(v);
}
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}
};
PrintLoops v;
s.accept(v);
}
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}
};
PrintLoops v;
s.accept(v);
}
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}
};
PrintLoops v;
s.accept(v);
}
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• 0 ≤ & < + (⇒ 0 ≤ & ≤ + − 1)
• 0 ≤ ( < , (⇒ 0 ≤ ( ≤ , − 1)
8 8 8 23 1 1 10
G I F
for (y=0; y<H; y++)
for (x=0; x<W; x++) {
S1: s = 0; //S1
for (ky=0; y<KS; ky++)
for (kx=0; x<KS; kx++)
S2: s += src[y+ky][x+kx] * kernel[ky][kx];
S3: dst[y][x] = s >> t;
}

è AC
– 1 8 1 8
• !"#
= (&, (, )&, )()
– 8. 1 1
• +"#
= (,, -, ./)
– 1 8 1 8 P
• 0 ≤ & < , (⇒ 0 ≤ ( ≤ , − 1)
• 0 ≤ ( < - (⇒ 0 ≤ & ≤ - − 1)
• 0 ≤ )& < ., (⇒ 0 ≤ )& ≤ ., − 1)
• 0 ≤ )( < .- (⇒ 0 ≤ )( ≤ .- − 1)
8 8 8 23 1 1 10
G I F
for (y=0; y<H; y++)
for (x=0; x<W; x++) {
S1: s = 0; //S1
S3: dst[y][x] = s >> t;
}

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C
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%"# = { (, * |
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H
W
1
≥ 2}
%"$ = (, *, 4(, 4*
1 0 0 0 0 0 0 0
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0 1 0 0 0 0 0 0
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0 0 1 0 0 0 0 0
0 0 −1 0 0 0 1 −1
0 0 0 1 0 0 0 0
0 0 0 −1 0 0 0 −1
(
*
4(
4*
H
W
KS
1
≥ 2}
%"#
F
for (y=0; y<H; y++)
for (x=0; x<W; x++) {
S1: s = 0; //S1
S3: dst[y][x] = s >> t;
}
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for (y=0; y<H; y++)
for (x=0; x<W; x++) {
S1: s = 0; //S1
for (ky=0; ky<KS; ky++)
for (kx=0; kx<KS; kx++)
S3: dst[y][x] = s >> t;
}
!"#
$, & = 0, $, 0, &, 0 )
!"* $, &, +$, +& = 0, $, 0, &, 1, +$, 0, +&, 0 )
!"- $, & = 0, $ 0, &, 2 )
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è 0 0 FA IS 3 0
è 0 0 ! 0 3 ,0. "#
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$("#
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!"#$%& ', ), *', *) = ' + *', ) + *) -
=
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0 1 0 1 0 0 0 0
'
)
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*)
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W
KS
1
!"45$6 ', ) = ', ) -
=
1 0 0 0 0
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W
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for (y=0; y<H; y++)
for (x=0; x<W; x++) {
S1: s = 0; //S1
S3: dst[y][x] = s >> t;
}

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!"# $, & =
0 0 0 0 0
1 0 0 0 0
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0 0 0 0 0
$
&
N
M
1
!"#,
$, & =
0 0 0 0 0
0 - 0 0 0
0 0 0 0 0
- 0 0 0 0
0 0 0 0 0
$
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N
M
1
for (i=0; i<N; i++)
for (j=0; j<M; j++)
S1(i, j);
for (j=0; j<M; j++)
for (i=0; i<N; i++)
S1(i, j);
. =
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 1 0 0 0
1 0 0 0 0
×
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#$%&
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#$%& = ()*, ),)
.$
.&
/$%&
×()$, )&, 1$, 1&, 1)&
≥
≥
=
4}

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– C 1 . 48 8 .4
4 . 8 8 . 48 423 1 1 10
1 1 01 8 310 .
for (i=0; i<N; i++) {
S: s[i] = 0;
for (j=0; j<M; j++) {
T: s[i] = s[i] + a[i][j] * x[j];
}
}
AI
!"#$
=
1 0 0 0 0 0
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)"
)$
*$
+
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1
≥
≥
≥
≥
≥
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=
0

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– 0
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8 44 12 0 0 0
080 0 . 4 20
for (i=0; i<N; i++) {
S: s[i] = 0;
for (j=0; j<M; j++) {
T: s[i] = s[i] + a[i][j] * x[j];
}
}
I F
!"#$
=
1 0 0 0 0 0
−1 0 0 1 0 0
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0 −1 0 1 0 0
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– !: #$
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=
1 0 0 0 0 0
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0 0 −1 0 1 0
1 −1 0 0 0 0
#$
#&
,&
-
M
1
≥
≥
≥
≥
≥
≥
=
0
for (i=0; i<N; i++) {
S: s[i] = 0;
for (j=0; j<M; j++) {
T: s[i] = s[i] + a[i][j] * x[j];
}
}
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DC & L 0 F
– D
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%"#$ = &(" )" − &($ )$ ≫ 0
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=
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0 0 1 0 0 0
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• / F 44 AA C 4
– x eHagl kc dHe
• vb e uM kph
– -0uM . 2 F P S y n L I
è H
– 8 A 8C 4 2: 2 C 2 F8 2
A 2 A 2 8 A A D

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– 0 8 4 20/9.4 /04 HC
è . 4
.9 98 9. 44 9 12 90 09 0/
Func matmul(Func a, Func b, int size)
{
Func c;
Var i, j;
RDom k(0, size);
c(i, j) = 0;
c(i, j) += a(k, j) * b(i, k);
return c;
}
for (c$3.s0.j, c$3.s0.j.loop_min, c$3.s0.j.loop_extent) {
for (c$3.s0.i, c$3.s0.i.loop_min, c$3.s0.i.loop_extent) {
c$3(c$3.s0.i, c$3.s0.j) = 0
}
}
for (c$3.s1.r78$x, 0, 100) {
c$3(c$3.s1.i, c$3.s1.j) = (c$3(c$3.s1.i, c$3.s1.j) +
(a$3(c$3.s1.r78$x, c$3.s1.j)*b$3(c$3.s1.i, c$3.s1.r78$x)))
}
}
}
.4 /0 .4 /0

2 02102 0 .. 2 2 25
Building polyhedral models...
Iteration Sets := (c$3.s0.j, c$3.s0.i)
Domain := [c$3.s0.j.loop_min, ((c$3.s0.j.loop_min + c$3.s0.j.loop_extent) + -1)], [c$3.s0.i.loop_min,
((c$3.s0.i.loop_min + c$3.s0.i.loop_extent) + -1)]
Schedule := (2, c$3.s0.j, 0, c$3.s0.i, 0)
Provides :=
c$3 := (c$3.s0.i, c$3.s0.j) : (c$3.s0.i, c$3.s0.j)
Iteration Sets := (c$3.s1.j, c$3.s1.i, c$3.s1.r78$x)
Domain := [c$3.s1.j.loop_min, ((c$3.s1.j.loop_min + c$3.s1.j.loop_extent) + -1)], [c$3.s1.i.loop_min,
((c$3.s1.i.loop_min + c$3.s1.i.loop_extent) + -1)], [0, 99]
Schedule := (3, c$3.s1.j, 0, c$3.s1.i, 0, c$3.s1.r78$x, 0)
Provides :=
c$3 := (c$3.s1.i, c$3.s1.j) : (c$3.s1.i, c$3.s1.j)
Calls :=
c$3 := (c$3.s1.i, c$3.s1.j) : (c$3.s1.i, c$3.s1.j)
a$3 := (c$3.s1.r78$x, c$3.s1.j) : (c$3.s1.r78$x, c$3.s1.j)
b$3 := (c$3.s1.i, c$3.s1.r78$x) : (c$3.s1.i, c$3.s1.r78$x)

0 5 5 5 0 2 11 50. 5 58
c$3(c$3.s0.i, c$3.s0.j) = 0
}
}
for (c$3.s1.r78$x, 0, 100) {
c$3(c$3.s1.i, c$3.s1.j) = (c$3(c$3.s1.i, c$3.s1.j) +
}
}
}
parallel (c$3.s0.j, c$3.s0.j.loop_min, c$3.s0.j.loop_extent) {
c$3(c$3.s0.i, c$3.s0.j) = 0
}
}
parallel (c$3.s1.j, c$3.s1.j.loop_min, c$3.s1.j.loop_extent) {
for (c$3.s1.r78$x, 0, 100) {
c$3(c$3.s1.i, c$3.s1.j) = (c$3(c$3.s1.i, c$3.s1.j) +
}
}
}
10
10

è 2 5 2
2 8 8 5 5 25 201 8 8 .
Building polyhedral models...
Iteration Sets := (f.s1.r4$x)
Domain := [2, 99]
Schedule := (1, f.s1.r4$x, 0)
Provides :=
f := (f.s1.r4$x) : (f.s1.r4$x)
Calls :=
f := ((f.s1.r4$x + -2)) : (f.s1.r4$x)
f := ((f.s1.r4$x + -1)) : (f.s1.r4$x)
Flow: f(f.s1.r4$x) -> f((f.s1.r4$x + -2)) : (=, -, =)
Flow: f(f.s1.r4$x) -> f((f.s1.r4$x + -1)) : (=, -, =)
f(x) = x;
f(r.x) = f(r.x-2) + f(r.x-1);
for (f.s0.x, f.s0.x.loop_min, f.s0.x.loop_extent) {
f(f.s0.x) = f.s0.x
}
for (f.s1.r4$x, 2, 98) {
f(f.s1.r4$x) = (f((f.s1.r4$x + -2)) + f((f.s1.r4$x + -1)))
}
2.
2.
FAC

è 5401
– odHag il n D .
– r L rAp
– H rA v R S Ia
è 5401
– Rtxs ehC a F eh
–
4 8 4 55 42 1 1 10

Prelude to halide_public

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