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"""
Local Laplacian.
"""
import halide as hl
# Just declare these at global scope, for simplicity
x, y, c, k = hl.vars("x y c k")
def _func_list(name, size):
"""Return a list containing `size` Funcs, named `name_n` for n in 0..size-1."""
return [hl.Func(f"{name}_{i}") for i in range(size)]
def _downsample(f):
"""Downsample with a 1 3 3 1 filter"""
downx, downy = hl.funcs("downx downy")
downx[x, y, hl._] = (
f[2 * x - 1, y, hl._]
+ 3.0 * (f[2 * x, y, hl._] + f[2 * x + 1, y, hl._])
+ f[2 * x + 2, y, hl._]
) / 8.0
downy[x, y, hl._] = (
downx[x, 2 * y - 1, hl._]
+ 3.0 * (downx[x, 2 * y, hl._] + downx[x, 2 * y + 1, hl._])
+ downx[x, 2 * y + 2, hl._]
) / 8.0
return downy
def _upsample(f):
"""Upsample using bilinear interpolation"""
upx, upy = hl.funcs("upx upy")
upx[x, y, hl._] = hl.lerp(
f[(x + 1) // 2, y, hl._],
f[(x - 1) // 2, y, hl._],
((x % 2) * 2 + 1) / 4.0,
)
upy[x, y, hl._] = hl.lerp(
upx[x, (y + 1) // 2, hl._],
upx[x, (y - 1) // 2, hl._],
((y % 2) * 2 + 1) / 4.0,
)
return upy
@hl.alias(local_laplacian_Mullapudi2016={"autoscheduler": "Mullapudi2016"})
@hl.generator()
class local_laplacian:
pyramid_levels = hl.GeneratorParam(8)
input_buf = hl.InputBuffer(hl.UInt(16), 3)
levels = hl.InputScalar(hl.Int(32))
alpha = hl.InputScalar(hl.Float(32))
beta = hl.InputScalar(hl.Float(32))
output_buf = hl.OutputBuffer(hl.UInt(16), 3)
def generate(self):
g = self
# THE ALGORITHM
J = g.pyramid_levels
# Make the remapping function as a lookup table.
fx = hl.f32(x) / 256.0
remap = hl.Func("remap")
remap[x] = g.alpha * fx * hl.exp(-fx * fx / 2.0)
# Set a boundary condition
clamped = hl.BoundaryConditions.repeat_edge(g.input_buf)
# Convert to floating point
floating = hl.Func("floating")
floating[x, y, c] = clamped[x, y, c] / 65535.0
# Get the luminance channel
gray = hl.Func("gray")
gray[x, y] = (
hl.f32(0.299) * floating[x, y, 0]
+ hl.f32(0.587) * floating[x, y, 1]
+ hl.f32(0.114) * floating[x, y, 2]
)
# Make the processed Gaussian pyramid.
gPyramid = _func_list("gPyramid", J)
# Do a lookup into a lut with 256 entires per intensity level
level = k * (1.0 / (g.levels - 1))
idx = gray[x, y] * hl.f32(g.levels - 1) * 256.0
idx = hl.clamp(hl.i32(idx), 0, (g.levels - 1) * 256)
gPyramid[0][x, y, k] = (
g.beta * (gray[x, y] - level) + level + remap[idx - 256 * k]
)
for j in range(1, J):
gPyramid[j][x, y, k] = _downsample(gPyramid[j - 1])[x, y, k]
# Get its laplacian pyramid
lPyramid = _func_list("lPyramid", J)
lPyramid[J - 1][x, y, k] = gPyramid[J - 1][x, y, k]
for j in range(J - 2, -1, -1):
lPyramid[j][x, y, k] = (
gPyramid[j][x, y, k] - _upsample(gPyramid[j + 1])[x, y, k]
)
# Make the Gaussian pyramid of the input
inGPyramid = _func_list("inGPyramid", J)
inGPyramid[0][x, y] = gray[x, y]
for j in range(1, J):
inGPyramid[j][x, y] = _downsample(inGPyramid[j - 1])[x, y]
# Make the laplacian pyramid of the output
outLPyramid = _func_list("outLPyramid", J)
for j in range(0, J):
# Split input pyramid value into integer and floating parts
level = inGPyramid[j][x, y] * hl.f32(g.levels - 1)
li = hl.clamp(hl.i32(level), 0, g.levels - 2)
lf = level - hl.f32(li)
# Linearly interpolate between the nearest processed pyramid levels
outLPyramid[j][x, y] = (1.0 - lf) * lPyramid[j][x, y, li] + (
lf * lPyramid[j][x, y, li + 1]
)
# Make the Gaussian pyramid of the output
outGPyramid = _func_list("outGPyramid", J)
outGPyramid[J - 1][x, y] = outLPyramid[J - 1][x, y]
for j in range(J - 2, -1, -1):
outGPyramid[j][x, y] = (
_upsample(outGPyramid[j + 1])[x, y] + outLPyramid[j][x, y]
)
# Reintroduce color (Connelly: use eps to avoid scaling up noise w/
# apollo3.png input)
color = hl.Func("color")
eps = hl.f32(0.01)
color[x, y, c] = (
outGPyramid[0][x, y] * (floating[x, y, c] + eps) / (gray[x, y] + eps)
)
# Convert back to 16-bit
g.output_buf[x, y, c] = hl.u16(hl.clamp(color[x, y, c], 0.0, 1.0) * 65535.0)
# ESTIMATES
# (This can be useful in conjunction with RunGen and benchmarks as well
# as autoschedulers, so we do it in all cases.)
g.input_buf.set_estimates([(0, 1536), (0, 2560), (0, 3)])
# Provide estimates on the parameters
g.levels.set_estimate(8)
g.alpha.set_estimate(1)
g.beta.set_estimate(1)
g.output_buf.set_estimates([(0, 1536), (0, 2560), (0, 3)])
# THE SCHEDULE
if g.using_autoscheduler():
# nothing
pass
elif g.target().has_gpu_feature():
# GPU schedule.
# 3.19ms on an RTX 2060.
remap.compute_root()
xi, yi = hl.vars("xi yi")
g.output_buf.compute_root().gpu_tile(x, y, xi, yi, 16, 8)
for j in range(0, J):
blockw = 16
blockh = 8
if j > 3:
blockw = 2
blockh = 2
if j > 0:
inGPyramid[j].compute_root().gpu_tile(x, y, xi, yi, blockw, blockh)
(
gPyramid[j]
.compute_root()
.reorder(k, x, y)
.gpu_tile(x, y, xi, yi, blockw, blockh)
)
outGPyramid[j].compute_root().gpu_tile(x, y, xi, yi, blockw, blockh)
else:
# CPU schedule.
# 21.4ms on an Intel i9-9960X using 32 threads at 3.7
# GHz, using the target x86-64-avx2.
# This app is dominated by data-dependent loads from
# memory, so we're better off leaving the AVX-512 units
# off in exchange for a higher clock, and we benefit from
# hyperthreading.
remap.compute_root()
yo = hl.Var("yo")
(
g.output_buf.reorder(c, x, y)
.split(y, yo, y, 64)
.parallel(yo)
.vectorize(x, 8)
)
gray.compute_root().parallel(y, 32).vectorize(x, 8)
for j in range(1, 5):
inGPyramid[j].compute_root().parallel(y, 32).vectorize(x, 8)
(
gPyramid[j]
.compute_root()
.reorder_storage(x, k, y)
.reorder(k, y)
.parallel(y, 8)
.vectorize(x, 8)
)
(
outGPyramid[j]
.store_at(g.output_buf, yo)
.compute_at(g.output_buf, y)
.fold_storage(y, 4)
.vectorize(x, 8)
)
outGPyramid[0].compute_at(g.output_buf, y).vectorize(x, 8)
for j in range(5, J):
inGPyramid[j].compute_root()
gPyramid[j].compute_root().parallel(k)
outGPyramid[j].compute_root()
if __name__ == "__main__":
hl.main()
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