def merge_spatial(input):
weight = hl.Func("raised_cosine_weights")
output = hl.Func("merge_spatial_output")
v, x, y = hl.Var('v'), hl.Var('x'), hl.Var('y')
# modified raised cosine window
weight[v] = 0.5 - 0.5 * hl.cos(2 * math.pi * (v + 0.5) / TILE_SIZE)
weight_00 = weight[idx_0(x)] * weight[idx_0(y)]
weight_10 = weight[idx_1(x)] * weight[idx_0(y)]
weight_01 = weight[idx_0(x)] * weight[idx_1(y)]
weight_11 = weight[idx_1(x)] * weight[idx_1(y)]
val_00 = input[idx_0(x), idx_0(y), tile_0(x), tile_0(y)]
val_10 = input[idx_1(x), idx_0(y), tile_1(x), tile_0(y)]
val_01 = input[idx_0(x), idx_1(y), tile_0(x), tile_1(y)]
val_11 = input[idx_1(x), idx_1(y), tile_1(x), tile_1(y)]
output[x, y] = hl.cast(hl.UInt(16), weight_00 * val_00
+ weight_10 * val_10
+ weight_01 * val_01
+ weight_11 * val_11)
weight.compute_root().vectorize(v, 32)
output.compute_root().parallel(y).vectorize(x, 32)
return output
def test_generate_halide(self):
zone = self.define_original_twoel()
decomposed = zone.split_recursive()
self.vars = {k: hl.Var(k) for k in "ijkl"}
i, j, k, l = [self.vars[k] for k in "ijkl"]
g_dens = hl.Func("g_dens")
g_dens[i,j] = i * j
g = hl.Func("g")
g[i,j,k,l] = hl.cos(i*j) * hl.sin(k*l)
self.inputs = {"g": g, "g_dens": g_dens}
self.clamps = {"g": g, "g_dens": g_dens}
self.funcs = {"g": g, "g_dens": g_dens}
self.loopnest_funcs = {}
func = decomposed.generate_halide(self, [8, 8, 8, 8])
def main():
# So far Funcs (such as the one below) have evaluated to a single
# scalar value for each point in their domain.
single_valued = hl.Func()
x, y = hl.Var("x"), hl.Var("y")
single_valued[x, y] = x + y
# One way to write a hl.Func that returns a collection of values is
# to add an additional dimension which indexes that
# collection. This is how we typically deal with color. For
# example, the hl.Func below represents a collection of three values
# for every x, y coordinate indexed by c.
color_image = hl.Func()
c = hl.Var("c")
color_image[x, y, c] = hl.select(
c == 0,
245, # Red value
c == 1,
42, # Green value
132) # Blue value
# Since this pattern appears quite often, Halide provides a
# syntatic sugar to write the code above as the following,
# using the "mux" function.
# color_image[x, y, c] = hl.mux(c, [245, 42, 132]);
# This method is often convenient because it makes it easy to
# operate on this hl.Func in a way that treats each item in the
# collection equally:
brighter = hl.Func()
brighter[x, y, c] = color_image[x, y, c] + 10
# However this method is also inconvenient for three reasons.
#
# 1) Funcs are defined over an infinite domain, so users of this
# hl.Func can for example access color_image(x, y, -17), which is
# not a meaningful value and is probably indicative of a bug.
#
# 2) It requires a hl.select, which can impact performance if not
# bounded and unrolled:
# brighter.bound(c, 0, 3).unroll(c)
#
# 3) With this method, all values in the collection must have the
# same type. While the above two issues are merely inconvenient,
# this one is a hard limitation that makes it impossible to
# express certain things in this way.
# It is also possible to represent a collection of values as a
# collection of Funcs:
func_array = [hl.Func() for i in range(3)]
func_array[0][x, y] = x + y
func_array[1][x, y] = hl.sin(x)
func_array[2][x, y] = hl.cos(y)
# This method avoids the three problems above, but introduces a
# new annoyance. Because these are separate Funcs, it is
# difficult to schedule them so that they are all computed
# together inside a single loop over x, y.
# A third alternative is to define a hl.Func as evaluating to a
# Tuple instead of an hl.Expr. A Tuple is a fixed-size collection of
# Exprs which may have different type. The following function
# evaluates to an integer value (x+y), and a floating point value
# (hl.sin(x*y)).
multi_valued = hl.Func("multi_valued")
multi_valued[x, y] = (x + y, hl.sin(x * y))
# Realizing a tuple-valued hl.Func returns a collection of
# Buffers. We call this a Realization. It's equivalent to a
# std::vector of hl.Buffer/Image objects:
if True:
im1, im2 = multi_valued.realize([80, 60])
assert im1.type() == hl.Int(32)
assert im2.type() == hl.Float(32)
assert im1[30, 40] == 30 + 40
assert np.isclose(im2[30, 40], math.sin(30 * 40))
# You can also pass a tuple of pre-allocated buffers to realize()
# rather than having new ones created. (The Buffers must have the correct
# types and have identical sizes.)
if True:
im1, im2 = hl.Buffer(hl.Int(32),
[80, 60]), hl.Buffer(hl.Float(32), [80, 60])
multi_valued.realize((im1, im2))
assert im1[30, 40] == 30 + 40
assert np.isclose(im2[30, 40], math.sin(30 * 40))
# All Tuple elements are evaluated together over the same domain
# in the same loop nest, but stored in distinct allocations. The
# equivalent C++ code to the above is:
if True:
multi_valued_0 = np.empty((80 * 60), dtype=np.int32)
multi_valued_1 = np.empty((80 * 60), dtype=np.int32)
for yy in range(80):
for xx in range(60):
multi_valued_0[xx + 60 * yy] = xx + yy
multi_valued_1[xx + 60 * yy] = math.sin(xx * yy)
# When compiling ahead-of-time, a Tuple-valued hl.Func evaluates
# into multiple distinct output halide_buffer_t structs. These appear in
# order at the end of the function signature:
# int multi_valued(...input buffers and params..., halide_buffer_t
# *output_1, halide_buffer_t *output_2)
# You can construct a Tuple by passing multiple Exprs to the
# Tuple constructor as we did above. Perhaps more elegantly, you
# can also take advantage of initializer lists and just
# enclose your Exprs in braces:
multi_valued_2 = hl.Func("multi_valued_2")
multi_valued_2[x, y] = (x + y, hl.sin(x * y))
# Calls to a multi-valued hl.Func cannot be treated as Exprs. The
# following is a syntax error:
# hl.Func consumer
# consumer[x, y] = multi_valued_2[x, y] + 10
# Instead you must index the returned object with square brackets
# to retrieve the individual Exprs:
integer_part = multi_valued_2[x, y][0]
floating_part = multi_valued_2[x, y][1]
assert type(integer_part) is hl.FuncTupleElementRef
assert type(floating_part) is hl.FuncTupleElementRef
consumer = hl.Func()
consumer[x, y] = (integer_part + 10, floating_part + 10.0)
# Tuple reductions.
if True:
# Tuples are particularly useful in reductions, as they allow
# the reduction to maintain complex state as it walks along
# its domain. The simplest example is an argmax.
# First we create an Image to take the argmax over.
input_func = hl.Func()
input_func[x] = hl.sin(x)
input = input_func.realize([100])
assert input.type() == hl.Float(32)
# Then we defined a 2-valued Tuple which tracks the maximum value
# its index.
arg_max = hl.Func()
# Pure definition.
# (using [()] for zero-dimensional Funcs is a convention of this python interface)
arg_max[()] = (0, input[0])
# Update definition.
r = hl.RDom([(1, 99)])
old_index = arg_max[()][0]
old_max = arg_max[()][1]
new_index = hl.select(old_max > input[r], r, old_index)
new_max = hl.max(input[r], old_max)
arg_max[()] = (new_index, new_max)
# The equivalent C++ is:
arg_max_0 = 0
arg_max_1 = float(input[0])
for r in range(1, 100):
old_index = arg_max_0
old_max = arg_max_1
new_index = r if (old_max > input[r]) else old_index
new_max = max(input[r], old_max)
# In a tuple update definition, all loads and computation
# are done before any stores, so that all Tuple elements
# are updated atomically with respect to recursive calls
# to the same hl.Func.
arg_max_0 = new_index
arg_max_1 = new_max
# Let's verify that the Halide and C++ found the same maximum
# value and index.
if True:
r0, r1 = arg_max.realize()
assert r0.type() == hl.Int(32)
assert r1.type() == hl.Float(32)
assert arg_max_0 == r0[()]
assert np.isclose(arg_max_1, r1[()])
# Halide provides argmax and hl.argmin as built-in reductions
# similar to sum, product, maximum, and minimum. They return
# a Tuple consisting of the point in the reduction domain
# corresponding to that value, and the value itself. In the
# case of ties they return the first value found. We'll use
# one of these in the following section.
# Tuples for user-defined types.
if True:
# Tuples can also be a convenient way to represent compound
# objects such as complex numbers. Defining an object that
# can be converted to and from a Tuple is one way to extend
# Halide's type system with user-defined types.
class Complex:
def __init__(self, r, i=None):
if type(r) is float and type(i) is float:
self.real = hl.Expr(r)
self.imag = hl.Expr(i)
elif i is not None:
self.real = r
self.imag = i
else:
self.real = r[0]
self.imag = r[1]
def as_tuple(self):
"Convert to a Tuple"
return (self.real, self.imag)
def __add__(self, other):
"Complex addition"
return Complex(self.real + other.real, self.imag + other.imag)
def __mul__(self, other):
"Complex multiplication"
return Complex(self.real * other.real - self.imag * other.imag,
self.real * other.imag + self.imag * other.real)
def __getitem__(self, idx):
return (self.real, self.imag)[idx]
def __len__(self):
return 2
def magnitude(self):
"Complex magnitude"
return (self.real * self.real) + (self.imag * self.imag)
# Other complex operators would go here. The above are
# sufficient for this example.
# Let's use the Complex struct to compute a Mandelbrot set.
mandelbrot = hl.Func()
# The initial complex value corresponding to an x, y coordinate
# in our hl.Func.
initial = Complex(x / 15.0 - 2.5, y / 6.0 - 2.0)
# Pure definition.
t = hl.Var("t")
mandelbrot[x, y, t] = Complex(0.0, 0.0)
# We'll use an update definition to take 12 steps.
r = hl.RDom([(1, 12)])
current = Complex(mandelbrot[x, y, r - 1])
# The following line uses the complex multiplication and
# addition we defined above.
mandelbrot[x, y, r] = (Complex(current * current) + initial)
# We'll use another tuple reduction to compute the iteration
# number where the value first escapes a circle of radius 4.
# This can be expressed as an hl.argmin of a boolean - we want
# the index of the first time the given boolean expression is
# false (we consider false to be less than true). The argmax
# would return the index of the first time the expression is
# true.
escape_condition = Complex(mandelbrot[x, y, r]).magnitude() < 16.0
first_escape = hl.argmin(escape_condition)
assert type(first_escape) is tuple
# We only want the index, not the value, but hl.argmin returns
# both, so we'll index the hl.argmin Tuple expression using
# square brackets to get the hl.Expr representing the index.
escape = hl.Func()
escape[x, y] = first_escape[0]
# Realize the pipeline and print the result as ascii art.
result = escape.realize([61, 25])
assert result.type() == hl.Int(32)
code = " .:-~*={&%#@"
for yy in range(result.height()):
for xx in range(result.width()):
index = result[xx, yy]
if index < len(code):
print("%c" % code[index], end="")
else:
pass # is lesson 13 cpp version buggy ?
print("")
print("Success!")
return 0
def main():
# So far Funcs (such as the one below) have evaluated to a single
# scalar value for each point in their domain.
single_valued = hl.Func()
x, y = hl.Var("x"), hl.Var("y")
single_valued[x, y] = x + y
# One way to write a hl.Func that returns a collection of values is
# to add an additional dimension which indexes that
# collection. This is how we typically deal with color. For
# example, the hl.Func below represents a collection of three values
# for every x, y coordinate indexed by c.
color_image = hl.Func()
c = hl.Var("c")
color_image[x, y, c] = hl.select(c == 0, 245, # Red value
c == 1, 42, # Green value
132) # Blue value
# This method is often convenient because it makes it easy to
# operate on this hl.Func in a way that treats each item in the
# collection equally:
brighter = hl.Func()
brighter[x, y, c] = color_image[x, y, c] + 10
# However this method is also inconvenient for three reasons.
#
# 1) Funcs are defined over an infinite domain, so users of this
# hl.Func can for example access color_image(x, y, -17), which is
# not a meaningful value and is probably indicative of a bug.
#
# 2) It requires a hl.select, which can impact performance if not
# bounded and unrolled:
# brighter.bound(c, 0, 3).unroll(c)
#
# 3) With this method, all values in the collection must have the
# same type. While the above two issues are merely inconvenient,
# this one is a hard limitation that makes it impossible to
# express certain things in this way.
# It is also possible to represent a collection of values as a
# collection of Funcs:
func_array = [hl.Func() for i in range(3)]
func_array[0][x, y] = x + y
func_array[1][x, y] = hl.sin(x)
func_array[2][x, y] = hl.cos(y)
# This method avoids the three problems above, but introduces a
# new annoyance. Because these are separate Funcs, it is
# difficult to schedule them so that they are all computed
# together inside a single loop over x, y.
# A third alternative is to define a hl.Func as evaluating to a
# Tuple instead of an hl.Expr. A Tuple is a fixed-size collection of
# Exprs which may have different type. The following function
# evaluates to an integer value (x+y), and a floating point value
# (hl.sin(x*y)).
multi_valued = hl.Func("multi_valued")
multi_valued[x, y] = (x + y, hl.sin(x * y))
# Realizing a tuple-valued hl.Func returns a collection of
# Buffers. We call this a Realization. It's equivalent to a
# std::vector of hl.Buffer/Image objects:
if True:
(im1, im2) = multi_valued.realize(80, 60)
assert type(im1) is hl.Buffer_int32
assert type(im2) is hl.Buffer_float32
assert im1(30, 40) == 30 + 40
assert numpy.isclose(im2(30, 40), math.sin(30 * 40))
# All Tuple elements are evaluated together over the same domain
# in the same loop nest, but stored in distinct allocations. The
# equivalent C++ code to the above is:
if True:
multi_valued_0 = numpy.empty((80*60), dtype=numpy.int32)
multi_valued_1 = numpy.empty((80*60), dtype=numpy.int32)
for yy in range(80):
for xx in range(60):
multi_valued_0[xx + 60*yy] = xx + yy
multi_valued_1[xx + 60*yy] = math.sin(xx*yy)
# When compiling ahead-of-time, a Tuple-valued hl.Func evaluates
# into multiple distinct output buffer_t structs. These appear in
# order at the end of the function signature:
# int multi_valued(...input buffers and params..., buffer_t *output_1, buffer_t *output_2)
# You can construct a Tuple by passing multiple Exprs to the
# Tuple constructor as we did above. Perhaps more elegantly, you
# can also take advantage of C++11 initializer lists and just
# enclose your Exprs in braces:
multi_valued_2 = hl.Func("multi_valued_2")
multi_valued_2[x, y] = (x + y, hl.sin(x * y))
# Calls to a multi-valued hl.Func cannot be treated as Exprs. The
# following is a syntax error:
# hl.Func consumer
# consumer[x, y] = multi_valued_2[x, y] + 10
# Instead you must index the returned object with square brackets
# to retrieve the individual Exprs:
integer_part = multi_valued_2[x, y][0]
floating_part = multi_valued_2[x, y][1]
assert type(integer_part) is hl.FuncTupleElementRef
assert type(floating_part) is hl.FuncTupleElementRef
consumer = hl.Func()
consumer[x, y] = (integer_part + 10, floating_part + 10.0)
# Tuple reductions.
if True:
# Tuples are particularly useful in reductions, as they allow
# the reduction to maintain complex state as it walks along
# its domain. The simplest example is an argmax.
# First we create an Image to take the argmax over.
input_func = hl.Func()
input_func[x] = hl.sin(x)
input = input_func.realize(100)
assert type(input) is hl.Buffer_float32
# Then we defined a 2-valued Tuple which tracks the maximum value
# its index.
arg_max = hl.Func()
# Pure definition.
# (using [()] for zero-dimensional Funcs is a convention of this python interface)
arg_max[()] = (0, input(0))
# Update definition.
r = hl.RDom(1, 99)
old_index = arg_max[()][0]
old_max = arg_max[()][1]
new_index = hl.select(old_max > input[r], r, old_index)
new_max = hl.max(input[r], old_max)
arg_max[()] = (new_index, new_max)
# The equivalent C++ is:
arg_max_0 = 0
arg_max_1 = float(input(0))
for r in range(1, 100):
old_index = arg_max_0
old_max = arg_max_1
new_index = r if (old_max > input(r)) else old_index
new_max = max(input(r), old_max)
# In a tuple update definition, all loads and computation
# are done before any stores, so that all Tuple elements
# are updated atomically with respect to recursive calls
# to the same hl.Func.
arg_max_0 = new_index
arg_max_1 = new_max
# Let's verify that the Halide and C++ found the same maximum
# value and index.
if True:
(r0, r1) = arg_max.realize()
assert type(r0) is hl.Buffer_int32
assert type(r1) is hl.Buffer_float32
assert arg_max_0 == r0(0)
assert numpy.isclose(arg_max_1, r1(0))
# Halide provides argmax and hl.argmin as built-in reductions
# similar to sum, product, maximum, and minimum. They return
# a Tuple consisting of the point in the reduction domain
# corresponding to that value, and the value itself. In the
# case of ties they return the first value found. We'll use
# one of these in the following section.
# Tuples for user-defined types.
if True:
# Tuples can also be a convenient way to represent compound
# objects such as complex numbers. Defining an object that
# can be converted to and from a Tuple is one way to extend
# Halide's type system with user-defined types.
class Complex:
def __init__(self, r, i=None):
if type(r) is float and type(i) is float:
self.real = hl.Expr(r)
self.imag = hl.Expr(i)
elif i is not None:
self.real = r
self.imag = i
else:
self.real = r[0]
self.imag = r[1]
def as_tuple(self):
"Convert to a Tuple"
return (self.real, self.imag)
def __add__(self, other):
"Complex addition"
return Complex(self.real + other.real, self.imag + other.imag)
def __mul__(self, other):
"Complex multiplication"
return Complex(self.real * other.real - self.imag * other.imag,
self.real * other.imag + self.imag * other.real)
def __getitem__(self, idx):
return (self.real, self.imag)[idx]
def __len__(self):
return 2
def magnitude(self):
"Complex magnitude"
return (self.real * self.real) + (self.imag * self.imag)
# Other complex operators would go here. The above are
# sufficient for this example.
# Let's use the Complex struct to compute a Mandelbrot set.
mandelbrot = hl.Func()
# The initial complex value corresponding to an x, y coordinate
# in our hl.Func.
initial = Complex(x/15.0 - 2.5, y/6.0 - 2.0)
# Pure definition.
t = hl.Var("t")
mandelbrot[x, y, t] = Complex(0.0, 0.0)
# We'll use an update definition to take 12 steps.
r = hl.RDom(1, 12)
current = Complex(mandelbrot[x, y, r-1])
# The following line uses the complex multiplication and
# addition we defined above.
mandelbrot[x, y, r] = (Complex(current*current) + initial)
# We'll use another tuple reduction to compute the iteration
# number where the value first escapes a circle of radius 4.
# This can be expressed as an hl.argmin of a boolean - we want
# the index of the first time the given boolean expression is
# false (we consider false to be less than true). The argmax
# would return the index of the first time the expression is
# true.
escape_condition = Complex(mandelbrot[x, y, r]).magnitude() < 16.0
first_escape = hl.argmin(escape_condition)
assert type(first_escape) is tuple
# We only want the index, not the value, but hl.argmin returns
# both, so we'll index the hl.argmin Tuple expression using
# square brackets to get the hl.Expr representing the index.
escape = hl.Func()
escape[x, y] = first_escape[0]
# Realize the pipeline and print the result as ascii art.
result = escape.realize(61, 25)
assert type(result) is hl.Buffer_int32
code = " .:-~*={&%#@"
for yy in range(result.height()):
for xx in range(result.width()):
index = result(xx, yy)
if index < len(code):
print("%c" % code[index], end="")
else:
pass # is lesson 13 cpp version buggy ?
print("")
print("Success!")
return 0