def get_blur(input): assert type(input) == hl.ImageParam assert input.dimensions() == 2 x, y = hl.Var("x"), hl.Var("y") clamped_input = hl.repeat_edge(input) input_uint16 = hl.Func("input_uint16") input_uint16[x, y] = hl.cast(hl.UInt(16), clamped_input[x, y]) ci = input_uint16 blur_x = hl.Func("blur_x") blur_y = hl.Func("blur_y") blur_x[x, y] = (ci[x, y] + ci[x + 1, y] + ci[x + 2, y]) / 3 blur_y[x, y] = hl.cast( hl.UInt(8), (blur_x[x, y] + blur_x[x, y + 1] + blur_x[x, y + 2]) / 3) # schedule xi, yi = hl.Var("xi"), hl.Var("yi") blur_y.tile(x, y, xi, yi, 8, 4).parallel(y).vectorize(xi, 8) blur_x.compute_at(blur_y, x).vectorize(x, 8) return blur_y
def get_blur(input): assert type(input) == hl.ImageParam assert input.dimensions() == 2 x, y = hl.Var("x"), hl.Var("y") clamped_input = hl.repeat_edge(input) input_uint16 = hl.Func("input_uint16") input_uint16[x,y] = hl.cast(hl.UInt(16), clamped_input[x,y]) ci = input_uint16 blur_x = hl.Func("blur_x") blur_y = hl.Func("blur_y") blur_x[x,y] = (ci[x,y]+ci[x+1,y]+ci[x+2,y])/3 blur_y[x,y] = hl.cast(hl.UInt(8), (blur_x[x,y]+blur_x[x,y+1]+blur_x[x,y+2])/3) # schedule xi, yi = hl.Var("xi"), hl.Var("yi") blur_y.tile(x, y, xi, yi, 8, 4).parallel(y).vectorize(xi, 8) blur_x.compute_at(blur_y, x).vectorize(x, 8) return blur_y
def main(): # Declare some Vars to use below. x, y = hl.Var("x"), hl.Var("y") # Load a grayscale image to use as an input. image_path = os.path.join(os.path.dirname(__file__), "../../tutorial/images/gray.png") input_data = imread(image_path) if True: # making the image smaller to go faster input_data = input_data[:160, :150] assert input_data.dtype == np.uint8 input = hl.Buffer(input_data) # You can define a hl.Func in multiple passes. Let's see a toy # example first. if True: # The first definition must be one like we have seen already # - a mapping from Vars to an hl.Expr: f = hl.Func("f") f[x, y] = x + y # We call this first definition the "pure" definition. # But the later definitions can include computed expressions on # both sides. The simplest example is modifying a single point: f[3, 7] = 42 # We call these extra definitions "update" definitions, or # "reduction" definitions. A reduction definition is an # update definition that recursively refers back to the # function's current value at the same site: if False: e = f[x, y] + 17 print("f[x, y] + 17", e) print("(f[x, y] + 17).type()", e.type()) print("(f[x, y]).type()", f[x, y].type()) f[x, y] = f[x, y] + 17 # If we confine our update to a single row, we can # recursively refer to values in the same column: f[x, 3] = f[x, 0] * f[x, 10] # Similarly, if we confine our update to a single column, we # can recursively refer to other values in the same row. f[0, y] = f[0, y] / f[3, y] # The general rule is: Each hl.Var used in an update definition # must appear unadorned in the same position as in the pure # definition in all references to the function on the left- # and right-hand sides. So the following definitions are # legal updates: f[x, 17] = x + 8 # x is used, so all uses of f must have x as the first argument. f[0, y] = y * 8 # y is used, so all uses of f must have y as the second argument. f[x, x + 1] = x + 8 f[y / 2, y] = f[0, y] * 17 # But these ones would cause an error: # f[x, 0) = f[x + 1, 0) <- First argument to f on the right-hand-side must be 'x', not 'x + 1'. # f[y, y + 1) = y + 8 <- Second argument to f on the left-hand-side must be 'y', not 'y + 1'. # f[y, x) = y - x <- Arguments to f on the left-hand-side are in the wrong places. # f[3, 4) = x + y <- Free variables appear on the right-hand-side but not the left-hand-side. # We'll realize this one just to make sure it compiles. The # second-to-last definition forces us to realize over a # domain that is taller than it is wide. f.realize(100, 101) # For each realization of f, each step runs in its entirety # before the next one begins. Let's trace the loads and # stores for a simpler example: g = hl.Func("g") g[x, y] = x + y # Pure definition g[2, 1] = 42 # First update definition g[x, 0] = g[x, 1] # Second update definition g.trace_loads() g.trace_stores() g.realize(4, 4) # Reading the log, we see that each pass is applied in turn. The equivalent C is: result = np.empty((4, 4), dtype=np.int) # Pure definition for yy in range(4): for xx in range(4): result[yy][xx] = xx + yy # First update definition result[1][2] = 42 # Second update definition for xx in range(4): result[0][xx] = result[1][xx] # end of section # Putting update passes inside loops. if True: # Starting with this pure definition: f = hl.Func("f") f[x, y] = x + y # Say we want an update that squares the first fifty rows. We # could do this by adding 50 update definitions: # f[x, 0) = f[x, 0) * f[x, 0) # f[x, 1) = f[x, 1) * f[x, 1) # f[x, 2) = f[x, 2) * f[x, 2) # ... # f[x, 49) = f[x, 49) * f[x, 49) # Or equivalently using a compile-time loop in our C++: # for (int i = 0 i < 50 i++) { # f[x, i) = f[x, i) * f[x, i) # # But it's more manageable and more flexible to put the loop # in the generated code. We do this by defining a "reduction # domain" and using it inside an update definition: r = hl.RDom(0, 50) f[x, r] = f[x, r] * f[x, r] halide_result = f.realize(100, 100) # The equivalent C is: c_result = np.empty((100, 100), dtype=np.int) for yy in range(100): for xx in range(100): c_result[yy][xx] = xx + yy for xx in range(100): for rr in range(50): # The loop over the reduction domain occurs inside of # the loop over any pure variables used in the update # step: c_result[rr][xx] = c_result[rr][xx] * c_result[rr][xx] # Check the results match: for yy in range(100): for xx in range(100): if halide_result(xx, yy) != c_result[yy][xx]: raise Exception( "halide_result(%d, %d) = %d instead of %d" % (xx, yy, halide_result(xx, yy), c_result[yy][xx])) return -1 # Now we'll examine a real-world use for an update definition: # computing a histogram. if True: # Some operations on images can't be cleanly expressed as a pure # function from the output coordinates to the value stored # there. The classic example is computing a histogram. The # natural way to do it is to iterate over the input image, # updating histogram buckets. Here's how you do that in Halide: histogram = hl.Func("histogram") # Histogram buckets start as zero. histogram[x] = 0 # Define a multi-dimensional reduction domain over the input image: r = hl.RDom(0, input.width(), 0, input.height()) # For every point in the reduction domain, increment the # histogram bucket corresponding to the intensity of the # input image at that point. histogram[input[r.x, r.y]] += 1 halide_result = histogram.realize(256) # The equivalent C is: c_result = np.empty((256), dtype=np.int) for xx in range(256): c_result[xx] = 0 for r_y in range(input.height()): for r_x in range(input.width()): c_result[input_data[r_x, r_y]] += 1 # Check the answers agree: for xx in range(256): if c_result[xx] != halide_result(xx): raise Exception("halide_result(%d) = %d instead of %d" % (xx, halide_result(xx), c_result[xx])) return -1 # Scheduling update steps if True: # The pure variables in an update step and can be # parallelized, vectorized, split, etc as usual. # Vectorizing, splitting, or parallelize the variables that # are part of the reduction domain is trickier. We'll cover # that in a later lesson. # Consider the definition: f = hl.Func("x") f[x, y] = x * y # Set the second row to equal the first row. f[x, 1] = f[x, 0] # Set the second column to equal the first column plus 2. f[1, y] = f[0, y] + 2 # The pure variables in each stage can be scheduled # independently. To control the pure definition, we schedule # as we have done in the past. The following code vectorizes # and parallelizes the pure definition only. f.vectorize(x, 4).parallel(y) # We use hl.Func::update(int) to get a handle to an update step # for the purposes of scheduling. The following line # vectorizes the first update step across x. We can't do # anything with y for this update step, because it doesn't # use y. f.update(0).vectorize(x, 4) # Now we parallelize the second update step in chunks of size # 4. yo, yi = hl.Var("yo"), hl.Var("yi") f.update(1).split(y, yo, yi, 4).parallel(yo) halide_result = f.realize(16, 16) # Here's the equivalent (serial) C: c_result = np.empty((16, 16), dtype=np.int) # Pure step. Vectorized in x and parallelized in y. for yy in range(16): # Should be a parallel for loop for x_vec in range(4): xx = [x_vec * 4, x_vec * 4 + 1, x_vec * 4 + 2, x_vec * 4 + 3] c_result[yy][xx[0]] = xx[0] * yy c_result[yy][xx[1]] = xx[1] * yy c_result[yy][xx[2]] = xx[2] * yy c_result[yy][xx[3]] = xx[3] * yy # First update. Vectorized in x. for x_vec in range(4): xx = [x_vec * 4, x_vec * 4 + 1, x_vec * 4 + 2, x_vec * 4 + 3] c_result[1][xx[0]] = c_result[0][xx[0]] c_result[1][xx[1]] = c_result[0][xx[1]] c_result[1][xx[2]] = c_result[0][xx[2]] c_result[1][xx[3]] = c_result[0][xx[3]] # Second update. Parallelized in chunks of size 4 in y. for yo in range(4): # Should be a parallel for loop for yi in range(4): yy = yo * 4 + yi c_result[yy][1] = c_result[yy][0] + 2 # Check the C and Halide results match: for yy in range(16): for xx in range(16): if halide_result(xx, yy) != c_result[yy][xx]: raise Exception( "halide_result(%d, %d) = %d instead of %d" % (xx, yy, halide_result(xx, yy), c_result[yy][xx])) return -1 # That covers how to schedule the variables within a hl.Func that # uses update steps, but what about producer-consumer # relationships that involve compute_at and store_at? Let's # examine a reduction as a producer, in a producer-consumer pair. if True: # Because an update does multiple passes over a stored array, # it's not meaningful to inline them. So the default schedule # for them does the closest thing possible. It computes them # in the innermost loop of their consumer. Consider this # trivial example: producer, consumer = hl.Func("producer"), hl.Func("consumer") producer[x] = x * 17 producer[x] += 1 consumer[x] = 2 * producer[x] halide_result = consumer.realize(10) # The equivalent C is: c_result = np.empty((10), dtype=np.int) for xx in range(10): producer_storage = np.empty((1), dtype=np.int) # Pure step for producer producer_storage[0] = xx * 17 # Update step for producer producer_storage[0] = producer_storage[0] + 1 # Pure step for consumer c_result[xx] = 2 * producer_storage[0] # Check the results match for xx in range(10): if halide_result(xx) != c_result[xx]: raise Exception("halide_result(%d) = %d instead of %d" % (xx, halide_result(xx), c_result[xx])) return -1 # For all other compute_at/store_at options, the reduction # gets placed where you would expect, somewhere in the loop # nest of the consumer. # Now let's consider a reduction as a consumer in a # producer-consumer pair. This is a little more involved. if True: if True: # Case 1: The consumer references the producer in the pure step only. producer, consumer = hl.Func("producer"), hl.Func("consumer") # The producer is pure. producer[x] = x * 17 consumer[x] = 2 * producer[x] consumer[x] += 1 # The valid schedules for the producer in this case are # the default schedule - inlined, and also: # # 1) producer.compute_at(x), which places the computation of # the producer inside the loop over x in the pure step of the # consumer. # # 2) producer.compute_root(), which computes all of the # producer ahead of time. # # 3) producer.store_root().compute_at(x), which allocates # space for the consumer outside the loop over x, but fills # it in as needed inside the loop. # # Let's use option 1. producer.compute_at(consumer, x) halide_result = consumer.realize(10) # The equivalent C is: c_result = np.empty((10), dtype=np.int) # Pure step for the consumer for xx in range(10): # Pure step for producer producer_storage = np.empty((1), dtype=np.int) producer_storage[0] = xx * 17 c_result[xx] = 2 * producer_storage[0] # Update step for the consumer for xx in range(10): c_result[xx] += 1 # All of the pure step is evaluated before any of the # update step, so there are two separate loops over x. # Check the results match for xx in range(10): if halide_result(xx) != c_result[xx]: raise Exception("halide_result(%d) = %d instead of %d" % (xx, halide_result(xx), c_result[xx])) return -1 if True: # Case 2: The consumer references the producer in the update step only producer, consumer = hl.Func("producer"), hl.Func("consumer") producer[x] = x * 17 consumer[x] = x consumer[x] += producer[x] # Again we compute the producer per x coordinate of the # consumer. This places producer code inside the update # step of the producer, because that's the only step that # uses the producer. producer.compute_at(consumer, x) # Note however, that we didn't say: # # producer.compute_at(consumer.update(0), x). # # Scheduling is done with respect to Vars of a hl.Func, and # the Vars of a hl.Func are shared across the pure and # update steps. halide_result = consumer.realize(10) # The equivalent C is: c_result = np.empty((10), dtype=np.int) # Pure step for the consumer for xx in range(10): c_result[xx] = xx # Update step for the consumer for xx in range(10): # Pure step for producer producer_storage = np.empty((1), dtype=np.int) producer_storage[0] = xx * 17 c_result[xx] += producer_storage[0] # Check the results match for xx in range(10): if halide_result(xx) != c_result[xx]: raise Exception("halide_result(%d) = %d instead of %d" % (xx, halide_result(xx), c_result[xx])) return -1 if True: # Case 3: The consumer references the producer in # multiple steps that share common variables producer, consumer = hl.Func("producer"), hl.Func("consumer") producer[x] = x * 17 consumer[x] = producer[x] * x consumer[x] += producer[x] # Again we compute the producer per x coordinate of the # consumer. This places producer code inside both the # pure and the update step of the producer. So there ends # up being two separate realizations of the producer, and # redundant work occurs. producer.compute_at(consumer, x) halide_result = consumer.realize(10) # The equivalent C is: c_result = np.empty((10), dtype=np.int) # Pure step for the consumer for xx in range(10): # Pure step for producer producer_storage = np.empty((1), dtype=np.int) producer_storage[0] = xx * 17 c_result[xx] = producer_storage[0] * xx # Update step for the consumer for xx in range(10): # Another copy of the pure step for producer producer_storage = np.empty((1), dtype=np.int) producer_storage[0] = xx * 17 c_result[xx] += producer_storage[0] # Check the results match for xx in range(10): if halide_result(xx) != c_result[xx]: raise Exception("halide_result(%d) = %d instead of %d" % (xx, halide_result(xx), c_result[xx])) return -1 if True: # Case 4: The consumer references the producer in # multiple steps that do not share common variables producer, consumer = hl.Func("producer"), hl.Func("consumer") producer[x, y] = x * y consumer[x, y] = x + y consumer[x, 0] = producer[x, x - 1] consumer[0, y] = producer[y, y - 1] # In this case neither producer.compute_at(consumer, x) # nor producer.compute_at(consumer, y) will work, because # either one fails to cover one of the uses of the # producer. So we'd have to inline producer, or use # producer.compute_root(). # Let's say we really really want producer to be # compute_at the inner loops of both consumer update # steps. Halide doesn't allow multiple different # schedules for a single hl.Func, but we can work around it # by making two wrappers around producer, and scheduling # those instead: # Attempt 2: producer_wrapper_1, producer_wrapper_2, consumer_2 = hl.Func( ), hl.Func(), hl.Func() producer_wrapper_1[x, y] = producer[x, y] producer_wrapper_2[x, y] = producer[x, y] consumer_2[x, y] = x + y consumer_2[x, 0] += producer_wrapper_1[x, x - 1] consumer_2[0, y] += producer_wrapper_2[y, y - 1] # The wrapper functions give us two separate handles on # the producer, so we can schedule them differently. producer_wrapper_1.compute_at(consumer_2, x) producer_wrapper_2.compute_at(consumer_2, y) halide_result = consumer_2.realize(10, 10) # The equivalent C is: c_result = np.empty((10, 10), dtype=np.int) # Pure step for the consumer for yy in range(10): for xx in range(10): c_result[yy][xx] = xx + yy # First update step for consumer for xx in range(10): producer_wrapper_1_storage = np.empty((1), dtype=np.int) producer_wrapper_1_storage[0] = xx * (xx - 1) c_result[0][xx] += producer_wrapper_1_storage[0] # Second update step for consumer for yy in range(10): producer_wrapper_2_storage = np.empty((1), dtype=np.int) producer_wrapper_2_storage[0] = yy * (yy - 1) c_result[yy][0] += producer_wrapper_2_storage[0] # Check the results match for yy in range(10): for xx in range(10): if halide_result(xx, yy) != c_result[yy][xx]: print("halide_result(%d, %d) = %d instead of %d", xx, yy, halide_result(xx, yy), c_result[yy][xx]) return -1 if True: # Case 5: Scheduling a producer under a reduction domain # variable of the consumer. # We are not just restricted to scheduling producers at # the loops over the pure variables of the consumer. If a # producer is only used within a loop over a reduction # domain (hl.RDom) variable, we can also schedule the # producer there. producer, consumer = hl.Func("producer"), hl.Func("consumer") r = hl.RDom(0, 5) producer[x] = x * 17 consumer[x] = x + 10 consumer[x] += r + producer[x + r] producer.compute_at(consumer, r) halide_result = consumer.realize(10) # The equivalent C is: c_result = np.empty((10), dtype=np.int) # Pure step for the consumer. for xx in range(10): c_result[xx] = xx + 10 # Update step for the consumer. for xx in range(10): for rr in range( 5 ): # The loop over the reduction domain is always the inner loop. # We've schedule the storage and computation of # the producer here. We just need a single value. producer_storage = np.empty((1), dtype=np.int) # Pure step of the producer. producer_storage[0] = (xx + rr) * 17 # Now use it in the update step of the consumer. c_result[xx] += rr + producer_storage[0] # Check the results match for xx in range(10): if halide_result(xx) != c_result[xx]: raise Exception("halide_result(%d) = %d instead of %d" % (xx, halide_result(xx), c_result[xx])) return -1 # A real-world example of a reduction inside a producer-consumer chain. if True: # The default schedule for a reduction is a good one for # convolution-like operations. For example, the following # computes a 5x5 box-blur of our grayscale test image with a # hl.clamp-to-edge boundary condition: # First add the boundary condition. clamped = hl.repeat_edge(input) # Define a 5x5 box that starts at (-2, -2) r = hl.RDom(-2, 5, -2, 5) # Compute the 5x5 sum around each pixel. local_sum = hl.Func("local_sum") local_sum[x, y] = 0 # Compute the sum as a 32-bit integer local_sum[x, y] += clamped[x + r.x, y + r.y] # Divide the sum by 25 to make it an average blurry = hl.Func("blurry") blurry[x, y] = hl.cast(hl.UInt(8), local_sum[x, y] / 25) halide_result = blurry.realize(input.width(), input.height()) # The default schedule will inline 'clamped' into the update # step of 'local_sum', because clamped only has a pure # definition, and so its default schedule is fully-inlined. # We will then compute local_sum per x coordinate of blurry, # because the default schedule for reductions is # compute-innermost. Here's the equivalent C: #cast_to_uint8 = lambda x_: np.array([x_], dtype=np.uint8)[0] local_sum = np.empty((1), dtype=np.int32) c_result = hl.Buffer(hl.UInt(8), input.width(), input.height()) for yy in range(input.height()): for xx in range(input.width()): # FIXME this loop is quite slow # Pure step of local_sum local_sum[0] = 0 # Update step of local_sum for r_y in range(-2, 2 + 1): for r_x in range(-2, 2 + 1): # The clamping has been inlined into the update step. clamped_x = min(max(xx + r_x, 0), input.width() - 1) clamped_y = min(max(yy + r_y, 0), input.height() - 1) local_sum[0] += input(clamped_x, clamped_y) # Pure step of blurry #c_result(x, y) = (uint8_t)(local_sum[0] / 25) #c_result[xx, yy] = cast_to_uint8(local_sum[0] / 25) c_result[xx, yy] = int(local_sum[0] / 25) # hl.cast done internally # Check the results match for yy in range(input.height()): for xx in range(input.width()): if halide_result(xx, yy) != c_result(xx, yy): raise Exception( "halide_result(%d, %d) = %d instead of %d" % (xx, yy, halide_result(xx, yy), c_result(xx, yy))) return -1 # Reduction helpers. if True: # There are several reduction helper functions provided in # Halide.h, which compute small reductions and schedule them # innermost into their consumer. The most useful one is # "sum". f1 = hl.Func("f1") r = hl.RDom(0, 100) f1[x] = hl.sum(r + x) * 7 # Sum creates a small anonymous hl.Func to do the reduction. It's equivalent to: f2, anon = hl.Func("f2"), hl.Func("anon") anon[x] = 0 anon[x] += r + x f2[x] = anon[x] * 7 # So even though f1 references a reduction domain, it is a # pure function. The reduction domain has been swallowed to # define the inner anonymous reduction. halide_result_1 = f1.realize(10) halide_result_2 = f2.realize(10) # The equivalent C is: c_result = np.empty((10), dtype=np.int) for xx in range(10): anon = np.empty((1), dtype=np.int) anon[0] = 0 for rr in range(100): anon[0] += rr + xx c_result[xx] = anon[0] * 7 # Check they all match. for xx in range(10): if halide_result_1(xx) != c_result[xx]: print("halide_result_1(%d) = %d instead of %d", x, halide_result_1(x), c_result[x]) return -1 if halide_result_2(xx) != c_result[xx]: print("halide_result_2(%d) = %d instead of %d", x, halide_result_2(x), c_result[x]) return -1 # A complex example that uses reduction helpers. if False: # non-sense to port SSE code to python, skipping this test # Other reduction helpers include "product", "minimum", # "maximum", "hl.argmin", and "argmax". Using hl.argmin and argmax # requires understanding tuples, which come in a later # lesson. Let's use minimum and maximum to compute the local # spread of our grayscale image. # First, add a boundary condition to the input. clamped = hl.Func("clamped") x_clamped = hl.clamp(x, 0, input.width() - 1) y_clamped = hl.clamp(y, 0, input.height() - 1) clamped[x, y] = input[x_clamped, y_clamped] box = hl.RDom(-2, 5, -2, 5) # Compute the local maximum minus the local minimum: spread = hl.Func("spread") spread[x, y] = (maximum(clamped(x + box.x, y + box.y)) - minimum(clamped(x + box.x, y + box.y))) # Compute the result in strips of 32 scanlines yo, yi = hl.Var("yo"), hl.Var("yi") spread.split(y, yo, yi, 32).parallel(yo) # Vectorize across x within the strips. This implicitly # vectorizes stuff that is computed within the loop over x in # spread, which includes our minimum and maximum helpers, so # they get vectorized too. spread.vectorize(x, 16) # We'll apply the boundary condition by padding each scanline # as we need it in a circular buffer (see lesson 08). clamped.store_at(spread, yo).compute_at(spread, yi) halide_result = spread.realize(input.width(), input.height()) # The C equivalent is almost too horrible to contemplate (and # took me a long time to debug). This time I want to time # both the Halide version and the C version, so I'll use sse # intrinsics for the vectorization, and openmp to do the # parallel for loop (you'll need to compile with -fopenmp or # similar to get correct timing). #ifdef __SSE2__ # Don't include the time required to allocate the output buffer. c_result = hl.Buffer(hl.UInt(8), input.width(), input.height()) #ifdef _OPENMP t1 = datetime.now() #endif # Run this one hundred times so we can average the timing results. for iters in range(100): pass # #pragma omp parallel for # for yo in range((input.height() + 31)/32): # y_base = hl.min(yo * 32, input.height() - 32) # # # Compute clamped in a circular buffer of size 8 # # (smallest power of two greater than 5). Each thread # # needs its own allocation, so it must occur here. # # clamped_width = input.width() + 4 # clamped_storage = np.empty((clamped_width * 8), dtype=np.uint8) # # for yi in range(32): # y = y_base + yi # # uint8_t *output_row = &c_result(0, y) # # # Compute clamped for this scanline, skipping rows # # already computed within this slice. # int min_y_clamped = (yi == 0) ? (y - 2) : (y + 2) # int max_y_clamped = (y + 2) # for (int cy = min_y_clamped cy <= max_y_clamped cy++) { # # Figure out which row of the circular buffer # # we're filling in using bitmasking: # uint8_t *clamped_row = clamped_storage + (cy & 7) * clamped_width # # # Figure out which row of the input we're reading # # from by clamping the y coordinate: # int clamped_y = std::hl.min(std::hl.max(cy, 0), input.height()-1) # uint8_t *input_row = &input(0, clamped_y) # # # Fill it in with the padding. # for (int x = -2 x < input.width() + 2 ): # int clamped_x = std::hl.min(std::hl.max(x, 0), input.width()-1) # *clamped_row++ = input_row[clamped_x] # # # # # Now iterate over vectors of x for the pure step of the output. # for (int x_vec = 0 x_vec < (input.width() + 15)/16 x_vec++) { # int x_base = std::hl.min(x_vec * 16, input.width() - 16) # # # Allocate storage for the minimum and maximum # # helpers. One vector is enough. # __m128i minimum_storage, maximum_storage # # # The pure step for the maximum is a vector of zeros # maximum_storage = (__m128i)_mm_setzero_ps() # # # The update step for maximum # for (int max_y = y - 2 max_y <= y + 2 max_y++) { # uint8_t *clamped_row = clamped_storage + (max_y & 7) * clamped_width # for (int max_x = x_base - 2 max_x <= x_base + 2 max_): # __m128i v = _mm_loadu_si128((__m128i const *)(clamped_row + max_x + 2)) # maximum_storage = _mm_max_epu8(maximum_storage, v) # # # # # The pure step for the minimum is a vector of # # ones. Create it by comparing something to # # itself. # minimum_storage = (__m128i)_mm_cmpeq_ps(_mm_setzero_ps(), # _mm_setzero_ps()) # # # The update step for minimum. # for (int min_y = y - 2 min_y <= y + 2 min_y++) { # uint8_t *clamped_row = clamped_storage + (min_y & 7) * clamped_width # for (int min_x = x_base - 2 min_x <= x_base + 2 min_): # __m128i v = _mm_loadu_si128((__m128i const *)(clamped_row + min_x + 2)) # minimum_storage = _mm_min_epu8(minimum_storage, v) # # # # # Now compute the spread. # __m128i spread = _mm_sub_epi8(maximum_storage, minimum_storage) # # # Store it. # _mm_storeu_si128((__m128i *)(output_row + x_base), spread) # # # # del clamped_storage # # end of hundred iterations # Skip the timing comparison if we don't have openmp # enabled. Otherwise it's unfair to C. #ifdef _OPENMP t2 = datetime.now() # Now run the Halide version again without the # jit-compilation overhead. Also run it one hundred times. for iters in range(100): spread.realize(halide_result) t3 = datetime.now() # Report the timings. On my machine they both take about 3ms # for the 4-megapixel input (fast!), which makes sense, # because they're using the same vectorization and # parallelization strategy. However I find the Halide easier # to read, write, debug, modify, and port. print("Halide spread took %f ms. C equivalent took %f ms" % ((t3 - t2).total_seconds() * 1000, (t2 - t1).total_seconds() * 1000)) #endif # _OPENMP # Check the results match: for yy in range(input.height()): for xx in range(input.width()): if halide_result(xx, yy) != c_result(xx, yy): raise Exception( "halide_result(%d, %d) = %d instead of %d" % (xx, yy, halide_result(xx, yy), c_result(xx, yy))) return -1 #endif # __SSE2__ else: print("(Skipped the SSE2 section of the code, " "since non-sense in python world.)") print("Success!") return 0
def get_bilateral_grid(input, r_sigma, s_sigma): x = hl.Var('x') y = hl.Var('y') z = hl.Var('z') c = hl.Var('c') xi = hl.Var("xi") yi = hl.Var("yi") zi = hl.Var("zi") # Add a boundary condition clamped = hl.repeat_edge(input) # Construct the bilateral grid r = hl.RDom([(0, s_sigma), (0, s_sigma)], 'r') val = clamped[x * s_sigma + r.x - s_sigma // 2, y * s_sigma + r.y - s_sigma // 2] val = hl.clamp(val, 0.0, 1.0) zi = hl.cast(int_t, val / r_sigma + 0.5) histogram = hl.Func('histogram') histogram[x, y, z, c] = 0.0 histogram[x, y, zi, c] += hl.select(c == 0, val, 1.0) # Blur the histogram using a five-tap filter blurx, blury, blurz = hl.Func('blurx'), hl.Func('blury'), hl.Func('blurz') blurz[x, y, z, c] = histogram[x, y, z - 2, c] + histogram[ x, y, z - 1, c] * 4 + histogram[x, y, z, c] * 6 + histogram[ x, y, z + 1, c] * 4 + histogram[x, y, z + 2, c] blurx[x, y, z, c] = blurz[x - 2, y, z, c] + blurz[x - 1, y, z, c] * 4 + blurz[ x, y, z, c] * 6 + blurz[x + 1, y, z, c] * 4 + blurz[x + 2, y, z, c] blury[x, y, z, c] = blurx[x, y - 2, z, c] + blurx[x, y - 1, z, c] * 4 + blurx[ x, y, z, c] * 6 + blurx[x, y + 1, z, c] * 4 + blurx[x, y + 2, z, c] # Take trilinear samples to compute the output val = hl.clamp(clamped[x, y], 0.0, 1.0) zv = val / r_sigma zi = hl.cast(int_t, zv) zf = zv - zi xf = hl.cast(float_t, x % s_sigma) / s_sigma yf = hl.cast(float_t, y % s_sigma) / s_sigma xi = x / s_sigma yi = y / s_sigma interpolated = hl.Func('interpolated') interpolated[x, y, c] = hl.lerp( hl.lerp( hl.lerp(blury[xi, yi, zi, c], blury[xi + 1, yi, zi, c], xf), hl.lerp(blury[xi, yi + 1, zi, c], blury[xi + 1, yi + 1, zi, c], xf), yf), hl.lerp( hl.lerp(blury[xi, yi, zi + 1, c], blury[xi + 1, yi, zi + 1, c], xf), hl.lerp(blury[xi, yi + 1, zi + 1, c], blury[xi + 1, yi + 1, zi + 1, c], xf), yf), zf) # Normalize bilateral_grid = hl.Func('bilateral_grid') bilateral_grid[x, y] = interpolated[x, y, 0] / interpolated[x, y, 1] target = hl.get_target_from_environment() if target.has_gpu_feature(): # GPU schedule # Currently running this directly from the Python code is very slow. # Probably because of the dispatch time because generated code # is same speed as C++ generated code. print("Compiling for GPU.") histogram.compute_root().reorder(c, z, x, y).gpu_tile(x, y, 8, 8) histogram.update().reorder(c, r.x, r.y, x, y).gpu_tile(x, y, xi, yi, 8, 8).unroll(c) blurx.compute_root().gpu_tile(x, y, z, xi, yi, zi, 16, 16, 1) blury.compute_root().gpu_tile(x, y, z, xi, yi, zi, 16, 16, 1) blurz.compute_root().gpu_tile(x, y, z, xi, yi, zi, 8, 8, 4) bilateral_grid.compute_root().gpu_tile(x, y, xi, yi, s_sigma, s_sigma) else: # CPU schedule print("Compiling for CPU.") histogram.compute_root().parallel(z) histogram.update().reorder(c, r.x, r.y, x, y).unroll(c) blurz.compute_root().reorder(c, z, x, y).parallel(y).vectorize(x, 4).unroll(c) blurx.compute_root().reorder(c, x, y, z).parallel(z).vectorize(x, 4).unroll(c) blury.compute_root().reorder(c, x, y, z).parallel(z).vectorize(x, 4).unroll(c) bilateral_grid.compute_root().parallel(y).vectorize(x, 4) return bilateral_grid