1 # Each band leaf assembles the rows its outputs read into one contiguous 2 # window and runs the two sweeps of the dense pool on it: along the columns of 3 # every window row, then along the rows, with output row zero's window 4 # starting at the window row that the image row would. Sample order is the 5 # dense order. 6 import Base 7 import ./tensor_access.bend as Access 8 import ./tensor_operations.bend as Operations 9 import ./tensor_band.bend as Bands 10 import ./tensor_band_window.bend as BandWindow 11 import ./traversal_partition.bend as Partition 12 import ./storage_buffer.bend as Storage 13 import ./tensor.bend as Tensors 14 import ./tensor_band_schedule.bend as BandSchedule 15 import ./kernel_cost.bend as Cost 16 import ./default_kernel_cost.bend as DefaultCost 17 18 type Context<-Element: Data> is Data: 19 Context{geometry: BandWindow.Geometry,pad: Element,fill: Element,workers: U32} 20 21 def window_size(window: BandWindow.RowWindow) -> BandSchedule.Size: 22 BandWindow.RowWindow{BandWindow.Rows{first,+count},above,below,rows} = window 23 BandSchedule.Size{1,count,count} 24 25 def plan_size(layout: Bands.Plan,+window: BandWindow.Geometry) -> BandSchedule.Size: 26 match layout: 27 case Bands.Rows{first,rows}: window_size(BandWindow.window(window,first,rows)) 28 case Bands.Split{left,right}: BandSchedule.merge(plan_size(left,window),plan_size(right,window)) 29 30 # Bytes price loading, storing and the loop that moves them (copy_byte_ns is 31 # measured on copy loops); operations count the rest. Per sample 32 # (Access.read_line and the operation): an offset and a subtraction, one bound 33 # check, a two-operation index, the padding select and the compare-and-select 34 # maximum: 8. Each line adds ten for its origin (Access.line_at). An output is 35 # one line along the rows; the lines along the columns are one for every 36 # window row, stride for every output row. 37 def parallel(window: BandWindow.Geometry,workers: U32,size: BandSchedule.Size) -> Bool: 38 BandWindow.Geometry{Bands.Geometry{batch,channels,ih,iw},kernel,stride,padding,oh,ow} = window 39 +config = DefaultCost.configuration() 40 +samples = U32.to_f32(kernel) 41 +lines = (U32.to_f32(stride) + 1.0 : F32) 42 +line_bytes = (samples * 4.0 + 8.0 : F32) 43 +line_operations = (samples * 8.0 + 10.0 : F32) 44 BandSchedule.sized(Bands.Geometry{batch,channels,oh,ow},workers,Cost.element_ns((lines * line_bytes : F32),(lines * line_operations : F32),config),config,size) 45 46 # The destination of the two sweeps of channels stored planes: along the 47 # columns into middle, [channels,height,out_width], then along the rows from 48 # origin into output. 49 def pooled(~Element: Data,~operation: Element -> Element -> Element,+pool: Access.Pool,+pad: Element,origin: U32,+channels: U32, 50 input: Storage.Buffer,middle: Storage.Buffer,output: Storage.Buffer) -> Storage.Buffer: 51 Access.Pool{+height,+width,+kernel,+stride,+padding,+out_height,+out_width} = pool 52 +pool = {Access.Pool{height,width,kernel,stride,padding,out_height,out_width} : Access.Pool} 53 Bands.destination(~Element,Operations.swept(~Element,~operation,U32.to_nat((channels * out_height * out_width : U32)), 54 Access.SweepContext{Access.pool_rows(pool,origin),pad}, 55 Bands.destination(~Element,Operations.swept(~Element,~operation,U32.to_nat((channels * height * out_width : U32)), 56 Access.SweepContext{Access.pool_columns(pool),pad},input,middle)),output)) 57 58 def windowed(~Element: Data,~operation: Element -> Element -> Element,+geometry: BandWindow.Geometry,+pad: Element,+fill: Element,+first: U32,+rows: U32, 59 +rows_read: BandWindow.RowWindow,core: Storage.Buffer,above: Storage.Buffer,below: Storage.Buffer) -> Bands.Bands(~Element): 60 BandWindow.Geometry{Bands.Geometry{batch,+channels,+height,+width},+kernel,+stride,+padding,+output_height,+output_width} = geometry 61 BandWindow.RowWindow{BandWindow.Rows{+output_first,+output_rows},+above_range,+below_range,+window} = rows_read 62 BandWindow.Rows{+window_first,+window_rows} = window 63 Partition.Leaf{pooled(~Element,~operation,Access.Pool{window_rows,width,kernel,stride,padding,output_rows,output_width},pad, 64 ((output_first - first / height * output_height) * stride + first / height * height - window_first : U32),channels, 65 BandWindow.assemble(~Element,fill,BandWindow.input_geometry(geometry),window,BandWindow.Rows{first,rows},above_range,below_range,core,above,below), 66 Tensors.buffer(~Element,fill,(channels * window_rows * output_width : U32)), 67 Tensors.buffer(~Element,fill,(channels * output_rows * output_width : U32))),output_first,output_rows,Unit{}} 68 69 def leaf(~Element: Data,~operation: Element -> Element -> Element,context: Context,first: U32,rows: U32,core: Storage.Buffer,halo: BandWindow.Halo) -> Bands.Bands(~Element): 70 Context{+geometry,+pad,+fill,workers} = context 71 BandWindow.Halo{above,below,+rows_read} = halo 72 +first = first 73 +rows = rows 74 windowed(~Element,~operation,geometry,pad,fill,first,rows,rows_read,core,above,below) 75 76 def prepared(~Element: Data,~operation: Element -> Element -> Element,+context: Context,+layout: Bands.Plan,owners: Bands.Bands(~Element) & BandWindow.Halos(~Element)) -> Bands.Bands(~Element): 77 Context{+window,pad,fill,workers} = context 78 (bands,halos) = owners 79 +geometry = BandWindow.input_geometry(window) 80 +enabled = parallel(window,workers,plan_size(layout,window)) 81 BandWindow.apply(~Element,~Context,~leaf(~Element,~operation),layout,enabled && Bands.same_image(geometry,layout),enabled,geometry,context,bands,halos) 82 83 def planned(~Element: Data,~operation: Element -> Element -> Element,+context: Context,owners: Bands.Bands(~Element) & Bands.Plan) -> Bands.Bands(~Element): 84 Context{window,pad,fill,workers} = context 85 (bands,+layout) = owners 86 prepared(~Element,~operation,context,layout,BandWindow.prepare(~Element,window,pad,layout,bands)) 87 88 def execute(~Element: Data,~operation: Element -> Element -> Element,context: Context,bands: Bands.Bands(~Element)) -> Bands.Bands(~Element): 89 planned(~Element,~operation,context,Bands.plan(~Element,bands))