def MatmulWith

bendtorch-core@0.1.0.0 · src/tensor/contracts/LAWS.bend:172

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/dot_fold.bend as DotFold
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed

172# What the transport form of matmul_replayed asks of P: P holds for both
173# inputs, replayed with any histories that keep their words, next to the
174# output, of the plan's shape, replayed over +0.0 with any history whose cell
175# (row, column) holds the total `matmul_ordered` states.
176def MatmulWith(+left: Shape.Shape, +right: Shape.Shape, +plan: Matrix.Plan<left, right>,
177  +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>,
178  -P: Result<&2, &1, Matrix.Error, Core.Dynamic & Core.Dynamic & Core.Dynamic> -> Type) -> Type:
179  @+left_kept: List<&2, StorageLaws.Op> ->
180  @left_words: {words(left, left_fill, left_kept, Shape.logical_numel(Shape.dimensions(left))) ==
181    words(left, left_fill, left_ops, Shape.logical_numel(Shape.dimensions(left))) : List<&2, F32>} ->
182  @-left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_kept)) == Shape.logical_numel(Shape.dimensions(left)) : Nat} ->
183  @+right_kept: List<&2, StorageLaws.Op> ->
184  @right_words: {words(right, right_fill, right_kept, Shape.logical_numel(Shape.dimensions(right))) ==
185    words(right, right_fill, right_ops, Shape.logical_numel(Shape.dimensions(right))) : List<&2, F32>} ->
186  @-right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_kept)) == Shape.logical_numel(Shape.dimensions(right)) : Nat} ->
187  @+output_ops: List<&2, StorageLaws.Op> ->
188  @cells: (@+row: Nat -> @row_below: {Nat.is_lt(row, matrix_rows(left, right, plan)) == True{} : Bool} ->
189    @+column: Nat -> @column_below: {Nat.is_lt(column, matrix_columns(left, right, plan)) == True{} : Bool} ->
190    {Replayed.value(Matrix.output_shape(left, right, plan), 0.0, output_ops,
191      U32.from_nat(Nat.add(Nat.mul(row, matrix_columns(left, right, plan)), column))) ==
192      DotFold.dot_fold(factors(row, column, matrix_inner(left, right, plan), matrix_columns(left, right, plan),
193        left, left_fill, left_ops, right, right_fill, right_ops, matrix_inner(left, right, plan)), 0.0) : F32}) ->
194  @-output_fits: {Lifecycle.logical_length(Replayed.storage(Matrix.output_shape(left, right, plan), 0.0, output_ops)) ==
195    Shape.logical_numel(Shape.dimensions(Matrix.output_shape(left, right, plan))) : Nat} ->
196    P(Done{(Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_kept), left_fits}},
197      Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_kept), right_fits}},
198      Core.Packed{Matrix.output_shape(left, right, plan),
199        Core.TTensor{Replayed.storage(Matrix.output_shape(left, right, plan), 0.0, output_ops), output_fits}})})