def output_source

bendtorch-core@0.1.0.0 · src/tensor/matmul_PROOF.bend:1527

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage
import bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend as Parallel

1527def output_source(+left: Shape.Shape, +right: Shape.Shape, +output: Shape.Shape, +rows: U32, +inner: U32, +right_inner: U32, +columns: U32,
1528  -le: {Shape.dimensions(left) == [rows, inner] : List<&2, U32>}, -re: {Shape.dimensions(right) == [right_inner, columns] : List<&2, U32>},
1529  -oe: {Shape.dimensions(output) == [rows, columns] : List<&2, U32>}, -compatible: {U32.to_nat(inner) == U32.to_nat(right_inner) : Nat},
1530  +depth: Nat, +length: Nat, -valid: {Storage.bounds(depth, length) == True{} : Bool},
1531  -exact: {length == Shape.logical_numel(Shape.dimensions(output)) : Nat},
1532  -a: Core.Tensor<left>, -b: Core.Tensor<right>,
1533  -kept_left: Core.Tensor<left>, -copy_left: Array<F32>, -taken_left: Parallel.Taken<Core.Packed{left, a}, (Core.Packed{left, kept_left}, copy_left)>,
1534  -kept_right: Core.Tensor<right>, -copy_right: Array<F32>, -taken_right: Parallel.Taken<Core.Packed{right, b}, (Core.Packed{right, kept_right}, copy_right)>) ->
1535  Laws.SourceMatmul<Core.Packed{left, a}, Core.Packed{right, b}, Matrix.parallel_output(output, U32.to_nat(inner), U32.to_nat(columns), depth, length,
1536    valid, exact, (Core.Packed{left, kept_left}, copy_left), (Core.Packed{right, kept_right}, copy_right))>:
1537  Laws.SourceMatmul{unit => Laws.MatmulSuccess{left, right, Matrix.Plan{output, rows, inner, right_inner, columns, le, re, oe, compatible},
1538    a, b, kept_left, kept_right,
1539    Core.TTensor{Storage.Owned{depth, length,
1540      Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1541      Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1542      valid}, exact},
1543    {==}, {==}, {==}, {==}, {==},
1544    Laws.ProductPrefix{
1545      other => {\{Parallel.Fact: p => p} : Parallel.Fact<{Core.checked_observe(left, kept_left, other) == Core.checked_observe(left, a, other) : Maybe<&2, F32>}> ->
1546        {Core.checked_observe(left, kept_left, other) == Core.checked_observe(left, a, other) : Maybe<&2, F32>}}(
1547        taken_keeps(left, a, kept_left, copy_left, taken_left, other)),
1548      other => {\{Parallel.Fact: p => p} : Parallel.Fact<{Core.checked_observe(right, kept_right, other) == Core.checked_observe(right, b, other) : Maybe<&2, F32>}> ->
1549        {Core.checked_observe(right, kept_right, other) == Core.checked_observe(right, b, other) : Maybe<&2, F32>}}(
1550        taken_keeps(right, b, kept_right, copy_right, taken_right, other)),
1551      position => earlier =>
1552        {\{Parallel.Taken: dl => bl => left_reads => left_same =>
1553          {\{Parallel.Taken: dr => br => right_reads => right_same =>
1554            {\{Parallel.Fact: p => p} :
1555              Parallel.Fact<Laws.ProductCell<inner, left, right, a, b, output,
1556                Core.TTensor{Storage.Owned{depth, length,
1557                  Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1558                  Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1559                  valid}, exact}, position>> ->
1560              Laws.ProductCell<inner, left, right, a, b, output,
1561                Core.TTensor{Storage.Owned{depth, length,
1562                  Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1563                  Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1564                  valid}, exact}, position>}(
1565              product_cell(left, right, output, rows, inner, right_inner, columns, le, re, oe, compatible, depth, length, valid, exact,
1566                a, b, dl, dr, copy_left, copy_right, bl, br, left_reads, right_reads, position, earlier))} :
1567            Parallel.Taken<Core.Packed{right, b}, (Core.Packed{right, kept_right}, copy_right)> ->
1568            Laws.ProductCell<inner, left, right, a, b, output,
1569              Core.TTensor{Storage.Owned{depth, length,
1570                Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1571                Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1572                valid}, exact}, position>}(taken_right)} :
1573          Parallel.Taken<Core.Packed{left, a}, (Core.Packed{left, kept_left}, copy_left)> ->
1574          Laws.ProductCell<inner, left, right, a, b, output,
1575            Core.TTensor{Storage.Owned{depth, length,
1576              Matrix.build(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1577              Matrix.build_balanced(depth, Matrix.product_splits(depth, U32.to_nat(inner)), U32.to_nat(inner), U32.to_nat(columns), length, 0n, copy_left, copy_right),
1578              valid}, exact}, position>}(taken_left)}}}