def source_at

bendtorch-core@0.1.0.0 · src/tensor/slice_PROOF.bend:736

import Base
import bendtorch-core@0.1.0.0/src/tensor/slice.bend as Slice
import bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedProof

736# The forward cell (o, k, r) reads input cell (o, start + k * step, r).
737def source_at(+outer: Nat, +extent: Nat, +inner: Nat, +start: Nat, +step: Nat, +length: Nat, +o: Nat, +k: Nat, +r: Nat,
738  +k_below: {Nat.is_lt(k, length) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool}) ->
739  {Slice.source(Slice.Plan{outer, extent, inner, start, step, length}, Laws.position(length, inner, o, k, r)) ==
740    Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}:
741  +row = Nat.add(Nat.mul(o, length), k)
742  +pos = Laws.position(length, inner, o, k, r)
743  %Equal.sym(Nat, Nat.div(pos, inner), row, BatchedProof.div_exact(row, inner, r, r_below)) :
744    {Nat.add(Nat.mul(Nat.add(Nat.mul(Nat.div(_, length), extent), Nat.add(start, Nat.mul(Nat.mod(_, length), step))), inner), Nat.mod(pos, inner)) ==
745      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
746  %Equal.sym(Nat, Nat.mod(pos, inner), r, BatchedProof.mod_exact(row, inner, r, r_below)) :
747    {Nat.add(Nat.mul(Nat.add(Nat.mul(Nat.div(row, length), extent), Nat.add(start, Nat.mul(Nat.mod(row, length), step))), inner), _) ==
748      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
749  %Equal.sym(Nat, Nat.div(row, length), o, BatchedProof.div_exact(o, length, k, k_below)) :
750    {Nat.add(Nat.mul(Nat.add(Nat.mul(_, extent), Nat.add(start, Nat.mul(Nat.mod(row, length), step))), inner), r) ==
751      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
752  %Equal.sym(Nat, Nat.mod(row, length), k, BatchedProof.mod_exact(o, length, k, k_below)) :
753    {Nat.add(Nat.mul(Nat.add(Nat.mul(o, extent), Nat.add(start, Nat.mul(_, step))), inner), r) ==
754      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
755  {==}