def scattered_at

bendtorch-core@0.1.0.0 · src/tensor/gather_PROOF.bend:610

import Base
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedProof

610# Input cell (o, i, r) runs the sum of (o, i, r).
611def scattered_at(+kind: Gather.Lookup, +outer: Nat, +rows: Nat, +inner: Nat, +count: Nat, +o: Nat, +i: Nat, +r: Nat,
612  +i_below: {Nat.is_lt(i, rows) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool}, -state: Array<F32> & Array<U32>) ->
613  {Gather.scattered(Gather.Plan{kind, outer, rows, inner, count}, Laws.position(rows, inner, o, i, r), state) == Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}:
614  +row = Nat.add(Nat.mul(o, rows), i)
615  +pos = Laws.position(rows, inner, o, i, r)
616  %Equal.sym(Nat, Nat.div(pos, inner), row, BatchedProof.div_exact(row, inner, r, r_below)) :
617    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, Nat.div(_, rows), Nat.mod(_, rows), Nat.mod(pos, inner), count, 0n, (0.0, state)) ==
618      Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
619  %Equal.sym(Nat, Nat.mod(pos, inner), r, BatchedProof.mod_exact(row, inner, r, r_below)) :
620    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, Nat.div(row, rows), Nat.mod(row, rows), _, count, 0n, (0.0, state)) ==
621      Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
622  %Equal.sym(Nat, Nat.div(row, rows), o, BatchedProof.div_exact(o, rows, i, i_below)) :
623    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, _, Nat.mod(row, rows), r, count, 0n, (0.0, state)) == Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
624  %Equal.sym(Nat, Nat.mod(row, rows), i, BatchedProof.mod_exact(o, rows, i, i_below)) :
625    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, _, r, count, 0n, (0.0, state)) == Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
626  {==}