math_checked_word.bend source

math_checked_word.bend on the hub · documented module

# Exact overflow-checked multiplication for metadata. Each Horner step starts# below word_max and forms at most 3*word_max, safely below the native Nat cap.# The loop has exactly 32 bit steps and never touches tensor payloads.import Baseimport ./machine_limits.bend as Machinedef bounded_result(valid: Bool,value: Nat) -> Maybe<&2,Nat>:  match valid:    case False{}: None{}    case True{}: Some{value}def bounded(+value: Nat,limit: Nat) -> Maybe<&2,Nat>:  bounded_result(Nat.is_le(value,limit),value)def multiply_step(bit: Bool,right: Nat,previous: Maybe<&2,Nat>,limit: Nat) -> Maybe<&2,Nat>:  match previous:    case None{}: None{}    case Some{value}: bounded(Nat.add(Nat.double(value),Bool.pick(Nat,bit,right,0n)),limit)def multiply_bits(width: Nat,bits: Word(width),+right: Nat,+limit: Nat) -> Maybe<&2,Nat>:  match width bits:    case 0n WNil{}: Some{0n}    case 1n+rest WCon{bit,tail}: multiply_step(bit,right,multiply_bits(rest,tail,right,limit),limit)def encoded(result: Maybe<&2,Nat>) -> Maybe<&2,U32>:  match result:    case None{}: None{}    case Some{value}: Some{U32.from_nat(value)}def multiply_bounded(left: U32,right: U32,limit: U32) -> Maybe<&2,U32>:  U32{bits} = left  encoded(multiply_bits(32n,bits,U32.to_nat(right),U32.to_nat(limit)))# Unit products already fit a word. Shapes and contiguous strides frequently# use them; returning the operand avoids the 32-step natural Horner traversal.def multiply_right(unit: Bool,left: U32,right: U32) -> Maybe<&2,U32>:  match unit:    case True{}: Some{left}    case False{}: multiply_bounded(left,right,Machine.word_max())def multiply_left(unit: Bool,+left: U32,+right: U32) -> Maybe<&2,U32>:  match unit:    case True{}: Some{right}    case False{}: multiply_right(U32.is_eq(right,1),left,right)def multiply(+left: U32,+right: U32) -> Maybe<&2,U32>:  multiply_left(U32.is_eq(left,1),left,right)