## Binary multiplication

See this description on Wikipedia

**Authors:** Jean-Christophe Filliâtre

**Topics:** Mathematics

**Tools:** Why3

see also the index (by topic, by tool, by reference, by year)

module BinaryMultiplication use import mach.int.Int use import number.Parity use import ref.Ref let binary_mult (a b: int) requires { b >= 0 } ensures { result = a * b } = let x = ref a in let y = ref b in let z = ref 0 in while !y <> 0 do invariant { 0 <= !y } invariant { !z + !x * !y = a * b } variant { !y } if odd !y then z := !z + !x; x := 2 * !x; y := !y / 2 done; !z end

download ZIP archive

# Why3 Proof Results for Project "binary_multiplication"

## Theory "binary_multiplication.BinaryMultiplication": fully verified in 0.74 s

Obligations | Alt-Ergo (0.99.1) |

VC for binary_mult | 0.74 |