<title>Combined unsigned and two's complement saturating multipliers</title>

Integer multipliers with overflow detection

“…It also works well for both array and tree multipliers and does not depend on the internal architecture of the simplified multiplier. This paper is an extension of our research presented in [8] and [9].…”

“…Recently, several techniques for overflow detection have been proposed to eliminate the need to compute all 2n bits of the product [6], [7], [8], [9], [10], [11]. Instead, they compute approximately n least significant product bits and have overflow detection logic that executes in parallel with the multiplication.…”

“…In [8], methods are presented that allow a single multiplier to perform both unsigned and two's complement multiplication with overflow detection and saturation. The overflow detection methods presented in [8] work well for array multipliers, but can increase the worst-case delay path of tree multipliers since they have linear delay.…”

“…The overflow detection methods presented in [8] work well for array multipliers, but can increase the worst-case delay path of tree multipliers since they have linear delay. In [9], overflow detection methods that have logarithmic delay and work well for combined unsigned and two's complement tree multipliers are presented.…”

On the Complexity of Fixed-Size Bit-Vector Logics with Binary Encoded Bit-Width

“…We show that the set of these benchmarks, with b ∈ N, is bit-width bounded, and therefore is in NP. This problem checks that a certain (unsigned) overflow detection unit, defined in [19], gives the same result as the following condition: if the b/2 most significant bits of the multiplicands are zero, then no overflow occurs. It requires 2 · (b − 2) variables and a fixed number of constants to formalize the overflow detection unit, as detailed in [19].…”