Abstract: Described herein is a technique to implement an efficient floating-point n-input sum of squares operation using faithful rounding to 1 unit in the place (ULP) instead of IEEE rounding. The resulting circuitry is useful to accelerate graphics algorithms that don't require fully IEEE compliant hardware. Multipliers that are 1ulp can be significantly smaller, faster and more power efficient than IEEE rounded multipliers.

Abstract: Described herein is a generalized optimal reduction scheme for reducing an array modulo a constant. The constant modulo operation calculates a result for array of bits xi, width n modulo an odd positive integer constant d, (e.g., x[n:0] mod d). Circuitry to perform such operation can be configured to compress the array of bits xi, width n into an array of bits yi width m. The techniques described herein enable the design of optimal circuitry via iterative exploration of all potential reduction strategies that are available given the input constraints.

Abstract: The techniques described in the detailed description above enable the manufacturing of circuits with increased performance and efficiency when performing division by a constant number. One embodiment provides circuitry including an input circuit to receive an input value including a plurality of bits, a logarithmic tree coupled with the input circuit, the logarithmic tree configured to compute an array of values based on a plurality of multi-bit groups of the plurality of bits of the input value, each value in the array of values includes a modulus of a corresponding multi-bit group with respect to the constant, a binary array adder to compute a quotient of the division operation based on the array of values, the input value, and the constant, and an output circuit to output the quotient.