A system performs logic simulation of a circuit design specified using a hardware description language such as Verilog. The system performs constraint solving based on an expression specified in the specification of the circuit design. The system identifies required bits for each variable in the expression. The number of required bits is less than the number of bits specified in the variable declaration. The system performs bit-level constraint solving by performing a bit operation on the set of required bits and a simplified processing of the remaining bits of the variable. Since the original circuit design is preserved with the original bit-widths for simulation, those required bits are used on the fly internally during constraint solving. Furthermore, dynamic bit reductions on arithmetic operations are performed on the fly. The system improves computational efficiency by restricting bit operations to fewer bits of variables and operators of the expression.

A multi-accumulator multiply-and-accumulate (MAC) unit can include a multiplier and a plurality of accumulators. The multiplier can be configured to multiply a given element of a corresponding column of a first matrix and a plurality of elements of a corresponding row of a second matrix to generate a plurality of corresponding partial product elements that can be accumulated by corresponding ones of the plurality of accumulators.

A cryptographic processing device for cryptographically processing data, having a memory configured to store a first operand and a second operand represented by the data to be cryptographically processed, wherein the first operand and the second operand each correspond to an indexed array of data words, and a cryptographic processor configured to determine, for cryptographically processing the data, a product of the first operand with the second operand by accumulating results of partial multiplications, each partial multiplication comprising the multiplication of a data word of the first operand with a data word of the second operand wherein the cryptographic processor is configured to perform the partial multiplications in successive blocks of partial multiplications, each block being associated with a result index range and a first operand index range and each block comprising all partial multiplications between data words of the first operand within the first operand index range with data words of the second operand such that a sum of indices of the data word of the first operand and of the data word of the second operand is within the result index range.

A system performs logic simulation of a circuit design specified using a hardware description language such as Verilog. The system performs constraint solving based on an expression specified in the specification of the circuit design. The system identifies required bits for each variable in the expression. The number of required bits is less than the number of bits specified in the variable declaration. The system performs bit-level constraint solving by performing a bit operation on the set of required bits and a simplified processing of the remaining bits of the variable. Since the original circuit design is preserved with the original bit-widths for simulation, those required bits are used on the fly internally during constraint solving. Furthermore, dynamic bit reductions on arithmetic operations are performed on the fly. The system improves computational efficiency by restricting bit operations to fewer bits of variables and operators of the expression.

A cryptographic processing device for cryptographically processing data, having a memory configured to store a first operand and a second operand represented by the data to be cryptographically processed, wherein the first operand and the second operand each correspond to an indexed array of data words, and a cryptographic processor configured to determine, for cryptographically processing the data, a product of the first operand with the second operand by accumulating results of partial multiplications, each partial multiplication comprising the multiplication of a data word of the first operand with a data word of the second operand wherein the cryptographic processor is configured to perform the partial multiplications in successive blocks of partial multiplications, each block being associated with a result index range and a first operand index range and each block comprising all partial multiplications between data words of the first operand within the first operand index range with data words of the second operand such that a sum of indices of the data word of the first operand and of the data word of the second operand is within the result index range.