Performing Constant Modulo Arithmetic

A method of determining y=x mod (2m−1), where x is an n-bit binary number, y is an m-bit binary number, and n>m, the method comprising:

• receiving, at addition logic, a first m-bit binary number β and a second m-bit binary number γ;
• and
• performing, at the addition logic, a summation in dependence on the first m-bit binary number β and the second m-bit binary number γ;
• generating, at the addition logic, an addition output in dependence on the summation;
• forming, at exception logic, a determination result indicating whether all of the bits of x are 1;
• and
• operating, at output logic, on the addition output in dependence on the determination result, wherein, in response to determining that the determination result indicates that all of the bits of x are 1, a XOR operation of the addition output with the binary value 1 is performed.

A non-transitory computer readable storage medium having stored thereon computer readable instructions that, when processed at a computer system for generating a manifestation of an integrated circuit, cause the computer system to generate a manifestation of a circuit configured to determine y=x mod (2m−1), where x is an n-bit binary number, y is an m-bit binary number, and n>m, the circuit comprising:

• addition logic configured to:
• receive a first m-bit binary number β and a second m-bit binary number γ,
• perform a summation in dependence on the first m-bit binary number β and the second m-bit binary number γ, and
• generate an addition output in dependence on the summation;
• exception logic configured to form a determination result indicating whether all of the bits of x are 1;
• and
• output logic configured to operate on the addition output in dependence on the determination result received from the exception logic, wherein the output logic is configured to, if the determination result indicates that all of the bits of x are 1, perform a XOR operation of the addition output with the binary value 1.