System and method for improved fractional binary to fractional residue converter and multipler
Methods and systems for residue number system based ALUs, processors, and other hardware provide the full range of arithmetic operations while taking advantage of the benefits of the residue numbers in certain operations.
1. A residue converter configured to convert a fractional binary value to a fractional residue value comprising:
an input register that receives a plurality of binary input digits, the plurality of binary input digits configured as a parallel binary input receiving a binary fractional value;
a modulus shift register that stores a plurality of modulus values and to output each of the plurality of modulus values in sequence;
a first plurality of digit processing units that performs one or more arithmetic operations on a plurality of binary input digits and on a sequence of modulus values, and to generate a plurality of digit values and modulus values, each digit processing unit comprising:
a modulus operand register that receives a modulus value from a prior processing stage, and configured to send a modulus value to a succeeding processing stage;
an additive operand register that receives a digit value from a prior processing stage;
a digit accumulator that stores a binary digit value;
a multiplier that multiplies the contents of said digit accumulator with the contents of said modulus operand register generating an accumulator modulus product; and
an adder that adds said accumulator modulus product with the contents of the additive operand register, and configured to send a least significant portion of the adder result to said digit accumulator, and a most significant portion of the result to a successive processing stage; and
a second plurality of digit processing units that receive digit values and modulus values from said first plurality of digit processing units, and to perform one or more modular arithmetic operations on a plurality of residue digits, each digit processing unit comprising:
a residue digit register that stores a residue digit;
a modular multiplier that receives a modulus value from an input modulus bus and a value from said residue digit register, and is sends a residue product result; and
a modular adder that receives said residue product result, and configured to receive a digit value from an input digit value bus;
wherein after a plurality of processing cycles, a fractional residue number equivalent to a binary fractional input is stored in the plurality of said residue digit registers.
2. The residue converter of claim 1 , wherein at least one said prior processing stage is said modulus shift register, and at least one said digit processing unit configured to send a digit value and a digit weight to a second plurality of digit processing units.
3. The residue converter of claim 1 , wherein the first plurality of digit processing units process numbers in binary format while the second plurality of digit processing units process digits in residue number format.