Residue number system in a photonic matrix accelerator

A photonic linear processor comprising:

• an optical transmitter comprising at least one light source and at least one amplitude modulator, the optical transmitter configured to:
• provide a first value associated with a first modulus;
• and
• provide a second value associated with the first modulus;
• at least one phase shifter configured to shift, by each of the first value and the second value, a phase of a first light signal;
• and
• at least one coherent receiver configured to:
• detect the shifted phase of the first light signal;
• and
• output the detected phase of the first light signal as representing a first residue of a sum of the first value and the second value, the first residue being associated with the first modulus,
• wherein the photonic linear processor is further configured to:
• represent a number using a combination of a residue number system (RNS) and a positional number system (PNS), comprising:
• representing the number using a plurality of digits of the PNS;
• and
• representing each digit of the plurality of digits using a plurality of residues,
• wherein each residue of the plurality of residues represents a remainder of a digit of the plurality of digits with respect to a modulus of a plurality of moduli of the RNS;
• and
• obtain at least one of the first value and the second value using at least one residue of the plurality of residues;
• detect an overflow of a first digit of the plurality of digits;
• and
• propagate the overflow from the first digit to a second digit,
• wherein the second digit has a higher order than the first digit,
• wherein:
• the plurality of moduli comprises a first set of moduli;
• the first set of moduli is configured to represent each digit of the plurality of digits;
• the plurality of moduli further comprises a second set of moduli;
• each modulus of the second set of moduli is different than each modulus of the first set of moduli;
• the second set of moduli includes the first modulus;
• and
• detecting the overflow of the first digit comprises detecting the overflow of the first digit using the outputted detected phase of the light signal representing the residue of the sum of the first value and the second value, associated with the first modulus.

A method of performing summation of values using phases of light, the method comprising:

• providing a first value associated with a first modulus;
• providing a second value associated with the first modulus;
• using at least one phase shifter, shifting, by each of the first value and the second value, a phase of a light signal;
• using at least one coherent receiver, detecting the shifted phase of the light signal;
• outputting the detected phase of the light signal as representing a first residue of a sum of the first value and the second value, the first residue being associated with the first modulus;
• providing a first vector comprising a first ordered sequence of values;
• providing a second vector comprising a second ordered sequence of values of equal length as the first ordered sequence of values;
• representing the first vector as a tuple of residue vectors, each residue vector of the tuple of residue vectors comprising a respective third ordered sequence of values of equal length as the first ordered sequence of values and each residue vector being associated with a respective modulus of a plurality of moduli of a residue number system (RNS), wherein the plurality of moduli includes the first modulus;
• for each residue vector of the tuple of residue vectors:
• multiplying corresponding values of the second ordered sequence of values and the respective third ordered sequence of values to produce a plurality of products, wherein the plurality of products for a first residue vector of the plurality of residue vectors includes the first value and the second value;
• using at least one phase shifter, shifting, by each product of the plurality products, a phase of a light signal, wherein a light signal for the first residue vector comprises the first light signal;
• and
• using at least one coherent receiver, detecting the shifted phase of each light signal;
• and
• outputting the detected phases of each light signal as a tuple of residues, the tuple of residues representing a dot product of the first vector and the second vector, wherein one residue of the tuple comprises the first residue of the sum of the first value and the second value associated with the first modulus.

A method of performing summation of values using phases of light, the method comprising:

• providing a first value associated with a first modulus;
• providing a second value associated with the first modulus;
• using at least one phase shifter, shifting, by each of the first value and the second value, a phase of a light signal;
• using at least one coherent receiver, detecting the shifted phase of the light signal;
• and
• outputting the detected phase of the light signal as representing a first residue of a sum of the first value and the second value, the first residue being associated with the first modulus;
• representing a number using a combination of a residue number system (RNS) and a positional number system (PNS), comprising:
• representing the number using a plurality of digits of the PNS;
• and
• representing each digit of the plurality of digits using a plurality of residues,
• wherein each residue of the plurality of residues represents a remainder of a digit of the plurality of digits with respect to a modulus of a plurality of moduli of the RNS;
• obtaining at least one of the first value and the second value using at least one residue of the plurality of residues;
• detecting an overflow of a first digit of the plurality of digits;
• and
• propagating the overflow from the first digit to a second digit, wherein the second digit has a higher order than the first digit,
• wherein:
• the plurality of moduli comprises a first set of moduli;
• the first set of moduli is configured to represent each digit of the plurality of digits;
• the plurality of moduli further comprises a second set of moduli;
• each modulus of the second set of moduli is different than each modulus of the first set of moduli;
• the second set of moduli includes the first modulus;
• and
• detecting the overflow of the first digit comprises detecting the overflow of the first digit using the outputted detected phase of the light signal representing the residue of the sum of the first value and the second value, associated with the first modulus.