Low-discrepancy deterministic bit-stream processing using Sobol sequences

A device configured to process a first set of data bits encoding a first numerical value and a second set of data bits encoding a second numerical value, the device comprising:

• a counter configured to generate an output;
• a first Sobol sequence source configured to generate a first Sobol sequence based on the output of the counter;
• a second Sobol sequence source configured to generate a second Sobol sequence based on the output of the counter, wherein the second Sobol sequence source is different from the first Sobol sequence source, and wherein the first Sobol sequence source and the second Sobol sequence source are directly driven by the counter;
• a first comparator configured to generate a first bit sequence based on the first Sobol sequence and a first constant number;
• a second comparator configured to generate a second bit sequence based on the second Sobol sequence and a second constant number;
• and
• computation logic configured to:
• perform a computational operation on the first bit sequence and the second bit sequence;
• and
• produce an output bit-stream having a set of data bits indicating a result of the computational operation, wherein the data bits of the output bit-stream represent the result based on a probability that any data bit in the set of data bits of the output bit-stream is high.

A device configured to process a first set of data bits encoding a first numerical value and a second set of data bits encoding a second numerical value, the device comprising:

• a first counter;
• a second counter configured to stall based on an output of the first counter;
• a first Sobol sequence source configured to generate a first Sobol sequence based on an output of the first counter;
• a second Sobol sequence source configured to generate a second Sobol sequence based on an output of the second counter, wherein the second Sobol sequence source is different from the first Sobol sequence source;
• a first comparator configured to generate a first bit sequence based on the first Sobol sequence and a first constant number;
• a second comparator configured to generate a second bit sequence based on the second Sobol sequence and a second constant number;
• and
• computation logic configured to:
• perform a computational operation on the first bit sequence and the second bit sequence;
• and
• produce an output bit-stream having a set of data bits indicating a result of the computational operation, wherein the data bits of the output bit-stream represent the result based on a probability that any data bit in the set of data bits of the output bit-stream is high.

A method comprising:

• receiving, at a bit stream generator, a first set of data bits encoding a first numerical value and a second set of data bits encoding a second numerical value;
• generating, at the bit stream generator, bit combinations representing a first bit sequence and a second bit sequence that encode the first and second numerical values, respectively, based on a proportion of the data bits in the sequence that are high relative to the total data bits in the sequence, wherein a subset of the bit combinations pairs a data bit of the first bit sequence with multiple different data bits of the second bit sequence, wherein generating the bit combinations comprises generating the first bit sequence using a first Sobol sequence source and generating the second bit sequence using a second Sobol sequence source different from the first Sobol sequence source;
• and
• producing, by computation logic, an output bit stream by performing a computational operation on the bit combinations, wherein the data bits of the output bit stream represent a result of the computational operation based on a probability that any data bit in the output bit stream is high.

A stochastic computational unit comprising:

• a bit-stream generator configured to generate bit combinations representing a first bit sequence and a second bit sequence that encode first and second numerical values, respectively, based on a proportion of the data bits in the sequence that are high relative to the total data bits in the sequence, wherein a subset of the bit combinations pairs a data bit of the first bit sequence with multiple different data bits of the second bit sequence, wherein the first bit sequence is generated using a first Sobol sequence source, wherein the second bit sequence is generated using a second Sobol sequence source different from the first Sobol sequence source, and
• stochastic processing circuitry configured to:
• perform a computational operation on the bit combinations;
• and
• produce an output bit-stream having a set of data bits indicating a result of the computational operation, wherein the data bits of the output bit-stream represent the result based on a probability that any data bit in the set of data bits of the output bit-stream is high.