A multiplication circuit is provided, the circuit is configured to perform a multiplication operation on two pieces of data: A and B, and includes: an addition subcircuit configured to obtain logarithmic field data a and b that corresponding to A and B, and perform an addition operation on a and b to obtain c, where c includes an integral part and a fractional part; an exponentiation operation subcircuit configured to perform an exponentiation operation in which a base is 2 and an exponent is the fractional part of c, to obtain an exponentiation operation result; a shift subcircuit configured to shift the exponentiation operation result based on the integral part of c to obtain a shift result; and an output subcircuit, configured to output a product of A and B based on signs of a and b and with reference to the shift result.

Low precision computers can be efficient at finding possible answers to search problems. However, sometimes the task demands finding better answers than a single low precision search. A computer system augments low precision computing with a small amount of high precision computing, to improve search quality with little additional computing.

A processor or other device, such as a programmable and/or massively parallel processor or other device, includes processing elements designed to perform arithmetic operations (possibly but not necessarily including, for example, one or more of addition, multiplication, subtraction, and division) on numerical values of low precision but high dynamic range (LPHDR arithmetic). Such a processor or other device may, for example, be implemented on a single chip. Whether or not implemented on a single chip, the number of LPHDR arithmetic elements in the processor or other device in certain embodiments of the present invention significantly exceeds (e.g., by at least 20 more than three times) the number of arithmetic elements, if any, in the processor or other device which are designed to perform high dynamic range arithmetic of traditional precision (such as 32 bit or 64 bit floating point arithmetic).

This application relates to apparatus and methods for the multiplication of signals. A multiplication circuit (100) has first and second time-encoding modulators (103a, 103b) configured to receive first and second combined signals (S.sub.C1, S.sub.C2) respectively, and generate respective first and second PWM signals (S.sub.PWM1, S.sub.PWM2), each with a cycle frequency that depends substantially on the square of the value of the input combined signal. The first combined signal (S.sub.C1) corresponds to a sum of a first and second input signals (S.sub.1, S.sub.2) and the second combined signal (S.sub.C2) corresponds to the difference between the first and second input signals (S.sub.1, S.sub.2). First and second time-decoding converters (104a, 104b) receive the first and second PWM signals and provide respective first and count values (D.sub.1, D.sub.2) based on a parameter related to the frequency of the respective first or second PWM signal. A subtractor (105) determine a difference between the first and second count values (D.sub.1, D.sub.2) and provides an output signal (D.sub.OUT) based on this difference.

In one embodiment, a method includes receiving a request for an operation to be performed; determining that the operation is associated with a machine-learning algorithm, and in response, route the operation to a computing circuit; performing, at the computing circuit, the operation, including: determining a linear domain product of a first log-domain number and a second log-domain number associated with the operation based on a summation of the first log-domain number and the second log-domain number and output a third log-domain number approximating the linear domain product of the first log-domain number and the second log-domain number; converting the third log-domain number to a first linear-domain number; summing the first linear-domain number and a second linear-domain number associated with the operation, and output a third linear-domain number as the summed result.

In one embodiment, a method includes receiving a request for an operation to be performed; determining that the operation is associated with a machine-learning algorithm, and in response, route the operation to a computing circuit; performing, at the computing circuit, the operation, including: determining a linear domain product of a first log-domain number and a second log-domain number associated with the operation based on a summation of the first log-domain number and the second log-domain number and output a third log-domain number approximating the linear domain product of the first log-domain number and the second log-domain number; converting the third log-domain number to a first linear-domain number; summing the first linear-domain number and a second linear-domain number associated with the operation, and output a third linear-domain number as the summed result.

A processor or other device, such as a programmable and/or massively parallel processor or other device, includes processing elements designed to perform arithmetic operations (possibly but not necessarily including, for example, one or more of addition, multiplication, subtraction, and division) on numerical values of low precision but high dynamic range (LPHDR arithmetic). Such a processor or other device may, for example, be implemented on a single chip. Whether or not implemented on a single chip, the number of LPHDR arithmetic elements in the processor or other device in certain embodiments of the present invention significantly exceeds (e.g., by at least 20 more than three times) the number of arithmetic elements, if any, in the processor or other device which are designed to perform high dynamic range arithmetic of traditional precision (such as 32 bit or 64 bit floating point arithmetic).

An arithmetic logic unit, comprising an addition unit for determining a sum of a first input and a second input; and a logarithmic addition unit for determining an output using the sum and a third input. The output is a multiply-accumulate output represented in a logarithmic domain when the first, second and third inputs are represented in the logarithmic domain.

In one embodiment, an apparatus comprises a multiplier circuit to: identify a plurality of partial products associated with a multiply operation; partition the plurality of partial products into a first set of partial products, a second set of partial products, and a third set of partial products; determine whether the multiply operation is associated with a square operation; upon a determination that the multiply operation is associated with the square operation, compute a result based on the first set of partial products and the third set of partial products; and upon a determination that the multiply operation is not associated with the square operation, compute the result based on the first set of partial products, the second set of partial products, and the third set of partial products.

This application relates to apparatus and methods for the multiplication of signals. A multiplication circuit (100) has first and second time-encoding modulators (103a, 103b) configured to receive first and second combined signals (S.sub.C1, S.sub.C2) respectively, and generate respective first and second PWM signals (S.sub.PWM1, S.sub.PWM2), each with a cycle frequency that depends substantially on the square of the value of the input combined signal. The first combined signal (S.sub.C1) corresponds to a sum of a first and second input signals (S.sub.1, S.sub.2) and the second combined signal (S.sub.C2) corresponds to the difference between the first and second input signals (S.sub.1, S.sub.2). First and second time-decoding converters (104a, 104b) receive the first and second PWM signals and provide respective first and count values (D.sub.1, D.sub.2) based on a parameter related to the frequency of the respective first or second PWM signal. A subtractor (105) determine a difference between the first and second count values (D.sub.1, D.sub.2) and provides an output signal (D.sub.OUT) based on this difference.