Sambanova Systems, Inc.

Xiaoyan Li

Mingran Wang

Yongning Sheng

Gregory Frederick Grohoski

Mark Luttrell

A computation unit includes input lines to provide a floating-point value, a first lookup table, a second lookup table, a range detector, and an output stage. The input lines include exponent lines and mantissa lines. The first lookup table has a first address input coupled to a first subset of the input lines to provide a first output. The second lookup table has a second address input coupled to a second subset of the input lines to provide a second output. The range detector is coupled to at least some of the input lines and indicates whether the floating-point value provided on the input lines is within a specified range on a range output. The output stage is operatively coupled to the first output, the second output and the range output, to generate a function output based on the first output, the second output, and the range output.

Calculating a floating-point function using multiple lookup tables

A computation unit comprises a floating point input having X bits including a sign bit, an E bit exponent and an M bit mantissa. A first circuit is operatively coupled to receive X-N bits of the input, including e1 bits of the exponent and ml bits of the mantissa, where e1&#x2264;E, and m1&#x2264;M, to output values over a first domain of the input. A second circuit is operatively coupled to receive X-K bits of the input, including e2 bits of the exponent, e2&#x3c;e1, and m2 bits of the mantissa, m2&#x3e;m1, to output values, over a second domain of the input. A range detector is operatively coupled to the input, to indicate a range in response to a value of the input. A selector can select the output of the first circuit or of the second circuit in response to the range detector.

Computation units for functions based on lookup tables

Herein are disclosed computation units for batch normalization. A computation unit may include a first circuit to traverse a batch of input elements xhaving a first format, to produce a mean &#x3bc;in the first format and a mean &#x3bc;in a second format, the second format having more bits than the first format. The computation unit may further include a second circuit operatively coupled to the first circuit to traverse the batch of input elements xto produce a standard deviation &#x3c3; for the batch using the mean &#x3bc;in the first format. The computation unit may also include a third circuit operatively coupled to the second circuit to traverse the batch of input elements xto produce a normalized set of values yusing the mean &#x3bc;in the second format and the standard deviation &#x3c3;.

Computational units for batch normalization

A computation unit computes a function f(I). The function f(I) has a target output range over a first domain of an input I encoded using a first format. A first circuit receives the encoded input I in the first format including X bits, to add an offset C to the encoded input I to generate an offset input SI=I+C, in a second format including fewer than X bits. The offset C is equal to a difference between the first domain in f(I) and a higher precision domain of the second format for the offset input SI. A second circuit is operatively coupled to receive the offset input SI in the second format, to output a value equal to a function f(SI) to provide an encoded output value f(I).

Look-up table with input offsetting

A computation unit that comprises (i) a multiplicand vector decomposer that generates a decomposed multiplicand vector which uses a sequence of first and second concatenated multiplicand sub-elements (12CMCSE) in a lower-precision format (LPF) to represent corresponding ones of multiplicand elements in a multiplicand vector in a higher-precision format (HPF), (ii) a multiplier vector decomposer that generates a decomposed multiplier vector which uses a sequence of first and second concatenated multiplier sub-elements (12CMLSE) in the LPF to represent corresponding ones of multiplier elements in a multiplier vector in the HPF, (iii) a multiplicand tensor encoder that encodes double reads of the sequence of the 12CMCSE in a decomposed multiplicand tensor, and (iv) a product vector generator that generates a product vector containing a sequence of first and second concatenated product sub-elements by executing general matrix-matrix multiplication (GeMM) operations between the double reads of the 12CMCSE and corresponding ones of the 12CMLSE.

Computationally efficient general matrix-matrix multiplication (GeMM)

Herein are disclosed computation units for element approximation. A computation unit may include a first circuit to compute a first projection &#x3c0; of an input element xfrom a first range to a second range. In the first circuit, the input element xmay have a first format and the projected element ymay have a second format. In addition, in the first circuit, the second format may have more bits than the first format. The computation unit may further include a second circuit operatively coupled to the first circuit to produce a reduction zin the first format using the projected element yin the second format. The computation unit may also include a third circuit operatively coupled to the second circuit to compute a second projection &#x3c1; of the reduction zfrom the second range to the first range to produce an approximation w.

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San Jose, CA, United States of America

Xiaoyan Li