Method and processing device for numerical data quantization or numerical data de-quantization

A processing device for numerical data de-quantization, comprising:

• a memory;
• and
• processing circuitry coupled with the memory and configured to:
• extract a mantissa of a de-quantized digital representation of a numerical data that is a result of processing a first set of quantized digital representations of a first set of numbers and a second set of quantized digital representations of a second set of numbers;
• extract an exponent adjustment from the numerical data;
• obtain a combined exponent scaling factor based on a first exponent scaling factor associated with the first set of quantized digital representations and a second exponent scaling factor associated with the second set of quantized digital representations;
• obtain an unbiased exponent of the numerical data based on the combined exponent scaling factor and the exponent adjustment;
• and
• output, to the memory, the de-quantized digital representation of the numerical data, the de-quantized digital representation including
• the mantissa of the de-quantized digital representation, and
• an exponent of the de-quantized digital representation based on the unbiased exponent of the numerical data.

A method of numerical data quantization, comprising:

• determining a maximum exponent from a set of exponents of a set of digital representations of a set of numbers;
• obtaining, by processing circuitry, a set of scaled exponents based on subtraction of the maximum exponent from each one of the set of exponents;
• performing, by the processing circuitry, one of:
• obtaining a set of quantized significands based on a set of mantissas of the set of digital representations of the set of numbers and the set of scaled exponents, or
• obtaining a set of quantized mantissas based on the set of mantissas;
• outputting a set of quantized digital representations of the set of numbers, based on the set of quantized significands, or based on the set of quantized mantissas and the set of scaled exponents;
• and
• outputting a biased exponent scaling factor associated with the set of quantized digital representations based on the maximum exponent.