Floating-point logarithmic number system scaling system for machine learning

A system comprising:

• an integrated circuit including a hardware inexact floating-point logarithmic number system (FPLNS) multiplier configured to perform FPLNS functions, the integrated circuit configured to:
• access registers containing a first floating-point binary value and a first logarithmic binary value of the first floating-point binary value, each of the first floating-point binary value and the first logarithmic binary value being in an FPLNS data format, the first floating-point binary value in the FPLNS format including a sign bit followed by exponent bits, the exponent bits followed by mantissa bits;
• access registers containing a second floating-point binary value and a second logarithmic binary value of the second floating-point binary value, each of the second floating-point binary value and the second logarithmic binary value being in an FPLNS data format, the second floating-point binary value in the FPLNS format;
• multiplying, by the FPLNS multiplier, the first floating-point binary value and the second floating-point binary value, the FPLNS multiplier configured to:
• add, by the FPLNS multiplier, the first logarithmic binary value to the second logarithmic binary value to form a first logarithmic sum,
• shift a bias constant by a number of bits of the mantissa of the first floating-point binary value to form a first shifted bias value,
• subtract a correction factor from the first shifted bias value to form a first corrected bias value, and
• subtract the first corrected bias value from the first logarithmic sum to form a first result;
• and
• the integrated circuit being further configured to perform an antilogarithm on the first result to generate a multiplication result of the multiplication of the first floating-point binary value and the second floating-point binary value.