Jacob, Anushya

There is provided a hardware unit for outputting a value of frac(x), where frac(x) is defined as x - floor(x), wherein the hardware unit is configured to:receive an input floating-point number x having a mantissa (m) of bit width 'mw', an exponent (e) of bit width 'ew', a sign bit (s) and an exponent bias (bias); calculate power (x_pow) of the input floating-point number x, wherein x_pow= e-bias; compare the x_pow to (i) -1 and (ii) mw; and output the value of frac(x) ), wherein: the hardware unit is configured to output the value of frac(x), if the comparison indicates -1 ≤ x_pow <mw, by applying a mask to the input floating-point number x to generate a masked result, and renormalizing the masked result; and the hardware unit is configured to output the value of frac(x) if the comparison indicates input floating-point number x is negative and -(mw+2) <x_pow<-1, by negating the bits of the input floating-point number x, followed by steps of right shifting the negated number and rounding, wherein if the rounded value is 1, the output value of frac(x) is a value below 1, otherwise the output value of frac(x) is the rounded value.