Method and apparatus for computing an approximation to the reciprocal of a floating point number in IEEE format

An apparatus for computing an approximation to the reciprocal of a floating point number x comprising:

• a first register storing the number x comprising a 1-bit sign, an e-bit exponent, and an f-bit fraction;
• a second register storing a mask m mask comprised of one zero bit corresponding to the sign bit of x, e one bits corresponding to the exponent bits of x, k zero bits corresponding to the first k fraction bits of x and f−k one bits corresponding to the remaining f−k fraction bits of x;
• a bitwise exclusive OR function combining the number x from the first register and the mask m from the second register to produce a bitwise exclusive OR output {circumflex over (x)}=xΛm;
• an index extractor extracting the first k bits of the fraction of x as an index I;
• a lookup table with 2k entries responding to the index i and outputting an entry T(i) as the ith entry of the table;
• and
• a multiplier computing the product {circumflex over (x)}×T(i) with floating point arithmetic an output r=T(i)×{circumflex over (x)} as an estimate of the reciprocal of x with 2×k+3 good bits.