3 ms·

Your kernel seems to be incorrect for 1.75 * 2.5. From paper we have 1.75 == (1+0.75)*2^0 for 2.5 == (1+0.25)*2^1 so result is (1+0.75+0.25+2^-4)*2^1 == 4.125

• raluk 2y ago
  Extra. I am not sure if that is clear from paper, but in example of 1.75 * 2.5 we can represent 1.75 also as (1-0.125) * 2. This gives good aproximations for numbers that are close but less than power of 2. This way abs(a*b) in (1+a)*(1+b) is allways small and strictly less than 0.25. Another example, if we have for example 1.9 * 1.9 then we need to account for overflow in (0.9 + 0.9) and this seems to induce similar overhead as expressing numbers as (1-0.05)*2 .