Computer scientists are a demanding bunch. For them, it’s not enough to get the right answer to a problem — the goal, almost always, is to get the answer as efficiently as possible. Take the act of ...

Once the domain of esoteric scientific and business computing, floating point calculations are now practically everywhere. From video games to large language models and kin, it would seem that a ...

Ars Technica has been separating the signal from the noise for over 25 years. With our unique combination of technical savvy and wide-ranging interest in the technological arts and sciences, Ars is ...

As defined by the IEEE 754 standard, floating-point values are represented in three fields: a significand or mantissa, a sign bit for the significand and an exponent field. The exponent is a biased ...

Mathematicians love a good puzzle. Even something as abstract as multiplying matrices (two-dimensional tables of numbers) can feel like a game when you try to find the most efficient way to do it.

This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the ...