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More floating point alternatives

53 points · 51 comments · vismit2000

klodolph · 1790043291 · focus · HN ↗
Worth mentioning is storing the logarithm of the number.
Seen it used in a couple places. Logarithmic depth buffer is one. Yamaha DX7 is another.
1. mtklein · 1790043950 · focus · HN ↗
  That's kind of exactly what floats are. You store the log2 of the number, a bit for its sign, and in what remaining bits you have left some fixed-point scaling between adjacent powers.
  1. mdspan · 1790049855 · focus · HN ↗
    I think they mean storing just an exponent instead of an exponent + mantissa. Makes multiplication much easier to implement.
  2. em3rgent0rdr · 1790050683 · focus · HN ↗
    No, that is not what floats are. A logarithmic number system literally just stores the logarithm of a number (and a sign bit) and manipulates it as a logarithm. The significand is 1, always. So multiplication & division are simply addition & subtraction, respectively. But this simplification for multiplication, division, roots, and powers is counterbalanced by more complex addition and subtraction.[1]
    [1] <a href="https://en.wikipedia.org/wiki/Logarithmic_number_system" rel="nofollow">https://en.wikipedia.org/wiki/Logarithmic_number_system
  3. pkaye · 1790062947 · focus · HN ↗
    Floats are actually rational numbers with denominators of power of 2.
    <a href="https://en.wikipedia.org/wiki/Dyadic_rational#In_computing" rel="nofollow">https://en.wikipedia.org/wiki/Dyadic_rational#In_computing

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