4 ms·

At FP2, you are probably better off with {-1, 0, 1, NaN} (sign+mantissa) rather than sign/exponent. You basically bit pack. FP3 gives you sign, 1x "exponent",

by kortex 4y ago

At FP2, you are probably better off with {-1, 0, 1, NaN} (sign+mantissa) rather than sign/exponent. You basically bit pack. FP3 gives you sign, 1x "exponent", 1x mantissa, so still kinda bit packing. I could see FP4 with sign, 1x exponent, 2x mantissa. Exponent would really just be a 4x multiplier, giving +/-0,1,2,3,4,8,12 Or invert all those, so you are expressing common fractions on 0..1

dragontamer 4y ago
Real life has the E3 series: 1, 2.2, 4.7, and then 10, 22, 47, 100, 220, 470, 1000, etc. Etc. EEs would recognize these values to be the Preferred Resistors values for projects (though more commonly the E6 series is used in projects, the E3 and E1 values are preferred) That's 3 values per decade, which is slightly more dispersed than a FP4 that consists of 1 sign + 3 exponent + 0 (implicit mantissa 1 bit). Or the values -128, -64, -32, -16, -8, -4, -2, -1, 1, 2, ... 128. Maybe we can take -128 and call that zero instead, cause zero is useful. -------- Given how even E3 is still useful in real world electrical engineering problems, I'm more inclined to allocate more bits to the exponent than the mantissa.
- ben_w 4y ago
  > Real life has the E3 series: 1, 2.2, 4.7, and then 10, 22, 47, 100, 220, 470, 1000, etc. Etc. Took me until today to realise that sequence is a rounded version of 10^(n/3) for integer n.
  - simcop2387 4y ago
    Almost so, there are some manual adjustments to help with overlap from tolerances at various places, but that pure math layout of it would be where you'd probably want to do it for ml
- stkdump 4y ago
  E3 is only relevant to decimal numbers. I don't see how computing can benefit from it, unless base conversion for human interaction is a particularly large part of the problem. And there is a reason why stuff like BCD isn't used anywhere near anything resembling high performance computing: it's practically never worth it.
Dylan16807 4y ago
If you're going to bother doing floats you should probably make them balanced around 1. And exponent seems to be much more important for these small sizes. The first paper that shows up for FP4 almost has negative mantissa bits. Their encoding has 0, 1/64, 1/16, 1/4, 1, 4, 16, 64.

by kortex 4y ago

dragontamer 4y ago

Real life has the E3 series: 1, 2.2, 4.7, and then 10, 22, 47, 100, 220, 470, 1000, etc. Etc. EEs would recognize these values to be the Preferred Resistors values for projects (though more commonly the E6 series is used in projects, the E3 and E1 values are preferred) That's 3 values per decade, which is slightly more dispersed than a FP4 that consists of 1 sign + 3 exponent + 0 (implicit mantissa 1 bit). Or the values -128, -64, -32, -16, -8, -4, -2, -1, 1, 2, ... 128. Maybe we can take -128 and call that zero instead, cause zero is useful. -------- Given how even E3 is still useful in real world electrical engineering problems, I'm more inclined to allocate more bits to the exponent than the mantissa.

ben_w 4y ago
> Real life has the E3 series: 1, 2.2, 4.7, and then 10, 22, 47, 100, 220, 470, 1000, etc. Etc. Took me until today to realise that sequence is a rounded version of 10^(n/3) for integer n.
- simcop2387 4y ago
  Almost so, there are some manual adjustments to help with overlap from tolerances at various places, but that pure math layout of it would be where you'd probably want to do it for ml
stkdump 4y ago
E3 is only relevant to decimal numbers. I don't see how computing can benefit from it, unless base conversion for human interaction is a particularly large part of the problem. And there is a reason why stuff like BCD isn't used anywhere near anything resembling high performance computing: it's practically never worth it.

Dylan16807 4y ago

If you're going to bother doing floats you should probably make them balanced around 1. And exponent seems to be much more important for these small sizes. The first paper that shows up for FP4 almost has negative mantissa bits. Their encoding has 0, 1/64, 1/16, 1/4, 1, 4, 16, 64.