nickva commented on issue #4650:
URL: https://github.com/apache/couchdb/issues/4650#issuecomment-1603205176
To go with float base-2 exponential binning (to capture as much range as
possible in each counters array) threw this together:
```erlang
-define(EXPONENT_BIAS, 1023).
-define(MANTISSA_BITS, 52).
-define(EXPONENT_BITS, 11).
bin_index(Val, Scale) when is_integer(Val) ->
bin_index(float(Val), Scale);
bin_index(Val, Scale) when is_float(Val), is_integer(Scale), Scale >=0,
Scale < ?MANTISSA_BITS ->
{Exponent, Mantissa} = exp(Val),
ExponentBits = Exponent bsl Scale,
MantissaBits = Mantissa bsr (?MANTISSA_BITS - Scale),
ExponentBits bor MantissaBits.
exp(Val) when is_float(Val) ->
<<0:1, Exponent:?EXPONENT_BITS, Mantissa:?MANTISSA_BITS>> =
<<Val/float>>,
{Exponent - ?EXPONENT_BIAS, Mantissa}.
```
At first thought of using just the exponent part directly, however the bins
are spaced out a bit too much. So then used the idea from
https://github.com/newrelic-experimental/newrelic-sketch-java/tree/main/src/main/java/com/newrelic/nrsketch/indexer
to add some more precision from the mantissa part into the bin index.
First exponent is shifted a bit "to make some room" for the extra bits
`Exponent bsl Scale`. `eeee bsl 2` => `eeee00`. Now we have a place for the 2
extra precision bits.
Then, we shift the mantissa bits to the right and leave only its two top
most significant bits. For example, `mmmmmm... bsr (52 -2)` => `0000mm`. And
finally, combine it by OR-ing into the shifted exponent part to get the index
`eeee00 bor 0000mm` => `eeeemm`.
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