🚀 go-pugleaf

Robert is right. You have 25 bits of accuracy for any given exponent. 
 But if splitting hairs is needed, consider this.

For an exponent of zero you can resolve the range of +1.000 to +1.999, 
or the range of -1.000 to -1.999  in steps of 58E-9.  You may notice 
that the span of -0.999 to +0.999 is NOT included.

If the exponent is -1 you can resolve the range of +0.500 to +0.999 or 
-0.500 to -0.999 in steps of 29E-9.   And, yet again, there is a span in 
the middle (albeit 1/2 as large) that is not included, and again the 
resolution is 2x finer.

 From a signal processing standpoint, when two signals are present, the 
larger of the two will bias the exponent 'gain' to fit the larger of the 
two.  Basicaly what this does is cause the largest error to occur as the 
signal approaches its  maximum or minimum.  This causes the noise floor 
to track the larger of the two signals at -150dB. And, when the larger 
of the two signals diminishes, so does the noise floor along with it.

What you end up with is a dynamic 150db noise free range _from_ the 
largest signal to the noise floor.

Best regards,
Keith Larson

>
>yeah, but if you're comparing apples to apples, the 24 bit fixed-point PCM
>word has the sign bit as part of the word (with 23 other bits).  so with
>regular, vanilla-flavored floating point, there is the sign bit + 24 "other
>bits", making it 25.
>
>how else can we look at it?: 32 bit float, subtract 8 bit exponent leaving
>24 bits, add "hidden 1 bit" and you've got 25.  for a signal that peaks at +
>or - 1 (or just a hair below like + or - 0.999999), the exponent gets as
>large -1 (represented as 126) and no larger and your largest quantization
>error is -150 dB below that, not -144 as would be the case with a 24 bit
>fixed-point value.  isn't that right, Jim, or did i screw up?
>