WOW... I just learned something important! So, my whole point here was that I had the idea that DAWs like Ardour support 32-bit considering only values from -1 to 1. But that is just wrong!

I just learned you can put a sound file with values in the hundreds / thousands in 32 bit float, load them into your DAW, and scale it down.

I tried it by creating a sine wave in Pd with values from -100 to 100, exported as 32-bit float with writesf~, loaded into soundforge, then scaled it down 40 dB, and the sine wave was there!

So yeah, Pd's audio resolution is the same as DAW which say they handle 32-bit float sound files. My whole issue was that Pd had a different way of dealing with 32-bit float, but not at all. In Principle, other softwares out there also deal with 32-bit float outside the boundaries of -1 to 1!!!

That just answers my question then... once and for all and for good.

I guess the discussion I ended up promoting is a parallel issue... let me rephrase it then. 

Regarding 24 bit DAC converters in sound cards, the 24 bits in there are just for values from -1 to 1, right?

If so, then 32 bit float isn't really "8 more bits". And you've been also saying 24 bit converters are fixed, not float. So there's a weird relationship between this conversion from 32 bit float files to the soundcard.

But then, I guess I'm happy with all I've learned so far.

thanks

2015-04-23 13:26 GMT-03:00 Jamie Bullock <jamie@jamiebullock.com>:

On 22 April 2015 at 19:44:26, William Huston (williamahuston@gmail.com) wrote:

On Wednesday, April 22, 2015, Jamie Bullock <jamie@jamiebullock.com> wrote:
>
> Pd is 32-bit *floating point*, so you have 32-bit resolution between -1 and 1.

I don't think that's right.

The range of a single precision floating point number is from

-3.4028234 × 10E38 to 3.4028234 × 10E38 (not from -1 to 1)

True, but I didn’t say the range of 32-bit float was -1 to 1!

There are only 23 bits of precision for the mantissa + 1 for sign in a single precision float.

Also true, but when I said “resolution” I didn’t mean “precision”. Because the exponent can be negative, resolution scales dynamically from 1..0 according to the value of the exponent, whilst precision stays fixed according to the number of bits in the mantissa. Thus for very small values the resolution (or quantisation step size) is far finer than can be represented with the mantissa alone. 

What I was trying to put across (poorly!) in my original reply is that unlike fixed point where for lower order values fewer bits are available in the binary representation, with floating point, just because e.g. -1..1 is a smaller range than -3.4 x 10E38..3.4 x 10E38 it doesn’t imply “fewer are bits available”, e.g.

Sign Exponent Mantissa

0 01111110   11111111111111111111111 -> 0.99999994

0 00000001 11111111111111111111111 -> 2.3509886E-38

1 01000000        0000000000000000000000 -> -1.0842022E-19

1              011111110        0000000000000000000000 -> -1.0

Strictly speaking, I guess only 31 bits “count” in the range -1..1 due to a maximum of 7-bits being significant in the exponent.

best,

Jamie