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 <ja...@jamiebullock.com>: > > On 22 April 2015 at 19:44:26, William Huston (williamahus...@gmail.com) > wrote: > > On Wednesday, April 22, 2015, Jamie Bullock <ja...@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 >
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