64bit processing - Why?
64bit processing - Why?
- Subject: 64bit processing - Why?
- From: Ethan Funk <email@hidden>
- Date: Thu, 30 Jul 2009 16:38:26 -0700
First off, I would like to weight in on this discussion by pointing
out that the sign bit has the same effect on the dynamic range of a
binary number as any of the other bits. The sign bit allows the
number to handle positive AND negative range - this doubles the
unsigned scalar range, adding 6 dB in the log scale, just like any
other bit.
Second, I'd like to know who (other than people from marketing
departments) need audio dynamic ranges in excess of 144 dB. I am sure
no one from this list has ever experience 144 dB of acoustic dynamic
range. If you would like to experience this your self, find an audio
amp that has more than 144 dB of dynamic range (good luck), hook it up
to some speakers and turn the volume up with no audio input until you
hear some hiss from the amp. You may need to get close to the speaker
for this. Step back from the speakers a bit until you can't hear the
hiss any more. If the room you are in is very, very quiet, you are
now experiencing 0 dBA of sound pressure - just less than the least
significant bit in a binary number representing audio data.
Now send a 1 to 2 kHz tone into the amplifier. It should be 1 to 2
kHz because this is the frequency range where your ears have the
widest dynamic range. Slowly turn up the tone level going into the
amplifier until your ears hurt. You are now experiencing
approximately 100 dBA of sound pressure. Raise the tone level another
20 dB. Now, at the 120 dBA of sound pressure your are experiencing,
you have permanently damage your hearing, and your neighbors are
calling the FAA because they think a jet plane is landing on their
street. But wait, you still have another 24 dB to go before a 32 bit
single precision binary float number runs out of range. So if by some
amazing chance, you have not yet destroyed your speakers and your
amplifier is not yet clipping, turn it up another 24 dB... Yes, 24 dB
above where you damaged your hearing. Once you get to 144 dBA of
sound pressure, that's 251 time more power than the damaging 120 dBA,
I would imaging blood would be drip from your punctured ear drums and
you would be signing up for a course in ASL (American Sign Language).
And remember, this was with the amplifier turned up high enough that
you could almost hear the noise with no audio input - the level just
below where you would actually hear the least significant bit.
The folks at Apple appear to have understood the human limits when
they choose single precision floats. Why waste processor resources
with doubles when it would require the humans to evolve a great deal,
not the machines, for the benefit to be appreciated.
Ethan...
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