ORIGINAL: Ron Kuper [Cakewalk]

We've prepared a test project that demonstrates this behavior in a clearly audible fashion. We'll post a link as soon as we can.

Ron Kuper [Cakewalk]
Sorry for jumping into this thread so late. We've been trying to coming up with a very simple example to illustrate the benefits of 64-bit double precision mixing. I've got one now. (Thanks to Aurelio Ramos, s/w engineer at Cakewalk, for coming up the idea for how to simply demonstrate this.)

In a nutshell: if you are processing 24-bit audio, and you start mixing many tracks where some volumes are > 0dB and some volumes are < 0dB, then due to the way floating point summation is done you are susceptible to loss of accuracy in the summation.

For those of you who are C/C++ programmers, the following program demonstrates this phenomenon:


void test()
{
const double dScale24 = (double)(1 << 23);
const double dGain = 2.0;
const double dAtten = 0.5;

const int nPCM24Orig = 0x5000FF;
double dSamp = (double)nPCM24Orig / dScale24;
float fSamp = (float)dSamp;

float fSum = 0;
fSum += (float)( dGain * fSamp );
fSum += (float)( dAtten * fSamp );
fSum += (float)( -dGain * fSamp );
fSum = (float)( dGain * fSum );
int nPCM24FromFloat = (int)(fSum * dScale24 + 0.5);

double dSum = 0;
dSum += (double)( dGain * dSamp );
dSum += (double)( dAtten * dSamp );
dSum += (double)( -dGain * dSamp );
dSum = (double)( dGain * dSum );
int nPCM24FromDouble = (int)(dSum * dScale24 + 0.5);

printf("Original: %lX, FromFloat: %lX, FromDouble: %lX\n", nPCM24Orig, nPCM24FromFloat, nPCM24FromDouble);
}
The program's output is:

Original: 5000FF, FromFloat: 500100, FromDouble: 5000FF

What this program does is perform the summation (X*2 + X/2 - X*2) * 2. You can imagine it as a 3 track project with the same file on each track. Track 1's gain is +6dB. Track 2's gain is -6dB. Track 3's gain is also +6dB but the track's phase is flipped. All 3 tracks are bused into a bus whose gain is +6dB. The answer should of course be X, i.e., the signal produced on the bus output should be the same as the track data but at unity gain.

What the program shows is if X is a 24-bit PCM sample, and the math is done using floats, the result is *not* X. The least significant bit is lost. If the gain adjustments are more dramatic, or more gain stages are used, then more bits can be lost.

We've prepared a test project that demonstrates this behavior in a clearly audible fashion. We'll post a link as soon as we can.

Using my abacus to translate the C++ hexidecimal into MHz, I've determined that Sonar 5 will sound 20 to 40 percent better.

LOL Kylen.. All of this math needs a break (unfortunately I love the math stuff as much as a good sounding mix - they are intrisictly related)

you've taken orange sunshine

ORIGINAL: Skyline In The Office
So...... if i sum up for my own benefit: for the best fidelity in S5P (end product being an audio CD or MP3) I should record at 44.1 kHz at 24bit with the 64 bit precision box ticked, yes?