[v4] ALSA: usb-audio: Fix max packet size calculation for USB audio

Rounding must take place before multiplication with the frame size, since 
each packet contains a whole number of frames.

We must also properly consider the data interval, as a larger data 
interval will result in larger packets, which, depending on the sampling 
frequency, can result in packet sizes that are less than integral 
multiples of the packet size for a lower data interval.

Detailed explanation and rationale:

The code before this commit had the following expression on line 613 to 
calculate the maximum isochronous packet size:

	maxsize = ((ep->freqmax + 0xffff) * (frame_bits >> 3)) 
			>> (16 - ep->datainterval);

Here, ep->freqmax is the maximum assumed sample frequency, calculated from the
nominal sample frequency plus 25%. It is ultimately derived from ep->freqn,
which is in the units of frames per packet, from get_usb_full_speed_rate()
or usb_high_speed_rate(), as applicable, in Q16.16 format.

The expression essentially adds the Q16.16 equivalent of 0.999... (i.e.  
the largest number less than one) to the sample rate, in order to get a 
rate whose integer part is rounded up from the fractional value. The 
multiplication with (frame_bits >> 3) yields the number of bytes in a 
packet, and the (16 >> ep->datainterval) then converts it from Q16.16 back 
to an integer, taking into consideration the bDataInterval field of the 
endpoint descriptor (which describes how often isochronous packets are 
transmitted relative to the (micro)frame rate (125us or 1ms, for USB high 
speed and full speed, respectively)). For this discussion we will initially
assume a bDataInterval of 0, so the second line of the expression just
converts the Q16.16 value to an integer.

In order to illustrate the problem, we will set frame_bits 64, which
corresponds to a frame size of 8 bytes.

The problem here is twofold. First, the rounding operation consists
of the addition of 0x0.ffff and subsequent conversion to integer, but as the
expression stands, the conversion to integer is done after multiplication
with the frame size, rather than before. This results in the resulting
maxsize becoming too large.

Let's take an example. We have a sample rate of 96 kHz, so our ep->freqn is
0xc0000 (see usb_high_speed_rate()). Add 25% (line 612) and we get 0xf0000.
The calculated maxsize is then ((0xf0000 + 0x0ffff) * 8) >> 16 = 127 .
However, if we do the number of bytes calculation in a less obscure way it's
more apparent what the true corresponding packet size is: we get
ceil(96000 * 1.25 / 8000) * 8 = 120, where 1.25 is the 25% from line 612, 
and the 8000 is the number of isochronous packets per second on a high 
speed USB connection (125 us microframe interval).

This is fixed by performing the complete rounding operation prior to
multiplication with the frame rate.

The second problem is that when considering the ep->datainterval, this 
must be done before rounding, in order to take the advantage of the fact 
that if the number of bytes per packet is not an integer, the resulting 
rounded-up integer is not necessarily a factor of two when the data 
interval is increased by the same factor.

For instance, assuming a freqency of 41 kHz, the resulting 
bytes-per-packet value for USB high speed is 41 kHz / 8000 = 5.125, or 
0x52000 in Q16.16 format. With a data interval of 1 (ep->datainterval = 0),
this means that 6 frames per packet are needed, whereas with a data 
interval of 2 we need 10.25, i.e. 11 frames needed.

Rephrasing the maxsize expression to:

	maxsize = (((ep->freqmax << ep->datainterval) + 0xffff) >> 16) *
			 (frame_bits >> 3);

for the above 96 kHz example we instead get 
((0xf0000 + 0xffff) >> 16) * 8 = 120 which is the correct value.

We can also do the calculation with a non-integer sample rate which is when
rounding comes into effect: say we have 44.1 kHz (resulting ep->freqn =
0x58333, and resulting ep->freqmax 0x58333 * 1.25 = 0x6e3ff (rounded down)):

Original maxsize = ((0x6e3ff + 0xffff) * 8) << 16 = 63 (63.124.. rounded down)
True maxsize = ceil(44100 * 1.25 / 8000) * 8 = 7 * 8 = 56
New maxsize = ((0x6e3ff + 0xffff) >> 16) * 8 = 7 * 8 = 56

This is also corroborated by the wMaxPacketSize check on line 616. Assume
that wMaxPacketSize = 104, with ep->maxpacksize then having the same value.
As 104 < 127, we get maxsize = 104. ep->freqmax is then recalculated to
(104 / 8) << 16 = 0xd0000 . Putting that rate into the original maxsize
calculation yields a maxsize of ((0xd0000 + 0xffff) * 8) >> 16 = 111
(with decimals 111.99988). Clearly, we should get back the 104 here,
which we would with the new expression: ((0xd0000 + 0xffff) >> 16) * 8 = 104 .

(The error has not been a problem because it only results in maxsize being 
a bit too big which just wastes a couple of bytes, either as a result of 
the first maxsize calculation, or because the resulting calculation will 
hit the wMaxPacketSize value before the packet is too big, resulting in 
fixing the size to wMaxPacketSize even though the packet is actually not 
too long.)

Tested with an Edirol UA-5 both at 44.1 kHz and 96 kHz.

Signed-off-by: Ricard Wanderlof <ricardw@axis.com>
---
V2: Added tested device to commit message. No other changes.
V3: Updated after input from Clemens. Since the expression is now getting
    rather convoluted, added a description in the comments in the code.
    New commit message to reflect the new version. Updated rationale below.
V4: Moved most of the rationale (slightly rephrased) to the commit message
    as suggested by Takashi.

Although the error is tolerable because it just wastes a couple of bytes 
in each packet, however, I'm working on a quirk for a device which stuffs 
an extra four (non sample) bytes into each isochronous packet, and that 
means that the maxsize calculation must take this into account. During 
this work it became obvious that there was something wrong with the 
maxsize calculation, as the resulting packet size when wMaxPacketSize was 
hit did not correspond to the packet size which triggered the if statement 
to start with.

Since this seems to me an obvious (after looking at it for a bit...) bug I'm
submitting this as a separate patch rather than part of an upcoming patch
series.

 sound/usb/endpoint.c |   19 +++++++++++++++++--
 1 file changed, 17 insertions(+), 2 deletions(-)

[v4] ALSA: usb-audio: Fix max packet size calculation for USB audio

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