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>
Signed-off-by: Takashi Iwai <tiwai@suse.de>

sound/usb/endpoint.c

@@ -610,8 +610,23 @@ static int data_ep_set_params(struct snd_usb_endpoint *ep,
 
 	/* assume max. frequency is 25% higher than nominal */
 	ep->freqmax = ep->freqn + (ep->freqn >> 2);
-	maxsize = ((ep->freqmax + 0xffff) * (frame_bits >> 3))
-				>> (16 - ep->datainterval);
+	/* Round up freqmax to nearest integer in order to calculate maximum
+	 * packet size, which must represent a whole number of frames.
+	 * This is accomplished by adding 0x0.ffff before converting the
+	 * Q16.16 format into integer.
+	 * In order to accurately calculate the maximum packet size when
+	 * the data interval is more than 1 (i.e. ep->datainterval > 0),
+	 * multiply by the data interval prior to rounding. For instance,
+	 * a freqmax of 41 kHz will result in a max packet size of 6 (5.125)
+	 * frames with a data interval of 1, but 11 (10.25) frames with a
+	 * data interval of 2.
+	 * (ep->freqmax << ep->datainterval overflows at 8.192 MHz for the
+	 * maximum datainterval value of 3, at USB full speed, higher for
+	 * USB high speed, noting that ep->freqmax is in units of
+	 * frames per packet in Q16.16 format.)
+	 */
+	maxsize = (((ep->freqmax << ep->datainterval) + 0xffff) >> 16) *
+			 (frame_bits >> 3);
 	/* but wMaxPacketSize might reduce this */
 	if (ep->maxpacksize && ep->maxpacksize < maxsize) {
 		/* whatever fits into a max. size packet */