### 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>

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