* Fixed mashing for even number of TOF bins.

[NikEfth]

Changes in this pull request

This PR fixes #1751. With even number of TOF abs, naive inversion does not work. If even we need to subtract 1.
Now, both -1 and 0 become a mashed TOF bin 0 but they have inverted detectors.

Testing performed

New tests introduced to explicitly check the transformation with even and odd TOF bins, with and without mashing.

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[KrisThielemans]

As this correct?

You put in changes for even number tof bins, but the number of timing_pos could also be even. Do we cope with this? Same convention?

We want the dp.timing_pos correspond to the centre of the (mashed) TOF bin.

Examples that seem to give undesirable results

• num_tof_bins is even

bin.timing_pos_num	centred_range for bin	centred_range for dp.timing_pos	actual (asymmetric) range
0	0.5	0.5 * mash	0.5 * mash - 0.5

dp.timing_pos wouldn't be integer if mash is even

• num_tof_bins is odd, but mash is even

bin.timing_pos_num	centred_range for bin	centred_range for dp.timing_pos	actual (asymmetric) range
0	0	0	-0.5

[NikEfth]

I can simplify by droping the convention that dp should be positive. It won't fix everything though.

[KrisThielemans]

I don't think that the "positive dps" is the problem. At the moment, I only see the approach followed by @danieldeidda #1334 as correct.

From my table above, I think we should put in some run-time checks and call error if (scanner.num_tof_bins is even and TOF_mashing_factor>1), or (TOF_mashing_factor is even). That's still better than not allowing even TOF bins at all. (Maybe those restrictions can be relaxed a bit).

I'm not sure what you're testing at the moment. Do you test any of the above cases? Shouldn't the test not fail?

[NikEfth]

Now I cleanly test for more cases. Bear with me for a couple of days, please.