Make median and quantile consistent to base R

[hcirellu]

median and quantile have unexpected results when comparing it with integer transfered to integer64.

main:

median(as.integer64(c(1, 3)))
# integer64
# [1] 3

PR:

median(as.integer64(c(1, 3)))
# integer64
# [1] 2

I had to fix two existing tests.

Closes #247

[hcirellu]

I also had to change the optimizer64 in a way that the comparing quantile is called with type=7, which is the default in R. In addition I needed to add a custom round function, that does not round to the next even number for the conversion from double to integer64.
This way it meets the integer64 logic of calculating the in-between values in sortqtl.integer64 and orderqtl.integer64 where the resulting value is calculated by the interpolation of the neighboring values, i.e.:

neighboring_values[1L,] + (neighboring_values[2L,] - neighboring_values[1L,])*(sel%%1)

This boils down to:

as.integer64(1L) + as.integer64(2L - 1L)*0.5
# integer64
# [1] 2

which is different to coercing the double result to integer64 for comparison:

as.integer64(1L + (2L - 1L)*0.5)
# integer64
# [1] 1

Is this ok? Or should the calculation in sortqtl.integer64 and orderqtl.integer64 be changed to meet the requirement that median(as.integer(1:2)) equals as.integer64(median(1:2)), which seems inconsistent with the interpolation of neighboring values using +, -, and * for integer64?
WDYT?

[MichaelChirico]

WDYT about

x32 = 100 * (1:100)
x64 = as.integer64(x32)

quantile(x32/100, names=FALSE)
# [1]   1.00  25.75  50.50  75.25 100.00
quantile(x32, names=FALSE)
# [1]   100  2575  5050  7525 10000
quantile(x64, names=FALSE)
# integer64
# [1] 100   2600  5000  7500  10000

[hcirellu]

That's in main. In this PR the result would be

quantile(x64, names=FALSE)
# integer64
# [1] 100   2575  5050  7525  10000

which is what I expect, because it is "identical" to the default behaviour in R. But that depends on the individual view.
When comparing the different modes (type=7 is the default)

setNames(`row.names<-`(Reduce(rbind, lapply(1:9, \(t) quantile(x32, type=t, names=FALSE)), init = data.frame(rep(list(numeric()),5))), c(paste0("type=", 1:9))), names(quantile(x32)))
#         0%      25%  50%      75%  100%
# type=1 100 2500.000 5000 7500.000 10000
# type=2 100 2550.000 5050 7550.000 10000
# type=3 100 2500.000 5000 7500.000 10000
# type=4 100 2500.000 5000 7500.000 10000
# type=5 100 2550.000 5050 7550.000 10000
# type=6 100 2525.000 5050 7575.000 10000
# type=7 100 2575.000 5050 7525.000 10000
# type=8 100 2541.667 5050 7558.333 10000
# type=9 100 2543.750 5050 7556.250 10000

it shows, that the results differ alot.
Do we want to support the types 1-9, too? (Right now we only support a non-existent type=0.)
For a consistent median based on qtile it seems, that we "need" a qtile with type=7. Or we implement median independent of quantile.

Or didn't I get your question right? Is it about adjusting the test from 1:100 to your proposal?