confusion about priorities

[robert.berger]

man page:
pri PRI priority of the process. Higher number means lower priority.

In my tests I manipulate priorites and run afterwards:

ps -C -e -o class,rtprio,pri,nice,cmd
ps -e -o class,rtprio,pri,nice,cmd | grep "fork_1.out"

-----
1) default prio

./fork_1.out

CLS RTPRIO PRI NI CMD
TS - 19 0 ./fork_1.out

-----
2) nice lower prio

nice -n 19 ./fork_1.out

CLS RTPRIO PRI NI CMD
TS - 0 19 ./fork_1.out

The above has a higher priority 19>0, man pages for ps say that higher number means lower priority, so this is inconsistent.
-----

3) nice higher prio
sudo nice -n -20 ./fork_1.out

CLS RTPRIO PRI NI CMD
TS - 39 -20 ./fork_1.out

Here the PRI is 39>19>0, although this shoul now be be highest possible priority in the TS class - inconsistent

-----

chrt -m
SCHED_OTHER min/max priority : 0/0
SCHED_FIFO min/max priority : 1/99
SCHED_RR min/max priority : 1/99
SCHED_BATCH min/max priority : 0/0
SCHED_IDLE min/max priority : 0/0

-----

4) highest rt prio

sudo chrt -r 99 ./fork_1.out

CLS RTPRIO PRI NI CMD
RR 99 139 - ./fork_1.out

139>39>19>0 this should be the highest available RT priority - inconsistent

-----

5) lowest rt prio

sudo chrt -f 1 ./fork_1.out

CLS RTPRIO PRI NI CMD
FF 1 41 - ./fork_1.out
FF 1 41 - ./fork_1.out

this should be the lowest available RT priority - inconsistent

------

Besides:
The RT-priorites go from 1 (lowest) to 99 (highest), which seems OK, but the same range maps to 41 to 139, which IMHO maps to a kernel static priority for 1 to 99.

Since the first nice priority (-n 20 maps to a Prio value of 39) the questions is what happened to 40?

What we see is:
Priority values from 0 to 139 with a gap at 40 seem to map to static kernel priorities of 139 to 1 (which would explain the gap).

Anyhow is this really how it's supposed to be?

What should prio is ps show?

ProblemType: Bug
DistroRelease: Ubuntu 12.04
Package: procps 1:3.2.8-11ubuntu6
ProcVersionSignature: Ubuntu 3.2.0-35.55-generic-pae 3.2.34
Uname: Linux 3.2.0-35-generic-pae i686
ApportVersion: 2.0.1-0ubuntu17.1
Architecture: i386
Date: Mon Apr 1 12:14:19 2013
InstallationMedia: Ubuntu 12.04 LTS "Precise Pangolin" - Release i386 (20120423)
MarkForUpload: True
SourcePackage: procps
UpgradeStatus: No upgrade log present (probably fresh install)