sched/deadline: Fix bandwidth reclaim equation in GRUB

sched/deadline: Fix bandwidth reclaim equation in GRUB

According to the GRUB[1] rule, the runtime is depreciated as:
  "dq = -max{u, (1 - Uinact - Uextra)} dt" (1)

To guarantee that deadline tasks doesn't starve lower class tasks,
we do not allocate the full bandwidth of the cpu to deadline tasks.
Maximum bandwidth usable by deadline tasks is denoted by "Umax".
Considering Umax, equation (1) becomes:
  "dq = -(max{u, (Umax - Uinact - Uextra)} / Umax) dt" (2)

Current implementation has a minor bug in equation (2), which this
patch fixes.

The reclamation logic is verified by a sample program which creates
multiple deadline threads and observing their utilization. The tests
were run on an isolated cpu(isolcpus=3) on a 4 cpu system.

Tests on 6.3.0
==============

RUN 1: runtime=7ms, deadline=period=10ms, RT capacity = 95%
TID[693]: RECLAIM=1, (r=7ms, d=10ms, p=10ms), Util: 93.33
TID[693]: RECLAIM=1, (r=7ms, d=10ms, p=10ms), Util: 93.35

RUN 2: runtime=1ms, deadline=period=100ms, RT capacity = 95%
TID[708]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 16.69
TID[708]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 16.69

RUN 3: 2 tasks
  Task 1: runtime=1ms, deadline=period=10ms
  Task 2: runtime=1ms, deadline=period=100ms
TID[631]: RECLAIM=1, (r=1ms, d=10ms, p=10ms), Util: 62.67
TID[632]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 6.37
TID[631]: RECLAIM=1, (r=1ms, d=10ms, p=10ms), Util: 62.38
TID[632]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 6.23

As seen above, the reclamation doesn't reclaim the maximum allowed
bandwidth and as the bandwidth of tasks gets smaller, the reclaimed
bandwidth also comes down.

Tests with this patch applied
=============================

RUN 1: runtime=7ms, deadline=period=10ms, RT capacity = 95%
TID[608]: RECLAIM=1, (r=7ms, d=10ms, p=10ms), Util: 95.19
TID[608]: RECLAIM=1, (r=7ms, d=10ms, p=10ms), Util: 95.16

RUN 2: runtime=1ms, deadline=period=100ms, RT capacity = 95%
TID[616]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 95.27
TID[616]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 95.21

RUN 3: 2 tasks
  Task 1: runtime=1ms, deadline=period=10ms
  Task 2: runtime=1ms, deadline=period=100ms
TID[620]: RECLAIM=1, (r=1ms, d=10ms, p=10ms), Util: 86.64
TID[621]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 8.66
TID[620]: RECLAIM=1, (r=1ms, d=10ms, p=10ms), Util: 86.45
TID[621]: RECLAIM=1, (r=1ms, d=100ms, p=100ms), Util: 8.73

Running tasks on all cpus allowing for migration also showed that
the utilization is reclaimed to the maximum. Running 10 tasks on
3 cpus SCHED_FLAG_RECLAIM - top shows:
%Cpu0  : 94.6 us,  0.0 sy,  0.0 ni,  5.4 id,  0.0 wa
%Cpu1  : 95.2 us,  0.0 sy,  0.0 ni,  4.8 id,  0.0 wa
%Cpu2  : 95.8 us,  0.0 sy,  0.0 ni,  4.2 id,  0.0 wa

[1]: Abeni, Luca & Lipari, Giuseppe & Parri, Andrea & Sun, Youcheng.
     (2015). Parallel and sequential reclaiming in multicore
     real-time global scheduling.

Signed-off-by: Vineeth Pillai (Google) <vineeth@bitbyteword.org>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Reviewed-by: Daniel Bristot de Oliveira <bristot@kernel.org>
Acked-by: Juri Lelli <juri.lelli@redhat.com>
Link: https://lore.kernel.org/r/20230530135526.2385378-1-vineeth@bitbyteword.org