CFS: Scheduler: How does each change in 'nice' value result in 10% change in CPU time?

[John Locke]

Can anyone explain how the weights that the 'nice' values are mapped
to actually result in an ~10% change in CPU time as you go from one
nice level to the next? I can't make out how the comment here actually
computes: (https://git.kernel.org/cgit/linux/kernel/git/stable/linux-stable.git/tree/kernel/sched/sched.h?id=refs/tags/v3.10.94#n918)

/*
 * Nice levels are multiplicative, with a gentle 10% change for every
 * nice level changed. I.e. when a CPU-bound task goes from nice 0 to
 * nice 1, it will get ~10% less CPU time than another CPU-bound task
 * that remained on nice 0.
 *
 * The "10% effect" is relative and cumulative: from _any_ nice level,
 * if you go up 1 level, it's -10% CPU usage, if you go down 1 level
 * it's +10% CPU usage. (to achieve that we use a multiplier of 1.25.
 * If a task goes up by ~10% and another task goes down by ~10% then
 * the relative distance between them is ~25%.)
 */
static const int prio_to_weight[40] = {

If I take an example of 2 tasks both with weight=1024 (NICE_0) they
should each get 50% of the CPU time. If 1 of the tasks is reniced to
NICE_1 then the NICE_0 task will get 1024/(1024+820)=56% of the CPU
time and  the NICE_1 task will get 44% of the CPU time. I'm obviously
not understanding something since I can't come at those 10% figures in
the comments.

Thanks.