Re: [PATCH 14/16] sched: make __update_entity_runnable_avg() fast

[Peter Zijlstra <peterz@infradead.org>]

On Wed, 2012-07-11 at 17:15 -0700, Paul Turner wrote:
> convergence
> 345> 47765

Ah, 345 is much saner indeed!

> And for posterity, a simple generator so that I don't lose it again:
> #include <math.h>
> #include <stdio.h>
> 
> #define SRR(x, y) (((x) + (1UL << ((y) - 1))) >> (y))
> #define N 32
> #define WMULT_SHIFT 32
> 
> const long WMULT_CONST = ((1UL << N) - 1);
> const double y = .97857206208770013451;

I used pow(0.5, 1.0/N), no point in loosing precision and mis-typing a
digit or somesuch nonsense ;-)

> 
> long approx_decay(int c) {
>         return (c * 4008) >> 12;
> }
> 
> long mult_inv_array[N];
> void calc_mult_inv() {
>         int i;
>         double yn = 0;
> 
>         printf("inverses\n");
>         for (i = 0; i < N; i++) {
>                 yn = (double)WMULT_CONST * pow(y, i);
>                 mult_inv_array[i] = yn;
>                 printf("%d: %8lx\n", i, mult_inv_array[i]);
>         }
> 
>         printf("\n");
> }
> 
> long mult_inv(long c, int n) {
>         return SRR(c * runnable_avg_yN_inv[n], WMULT_SHIFT);

This works much better when you do:

  s/runnable_avg_yN_inv/mult_inv_array/

> }
> 
> void calc_yn_sum(int n)
> {
>         int i;
>         double sum = 0, sum_fl = 0, diff = 0;
>         long approx = 0, approx_fm = 0, approx_fm2 = 0;
> 
>         printf("sum y^n\n");
>         printf("   %8s  %8s  %8s  %8s %8s\n", "exact", "floor", "shift",
>                "fastmul1", "fastmul2");
>         for (i = 1; i < n; i++) {
>                 sum = (y * sum + y * 1024);
>                 sum_fl = floor(y * sum_fl+ y * 1024);
>                 approx = approx_decay(approx) + approx_decay(1024);
>                 approx_fm = mult_inv(approx_fm, 1) + mult_inv(1024, 1);
>                 approx_fm2 += mult_inv(1024, i);
> 
>                 /*diff = sum;*/
>                 printf("%2d: %8.0f  %8.0f  %8ld  %8ld  %8ld\n", i, sum,
>                                 sum_fl - diff,
>                                 approx - (long)diff,
>                                 approx_fm - (long)diff,
>                                 approx_fm2 - (long)diff);
> 
>         }
>         printf("\n");
> }
> 
> void calc_conv(long n) {
>         long old_n;
>         int i = -1;
> 
>         printf("convergence\n");
>         do {
>                 old_n = n;
>                 n = mult_inv(n, 1) + 1024;
>                 i++;
>         } while (n != old_n);
>         printf("%d> %ld\n", i - 1, n);
>         printf("\n");
> }
> 
> void main() {
>         calc_mult_inv();
>         calc_conv(1024);
>         calc_yn_sum(N);
> }
> 
>