Bound better the loop size for the estimator to increase the shift

[ameligrana]

This should be okay since significand_sum_hi < group_length <= m[4]

[github-actions]

Benchmark Results

	f537014	69f527f	f537014 / 69f527f
TTFX excluding time to load	0.0384 ± 0 s	0.0388 ± 0 s	0.961 ± 0,1.01 ± 0,0.99 ± 0
code size in bytes	1.55e+04 ± 0 h	1.55e+04 ± 0 h	1 ± 0
code size in lines	573 ± 0 h	571 ± 0 h	1 ± 0
code size in syntax nodes	4.15e+03 ± 0 h	4.15e+03 ± 0 h	1 ± 0
constructor empty	1.53 ± 0.14 μs	1.65 ± 0.39 μs	0.853 ± 0.29,0.995 ± 0.2,0.93 ± 0.24
constructor n=100 σ=0.1	6.02 ± 0.18 μs	6.04 ± 0.21 μs	0.97 ± 0.086,1.74,0.997 ± 0.046
constructor n=100 σ=1.0	6.57 ± 0.17 μs	6.71 ± 1.2 μs	0.979 ± 0.64,1.01 ± 0.023,0.979 ± 0.18
constructor n=100 σ=10.0	8.19 ± 1.5 μs	16.8 μs	1.54,0.997 ± 0.026,0.486
constructor n=100 σ=100.0	8.5 ± 0.25 μs	8.67 ± 43 μs	0.872 ± 2.6,0.876 ± 0.093,0.98 ± 4.8
constructor n=1000 σ=0.1	0.0476 ± 0.0013 ms	0.0477 ± 0.0013 ms	1.02 ± 0.064,0.985 ± 0.069,0.998 ± 0.039
constructor n=1000 σ=1.0	0.0572 ± 0.0026 ms	0.0507 ± 0.0017 ms	1.09 ± 0.23,0.996 ± 0.041,1.13 ± 0.064
constructor n=1000 σ=10.0	0.058 ± 0.001 ms	0.0581 ± 0.0011 ms	0.998 ± 0.054,1 ± 0.023,0.998 ± 0.026
constructor n=1000 σ=100.0	0.0698 ± 0.0034 ms	0.07 ± 0.0036 ms	0.989 ± 0.11,1.01 ± 0.14,0.997 ± 0.071
constructor n=10000 σ=0.1	0.492 ± 0.03 ms	0.485 ± 0.025 ms	1.02 ± 0.11,0.996 ± 0.092,1.02 ± 0.081
constructor n=10000 σ=1.0	0.531 ± 0.015 ms	0.493 ± 0.02 ms	0.998 ± 0.1,1 ± 0.063,1.08 ± 0.055
constructor n=10000 σ=10.0	0.569 ± 0.027 ms	0.576 ± 0.018 ms	1 ± 0.049,0.995 ± 0.13,0.986 ± 0.056
constructor n=10000 σ=100.0	0.662 ± 0.021 ms	0.663 ± 0.015 ms	0.986 ± 0.078,1 ± 0.092,0.998 ± 0.039
constructor zeros	3.65 ± 2.4 μs	3 ± 0.24 μs	0.894 ± 0.24,0.988 ± 0.079,1.21 ± 0.8
delete ∘ rand n=100 σ=0.1	4.69 ± 0.19 μs	4.68 ± 0.24 μs	1.01 ± 0.071,0.998 ± 0.068,1 ± 0.066
delete ∘ rand n=100 σ=1.0	4.96 ± 0.22 μs	4.95 ± 0.22 μs	1.01 ± 0.063,0.993 ± 0.06,1 ± 0.063
delete ∘ rand n=100 σ=10.0	5.56 ± 0.28 μs	5.57 ± 0.29 μs	1.01 ± 0.076,0.984 ± 0.071,0.998 ± 0.072
delete ∘ rand n=100 σ=100.0	8.8 ± 0.47 μs	8.63 ± 0.35 μs	1.01 ± 0.056,0.988 ± 0.055,1.02 ± 0.068
delete ∘ rand n=1000 σ=0.1	0.0468 ± 0.001 ms	0.0468 ± 0.0012 ms	1.01 ± 0.034,1 ± 0.03,1 ± 0.033
delete ∘ rand n=1000 σ=1.0	0.0506 ± 0.0011 ms	0.0504 ± 0.0011 ms	1 ± 0.03,0.994 ± 0.037,1 ± 0.031
delete ∘ rand n=1000 σ=10.0	0.0528 ± 0.0011 ms	0.0524 ± 0.00095 ms	1 ± 0.026,0.995 ± 0.026,1.01 ± 0.029
delete ∘ rand n=1000 σ=100.0	0.061 ± 0.001 ms	0.0608 ± 0.00098 ms	1.01 ± 0.024,0.989 ± 0.022,1 ± 0.023
delete ∘ rand n=10000 σ=0.1	0.519 ± 0.02 ms	0.512 ± 0.014 ms	0.999 ± 0.052,0.989 ± 0.051,1.01 ± 0.048
delete ∘ rand n=10000 σ=1.0	0.553 ± 0.0089 ms	0.556 ± 0.015 ms	0.978 ± 0.048,0.991 ± 0.037,0.994 ± 0.031
delete ∘ rand n=10000 σ=10.0	0.556 ± 0.014 ms	0.552 ± 0.014 ms	1 ± 0.041,0.979 ± 0.034,1.01 ± 0.036
delete ∘ rand n=10000 σ=100.0	0.55 ± 0.017 ms	0.547 ± 0.016 ms	1.01 ± 0.044,0.985 ± 0.042,1.01 ± 0.043
intermixed_h n=100 σ=0.1	12.4 ± 1.4 μs	12.3 ± 1.5 μs	0.987 ± 0.14,0.994 ± 0.21,1.01 ± 0.17
intermixed_h n=100 σ=1.0	17.5 μs	11.5 ± 1.1 μs	0.78 ± 0.11,1.02 ± 0.27,1.53
intermixed_h n=100 σ=10.0	12 ± 1.7 μs	11.9 ± 1.7 μs	1 ± 0.35,0.989 ± 0.32,1 ± 0.21
intermixed_h n=100 σ=100.0	11.7 ± 0.88 μs	12.1 ± 1.5 μs	0.882 ± 0.25,0.896 ± 0.25,0.968 ± 0.14
intermixed_h n=1000 σ=0.1	0.141 ± 0.079 ms	0.156 ± 0.084 ms	0.935 ± 0.43,0.953 ± 0.54,0.907 ± 0.71
intermixed_h n=1000 σ=1.0	0.114 ± 0.0081 ms	0.115 ± 0.0076 ms	1.03 ± 0.11,1.01 ± 0.11,0.991 ± 0.096
intermixed_h n=1000 σ=10.0	0.109 ± 0.011 ms	0.109 ± 0.01 ms	0.981 ± 0.12,0.998 ± 0.14,1 ± 0.13
intermixed_h n=1000 σ=100.0	0.115 ± 0.011 ms	0.116 ± 0.011 ms	0.973,0.985 ± 0.14,0.993 ± 0.13
intermixed_h n=10000 σ=0.1	1.16 ± 0.12 ms	1.19 ± 0.12 ms	0.946 ± 0.19,1.01 ± 0.26,0.971 ± 0.14
intermixed_h n=10000 σ=1.0	1.21 ± 0.18 ms	1.18 ± 0.15 ms	0.952 ± 0.2,0.996 ± 0.2,1.03 ± 0.2
intermixed_h n=10000 σ=10.0	1.13 ± 0.18 ms	1.13 ± 0.17 ms	1.02 ± 0.21,1 ± 0.25,1 ± 0.22
intermixed_h n=10000 σ=100.0	1.14 ± 0.19 ms	1.11 ± 0.16 ms	0.975 ± 0.22,0.974 ± 0.2,1.03 ± 0.23
pathological 1	0.0466 ± 0.00059 μs	0.0465 ± 0.00056 μs	1.01 ± 0.011,0.999 ± 0.01,1 ± 0.018
pathological 1′	0.121 ± 0.0015 μs	0.133 ± 0.0017 μs	0.83 ± 0.012,0.851 ± 0.015,0.908 ± 0.016
pathological 2	0.0634 ± 0.00057 μs	0.0633 ± 0.0007 μs	1 ± 0.0075,1 ± 0.0065,1 ± 0.014
pathological 2′	0.135 ± 0.0018 μs	0.147 ± 0.0021 μs	0.908 ± 0.014,0.86 ± 0.017,0.922 ± 0.018
pathological 2′′	0.18 ± 0.0062 μs	0.187 ± 0.012 μs	0.951 ± 0.05,0.877 ± 0.07,0.965 ± 0.071
pathological 3	18.7 ± 0.3 ns	18.7 ± 0.31 ns	1 ± 0.023,1.01 ± 0.027,1 ± 0.023
pathological 4	0.0629 ± 0.0006 μs	0.0627 ± 0.00073 μs	1 ± 0.0079,0.975 ± 0.0082,1 ± 0.015
pathological 4′	0.138 ± 0.0019 μs	0.151 ± 0.002 μs	0.937 ± 0.014,0.857 ± 0.019,0.912 ± 0.017
pathological 4′′	0.185 ± 0.007 μs	0.181 ± 0.0039 μs	0.967 ± 0.081,1.02,1.02 ± 0.044
pathological 5a	0.0462 ± 0.00073 μs	0.0461 ± 0.00059 μs	0.996 ± 0.0093,0.995 ± 0.011,1 ± 0.02
pathological 5b	0.0462 ± 0.00069 μs	0.0461 ± 0.00061 μs	1 ± 0.011,0.988 ± 0.011,1 ± 0.02
pathological 5b′	0.259 ± 0.003 μs	0.265 ± 0.0029 μs	0.957 ± 0.011,0.895 ± 0.01,0.977 ± 0.015
pathological 5b′′	0.275 ± 0.0076 μs	0.277 ± 0.013 μs	0.919 ± 0.02,0.944 ± 0.19,0.993 ± 0.055
pathological 6	0.273 ± 0.0031 μs	0.278 ± 0.0028 μs	0.9 ± 0.0098,0.951 ± 0.011,0.983 ± 0.015
pathological large compaction (133380-op)	13.6 ± 0.14 ms	13.7 ± 0.14 ms	0.972 ± 0.038,0.988 ± 0.031,0.996 ± 0.015
pathological medium compaction (1254-op)	0.107 ± 0.0048 ms	0.11 ± 0.019 ms	0.915 ± 0.12,0.987 ± 0.07,0.967 ± 0.18
pathological old compaction (6-op)	0.236 μs	0.235 μs	0.98,1.01,1
pathological small compaction (18-op)	0.652 ± 0.008 μs	0.653 ± 0.0065 μs	0.995 ± 0.01,0.917 ± 0.014,1 ± 0.016
pathological tiny compaction (6-op)	0.298 ± 0.0022 μs	0.299 ± 0.0026 μs	0.987 ± 0.011,0.962 ± 0.013,0.999 ± 0.011
sample (bulk) n=1000 k=10000 σ=1	0.179 ± 0.023 ms	0.179 ± 0.023 ms	1 ± 0.18,0.992 ± 0.18,0.998 ± 0.18
sample (bulk) n=1000 k=10000 σ=100	0.126 ± 0.053 ms	0.127 ± 0.053 ms	0.993 ± 0.56,0.983 ± 0.56,0.988 ± 0.58
sample (bulk) n=1000 k=1000000 σ=1	17.7 ± 2.3 ms	17.6 ± 2.7 ms	0.976 ± 0.14,0.99 ± 0.17,1.01 ± 0.2
sample (bulk) n=1000 k=1000000 σ=100	9.78 ± 4.9 ms	10.5 ± 5 ms	1.08 ± 0.8,0.905 ± 0.65,0.932 ± 0.64
sample (bulk) n=1000000 k=10000 σ=1	0.374 ± 0.044 ms	0.384 ± 0.017 ms	0.984 ± 0.12,1.04 ± 0.21,0.974 ± 0.12
sample (bulk) n=1000000 k=10000 σ=100	0.144 ± 0.031 ms	0.145 ± 0.025 ms	1.14 ± 0.5,0.878 ± 0.35,1 ± 0.28
sample (bulk) n=1000000 k=1000000 σ=1	22.9 ± 0.98 ms	22.5 ± 1.4 ms	0.982 ± 0.034,1.06 ± 0.053,1.01 ± 0.076
sample (bulk) n=1000000 k=1000000 σ=100	10.6 ± 3.8 ms	11.2 ± 4.5 ms	1.09 ± 0.6,1.14 ± 0.65,0.954 ± 0.51
sample n=100 σ=0.1	28.6 ± 5.9 ns	27.8 ± 0.94 ns	1 ± 0.04,1 ± 0.035,1.03 ± 0.21
sample n=100 σ=1.0	0.0325 ± 0.0029 μs	0.0324 ± 0.0028 μs	1 ± 0.12,1.01 ± 0.12,1 ± 0.12
sample n=100 σ=10.0	21.2 ± 5.4 ns	21.4 ± 5.4 ns	1 ± 0.35,0.987 ± 0.35,0.99 ± 0.36
sample n=100 σ=100.0	18.6 ± 4.9 ns	18.5 ± 4.7 ns	1 ± 0.36,0.979 ± 0.35,1.01 ± 0.37
sample n=1000 σ=0.1	25.5 ± 7.7 ns	25.4 ± 5.9 ns	0.986 ± 0.34,1 ± 0.39,1 ± 0.38
sample n=1000 σ=1.0	0.0352 ± 0.0028 μs	0.0357 ± 0.0028 μs	0.989 ± 0.1,0.995 ± 0.11,0.988 ± 0.11
sample n=1000 σ=10.0	22.7 ± 5.9 ns	22.2 ± 6 ns	0.984 ± 0.35,1 ± 0.39,1.02 ± 0.39
sample n=1000 σ=100.0	18.5 ± 4.8 ns	18.7 ± 5 ns	0.996 ± 0.36,0.977 ± 0.35,0.989 ± 0.37
sample n=10000 σ=0.1	0.0352 ± 0.0011 μs	0.0355 ± 0.0013 μs	0.987 ± 0.058,1.01 ± 0.045,0.992 ± 0.047
sample n=10000 σ=1.0	0.0371 ± 0.0011 μs	0.0379 ± 0.0024 μs	0.99 ± 0.054,0.971 ± 0.087,0.979 ± 0.069
sample n=10000 σ=10.0	24.3 ± 6.1 ns	23.3 ± 6.7 ns	0.906 ± 0.37,0.992 ± 0.35,1.04 ± 0.4
sample n=10000 σ=100.0	18.5 ± 4.8 ns	18.8 ± 5.4 ns	1.08 ± 0.38,0.944 ± 0.38,0.982 ± 0.38
summarysize n=100 σ=0.1	1.15e+05 ± 0 h	1.15e+05 ± 0 h	1 ± 0
summarysize n=100 σ=1.0	1.15e+05 ± 0 h	1.15e+05 ± 0 h	1 ± 0
summarysize n=100 σ=10.0	1.15e+05 ± 0 h	1.15e+05 ± 0 h	1 ± 0
summarysize n=100 σ=100.0	1.15e+05 ± 0 h	1.15e+05 ± 0 h	1 ± 0
summarysize n=1000 σ=0.1	1.44e+05 ± 0 h	1.44e+05 ± 0 h	1 ± 0
summarysize n=1000 σ=1.0	1.44e+05 ± 0 h	1.44e+05 ± 0 h	1 ± 0
summarysize n=1000 σ=10.0	1.44e+05 ± 0 h	1.44e+05 ± 0 h	1 ± 0
summarysize n=1000 σ=100.0	1.44e+05 ± 0 h	1.44e+05 ± 0 h	1 ± 0
summarysize n=10000 σ=0.1	1e+06 ± 0 h	1e+06 ± 0 h	1 ± 0
summarysize n=10000 σ=1.0	1e+06 ± 0 h	1e+06 ± 0 h	1 ± 0
summarysize n=10000 σ=10.0	1e+06 ± 0 h	1e+06 ± 0 h	1 ± 0
summarysize n=10000 σ=100.0	1e+06 ± 0 h	1e+06 ± 0 h	1 ± 0
update ∘ rand n=100 σ=0.1	0.0897 ± 0.0026 μs	0.0898 ± 0.0025 μs	1.01 ± 0.038,1.01 ± 0.039,0.999 ± 0.04
update ∘ rand n=100 σ=1.0	0.0961 ± 0.003 μs	0.0973 ± 0.0041 μs	0.999 ± 0.073,1 ± 0.047,0.988 ± 0.051
update ∘ rand n=100 σ=10.0	0.112 ± 0.007 μs	0.113 ± 0.007 μs	1 ± 0.098,0.995 ± 0.091,0.994 ± 0.087
update ∘ rand n=100 σ=100.0	0.169 ± 0.0098 μs	0.17 ± 0.0099 μs	0.98 ± 0.08,0.979 ± 0.083,0.993 ± 0.082
update ∘ rand n=1000 σ=0.1	0.0909 ± 0.0026 μs	0.0908 ± 0.0028 μs	1.01 ± 0.043,1.01 ± 0.04,1 ± 0.042
update ∘ rand n=1000 σ=1.0	0.098 ± 0.0031 μs	0.0973 ± 0.0027 μs	1.01 ± 0.044,1.01 ± 0.044,1.01 ± 0.042
update ∘ rand n=1000 σ=10.0	0.109 ± 0.0026 μs	0.108 ± 0.0027 μs	1.01 ± 0.043,0.997 ± 0.036,1.01 ± 0.035
update ∘ rand n=1000 σ=100.0	0.174 ± 0.0045 μs	0.175 ± 0.0067 μs	0.983 ± 0.035,0.982 ± 0.038,0.996 ± 0.046
update ∘ rand n=10000 σ=0.1	0.0999 ± 0.00097 μs	0.0996 ± 0.00017 μs	1 ± 0.035,0.992 ± 0.025,1 ± 0.0099
update ∘ rand n=10000 σ=1.0	0.103 ± 0.0015 μs	0.103 ± 0.0014 μs	0.977 ± 0.021,0.989 ± 0.019,0.996 ± 0.02
update ∘ rand n=10000 σ=10.0	0.105 ± 0.0013 μs	0.106 ± 0.0016 μs	0.984 ± 0.028,1 ± 0.03,0.99 ± 0.019
update ∘ rand n=10000 σ=100.0	0.148 ± 0.0013 μs	0.148 ± 0.0021 μs	0.993 ± 0.021,0.978 ± 0.017,0.999 ± 0.016
time_to_load	0.0489 ± 7.2e-05 s	0.0492 ± 0.00038 s	0.991 ± 0.017,1 ± 0.012,0.994 ± 0.0078

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[ameligrana]

This seems an improvement to me.

[LilithHafner]

Almost all of our benchmarks that hit this line are on small weight vectors with low m[4], so those benchmarks over-represent the improvement of this PR. That said, I doubt it's a meaningful regression on large samplers. So performance wise LGTM.

If we're tightening this bound, I would like to see a test that stresses it (e.g. one that fails if that +1 is missing but passes with the +1) and while making that test, of course, if you find one that requires +2 then that's an issue.