Optimize Three-Way Partition

[gevtushenko]

Description

closes #168

This PR changes three-way partition implementation to use one decoupled look-back instead of two. The change improves performance for 32-bit offsets without tuning, but leads to significant regressions (up to 40%) for 64-bit offsets. Since three-way partition doesn't provide device API for 64-bit offsets, we can proceed with the change focusing on 32-bit offsets for now. The regression will be addressed later as part of #220.

H100/HBM3

Entropy	I8	I16	I32	I64	I128	F32	F64
0	-38.61%	-38.65%	-34.61%	-30.08%	-37.93%	-15.22%	-30.90%
0.544	-38.59%	-38.56%	-36.25%	-29.25%	-37.84%	-16.28%	-29.93%
1	-38.24%	-38.24%	-35.97%	-29.61%	-37.76%	-15.69%	-30.33%

T{ct}	OffsetT{ct}	Elements{io}	Entropy	Cmp Noise	%Diff
I8	I32	2^16	1	2.54%	5.82%
I8	I32	2^20	1	1.53%	-9.53%
I8	I32	2^24	1	0.69%	-31.45%
I8	I32	2^28	1	0.18%	-38.24%
I8	I32	2^16	0.544	2.31%	0.42%
I8	I32	2^20	0.544	2.05%	-11.28%
I8	I32	2^24	0.544	0.73%	-32.28%
I8	I32	2^28	0.544	0.17%	-38.59%
I8	I32	2^16	0	2.73%	-1.27%
I8	I32	2^20	0	1.90%	-12.70%
I8	I32	2^24	0	0.76%	-32.43%
I8	I32	2^28	0	0.15%	-38.61%
I8	I64	2^16	1	1.71%	30.64%
I8	I64	2^20	1	1.69%	22.04%
I8	I64	2^24	1	0.66%	6.52%
I8	I64	2^28	1	0.20%	2.84%
I8	I64	2^16	0.544	2.04%	26.12%
I8	I64	2^20	0.544	1.79%	18.41%
I8	I64	2^24	0.544	0.65%	4.72%
I8	I64	2^28	0.544	0.21%	2.22%
I8	I64	2^16	0	1.52%	22.84%
I8	I64	2^20	0	1.60%	17.40%
I8	I64	2^24	0	0.64%	4.21%
I8	I64	2^28	0	0.21%	1.54%
I16	I32	2^16	1	2.36%	4.34%
I16	I32	2^20	1	1.70%	-8.23%
I16	I32	2^24	1	0.90%	-31.69%
I16	I32	2^28	1	0.22%	-38.24%
I16	I32	2^16	0.544	2.52%	-1.88%
I16	I32	2^20	0.544	1.49%	-10.88%
I16	I32	2^24	0.544	0.90%	-32.21%
I16	I32	2^28	0.544	0.21%	-38.56%
I16	I32	2^16	0	2.67%	-4.22%
I16	I32	2^20	0	1.99%	-12.02%
I16	I32	2^24	0	0.85%	-32.77%
I16	I32	2^28	0	0.20%	-38.65%
I16	I64	2^16	1	1.55%	52.42%
I16	I64	2^20	1	1.90%	16.07%
I16	I64	2^24	1	0.86%	-10.62%
I16	I64	2^28	1	0.29%	-20.91%
I16	I64	2^16	0.544	1.76%	51.82%
I16	I64	2^20	0.544	2.05%	16.65%
I16	I64	2^24	0.544	0.86%	-11.43%
I16	I64	2^28	0.544	0.29%	-21.32%
I16	I64	2^16	0	2.38%	49.49%
I16	I64	2^20	0	1.76%	14.63%
I16	I64	2^24	0	0.85%	-13.30%
I16	I64	2^28	0	0.28%	-22.89%
I32	I32	2^16	1	1.80%	-10.60%
I32	I32	2^20	1	1.52%	-14.66%
I32	I32	2^24	1	1.22%	-29.94%
I32	I32	2^28	1	0.29%	-35.97%
I32	I32	2^16	0.544	1.73%	-9.31%
I32	I32	2^20	0.544	1.63%	-12.20%
I32	I32	2^24	0.544	1.18%	-30.12%
I32	I32	2^28	0.544	0.29%	-36.25%
I32	I32	2^16	0	2.06%	-9.51%
I32	I32	2^20	0	1.87%	-11.53%
I32	I32	2^24	0	1.06%	-28.54%
I32	I32	2^28	0	0.25%	-34.61%
I32	I64	2^16	1	1.69%	25.42%
I32	I64	2^20	1	1.69%	18.76%
I32	I64	2^24	1	1.23%	3.39%
I32	I64	2^28	1	0.38%	-1.54%
I32	I64	2^16	0.544	1.78%	23.51%
I32	I64	2^20	0.544	1.84%	19.14%
I32	I64	2^24	0.544	1.09%	2.92%
I32	I64	2^28	0.544	0.32%	-1.56%
I32	I64	2^16	0	1.51%	25.89%
I32	I64	2^20	0	1.63%	17.38%
I32	I64	2^24	0	1.00%	3.47%
I32	I64	2^28	0	0.31%	-0.58%
I64	I32	2^16	1	2.51%	-9.20%
I64	I32	2^20	1	1.86%	-10.67%
I64	I32	2^24	1	1.05%	-30.86%
I64	I32	2^28	1	0.30%	-29.61%
I64	I32	2^16	0.544	2.71%	-8.47%
I64	I32	2^20	0.544	1.74%	-12.92%
I64	I32	2^24	0.544	1.10%	-30.39%
I64	I32	2^28	0.544	0.31%	-29.25%
I64	I32	2^16	0	2.82%	-11.54%
I64	I32	2^20	0	1.56%	-14.11%
I64	I32	2^24	0	1.12%	-31.52%
I64	I32	2^28	0	0.32%	-30.08%
I64	I64	2^16	1	1.45%	16.71%
I64	I64	2^20	1	2.12%	-3.95%
I64	I64	2^24	1	1.06%	-18.66%
I64	I64	2^28	1	0.28%	-21.86%
I64	I64	2^16	0.544	1.38%	15.98%
I64	I64	2^20	0.544	2.04%	-5.02%
I64	I64	2^24	0.544	1.01%	-18.27%
I64	I64	2^28	0.544	0.26%	-21.69%
I64	I64	2^16	0	1.82%	15.99%
I64	I64	2^20	0	2.08%	-4.97%
I64	I64	2^24	0	1.07%	-20.57%
I64	I64	2^28	0	0.30%	-24.03%
I128	I32	2^16	1	2.61%	-8.39%
I128	I32	2^20	1	3.22%	-19.74%
I128	I32	2^24	1	0.92%	-36.30%
I128	I32	2^28	1	0.23%	-37.76%
I128	I32	2^16	0.544	2.63%	-9.50%
I128	I32	2^20	0.544	3.25%	-19.97%
I128	I32	2^24	0.544	0.88%	-36.40%
I128	I32	2^28	0.544	0.50%	-37.84%
I128	I32	2^16	0	2.60%	-9.86%
I128	I32	2^20	0	3.29%	-21.08%
I128	I32	2^24	0	0.92%	-36.43%
I128	I32	2^28	0	0.25%	-37.93%
I128	I64	2^16	1	1.92%	6.66%
I128	I64	2^20	1	2.09%	-4.73%
I128	I64	2^24	1	1.19%	-22.12%
I128	I64	2^28	1	0.30%	-25.92%
I128	I64	2^16	0.544	2.33%	8.84%
I128	I64	2^20	0.544	2.10%	-4.98%
I128	I64	2^24	0.544	1.19%	-22.38%
I128	I64	2^28	0.544	0.50%	-26.04%
I128	I64	2^16	0	2.29%	7.97%
I128	I64	2^20	0	2.22%	-6.01%
I128	I64	2^24	0	1.19%	-23.13%
I128	I64	2^28	0	0.31%	-26.84%
F32	I32	2^16	1	2.51%	-9.32%
F32	I32	2^20	1	1.52%	-5.02%
F32	I32	2^24	1	1.11%	-10.23%
F32	I32	2^28	1	0.38%	-15.69%
F32	I32	2^16	0.544	2.09%	-8.11%
F32	I32	2^20	0.544	1.77%	-5.80%
F32	I32	2^24	0.544	1.36%	-10.76%
F32	I32	2^28	0.544	0.53%	-16.28%
F32	I32	2^16	0	1.54%	-8.92%
F32	I32	2^20	0	1.51%	-5.76%
F32	I32	2^24	0	1.43%	-8.33%
F32	I32	2^28	0	0.59%	-15.22%
F32	I64	2^16	1	1.95%	18.90%
F32	I64	2^20	1	1.67%	16.84%
F32	I64	2^24	1	1.18%	2.87%
F32	I64	2^28	1	0.37%	-1.92%
F32	I64	2^16	0.544	1.69%	20.68%
F32	I64	2^20	0.544	1.76%	15.92%
F32	I64	2^24	0.544	1.13%	2.12%
F32	I64	2^28	0.544	0.34%	-1.74%
F32	I64	2^16	0	1.67%	19.46%
F32	I64	2^20	0	2.33%	17.25%
F32	I64	2^24	0	1.03%	2.94%
F32	I64	2^28	0	0.29%	-0.89%
F64	I32	2^16	1	1.96%	-8.65%
F64	I32	2^20	1	1.64%	-12.57%
F64	I32	2^24	1	1.10%	-31.88%
F64	I32	2^28	1	0.31%	-30.33%
F64	I32	2^16	0.544	1.86%	-8.60%
F64	I32	2^20	0.544	1.92%	-13.45%
F64	I32	2^24	0.544	1.23%	-31.34%
F64	I32	2^28	0.544	0.33%	-29.93%
F64	I32	2^16	0	2.70%	-10.08%
F64	I32	2^20	0	1.93%	-14.33%
F64	I32	2^24	0	1.19%	-32.73%
F64	I32	2^28	0	0.31%	-30.90%
F64	I64	2^16	1	2.20%	16.84%
F64	I64	2^20	1	2.02%	-4.65%
F64	I64	2^24	1	1.13%	-19.54%
F64	I64	2^28	1	0.32%	-23.02%
F64	I64	2^16	0.544	1.97%	19.02%
F64	I64	2^20	0.544	2.05%	-4.65%
F64	I64	2^24	0.544	1.09%	-19.06%
F64	I64	2^28	0.544	0.27%	-22.48%
F64	I64	2^16	0	2.03%	15.75%
F64	I64	2^20	0	2.02%	-6.81%
F64	I64	2^24	0	1.14%	-21.69%
F64	I64	2^28	0	0.29%	-25.25%

H100/HBM2e

Entropy	I8	I16	I32	I64	I128	F32	F64
0	-36.92%	-37.54%	-30.16%	-27.19%	-31.41%	-16.93%	-27.99%
0.544	-36.66%	-37.38%	-31.57%	-26.44%	-31.44%	-18.98%	-27.35%
1	-36.06%	-37.05%	-30.36%	-26.52%	-31.35%	-18.23%	-27.44%

A100

Entropy	I8	I16	I32	I64	I128	F32	F64
0	-24.98%	-19.93%	-5.22%	-14.80%	-2.78%	-5.24%	-20.26%
0.544	-25.44%	-19.82%	-5.85%	-14.90%	-2.89%	-5.85%	-20.43%
1	-24.12%	-19.69%	-5.97%	-14.99%	-2.95%	-5.96%	-20.44%

V100

Entropy	I8	I16	I32	I64	I128	F32	F64
0	-22.54%	-21.69%	-12.36%	-19.48%	-9.62%	-12.41%	-19.46%
0.544	-23.11%	-22.11%	-10.99%	-20.39%	-8.83%	-11.02%	-20.30%
1	-22.70%	-22.10%	-10.92%	-20.61%	-10.57%	-10.93%	-20.54%

Checklist

• New or existing tests cover these changes.
• The documentation is up to date with these changes.

[miscco]

Only nits, that do not warrant to rerun CI