Reduce for CPU

[jszuppe]

Device: Intel(R) Core(TM) i5-6600K CPU @ 3.50GHz (4/4 cores/threads)

=== accumulate with stl ===
size,time (ms)
2,0.000133
4,0.000133
8,0.000133
16,0.000135
32,0.000136
64,0.000139
128,0.000151
256,0.000165
512,0.000189
1024,0.000238
2048,0.000463
4096,0.000758
8192,0.001401
16384,0.002684
32768,0.005183
65536,0.009545
131072,0.018869
262144,0.033239
524288,0.059656
1048576,0.119746
2097152,0.295889
4194304,0.606165
8388608,1.219240
16777216,2.450350
33554432,4.898130

[master]

=== accumulate with compute ===
size,time (ms)
2,0.022182
4,0.021758
8,0.021698
16,0.021807
32,0.024980
64,0.021770
128,0.025144
256,0.025538
512,0.025886
1024,0.026272
2048,0.026631
4096,0.024762
8192,0.030600
16384,0.034140
32768,0.043930
65536,0.063510
131072,0.102598
262144,0.181727
524288,0.377996
1048576,0.655540
2097152,1.303180
4194304,2.582180
8388608,5.143530
16777216,10.262900
33554432,20.502700

[pr_reduce_on_cpu]

=== accumulate with compute ===
size,time (ms)
2,0.022874
4,0.022268
8,0.022637
16,0.022521
32,0.022562
64,0.023775
128,0.025854
256,0.025927
512,0.026442
1024,0.023142
2048,0.026977
4096,0.028208
8192,0.031033
16384,0.034424
32768,0.043838
65536,0.053461
131072,0.055120
262144,0.080476
524288,0.092360
1048576,0.131765
2097152,0.228212
4194304,0.421832
8388608,0.832666
16777216,1.697780
33554432,3.461450

You can see that STL is very fast with the reduction (5x faster compare to our serial_reduce used currently in master for reduction on CPUs). I assume it uses SSE/AVX. When reducing vector of int4_s instead of vector of int_s, the performance of serial_reduce becomes almost identical to the performance of STL (for big inputs).

New implementation is faster compared to STL for inputs bigger than 2097152 (for reduction with plus<int> function).

[coveralls]

Coverage decreased (-0.2%) to 80.4% when pulling 97f0225 on haahh:pr_reduce_cpu into a3f72e6 on boostorg:develop.

[coveralls]

Coverage decreased (-0.2%) to 80.409% when pulling 4093481 on haahh:pr_reduce_cpu into a3f72e6 on boostorg:develop.

[kylelutz]

Looks good! Merged!