new scalar umul128 method about positional-popcount HOT 11 CLOSED

n = 1000000 
iterations = 10 
array size: 1.907 MB
avx256popcnt                            	cycles per 16-bit word:  0.316; ref cycles per 16-bit word: 0.259 
pospopcnt_u16                           	cycles per 16-bit word:  0.344; ref cycles per 16-bit word: 0.275 
pospopcnt_u16_scalar_naive              	cycles per 16-bit word:  3.936; ref cycles per 16-bit word: 3.463 
pospopcnt_u16_scalar_naive_nosimd       	cycles per 16-bit word:  18.055; ref cycles per 16-bit word: 14.282 
pospopcnt_u16_scalar_partition          	cycles per 16-bit word:  3.364; ref cycles per 16-bit word: 2.643 
pospopcnt_u16_scalar_hist1x4            	cycles per 16-bit word:  3.124; ref cycles per 16-bit word: 2.456 
pospopcnt_u16_scalar_umul128            	cycles per 16-bit word:  2.415; ref cycles per 16-bit word: 1.898 
pospopcnt_u16_scalar_umul128_unroll2    	cycles per 16-bit word:  2.969; ref cycles per 16-bit word: 2.333 
pospopcnt_u16_sse_single                	cycles per 16-bit word:  4.308; ref cycles per 16-bit word: 3.385 
pospopcnt_u16_sse_mula                  	cycles per 16-bit word:  2.135; ref cycles per 16-bit word: 1.740 
pospopcnt_u16_sse_mula_unroll4          	cycles per 16-bit word:  1.736; ref cycles per 16-bit word: 1.428 
pospopcnt_u16_sse_mula_unroll8          	cycles per 16-bit word:  1.535; ref cycles per 16-bit word: 1.251 
pospopcnt_u16_sse_mula_unroll16         	cycles per 16-bit word:  1.536; ref cycles per 16-bit word: 1.208 
pospopcnt_u16_sse2_sad                  	cycles per 16-bit word:  1.384; ref cycles per 16-bit word: 1.116 
pospopcnt_u16_sse2_csa                  	cycles per 16-bit word:  0.428; ref cycles per 16-bit word: 0.357 
pospopcnt_u16_avx2_popcnt               	cycles per 16-bit word:  3.133; ref cycles per 16-bit word: 2.469 
pospopcnt_u16_avx2                      	cycles per 16-bit word:  4.074; ref cycles per 16-bit word: 3.225 
pospopcnt_u16_avx2_naive_counter        	cycles per 16-bit word:  4.002; ref cycles per 16-bit word: 3.144 
pospopcnt_u16_avx2_single               	cycles per 16-bit word:  3.704; ref cycles per 16-bit word: 2.920 
pospopcnt_u16_avx2_lemire               	cycles per 16-bit word:  2.193; ref cycles per 16-bit word: 1.733 
pospopcnt_u16_avx2_lemire2              	cycles per 16-bit word:  1.502; ref cycles per 16-bit word: 1.191 
pospopcnt_u16_avx2_mula                 	cycles per 16-bit word:  1.426; ref cycles per 16-bit word: 1.135 
pospopcnt_u16_avx2_mula_unroll4         	cycles per 16-bit word:  0.960; ref cycles per 16-bit word: 0.772 
pospopcnt_u16_avx2_mula_unroll8         	cycles per 16-bit word:  0.816; ref cycles per 16-bit word: 0.641 
pospopcnt_u16_avx2_mula_unroll16        	cycles per 16-bit word:  0.844; ref cycles per 16-bit word: 0.663 
pospopcnt_u16_avx2_mula3                	cycles per 16-bit word:  0.517; ref cycles per 16-bit word: 0.440 
pospopcnt_u16_avx2_csa                  	cycles per 16-bit word:  0.329; ref cycles per 16-bit word: 0.275 

pospopcnt_u16_scalar_umul128            	instructions per cycle 3.53, cycles per 16-bit word:  2.414, instructions per 16-bit word 8.528 
min:  2413517 cycles,  8527767 instructions, 	     248 branch mis.,     8206 cache ref.,        0 cache mis.
avg: 2426353.7 cycles, 8527767.2 instructions, 	   248.8 branch mis.,  11234.4 cache ref.,      1.0 cache mis.

pospopcnt_u16_scalar_umul128_unroll2    	instructions per cycle 2.94, cycles per 16-bit word:  2.389, instructions per 16-bit word 7.027 
min:  2389269 cycles,  7026782 instructions, 	     248 branch mis.,    10193 cache ref.,        0 cache mis.
avg: 2400136.8 cycles, 7026782.2 instructions, 	   249.3 branch mis.,  11906.7 cache ref.,      0.8 cache mis.