Performance of Random Number Generators¶

The performance is measured on an MacBook Pro with an Intel Core i7-4960HQ CPU running macOS Sierra (version 10.12.4).

Three compilers are tested, LLVM clang (version Apple 8.1.0), GNU GCC (version 6.3.0), and Intel C++ compiler (version 17.0.2). They are labeled as “LLVM”, “GCC” and “Intel”, respectively.

Two usage cases of RNGs are considered. The first is generating random integers within a loop, each iteration generate a single random integer,

// RNGType is the type of RNG tested
RNGType rng;
::mckl::UniformBitsDistribution<RNGType::result_type> ubits;
for (std:size_t i = 0; i != n; ++i)
    r[i] = ::mckl::rand(rng, ubits);

For RNGs that output random integers uniform on the set \(\{0,\dots,2^W - 1\}\), where \(W\) is the number of bits in its output integer type, this is equivalent to

for (std::size_t i = 0; i != n; ++i)
    r[i] = rng();

The second is the vectorized performance,

::mckl::rand(rng, ubits, n, r.data());

For RNGs that output random integers uniform on the set \(\{0,\dots,2^W - 1\}\), where \(W\) is the number of bits in its output integer type, this is equivalent to

::mckl::rand(rng, n, r.data());

See Vectorized Random Number Generating. In both cases, we repeat the simulations 100 times, each time with \(n\) chosen randomly between 5,000 and 10,000. The total number of cycles of the 100 simulations are recorded, and then divided by the total number of bytes generated. It gives the performance measurement in cpB. The two cases are labeled “Single” and “Batch”, respectively, in the tables below.

Performance of RNGs in the Standard Library¶
		Single			Batch
RNG	LLVM	GCC	Intel	LLVM	GCC	Intel
`std::mt19937`	4.56	4.21	5.03	4.56	3.99	5.03
`std::mt19937_64`	2.35	2.21	2.46	2.35	2.18	2.46
`std::minstd_rand0`	9.68	10.1	10.9	9.68	10.1	10.9
`std::minstd_rand`	7.61	8.56	9.59	7.54	8.56	9.57
`std::ranlux24_base`	12.4	5.98	13.7	12.6	6.15	12.1
`std::ranlux48_base`	5.83	3.11	6.59	5.83	3.07	6.69
`std::ranlux24`	130	94.2	130	130	93.7	113
`std::ranlux48`	223	159	243	224	159	230
`std::knuth_b`	43.7	49.6	30.5	37.8	48.8	30.4

Performance of RNGs in the Random123 Library¶
		Single			Batch
RNG	LLVM	GCC	Intel	LLVM	GCC	Intel
`r123::AESNI4x32`	6.58	1.56	8.93	6.61	1.52	8.83
`r123::ARS4x32`	5.13	1.18	6.39	5.19	1.18	6.30
`r123::Philox2x32`	10.1	3.04	12.6	10.1	3.07	12.6
`r123::Philox4x32`	6.14	2.86	13.1	6.17	2.81	13.1
`r123::Philox2x64`	2.19	1.77	10.3	2.15	1.56	10.2
`r123::Philox4x64`	2.25	1.72	12.0	2.25	1.67	11.9
`r123::Threefry2x32`	11.6	4.59	10.8	11.7	4.59	10.9
`r123::Threefry4x32`	6.94	3.86	7.86	6.84	3.87	7.80
`r123::Threefry2x64`	3.38	2.25	3.17	3.30	2.32	3.17
`r123::Threefry4x64`	2.62	1.97	6.75	2.53	1.97	6.72

Performance of `AESEngine`¶
		Single			Batch
RNG	LLVM	GCC	Intel	LLVM	GCC	Intel
`AES128`	1.53	1.90	1.87	0.64	0.63	0.63
`AES192`	2.19	2.28	2.25	0.76	0.76	0.76
`AES256`	2.57	2.63	2.63	0.89	0.89	0.89
`ARS`	1.04	1.33	1.01	0.32	0.32	0.32
`AES128_64`	1.14	1.36	1.48	0.63	0.63	0.63
`AES192_64`	1.62	1.62	1.78	0.76	0.76	0.76
`AES256_64`	1.93	1.96	2.06	0.88	0.88	0.88
`ARS_64`	0.73	0.86	0.67	0.32	0.32	0.32

Performance of `PhiloxEngine`¶
		Single			Batch
RNG	LLVM	GCC	Intel	LLVM	GCC	Intel
`Philox2x32`	4.71	4.52	5.57	0.61	0.61	0.61
`Philox4x32`	3.74	6.27	4.34	0.63	0.63	0.63
`Philox2x64`	2.70	2.38	3.07	1.42	1.42	1.43
`Philox4x64`	2.79	2.67	2.48	1.45	1.45	1.45
`Philox2x32_64`	4.08	4.08	5.32	0.61	0.61	0.61
`Philox4x32_64`	3.46	6.07	4.06	0.61	0.61	0.63
`Philox2x64_64`	2.09	2.08	2.82	1.42	1.42	1.42
`Philox4x64_64`	2.28	2.16	2.08	1.45	1.45	1.45

Performance of `ThreefryEngine`¶
		Single			Batch
RNG	LLVM	GCC	Intel	LLVM	GCC	Intel
`Threefry2x32`	7.34	6.61	7.16	0.99	0.99	0.94
`Threefry4x32`	5.33	6.81	5.32	1.01	0.99	0.98
`Threefry2x64`	4.02	3.33	4.28	0.92	0.92	0.89
`Threefry4x64`	3.27	2.89	3.52	0.95	0.91	0.86
`Threefry8x64`	3.04	2.19	3.13	0.89	0.86	0.86
`Threefry16x64`	3.99	3.46	3.60	0.91	1.02	0.86
`Threefish256`	8.78	8.89	9.16	2.97	2.76	2.81
`Threefish512`	6.72	6.55	6.83	2.92	2.78	2.79
`Threefish1024`	10.6	9.21	9.44	3.41	3.84	3.26
`Threefry2x32_64`	6.53	5.50	6.59	0.98	0.98	0.94
`Threefry4x32_64`	4.78	6.61	4.85	1.01	0.98	0.96
`Threefry2x64_64`	3.29	3.13	4.03	0.92	0.91	0.88
`Threefry4x64_64`	2.57	2.62	2.95	0.94	0.89	0.85
`Threefry8x64_64`	1.97	1.93	2.50	0.88	0.86	0.86
`Threefry16x64_64`	2.50	2.48	2.43	0.91	0.99	0.85
`Threefish256_64`	8.05	8.35	8.43	2.95	2.75	2.79
`Threefish512_64`	5.67	5.58	6.05	2.89	2.78	2.78
`Threefish1024_64`	8.70	8.29	8.43	3.38	3.80	3.22

Performance of `MKLEngine`¶
		Single			Batch
RNG	LLVM	GCC	Intel	LLVM	GCC	Intel
`MKL_ARS5`	2.37	2.38	2.35	0.41	0.41	0.41
`MKL_PHILOX4X32X10`	2.95	2.98	2.95	0.76	0.77	0.77
`MKL_MCG59`	2.09	2.13	2.10	0.44	0.44	0.44
`MKL_MT19937`	2.00	2.09	2.09	0.32	0.32	0.32
`MKL_MT2203`	1.99	2.00	1.97	0.25	0.26	0.25
`MKL_SFMT19937`	1.97	2.00	2.00	0.22	0.22	0.22
`MKL_ARS5_64`	1.15	1.15	1.11	0.39	0.39	0.39
`MKL_PHILOX4X32X10_64`	1.58	1.58	1.52	0.75	0.76	0.76
`MKL_MCG59_64`	0.98	0.98	0.94	0.42	0.42	0.42
`MKL_MT19937_64`	0.92	0.92	0.89	0.32	0.32	0.32
`MKL_MT2203_64`	0.88	0.83	0.80	0.25	0.25	0.25
`MKL_SFMT19937_64`	0.89	0.91	0.85	0.20	0.20	0.20