...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
We've run our performance tests both for our own code, and against other open source implementations of the same functions. The results are presented below to give you a rough idea of how they all compare.
Caution  

You should exercise extreme caution when interpreting these results, relative performance may vary by platform, the tests use data that gives good code coverage of our code, but which may skew the results towards the corner cases. Finally, remember that different libraries make different choices with regard to performance verses numerical stability. 
All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM, Windows Vista machine, with the test program compiled with Microsoft Visual C++ 2009 using the /Ox option.
Function 
Boost 
GSL1.9 
Cephes 

1.00
(4.873e007s)

N/A 
1.00
(6.699e007s)


1.00
(1.664e007s)

1.00
(2.677e007s)

1.00
(1.189e007s)


1.00
(8.760e008s)

1.00
(1.248e007s)

1.00
(8.169e008s)


1.80
(2.997e007s)

1.54
(2.569e007s)

1.00
(1.666e007s)


2.20
(3.045e007s)

4.14
(5.713e007s)

1.00
(1.381e007s)


1.00
(1.483e007s)

1.00
(7.052e007s)

1.00
(1.722e007s)


1.00
(6.182e007s)

3.57
(2.209e006s)

4.29
(2.651e006s)


1.00
(1.943e006s)

N/A 
+INF ^{[1]} 

1.00
(1.670e006s)

1.16
(1.935e006s)

1.16
(1.935e006s)


ibeta_inv and ibetac_inv 
1.00
(6.075e006s)

N/A 
2.45
(1.489e005s)

17.89^{[2]}
(4.248e005s)

1.00
(5.214e006s)

1.00
(2.374e006s)


1.00
(5.924e006s)

1.00
(4.487e006s)

1.00
(4.823e006s)


1.00
(2.783e006s)

1.00
(3.927e006s)

N/A 

1.00
(4.465e006s)

1.00
(1.230e005s)

1.00
(4.977e006s)


^{[1] } Cephes gets stuck in an infinite loop while trying to execute our test cases. ^{[2] } The performance here is dominated by a few cases where the parameters grow very large: faster asymptotic expansions are available, but are of limited (or even frankly terrible) precision. The same issue effects all of our Bessel function implementations, but doesn't necessarily show in the current performance data. More investigation is needed here. 
All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM, Windows Vista machine, with the test program compiled with Microsoft Visual C++ 2009, and R2.9.2 compiled in "standalone mode" with MinGW4.3 (R2.9.2 appears not to be buildable with Visual C++).
Table 55. A Comparison to the R Statistical Library on Windows XP
Statistical Function 
Boost 
R 
DCDFLIB 

1.08
(1.385e006s)

1.00
(1.278e006s)

1.06
(1.349e006s)


Beta Distribution Quantile 
1.00
(4.975e006s)

67.66^{[1]}
(3.366e004s)

4.23
(2.103e005s)

1.06
(4.503e007s)

1.81
(7.680e007s)

1.00
(4.239e007s)


Binomial Distribution Quantile 
1.00
(3.254e006s)

1.15
(3.746e006s)

7.25
(2.358e005s)

1.00
(1.134e007s)

1.08
(1.227e007s)

NA 

Cauchy Distribution Quantile 
1.00
(1.203e007s)

1.00
(1.203e007s)

NA 
1.21
(5.021e007s)

2.83
(1.176e006s)

1.00
(4.155e007s)


Chi Squared Distribution Quantile 
1.00
(1.930e006s)

2.72
(5.243e006s)

5.73
(1.106e005s)

1.00
(3.798e008s)

5.89
(2.236e007s)

NA 

Exponential Distribution Quantile 
1.41
(9.006e008s)

1.00
(6.380e008s)

NA 
1.00
(9.556e007s)

1.34
(1.283e006s)

1.24
(1.183e006s)


Fisher F Distribution Quantile 
1.00
(6.987e006s)

1.33
(9.325e006s)

3.16
(2.205e005s)

1.52
(6.240e007s)

3.11
(1.279e006s)

1.00
(4.111e007s)


Gamma Distribution Quantile 
1.24
(2.179e006s)

6.25
(1.102e005s)

1.00
(1.764e006s)

__hypergeometric_distrib CDF 
3.60^{[2]}
(5.987e007s)

1.00
(1.665e007s)

NA 
__hypergeometric_distrib Quantile 
1.00
(5.684e007s)

3.53
(2.004e006s)

NA 
1.00
(1.714e007s)

5.24
(8.984e007s)

NA 

Logistic Distribution Quantile 
1.02
(2.084e007s)

1.00
(2.043e007s)

NA 
1.00
(3.579e007s)

1.49
(5.332e007s)

NA 

Lognormal Distribution Quantile 
1.00
(9.622e007s)

1.57
(1.507e006s)

NA 
1.00
(6.227e007s)

2.25
(1.403e006s)

2.21
(1.378e006s)


Negative Binomial Distribution Quantile 
1.00
(8.594e006s)

43.43^{[3]}
(3.732e004s)

3.48
(2.994e005s)

2.16
(3.926e006s)

79.93
(1.450e004s)

1.00
(1.814e006s)


Noncentral Chi Squared Distribution Quantile 
5.00
(3.393e004s)

393.90^{[4]}
(2.673e002s)

1.00
(6.786e005s)

1.59
(1.128e005s)

1.00
(7.087e006s)

1.00
(4.274e006s)


Noncentral F Distribution Quantile 
1.00
(4.750e004s)

1.62
(7.681e004s)

1.00
(4.274e006s)

3.41
(1.852e005s)

1.00
(5.436e006s)

NA 

noncentral T distribution Quantile 
1.31
(5.768e004s)

1.00^{[5]}
(4.411e004s)

NA 
1.00
(8.373e008s)

1.68
(1.409e007s)

6.01
(5.029e007s)


Normal Distribution Quantile 
1.29
(1.521e007s)

1.00
(1.182e007s)

10.85
(1.283e006s)

1.18
(5.193e007s)

2.98
(1.314e006s)

1.00
(4.410e007s)


1.00
(1.203e006s)

2.20
(2.642e006s)

7.86
(9.457e006s)


1.00
(8.655e007s)

1.06
(9.166e007s)

1.04
(8.999e007s)


Students t Distribution Quantile 
1.00
(2.294e006s)

1.36
(3.131e006s)

4.82
(1.106e005s)

1.00
(1.865e007s)

2.33
(4.341e007s)

NA 

Weibull Distribution Quantile 
1.00
(3.608e007s)

1.22
(4.410e007s)

NA 
^{[1] } There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. ^{[2] } This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision. ^{[3] } The R library appears to use a linearsearch strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases ^{[4] } There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. ^{[5] } There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. 
All the results were measured on a 2.0GHz Intel T5800 Core 2 Duo, 4Gb RAM, Ubuntu Linux 9 machine, with the test program and R2.9.2 compiled with GNU G++ 4.3.3 using O3 DNDEBUG=1.
Table 56. A Comparison to the R Statistical Library on Linux
Statistical Function 
Boost 
R 
DCDFLIB 

2.09
(3.189e006s)

1.00
(1.526e006s)

1.19
(1.822e006s)


Beta Distribution Quantile 
1.00
(1.185e005s)

30.51^{[1]}
(3.616e004s)

2.52
(2.989e005s)

4.41
(9.175e007s)

3.59
(7.476e007s)

1.00
(2.081e007s)


Binomial Distribution Quantile 
1.57
(6.925e006s)

1.00
(4.407e006s)

7.43
(3.274e005s)

1.00
(1.594e007s)

1.04
(1.654e007s)

NA 

Cauchy Distribution Quantile 
1.21
(1.752e007s)

1.00
(1.448e007s)

NA 
2.61
(1.376e006s)

2.36
(1.243e006s)

1.00
(5.270e007s)


Chi Squared Distribution Quantile 
1.00
(4.252e006s)

1.34
(5.700e006s)

3.47
(1.477e005s)

1.00
(1.342e007s)

1.25
(1.677e007s)

NA 

Exponential Distribution Quantile 
1.00
(8.827e008s)

1.07
(9.470e008s)

NA 
1.62
(2.324e006s)

1.19
(1.711e006s)

1.00
(1.437e006s)


Fisher F Distribution Quantile 
1.53
(1.577e005s)

1.00
(1.033e005s)

2.63
(2.719e005s)

3.18
(1.582e006s)

2.63
(1.309e006s)

1.00
(4.980e007s)


Gamma Distribution Quantile 
2.19
(4.770e006s)

6.94
(1.513e005s)

1.00
(2.179e006s)

__hypergeometric_distrib CDF 
2.20^{[2]}
(3.522e007s)

1.00
(1.601e007s)

NA 
__hypergeometric_distrib Quantile 
1.00
(8.279e007s)

2.57
(2.125e006s)

NA 
1.00
(9.398e008s)

2.75
(2.588e007s)

NA 

Logistic Distribution Quantile 
1.00
(9.893e008s)

1.30
(1.285e007s)

NA 
1.00
(1.831e007s)

1.39
(2.539e007s)

NA 

Lognormal Distribution Quantile 
1.10
(5.551e007s)

1.00
(5.037e007s)

NA 
1.08
(1.563e006s)

1.00
(1.444e006s)

1.00
(1.444e006s)


Negative Binomial Distribution Quantile 
1.00
(1.700e005s)

25.92^{[3]}
(4.407e004s)

1.93
(3.274e005s)

5.06
(2.841e005s)

25.01
(1.405e004s)

1.00
(5.617e006s)


Noncentral Chi Squared Distribution Quantile 
8.47
(1.879e003s)

144.91^{[4]}
(3.214e002s)

1.00
(2.218e004s)

10.33
(5.868e005s)

1.42
(8.058e006s)

1.00
(5.682e006s)


Noncentral F Distribution Quantile 
5.64
(7.869e004s)

6.63
(9.256e004s)

1.00
(1.396e004s)

4.91
(3.357e005s)

1.00
(6.844e006s)

NA 

noncentral T distribution Quantile 
1.57
(9.265e004s)

1.00^{[5]}
(5.916e004s)

NA 
1.00
(1.074e007s)

1.16
(1.245e007s)

5.36
(5.762e007s)


Normal Distribution Quantile 
1.28
(1.902e007s)

1.00
(1.490e007s)

10.35
(1.542e006s)

2.43
(1.198e006s)

2.25
(1.110e006s)

1.00
(4.937e007s)


1.11
(3.032e006s)

1.00
(2.724e006s)

4.07
(1.110e005s)


2.17
(2.020e006s)

1.00
(9.321e007s)

1.10
(1.021e006s)


Students t Distribution Quantile 
1.18
(3.972e006s)

1.00
(3.364e006s)

3.89
(1.308e005s)

1.00
(3.662e007s)

1.04
(3.808e007s)

NA 

Weibull Distribution Quantile 
1.00
(4.112e007s)

1.05
(4.317e007s)

NA 
^{[1] } There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. ^{[2] } This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision. ^{[3] } The R library appears to use a linearsearch strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases ^{[4] } There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. ^{[5] } There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. 