Implementation of Hardware-Accelerated Scalable Parallel Random Number Generators

Table 7

Numerical results for the errors for $\pi$ estimation.

Number of random samples $N$	Mean error	Standard deviation of error	95% Confidence interval upper limit of error
$8\times {10}^4$	$2.4\times {10}^{-3}$	$2.1\times {10}^{-3}$	$6.5\times {10}^{-3}$
$8\times {10}^5$	$3.1\times {10}^{-3}$	$1.4\times {10}^{-3}$	$5.5\times {10}^{-3}$
$8\times {10}^6$	$2.1\times {10}^{-4}$	$1.2\times {10}^{-4}$	$4.5\times {10}^{-4}$
$8\times {10}^7$	$1.2\times {10}^{-4}$	$1.5\times {10}^{-4}$	$4.1\times {10}^{-4}$
$8\times {10}^8$	$1.2\times {10}^{-4}$	$1.1\times {10}^{-4}$	$3.4\times {10}^{-4}$
$8\times {10}^9$	$3.0\times {10}^{-5}$	$2.8\times {10}^{-5}$	$8.5\times {10}^{-5}$
$8\times {10}^{10}$	$5.6\times {10}^{-6}$	$3.2\times {10}^{-6}$	$1.2\times {10}^{-5}$
$8\times {10}^{11}$	$1.2\times {10}^{-6}$	$8.1\times {10}^{-7}$	$2.8\times {10}^{-6}$