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# G.2.5 Performance Requirements for Random Number Generation

1

In the strict mode, the performance of Numerics.Float_Random
and Numerics.Discrete_Random shall be as specified here.

#### Implementation Requirements

2

Two different calls to the time-dependent Reset
procedure shall reset the generator to different states, provided that
the calls are separated in time by at least one second and not more than
fifty years.

3

The implementation's representations of generator
states and its algorithms for generating random numbers shall yield a
period of at least 2^{31}-2;
much longer periods are desirable but not required.

4

The implementations of Numerics.Float_Random.Random
and Numerics.Discrete_Random.Random shall pass at least 85% of the individual
trials in a suite of statistical tests. For Numerics.Float_Random, the
tests are applied directly to the floating point values generated (i.e.,
they are not converted to integers first), while for Numerics.Discrete_Random
they are applied to the generated values of various discrete types. Each
test suite performs 6 different tests, with each test repeated 10 times,
yielding a total of 60 individual trials. An individual trial is deemed
to pass if the chi-square value (or other statistic) calculated for the
observed counts or distribution falls within the range of values corresponding
to the 2.5 and 97.5 percentage points for the relevant degrees of freedom
(i.e., it shall be neither too high nor too low). For the purpose of
determining the degrees of freedom, measurement categories are combined
whenever the expected counts are fewer than 5.

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