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<p>
All three of the double-exponential integrators are thread safe as long
as BOOST_MATH_NO_ATOMIC_INT is not set. Since the integrators store a large
amount of fairly hard to compute data, it is recomended that these objects
are stored and reused as much as possible.
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<p>
Internally all three of the double-exponential integrators use the same
caching strategy: they allocate all the vectors needed to store the maximum
permitted levels, but only populate the first few levels when constructed.
This means a minimal amount of memory is actually allocated when the integrator
is first constructed, and already populated levels can be accessed via
a lockfree atomic read, and only populating new levels requires a thread
lock.
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In addition, the three built in types (plus <code class="computeroutput"><span class="identifier">__float128</span></code>
when available), have the first 7 levels pre-computed: this is generally
sufficient for the vast majority of integrals - even at quad precision
- and means that integrators for these types are relatively cheap to construct.
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