s, and this can be a very serious problem when executing 
Branch and Bound algorithms which expect the mid-value to be inside the 
lower/upper interval.
<p>

We solved the problem by rewritting the trigonometric functions in
order to make them both consistant and correct. We used the following property:
when -pi/4&lt;=a&lt;=pi/4 the rounding in 64 bits of the 80 bits low/std/high value returned
by the x87 are correct. Moreover, when 0&lt;a&lt;2**53 then (a mod (2Pi_low)) and
(a mod (2Pi_high)) are in the sa