Returns the sum of elements in this stream. Summation is a special case of a reduction. If floating-point summation were exact, this method would be equivalent to:


     return reduce(0, Double::sum);

However, since floating-point summation is not exact, the above code is not necessarily equivalent to the summation computation done by this method.

The value of a floating-point sum is a function both of the input values as well as the order of addition operations. The order of addition operations of this method is intentionally not defined to allow for implementation flexibility to improve the speed and accuracy of the computed result. In particular, this method may be implemented using compensated summation or other technique to reduce the error bound in the numerical sum compared to a simple summation of double values. Because of the unspecified order of operations and the possibility of using differing summation schemes, the output of this method may vary on the same input elements.

Various conditions can result in a non-finite sum being computed. This can occur even if the all the elements being summed are finite. If any element is non-finite, the sum will be non-finite:

If any element is a NaN, then the final sum will be NaN.
If the elements contain one or more infinities, the sum will be infinite or NaN.
- If the elements contain infinities of opposite sign, the sum will be NaN.
- If the elements contain infinities of one sign and an intermediate sum overflows to an infinity of the opposite sign, the sum may be NaN.

It is possible for intermediate sums of finite values to overflow into opposite-signed infinities; if that occurs, the final sum will be NaN even if the elements are all finite. If all the elements are zero, the sign of zero is not guaranteed to be preserved in the final sum.

This is a terminal operation.

Returns: the sum of elements in this stream

@apiNote Elements sorted by increasing absolute magnitude tend to yield more accurate results.