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2. 2Sum - Wikipedia

   en.wikipedia.org/wiki/2Sum

   Fast2Sum is often used implicitly in other algorithms such as compensated summation algorithms; [1] Kahan's summation algorithm was published first in 1965, [3] and Fast2Sum was later factored out of it by Dekker in 1971 for double-double arithmetic algorithms. [4] The names 2Sum and Fast2Sum appear to have been applied retroactively by ...

3. Kahan summation algorithm - Wikipedia

   en.wikipedia.org/wiki/Kahan_summation_algorithm

   For summing [, +,,] in double precision, Kahan's algorithm yields 0.0, whereas Neumaier's algorithm yields the correct value 2.0. Higher-order modifications of better accuracy are also possible. For example, a variant suggested by Klein, [ 12 ] which he called a second-order "iterative Kahan–Babuška algorithm".

4. Floating-point error mitigation - Wikipedia

   en.wikipedia.org/wiki/Floating-point_error...

   Extension of precision is using of larger representations of real values than the one initially considered. The IEEE 754 standard defines precision as the number of digits available to represent real numbers. A programming language can include single precision (32 bits), double precision (64 bits), and quadruple precision (128 bits). While ...

5. Double-precision floating-point format - Wikipedia

   en.wikipedia.org/wiki/Double-precision_floating...

   Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.

6. Floating-point arithmetic - Wikipedia

   en.wikipedia.org/wiki/Floating-point_arithmetic

   These include: as noted above, computing all expressions and intermediate results in the highest precision supported in hardware (a common rule of thumb is to carry twice the precision of the desired result, i.e. compute in double precision for a final single-precision result, or in double extended or quad precision for up to double-precision ...

7. Pairwise summation - Wikipedia

   en.wikipedia.org/wiki/Pairwise_summation

   Pairwise summation is the default summation algorithm in NumPy [9] and the Julia technical-computing language, [10] where in both cases it was found to have comparable speed to naive summation (thanks to the use of a large base case).