| Value | Meaning |
|---|---|
| appropriate | Performs pairwise summation for floating point based types and fast summation for integral based types. |
| pairwise | Pairwise summation algorithm. |
| precise | Precise summation algorithm. The value of the sum is rounded to the nearest representable floating-point number using the $(LUCKY round-half-to-even rule). The result can differ from the exact value on 32bit x86, nextDown(proir) <= result && result <= nextUp(proir). The current implementation re-establish special value semantics across iterations (i.e. handling ±inf). References: "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates", Mark Dickinson's post at bugs.python.org. |
| decimal | Precise decimal summation algorithm. The elements of the sum are converted to a shortest decimal representation that being converted back would result the same floating-point number. The resulting decimal elements are summed without rounding. The decimal sum is converted back to a binary floating point representation using round-half-to-even rule. See_also: The Ryu algorithm |
| kahan | Kahan summation algorithm. |
| kbn | $(LUCKY Kahan-Babuška-Neumaier summation algorithm). KBN gives more accurate results then Kahan. |
| kb2 | $(LUCKY Generalized Kahan-Babuška summation algorithm), order 2. KB2 gives more accurate results then Kahan and KBN. |
| naive | Naive algorithm (one by one). |
| fast | SIMD optimized summation algorithm. |
Summation algorithms.