and consistency mechanisms in the case of the reduction unit 260 the finite size of the accumulation buffer 266 typically on the order of 64 entries limits the number of active keys which thus limits the number of independent accumulations undertaken at one time however not all parts of the reduction operation need the consistency and coherence provided by the reduction unit 260 itself and instead can be implemented with local coherence and consistency and a globally coherent and consistent meta operation much as in the above example in which resources with weaker invariance guarantees were used in conjunction with meta tokens passed through the hardware based interaction mechanisms local reduction or interaction mechanisms such arithmetic units collocated with the cache banks described in following paragraphs can be used along with meta tokens passed through the reduction unit to provide the same semantics offered by directly using the reduction unit but with a larger number of accumulation buffer entries in another implementation to supplement a reduction unit such as reduction unit 260 will include arithmetic units collocated with cache banks using an implementation based on scatter add which is described in u201c scatter add in parallel architectures 11th international symposium on high performance computer architecture 2005 by jung ho ahm and william j dally these arithmetic units provide the same arithmetic operators as the tree based unit 262 f first level 262 m middle levels and 262 l last level but use the memory system as the accumulation buffer 266 and the mau 240 as the access interface as opposed to the dedicated emit fifo and.