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Decimal Arithmetic

William Kahan, Basic Issues in Floating Point Arithmetic and Error Analysis, here. There is the possibility that some people exist who if granted three wishes by an all-powerful Genie would use  two of them to get 1. all hardware vendors to implement decimal arithmetic and 2. make Java Big Decimal faster. I guess that is why we cannot have nice things.

McIntosh and Sham , IBM Toronto Lab, Compiler Exploitation of Decimal Floating-Point Hardware, 2008, here. Why care about decimal arithmetic hardware? These folks list some reasons. Oh, avoids rounding in some cases. How about get me AVX3.2 and a 10GB link to my home computer first? Oh. and make big flat screens high res and cheap and get me a  non temporary ICC license. And a restricted range vector exponential that is super fast. Make the 10GB link wireless and make Verizon FIOS support IMAP until that happens. 7.0 * 0.015 = 7.10499999… meh

Lefevre, Stehle, and Zimmermann, Worst Cases for the Exponential Function on the IEEE 754r decimal64 Format, here. interesting, but why do I care if decimal arithmetic hardware works, unless it is cheaper and faster than binary. Is this gonna be one of those creepy reasons like – because we need new languages to express our programming ideas in?

Abstract. We searched for the worst cases for correct rounding of the exponential function in the IEEE 754r decimal64 format, and computed all the bad cases whose distance from a breakpoint (for all rounding modes) is less than 10−15 ulp, and we give the worst ones. In partic- ular, the worst case for |x| ≥ 3 × 10−11 is exp(9.407822313572878 × 10−2) = 1.09864568206633850000000000000000278…. This work can be extended to other elementary functions in the decimal64 format and allows the design of reasonably fast routines that will evaluate these functions with correct rounding, at least in some domains.

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