Editing IBM hexadecimal floating-point (section)

== The decision for hexadecimal floating-point ==

The article "Architecture of the IBM System/360" explains the choice as being because "the frequency of pre-shift, overflow, and precision-loss post-shift on floating-point addition are substantially reduced by this choice."<ref name="IBM Journal of R&D">{{cite journal |last1=Amdahl |first1=Gene |last2=Blaauw |first2=Gerrit |last3=Brooks, Jr |first3=Frederick |title=Architecture of the IBM System/360 |journal=IBM Journal of Research and Development |volume=1964 |page=87 |url=https://www.researchgate.net/publication/220498837 |access-date=4 September 2023}}</ref> This allowed higher performance for the large System/360 models, and reduced cost for the small ones. The authors were aware of the potential for precision loss, but assumed that this would not be significant for 64-bit floating-point variables. Unfortunately, the designers seem not to have been aware of [[Benford's Law]] which means that a large proportion of numbers will suffer reduced precision.

The book "Computer Architecture" by two of the System/360 architects quotes Sweeney's study of 1958-65 which showed that using a base greater than 2 greatly reduced the number of shifts required for alignment and normalisation, in particular the number of ''different'' shifts needed. They used a larger base to make the implementations run faster, and the choice of base 16 was natural given 8-bit bytes. The intention was that 32-bit floats would only be used for calculations that would not propagate rounding errors, and 64-bit double precision would be used for all scientific and engineering calculations. The initial implementation of double precision lacked a guard digit to allow proper rounding, but this was changed soon after the first customer deliveries.<ref>{{cite book |last1=Blaauw |first1=Gerrit A. |last2=Brooks |first2=Frederick P. |title=Computer Architecture |date=1997 |publisher=Addison-Weslet |location=Reading, Massachusetts |isbn=0-201-10557-8 |edition=1st }}</ref>