http://gcc.gnu.org/bugzilla/show_bug.cgi?id=60843
--- Comment #3 from joseph at codesourcery dot com <joseph at codesourcery dot com> --- On Wed, 30 Apr 2014, kdevel at vogtner dot de wrote: > The problem is the erroneous wording "reduction modulo 2^N". *Reduction* by > definition results in the least *nonnegative* number out of the list of > congruent numbers, cf. http://www.youtube.com/watch?v=SO6l6sDwEFg&t=5m50s It's perfectly normal English usage for "X with qualifier" to be outside what would be understood by X without the qualifier. I think the use in the GCC manual is a perfectly ordinary and well-understood use of the term. The GCC manual is not trying to refer to any particular set of definitions as normative references, and it's not trying to give formal definitions. If anything, I'd say strictly reduction modulo 2^N is a map from Z to Z / 2^N Z, i.e. producing an equivalence class of integers rather than a single integer (and for modulo arithmetic, integer types are interpreted as having values that are such equivalence classes).
