the nth position if and only if n is in the list. The implied probability of a gap of n is 1/2n. This is also the special case of Golomb coding where the parameter M is 1; this parameter is only normally selected when , or roughly the term occurs in at least 38% of documents. Language support The APL programming language fully supports bit arrays of arbitrary shape and size as a Boolean datatype distinct from integers. All major implementations (Dyalog APL, APL2, APL Next, NARS2000, Gnu APL, etc.) pack the bits densely into whatever size the machine word is. Bits may be accessed individually via the usual indexing notation (A[3]) as well as through all of the usual primitive functions and operators where they are often operated on using a special case algorithm such as summing the bits via a table lookup of bytes. The C programming language's bit fields, pseudo-objects found in structs with size equal to some number of bits, are in fact small bit arrays; they are limited in that they cannot span words. Although they give a convenient syntax, the bits are still accessed using bytewise operators on most machines, and they can only be defined statically (like C's static arrays, their sizes are fixed at compile-time). It is also a common idiom for C programmers to use words as small bit arrays and access bits of them using bit operators. A widely available header file included in the X11 system, xtrapbits.h, is “a portable way for systems to define bit field manipulation of arrays of bits.” A more explanatory description of aforementioned approach can be found in the comp.lang.c faq. In C++, although individual bools typically occupy the same space as a byte or an integer, the STL type vector<bool> is a partial template specialization in which bits are packed as a space efficiency optimization. Since bytes (and not bits) are the smallest addressable unit in C++, the [] operator does not return a reference to an element, but instead returns a proxy reference. This might seem a minor point, but it means that vector<bool> is not a standard STL container, which is why the use of vector<bool> is generally discouraged. Another unique STL class, bitset, creates a vector of bits fixed at a particular size at compile-time, and in its interface and syntax more resembles the idiomatic use of words as bit