boost/boost_1_91_0/libs/iterator/doc/RandomAccessTraversal.rst

Random Access Traversal Concept

A class or built-in type X models the Random Access Traversal concept if the following expressions are valid and respect the stated semantics. In the table below, Distance is iterator_traits<X>::difference_type and n represents a constant object of type Distance.

Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal)
Expression	Return Type	Operational Semantics	Assertion/ Precondition
r += n	X&	{ Distance m = n; if (m >= 0) while (m--) ++r; else while (m++) --r; return r; }
a + n, n + a	X	{ X tmp = a; return tmp += n; }
r -= n	X&	return r += -n
a - n	X	{ X tmp = a; return tmp -= n; }
b - a	Distance	a < b ? distance(a,b) : -distance(b,a)	pre: there exists a value n of Distance such that a + n == b. b == a + (b - a).
a[n]	convertible to T	*(a + n)	pre: a is a Readable Iterator
a[n] = v	convertible to T	*(a + n) = v	pre: a is a Writable iterator
a < b	convertible to bool	b - a > 0	< is a total ordering relation
a > b	convertible to bool	b < a	> is a total ordering relation
a >= b	convertible to bool	!(a < b)
a <= b	convertible to bool	!(a > b)
iterator_traversal<X>::type	Convertible to random_access_traversal_tag