Ranges are finite numerical intervals, e.g. “all integers
i such that
(m <= i) and
(i < n)”. The high end bound is sometimes exclusive,
(i < n), and sometimes inclusive,
(i <= n).
In Wuffs syntax, similar to Rust syntax, the exclusive range is
m .. n and the inclusive range is
m ..= n. The conventional mathematical syntax is
[m, n) or
[m, n[ for exclusive and
[m, n] for inclusive, but Wuffs is a programming language, and programming language tools prefer brackets to always be balanced.
In Wuffs' C form, the exclusive range is
wuffs_base__range_ie_T and the inclusive range is
ie means inclusive on the low end, exclusive on the high end. The
T is a numerical type like
Both of the
ie flavors are useful in practice:
m ..= n is more convenient when computing interval arithmetic,
m .. n is more convenient when working with slices. The
ee flavors also exist in theory, but aren't widely used. In Wuffs, the low end is always inclusive.
For example, with
ie, the number of elements in “
uint32_t values in the half-open interval
m .. n” is equal to
max(0, n - m). Furthermore, that number of elements (in one dimension, a length, in two dimensions, a width or height) is itself representable as a
uint32_t without overflow, again for
n. In the contrasting
ii flavor, the size of the closed interval
0 ..= ((1<<32) - 1) is
1<<32, which cannot be represented as a
In Wuffs' C form, because of this potential overflow, the
ie flavor has length / width / height methods, but the
ii flavor does not.
ii (closed) flavor is useful when refining e.g. “the set of all
uint32_t values” to a contiguous subset: “
uint32_t values in the closed interval
m ..= n”, for
n. An unrefined type (in other words, the set of all
uint32_t values) is not representable in the
ie flavor because if
((1<<32) - 1) then
(n + 1) will overflow.
It is valid for
m >= n (for the
ie case) or for
m > n (for the
ii case), in which case the range is empty. There are multiple valid representations of an empty range:
(m=1, n=0) and
(m=99, n=77) are equivalent.
Rects are just the 2-dimensional form of (1-dimensional) ranges. For example,
wuffs_base__rect_ii_u32 is a rectangle on the integer grid, containing all points
(x, y) such that
(min_incl_x <= x) and
(x <= max_incl_x), and likewise for
Once again, it is valid for
min > max, and there are multiple valid representations of an empty rectangle.
When rects are used in graphics, the X and Y axes increase right and down.