Now it's possible to specify sort order of each index part.

Related dev. issue(s): https://github.com/tarantool/tarantool/issues/5529
Related doc issue: https://github.com/tarantool/doc/issues/3747 (Lua API)
Related doc issue: https://github.com/tarantool/doc/issues/3748 (C API)

Product: Tarantool
Since: master
Root document: https://www.tarantool.io/en/doc/latest/reference/reference_lua/box_space/create_index/
SME: @ mkostoevr

Details

Sort order specifies the way indexes iterate over tuples with
different fields in the same part. It can be either ascending
(which is the case by default) and descending.

Tuples with different ascending parts are sorted in indexes from
lesser to greater, whereas tuples with different descending parts
are sorted in the opposte order: from greater to lesser.

Given example:

box.cfg{}

s = box.schema.create_space('tester')
pk = s:create_index('pk', {parts = {
  {1, 'unsigned', sort_order = 'desc'},
  {2, 'unsigned', sort_order = 'asc'},
  {3, 'unsigned', sort_order = 'desc'},
}})

s:insert({1, 1, 1})
s:insert({1, 1, 2})
s:insert({1, 2, 1})
s:insert({1, 2, 2})
s:insert({2, 1, 1})
s:insert({2, 1, 2})
s:insert({2, 2, 1})
s:insert({2, 2, 2})
s:insert({3, 1, 1})
s:insert({3, 1, 2})
s:insert({3, 2, 1})
s:insert({3, 2, 2})

In this case field 1 and 3 are descending, whereas field 2 is
ascending. So s:select() will return this result:

---
- [3, 1, 2]
- [3, 1, 1]
- [3, 2, 2]
- [3, 2, 1]
- [2, 1, 2]
- [2, 1, 1]
- [2, 2, 2]
- [2, 2, 1]
- [1, 1, 2]
- [1, 1, 1]
- [1, 2, 2]
- [1, 2, 1]
...

Beware, that when using other sort order than 'asc' for any field
'GE', 'GT', 'LE' and 'LT' iterator lose their meaning and specify
'forward inclusive', 'forward exclusive', 'reverse inclusive' and
'reverse exclusive' iteration direction respectively. Given example
above, s:select({2}, {iterator = 'GT'}) will return this:

---
- [1, 1, 2]
- [1, 1, 1]
- [1, 2, 2]
- [1, 2, 1]
...

And s:select({1}, {iterator = 'LT'}) will give us:

---
- [2, 2, 1]
- [2, 2, 2]
- [2, 1, 1]
- [2, 1, 2]
- [3, 2, 1]
- [3, 2, 2]
- [3, 1, 1]
- [3, 1, 2]
...

In order to be more clear alternative iterator aliases can be used:
'FORWARD_INCLUSIVE', 'FORWARD_EXCLUSIVE', 'REVERSE_INCLUSIVE',
'REVERSE_EXCLUSIVE':

> s:select({1}, {iterator = 'REVERSE_EXCLUSIVE'})
---
- [2, 2, 1]
- [2, 2, 2]
- [2, 1, 1]
- [2, 1, 2]
- [3, 2, 1]
- [3, 2, 2]
- [3, 1, 1]
- [3, 1, 2]
...

Requested by @ mkostoevr in https://github.com/tarantool/tarantool/commit/b1990b219727ad8c43e5291ff7444546818a0fb7.

Start with the root document at reference/reference_lua/box_space/create_index/ and review the related development issue 5529 for context. Document per-part ascending and descending sort_order, the resulting select order, and the iterator alias behavior shown in this issue. Done means the Lua API page clearly explains these semantics with the supplied examples.