primitives: introduce FieldVec type

This will allow `Polynomial` to work without an allocator (at least for
"small" checksums. Here a "small" checksum is one of length at most 6
(which covers bech32 and bech32m).

The descriptor checksum (8 characters), codex32 (13 characters) and "long
codex32" (15 characters) will not work with no-alloc.

I would like to fix this but it results in large types, especially a large
InvalidResidueError type (see last commit of this PR), so probably it will
need to be feature-gated or something. For now we just punt on it.

This PR introduces the `primitives::correction` module but only puts a
single constant into it for now.

Author: apoelstra

src/primitives/correction.rs

@@ -0,0 +1,35 @@
+// SPDX-License-Identifier: MIT
+
+//! Error Correction
+//!
+//! Implements the Berlekamp-Massey algorithm to locate errors, with Forney's
+//! equation to identify the error values, in a BCH-encoded string.
+//!
+
+/// **One more than** the maximum length (in characters) of a checksum which
+/// can be error-corrected without an allocator.
+///
+/// When the **alloc** feature is enabled, this constant is practically irrelevant.
+/// When the feature is disabled, it represents a length beyond which this library
+/// does not support error correction.
+///
+/// If you need this value to be increased, please file an issue describing your
+/// usecase. Bear in mind that an increased value will increase memory usage for
+/// all users, and the focus of this library is the Bitcoin ecosystem, so we may
+/// not be able to accept your request.
+// This constant is also used when comparing bech32 residues against the
+// bech32/bech32m targets, which should work with no-alloc. Therefore this
+// constant must be > 6 (the length of the bech32(m) checksum).
+//
+// Otherwise it basically represents a tradeoff between stack usage and the
+// size of error types, vs functionality in a no-alloc setting. The value
+// of 7 covers bech32 and bech32m. To get the descriptor checksum we need a
+// value and the descriptor checksum. To also get codex32 it should be >13,
+// and for "long codex32" >15 ... but consider that no-alloc contexts are
+// likely to be underpowered and will struggle to do correction on these
+// big codes anyway.
+//
+// Perhaps we will want to add a feature gate, off by default, that boosts
+// this to 16, or maybe even higher. But we will wait for implementors who
+// complain.
+pub const NO_ALLOC_MAX_LENGTH: usize = 7;