Extend Field and Checksum for error correction

src/lib.rs

@@ -95,14 +95,18 @@
 //!
 //! ```
 //! # #[cfg(feature = "alloc")] {
-//! use bech32::Checksum;
+//! use bech32::{Checksum, Fe32, Fe1024};
 //!
 //! /// The codex32 checksum algorithm, defined in BIP-93.
 //! #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 //! pub enum Codex32 {}
 //!
 //! impl Checksum for Codex32 {
 //! type MidstateRepr = u128;
+//! type CorrectionField = bech32::primitives::gf32_ext::Fe32Ext<2>;
+//! const ROOT_GENERATOR: Self::CorrectionField = Fe1024::new([Fe32::_9, Fe32::_9]);
+//! const ROOT_EXPONENTS: core::ops::RangeInclusive<usize> = 77..=84;
+//!
 //! const CHECKSUM_LENGTH: usize = 13;
 //! const CODE_LENGTH: usize = 93;
 //! // Copied from BIP-93

src/primitives/checksum.rs

@@ -23,6 +23,10 @@ use crate::Fe32;
 ///
 /// For users, this can be treated as a marker trait; none of the associated data
 /// are end-user relevant.
+///
+/// For developers, implementations of this trait can be computed by starting with
+/// a couple of values and using the [`PrintImpl`] object to generate the rest.
+/// See the documentation for that type and its unit tests for examples.
 pub trait Checksum {
  /// An unsigned integer type capable of holding a packed version of the generator
  /// polynomial (without its leading 1) and target residue (which will have the
@@ -37,6 +41,16 @@ pub trait Checksum {
  /// be pretty efficient no matter what.
  type MidstateRepr: PackedFe32;
 
+ /// The extension field in which error correction happens.
+ type CorrectionField: super::ExtensionField<BaseField = Fe32>;
+
+ /// The generator of the consecutive roots of the generator polynomial.
+ const ROOT_GENERATOR: Self::CorrectionField;
+
+ /// The consecutive powers of [`Self::ROOT_GENERATOR`] which are roots
+ /// of the generator polynomial.
+ const ROOT_EXPONENTS: core::ops::RangeInclusive<usize>;
+
  /// The length of the code.
  ///
  /// The length of the code is how long a coded message can be (including the
@@ -224,7 +238,7 @@ impl<'a, ExtField> PrintImpl<'a, ExtField> {
 #[cfg(feature = "alloc")]
 impl<'a, ExtField> fmt::Display for PrintImpl<'a, ExtField>
 where
- ExtField: super::ExtensionField + From<Fe32>,
+ ExtField: super::Bech32Field + super::ExtensionField<BaseField = Fe32>,
 {
  fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
  // Generator polynomial as a polynomial over GF1024
@@ -234,7 +248,7 @@ where
  v.extend(self.generator.iter().cloned().map(ExtField::from));
  Polynomial::new(v)
  };
- let (_gen, length, _exponents) = gen_poly.bch_generator_primitive_element();
+ let (gen, length, exponents) = gen_poly.bch_generator_primitive_element();
 
  write!(f, "// Code block generated by Checksum::print_impl polynomial ")?;
  for fe in self.generator {
@@ -251,6 +265,18 @@ where
  " type MidstateRepr = {}; // checksum packs into {} bits",
  self.midstate_repr, self.bit_len
  )?;
+ f.write_str("\n")?;
+ writeln!(f, " type CorrectionField = {};", core::any::type_name::<ExtField>())?;
+ f.write_str(" const ROOT_GENERATOR: Self::CorrectionField = ")?;
+ gen.format_as_rust_code(f)?;
+ f.write_str(";\n")?;
+ writeln!(
+ f,
+ " const ROOT_EXPONENTS: core::ops::RangeInclusive<usize> = {}..={};",
+ exponents.start(),
+ exponents.end()
+ )?;
+ f.write_str("\n")?;
  writeln!(f, " const CODE_LENGTH: usize = {};", length)?;
  writeln!(f, " const CHECKSUM_LENGTH: usize = {};", gen_poly.degree())?;
  writeln!(f, " const GENERATOR_SH: [{}; 5] = [", self.midstate_repr)?;
@@ -263,9 +289,10 @@ where
  writeln!(f, " ];")?;
  writeln!(
  f,
- " const TARGET_RESIDUE: {} = {:?};",
+ " const TARGET_RESIDUE: {} = 0x{:0width$x};",
  self.midstate_repr,
- u128::pack(self.target.iter().copied().map(From::from))
+ u128::pack(self.target.iter().copied().map(From::from)),
+ width = self.hex_width,
  )?;
  f.write_str("}")
  }