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Radix64 Encoding: Order-Preserving Strings in 64 Bits

Problem: Compact, Order-Preserving Identifiers for Short Symbols

In domains like high-frequency trading, structured storage, or financial indexing, identifiers such as stock symbols (e.g., "AAPL", "GOOG", "TSLA") are:

  • Short — typically ≤ 8 characters
  • Drawn from a small alphabet — ~32 to 40 printable characters
  • Compared lexicographically — e.g., "ABC" < "XYZ" must hold

These structural constraints can be exploited to encode each symbol into a compact, fixed-width binary key while preserving their natural sort order.

Specifically, such systems often need:

  • Lexicographic ordering — to maintain sorted maps, symbol trees, or search indices
  • Fixed-size keys — for CPU- and cache-friendly performance
  • Support for variable-length symbols — without breaking ordering
  • Ability to pack extra metadata — like 16-bit contract IDs or timestamps

But typical representations fall short:

  • std::string / char[] are variable-length and inefficient as keys
  • strcmp is slow, branching, and non-SIMD friendly
  • Standard Base64 isn't order-preserving
  • Hashes destroy ordering and increase collision risk

➤ Radix64 encoding solves this by leveraging the symbol structure — short, constrained, ordered strings — to pack lex-order-preserving representations into just 64 bits.

Solution: Order-Preserving Radix64 Encoding

Radix64 solves this by:

  • Encoding up to 8 characters as a 48-bit big-endian base-64 integer
  • Padding shorter strings with the lowest code to preserve prefix order
  • Optionally combining a 16-bit integer (e.g., contract ID) in the LSBs
  • Making unsigned integer comparison exactly match lexicographic order

So you can now represent things like:

"AAPL"    → 48-bit radix64 prefix
contract  → 16-bit index
key       → 64-bit sortable, compact ID

Used as keys in:

  • Fast symbol lookup tables
  • Order books and trading systems
  • Encoded identifiers for datasets or HDF5 groups
  • Key-value stores, B-trees, or radix trees

Read the full radix64 guide