Notes on NaNs

syndicate/mc/preserve.md

@@ -321,10 +321,17 @@ Any `Value` may be represented using the
 [compact binary syntax](#compact-binary-syntax) by directly prefixing
 the binary form of the `Value` with ASCII `SOH` (`%x01`), or by
 enclosing a hexadecimal representation of the binary form of the
-`Value` in the tokens `#hexvalue{` and `}`.
+`Value` in the tokens `#hexvalue{` and `}`.[^rationale-switch-to-binary]
 
            Compact = %x01 <binary data> / %s"#hexvalue{" *(ws / HEXDIG) ws "}"
 
+  [^rationale-switch-to-binary]: **Rationale.** The textual syntax
+    cannot express every `Value`: specifically, it cannot express the
+    several million floating-point NaNs, or the two floating-point
+    Infinities. Since the compact binary format for `Value`s expresses
+    each `Value` with precision, embedding binary `Value`s solves the
+    problem.
+
 `Boolean`s are the simple literal strings `#true` and `#false`.
 
            Boolean = %s"#true" / %s"#false"
@@ -1370,9 +1377,9 @@ encoding ordering? We'd have to only use streaming forms, and avoid
 the small integer encoding, and not store record arities, and sort
 sets and dictionaries, and mask floats and doubles (perhaps
 [like this](https://stackoverflow.com/questions/43299299/sorting-floating-point-values-using-their-byte-representation)),
-and I don't know what to do about SignedIntegers. Perhaps make them
+and pick a specific `NaN`, and I don't know what to do about
-more like float formats, with the byte count acting as a kind of
+SignedIntegers. Perhaps make them more like float formats, with the
-exponent underneath the sign bit.
+byte count acting as a kind of exponent underneath the sign bit.
 
  - Perhaps define separate additional canonicalization restrictions?
    Doesn't help the ordering, but does help the equivalence.