Add a note, expand other notes, add dates into notes.

1 files changed, 26 insertions, 1 deletions

diff --git a/notes/250329-numbers.md b/notes/250329-numbers.md
index 6507a67..5bbfde3 100644
--- a/notes/250329-numbers.md
+++ b/notes/250329-numbers.md
@@ -1,11 +1,15 @@
+# Number tower
 
+_2025 March_
+
+```
 exacts:
 
   uint : 0...n
 
   sint : -n...-1 | uint
 
-  ratn : ( p: sint, q: sint )
+  ratn : ( p: sint, q: uint )
 
   comp : ( r: ratn, i: ratn )
 
@@ -43,3 +47,24 @@ inexact operations:
   double + double = double
 
   cmp128 + double = cmp128  [ cmp128 + ( r = double , i = 0 ) ]
+```
+
+_2025 December_
+
+Mixing exact and inexact numbers implicitly should not be allowed.  It
+should be a type error.  Conversion must be explicit.
+
+Basically there are two numeric towers, not one.  The exact numbers
+use integers all the way down; for example, an exact complex is a pair
+of exact rationals which are each a pair of integers.  Inexact numbers
+use double, with the only other type being `complex128` which is a
+pair of doubles.
+
+Not sure yet how exactly to deal with unsigned integers.  All I know
+is that I don't want there to be unsigned rational numbers; that's
+just excessive.  A rational number always has a signed numerator and
+an unsigned denominator.
+
+See also:
+
+https://www.deinprogramm.de/sperber/papers/numerical-tower.pdf