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# Number tower
_2025 March_
```
exacts:
uint : 0...n
sint : -n...-1 | uint
ratn : ( p: sint, q: uint )
comp : ( r: ratn, i: ratn )
inexacts:
double : ieee754 double with +inf, -inf, +nan, -nan
cmp128 : ( r: double , i: double )
exact operations:
uint + uint = uint
sint + uint = sint
ratn + uint = ratn [ ratn + ( p = uint , q = 0 ) ]
ratn + sint = ratn [ ratn + ( p = sint , q = 0 ) ]
ratn + ratn = ratn
comp + uint = comp [ comp + ( r = ( p = uint , q = 0 ) , i = 0 ) ]
comp + sint = comp [ comp + ( r = ( p = sint , q = 0 ) , i = 0 ) ]
comp + ratn = comp [ comp + ( r = ratn , i = 0 ) ]
comp + comp = comp
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
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