sl0ppty: PI is 180

Angles here are degrees, and pi in an angle language is not a number -- it is a
half turn. So `PI` is 180, `TAU` is 360, and a formula written the radian way
ports across as written:

    sin(TAU * x / cols)      one cycle over the pane's width
    sin(TAU * p * 3 / perim) three lobes fitted exactly to a border
    PI / 2                   a quarter turn
    PI / 6                   thirty degrees, exactly

That last line is the argument. A numeric pi would be 3 in this language, and
`3.14159 / 6` in integers is 0 -- so radians cannot express a sixth of a turn
here at all, while degrees give it as a whole number. The pun is not a
compromise; it is the more precise reading of the two.

Which is why there is no `deg2rad` or `rad2deg` beside them, and asking for one
says `unknown function`. There is one angle unit. A conversion could only lose
the angle (`deg2rad(90)` is 1, and `sin(1)` is nearly nothing) or invent a second
scale for the language to disagree with itself about.

Spelled-out numbers rather than variables: they read no environment, carry no
dependency, and fold into the program like the literals they are. The browser
preview learned the same two, from the same table.

Verified: 12 cases in `tests/expr_test.c`, including that `deg2rad` and
`rad2deg` are refused; the cross-check agrees with the compiler on 700
evaluations, now including `sin(TAU * x / cols)` and friends.

Two smaller things ride along, both from the repl. `PI`/`TAU` tab-complete, and
its drift test grew a third table to check -- it already caught `sin`/`cos`
missing before I did. And it now checks the script *parses* before starting a
pane that runs it: I broke the indentation of one line here, and the failure
arrived as `IndexError: list index out of range` from a pane that died before
its prompt, which is a long way from "line 212".

1 files changed, 7 insertions, 0 deletions

diff --git a/config/config.kdl b/config/config.kdl
index 6fc59d2..9ee458a 100644
--- a/config/config.kdl
+++ b/config/config.kdl
@@ -475,6 +475,13 @@ states {
 //                                  breathe with nothing to rescale. Any angle
 //                                  wraps, negative ones included, since `t / 4`
 //                                  does not stop at 360.
+//   constants   PI TAU        180 and 360: pi as an *angle*, which is all it can
+//                             be here -- a half turn and a whole one. So a
+//                             radian-shaped formula ports across as written,
+//                             `sin(TAU * x / cols)` is one cycle over the pane,
+//                             and the common fractions stay exact where
+//                             `3.14159 / 6` in integers would be 0. There is no
+//                             deg2rad/rad2deg: one unit, nothing to convert.
 //
 // There are no loops and no recursion, on purpose: a config cannot spin, and
 // there is nothing to sandbox. An expression that does not compile drops that