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, 18 insertions, 0 deletions

diff --git a/tests/expr_test.c b/tests/expr_test.c
index b84e355..f775065 100644
--- a/tests/expr_test.c
+++ b/tests/expr_test.c
@@ -132,6 +132,24 @@ int main(void) {
   eq("128 + sin(270) / 2", 1); /* -255/2 truncates toward zero, so 128 - 127 */
   eq("abs(sin(270))", 255);
 
+  printf("\n-- PI and TAU are angles, not numbers\n");
+  eq("PI", 180);
+  eq("TAU", 360);
+  eq("PI * 2 == TAU", 1);
+  /* The point of the pun: a formula written the radian way works as written. */
+  eq("sin(PI)", 0);
+  eq("sin(PI / 2)", 255);
+  eq("cos(TAU)", 255);
+  eq("sin(TAU * 3 / 4)", -255);
+  /* ...and exactly, which real radians could not manage in integers: a sixth of
+   * a turn is 30 whole degrees, where 3.14159 / 6 would be 0. */
+  eq("sin(PI / 6)", 127);
+  eq("sin(PI / 3)", 221);
+  eq("sin(PI / 4)", 180);
+  /* No conversions, because there is one unit and nothing to convert. */
+  refused("deg2rad is not a thing", "deg2rad(90)");
+  refused("nor rad2deg", "rad2deg(1)");
+
   printf("\n-- variables\n");
   eq("x", 3);
   eq("y", 4);