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".

2 files changed, 12 insertions, 1 deletions

diff --git a/contrib/shader-repl b/contrib/shader-repl
index f154bb8..4410a24 100755
--- a/contrib/shader-repl
+++ b/contrib/shader-repl
@@ -65,6 +65,8 @@ PROPS = ["amount=", "color=", "channel=", "where=", "at=", "radius=", "band=",
 VALUES = ['"chrome"', '"content"', '"fg"', '"bg"', '"both"']
 VARS = ["x", "y", "cols", "rows", "curx", "cury", "cursor", "focused", "t",
         "since"]
+# Angles are degrees, so pi is a half turn: `PI` is 180 and `TAU` is 360.
+CONSTS = ["PI", "TAU"]
 FUNCS = ["min(", "max(", "abs(", "clamp(", "dist(", "sin(", "cos("]
 
 HISTORY = os.path.join(
@@ -77,7 +79,7 @@ def complete(text, state):
     inside an expression, but a prompt that guesses which you meant and offers
     nothing when it guesses wrong is worse company than one that offers
     everything starting with what you typed."""
-    words = COMMANDS + SHADERS + PROPS + VALUES + VARS + FUNCS
+    words = COMMANDS + SHADERS + PROPS + VALUES + VARS + CONSTS + FUNCS
     hits = [w for w in words if w.startswith(text)]
     return hits[state] if state < len(hits) else None
 
@@ -207,6 +209,8 @@ def main():
                 print("  shaders: " + " ".join(SHADERS))
                 print("  keys:    " + " ".join(p.rstrip("=") for p in PROPS))
                 print("  vars:    " + " ".join(VARS))
+                print("  consts:  " + " ".join(CONSTS)
+                      + "   (degrees, so PI is a half turn)")
                 print("  funcs:   " + " ".join(f.rstrip("(") for f in FUNCS))
                 print("  tab completes all of it; up/down and ctrl-r are history")
                 continue
diff --git a/contrib/shadertoy.html b/contrib/shadertoy.html
index 070f139..b1c9614 100644
--- a/contrib/shadertoy.html
+++ b/contrib/shadertoy.html
@@ -134,6 +134,12 @@
 
 const DEP = { POS: 1, CURSOR: 2, TIME: 4, FOCUS: 8, SIZE: 16 };
 
+/* Pi is not a number in an angle language, it is a half turn -- and angles here
+   are degrees, so `PI` is 180 and `TAU` is 360. A radian-shaped formula ports
+   across unchanged, and the common fractions of a turn stay whole. Same table as
+   src/expr.c, spelled-out numbers rather than variables. */
+const CONSTS = { PI: 180, TAU: 360 };
+
 const VARS = {
   x:       { dep: DEP.POS },
   y:       { dep: DEP.POS },
@@ -206,6 +212,7 @@ function compile(src) {
         ws(); if (src[i] !== ")") fail("expected )"); i++;
         return makeCall(name, args);
       }
+      if (name in CONSTS) { const k = CONSTS[name]; return () => k; }
       const v = VARS[name];
       if (!v) { i = s; fail("unknown name"); }
       deps |= v.dep;