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".

3 files changed, 44 insertions, 1 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);
diff --git a/tests/test_shader_repl.py b/tests/test_shader_repl.py
index c3c46cf..8736420 100755
--- a/tests/test_shader_repl.py
+++ b/tests/test_shader_repl.py
@@ -10,6 +10,7 @@ becomes a list of what was true once.
 The rest is the loop itself, driven the way a person drives it -- typed lines,
 history, a tab -- in a real session with a real pty.
 """
+import ast
 import os
 import re
 import subprocess
@@ -34,7 +35,8 @@ def repl_lists():
         body = re.search(r"^%s = (\[[^\]]*\])" % var, src, re.M).group(1)
         return [w.strip().strip('"\'').rstrip("=(").strip('"')
                 for w in re.findall(r'["\'][^"\']+["\']', body)]
-    return {v: names(v) for v in ("COMMANDS", "SHADERS", "PROPS", "VARS", "FUNCS")}
+    return {v: names(v)
+            for v in ("COMMANDS", "SHADERS", "PROPS", "VARS", "CONSTS", "FUNCS")}
 
 
 def source_names(path, pattern):
@@ -70,6 +72,19 @@ def session(cfg_path, data_home):
                    cols=84, rows=16, config=cfg_path, env=env)
 
 
+def test_the_script_is_a_script():
+    """First, because everything below it starts a pane that runs this file: a
+    syntax error otherwise shows up as `IndexError: list index out of range` from
+    a pane that died before printing its prompt, which is a long way from saying
+    line 212 is indented wrong."""
+    try:
+        ast.parse(open(REPL).read())
+        ok, why = True, ""
+    except SyntaxError as exc:
+        ok, why = False, "%s line %s: %s" % (exc.__class__.__name__, exc.lineno, exc.msg)
+    check("contrib/shader-repl parses", ok, why)
+
+
 def test_the_completion_list_matches_the_code():
     lists = repl_lists()
 
@@ -90,6 +105,10 @@ def test_the_completion_list_matches_the_code():
           variables <= set(lists["VARS"]),
           "missing: %s" % sorted(variables - set(lists["VARS"])))
 
+    consts = source_names("expr.c", r'\{"([A-Z]+)", \d+\},?\s')
+    check("every constant can be completed", consts <= set(lists["CONSTS"]),
+          "missing: %s" % sorted(consts - set(lists["CONSTS"])))
+
     funcs = source_names("expr.c", r'\{"([a-z]+)", \d, OP_[A-Z]+\}')
     check("every expression function can be completed",
           funcs <= set(lists["FUNCS"]),
@@ -185,6 +204,7 @@ def test_help_lists_what_there_is():
 
 
 if __name__ == "__main__":
+    test_the_script_is_a_script()
     test_the_completion_list_matches_the_code()
     test_every_offered_shader_is_accepted_by_a_session()
     test_history_survives_the_next_run()
diff --git a/tests/test_shadertoy.py b/tests/test_shadertoy.py
index 2f88225..99e724a 100644
--- a/tests/test_shadertoy.py
+++ b/tests/test_shadertoy.py
@@ -123,6 +123,11 @@ EXPRS = [
     "abs(sin(x * 9 + t / 6))",
     "clamp(sin(t / 5) + 128, 0, 255)",
     "sin(sin(t / 3))",
+    # pi as an angle: a half turn, in the degrees this language counts in
+    "PI", "TAU", "PI * 2 == TAU",
+    "sin(PI)", "sin(PI / 2)", "sin(PI / 6)", "cos(TAU)",
+    "sin(TAU * x / cols)", "sin(TAU * y / rows + t / 5)",
+    "128 + sin(TAU * t / 4000) / 2",
 ]