Merge pull request #1866 from brownplt/jsnums-test-atan2-quadrants

Add jsnums-test spec for atan2 quadrant correctness

Author: jpolitz

tests/jsnums-test/jsnums-test.js

@@ -41,6 +41,52 @@ R(["pyret-base/js/js-numbers"], function(JNlib) {
       expect(function() { JN.makeBignum(+1.5).acos(); }).toThrow('domainError');
 
     });
+
+    it("atan2 four quadrants and boundaries", function() {
+      // atan2(y, x) takes y first, x second (math convention).
+      // The x<0 and (x>0, y<0) branches historically leaked bare
+      // Math.PI / 2*Math.PI through `add`, because JS-number+JS-number
+      // short-circuits and returns its raw sum.
+
+      // x > 0, y = 0: must be exact integer 0, NOT Roughnum 0.0.
+      // Multiples of π are intrinsically irrational, but this case is
+      // representable exactly and "atan2(0, 5) == 0" is the kind of
+      // thing math teachers expect to be unambiguous. Implementation
+      // routes through atan(divide(0, x)) -> atan(0) -> integer 0.
+      expect(JN.isInteger(JN.atan2(0, 1))).toBe(true);
+      expect(JN.equals(JN.atan2(0, 1), 0)).toBe(true);
+      expect(JN.isInteger(JN.atan2(0, 5))).toBe(true);
+      expect(JN.equals(JN.atan2(0, 5), 0)).toBe(true);
+      expect(JN.isInteger(JN.atan2(0, JN.makeBignum(5)))).toBe(true);
+      expect(JN.equals(JN.atan2(0, JN.makeBignum(5)), 0)).toBe(true);
+
+      // x > 0, y > 0  (1st quadrant interior): atan(y/x), irrational.
+      expect(JN.isRoughnum(JN.atan2(1, 1))).toBe(true);
+
+      // x = 0, y > 0: π/2 (Roughnum)
+      expect(JN.isRoughnum(JN.atan2(1, 0))).toBe(true);
+      expect(JN.toFixnum(JN.atan2(1, 0))).toEqual(Math.PI / 2);
+
+      // x < 0, y >= 0  (2nd quadrant): atan(y/x) + π
+      expect(JN.isRoughnum(JN.atan2(1, -1))).toBe(true);
+      expect(JN.isRoughnum(JN.atan2(0, -1))).toBe(true);
+      // atan2(0, -1) = π exactly. This case used to leak Math.PI as a raw JS double.
+      expect(JN.toFixnum(JN.atan2(0, -1))).toEqual(Math.PI);
+
+      // x < 0, y < 0  (3rd quadrant): atan(y/x) + π
+      expect(JN.isRoughnum(JN.atan2(-1, -1))).toBe(true);
+
+      // x = 0, y < 0: 3π/2. Note: jsnums returns angles in [0, 2π) here,
+      // unlike JS Math.atan2 which would give -π/2 for this case.
+      expect(JN.isRoughnum(JN.atan2(-1, 0))).toBe(true);
+      expect(JN.toFixnum(JN.atan2(-1, 0))).toEqual(3 * Math.PI / 2);
+
+      // x > 0, y < 0  (4th quadrant): atan(y/x) + 2π. Used to leak 2*Math.PI.
+      expect(JN.isRoughnum(JN.atan2(-1, 1))).toBe(true);
+
+      // (0, 0) is out of domain.
+      expect(function() { JN.atan2(0, 0); }).toThrow('domainError');
+    });
   });
 
   jazz.execute();