[
{ "name": "zero", "args": [0], "expect": 0 },
{ "name": "one is pi/4", "args": [1], "expect": 0.7853981633974483 },
{ "name": "minus one is -pi/4", "args": [-1], "expect": -0.7853981633974483 },
{ "name": "square root of 3 is pi/3 (60 degrees)", "args": [1.7320508075688772], "expect": 1.0471975511965976 },
{ "name": "1 over root 3 is pi/6 (30 degrees)", "args": [0.5773502691896257], "expect": 0.5235987755982988 },
{ "name": "tiny: atan(x) rounds to x", "args": [1e-10], "expect": 1e-10 },
{ "name": "exactly 2^-29, the first value that goes through the polynomial", "args": [1.862645149230957e-9], "expect": 1.862645149230957e-9 },
{ "name": "small but not tiny: the cubic term shows", "args": [1e-5], "expect": 9.999999999666668e-6 },
{ "name": "0.1", "args": [0.1], "expect": 0.09966865249116204 },
{ "name": "just below the 7/16 boundary", "args": [0.43749999999999994], "expect": 0.41241044159738727 },
{ "name": "exactly 7/16: first value reduced against atan(0.5)", "args": [0.4375], "expect": 0.4124104415973873 },
{ "name": "0.5 lands on the atan(0.5) constant", "args": [0.5], "expect": 0.4636476090008061 },
{ "name": "exactly 11/16: reduced against atan(1)", "args": [0.6875], "expect": 0.6022873461349642 },
{ "name": "exactly 19/16: reduced against atan(1.5)", "args": [1.1875], "expect": 0.870903457075653 },
{ "name": "1.5 lands on the atan(1.5) constant", "args": [1.5], "expect": 0.982793723247329 },
{ "name": "exactly 39/16: reduced against pi/2", "args": [2.4375], "expect": 1.1814796049617557 },
{ "name": "ten", "args": [10], "expect": 1.4711276743037347 },
{ "name": "negative is odd: atan(-x) = -atan(x)", "args": [-7.5], "expect": -1.4382447944982226 },
{ "name": "huge but below 2^66", "args": [5e18], "expect": 1.5707963267948966 },
{ "name": "2^66 and above is pi/2 (2^70 here)", "args": [1.1805916207174113e21], "expect": 1.5707963267948966 },
{ "name": "hugely negative is -pi/2", "args": [-1e300], "expect": -1.5707963267948966 },
{ "name": "a string is an error, not a coercion", "args": ["1"], "expectError": "x must be a finite number" }
]