Math.atan2() should not return "inverse tangent of ny / nx"

[Josh-Cena]

Description: Math.atan2(1, -1), according to the spec, should be equivalent to Math.atan(1 / -1), because it falls into step 12:

12. Return an implementation-approximated Number value representing the result of the inverse tangent of the quotient ℝ(ny) / ℝ(nx).

"Inverse tangent" is commonly defined to have range $\displaystyle \left[-\frac{\pi}{2},\frac{\pi}{2}\right]$, which is also consistent with the behavior of Math.atan() (which is specified with the exact same wording). However, for x < 0, Math.atan2() does not use this range, and thus should be specified separately.

eshost Output:

$ eshost -s -e "Math.atan2(1, -1)"
#### JavaScriptCore, SpiderMonkey, V8
2.356194490192345

[jmdyck]

Step 12 was introduced by PR #2122. Before that, the specification of Math.atan2 was:

Returns an implementation-approximated value representing the result of the arc tangent of the quotient y / x of the arguments y and x, where the signs of y and x are used to determine the quadrant of the result. [...] The result is expressed in radians and ranges from -π to +π.

(plus a bunch of edge-cases for which particular values were required).

PR #2122 should perhaps have used wording closer to that for step 12.

[Josh-Cena]

Returns an implementation-approximated value representing the result of the arc tangent of the quotient y / x of the arguments y and x, where the signs of y and x are used to determine the quadrant of the result. [...] The result is expressed in radians and ranges from -π to +π.

I find this quite vague, isn't it? It doesn't tell me which quadrant the result is in, for each sign combination.

[jmdyck]

Isn't it obvious? E.g., if y is positive and x is negative, then it's in the quadrant defined by y > 0 and x < 0.

[Josh-Cena]

Ah, I see what it means. It still feels weird, though, because that deviates from what "arc tangent" usually means in terms of a well-defined function. I wonder if it isn't better to simply transform the values using $\pi - \arctan\frac{y}{x}$.