Mathf.Sin(Mathf.PI) returns non zero number

[KellyThomas]

Godot version:
aeb1c67

OS/device including version:
Window 7

Issue description:
C# Godot's Mathf.Sin(Mathf.PI) returns a negative non zero number.

Two of the signature characteristics of the sine function are:

• it will return zero when the parameter value is an integer multiple of pi
• it will return a non-negative number when the parameter value is within the range zero to pi inclusive.

Steps to reproduce:
If we attach the following gdscript to a Node:

extends Node

func _ready():
    print("-GDSCRIPT-")
    print("PI: %.13f" % PI)
    print("sin(PI): %.13f" % sin(PI))
    print("sqrt(sin(PI)): %.13f" % sqrt(sin(PI)))

It will produce this output:

-GDSCRIPT-
PI: 3.1415926535900
sin(PI): 0.0000000000000
sqrt(sin(PI)): 0.0000000110660

But if we attach this c sharp to a Node:

using Godot;

public class TestNode : Node
{
    public override void _Ready()
    {
        GD.Print("-CSHARP: Mathf-");
        GD.Print($"Mathf.PI: {Mathf.PI:F13}");
        GD.Print($"Mathf.Sin(Mathf.PI): {Mathf.Sin(Mathf.PI):F13}");
        GD.Print($"Mathf.Sqrt(Mathf.Sin(Mathf.PI)): {Mathf.Sqrt(Mathf.Sin(Mathf.PI)):F13}");
    }
}

It will generate this output:

-CSHARP: Mathf-
Mathf.PI: 3.1415930000000
Mathf.Sin(Mathf.PI): -0.0000000874228
Mathf.Sqrt(Mathf.Sin(Mathf.PI)): NaN

[ghost]

cc: @neikeq

[bruvzg]

Output looks OK, Mathf use single floats, and you shouldn't expect more then 7 digits precision, GDscript use double floats and should give 15-16 digits, but print output only 12 (there's PR to fix it #17316).

[KellyThomas]

Hmm.. I guess your right.

The issue was exposed by porting some gdscript that assumed sin() returned positive for the range 0 to PI. First I was using System.Math and everything worked (also using doubles) but when I changed to Godot.Math then stuff started disappearing from my screen as they were assigned a position values of NaN.

(float)Math.Sin((float)Math.PI) is returning same as Mathf.Sin(Mathf.PI) so it does look like the best we can expect.

[bruvzg]

assumed sin() returned positive for the range 0 to PI

Single precision PI representation is bigger than PI (it's 3.1415927410, real PI is 3.1415926535...).

[akien-mga]

That's not a bug, that's just how floating point precision works. You should never assume that any float or double operation will return a pure integer 0. 0 does not exist as the result of a floating point operation, you should always check that abs(<your operation>) < epsilon.