FULL PRODUCT VERSION :
java version "1.8.0_121"
Java(TM) SE Runtime Environment (build 1.8.0_121-b13)
Java HotSpot(TM) 64-Bit Server VM (build 25.121-b13, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
Microsoft Windows [Version 6.1.7601]

A DESCRIPTION OF THE PROBLEM :
The computation of quaternions from a rotation matrix fails (as in produces incorrect result) when some but not all parts of a rotation Matrix are small instead of zero, e.g
-1.2246467991473532E-16 as opposed to 0.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
Quat4f quat = new Quat4f();
Matrix3d rotation = new Matrix3d();
rotation.setM00(0.);
rotation.setM01(0.);
rotation.setM02(1.);
rotation.setM10(0.);
rotation.setM11(-1.);
rotation.setM12(0.);
rotation.setM20(1.0);
rotation.setM21(0.);
rotation.setM22(0.);
quat.set(rotation);
System.out.println(quat);

Quat4f quat2 = new Quat4f();
Matrix3d rotation2 = new Matrix3d();
rotation2.setM00(-6.123233995736766E-17);
rotation2.setM01(7.498798913309288E-33);
rotation2.setM02(1.);
rotation2.setM10(-1.2246467991473532E-16);
rotation2.setM11(-1.);
rotation2.setM12(0.);
rotation2.setM20(1.0);
rotation2.setM21(-1.2246467991473532E-16);
rotation2.setM22(6.123233995736766E-17);
quat2.set(rotation2);
System.out.println(quat2);

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
The two Quaternions should have alomst the same values.
(0.70710677, 0.0, 0.70710677, 0.0)
ACTUAL -
First case with the "cleaned" matrix is as expected
(0.70710677, 0.0, 0.70710677, 0.0)

Second case with the original values is wrong!
(-5.8113327E-9, 0.0, -5.8113327E-9, 5.268356E-9)


REPRODUCIBILITY :
This bug can be reproduced always.

---------- BEGIN SOURCE ----------
Quat4f quat = new Quat4f();
Matrix3d rotation = new Matrix3d();
rotation.setM00(0.);
rotation.setM01(0.);
rotation.setM02(1.);
rotation.setM10(0.);
rotation.setM11(-1.);
rotation.setM12(0.);
rotation.setM20(1.0);
rotation.setM21(0.);
rotation.setM22(0.);
quat.set(rotation);
System.out.println(quat);

Quat4f quat2 = new Quat4f();
Matrix3d rotation2 = new Matrix3d();
rotation2.setM00(-6.123233995736766E-17);
rotation2.setM01(7.498798913309288E-33);
rotation2.setM02(1.);
rotation2.setM10(-1.2246467991473532E-16);
rotation2.setM11(-1.);
rotation2.setM12(0.);
rotation2.setM20(1.0);
rotation2.setM21(-1.2246467991473532E-16);
rotation2.setM22(6.123233995736766E-17);
quat2.set(rotation2);
System.out.println(quat2);
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
Round values for input.