const float PI = 3.14159265358979323846f;
float8 torsionParams = PARAMS[index];
float4 v0 = (float4) (pos1.xyz-pos2.xyz, 0.0f);
float4 v1 = (float4) (pos3.xyz-pos2.xyz, 0.0f);
float4 v2 = (float4) (pos3.xyz-pos4.xyz, 0.0f);
float4 cp0 = cross(v0, v1);
float4 cp1 = cross(v1, v2);
float cosangle = dot(normalize(cp0), normalize(cp1));
float dihedralAngle;
if (cosangle > 0.99f || cosangle < -0.99f) {
    // We're close to the singularity in acos(), so take the cross product and use asin() instead.

    float4 cross_prod = cross(cp0, cp1);
    float scale = dot(cp0, cp0)*dot(cp1, cp1);
    dihedralAngle = asin(sqrt(dot(cross_prod, cross_prod)/scale));
    if (cosangle < 0.0f)
        dihedralAngle = PI-dihedralAngle;
}
else
   dihedralAngle = acos(cosangle);
dihedralAngle = (dot(v0, cp1) >= 0 ? dihedralAngle : -dihedralAngle);
if (dihedralAngle < 0.0f)
    dihedralAngle += PI;
else
    dihedralAngle -= PI;
cosangle = -cosangle;
float cosFactor = cosangle;
float dEdAngle = -torsionParams.s1;
float rbEnergy = torsionParams.s0;
rbEnergy += torsionParams.s1*cosFactor;
dEdAngle -= 2.0f*torsionParams.s2*cosFactor;
cosFactor *= cosangle;
dEdAngle -= 3.0f*torsionParams.s3*cosFactor;
rbEnergy += torsionParams.s2*cosFactor;
cosFactor *= cosangle;
dEdAngle -= 4.0f*torsionParams.s4*cosFactor;
rbEnergy += torsionParams.s3*cosFactor;
cosFactor *= cosangle;
dEdAngle -= 5.0f*torsionParams.s5*cosFactor;
rbEnergy += torsionParams.s4*cosFactor;
rbEnergy += torsionParams.s5*cosFactor*cosangle;
energy += rbEnergy;
dEdAngle *= sin(dihedralAngle);
float normCross1 = dot(cp0, cp0);
float normSqrBC = dot(v1, v1);
float normBC = sqrt(normSqrBC);
float normCross2 = dot(cp1, cp1);
float dp = 1.0f/normSqrBC;
float4 ff = (float4) ((-dEdAngle*normBC)/normCross1, dot(v0, v1)*dp, dot(v2, v1)*dp, (dEdAngle*normBC)/normCross2);
float4 force1 = ff.x*cp0;
float4 force4 = ff.w*cp1;
float4 s = ff.y*force1 - ff.z*force4;
float4 force2 = s-force1;
float4 force3 = -s-force4;