34935-vm/assets/cesium/packages/engine/Source/Shaders/Builtin/Functions/cosineAndSine.glsl

/**
 * @private
 */
vec2 cordic(float angle)
{
// Scale the vector by the appropriate factor for the 24 iterations to follow.
    vec2 vector = vec2(6.0725293500888267e-1, 0.0);
// Iteration 1
    float sense = (angle < 0.0) ? -1.0 : 1.0;
 //   float factor = sense * 1.0;  // 2^-0
    mat2 rotation = mat2(1.0, sense, -sense, 1.0);
    vector = rotation * vector;
    angle -= sense * 7.8539816339744828e-1;  // atan(2^-0)
// Iteration 2
    sense = (angle < 0.0) ? -1.0 : 1.0;
    float factor = sense * 5.0e-1;  // 2^-1
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 4.6364760900080609e-1;  // atan(2^-1)
// Iteration 3
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 2.5e-1;  // 2^-2
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 2.4497866312686414e-1;  // atan(2^-2)
// Iteration 4
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 1.25e-1;  // 2^-3
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 1.2435499454676144e-1;  // atan(2^-3)
// Iteration 5
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 6.25e-2;  // 2^-4
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 6.2418809995957350e-2;  // atan(2^-4)
// Iteration 6
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 3.125e-2;  // 2^-5
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 3.1239833430268277e-2;  // atan(2^-5)
// Iteration 7
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 1.5625e-2;  // 2^-6
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 1.5623728620476831e-2;  // atan(2^-6)
// Iteration 8
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 7.8125e-3;  // 2^-7
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 7.8123410601011111e-3;  // atan(2^-7)
// Iteration 9
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 3.90625e-3;  // 2^-8
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 3.9062301319669718e-3;  // atan(2^-8)
// Iteration 10
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 1.953125e-3;  // 2^-9
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 1.9531225164788188e-3;  // atan(2^-9)
// Iteration 11
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 9.765625e-4;  // 2^-10
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 9.7656218955931946e-4;  // atan(2^-10)
// Iteration 12
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 4.8828125e-4;  // 2^-11
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 4.8828121119489829e-4;  // atan(2^-11)
// Iteration 13
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 2.44140625e-4;  // 2^-12
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 2.4414062014936177e-4;  // atan(2^-12)
// Iteration 14
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 1.220703125e-4;  // 2^-13
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 1.2207031189367021e-4;  // atan(2^-13)
// Iteration 15
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 6.103515625e-5;  // 2^-14
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 6.1035156174208773e-5;  // atan(2^-14)
// Iteration 16
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 3.0517578125e-5;  // 2^-15
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 3.0517578115526096e-5;  // atan(2^-15)
// Iteration 17
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 1.52587890625e-5;  // 2^-16
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 1.5258789061315762e-5;  // atan(2^-16)
// Iteration 18
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 7.62939453125e-6;  // 2^-17
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 7.6293945311019700e-6;  // atan(2^-17)
// Iteration 19
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 3.814697265625e-6;  // 2^-18
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 3.8146972656064961e-6;  // atan(2^-18)
// Iteration 20
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 1.9073486328125e-6;  // 2^-19
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 1.9073486328101870e-6;  // atan(2^-19)
// Iteration 21
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 9.5367431640625e-7;  // 2^-20
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 9.5367431640596084e-7;  // atan(2^-20)
// Iteration 22
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 4.76837158203125e-7;  // 2^-21
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 4.7683715820308884e-7;  // atan(2^-21)
// Iteration 23
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 2.384185791015625e-7;  // 2^-22
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
    angle -= sense * 2.3841857910155797e-7;  // atan(2^-22)
// Iteration 24
    sense = (angle < 0.0) ? -1.0 : 1.0;
    factor = sense * 1.1920928955078125e-7;  // 2^-23
    rotation[0][1] = factor;
    rotation[1][0] = -factor;
    vector = rotation * vector;
//    angle -= sense * 1.1920928955078068e-7;  // atan(2^-23)

    return vector;
}

/**
 * Computes the cosine and sine of the provided angle using the CORDIC algorithm.
 *
 * @name czm_cosineAndSine
 * @glslFunction
 *
 * @param {float} angle The angle in radians.
 *
 * @returns {vec2} The resulting cosine of the angle (as the x coordinate) and sine of the angle (as the y coordinate).
 *
 * @example
 * vec2 v = czm_cosineAndSine(czm_piOverSix);
 * float cosine = v.x;
 * float sine = v.y;
 */
vec2 czm_cosineAndSine(float angle)
{
    if (angle < -czm_piOverTwo || angle > czm_piOverTwo)
    {
        if (angle < 0.0)
        {
            return -cordic(angle + czm_pi);
        }
        else
        {
            return -cordic(angle - czm_pi);
        }
    }
    else
    {
        return cordic(angle);
    }
}