JSDoc: Source: gl-matrix/mat4.js

# Source: gl-matrix/mat4.js

    /* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.

    Permission is hereby granted, free of charge, to any person obtaining a copy
    of this software and associated documentation files (the "Software"), to deal
    in the Software without restriction, including without limitation the rights
    to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
    copies of the Software, and to permit persons to whom the Software is
    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in
    all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
    AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
    THE SOFTWARE. */

    var glMatrix = require("./common.js");

    /**
     * @class 4x4 Matrix
     * @name mat4
     */
    var mat4 = {
      scalar: {},
      SIMD: {}
    };

    /**
     * Creates a new identity mat4
     *
     * @returns {mat4} a new 4x4 matrix
     */
    mat4.create = function() {
        var out = new glMatrix.ARRAY_TYPE(16);
        out[0] = 1;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 0;
        out[5] = 1;
        out[6] = 0;
        out[7] = 0;
        out[8] = 0;
        out[9] = 0;
        out[10] = 1;
        out[11] = 0;
        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;
        return out;
    };

    /**
     * Creates a new mat4 initialized with values from an existing matrix
     *
     * @param {mat4} a matrix to clone
     * @returns {mat4} a new 4x4 matrix
     */
    mat4.clone = function(a) {
        var out = new glMatrix.ARRAY_TYPE(16);
        out[0] = a[0];
        out[1] = a[1];
        out[2] = a[2];
        out[3] = a[3];
        out[4] = a[4];
        out[5] = a[5];
        out[6] = a[6];
        out[7] = a[7];
        out[8] = a[8];
        out[9] = a[9];
        out[10] = a[10];
        out[11] = a[11];
        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
        return out;
    };

    /**
     * Copy the values from one mat4 to another
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.copy = function(out, a) {
        out[0] = a[0];
        out[1] = a[1];
        out[2] = a[2];
        out[3] = a[3];
        out[4] = a[4];
        out[5] = a[5];
        out[6] = a[6];
        out[7] = a[7];
        out[8] = a[8];
        out[9] = a[9];
        out[10] = a[10];
        out[11] = a[11];
        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
        return out;
    };

    /**
     * Create a new mat4 with the given values
     *
     * @param {Number} m00 Component in column 0, row 0 position (index 0)
     * @param {Number} m01 Component in column 0, row 1 position (index 1)
     * @param {Number} m02 Component in column 0, row 2 position (index 2)
     * @param {Number} m03 Component in column 0, row 3 position (index 3)
     * @param {Number} m10 Component in column 1, row 0 position (index 4)
     * @param {Number} m11 Component in column 1, row 1 position (index 5)
     * @param {Number} m12 Component in column 1, row 2 position (index 6)
     * @param {Number} m13 Component in column 1, row 3 position (index 7)
     * @param {Number} m20 Component in column 2, row 0 position (index 8)
     * @param {Number} m21 Component in column 2, row 1 position (index 9)
     * @param {Number} m22 Component in column 2, row 2 position (index 10)
     * @param {Number} m23 Component in column 2, row 3 position (index 11)
     * @param {Number} m30 Component in column 3, row 0 position (index 12)
     * @param {Number} m31 Component in column 3, row 1 position (index 13)
     * @param {Number} m32 Component in column 3, row 2 position (index 14)
     * @param {Number} m33 Component in column 3, row 3 position (index 15)
     * @returns {mat4} A new mat4
     */
    mat4.fromValues = function(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
        var out = new glMatrix.ARRAY_TYPE(16);
        out[0] = m00;
        out[1] = m01;
        out[2] = m02;
        out[3] = m03;
        out[4] = m10;
        out[5] = m11;
        out[6] = m12;
        out[7] = m13;
        out[8] = m20;
        out[9] = m21;
        out[10] = m22;
        out[11] = m23;
        out[12] = m30;
        out[13] = m31;
        out[14] = m32;
        out[15] = m33;
        return out;
    };

    /**
     * Set the components of a mat4 to the given values
     *
     * @param {mat4} out the receiving matrix
     * @param {Number} m00 Component in column 0, row 0 position (index 0)
     * @param {Number} m01 Component in column 0, row 1 position (index 1)
     * @param {Number} m02 Component in column 0, row 2 position (index 2)
     * @param {Number} m03 Component in column 0, row 3 position (index 3)
     * @param {Number} m10 Component in column 1, row 0 position (index 4)
     * @param {Number} m11 Component in column 1, row 1 position (index 5)
     * @param {Number} m12 Component in column 1, row 2 position (index 6)
     * @param {Number} m13 Component in column 1, row 3 position (index 7)
     * @param {Number} m20 Component in column 2, row 0 position (index 8)
     * @param {Number} m21 Component in column 2, row 1 position (index 9)
     * @param {Number} m22 Component in column 2, row 2 position (index 10)
     * @param {Number} m23 Component in column 2, row 3 position (index 11)
     * @param {Number} m30 Component in column 3, row 0 position (index 12)
     * @param {Number} m31 Component in column 3, row 1 position (index 13)
     * @param {Number} m32 Component in column 3, row 2 position (index 14)
     * @param {Number} m33 Component in column 3, row 3 position (index 15)
     * @returns {mat4} out
     */
    mat4.set = function(out, m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
        out[0] = m00;
        out[1] = m01;
        out[2] = m02;
        out[3] = m03;
        out[4] = m10;
        out[5] = m11;
        out[6] = m12;
        out[7] = m13;
        out[8] = m20;
        out[9] = m21;
        out[10] = m22;
        out[11] = m23;
        out[12] = m30;
        out[13] = m31;
        out[14] = m32;
        out[15] = m33;
        return out;
    };

    /**
     * Set a mat4 to the identity matrix
     *
     * @param {mat4} out the receiving matrix
     * @returns {mat4} out
     */
    mat4.identity = function(out) {
        out[0] = 1;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 0;
        out[5] = 1;
        out[6] = 0;
        out[7] = 0;
        out[8] = 0;
        out[9] = 0;
        out[10] = 1;
        out[11] = 0;
        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;
        return out;
    };

    /**
     * Transpose the values of a mat4 not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.scalar.transpose = function(out, a) {
        // If we are transposing ourselves we can skip a few steps but have to cache some values
        if (out === a) {
            var a01 = a[1], a02 = a[2], a03 = a[3],
                a12 = a[6], a13 = a[7],
                a23 = a[11];

            out[1] = a[4];
            out[2] = a[8];
            out[3] = a[12];
            out[4] = a01;
            out[6] = a[9];
            out[7] = a[13];
            out[8] = a02;
            out[9] = a12;
            out[11] = a[14];
            out[12] = a03;
            out[13] = a13;
            out[14] = a23;
        } else {
            out[0] = a[0];
            out[1] = a[4];
            out[2] = a[8];
            out[3] = a[12];
            out[4] = a[1];
            out[5] = a[5];
            out[6] = a[9];
            out[7] = a[13];
            out[8] = a[2];
            out[9] = a[6];
            out[10] = a[10];
            out[11] = a[14];
            out[12] = a[3];
            out[13] = a[7];
            out[14] = a[11];
            out[15] = a[15];
        }

        return out;
    };

    /**
     * Transpose the values of a mat4 using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.SIMD.transpose = function(out, a) {
        var a0, a1, a2, a3,
            tmp01, tmp23,
            out0, out1, out2, out3;

        a0 = SIMD.Float32x4.load(a, 0);
        a1 = SIMD.Float32x4.load(a, 4);
        a2 = SIMD.Float32x4.load(a, 8);
        a3 = SIMD.Float32x4.load(a, 12);

        tmp01 = SIMD.Float32x4.shuffle(a0, a1, 0, 1, 4, 5);
        tmp23 = SIMD.Float32x4.shuffle(a2, a3, 0, 1, 4, 5);
        out0  = SIMD.Float32x4.shuffle(tmp01, tmp23, 0, 2, 4, 6);
        out1  = SIMD.Float32x4.shuffle(tmp01, tmp23, 1, 3, 5, 7);
        SIMD.Float32x4.store(out, 0,  out0);
        SIMD.Float32x4.store(out, 4,  out1);

        tmp01 = SIMD.Float32x4.shuffle(a0, a1, 2, 3, 6, 7);
        tmp23 = SIMD.Float32x4.shuffle(a2, a3, 2, 3, 6, 7);
        out2  = SIMD.Float32x4.shuffle(tmp01, tmp23, 0, 2, 4, 6);
        out3  = SIMD.Float32x4.shuffle(tmp01, tmp23, 1, 3, 5, 7);
        SIMD.Float32x4.store(out, 8,  out2);
        SIMD.Float32x4.store(out, 12, out3);

        return out;
    };

    /**
     * Transpse a mat4 using SIMD if available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.transpose = glMatrix.USE_SIMD ? mat4.SIMD.transpose : mat4.scalar.transpose;

    /**
     * Inverts a mat4 not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.scalar.invert = function(out, a) {
        var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
            a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
            a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
            a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],

            b00 = a00 * a11 - a01 * a10,
            b01 = a00 * a12 - a02 * a10,
            b02 = a00 * a13 - a03 * a10,
            b03 = a01 * a12 - a02 * a11,
            b04 = a01 * a13 - a03 * a11,
            b05 = a02 * a13 - a03 * a12,
            b06 = a20 * a31 - a21 * a30,
            b07 = a20 * a32 - a22 * a30,
            b08 = a20 * a33 - a23 * a30,
            b09 = a21 * a32 - a22 * a31,
            b10 = a21 * a33 - a23 * a31,
            b11 = a22 * a33 - a23 * a32,

            // Calculate the determinant
            det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

        if (!det) {
            return null;
        }
        det = 1.0 / det;

        out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
        out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
        out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
        out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
        out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
        out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
        out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
        out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
        out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
        out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
        out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
        out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
        out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
        out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
        out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
        out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;

        return out;
    };

    /**
     * Inverts a mat4 using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.SIMD.invert = function(out, a) {
      var row0, row1, row2, row3,
          tmp1,
          minor0, minor1, minor2, minor3,
          det,
          a0 = SIMD.Float32x4.load(a, 0),
          a1 = SIMD.Float32x4.load(a, 4),
          a2 = SIMD.Float32x4.load(a, 8),
          a3 = SIMD.Float32x4.load(a, 12);

      // Compute matrix adjugate
      tmp1 = SIMD.Float32x4.shuffle(a0, a1, 0, 1, 4, 5);
      row1 = SIMD.Float32x4.shuffle(a2, a3, 0, 1, 4, 5);
      row0 = SIMD.Float32x4.shuffle(tmp1, row1, 0, 2, 4, 6);
      row1 = SIMD.Float32x4.shuffle(row1, tmp1, 1, 3, 5, 7);
      tmp1 = SIMD.Float32x4.shuffle(a0, a1, 2, 3, 6, 7);
      row3 = SIMD.Float32x4.shuffle(a2, a3, 2, 3, 6, 7);
      row2 = SIMD.Float32x4.shuffle(tmp1, row3, 0, 2, 4, 6);
      row3 = SIMD.Float32x4.shuffle(row3, tmp1, 1, 3, 5, 7);

      tmp1   = SIMD.Float32x4.mul(row2, row3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor0 = SIMD.Float32x4.mul(row1, tmp1);
      minor1 = SIMD.Float32x4.mul(row0, tmp1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row1, tmp1), minor0);
      minor1 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor1);
      minor1 = SIMD.Float32x4.swizzle(minor1, 2, 3, 0, 1);

      tmp1   = SIMD.Float32x4.mul(row1, row2);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor0);
      minor3 = SIMD.Float32x4.mul(row0, tmp1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row3, tmp1));
      minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor3);
      minor3 = SIMD.Float32x4.swizzle(minor3, 2, 3, 0, 1);

      tmp1   = SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(row1, 2, 3, 0, 1), row3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      row2   = SIMD.Float32x4.swizzle(row2, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor0);
      minor2 = SIMD.Float32x4.mul(row0, tmp1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row2, tmp1));
      minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor2);
      minor2 = SIMD.Float32x4.swizzle(minor2, 2, 3, 0, 1);

      tmp1   = SIMD.Float32x4.mul(row0, row1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor2);
      minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row2, tmp1), minor3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row3, tmp1), minor2);
      minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row2, tmp1));

      tmp1   = SIMD.Float32x4.mul(row0, row3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row2, tmp1));
      minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor2);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor1);
      minor2 = SIMD.Float32x4.sub(minor2, SIMD.Float32x4.mul(row1, tmp1));

      tmp1   = SIMD.Float32x4.mul(row0, row2);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor1);
      minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row1, tmp1));
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row3, tmp1));
      minor3 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor3);

      // Compute matrix determinant
      det   = SIMD.Float32x4.mul(row0, minor0);
      det   = SIMD.Float32x4.add(SIMD.Float32x4.swizzle(det, 2, 3, 0, 1), det);
      det   = SIMD.Float32x4.add(SIMD.Float32x4.swizzle(det, 1, 0, 3, 2), det);
      tmp1  = SIMD.Float32x4.reciprocalApproximation(det);
      det   = SIMD.Float32x4.sub(
                   SIMD.Float32x4.add(tmp1, tmp1),
                   SIMD.Float32x4.mul(det, SIMD.Float32x4.mul(tmp1, tmp1)));
      det   = SIMD.Float32x4.swizzle(det, 0, 0, 0, 0);
      if (!det) {
          return null;
      }

      // Compute matrix inverse
      SIMD.Float32x4.store(out, 0,  SIMD.Float32x4.mul(det, minor0));
      SIMD.Float32x4.store(out, 4,  SIMD.Float32x4.mul(det, minor1));
      SIMD.Float32x4.store(out, 8,  SIMD.Float32x4.mul(det, minor2));
      SIMD.Float32x4.store(out, 12, SIMD.Float32x4.mul(det, minor3));
      return out;
    }

    /**
     * Inverts a mat4 using SIMD if available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.invert = glMatrix.USE_SIMD ? mat4.SIMD.invert : mat4.scalar.invert;

    /**
     * Calculates the adjugate of a mat4 not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.scalar.adjoint = function(out, a) {
        var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
            a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
            a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
            a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

        out[0]  =  (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22));
        out[1]  = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
        out[2]  =  (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12));
        out[3]  = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
        out[4]  = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
        out[5]  =  (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22));
        out[6]  = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
        out[7]  =  (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12));
        out[8]  =  (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21));
        out[9]  = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
        out[10] =  (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11));
        out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
        out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
        out[13] =  (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21));
        out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
        out[15] =  (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11));
        return out;
    };

    /**
     * Calculates the adjugate of a mat4 using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    mat4.SIMD.adjoint = function(out, a) {
      var a0, a1, a2, a3;
      var row0, row1, row2, row3;
      var tmp1;
      var minor0, minor1, minor2, minor3;

      a0 = SIMD.Float32x4.load(a, 0);
      a1 = SIMD.Float32x4.load(a, 4);
      a2 = SIMD.Float32x4.load(a, 8);
      a3 = SIMD.Float32x4.load(a, 12);

      // Transpose the source matrix.  Sort of.  Not a true transpose operation
      tmp1 = SIMD.Float32x4.shuffle(a0, a1, 0, 1, 4, 5);
      row1 = SIMD.Float32x4.shuffle(a2, a3, 0, 1, 4, 5);
      row0 = SIMD.Float32x4.shuffle(tmp1, row1, 0, 2, 4, 6);
      row1 = SIMD.Float32x4.shuffle(row1, tmp1, 1, 3, 5, 7);

      tmp1 = SIMD.Float32x4.shuffle(a0, a1, 2, 3, 6, 7);
      row3 = SIMD.Float32x4.shuffle(a2, a3, 2, 3, 6, 7);
      row2 = SIMD.Float32x4.shuffle(tmp1, row3, 0, 2, 4, 6);
      row3 = SIMD.Float32x4.shuffle(row3, tmp1, 1, 3, 5, 7);

      tmp1   = SIMD.Float32x4.mul(row2, row3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor0 = SIMD.Float32x4.mul(row1, tmp1);
      minor1 = SIMD.Float32x4.mul(row0, tmp1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row1, tmp1), minor0);
      minor1 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor1);
      minor1 = SIMD.Float32x4.swizzle(minor1, 2, 3, 0, 1);

      tmp1   = SIMD.Float32x4.mul(row1, row2);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor0);
      minor3 = SIMD.Float32x4.mul(row0, tmp1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row3, tmp1));
      minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor3);
      minor3 = SIMD.Float32x4.swizzle(minor3, 2, 3, 0, 1);

      tmp1   = SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(row1, 2, 3, 0, 1), row3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      row2   = SIMD.Float32x4.swizzle(row2, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor0);
      minor2 = SIMD.Float32x4.mul(row0, tmp1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor0 = SIMD.Float32x4.sub(minor0, SIMD.Float32x4.mul(row2, tmp1));
      minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row0, tmp1), minor2);
      minor2 = SIMD.Float32x4.swizzle(minor2, 2, 3, 0, 1);

      tmp1   = SIMD.Float32x4.mul(row0, row1);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor2);
      minor3 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row2, tmp1), minor3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor2 = SIMD.Float32x4.sub(SIMD.Float32x4.mul(row3, tmp1), minor2);
      minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row2, tmp1));

      tmp1   = SIMD.Float32x4.mul(row0, row3);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row2, tmp1));
      minor2 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor2);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row2, tmp1), minor1);
      minor2 = SIMD.Float32x4.sub(minor2, SIMD.Float32x4.mul(row1, tmp1));

      tmp1   = SIMD.Float32x4.mul(row0, row2);
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 1, 0, 3, 2);
      minor1 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row3, tmp1), minor1);
      minor3 = SIMD.Float32x4.sub(minor3, SIMD.Float32x4.mul(row1, tmp1));
      tmp1   = SIMD.Float32x4.swizzle(tmp1, 2, 3, 0, 1);
      minor1 = SIMD.Float32x4.sub(minor1, SIMD.Float32x4.mul(row3, tmp1));
      minor3 = SIMD.Float32x4.add(SIMD.Float32x4.mul(row1, tmp1), minor3);

      SIMD.Float32x4.store(out, 0,  minor0);
      SIMD.Float32x4.store(out, 4,  minor1);
      SIMD.Float32x4.store(out, 8,  minor2);
      SIMD.Float32x4.store(out, 12, minor3);
      return out;
    };

    /**
     * Calculates the adjugate of a mat4 using SIMD if available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
     mat4.adjoint = glMatrix.USE_SIMD ? mat4.SIMD.adjoint : mat4.scalar.adjoint;

    /**
     * Calculates the determinant of a mat4
     *
     * @param {mat4} a the source matrix
     * @returns {Number} determinant of a
     */
    mat4.determinant = function (a) {
        var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
            a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
            a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
            a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],

            b00 = a00 * a11 - a01 * a10,
            b01 = a00 * a12 - a02 * a10,
            b02 = a00 * a13 - a03 * a10,
            b03 = a01 * a12 - a02 * a11,
            b04 = a01 * a13 - a03 * a11,
            b05 = a02 * a13 - a03 * a12,
            b06 = a20 * a31 - a21 * a30,
            b07 = a20 * a32 - a22 * a30,
            b08 = a20 * a33 - a23 * a30,
            b09 = a21 * a32 - a22 * a31,
            b10 = a21 * a33 - a23 * a31,
            b11 = a22 * a33 - a23 * a32;

        // Calculate the determinant
        return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
    };

    /**
     * Multiplies two mat4's explicitly using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand, must be a Float32Array
     * @param {mat4} b the second operand, must be a Float32Array
     * @returns {mat4} out
     */
    mat4.SIMD.multiply = function (out, a, b) {
        var a0 = SIMD.Float32x4.load(a, 0);
        var a1 = SIMD.Float32x4.load(a, 4);
        var a2 = SIMD.Float32x4.load(a, 8);
        var a3 = SIMD.Float32x4.load(a, 12);

        var b0 = SIMD.Float32x4.load(b, 0);
        var out0 = SIMD.Float32x4.add(
                       SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 0, 0, 0, 0), a0),
                       SIMD.Float32x4.add(
                           SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 1, 1, 1, 1), a1),
                           SIMD.Float32x4.add(
                               SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 2, 2, 2, 2), a2),
                               SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b0, 3, 3, 3, 3), a3))));
        SIMD.Float32x4.store(out, 0, out0);

        var b1 = SIMD.Float32x4.load(b, 4);
        var out1 = SIMD.Float32x4.add(
                       SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 0, 0, 0, 0), a0),
                       SIMD.Float32x4.add(
                           SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 1, 1, 1, 1), a1),
                           SIMD.Float32x4.add(
                               SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 2, 2, 2, 2), a2),
                               SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b1, 3, 3, 3, 3), a3))));
        SIMD.Float32x4.store(out, 4, out1);

        var b2 = SIMD.Float32x4.load(b, 8);
        var out2 = SIMD.Float32x4.add(
                       SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 0, 0, 0, 0), a0),
                       SIMD.Float32x4.add(
                           SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 1, 1, 1, 1), a1),
                           SIMD.Float32x4.add(
                                   SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 2, 2, 2, 2), a2),
                                   SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b2, 3, 3, 3, 3), a3))));
        SIMD.Float32x4.store(out, 8, out2);

        var b3 = SIMD.Float32x4.load(b, 12);
        var out3 = SIMD.Float32x4.add(
                       SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 0, 0, 0, 0), a0),
                       SIMD.Float32x4.add(
                            SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 1, 1, 1, 1), a1),
                            SIMD.Float32x4.add(
                                SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 2, 2, 2, 2), a2),
                                SIMD.Float32x4.mul(SIMD.Float32x4.swizzle(b3, 3, 3, 3, 3), a3))));
        SIMD.Float32x4.store(out, 12, out3);

        return out;
    };

    /**
     * Multiplies two mat4's explicitly not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @returns {mat4} out
     */
    mat4.scalar.multiply = function (out, a, b) {
        var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
            a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
            a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
            a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

        // Cache only the current line of the second matrix
        var b0  = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
        out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
        out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
        out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
        out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

        b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
        out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
        out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
        out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
        out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

        b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
        out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
        out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
        out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
        out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

        b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
        out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
        out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
        out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
        out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
        return out;
    };

    /**
     * Multiplies two mat4's using SIMD if available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @returns {mat4} out
     */
    mat4.multiply = glMatrix.USE_SIMD ? mat4.SIMD.multiply : mat4.scalar.multiply;

    /**
     * Alias for {@link mat4.multiply}
     * @function
     */
    mat4.mul = mat4.multiply;

    /**
     * Translate a mat4 by the given vector not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to translate
     * @param {vec3} v vector to translate by
     * @returns {mat4} out
     */
    mat4.scalar.translate = function (out, a, v) {
        var x = v[0], y = v[1], z = v[2],
            a00, a01, a02, a03,
            a10, a11, a12, a13,
            a20, a21, a22, a23;

        if (a === out) {
            out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
            out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
            out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
            out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
        } else {
            a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
            a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
            a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];

            out[0] = a00; out[1] = a01; out[2] = a02; out[3] = a03;
            out[4] = a10; out[5] = a11; out[6] = a12; out[7] = a13;
            out[8] = a20; out[9] = a21; out[10] = a22; out[11] = a23;

            out[12] = a00 * x + a10 * y + a20 * z + a[12];
            out[13] = a01 * x + a11 * y + a21 * z + a[13];
            out[14] = a02 * x + a12 * y + a22 * z + a[14];
            out[15] = a03 * x + a13 * y + a23 * z + a[15];
        }

        return out;
    };

    /**
     * Translates a mat4 by the given vector using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to translate
     * @param {vec3} v vector to translate by
     * @returns {mat4} out
     */
    mat4.SIMD.translate = function (out, a, v) {
        var a0 = SIMD.Float32x4.load(a, 0),
            a1 = SIMD.Float32x4.load(a, 4),
            a2 = SIMD.Float32x4.load(a, 8),
            a3 = SIMD.Float32x4.load(a, 12),
            vec = SIMD.Float32x4(v[0], v[1], v[2] , 0);

        if (a !== out) {
            out[0] = a[0]; out[1] = a[1]; out[2] = a[2]; out[3] = a[3];
            out[4] = a[4]; out[5] = a[5]; out[6] = a[6]; out[7] = a[7];
            out[8] = a[8]; out[9] = a[9]; out[10] = a[10]; out[11] = a[11];
        }

        a0 = SIMD.Float32x4.mul(a0, SIMD.Float32x4.swizzle(vec, 0, 0, 0, 0));
        a1 = SIMD.Float32x4.mul(a1, SIMD.Float32x4.swizzle(vec, 1, 1, 1, 1));
        a2 = SIMD.Float32x4.mul(a2, SIMD.Float32x4.swizzle(vec, 2, 2, 2, 2));

        var t0 = SIMD.Float32x4.add(a0, SIMD.Float32x4.add(a1, SIMD.Float32x4.add(a2, a3)));
        SIMD.Float32x4.store(out, 12, t0);

        return out;
    };

    /**
     * Translates a mat4 by the given vector using SIMD if available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to translate
     * @param {vec3} v vector to translate by
     * @returns {mat4} out
     */
    mat4.translate = glMatrix.USE_SIMD ? mat4.SIMD.translate : mat4.scalar.translate;

    /**
     * Scales the mat4 by the dimensions in the given vec3 not using vectorization
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to scale
     * @param {vec3} v the vec3 to scale the matrix by
     * @returns {mat4} out
     **/
    mat4.scalar.scale = function(out, a, v) {
        var x = v[0], y = v[1], z = v[2];

        out[0] = a[0] * x;
        out[1] = a[1] * x;
        out[2] = a[2] * x;
        out[3] = a[3] * x;
        out[4] = a[4] * y;
        out[5] = a[5] * y;
        out[6] = a[6] * y;
        out[7] = a[7] * y;
        out[8] = a[8] * z;
        out[9] = a[9] * z;
        out[10] = a[10] * z;
        out[11] = a[11] * z;
        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
        return out;
    };

    /**
     * Scales the mat4 by the dimensions in the given vec3 using vectorization
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to scale
     * @param {vec3} v the vec3 to scale the matrix by
     * @returns {mat4} out
     **/
    mat4.SIMD.scale = function(out, a, v) {
        var a0, a1, a2;
        var vec = SIMD.Float32x4(v[0], v[1], v[2], 0);

        a0 = SIMD.Float32x4.load(a, 0);
        SIMD.Float32x4.store(
            out, 0, SIMD.Float32x4.mul(a0, SIMD.Float32x4.swizzle(vec, 0, 0, 0, 0)));

        a1 = SIMD.Float32x4.load(a, 4);
        SIMD.Float32x4.store(
            out, 4, SIMD.Float32x4.mul(a1, SIMD.Float32x4.swizzle(vec, 1, 1, 1, 1)));

        a2 = SIMD.Float32x4.load(a, 8);
        SIMD.Float32x4.store(
            out, 8, SIMD.Float32x4.mul(a2, SIMD.Float32x4.swizzle(vec, 2, 2, 2, 2)));

        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
        return out;
    };

    /**
     * Scales the mat4 by the dimensions in the given vec3 using SIMD if available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to scale
     * @param {vec3} v the vec3 to scale the matrix by
     * @returns {mat4} out
     */
    mat4.scale = glMatrix.USE_SIMD ? mat4.SIMD.scale : mat4.scalar.scale;

    /**
     * Rotates a mat4 by the given angle around the given axis
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @param {vec3} axis the axis to rotate around
     * @returns {mat4} out
     */
    mat4.rotate = function (out, a, rad, axis) {
        var x = axis[0], y = axis[1], z = axis[2],
            len = Math.sqrt(x * x + y * y + z * z),
            s, c, t,
            a00, a01, a02, a03,
            a10, a11, a12, a13,
            a20, a21, a22, a23,
            b00, b01, b02,
            b10, b11, b12,
            b20, b21, b22;

        if (Math.abs(len) < glMatrix.EPSILON) { return null; }

        len = 1 / len;
        x *= len;
        y *= len;
        z *= len;

        s = Math.sin(rad);
        c = Math.cos(rad);
        t = 1 - c;

        a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
        a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
        a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];

        // Construct the elements of the rotation matrix
        b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s;
        b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s;
        b20 = x * z * t + y * s; b21 = y * z * t - x * s; b22 = z * z * t + c;

        // Perform rotation-specific matrix multiplication
        out[0] = a00 * b00 + a10 * b01 + a20 * b02;
        out[1] = a01 * b00 + a11 * b01 + a21 * b02;
        out[2] = a02 * b00 + a12 * b01 + a22 * b02;
        out[3] = a03 * b00 + a13 * b01 + a23 * b02;
        out[4] = a00 * b10 + a10 * b11 + a20 * b12;
        out[5] = a01 * b10 + a11 * b11 + a21 * b12;
        out[6] = a02 * b10 + a12 * b11 + a22 * b12;
        out[7] = a03 * b10 + a13 * b11 + a23 * b12;
        out[8] = a00 * b20 + a10 * b21 + a20 * b22;
        out[9] = a01 * b20 + a11 * b21 + a21 * b22;
        out[10] = a02 * b20 + a12 * b21 + a22 * b22;
        out[11] = a03 * b20 + a13 * b21 + a23 * b22;

        if (a !== out) { // If the source and destination differ, copy the unchanged last row
            out[12] = a[12];
            out[13] = a[13];
            out[14] = a[14];
            out[15] = a[15];
        }
        return out;
    };

    /**
     * Rotates a matrix by the given angle around the X axis not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.scalar.rotateX = function (out, a, rad) {
        var s = Math.sin(rad),
            c = Math.cos(rad),
            a10 = a[4],
            a11 = a[5],
            a12 = a[6],
            a13 = a[7],
            a20 = a[8],
            a21 = a[9],
            a22 = a[10],
            a23 = a[11];

        if (a !== out) { // If the source and destination differ, copy the unchanged rows
            out[0]  = a[0];
            out[1]  = a[1];
            out[2]  = a[2];
            out[3]  = a[3];
            out[12] = a[12];
            out[13] = a[13];
            out[14] = a[14];
            out[15] = a[15];
        }

        // Perform axis-specific matrix multiplication
        out[4] = a10 * c + a20 * s;
        out[5] = a11 * c + a21 * s;
        out[6] = a12 * c + a22 * s;
        out[7] = a13 * c + a23 * s;
        out[8] = a20 * c - a10 * s;
        out[9] = a21 * c - a11 * s;
        out[10] = a22 * c - a12 * s;
        out[11] = a23 * c - a13 * s;
        return out;
    };

    /**
     * Rotates a matrix by the given angle around the X axis using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.SIMD.rotateX = function (out, a, rad) {
        var s = SIMD.Float32x4.splat(Math.sin(rad)),
            c = SIMD.Float32x4.splat(Math.cos(rad));

        if (a !== out) { // If the source and destination differ, copy the unchanged rows
          out[0]  = a[0];
          out[1]  = a[1];
          out[2]  = a[2];
          out[3]  = a[3];
          out[12] = a[12];
          out[13] = a[13];
          out[14] = a[14];
          out[15] = a[15];
        }

        // Perform axis-specific matrix multiplication
        var a_1 = SIMD.Float32x4.load(a, 4);
        var a_2 = SIMD.Float32x4.load(a, 8);
        SIMD.Float32x4.store(out, 4,
                             SIMD.Float32x4.add(SIMD.Float32x4.mul(a_1, c), SIMD.Float32x4.mul(a_2, s)));
        SIMD.Float32x4.store(out, 8,
                             SIMD.Float32x4.sub(SIMD.Float32x4.mul(a_2, c), SIMD.Float32x4.mul(a_1, s)));
        return out;
    };

    /**
     * Rotates a matrix by the given angle around the X axis using SIMD if availabe and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.rotateX = glMatrix.USE_SIMD ? mat4.SIMD.rotateX : mat4.scalar.rotateX;

    /**
     * Rotates a matrix by the given angle around the Y axis not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.scalar.rotateY = function (out, a, rad) {
        var s = Math.sin(rad),
            c = Math.cos(rad),
            a00 = a[0],
            a01 = a[1],
            a02 = a[2],
            a03 = a[3],
            a20 = a[8],
            a21 = a[9],
            a22 = a[10],
            a23 = a[11];

        if (a !== out) { // If the source and destination differ, copy the unchanged rows
            out[4]  = a[4];
            out[5]  = a[5];
            out[6]  = a[6];
            out[7]  = a[7];
            out[12] = a[12];
            out[13] = a[13];
            out[14] = a[14];
            out[15] = a[15];
        }

        // Perform axis-specific matrix multiplication
        out[0] = a00 * c - a20 * s;
        out[1] = a01 * c - a21 * s;
        out[2] = a02 * c - a22 * s;
        out[3] = a03 * c - a23 * s;
        out[8] = a00 * s + a20 * c;
        out[9] = a01 * s + a21 * c;
        out[10] = a02 * s + a22 * c;
        out[11] = a03 * s + a23 * c;
        return out;
    };

    /**
     * Rotates a matrix by the given angle around the Y axis using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.SIMD.rotateY = function (out, a, rad) {
        var s = SIMD.Float32x4.splat(Math.sin(rad)),
            c = SIMD.Float32x4.splat(Math.cos(rad));

        if (a !== out) { // If the source and destination differ, copy the unchanged rows
            out[4]  = a[4];
            out[5]  = a[5];
            out[6]  = a[6];
            out[7]  = a[7];
            out[12] = a[12];
            out[13] = a[13];
            out[14] = a[14];
            out[15] = a[15];
        }

        // Perform axis-specific matrix multiplication
        var a_0 = SIMD.Float32x4.load(a, 0);
        var a_2 = SIMD.Float32x4.load(a, 8);
        SIMD.Float32x4.store(out, 0,
                             SIMD.Float32x4.sub(SIMD.Float32x4.mul(a_0, c), SIMD.Float32x4.mul(a_2, s)));
        SIMD.Float32x4.store(out, 8,
                             SIMD.Float32x4.add(SIMD.Float32x4.mul(a_0, s), SIMD.Float32x4.mul(a_2, c)));
        return out;
    };

    /**
     * Rotates a matrix by the given angle around the Y axis if SIMD available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
     mat4.rotateY = glMatrix.USE_SIMD ? mat4.SIMD.rotateY : mat4.scalar.rotateY;

    /**
     * Rotates a matrix by the given angle around the Z axis not using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.scalar.rotateZ = function (out, a, rad) {
        var s = Math.sin(rad),
            c = Math.cos(rad),
            a00 = a[0],
            a01 = a[1],
            a02 = a[2],
            a03 = a[3],
            a10 = a[4],
            a11 = a[5],
            a12 = a[6],
            a13 = a[7];

        if (a !== out) { // If the source and destination differ, copy the unchanged last row
            out[8]  = a[8];
            out[9]  = a[9];
            out[10] = a[10];
            out[11] = a[11];
            out[12] = a[12];
            out[13] = a[13];
            out[14] = a[14];
            out[15] = a[15];
        }

        // Perform axis-specific matrix multiplication
        out[0] = a00 * c + a10 * s;
        out[1] = a01 * c + a11 * s;
        out[2] = a02 * c + a12 * s;
        out[3] = a03 * c + a13 * s;
        out[4] = a10 * c - a00 * s;
        out[5] = a11 * c - a01 * s;
        out[6] = a12 * c - a02 * s;
        out[7] = a13 * c - a03 * s;
        return out;
    };

    /**
     * Rotates a matrix by the given angle around the Z axis using SIMD
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.SIMD.rotateZ = function (out, a, rad) {
        var s = SIMD.Float32x4.splat(Math.sin(rad)),
            c = SIMD.Float32x4.splat(Math.cos(rad));

        if (a !== out) { // If the source and destination differ, copy the unchanged last row
            out[8]  = a[8];
            out[9]  = a[9];
            out[10] = a[10];
            out[11] = a[11];
            out[12] = a[12];
            out[13] = a[13];
            out[14] = a[14];
            out[15] = a[15];
        }

        // Perform axis-specific matrix multiplication
        var a_0 = SIMD.Float32x4.load(a, 0);
        var a_1 = SIMD.Float32x4.load(a, 4);
        SIMD.Float32x4.store(out, 0,
                             SIMD.Float32x4.add(SIMD.Float32x4.mul(a_0, c), SIMD.Float32x4.mul(a_1, s)));
        SIMD.Float32x4.store(out, 4,
                             SIMD.Float32x4.sub(SIMD.Float32x4.mul(a_1, c), SIMD.Float32x4.mul(a_0, s)));
        return out;
    };

    /**
     * Rotates a matrix by the given angle around the Z axis if SIMD available and enabled
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
     mat4.rotateZ = glMatrix.USE_SIMD ? mat4.SIMD.rotateZ : mat4.scalar.rotateZ;

    /**
     * Creates a matrix from a vector translation
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.translate(dest, dest, vec);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {vec3} v Translation vector
     * @returns {mat4} out
     */
    mat4.fromTranslation = function(out, v) {
        out[0] = 1;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 0;
        out[5] = 1;
        out[6] = 0;
        out[7] = 0;
        out[8] = 0;
        out[9] = 0;
        out[10] = 1;
        out[11] = 0;
        out[12] = v[0];
        out[13] = v[1];
        out[14] = v[2];
        out[15] = 1;
        return out;
    }

    /**
     * Creates a matrix from a vector scaling
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.scale(dest, dest, vec);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {vec3} v Scaling vector
     * @returns {mat4} out
     */
    mat4.fromScaling = function(out, v) {
        out[0] = v[0];
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 0;
        out[5] = v[1];
        out[6] = 0;
        out[7] = 0;
        out[8] = 0;
        out[9] = 0;
        out[10] = v[2];
        out[11] = 0;
        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;
        return out;
    }

    /**
     * Creates a matrix from a given angle around a given axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotate(dest, dest, rad, axis);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @param {vec3} axis the axis to rotate around
     * @returns {mat4} out
     */
    mat4.fromRotation = function(out, rad, axis) {
        var x = axis[0], y = axis[1], z = axis[2],
            len = Math.sqrt(x * x + y * y + z * z),
            s, c, t;

        if (Math.abs(len) < glMatrix.EPSILON) { return null; }

        len = 1 / len;
        x *= len;
        y *= len;
        z *= len;

        s = Math.sin(rad);
        c = Math.cos(rad);
        t = 1 - c;

        // Perform rotation-specific matrix multiplication
        out[0] = x * x * t + c;
        out[1] = y * x * t + z * s;
        out[2] = z * x * t - y * s;
        out[3] = 0;
        out[4] = x * y * t - z * s;
        out[5] = y * y * t + c;
        out[6] = z * y * t + x * s;
        out[7] = 0;
        out[8] = x * z * t + y * s;
        out[9] = y * z * t - x * s;
        out[10] = z * z * t + c;
        out[11] = 0;
        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;
        return out;
    }

    /**
     * Creates a matrix from the given angle around the X axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotateX(dest, dest, rad);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.fromXRotation = function(out, rad) {
        var s = Math.sin(rad),
            c = Math.cos(rad);

        // Perform axis-specific matrix multiplication
        out[0]  = 1;
        out[1]  = 0;
        out[2]  = 0;
        out[3]  = 0;
        out[4] = 0;
        out[5] = c;
        out[6] = s;
        out[7] = 0;
        out[8] = 0;
        out[9] = -s;
        out[10] = c;
        out[11] = 0;
        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;
        return out;
    }

    /**
     * Creates a matrix from the given angle around the Y axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotateY(dest, dest, rad);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.fromYRotation = function(out, rad) {
        var s = Math.sin(rad),
            c = Math.cos(rad);

        // Perform axis-specific matrix multiplication
        out[0]  = c;
        out[1]  = 0;
        out[2]  = -s;
        out[3]  = 0;
        out[4] = 0;
        out[5] = 1;
        out[6] = 0;
        out[7] = 0;
        out[8] = s;
        out[9] = 0;
        out[10] = c;
        out[11] = 0;
        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;
        return out;
    }

    /**
     * Creates a matrix from the given angle around the Z axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotateZ(dest, dest, rad);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    mat4.fromZRotation = function(out, rad) {
        var s = Math.sin(rad),
            c = Math.cos(rad);

        // Perform axis-specific matrix multiplication
        out[0]  = c;
        out[1]  = s;
        out[2]  = 0;
        out[3]  = 0;
        out[4] = -s;
        out[5] = c;
        out[6] = 0;
        out[7] = 0;
        out[8] = 0;
        out[9] = 0;
        out[10] = 1;
        out[11] = 0;
        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;
        return out;
    }

    /**
     * Creates a matrix from a quaternion rotation and vector translation
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.translate(dest, vec);
     *     var quatMat = mat4.create();
     *     quat4.toMat4(quat, quatMat);
     *     mat4.multiply(dest, quatMat);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat4} q Rotation quaternion
     * @param {vec3} v Translation vector
     * @returns {mat4} out
     */
    mat4.fromRotationTranslation = function (out, q, v) {
        // Quaternion math
        var x = q[0], y = q[1], z = q[2], w = q[3],
            x2 = x + x,
            y2 = y + y,
            z2 = z + z,

            xx = x * x2,
            xy = x * y2,
            xz = x * z2,
            yy = y * y2,
            yz = y * z2,
            zz = z * z2,
            wx = w * x2,
            wy = w * y2,
            wz = w * z2;

        out[0] = 1 - (yy + zz);
        out[1] = xy + wz;
        out[2] = xz - wy;
        out[3] = 0;
        out[4] = xy - wz;
        out[5] = 1 - (xx + zz);
        out[6] = yz + wx;
        out[7] = 0;
        out[8] = xz + wy;
        out[9] = yz - wx;
        out[10] = 1 - (xx + yy);
        out[11] = 0;
        out[12] = v[0];
        out[13] = v[1];
        out[14] = v[2];
        out[15] = 1;

        return out;
    };

    /**
     * Returns the translation vector component of a transformation
     *  matrix. If a matrix is built with fromRotationTranslation,
     *  the returned vector will be the same as the translation vector
     *  originally supplied.
     * @param  {vec3} out Vector to receive translation component
     * @param  {mat4} mat Matrix to be decomposed (input)
     * @return {vec3} out
     */
    mat4.getTranslation = function (out, mat) {
      out[0] = mat[12];
      out[1] = mat[13];
      out[2] = mat[14];

      return out;
    };

    /**
     * Returns a quaternion representing the rotational component
     *  of a transformation matrix. If a matrix is built with
     *  fromRotationTranslation, the returned quaternion will be the
     *  same as the quaternion originally supplied.
     * @param {quat} out Quaternion to receive the rotation component
     * @param {mat4} mat Matrix to be decomposed (input)
     * @return {quat} out
     */
    mat4.getRotation = function (out, mat) {
      // Algorithm taken from http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
      var trace = mat[0] + mat[5] + mat[10];
      var S = 0;

      if (trace > 0) {
        S = Math.sqrt(trace + 1.0) * 2;
        out[3] = 0.25 * S;
        out[0] = (mat[6] - mat[9]) / S;
        out[1] = (mat[8] - mat[2]) / S;
        out[2] = (mat[1] - mat[4]) / S;
      } else if ((mat[0] > mat[5])&(mat[0] > mat[10])) {
        S = Math.sqrt(1.0 + mat[0] - mat[5] - mat[10]) * 2;
        out[3] = (mat[6] - mat[9]) / S;
        out[0] = 0.25 * S;
        out[1] = (mat[1] + mat[4]) / S;
        out[2] = (mat[8] + mat[2]) / S;
      } else if (mat[5] > mat[10]) {
        S = Math.sqrt(1.0 + mat[5] - mat[0] - mat[10]) * 2;
        out[3] = (mat[8] - mat[2]) / S;
        out[0] = (mat[1] + mat[4]) / S;
        out[1] = 0.25 * S;
        out[2] = (mat[6] + mat[9]) / S;
      } else {
        S = Math.sqrt(1.0 + mat[10] - mat[0] - mat[5]) * 2;
        out[3] = (mat[1] - mat[4]) / S;
        out[0] = (mat[8] + mat[2]) / S;
        out[1] = (mat[6] + mat[9]) / S;
        out[2] = 0.25 * S;
      }

      return out;
    };

    /**
     * Creates a matrix from a quaternion rotation, vector translation and vector scale
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.translate(dest, vec);
     *     var quatMat = mat4.create();
     *     quat4.toMat4(quat, quatMat);
     *     mat4.multiply(dest, quatMat);
     *     mat4.scale(dest, scale)
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat4} q Rotation quaternion
     * @param {vec3} v Translation vector
     * @param {vec3} s Scaling vector
     * @returns {mat4} out
     */
    mat4.fromRotationTranslationScale = function (out, q, v, s) {
        // Quaternion math
        var x = q[0], y = q[1], z = q[2], w = q[3],
            x2 = x + x,
            y2 = y + y,
            z2 = z + z,

            xx = x * x2,
            xy = x * y2,
            xz = x * z2,
            yy = y * y2,
            yz = y * z2,
            zz = z * z2,
            wx = w * x2,
            wy = w * y2,
            wz = w * z2,
            sx = s[0],
            sy = s[1],
            sz = s[2];

        out[0] = (1 - (yy + zz)) * sx;
        out[1] = (xy + wz) * sx;
        out[2] = (xz - wy) * sx;
        out[3] = 0;
        out[4] = (xy - wz) * sy;
        out[5] = (1 - (xx + zz)) * sy;
        out[6] = (yz + wx) * sy;
        out[7] = 0;
        out[8] = (xz + wy) * sz;
        out[9] = (yz - wx) * sz;
        out[10] = (1 - (xx + yy)) * sz;
        out[11] = 0;
        out[12] = v[0];
        out[13] = v[1];
        out[14] = v[2];
        out[15] = 1;

        return out;
    };

    /**
     * Creates a matrix from a quaternion rotation, vector translation and vector scale, rotating and scaling around the given origin
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.translate(dest, vec);
     *     mat4.translate(dest, origin);
     *     var quatMat = mat4.create();
     *     quat4.toMat4(quat, quatMat);
     *     mat4.multiply(dest, quatMat);
     *     mat4.scale(dest, scale)
     *     mat4.translate(dest, negativeOrigin);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat4} q Rotation quaternion
     * @param {vec3} v Translation vector
     * @param {vec3} s Scaling vector
     * @param {vec3} o The origin vector around which to scale and rotate
     * @returns {mat4} out
     */
    mat4.fromRotationTranslationScaleOrigin = function (out, q, v, s, o) {
      // Quaternion math
      var x = q[0], y = q[1], z = q[2], w = q[3],
          x2 = x + x,
          y2 = y + y,
          z2 = z + z,

          xx = x * x2,
          xy = x * y2,
          xz = x * z2,
          yy = y * y2,
          yz = y * z2,
          zz = z * z2,
          wx = w * x2,
          wy = w * y2,
          wz = w * z2,

          sx = s[0],
          sy = s[1],
          sz = s[2],

          ox = o[0],
          oy = o[1],
          oz = o[2];

      out[0] = (1 - (yy + zz)) * sx;
      out[1] = (xy + wz) * sx;
      out[2] = (xz - wy) * sx;
      out[3] = 0;
      out[4] = (xy - wz) * sy;
      out[5] = (1 - (xx + zz)) * sy;
      out[6] = (yz + wx) * sy;
      out[7] = 0;
      out[8] = (xz + wy) * sz;
      out[9] = (yz - wx) * sz;
      out[10] = (1 - (xx + yy)) * sz;
      out[11] = 0;
      out[12] = v[0] + ox - (out[0] * ox + out[4] * oy + out[8] * oz);
      out[13] = v[1] + oy - (out[1] * ox + out[5] * oy + out[9] * oz);
      out[14] = v[2] + oz - (out[2] * ox + out[6] * oy + out[10] * oz);
      out[15] = 1;

      return out;
    };

    /**
     * Calculates a 4x4 matrix from the given quaternion
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat} q Quaternion to create matrix from
     *
     * @returns {mat4} out
     */
    mat4.fromQuat = function (out, q) {
        var x = q[0], y = q[1], z = q[2], w = q[3],
            x2 = x + x,
            y2 = y + y,
            z2 = z + z,

            xx = x * x2,
            yx = y * x2,
            yy = y * y2,
            zx = z * x2,
            zy = z * y2,
            zz = z * z2,
            wx = w * x2,
            wy = w * y2,
            wz = w * z2;

        out[0] = 1 - yy - zz;
        out[1] = yx + wz;
        out[2] = zx - wy;
        out[3] = 0;

        out[4] = yx - wz;
        out[5] = 1 - xx - zz;
        out[6] = zy + wx;
        out[7] = 0;

        out[8] = zx + wy;
        out[9] = zy - wx;
        out[10] = 1 - xx - yy;
        out[11] = 0;

        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;

        return out;
    };

    /**
     * Generates a frustum matrix with the given bounds
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {Number} left Left bound of the frustum
     * @param {Number} right Right bound of the frustum
     * @param {Number} bottom Bottom bound of the frustum
     * @param {Number} top Top bound of the frustum
     * @param {Number} near Near bound of the frustum
     * @param {Number} far Far bound of the frustum
     * @returns {mat4} out
     */
    mat4.frustum = function (out, left, right, bottom, top, near, far) {
        var rl = 1 / (right - left),
            tb = 1 / (top - bottom),
            nf = 1 / (near - far);
        out[0] = (near * 2) * rl;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 0;
        out[5] = (near * 2) * tb;
        out[6] = 0;
        out[7] = 0;
        out[8] = (right + left) * rl;
        out[9] = (top + bottom) * tb;
        out[10] = (far + near) * nf;
        out[11] = -1;
        out[12] = 0;
        out[13] = 0;
        out[14] = (far * near * 2) * nf;
        out[15] = 0;
        return out;
    };

    /**
     * Generates a perspective projection matrix with the given bounds
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {number} fovy Vertical field of view in radians
     * @param {number} aspect Aspect ratio. typically viewport width/height
     * @param {number} near Near bound of the frustum
     * @param {number} far Far bound of the frustum
     * @returns {mat4} out
     */
    mat4.perspective = function (out, fovy, aspect, near, far) {
        var f = 1.0 / Math.tan(fovy / 2),
            nf = 1 / (near - far);
        out[0] = f / aspect;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 0;
        out[5] = f;
        out[6] = 0;
        out[7] = 0;
        out[8] = 0;
        out[9] = 0;
        out[10] = (far + near) * nf;
        out[11] = -1;
        out[12] = 0;
        out[13] = 0;
        out[14] = (2 * far * near) * nf;
        out[15] = 0;
        return out;
    };

    /**
     * Generates a perspective projection matrix with the given field of view.
     * This is primarily useful for generating projection matrices to be used
     * with the still experiemental WebVR API.
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {Object} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
     * @param {number} near Near bound of the frustum
     * @param {number} far Far bound of the frustum
     * @returns {mat4} out
     */
    mat4.perspectiveFromFieldOfView = function (out, fov, near, far) {
        var upTan = Math.tan(fov.upDegrees * Math.PI/180.0),
            downTan = Math.tan(fov.downDegrees * Math.PI/180.0),
            leftTan = Math.tan(fov.leftDegrees * Math.PI/180.0),
            rightTan = Math.tan(fov.rightDegrees * Math.PI/180.0),
            xScale = 2.0 / (leftTan + rightTan),
            yScale = 2.0 / (upTan + downTan);

        out[0] = xScale;
        out[1] = 0.0;
        out[2] = 0.0;
        out[3] = 0.0;
        out[4] = 0.0;
        out[5] = yScale;
        out[6] = 0.0;
        out[7] = 0.0;
        out[8] = -((leftTan - rightTan) * xScale * 0.5);
        out[9] = ((upTan - downTan) * yScale * 0.5);
        out[10] = far / (near - far);
        out[11] = -1.0;
        out[12] = 0.0;
        out[13] = 0.0;
        out[14] = (far * near) / (near - far);
        out[15] = 0.0;
        return out;
    }

    /**
     * Generates a orthogonal projection matrix with the given bounds
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {number} left Left bound of the frustum
     * @param {number} right Right bound of the frustum
     * @param {number} bottom Bottom bound of the frustum
     * @param {number} top Top bound of the frustum
     * @param {number} near Near bound of the frustum
     * @param {number} far Far bound of the frustum
     * @returns {mat4} out
     */
    mat4.ortho = function (out, left, right, bottom, top, near, far) {
        var lr = 1 / (left - right),
            bt = 1 / (bottom - top),
            nf = 1 / (near - far);
        out[0] = -2 * lr;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 0;
        out[5] = -2 * bt;
        out[6] = 0;
        out[7] = 0;
        out[8] = 0;
        out[9] = 0;
        out[10] = 2 * nf;
        out[11] = 0;
        out[12] = (left + right) * lr;
        out[13] = (top + bottom) * bt;
        out[14] = (far + near) * nf;
        out[15] = 1;
        return out;
    };

    /**
     * Generates a look-at matrix with the given eye position, focal point, and up axis
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {vec3} eye Position of the viewer
     * @param {vec3} center Point the viewer is looking at
     * @param {vec3} up vec3 pointing up
     * @returns {mat4} out
     */
    mat4.lookAt = function (out, eye, center, up) {
        var x0, x1, x2, y0, y1, y2, z0, z1, z2, len,
            eyex = eye[0],
            eyey = eye[1],
            eyez = eye[2],
            upx = up[0],
            upy = up[1],
            upz = up[2],
            centerx = center[0],
            centery = center[1],
            centerz = center[2];

        if (Math.abs(eyex - centerx) < glMatrix.EPSILON &&
            Math.abs(eyey - centery) < glMatrix.EPSILON &&
            Math.abs(eyez - centerz) < glMatrix.EPSILON) {
            return mat4.identity(out);
        }

        z0 = eyex - centerx;
        z1 = eyey - centery;
        z2 = eyez - centerz;

        len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
        z0 *= len;
        z1 *= len;
        z2 *= len;

        x0 = upy * z2 - upz * z1;
        x1 = upz * z0 - upx * z2;
        x2 = upx * z1 - upy * z0;
        len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
        if (!len) {
            x0 = 0;
            x1 = 0;
            x2 = 0;
        } else {
            len = 1 / len;
            x0 *= len;
            x1 *= len;
            x2 *= len;
        }

        y0 = z1 * x2 - z2 * x1;
        y1 = z2 * x0 - z0 * x2;
        y2 = z0 * x1 - z1 * x0;

        len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
        if (!len) {
            y0 = 0;
            y1 = 0;
            y2 = 0;
        } else {
            len = 1 / len;
            y0 *= len;
            y1 *= len;
            y2 *= len;
        }

        out[0] = x0;
        out[1] = y0;
        out[2] = z0;
        out[3] = 0;
        out[4] = x1;
        out[5] = y1;
        out[6] = z1;
        out[7] = 0;
        out[8] = x2;
        out[9] = y2;
        out[10] = z2;
        out[11] = 0;
        out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
        out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
        out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
        out[15] = 1;

        return out;
    };

    /**
     * Returns a string representation of a mat4
     *
     * @param {mat4} a matrix to represent as a string
     * @returns {String} string representation of the matrix
     */
    mat4.str = function (a) {
        return 'mat4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' +
                        a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' +
                        a[8] + ', ' + a[9] + ', ' + a[10] + ', ' + a[11] + ', ' +
                        a[12] + ', ' + a[13] + ', ' + a[14] + ', ' + a[15] + ')';
    };

    /**
     * Returns Frobenius norm of a mat4
     *
     * @param {mat4} a the matrix to calculate Frobenius norm of
     * @returns {Number} Frobenius norm
     */
    mat4.frob = function (a) {
        return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2) + Math.pow(a[9], 2) + Math.pow(a[10], 2) + Math.pow(a[11], 2) + Math.pow(a[12], 2) + Math.pow(a[13], 2) + Math.pow(a[14], 2) + Math.pow(a[15], 2) ))
    };

    /**
     * Adds two mat4's
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @returns {mat4} out
     */
    mat4.add = function(out, a, b) {
        out[0] = a[0] + b[0];
        out[1] = a[1] + b[1];
        out[2] = a[2] + b[2];
        out[3] = a[3] + b[3];
        out[4] = a[4] + b[4];
        out[5] = a[5] + b[5];
        out[6] = a[6] + b[6];
        out[7] = a[7] + b[7];
        out[8] = a[8] + b[8];
        out[9] = a[9] + b[9];
        out[10] = a[10] + b[10];
        out[11] = a[11] + b[11];
        out[12] = a[12] + b[12];
        out[13] = a[13] + b[13];
        out[14] = a[14] + b[14];
        out[15] = a[15] + b[15];
        return out;
    };

    /**
     * Subtracts matrix b from matrix a
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @returns {mat4} out
     */
    mat4.subtract = function(out, a, b) {
        out[0] = a[0] - b[0];
        out[1] = a[1] - b[1];
        out[2] = a[2] - b[2];
        out[3] = a[3] - b[3];
        out[4] = a[4] - b[4];
        out[5] = a[5] - b[5];
        out[6] = a[6] - b[6];
        out[7] = a[7] - b[7];
        out[8] = a[8] - b[8];
        out[9] = a[9] - b[9];
        out[10] = a[10] - b[10];
        out[11] = a[11] - b[11];
        out[12] = a[12] - b[12];
        out[13] = a[13] - b[13];
        out[14] = a[14] - b[14];
        out[15] = a[15] - b[15];
        return out;
    };

    /**
     * Alias for {@link mat4.subtract}
     * @function
     */
    mat4.sub = mat4.subtract;

    /**
     * Multiply each element of the matrix by a scalar.
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to scale
     * @param {Number} b amount to scale the matrix's elements by
     * @returns {mat4} out
     */
    mat4.multiplyScalar = function(out, a, b) {
        out[0] = a[0] * b;
        out[1] = a[1] * b;
        out[2] = a[2] * b;
        out[3] = a[3] * b;
        out[4] = a[4] * b;
        out[5] = a[5] * b;
        out[6] = a[6] * b;
        out[7] = a[7] * b;
        out[8] = a[8] * b;
        out[9] = a[9] * b;
        out[10] = a[10] * b;
        out[11] = a[11] * b;
        out[12] = a[12] * b;
        out[13] = a[13] * b;
        out[14] = a[14] * b;
        out[15] = a[15] * b;
        return out;
    };

    /**
     * Adds two mat4's after multiplying each element of the second operand by a scalar value.
     *
     * @param {mat4} out the receiving vector
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @param {Number} scale the amount to scale b's elements by before adding
     * @returns {mat4} out
     */
    mat4.multiplyScalarAndAdd = function(out, a, b, scale) {
        out[0] = a[0] + (b[0] * scale);
        out[1] = a[1] + (b[1] * scale);
        out[2] = a[2] + (b[2] * scale);
        out[3] = a[3] + (b[3] * scale);
        out[4] = a[4] + (b[4] * scale);
        out[5] = a[5] + (b[5] * scale);
        out[6] = a[6] + (b[6] * scale);
        out[7] = a[7] + (b[7] * scale);
        out[8] = a[8] + (b[8] * scale);
        out[9] = a[9] + (b[9] * scale);
        out[10] = a[10] + (b[10] * scale);
        out[11] = a[11] + (b[11] * scale);
        out[12] = a[12] + (b[12] * scale);
        out[13] = a[13] + (b[13] * scale);
        out[14] = a[14] + (b[14] * scale);
        out[15] = a[15] + (b[15] * scale);
        return out;
    };

    /**
     * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
     *
     * @param {mat4} a The first matrix.
     * @param {mat4} b The second matrix.
     * @returns {Boolean} True if the matrices are equal, false otherwise.
     */
    mat4.exactEquals = function (a, b) {
        return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3] &&
               a[4] === b[4] && a[5] === b[5] && a[6] === b[6] && a[7] === b[7] &&
               a[8] === b[8] && a[9] === b[9] && a[10] === b[10] && a[11] === b[11] &&
               a[12] === b[12] && a[13] === b[13] && a[14] === b[14] && a[15] === b[15];
    };

    /**
     * Returns whether or not the matrices have approximately the same elements in the same position.
     *
     * @param {mat4} a The first matrix.
     * @param {mat4} b The second matrix.
     * @returns {Boolean} True if the matrices are equal, false otherwise.
     */
    mat4.equals = function (a, b) {
        var a0  = a[0],  a1  = a[1],  a2  = a[2],  a3  = a[3],
            a4  = a[4],  a5  = a[5],  a6  = a[6],  a7  = a[7],
            a8  = a[8],  a9  = a[9],  a10 = a[10], a11 = a[11],
            a12 = a[12], a13 = a[13], a14 = a[14], a15 = a[15];

        var b0  = b[0],  b1  = b[1],  b2  = b[2],  b3  = b[3],
            b4  = b[4],  b5  = b[5],  b6  = b[6],  b7  = b[7],
            b8  = b[8],  b9  = b[9],  b10 = b[10], b11 = b[11],
            b12 = b[12], b13 = b[13], b14 = b[14], b15 = b[15];

        return (Math.abs(a0 - b0) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
                Math.abs(a1 - b1) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
                Math.abs(a2 - b2) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a2), Math.abs(b2)) &&
                Math.abs(a3 - b3) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a3), Math.abs(b3)) &&
                Math.abs(a4 - b4) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a4), Math.abs(b4)) &&
                Math.abs(a5 - b5) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a5), Math.abs(b5)) &&
                Math.abs(a6 - b6) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a6), Math.abs(b6)) &&
                Math.abs(a7 - b7) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a7), Math.abs(b7)) &&
                Math.abs(a8 - b8) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a8), Math.abs(b8)) &&
                Math.abs(a9 - b9) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a9), Math.abs(b9)) &&
                Math.abs(a10 - b10) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a10), Math.abs(b10)) &&
                Math.abs(a11 - b11) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a11), Math.abs(b11)) &&
                Math.abs(a12 - b12) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a12), Math.abs(b12)) &&
                Math.abs(a13 - b13) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a13), Math.abs(b13)) &&
                Math.abs(a14 - b14) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a14), Math.abs(b14)) &&
                Math.abs(a15 - b15) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a15), Math.abs(b15)));
    };

    module.exports = mat4;