// Copyright 2018 Wenbin He. All rights reserved.
// Use of this source code is governed by a MIT-style license that can be
// found in the LICENSE file.

function DensityEstimator(verts) {
  // public variables and functions --------------------------------------------
  // set surfaces
  this.nverts = 0;
  this.area = 0.;
  this.verts_textures = [];

  // local references of canvas, gl, and program
  var canvas_ = DensityEstimator.canvas,
      gl_ = DensityEstimator.gl,
      program_ = DensityEstimator.program;

  this.SetSurfaces = function(verts) {
    // reset surfaces
    this.nverts = 0;
    this.area = 0.;
    for (var i = 0, il = this.verts_textures.length; i < il; ++i)
      gl_.deleteTexture(this.verts_textures[i].texture);
    this.verts_textures.length = 0;

    // Only keep triangles whose areas are greater than zero.
    var valid_verts = [];
    if (verts !== undefined) {
      for (var i = 0, il = verts.length; i < il; i += 9) {
        var a = verts.slice(i,     i + 3),
            b = verts.slice(i + 3, i + 6),
            c = verts.slice(i + 6, i + 9);
        var area = TriangleArea(a, b, c);
        if (area > 0.) {
          valid_verts.push(a);
          valid_verts.push(b);
          valid_verts.push(c);
          this.area += area;
        }
      }
    }

    this.nverts = valid_verts.length;
    console.log("Number of valid triangles: " + this.nverts / 3);
    console.log("Total area: " + this.area);

    // Copy the surfaces into textures.
    var max_texture_size = gl_.getParameter(gl_.MAX_TEXTURE_SIZE);
    // console.log("WebGL2 maximum texture size: " +
    //             max_texture_size + " x " + max_texture_size);
    while (valid_verts.length > 0) {
      var curr_verts = valid_verts.splice(0, Math.min(valid_verts.length,
                                                      max_texture_size * 3));

      var texture = gl_.createTexture();
      gl_.bindTexture(gl_.TEXTURE_2D, texture);
      gl_.texStorage2D(gl_.TEXTURE_2D, 1, gl_.RGB32F, 3, curr_verts.length / 3);

      gl_.texParameteri(gl_.TEXTURE_2D, gl_.TEXTURE_MIN_FILTER, gl_.NEAREST);
      gl_.texParameteri(gl_.TEXTURE_2D, gl_.TEXTURE_MAG_FILTER, gl_.NEAREST);
      gl_.texParameteri(gl_.TEXTURE_2D, gl_.TEXTURE_WRAP_S, gl_.CLAMP_TO_EDGE);
      gl_.texParameteri(gl_.TEXTURE_2D, gl_.TEXTURE_WRAP_T, gl_.CLAMP_TO_EDGE);

      gl_.texSubImage2D(gl_.TEXTURE_2D, 0, 0, 0,
                        3, curr_verts.length / 3,
                        gl_.RGB, gl_.FLOAT,
                        new Float32Array(curr_verts.flat()));

      gl_.bindTexture(gl_.TEXTURE_2D, null);

      this.verts_textures.push(
          {"w": 3, "h": curr_verts.length / 3, "texture": texture});
    }
  }

  this.SetSurfaces(verts);

  // SDE computation
  this.Compute = function(xmin, ymin, zmin,
                          xmax, ymax, zmax,  // Physical domain that density estimation is performed on.
                          xdim, ydim, zdim,  // Grid resolution of the physical domain.
                          H,  // bandwidth matrix
                          normed=false,  // If true, normalize SDE by the area of the surface.
                          red_only=true) {  // If true, only output the red channel.
    console.time("SDE computation time");
    // Copy the parameters from CPU to GPU.
    var Hi = MatInv(H);  // inverse of the bandwidth matrix
    if (Hi === undefined) {
      alert("The input bandwidth matrix is not invertible.");
      return;
    }

    var Hi_sqrt = MatSqrt(Hi);  // square root of Hi (i.e., Hi_sqrt x Hi_sqrt = Hi)
    if (Hi_sqrt === undefined) {
      alert("The input bandwidth matrix is not positive semidefinite.");
      return;
    }
    Hi_sqrt = new Float32Array(Hi_sqrt.flat());

    gl_.useProgram(program_);

    var uMinLoc = gl_.getUniformLocation(program_, "uMin");
    var uMaxLoc = gl_.getUniformLocation(program_, "uMax");
    var uDimLoc = gl_.getUniformLocation(program_, "uDim");
    gl_.uniform3fv(uMinLoc, new Float32Array([xmin, ymin, zmin]));
    gl_.uniform3fv(uMaxLoc, new Float32Array([xmax, ymax, zmax]));
    gl_.uniform3fv(uDimLoc, new Float32Array([xdim, ydim, zdim]));

    var uHiSqrtLoc = gl_.getUniformLocation(program_, "uHiSqrt");
    gl_.uniformMatrix3fv(uHiSqrtLoc, false, Hi_sqrt);

    // Create a 3D texture to store the density estimation result.
    var sde_texture = gl_.createTexture();
    gl_.bindTexture(gl_.TEXTURE_3D, sde_texture);
    gl_.texStorage3D(gl_.TEXTURE_3D, 1, gl_.R32F, xdim, ydim, zdim);

    gl_.texParameteri(gl_.TEXTURE_3D, gl_.TEXTURE_MIN_FILTER, gl_.NEAREST);
    gl_.texParameteri(gl_.TEXTURE_3D, gl_.TEXTURE_MAG_FILTER, gl_.NEAREST);
    gl_.texParameteri(gl_.TEXTURE_3D, gl_.TEXTURE_WRAP_S, gl_.CLAMP_TO_EDGE);
    gl_.texParameteri(gl_.TEXTURE_3D, gl_.TEXTURE_WRAP_T, gl_.CLAMP_TO_EDGE);

    gl_.bindTexture(gl_.TEXTURE_3D, null);

    // Create a framebuffer.
    var fbo = gl_.createFramebuffer();
    gl_.bindFramebuffer(gl_.FRAMEBUFFER, fbo);
    gl_.framebufferTextureLayer(
        gl_.FRAMEBUFFER, gl_.COLOR_ATTACHMENT0, sde_texture, 0, 0);

    if (gl_.checkFramebufferStatus(gl_.FRAMEBUFFER) !=
        gl_.FRAMEBUFFER_COMPLETE) {
      alert("The framebuffer is not complete.");
      return;
    }

    gl_.bindFramebuffer(gl_.FRAMEBUFFER, null);

    // Create a vertex buffer object.
    var aPosLoc = gl_.getAttribLocation(program_, "aPos");
    var aUvLoc = gl_.getAttribLocation(program_, "aUv");

    gl_.enableVertexAttribArray(aPosLoc);
    gl_.enableVertexAttribArray(aUvLoc);

    var quad = new Float32Array([-1., -1., 0., 0., 1., -1., 1., 0.,
                                 -1., 1., 0., 1., 1., 1., 1., 1.]);
    var vbo = gl_.createBuffer();
    gl_.bindBuffer(gl_.ARRAY_BUFFER, vbo);
    gl_.bufferData(gl_.ARRAY_BUFFER, quad, gl_.STATIC_DRAW);
    gl_.vertexAttribPointer(aPosLoc, 2, gl_.FLOAT, gl_.FALSE, 16, 0);
    gl_.vertexAttribPointer(aUvLoc, 2, gl_.FLOAT, gl_.FALSE, 16, 8);

    // setup viewport
    gl_.viewport(0, 0, xdim, ydim);

    // setup gamma texture
    var uGammaTextureLoc = gl_.getUniformLocation(program_, "uGammaTexture");

    gl_.activeTexture(gl_.TEXTURE0);
    gl_.bindTexture(gl_.TEXTURE_2D, DensityEstimator.gamma_texture);
    gl_.uniform1i(uGammaTextureLoc, 0);

    // computation
    var uZLoc = gl_.getUniformLocation(program_, "uZ");
    var uVertsTextureHeightLoc =
        gl_.getUniformLocation(program_, "uVertsTextureHeight");
    var uVertsTextureLoc = gl_.getUniformLocation(program_, "uVertsTexture");

    var interm_res = new Float32Array(zdim * ydim * xdim * 4);
    var res = new Float32Array(zdim * ydim * xdim * 4);
    res.fill(0.);

    gl_.bindFramebuffer(gl_.FRAMEBUFFER, fbo);
    for (var i = 0, il = this.verts_textures.length; i < il; ++i) {
      gl_.uniform1i(uVertsTextureHeightLoc, this.verts_textures[i].h);

      gl_.activeTexture(gl_.TEXTURE1);
      gl_.bindTexture(gl_.TEXTURE_2D, this.verts_textures[i].texture);
      gl_.uniform1i(uVertsTextureLoc, 1);

      for (var j = 0; j < zdim; ++j) {
        gl_.uniform1f(uZLoc, j / (zdim - 1) * (zmax - zmin) + zmin);

        gl_.framebufferTextureLayer(
            gl_.FRAMEBUFFER, gl_.COLOR_ATTACHMENT0, sde_texture, 0, j);
        gl_.drawArrays(gl_.TRIANGLE_STRIP, 0, 4);

        // Copy the density estimation result from GPU to CPU.
        gl_.readBuffer(gl_.COLOR_ATTACHMENT0);
        gl_.readPixels(0, 0, xdim, ydim, gl_.RGBA, gl_.FLOAT,
                       interm_res, j * ydim * xdim * 4);
      }

      // Aggregate the intermediate density estimation result into the final result.
      res.forEach(function(e, i, a) {
        a[i] += interm_res[i];
      });
    }

    // Release buffers and textures
    gl_.activeTexture(gl_.TEXTURE0);
    gl_.bindTexture(gl_.TEXTURE_2D, null);
    gl_.activeTexture(gl_.TEXTURE1);
    gl_.bindTexture(gl_.TEXTURE_2D, null);

    gl_.bindFramebuffer(gl_.FRAMEBUFFER, null);
    gl_.bindBuffer(gl_.ARRAY_BUFFER, null);

    gl_.deleteBuffer(vbo);
    gl_.deleteFramebuffer(fbo);
    gl_.deleteTexture(sde_texture);

    gl_.useProgram(null);

    // Normalize SDE by the area of the surface.
    if (normed) {
      for (var i = 0, il = zdim * ydim * xdim * 4; i < il; i += 4)
        res[i] /= this.area;
    }

    if (red_only) {
      res = res.filter(function(e, i, a) {
              return i % 4 === 0;
            });
    }

    console.timeEnd("SDE computation time");

    return res;
  };
  // ---------------------------------------------------------------------------

  // private variables and functions -------------------------------------------
  // constants
  var kEps = 1e-10;
  var kMaxSweeps = 64;

  // subtraction of vectors
  function VecSub(va, vb) {
    return [va[0] - vb[0], va[1] - vb[1], va[2] - vb[2]];
  }

  // cross product of vectors
  function VecCross(va, vb) {
    return [va[1] * vb[2] - va[2] * vb[1],
            va[2] * vb[0] - va[0] * vb[2],
            va[0] * vb[1] - va[1] * vb[0]];
  }

  // length of a vector
  function VecLength(v) {
    return Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
  }

  // area of a triangle
  function TriangleArea(a, b, c) {
    var ab = VecSub(b, a), ac = VecSub(c, a);
    return .5 * VecLength(VecCross(ab, ac));
  }

  // multiplication of matrices
  function MatMul(ma, mb) {
    return [[ma[0][0] * mb[0][0] + ma[0][1] * mb[1][0] + ma[0][2] * mb[2][0],
             ma[0][0] * mb[0][1] + ma[0][1] * mb[1][1] + ma[0][2] * mb[2][1],
             ma[0][0] * mb[0][2] + ma[0][1] * mb[1][2] + ma[0][2] * mb[2][2]],
            [ma[1][0] * mb[0][0] + ma[1][1] * mb[1][0] + ma[1][2] * mb[2][0],
             ma[1][0] * mb[0][1] + ma[1][1] * mb[1][1] + ma[1][2] * mb[2][1],
             ma[1][0] * mb[0][2] + ma[1][1] * mb[1][2] + ma[1][2] * mb[2][2]],
            [ma[2][0] * mb[0][0] + ma[2][1] * mb[1][0] + ma[2][2] * mb[2][0],
             ma[2][0] * mb[0][1] + ma[2][1] * mb[1][1] + ma[2][2] * mb[2][1],
             ma[2][0] * mb[0][2] + ma[2][1] * mb[1][2] + ma[2][2] * mb[2][2]]];
  }

  // determinant of a matrix
  function MatDet(m) {
    return m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1]) -
           m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0]) +
           m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
  }

  // transpose of a matrix
  function MatTrs(m) {
    return [[m[0][0], m[1][0], m[2][0]],
            [m[0][1], m[1][1], m[2][1]],
            [m[0][2], m[1][2], m[2][2]]];
  }

  // inverse of a matrix
  function MatInv(m) {
    var p00 = m[1][1] * m[2][2] - m[1][2] * m[2][1];
    var p10 = m[1][2] * m[2][0] - m[1][0] * m[2][2];
    var p20 = m[1][0] * m[2][1] - m[1][1] * m[2][0];

    var t = m[0][0] * p00 + m[0][1] * p10 + m[0][2] * p20;
    if (t == 0.) return;

    var t = 1. / t;

    return [[p00 * t,
             (m[0][2] * m[2][1] - m[0][1] * m[2][2]) * t,
             (m[0][1] * m[1][2] - m[0][2] * m[1][1]) * t],
            [p10 * t,
             (m[0][0] * m[2][2] - m[0][2] * m[2][0]) * t,
             (m[0][2] * m[1][0] - m[0][0] * m[1][2]) * t],
            [p20 * t,
             (m[0][1] * m[2][0] - m[0][0] * m[2][1]) * t,
             (m[0][0] * m[1][1] - m[0][1] * m[1][0]) * t]];
  }

  // eigen decomposition of a matrix
  function MatEig(m) {
    if (m[0][1] != m[1][0] ||
        m[0][2] != m[2][0] ||
        m[1][2] != m[2][1])
      return;

    var res = {val : [0., 0., 0.],
               vec : [[1., 0., 0.],
                      [0., 1., 0.],
                      [0., 0., 1.]]};

    var m00 = m[0][0], m11 = m[1][1], m22 = m[2][2],
        m01 = m[0][1], m02 = m[0][2], m12 = m[1][2];

    for (var i = 0; i < kMaxSweeps; ++i) {
      if ((Math.abs(m01) < kEps) && (Math.abs(m02) < kEps) &&
          (Math.abs(m12) < kEps)) break;

      if (m01 != 0.) {
        var u = (m11 - m00) * .5 / m01;
        var u2 = u * u;
        var u2p1 = u2 + 1.;
        var t = (u2p1 != u2) ?
                ((u < 0.) ? -1. : 1.) * (Math.sqrt(u2p1) - Math.abs(u)) :
                .5 / u;
        var c = 1. / Math.sqrt(t * t + 1.);
        var s = c * t;
        m00 -= t * m01;
        m11 += t * m01;
        m01 = 0.;

        var tmp = c * m02 - s * m12;
        m12 = s * m02 + c * m12;
        m02 = tmp;

        for (var j = 0; j < 3; ++j) {
          var tmp = c * res.vec[j][0] - s * res.vec[j][1];
          res.vec[j][1] = s * res.vec[j][0] + c * res.vec[j][1];
          res.vec[j][0] = tmp;
        }
      }

      if (m02 != 0.) {
        var u = (m22 - m00) * .5 / m02;
        var u2 = u * u;
        var u2p1 = u2 + 1.;
        var t = (u2p1 != u2) ?
                ((u < 0.) ? -1. : 1.) * (Math.sqrt(u2p1) - Math.abs(u)) :
                .5 / u;
        var c = 1. / Math.sqrt(t * t + 1.);
        var s = c * t;

        m00 -= t * m02;
        m22 += t * m02;
        m02 = 0.;

        var tmp = c * m01 - s * m12;
        m12 = s * m01 + c * m12;
        m01 = tmp;

        for (var j = 0; j < 3; ++j) {
          var tmp = c * res.vec[j][0] - s * res.vec[j][2];
          res.vec[j][2] = s * res.vec[j][0] + c * res.vec[j][2];
          res.vec[j][0] = tmp;
        }
      }

      if (m12 != 0.) {
        var u = (m22 - m11) * .5 / m12;
        var u2 = u * u;
        var u2p1 = u2 + 1.;
        var t = (u2p1 != u2) ?
                ((u < 0.) ? -1. : 1.) * (Math.sqrt(u2p1) - Math.abs(u)) :
                .5 / u;
        var c = 1. / Math.sqrt(t * t + 1.);
        var s = c * t;

        m11 -= t * m12;
        m22 += t * m12;
        m12 = 0.;

        var tmp = c * m01 - s * m02;
        m02 = s * m01 + c * m02;
        m01 = tmp;

        for (var j = 0; j < 3; ++j) {
          var tmp = c * res.vec[j][1] - s * res.vec[j][2];
          res.vec[j][2] = s * res.vec[j][1] + c * res.vec[j][2];
          res.vec[j][1] = tmp;
        }
      }
    }

    res.val[0] = m00;
    res.val[1] = m11;
    res.val[2] = m22;

    return res;
  }

  // square root of a matrix
  function MatSqrt(m) {
    var eig = MatEig(m);
    if (eig === undefined) return;
    if (eig.val[0] < 0. || eig.val[1] < 0. || eig.val[2] < 0.)
      return;

    var diag = [[Math.sqrt(eig.val[0]), 0., 0.],
                [0., Math.sqrt(eig.val[1]), 0.],
                [0., 0., Math.sqrt(eig.val[2])]];

    return MatMul(MatMul(eig.vec, diag), MatTrs(eig.vec));
  }
  // ---------------------------------------------------------------------------
}

// static variables and functions ----------------------------------------------
// canvas and gl
DensityEstimator.canvas = document.createElement("canvas");

DensityEstimator.gl =
    DensityEstimator.canvas.getContext("webgl2");
if (!DensityEstimator.gl) {
  alert("WebGL2 is not supported by this browser.");
}

DensityEstimator.ext =
    DensityEstimator.gl.getExtension("EXT_color_buffer_float");
if (!DensityEstimator.ext) {
  alert("EXT_color_buffer_float is not supported by this browser.");
}

DensityEstimator.oes =
    DensityEstimator.gl.getExtension("OES_texture_float_linear");
if (!DensityEstimator.oes) {
  alert("OES_texture_float_linear is not supported by this browser.");
}

// gamma
DensityEstimator.gamma_table = new Float32Array([
0.0, 0.0015914964, 0.0031826745, 0.004773217, 0.0063628056, 0.0079511255, 0.009537862, 0.011122703, 0.012705337, 0.014285457, 0.01586276, 0.01743694, 0.019007703, 0.020574756, 0.022137806, 0.023696572, 0.02525077, 0.026800126, 0.028344372, 0.029883241,
0.03141648, 0.03294383, 0.034465052, 0.0359799, 0.037488148, 0.038989566, 0.040483933, 0.041971043, 0.043450683, 0.044922665, 0.04638679, 0.04784288, 0.049290754, 0.05073025, 0.0521612, 0.05358346, 0.054996878, 0.056401316, 0.057796642, 0.059182733,
0.06055947, 0.06192675, 0.06328446, 0.06463251, 0.065970816, 0.06729929, 0.068617865, 0.069926456, 0.07122502, 0.07251348, 0.07379181, 0.07505995, 0.07631787, 0.07756553, 0.078802906, 0.08002998, 0.08124674, 0.08245317, 0.083649255, 0.084835015,
0.086010434, 0.08717553, 0.08833031, 0.0894748, 0.09060901, 0.091732964, 0.0928467, 0.093950234, 0.095043615, 0.09612688, 0.09720006, 0.0982632, 0.09931635, 0.10035957, 0.101392895, 0.10241638, 0.10343009, 0.10443409, 0.10542842, 0.106413156,
0.107388355, 0.10835409, 0.109310426, 0.110257424, 0.11119516, 0.11212371, 0.113043144, 0.11395352, 0.11485494, 0.11574745, 0.11663114, 0.117506094, 0.11837238, 0.11923007, 0.12007925, 0.120919995, 0.12175239, 0.122576505, 0.123392425, 0.12420023,
0.125, 0.0, 0.0015914168, 0.0031825155, 0.004772978, 0.0063624876, 0.007950728, 0.009537385, 0.011122146, 0.0127047, 0.014284741, 0.015861964, 0.017436065, 0.01900675, 0.020573722, 0.022136692, 0.023695378, 0.025249496, 0.026798774, 0.02834294,
0.02988173, 0.03141489, 0.03294216, 0.0344633, 0.03597807, 0.037486237, 0.038987577, 0.040481865, 0.041968893, 0.043448456, 0.044920355, 0.0463844, 0.047840413, 0.04928821, 0.050727624, 0.052158497, 0.053580675, 0.054994013, 0.056398373, 0.057793617,
0.05917963, 0.06055629, 0.061923485, 0.06328112, 0.06462909, 0.065967314, 0.067295715, 0.0686142, 0.069922715, 0.071221195, 0.07250959, 0.07378783, 0.07505589, 0.07631373, 0.07756131, 0.07879861, 0.080025606, 0.081242286, 0.08244863, 0.08364464,
0.08483032, 0.08600566, 0.087170675, 0.08832538, 0.08946978, 0.09060392, 0.09172779, 0.09284145, 0.09394491, 0.095038205, 0.096121386, 0.097194485, 0.09825755, 0.09931062, 0.100353755, 0.101387, 0.10241041, 0.10342405, 0.104427956, 0.10542221,
0.10640687, 0.10738199, 0.10834765, 0.1093039, 0.11025082, 0.11118848, 0.11211695, 0.1130363, 0.1139466, 0.114847936, 0.11574037, 0.11662398, 0.11749885, 0.11836506, 0.11922267, 0.12007177, 0.12091244, 0.12174475, 0.122568786, 0.12338463,
0.12419236, 0.12499204, 0.0, 0.0015911781, 0.003182038, 0.0047722617, 0.0063615325, 0.007949534, 0.0095359525, 0.011120475, 0.012702791, 0.014282593, 0.015859576, 0.017433438, 0.019003885, 0.020570619, 0.02213335, 0.023691798, 0.025245678, 0.026794715,
0.028338643, 0.029877195, 0.031410113, 0.032937147, 0.03445805, 0.03597258, 0.03748051, 0.03898161, 0.04047566, 0.04196245, 0.043441772, 0.044913433, 0.04637724, 0.04783301, 0.04928057, 0.050719745, 0.052150384, 0.053572323, 0.054985423, 0.05638954,
0.057784546, 0.05917032, 0.06054674, 0.0619137, 0.06327109, 0.064618826, 0.065956816, 0.06728497, 0.06860322, 0.069911495, 0.071209736, 0.07249789, 0.073775895, 0.075043716, 0.076301314, 0.07754866, 0.07878572, 0.08001248, 0.08122892, 0.08243503,
0.0836308, 0.08481623, 0.08599134, 0.08715612, 0.08831058, 0.08945475, 0.09058864, 0.09171228, 0.09282569, 0.09392891, 0.09502198, 0.09610491, 0.09717777, 0.0982406, 0.09929344, 0.100336336, 0.101369336, 0.10239251, 0.10340591, 0.10440958,
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3.3888944e-05, 3.418855e-05, 3.4468605e-05, 3.4729987e-05, 3.497356e-05, 3.5200188e-05, 3.541072e-05, 3.5606e-05, 3.578686e-05, 3.5954097e-05, 3.610851e-05, 3.6250858e-05, 3.6381887e-05, 3.6502308e-05, 3.661282e-05, 3.6714075e-05, 3.6806712e-05, 3.689134e-05, 3.696853e-05, 3.7038826e-05,
3.7102756e-05, 3.7160804e-05, 3.7213435e-05, 3.7261078e-05, 3.7304148e-05, 3.734302e-05, 3.7378053e-05, 3.740958e-05, 3.7437905e-05, 3.7463324e-05, 3.7486094e-05, 3.7506463e-05, 3.752466e-05, 3.754089e-05, 3.7555343e-05, 3.7568196e-05, 3.757961e-05, 3.7589733e-05, 3.7598693e-05, 3.7606616e-05,
3.761361e-05, 3.7619775e-05, 3.76252e-05, 3.7629972e-05, 3.7634156e-05, 3.7637827e-05, 3.7641035e-05, 3.764384e-05, 3.764629e-05, 3.7648424e-05, 3.765028e-05, 3.765189e-05, 3.765329e-05, 3.7654503e-05, 3.765555e-05, 3.7656457e-05, 3.7657235e-05, 3.765791e-05, 3.7658487e-05, 3.7658985e-05,
0.0, 1.1643807e-06, 2.326849e-06, 3.485502e-06, 4.638456e-06, 5.783856e-06, 6.919883e-06, 8.044766e-06, 9.156788e-06, 1.0254293e-05, 1.1335697e-05, 1.2399491e-05, 1.3444252e-05, 1.446864e-05, 1.5471414e-05, 1.6451428e-05, 1.7407636e-05, 1.8339098e-05, 1.9244979e-05, 2.012455e-05,
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3.2273085e-05, 3.257927e-05, 3.286584e-05, 3.3133627e-05, 3.3383472e-05, 3.361622e-05, 3.38327e-05, 3.403374e-05, 3.4220146e-05, 3.439272e-05, 3.4552242e-05, 3.469947e-05, 3.4835146e-05, 3.4959983e-05, 3.5074667e-05, 3.517987e-05, 3.527622e-05, 3.5364337e-05, 3.54448e-05, 3.5518155e-05,
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3.003649e-05, 3.0108518e-05, 3.0174175e-05, 3.023393e-05, 3.0288229e-05, 3.0337495e-05, 3.0382123e-05, 3.0422492e-05, 3.0458948e-05, 3.0491823e-05, 3.052142e-05, 3.0548028e-05, 3.057191e-05, 3.0593317e-05, 3.061247e-05, 3.0629588e-05, 3.0644856e-05, 3.0658455e-05, 3.0670555e-05, 3.0681298e-05,
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1.7490433e-05, 1.7601069e-05, 1.77034e-05, 1.7797889e-05, 1.7884993e-05, 1.7965154e-05, 1.8038803e-05, 1.8106355e-05, 1.8168215e-05, 1.8224766e-05, 1.8276378e-05, 1.8323404e-05, 1.8366183e-05, 1.8405035e-05, 1.8440258e-05, 1.8472143e-05, 1.8500958e-05, 1.8526955e-05, 1.855037e-05, 1.8571427e-05,
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1.8727851e-05, 1.8729206e-05, 1.8730378e-05, 1.8731393e-05, 1.8732271e-05, 1.8733026e-05, 1.8733677e-05, 1.8734238e-05, 1.873472e-05, 1.873513e-05, 1.8735484e-05, 1.8735785e-05, 1.8736042e-05, 1.873626e-05, 1.8736446e-05, 1.8736604e-05, 1.8736739e-05, 0.0, 6.015277e-07, 1.2019882e-06,
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1.19489905e-05, 1.2317997e-05, 1.26717e-05, 1.3010143e-05, 1.33334215e-05, 1.3641678e-05, 1.3935101e-05, 1.4213922e-05, 1.4478408e-05, 1.4728864e-05, 1.4965624e-05, 1.5189054e-05, 1.539954e-05, 1.5597494e-05, 1.5783342e-05, 1.5957525e-05, 1.6120499e-05, 1.6272725e-05, 1.6414668e-05, 1.65468e-05,
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1.7811755e-05, 1.7829638e-05, 1.784566e-05, 1.7859988e-05, 1.7872784e-05, 1.7884191e-05, 1.7894345e-05, 1.7903369e-05, 1.7911372e-05, 1.7918463e-05, 1.7924733e-05, 1.793027e-05, 1.7935148e-05, 1.7939443e-05, 1.7943215e-05, 1.7946524e-05, 1.7949424e-05, 1.7951957e-05, 1.7954171e-05, 1.79561e-05,
1.7957778e-05, 1.7959235e-05, 1.79605e-05, 1.7961596e-05, 1.7962542e-05, 1.796336e-05, 1.7964065e-05, 1.7964672e-05, 1.7965192e-05, 1.796564e-05, 1.7966022e-05, 1.796635e-05, 1.796663e-05, 1.7966868e-05, 1.796707e-05, 1.7967242e-05, 1.7967388e-05, 1.7967512e-05, 0.0, 5.7808523e-07,
1.1551402e-06, 1.7301403e-06, 2.3020718e-06, 2.869938e-06, 3.4327632e-06, 3.9895995e-06, 4.5395295e-06, 5.0816734e-06, 5.615191e-06, 6.139287e-06, 6.653213e-06, 7.156272e-06, 7.647821e-06, 8.127273e-06, 8.594097e-06, 9.0478225e-06, 9.488038e-06, 9.914392e-06, 1.0326592e-05, 1.0724408e-05,
1.1107664e-05, 1.1476248e-05, 1.1830097e-05, 1.21692065e-05, 1.24936205e-05, 1.2803434e-05, 1.3098789e-05, 1.3379869e-05, 1.3646899e-05, 1.39001395e-05, 1.4139888e-05, 1.4366468e-05, 1.4580235e-05, 1.47815645e-05, 1.4970853e-05, 1.5148515e-05, 1.5314978e-05, 1.5470681e-05, 1.561607e-05, 1.5751595e-05,
1.5877713e-05, 1.5994874e-05, 1.610353e-05, 1.6204127e-05, 1.6297106e-05, 1.6382899e-05, 1.6461925e-05, 1.6534597e-05, 1.6601314e-05, 1.6662461e-05, 1.6718408e-05, 1.676951e-05, 1.6816113e-05, 1.685854e-05, 1.6897098e-05, 1.6932085e-05, 1.6963779e-05, 1.699244e-05, 1.7018318e-05, 1.7041642e-05,
1.7062632e-05, 1.7081487e-05, 1.70984e-05, 1.7113543e-05, 1.7127082e-05, 1.7139166e-05, 1.7149932e-05, 1.715951e-05, 1.7168017e-05, 1.7175558e-05, 1.7182236e-05, 1.7188137e-05, 1.7193343e-05, 1.719793e-05, 1.7201965e-05, 1.7205508e-05, 1.7208613e-05, 1.721133e-05, 1.7213706e-05, 1.7215778e-05,
1.7217584e-05, 1.7219154e-05, 1.7220516e-05, 1.7221697e-05, 1.7222721e-05, 1.7223603e-05, 1.7224365e-05, 1.7225022e-05, 1.7225588e-05, 1.7226072e-05, 1.7226488e-05, 1.7226843e-05, 1.7227147e-05, 1.7227407e-05, 1.7227627e-05, 1.7227814e-05, 1.7227974e-05, 1.7228109e-05, 1.7228223e-05, 0.0,
5.555007e-07, 1.1100071e-06, 1.66253e-06, 2.2120912e-06, 2.7577287e-06, 3.298501e-06, 3.8334933e-06, 4.361821e-06, 4.8826355e-06, 5.3951258e-06, 5.8985256e-06, 6.3921143e-06, 6.8752197e-06, 7.347223e-06, 7.807558e-06, 8.255716e-06, 8.691243e-06, 9.113745e-06, 9.522884e-06, 9.918382e-06,
1.0300017e-05, 1.0667623e-05, 1.1021093e-05, 1.1360372e-05, 1.1685454e-05, 1.1996389e-05, 1.2293268e-05, 1.257623e-05, 1.2845457e-05, 1.3101166e-05, 1.3343613e-05, 1.3573086e-05, 1.37899015e-05, 1.39944e-05, 1.418695e-05, 1.4367932e-05, 1.453775e-05, 1.4696816e-05, 1.4845555e-05, 1.4984398e-05,
1.5113781e-05, 1.5234143e-05, 1.5345919e-05, 1.5449546e-05, 1.5545455e-05, 1.5634067e-05, 1.5715801e-05, 1.579106e-05, 1.5860243e-05, 1.592373e-05, 1.5981894e-05, 1.603509e-05, 1.608366e-05, 1.6127935e-05, 1.6168224e-05, 1.6204824e-05, 1.623802e-05, 1.6268075e-05, 1.6295246e-05, 1.6319762e-05,
1.6341852e-05, 1.6361719e-05, 1.637956e-05, 1.6395552e-05, 1.6409866e-05, 1.6422655e-05, 1.6434062e-05, 1.6444223e-05, 1.6453256e-05, 1.6461274e-05, 1.6468379e-05, 1.6474665e-05, 1.6480219e-05, 1.6485115e-05, 1.6489428e-05, 1.6493217e-05, 1.6496542e-05, 1.6499456e-05, 1.6502005e-05, 1.6504231e-05,
1.6506172e-05, 1.650786e-05, 1.650933e-05, 1.6510603e-05, 1.6511705e-05, 1.651266e-05, 1.6513484e-05, 1.6514196e-05, 1.6514807e-05, 1.6515332e-05, 1.6515783e-05, 1.651617e-05, 1.6516498e-05, 1.651678e-05, 1.6517022e-05, 1.6517226e-05, 1.65174e-05, 1.6517548e-05, 1.6517672e-05, 1.6517779e-05,
0.0, 5.337452e-07, 1.0665308e-06, 1.597402e-06, 2.1254152e-06, 2.6496414e-06, 3.1691727e-06, 3.6831266e-06, 4.1906496e-06, 4.6909227e-06, 5.1831653e-06, 5.6666377e-06, 6.1406454e-06, 6.6045413e-06, 7.05773e-06, 7.499666e-06, 7.92986e-06, 8.347875e-06, 8.753334e-06, 9.145913e-06,
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1.4376824e-05, 1.4500329e-05, 1.4615183e-05, 1.4721811e-05, 1.482063e-05, 1.4912056e-05, 1.4996497e-05, 1.5074354e-05, 1.5146018e-05, 1.521187e-05, 1.5272277e-05, 1.5327596e-05, 1.5378171e-05, 1.5424328e-05, 1.5466385e-05, 1.5504638e-05, 1.5539375e-05, 1.5570868e-05, 1.5599368e-05, 1.5625119e-05,
1.5648346e-05, 1.5669262e-05, 1.5688065e-05, 1.570494e-05, 1.5720061e-05, 1.5733587e-05, 1.5745667e-05, 1.5756437e-05, 1.5766023e-05, 1.5774542e-05, 1.5782098e-05, 1.5788792e-05, 1.5794709e-05, 1.5799935e-05, 1.5804539e-05, 1.5808591e-05, 1.581215e-05, 1.5815272e-05, 1.5818005e-05, 1.5820395e-05,
1.582248e-05, 1.5824296e-05, 1.5825877e-05, 1.582725e-05, 1.582844e-05, 1.582947e-05, 1.5830361e-05, 1.583113e-05, 1.5831793e-05, 1.5832362e-05, 1.583285e-05, 1.583327e-05, 1.5833628e-05, 1.5833935e-05, 1.5834197e-05, 1.583442e-05, 1.5834608e-05, 1.583477e-05, 1.5834907e-05, 1.5835021e-05,
1.583512e-05, 0.0, 5.1279045e-07, 1.0246548e-06, 1.5346719e-06, 2.0419309e-06, 2.5455358e-06, 3.0446104e-06, 3.5383034e-06, 4.025792e-06, 4.506286e-06, 4.979033e-06, 5.4433194e-06, 5.898477e-06, 6.3438824e-06, 6.778961e-06, 7.2031903e-06, 7.6160977e-06, 8.017265e-06, 8.406329e-06,
8.782979e-06, 9.146961e-06, 9.498071e-06, 9.836163e-06, 1.0161139e-05, 1.04729515e-05, 1.0771603e-05, 1.1057143e-05, 1.1329662e-05, 1.15892935e-05, 1.1836211e-05, 1.2070624e-05, 1.2292772e-05, 1.2502928e-05, 1.2701389e-05, 1.2888479e-05, 1.3064539e-05, 1.3229933e-05, 1.3385033e-05, 1.3530227e-05,
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1.4981078e-05, 1.5003078e-05, 1.5022881e-05, 1.5040675e-05, 1.5056637e-05, 1.5070931e-05, 1.5083711e-05, 1.5095119e-05, 1.5105285e-05, 1.5114328e-05, 1.51223585e-05, 1.512948e-05, 1.51357835e-05, 1.5141354e-05, 1.514627e-05, 1.5150599e-05, 1.5154406e-05, 1.5157749e-05, 1.5160678e-05, 1.5163242e-05,
1.5165481e-05, 1.5167435e-05, 1.5169136e-05, 1.51706145e-05, 1.5171898e-05, 1.517301e-05, 1.5173972e-05, 1.5174803e-05, 1.5175519e-05, 1.5176136e-05, 1.5176666e-05, 1.5177121e-05, 1.5177511e-05, 1.5177845e-05, 1.517813e-05, 1.51783715e-05, 1.5178579e-05, 1.5178754e-05, 1.5178903e-05, 1.5179029e-05,
1.5179136e-05, 1.51792265e-05, 0.0, 4.926091e-07, 9.843245e-07, 1.4742577e-06, 1.9615295e-06, 2.4452756e-06, 2.9246512e-06, 3.3988345e-06, 3.867032e-06, 4.328482e-06, 4.7824597e-06, 5.228277e-06, 5.66529e-06, 6.092898e-06, 6.5105487e-06, 6.9177386e-06, 7.3140136e-06, 7.698973e-06,
8.072266e-06, 8.433596e-06, 8.782719e-06, 9.119444e-06, 9.443628e-06, 9.75518e-06, 1.0054058e-05, 1.0340267e-05, 1.0613854e-05, 1.0874911e-05, 1.1123569e-05, 1.1359997e-05, 1.15843995e-05, 1.1797009e-05, 1.1998092e-05, 1.2187937e-05, 1.2366855e-05, 1.2535182e-05, 1.2693264e-05, 1.2841465e-05,
1.298016e-05, 1.3109732e-05, 1.323057e-05, 1.3343068e-05, 1.3447617e-05, 1.3544612e-05, 1.36344415e-05, 1.3717492e-05, 1.3794143e-05, 1.3864765e-05, 1.392972e-05, 1.3989361e-05, 1.4044028e-05, 1.409405e-05, 1.4139745e-05, 1.4181414e-05, 1.42193485e-05, 1.4253824e-05, 1.4285102e-05, 1.4313432e-05,
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1.45341855e-05, 1.4536285e-05, 1.4538114e-05, 1.4539706e-05, 1.4541089e-05, 1.4542288e-05, 1.4543328e-05, 1.4544225e-05, 1.4545e-05, 1.4545669e-05, 1.4546244e-05, 1.4546737e-05, 1.454716e-05, 1.4547522e-05, 1.45478325e-05, 1.4548096e-05, 1.4548322e-05, 1.4548513e-05, 1.4548676e-05, 1.4548814e-05,
1.454893e-05, 1.45490285e-05, 1.4549112e-05, 0.0, 4.7317468e-07, 9.4548716e-07, 1.4160801e-06, 1.8841055e-06, 2.3487294e-06, 2.809137e-06, 3.2645357e-06, 3.7141608e-06, 4.1572775e-06, 4.5931865e-06, 5.021226e-06, 5.440775e-06, 5.8512555e-06, 6.2521353e-06, 6.64293e-06, 7.023204e-06,
7.392571e-06, 7.750696e-06, 8.097294e-06, 8.432132e-06, 8.755025e-06, 9.065841e-06, 9.364493e-06, 9.650943e-06, 9.925197e-06, 1.0187304e-05, 1.0437355e-05, 1.0675477e-05, 1.0901837e-05, 1.1116633e-05, 1.1320092e-05, 1.1512472e-05, 1.1694054e-05, 1.186514e-05, 1.2026053e-05, 1.217713e-05,
1.2318724e-05, 1.2451195e-05, 1.2574916e-05, 1.26902605e-05, 1.2797608e-05, 1.289734e-05, 1.29898335e-05, 1.3075465e-05, 1.3154606e-05, 1.3227622e-05, 1.329487e-05, 1.3356699e-05, 1.3413447e-05, 1.3465443e-05, 1.3513001e-05, 1.3556427e-05, 1.3596011e-05, 1.3632031e-05, 1.3664753e-05, 1.3694427e-05,
1.3721292e-05, 1.3745573e-05, 1.3767479e-05, 1.3787211e-05, 1.3804954e-05, 1.3820882e-05, 1.3835155e-05, 1.38479245e-05, 1.385933e-05, 1.38694995e-05, 1.3878552e-05, 1.3886596e-05, 1.3893733e-05, 1.3900053e-05, 1.3905643e-05, 1.3910576e-05, 1.3914923e-05, 1.3918749e-05, 1.3922108e-05, 1.3925055e-05,
1.39276335e-05, 1.3929888e-05, 1.39318545e-05, 1.3933568e-05, 1.3935058e-05, 1.3936351e-05, 1.3937472e-05, 1.3938443e-05, 1.39392805e-05, 1.3940004e-05, 1.3940627e-05, 1.3941161e-05, 1.3941621e-05, 1.3942014e-05, 1.3942351e-05, 1.3942639e-05, 1.3942884e-05, 1.3943093e-05, 1.39432705e-05, 1.3943421e-05,
1.3943549e-05, 1.3943656e-05, 1.3943748e-05, 1.3943824e-05, 0.0, 4.544615e-07, 9.080913e-07, 1.3600622e-06, 1.8095564e-06, 2.2557695e-06, 2.6979153e-06, 3.1352297e-06, 3.5669755e-06, 3.9924444e-06, 4.410962e-06, 4.821891e-06, 5.224633e-06, 5.618632e-06, 6.003375e-06, 6.378397e-06,
6.7432784e-06, 7.0976484e-06, 7.4411855e-06, 7.773618e-06, 8.09472e-06, 8.4043195e-06, 8.702287e-06, 8.988543e-06, 9.2630535e-06, 9.525824e-06, 9.776906e-06, 1.0016388e-05, 1.0244397e-05, 1.04610945e-05, 1.0666672e-05, 1.0861354e-05, 1.10453875e-05, 1.1219046e-05, 1.13826245e-05, 1.1536434e-05,
1.16808005e-05, 1.1816065e-05, 1.1942579e-05, 1.2060698e-05, 1.2170786e-05, 1.2273209e-05, 1.2368333e-05, 1.2456523e-05, 1.2538143e-05, 1.261355e-05, 1.26830955e-05, 1.2747123e-05, 1.2805968e-05, 1.2859958e-05, 1.2909406e-05, 1.2954616e-05, 1.2995881e-05, 1.3033478e-05, 1.3067677e-05, 1.3098731e-05,
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1.1097925e-06, 1.1154435e-06, 1.1205699e-06, 1.12521e-06, 1.1294009e-06, 1.1331774e-06, 1.1365734e-06, 1.13962e-06, 1.1423477e-06, 1.1447842e-06, 1.1469559e-06, 1.1488873e-06, 1.1506013e-06, 1.1521191e-06, 1.1534601e-06, 1.1546424e-06, 1.1556825e-06, 1.1565955e-06, 1.1573952e-06, 1.1580942e-06,
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4.2342197e-08, 8.458685e-08, 1.266371e-07, 1.6839742e-07, 2.0977433e-07, 2.5067692e-07, 2.9101756e-07, 3.3071242e-07, 3.69682e-07, 4.0785156e-07, 4.4515158e-07, 4.815182e-07, 5.168933e-07, 5.51225e-07, 5.8446767e-07, 6.165821e-07, 6.475355e-07, 6.7730156e-07, 7.058605e-07, 7.3319853e-07,
7.5930825e-07, 7.841879e-07, 8.0784145e-07, 8.302781e-07, 8.515122e-07, 8.7156246e-07, 8.9045193e-07, 9.0820754e-07, 9.2485953e-07, 9.4044117e-07, 9.549884e-07, 9.685391e-07, 9.811333e-07, 9.928121e-07, 1.0036176e-06, 1.0135929e-06, 1.0227809e-06, 1.0312249e-06, 1.0389676e-06, 1.0460518e-06,
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4.886391e-07, 5.1306034e-07, 5.3652633e-07, 5.59022e-07, 5.805372e-07, 6.0106663e-07, 6.2060997e-07, 6.391714e-07, 6.5675925e-07, 6.7338595e-07, 6.890676e-07, 7.038237e-07, 7.176767e-07, 7.3065195e-07, 7.4277693e-07, 7.5408127e-07, 7.6459634e-07, 7.7435465e-07, 7.833899e-07, 7.917365e-07,
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1.2441026e-07, 1.4438861e-07, 1.6402788e-07, 1.8328674e-07, 2.0212651e-07, 2.2051137e-07, 2.3840857e-07, 2.5578862e-07, 2.726254e-07, 2.888962e-07, 3.0458182e-07, 3.1966655e-07, 3.341382e-07, 3.4798805e-07, 3.6121065e-07, 3.7380383e-07, 3.8576854e-07, 3.9710864e-07, 4.078308e-07, 4.1794425e-07,
4.2746052e-07, 4.3639332e-07, 4.4475823e-07, 4.5257255e-07, 4.5985502e-07, 4.666255e-07, 4.7290496e-07, 4.7871504e-07, 4.8407804e-07, 4.890165e-07, 4.9355316e-07, 4.977108e-07, 5.015121e-07, 5.0497925e-07, 5.081341e-07, 5.109981e-07, 5.1359183e-07, 5.1593526e-07, 5.1804756e-07, 5.19947e-07,
5.21651e-07, 5.231761e-07, 5.245379e-07, 5.257509e-07, 5.26829e-07, 5.277849e-07, 5.2863044e-07, 5.293767e-07, 5.300336e-07, 5.3061075e-07, 5.311165e-07, 5.315586e-07, 5.319443e-07, 5.3227996e-07, 5.325714e-07, 5.3282383e-07, 5.33042e-07, 5.3323015e-07, 5.33392e-07, 5.3353085e-07,
5.3364977e-07, 5.337514e-07, 5.33838e-07, 5.3391165e-07, 5.339741e-07, 5.34027e-07, 5.3407166e-07, 5.3410935e-07, 5.3414095e-07, 5.341675e-07, 5.341897e-07, 5.3420825e-07, 5.342237e-07, 5.3423656e-07, 5.3424725e-07, 5.3425606e-07, 5.3426334e-07, 5.342693e-07, 5.3427425e-07, 5.342783e-07,
5.342816e-07, 5.3428425e-07, 5.3428647e-07, 5.3428823e-07, 5.342897e-07, 5.3429085e-07, 5.342918e-07, 5.3429255e-07, 5.342932e-07, 5.342937e-07, 5.342941e-07, 5.342944e-07, 5.342946e-07, 5.342948e-07, 5.34295e-07, 0.0, 2.005662e-08, 4.0064048e-08, 5.997345e-08, 7.973673e-08,
9.930685e-08, 1.1863819e-07, 1.3768687e-07, 1.5641102e-07, 1.747711e-07, 1.927301e-07, 2.1025379e-07, 2.2731089e-07, 2.4387325e-07, 2.5991588e-07, 2.754172e-07, 2.9035886e-07, 3.0472597e-07, 3.1850698e-07, 3.3169354e-07, 3.4428064e-07, 3.5626633e-07, 3.6765155e-07, 3.7844023e-07, 3.8863877e-07,
3.982561e-07, 4.0730342e-07, 4.1579392e-07, 4.2374262e-07, 4.3116614e-07, 4.380825e-07, 4.4451082e-07, 4.5047116e-07, 4.559843e-07, 4.610716e-07, 4.6575465e-07, 4.700553e-07, 4.7399533e-07, 4.7759636e-07, 4.8087963e-07, 4.838662e-07, 4.8657625e-07, 4.890297e-07, 4.9124543e-07, 4.932418e-07,
4.9503626e-07, 4.9664544e-07, 4.98085e-07, 4.993699e-07, 5.005139e-07, 5.0153017e-07, 5.024308e-07, 5.0322706e-07, 5.039294e-07, 5.0454753e-07, 5.0509016e-07, 5.055655e-07, 5.0598084e-07, 5.0634293e-07, 5.0665784e-07, 5.0693114e-07, 5.071677e-07, 5.0737214e-07, 5.0754824e-07, 5.076996e-07,
5.078295e-07, 5.079406e-07, 5.080355e-07, 5.0811633e-07, 5.08185e-07, 5.0824326e-07, 5.082925e-07, 5.083341e-07, 5.083691e-07, 5.083985e-07, 5.0842317e-07, 5.084438e-07, 5.08461e-07, 5.0847535e-07, 5.0848723e-07, 5.0849707e-07, 5.0850525e-07, 5.0851196e-07, 5.085175e-07, 5.08522e-07,
5.085258e-07, 5.085288e-07, 5.085313e-07, 5.085333e-07, 5.085349e-07, 5.085363e-07, 5.0853737e-07, 5.085382e-07, 5.085389e-07, 5.085395e-07, 5.085399e-07, 5.0854027e-07, 5.0854055e-07, 5.085408e-07, 5.0854095e-07, 5.085411e-07, 0.0, 1.9125217e-08, 3.8203343e-08, 5.7187638e-08,
7.603206e-08, 9.469159e-08, 1.1312259e-07, 1.3128304e-07, 1.4913292e-07, 1.6663438e-07, 1.8375206e-07, 2.0045324e-07, 2.1670803e-07, 2.3248955e-07, 2.4777395e-07, 2.6254065e-07, 2.7677223e-07, 2.9045444e-07, 3.0357637e-07, 3.1613015e-07, 3.2811107e-07, 3.3951733e-07, 3.5035006e-07, 3.60613e-07,
3.7031245e-07, 3.7945705e-07, 3.880576e-07, 3.9612684e-07, 4.0367922e-07, 4.1073076e-07, 4.172987e-07, 4.2340147e-07, 4.2905828e-07, 4.342891e-07, 4.3911433e-07, 4.4355474e-07, 4.4763118e-07, 4.513645e-07, 4.5477543e-07, 4.5788428e-07, 4.6071108e-07, 4.6327526e-07, 4.6559566e-07, 4.6769046e-07,
4.695771e-07, 4.712722e-07, 4.727916e-07, 4.741503e-07, 4.753624e-07, 4.764412e-07, 4.7739906e-07, 4.782475e-07, 4.7899726e-07, 4.796583e-07, 4.8023975e-07, 4.807499e-07, 4.811966e-07, 4.8158665e-07, 4.819266e-07, 4.8222205e-07, 4.824783e-07, 4.8270005e-07, 4.8289144e-07, 4.830563e-07,
4.831979e-07, 4.833193e-07, 4.8342315e-07, 4.835117e-07, 4.8358714e-07, 4.836512e-07, 4.837055e-07, 4.8375136e-07, 4.837901e-07, 4.838226e-07, 4.8384993e-07, 4.8387284e-07, 4.83892e-07, 4.8390797e-07, 4.839212e-07, 4.8393224e-07, 4.8394134e-07, 4.839489e-07, 4.839551e-07, 4.839602e-07,
4.839644e-07, 4.839678e-07, 4.8397067e-07, 4.8397294e-07, 4.8397476e-07, 4.839763e-07, 4.839775e-07, 4.839785e-07, 4.839793e-07, 4.8397993e-07, 4.8398044e-07, 4.8398084e-07, 4.839812e-07, 4.839814e-07, 4.8398164e-07, 4.839818e-07, 4.839819e-07
]);

DensityEstimator.gamma_texture = DensityEstimator.gl.createTexture();
DensityEstimator.gl.bindTexture(
    DensityEstimator.gl.TEXTURE_2D, DensityEstimator.gamma_texture);

DensityEstimator.gl.texImage2D(
    DensityEstimator.gl.TEXTURE_2D, 0, DensityEstimator.gl.R32F, 101, 477, 0,
    DensityEstimator.gl.RED, DensityEstimator.gl.FLOAT,
    DensityEstimator.gamma_table);

DensityEstimator.gl.texParameteri(
    DensityEstimator.gl.TEXTURE_2D,
    DensityEstimator.gl.TEXTURE_MAG_FILTER,
    DensityEstimator.gl.LINEAR);
DensityEstimator.gl.texParameteri(
    DensityEstimator.gl.TEXTURE_2D,
    DensityEstimator.gl.TEXTURE_MIN_FILTER,
    DensityEstimator.gl.LINEAR);
DensityEstimator.gl.texParameteri(
    DensityEstimator.gl.TEXTURE_2D,
    DensityEstimator.gl.TEXTURE_WRAP_S,
    DensityEstimator.gl.CLAMP_TO_EDGE);
DensityEstimator.gl.texParameteri(
    DensityEstimator.gl.TEXTURE_2D,
    DensityEstimator.gl.TEXTURE_WRAP_T,
    DensityEstimator.gl.CLAMP_TO_EDGE);

DensityEstimator.gl.bindTexture(DensityEstimator.gl.TEXTURE_2D, null);

// shaders
DensityEstimator.vertex_glsl = [
  "#version 300 es",
  "precision highp float;",
  "in vec2 aPos;",
  "in vec2 aUv;",
  "out vec2 vUv;",
  "void main() {",
    "gl_Position = vec4(aPos, 0., 1.);",
    "vUv = aUv;",
  "}"
].join("\n");

DensityEstimator.fragment_glsl = [
  "#version 300 es",
  "precision highp float;",
  "#define kPi 3.141592653589793",
  "#define kSqrt2Recip 0.7071067811865475",
  "#define kSqrt2PiRecip 0.3989422804014327",
  "uniform float uZ;",
  "uniform vec3 uMin, uMax, uDim;",
  "uniform mat3 uHiSqrt;",
  "uniform sampler2D uGammaTexture;",
  "uniform int uVertsTextureHeight;",
  "uniform sampler2D uVertsTexture;",
  "in vec2 vUv;",
  "out vec4 fragColor;",

  "// https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions",
  "// maximum error: 2.5×10−5",
  "float erf(float x) {",
    "float t = 1. / (1. + .47047 * abs(x));",
    "float res = 1. - t * (.3480242 + t * (-.0958798 + t * .7478556)) *",
                     "exp(-(x * x));",
    "return res * sign(x);",
  "}",

  // "// maximum error: 1.5×10−7",
  // "float erf(float x) {",
  //   "float t = 1. / (1. + .3275911 * abs(x));",
  //   "float res = 1. - t * (.254829592 + t * (-.284496736 + t * (1.421413741 +",
  //                    "t * (-1.453152027 + t * 1.061405429)))) * exp(-(x * x));",
  //   "return res * sign(x);",
  // "}",

  "float TriangleArea(vec3 a, vec3 b, vec3 c) {",
    "vec3 ab = b - a, ac = c - a;",
    "return .5 * length(cross(ab, ac));",
  "}",

  "vec4 PlaneOfTriangle(vec3 a, vec3 b, vec3 c) {",
    "vec3 ab = b - a, ac = c - a;",
    "vec4 nd;",
    "nd.xyz = normalize(cross(ab, ac));",
    "nd.w = dot(nd.xyz, a);",
    "return nd;",
  "}",

  "vec3 ProjOnPlane(vec3 v, vec4 nd) {",
    "return v - nd.xyz * nd.w;",
  "}",

  "float Sign(float ax, float ay, float bx, float by, float cx, float cy) {",
    "return (ax - cx) * (by - cy) - (bx - cx) * (ay - cy);",
  "}",

  "bool PointInTriangle(float x, float y,",
                       "float ax, float ay,",
                       "float bx, float by,",
                       "float cx, float cy) {",
    "bool b1 = Sign(x, y, ax, ay, bx, by) < 0.;",
    "bool b2 = Sign(x, y, bx, by, cx, cy) < 0.;",
    "bool b3 = Sign(x, y, cx, cy, ax, ay) < 0.;",
    "return (b1 == b2) && (b2 == b3);",
  "}",

  "float NormPdf(float x) {",
    "return kSqrt2PiRecip * exp(-.5 * x * x);",
  "}",

  "float NormCdf(float x) {",
    "return .5 * (1. + erf(x * kSqrt2Recip));",
  "}",

  "float Gamma(float h, float a) {",
    "return texture(uGammaTexture, vec2(a * 100. / 101. + .5 / 101.,",
                                       "h * 100. / 477. + .5 / 477.)).r;",
  "}",

  "float GammaSwitch(float h, float a) {",
    "h = abs(h);",
    "if (h > 4.76) return 0.;",

    "if (a < -1.) {",
      "float cdf0 = NormCdf(h), cdf1 = NormCdf(-a * h);",
      "return -.5 * (cdf0 + cdf1) + cdf0 * cdf1 + Gamma(-a * h, 1. / -a);",
    "}",
    "if (a > 1.) {",
      "float cdf0 = NormCdf(h), cdf1 = NormCdf(a * h);",
      "return .5 * (cdf0 + cdf1) - cdf0 * cdf1 - Gamma(a * h, 1. / a);",
    "}",
    "if (a < 0.) return -Gamma(h, -a);",
    "return Gamma(h, a);",
  "}",

  "void main() {",
    "float HiSqrtDet = determinant(uHiSqrt);",
    "// physical position of the grid point",
    "vec3 x;",
    "x.xy = (vUv * uDim.xy - vec2(.5, .5)) / (uDim.xy - vec2(1., 1.));",
    "x.xy = x.xy * (uMax.xy - uMin.xy) + uMin.xy;",
    "x.z = uZ;",

    "vec3 a, b, c, ax, bx, cx;",
    "vec3 aPrime, bPrime, cPrime;",
    "vec3 aabbMin, aabbMax, four3D = vec3(4.), zero3D = vec3(0.);",
    "vec4 nd;",
    "vec3 aProj, bProj, cProj;",
    "vec3 uAxis, vAxis;",
    "vec2 a2D, b2D, c2D, zero2D = vec2(0.);",
    "vec2 bc2D, ca2D, ab2D;",
    "vec3 alpha;  // Used to store the bivariate normal integral over",
                 "// the area defined by each edge of a triangle.",
    "float bxc, cxa, axb;",
    "float h, a1, a2;",
    "vec3 coss;",
    "vec2 a2DNorm, b2DNorm, c2DNorm;",
    "int cossMinId;",
    "float res = 0.;",
    "for (int i = 0; i < uVertsTextureHeight; ++i) {",
      "// three vertices of the current triangle",
      "float currHeight = (float(i) + .5) / float(uVertsTextureHeight);",
      "a = texture(uVertsTexture, vec2(.5 / 3., currHeight)).xyz;",
      "b = texture(uVertsTexture, vec2(1.5 / 3., currHeight)).xyz;",
      "c = texture(uVertsTexture, vec2(2.5 / 3., currHeight)).xyz;",

      "// Transform the triangle based on the grid point position and the bandwidth matrix.",
      "ax = x - a;",
      "bx = x - b;",
      "cx = x - c;",
      "aPrime = uHiSqrt * ax;",
      "bPrime = uHiSqrt * bx;",
      "cPrime = uHiSqrt * cx;",

      "aabbMin = min(min(aPrime, bPrime), cPrime);",
      "aabbMax = max(max(aPrime, bPrime), cPrime);",

      "if (all(lessThan((aabbMin - four3D) * (aabbMax + four3D), zero3D))) {",
        "float ct = TriangleArea(a, b, c) /",
                   "TriangleArea(aPrime, bPrime, cPrime) *",
                   "HiSqrtDet;",

        "// Map the triangle into 2D.",
        "nd = PlaneOfTriangle(aPrime, bPrime, cPrime);",
        "aProj = ProjOnPlane(aPrime, nd);",
        "bProj = ProjOnPlane(bPrime, nd);",
        "cProj = ProjOnPlane(cPrime, nd);",

        "uAxis = normalize(aProj - bProj);",
        "vAxis = cross(uAxis, nd.xyz);",

        "a2D.x = dot(aProj, uAxis);",
        "a2D.y = dot(aProj, vAxis);",

        "b2D.x = dot(bProj, uAxis);",
        "b2D.y = dot(bProj, vAxis);",

        "c2D.x = dot(cProj, uAxis);",
        "c2D.y = dot(cProj, vAxis);",

        "// Compute SDE based on bivariate normal integrals.",
        "if (any(notEqual(a2D, zero2D)) &&",
            "any(notEqual(b2D, zero2D)) &&",
            "any(notEqual(c2D, zero2D))) {",
          "// segment bc",
          "bc2D = c2D - b2D;",
          "bxc = b2D.x * c2D.y - b2D.y * c2D.x;",
          "if (bxc != 0.) {",
            "h = bxc / length(bc2D);",
            "a1 = dot(b2D, bc2D) / bxc;",
            "a2 = dot(c2D, bc2D) / bxc;",
            "alpha.x = abs(GammaSwitch(h, a1) - GammaSwitch(h, a2));",
          "} else {",
            "alpha.x = dot(b2D, c2D) < 0. ? .5 : 0.;",
          "}",

          "// segment ca",
          "ca2D = a2D - c2D;",
          "cxa = c2D.x * a2D.y - c2D.y * a2D.x;",
          "if (cxa != 0.) {",
            "h = cxa / length(ca2D);",
            "a1 = dot(c2D, ca2D) / cxa;",
            "a2 = dot(a2D, ca2D) / cxa;",
            "alpha.y = abs(GammaSwitch(h, a1) - GammaSwitch(h, a2));",
          "} else {",
            "alpha.y = dot(c2D, a2D) < 0. ? .5 : 0.;",
          "}",

          "// segment ab",
          "ab2D = b2D - a2D;",
          "axb = a2D.x * b2D.y - a2D.y * b2D.x;",
          "if (axb != 0.) {",
            "h = axb / length(ab2D);",
            "a1 = dot(a2D, ab2D) / axb;",
            "a2 = dot(b2D, ab2D) / axb;",
            "alpha.z = abs(GammaSwitch(h, a1) - GammaSwitch(h, a2));",
          "} else {",
            "alpha.z = dot(a2D, b2D) < 0. ? .5 : 0.;",
          "}",

          "// Combine alpha bc, ca, and ab.",
          "if (PointInTriangle(0., 0., a2D.x, a2D.y,",
                              "b2D.x, b2D.y, c2D.x, c2D.y)) {",
            "res += (1. - dot(alpha, vec3(1.))) * NormPdf(nd.w) * ct;",
          "} else {",
            "a2DNorm = normalize(a2D);",
            "b2DNorm = normalize(b2D);",
            "c2DNorm = normalize(c2D);",
            "coss.x = dot(b2DNorm, c2DNorm);",
            "coss.y = dot(c2DNorm, a2DNorm);",
            "coss.z = dot(a2DNorm, b2DNorm);",

            "cossMinId = coss.y < coss.x ? (coss.z < coss.y ? 2 : 1) :",
                                          "(coss.z < coss.x ? 2 : 0);",

            "res += abs(dot(alpha, vec3(1.)) - 2. * alpha[cossMinId])",
                   "* NormPdf(nd.w) * ct;",
          "}",
        "}",

        "// Handle spacial cases.",
        "else if (all(equal(a2D, zero2D))) {",
          "// segment bc",
          "bc2D = c2D - b2D;",
          "bxc = b2D.x * c2D.y - b2D.y * c2D.x;",
          "if (bxc != 0.) {",
            "h = bxc / length(bc2D);",
            "a1 = dot(b2D, bc2D) / bxc;",
            "a2 = dot(c2D, bc2D) / bxc;",
            "alpha.x = abs(GammaSwitch(h, a1) - GammaSwitch(h, a2));",
          "} else {",
            "alpha.x = dot(b2D, c2D) < 0. ? .5 : 0.;",
          "}",

          "b2DNorm = normalize(b2D);",
          "c2DNorm = normalize(c2D);",

          "res += (acos(dot(b2DNorm, c2DNorm)) /",
                  "kPi * .5 - alpha.x) * NormPdf(nd.w) * ct;",
        "}",

        "else if (all(equal(b2D, zero2D))) {",
          "// segment ca",
          "ca2D = a2D - c2D;",
          "cxa = c2D.x * a2D.y - c2D.y * a2D.x;",
          "if (cxa != 0.) {",
            "h = cxa / length(ca2D);",
            "a1 = dot(c2D, ca2D) / cxa;",
            "a2 = dot(a2D, ca2D) / cxa;",
            "alpha.y = abs(GammaSwitch(h, a1) - GammaSwitch(h, a2));",
          "} else {",
            "alpha.y = dot(c2D, a2D) < 0. ? .5 : 0.;",
          "}",

          "c2DNorm = normalize(c2D);",
          "a2DNorm = normalize(a2D);",

          "res += (acos(dot(c2DNorm, a2DNorm)) /",
                  "kPi * .5 - alpha.y) * NormPdf(nd.w) * ct;",
        "}",

        "else if (all(equal(c2D, zero2D))) {",
          "// segment ab",
          "ab2D = b2D - a2D;",
          "axb = a2D.x * b2D.y - a2D.y * b2D.x;",
          "if (axb != 0.) {",
            "h = axb / length(ab2D);",
            "a1 = dot(a2D, ab2D) / axb;",
            "a2 = dot(b2D, ab2D) / axb;",
            "alpha.z = abs(GammaSwitch(h, a1) - GammaSwitch(h, a2));",
          "} else {",
            "alpha.z = dot(a2D, b2D) < 0. ? .5 : 0.;",
          "}",

          "a2DNorm = normalize(a2D);",
          "b2DNorm = normalize(b2D);",

          "res += (acos(dot(a2DNorm, b2DNorm)) /",
                  "kPi * .5 - alpha.x) * NormPdf(nd.w) * ct;",
        "}",
      "}",
    "}",

    "fragColor = vec4(res, 0., 0., 1.);",
  "}"
].join("\n");

DensityEstimator.GetShader = function(gl, type, code) {
  var shader = gl.createShader(type);

  gl.shaderSource(shader, code);
  gl.compileShader(shader);

  if (gl.getShaderParameter(shader, gl.COMPILE_STATUS) === false) {
    console.error("Shader couldn\'t compile.");
  }

  if (gl.getShaderInfoLog(shader) !== "") {
    console.warn(type === gl.VERTEX_SHADER ? "Vertex:" : "Fragment:",
                 gl.getShaderInfoLog(shader));
  }

  return shader;
}

DensityEstimator.program = DensityEstimator.gl.createProgram();

DensityEstimator.gl.attachShader(
    DensityEstimator.program,
    DensityEstimator.GetShader(
        DensityEstimator.gl,
        DensityEstimator.gl.VERTEX_SHADER,
        DensityEstimator.vertex_glsl));

DensityEstimator.gl.attachShader(
    DensityEstimator.program,
    DensityEstimator.GetShader(
        DensityEstimator.gl,
        DensityEstimator.gl.FRAGMENT_SHADER,
        DensityEstimator.fragment_glsl));

DensityEstimator.gl.linkProgram(DensityEstimator.program);
// ---------------------------------------------------------------------------