OpenGL torus with texture mapping and normals

torus.cpp

/*
r = torus ring radius
c = torus tube radius
rSeg, cSeg = number of segments/detail
*/

void drawTorus(double, double, int, int, int);

void drawTorus(double r = 0.07, double c = 0.15,
               int rSeg = 16, int cSeg = 8,
               int texture = 0)
{
  glFrontFace(GL_CW);

  glBindTexture(GL_TEXTURE_2D, texture);
  glTexEnvf(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);

  const double PI = 3.1415926535897932384626433832795;
  const double TAU = 2 * PI;

  for (int i = 0; i < rSeg; i++) {
    glBegin(GL_QUAD_STRIP);
    for (int j = 0; j <= cSeg; j++) {
      for (int k = 0; k <= 1; k++) {
        double s = (i + k) % rSeg + 0.5;
        double t = j % (cSeg + 1);

        double x = (c + r * cos(s * TAU / rSeg)) * cos(t * TAU / cSeg);
        double y = (c + r * cos(s * TAU / rSeg)) * sin(t * TAU / cSeg);
        double z = r * sin(s * TAU / rSeg);

        double u = (i + k) / (float) rSeg;
        double v = t / (float) cSeg;

        glTexCoord2d(u, v);
        glNormal3f(2 * x, 2 * y, 2 * z);
        glVertex3d(2 * x, 2 * y, 2 * z);
      }
    }
    glEnd();
  }

  glFrontFace(GL_CCW);
}

I'm pretty sure normals are incorrect here