rounded residual translation.json

{
  "formula": "T_d(y,rho)=(y+Q_Z(rho+d), rho+d-Q_Z(rho+d))",
  "premise": "y in5Z, rho in[-2,2], x=y+rho; source durations and admitted endpoints remain nonnegative",
  "examples": [
    {
      "x": 777,
      "d": -24,
      "Q_x": 775,
      "rho": 2,
      "rounded_shift": -20,
      "new_rounded": 755,
      "new_residual": -2
    },
    {
      "x": 595,
      "d": -24,
      "Q_x": 595,
      "rho": 0,
      "rounded_shift": -25,
      "new_rounded": 570,
      "new_residual": 1
    },
    {
      "x": 438,
      "d": 27,
      "Q_x": 440,
      "rho": -2,
      "rounded_shift": 25,
      "new_rounded": 465,
      "new_residual": 0
    },
    {
      "x": 433,
      "d": 27,
      "Q_x": 435,
      "rho": -2,
      "rounded_shift": 25,
      "new_rounded": 460,
      "new_residual": 0
    }
  ],
  "information": "Keeping the residual restores a lossless coordinate representation, not reduced source information."
}