%% Knuth's AoCP, vol 1, 2nd ed, pp 155--156
\int_new:N \l_easter_Y_int
\int_new:N \l_easter_G_int
\int_new:N \l_easter_C_int
\int_new:N \l_easter_X_int
\int_new:N \l_easter_Z_int
\int_new:N \l_easter_D_int
\int_new:N \l_easter_E_int
\int_new:N \l_easter_N_int
\int_new:N \l_easter_M_int
\int_new:N \l_easter_julian_day_int

\cs_new:Nn \easter_sunday:n {

  \int_set:Nn \l_easter_Y_int { #1 }

  \int_set:Nn \l_easter_G_int {
    \int_mod:nn { \l_easter_Y_int } { 19 } + 1
  }

  \int_set:Nn \l_easter_C_int {
    \int_div_truncate:nn { \l_easter_Y_int } { 100 } + 1
  }

  \int_set:Nn \l_easter_X_int {
    \int_div_truncate:nn { 3 * \l_easter_C_int } { 4 } - 12
  }

  \int_set:Nn \l_easter_Z_int {
    \int_div_truncate:nn { 8 * \l_easter_C_int + 5 } { 25 } - 5
  }

  \int_set:Nn \l_easter_D_int {
    \int_div_truncate:nn { 5 * \l_easter_Y_int } { 4 } - \l_easter_X_int - 10
  }

  \int_set:Nn \l_easter_E_int {
    \int_mod:nn { 11 * \l_easter_G_int + 20 + \l_easter_Z_int
      - \l_easter_X_int } { 30 }
  }

  % \int_mod:nn behaves strangely.
  \int_compare:nNnT { \l_easter_E_int } < { 0 }
  {
    \int_add:Nn \l_easter_E_int { 30 }
  }

  \int_compare:nNnTF { \l_easter_E_int } = { 25 }
  { % true
    \int_compare:nNnT { \l_easter_G_int } > { 11 }
    { % true
      \int_incr:N \l_easter_E_int
    }
  }
  { % false
    \int_compare:nNnT { \l_easter_E_int } = { 24 }
    { % true
      \int_incr:N \l_easter_E_int
    }
  }

  \int_set:Nn \l_easter_N_int { 44 - \l_easter_E_int }

  \int_compare:nNnT { \l_easter_N_int } < { 21 }
  { % true
    \int_add:Nn \l_easter_N_int { 30 }
  }

  \int_add:Nn \l_easter_N_int {
    7 - \int_mod:nn { \l_easter_D_int + \l_easter_N_int } { 7 }
  }

  \int_compare:nNnTF { \l_easter_N_int } > { 31 }
  { % true
    \int_sub:Nn \l_easter_N_int { 31 }
    \int_set:Nn \l_easter_M_int { 4 } % April
  }
  { % false
    \int_set:Nn \l_easter_M_int { 3 } % March
  }

  \pgfcalendardatetojulian { \l_easter_Y_int -
     \l_easter_M_int - \l_easter_N_int
  } { \l_easter_julian_day_int }

}

\pgfkeys{/pgf/calendar/Easter/.default = 0}
\pgfkeys{/pgf/calendar/Easter/.code =
  {
    \easter_sunday:n { \pgfcalendarifdateyear }
    \int_compare:nNnT { \pgfcalendarifdatejulian }
    =  {\l_easter_julian_day_int + #1}
    { \pgfcalendarmatchestrue }
  }
}

