\Delta d = \mathrm{days}(d_2) - \mathrm{days}(d_1)
\Delta y = y_2 - y_1,\quad \Delta m = m_2 - m_1,\quad \Delta d' = d_2 - d_1
\mathrm{add}(y,m,d; \Delta y,\Delta m,\Delta d) = \mathrm{clampEOM}\bigl(y+\Delta y,\; m+\Delta m,\; d\bigr) + \Delta d
\mathrm{bizdays}(d_1,d_2,H)=\sum_{t=d_1}^{d_2-1}\mathbf{1}\bigl(\mathrm{weekday}(t)\in\{1,\dots,5\}\land t\notin H\bigr)
\mathrm{week}(d)=\mathrm{ISOWeekNumber}(d),\quad \mathrm{weekday}_{\mathrm{ISO}}\in\{1\ldots7\}
Date difference (days): \[ \Delta d = \mathrm{days}(d_2) - \mathrm{days}(d_1) \] Y–M–D breakdown (proleptic Gregorian): \[ \Delta y = y_2 - y_1,\quad \Delta m = m_2 - m_1,\quad \Delta d' = d_2 - d_1 \] Adjust \(\Delta m,\Delta d'\) by borrowing/carrying based on month lengths and leap-year rules. Add/Subtract with end-of-month safety: \[ \mathrm{add}(y,m,d; \Delta y,\Delta m,\Delta d) = \mathrm{clampEOM}\bigl(y+\Delta y,\; m+\Delta m,\; d\bigr) + \Delta d \] where \(\mathrm{clampEOM}\) sets the day to the month's last valid day if needed. Business days, excluding weekends & holidays: \[ \mathrm{bizdays}(d_1,d_2,H)=\sum_{t=d_1}^{d_2-1}\mathbf{1}\bigl(\mathrm{weekday}(t)\in\{1,\dots,5\}\land t\notin H\bigr) \] ISO week number (ISO 8601): \[ \mathrm{week}(d)=\mathrm{ISOWeekNumber}(d),\quad \mathrm{weekday}_{\mathrm{ISO}}\in\{1\ldots7\} \]