Forecast Sheet: count hindcast rows against the work limit (#3199)

* Forecast Sheet: count hindcast rows against the work limit

MAX_WORK bounded history rows x forecast rows, but a Forecast Start
inside the history adds a hindcast row for every history point after
it, each holding the same ETS formulas that refit the model over the
history before the start. Those rows were not counted, so a start in
the middle of 10,000 rows of history built millions of uncharged
model fits per recalculation.

The forecast row cap is now computed from the rows the model is fit
to, after subtracting the hindcast rows; a start so early that the
hindcast alone passes the limit is refused, and the default number of
periods stays within the cap.

* address review: base the in-history forecast cap on the slots the fit range spans

* address review: document the hindcast-aware forecast work limit

* address review: document the fitted-row minimum in the forecast work limit

* address review: say the forecast start row counts toward the hindcast work limit

crates/engine/src/cmd/forecast.rs

@@ -36,13 +36,28 @@ fn max_periods(history: usize) -> u32 {
     u32::try_from(MAX_WORK / h).unwrap_or(u32::MAX).clamp(1, MAX_PERIODS)
 }
 
+/// Most forecast rows when the model is fit to the first `fit` of `history` rows, which span
+/// `slots` timeline slots once their gaps are filled. With a Forecast Start inside the history,
+/// every row after it is forecast too (a hindcast row holds the same ETS formulas, each refitting
+/// the model over the `slots` slots), so those rows (counted from the raw rows) count against
+/// [`MAX_WORK`] before any forecast row does. `None` when the hindcast alone exceeds it.
+fn max_periods_from(history: usize, fit: usize, slots: usize) -> Option<u32> {
+    if fit >= history {
+        return Some(max_periods(history));
+    }
+    let f = u64::try_from(slots.max(fit)).unwrap_or(u64::MAX).max(1);
+    let hindcast = u64::try_from(history - fit).unwrap_or(u64::MAX);
+    let rest = (MAX_WORK / f).checked_sub(hindcast).filter(|r| *r >= 1)?;
+    Some(u32::try_from(rest).unwrap_or(u32::MAX).min(MAX_PERIODS))
+}
+
 pub fn specs() -> Vec<CommandSpec> {
     vec![cmd!(
         "data.forecastSheet",
         "Forecast Sheet",
         ["Data", "Forecast"],
         None,
-        "{timeline?: \"A2:A25\", values?: \"B2:B25\" (default: the first two columns of `range`, the selection or the current region; a text first cell is the header), end?: timeline value or date text | periods?: n (default: a third of the history, at least 1; ≤10,000 and history × periods ≤ 500,000; history ≤ 10,000 rows), forecastStart?: a timeline value or date text on the history, before its last point (hindcast: the model is fit to the points before it, the forecast columns start there and run over the actuals; default and the last point: forecast after the history), confidenceInterval?: bool (default true), confidence?: 0.95 or 95, seasonality?: \"auto\" | 0 (none) | 2–8,760, fillMissing?: interpolate|zeros, aggregate?: average|count|counta|max|median|min|sum, statistics?: bool, chart?: line|column} → {sheet, table, chart, history, periods}. Inserts a sheet before the active one: timeline, values, Forecast (FORECAST.ETS), Lower/Upper Confidence Bound (FORECAST.ETS.CONFINT), optional FORECAST.ETS.STAT table, and a chart.",
+        "{timeline?: \"A2:A25\", values?: \"B2:B25\" (default: the first two columns of `range`, the selection or the current region; a text first cell is the header), end?: timeline value or date text | periods?: n (default: a third of the history, at least 1; ≤10,000 and history × periods ≤ 500,000, or with a forecastStart inside the history (hindcast rows are forecast too) (the greater of the fitted rows and fitted slots × (periods + rows from forecastStart on, that row included)) ≤ 500,000; history ≤ 10,000 rows), forecastStart?: a timeline value or date text on the history, before its last point (hindcast: the model is fit to the points before it, the forecast columns start there and run over the actuals; default and the last point: forecast after the history), confidenceInterval?: bool (default true), confidence?: 0.95 or 95, seasonality?: \"auto\" | 0 (none) | 2–8,760, fillMissing?: interpolate|zeros, aggregate?: average|count|counta|max|median|min|sum, statistics?: bool, chart?: line|column} → {sheet, table, chart, history, periods}. Inserts a sheet before the active one: timeline, values, Forecast (FORECAST.ETS), Lower/Upper Confidence Bound (FORECAST.ETS.CONFINT), optional FORECAST.ETS.STAT table, and a chart.",
         has_doc,
         forecast_sheet
     )]
@@ -257,13 +272,23 @@ fn forecast_sheet(s: &mut Session, p: &Json) -> Result<Json> {
             }
         }
     };
-    let cap = max_periods(rows.len());
+    // The slots the model is fit over: the fit rows' span of the timeline, gaps included.
+    let slots = match (fit < rows.len(), times.get(fit.wrapping_sub(1)), times.first()) {
+        (true, Some(last_fit), Some(first)) => match (timeline.steps_after_last(*last_fit), timeline.steps_after_last(*first)) {
+            (Some(b), Some(a)) => ((b - a).round() + 1.0).clamp(0.0, 1e9) as usize,
+            _ => fit,
+        },
+        _ => fit,
+    };
+    let cap = max_periods_from(rows.len(), fit, slots).ok_or_else(|| {
+        EngineError::Other("The forecast start is too early for this much history: choose a later forecast start or less history.".into())
+    })?;
     let periods = match end {
         Some(end) => steps_to(&timeline, end, cap)?,
         None => match number(p, "periods")? {
             Some(n) if n >= 1.0 && n.ceil() <= f64::from(cap) => n.ceil() as u32,
             Some(_) => return Err(bad(CMD, format!("`periods` is from 1 to {cap} for {} rows of history", rows.len()))),
-            None => default_periods(rows.len()),
+            None => default_periods(rows.len()).min(cap),
         },
     };
     let future: Vec<f64> =
@@ -532,6 +557,51 @@ mod tests {
         assert_eq!(s.doc().unwrap().wb.sheets.len(), sheets - 1);
     }
 
+    #[test]
+    fn hindcast_rows_count_against_the_work_limit() {
+        use super::{MAX_WORK, max_periods, max_periods_from};
+        assert_eq!(max_periods_from(1_300, 1_300, 1_300), Some(max_periods(1_300)));
+        // 2,000 rows fit to the first 1,899: 101 hindcast rows, then 162 forecast rows.
+        assert_eq!(max_periods_from(2_000, 1_899, 1_899), Some(162));
+        // Fit to the first 1,000: the 1,000 hindcast rows alone are twice the limit.
+        assert_eq!(max_periods_from(2_000, 1_000, 1_000), None);
+        // 800 rows fit to the first 400, which span 571 slots (gaps filled): each formula refits
+        // 571 slots, so 475 forecast rows after the 400 hindcast rows, not 850.
+        assert_eq!(max_periods_from(800, 400, 571), Some(475));
+        assert!((475 + 400) * 571 <= MAX_WORK as usize);
+        for (h, f) in [(2_000usize, 1_899usize), (10_000, 9_990), (100, 2), (60, 50)] {
+            if let Some(p) = max_periods_from(h, f, f) {
+                assert!((u64::from(p) + (h - f) as u64) * f as u64 <= MAX_WORK, "{h} {f}");
+            }
+        }
+        let mut s = Session::new();
+        s.new_workbook();
+        let mut rows = vec![json!(["t", "y"])];
+        rows.extend((1..=2_000).map(|t| json!([t, (t % 7) as f64 + t as f64 * 0.5])));
+        s.execute("range.setValues", json!({"range": "A1", "values": rows})).unwrap();
+        let sheets = s.doc().unwrap().wb.sheets.len();
+        let err = s.execute("data.forecastSheet", json!({"range": "A1:B2001", "forecastStart": 1_001})).expect_err("hindcast too long");
+        assert!(err.to_string().contains("forecast start is too early"), "{err}");
+        let err = s.execute("data.forecastSheet", json!({"range": "A1:B2001", "forecastStart": 1_900, "periods": 163})).expect_err("past the cap");
+        assert!(err.to_string().contains("from 1 to 162"), "{err}");
+        assert_eq!(s.doc().unwrap().wb.sheets.len(), sheets);
+    }
+
+    #[test]
+    fn the_hindcast_cap_follows_the_slots_the_fit_spans_not_its_rows() {
+        // 800 rows, 20% of the slots missing: the first 400 rows span 500 slots, so each ETS
+        // formula refits 500 slots and the cap is 1,000 - 400 = 600 (it was 850 by rows).
+        let mut s = Session::new();
+        s.new_workbook();
+        let times: Vec<u32> = (1u32..).filter(|t| !matches!(t % 10, 3 | 6)).take(800).collect();
+        let mut rows = vec![json!(["t", "y"])];
+        rows.extend(times.iter().map(|t| json!([t, (t % 7) as f64 + f64::from(*t) * 0.5])));
+        s.execute("range.setValues", json!({"range": "A1", "values": rows})).unwrap();
+        let start = times[400];
+        let err = s.execute("data.forecastSheet", json!({"range": "A1:B801", "forecastStart": start, "periods": 601})).expect_err("past the cap");
+        assert!(err.to_string().contains("from 1 to 600"), "{err}");
+    }
+
     #[test]
     fn history_and_periods_are_capped() {
         use super::{MAX_HISTORY, MAX_PERIODS, MAX_WORK, default_periods, max_periods};