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

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.

crates/engine/src/cmd/forecast.rs

@@ -36,6 +36,21 @@ 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",
@@ -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> =
@@ -530,6 +555,51 @@ 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};