LINEST: treat only identical raw values as a constant predictor

The 64-ulp spread threshold still classified distinct representable
predictors such as [1e15, 1e15 + 1, 1e15 + 2] as constant and dropped
them. A column is now constant only when every raw value is the same
double; the 1e15 case is added to the offset regression test.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

crates/functions/src/stat/regression.rs

@@ -130,10 +130,6 @@ fn norm2(v: &[f64]) -> f64 {
     m * v.iter().map(|x| (x / m) * (x / m)).sum::<f64>().sqrt()
 }
 
-/// A column whose values differ by no more than this many ulps of its largest magnitude is
-/// taken to be constant: the differences are rounding in how it was computed, not data.
-const CONSTANT_ULPS: f64 = 64.0;
-
 /// Result of [`qr_solve`]: the least-squares solution on the kept columns, in the caller's
 /// column scale, and what the standard errors need.
 struct QrFit {
@@ -276,11 +272,12 @@ fn regress(y: &[f64], x: &[Vec<f64>], k: usize, constant: bool) -> R<Fit> {
     let yc: Vec<f64> = y.iter().map(|v| v - ym).collect();
     let sstot: f64 = if constant { yc.iter().map(|v| v * v).sum() } else { y.iter().map(|v| v * v).sum() };
     // Only centring leaves rounding residue behind; without an intercept a constant column is data.
+    // Constant means every raw value is the same double: distinct values, however close, vary.
     let constant_cols: Vec<bool> = (0..k)
         .map(|j| {
-            let col = x.iter().map(|r| r.get(j).copied().unwrap_or(0.0));
-            let (lo, hi, big) = col.fold((f64::INFINITY, f64::NEG_INFINITY, 0.0f64), |(lo, hi, big), v| (lo.min(v), hi.max(v), big.max(v.abs())));
-            constant && hi - lo <= CONSTANT_ULPS * f64::EPSILON * big
+            let mut col = x.iter().map(|r| r.get(j).copied().unwrap_or(0.0));
+            let first = col.next();
+            constant && first.is_some_and(|f| col.all(|v| v == f))
         })
         .collect();
     let QrFit { coef, dropped, ssresid, diag, quad } = qr_solve(cols, yc, &xm, &constant_cols);

crates/functions/src/stat/tests.rs

@@ -582,6 +582,15 @@ fn linest_drops_collinear_columns() {
     let r = linest_rows(&[0.0, 1.0, 2.0], &[vec![1e13, 1e13 + 1.0, 1e13 + 2.0]], true);
     rel_close(r[0][0], 1.0, 1e-9, "slope on a predictor with a 1e13 offset");
     assert_eq!(r[3][1], Some(1.0), "df: the predictor is kept");
+    // Same at 1e15, where the spread is only a few ulps of the offset: still distinct doubles.
+    let x15 = [1e15, 1e15 + 1.0, 1e15 + 2.0];
+    let r = linest_rows(&[0.0, 1.0, 2.0], &[x15.to_vec()], true);
+    rel_close(r[0][0], 1.0, 1e-9, "slope on a predictor with a 1e15 offset");
+    rel_close(r[0][1], -1e15, 1e-9, "intercept on a predictor with a 1e15 offset");
+    assert_eq!(r[3][1], Some(1.0), "df: the 1e15 predictor is kept");
+    assert!(r[4][1].is_some_and(|v| v.abs() < 1e-9), "ssresid: the 1e15 line is exact, got {:?}", r[4][1]);
+    let fitted = rows_of(&ev("TREND", vec![c(&[0.0, 1.0, 2.0]), c(&x15)]));
+    close(fitted[2][0].clone(), 2.0);
     // More predictors than observations: the surplus columns drop, no panic.
     let r = linest_rows(&[1.0, 2.0], &[vec![1.0, 2.0], vec![2.0, 1.0], vec![0.0, 5.0]], true);
     assert_eq!(r[0].len(), 4);