G711: stabilize large-degree t density

crates/functions/src/stat/distributions.rs

@@ -19,7 +19,14 @@ fn t_cdf(t: f64, v: f64) -> f64 {
 }
 
 fn t_pdf(t: f64, v: f64) -> f64 {
-    (ln_gamma((v + 1.0) / 2.0) - ln_gamma(v / 2.0) - 0.5 * (v * std::f64::consts::PI).ln() - (v + 1.0) / 2.0 * (1.0 + t * t / v).ln()).exp()
+    let z = v / 2.0;
+    let log_gamma_ratio = if z >= 16.0 {
+        let inv_z = 1.0 / z;
+        0.5 * z.ln() - inv_z / 8.0 + inv_z.powi(3) / 192.0 - inv_z.powi(5) / 640.0 + 17.0 * inv_z.powi(7) / 14_336.0
+    } else {
+        ln_gamma(z + 0.5) - ln_gamma(z)
+    };
+    (log_gamma_ratio - 0.5 * (v * std::f64::consts::PI).ln() - (v + 1.0) / 2.0 * (1.0 + t * t / v).ln()).exp()
 }
 
 /// t ≥ 0 with P(T > t) = q, q in (0, 0.5].

crates/functions/src/stat/tests.rs

@@ -404,6 +404,12 @@ fn t_chi_f() {
     is_err(ev("F.DIST", vec![n(1.0), n(0.0), n(4.0), b(true)]), CellError::Num);
 }
 
+#[test]
+fn t_density_is_stable_for_large_degrees() {
+    close_tol(ev("T.DIST", vec![n(0.0), n(100_000_000.0), b(false)]), 0.398942279404077, 1e-12);
+    close_tol(ev("T.DIST", vec![n(0.0), n(10_000_000_000.0), b(false)]), 0.3989422803914591, 1e-12);
+}
+
 #[test]
 fn binom_inv_huge_trials_returns() {
     // Above 2^53 neighbouring f64 values are more than 1 apart; the bisection must still end.

docs/function-parity.md

@@ -1,6 +1,6 @@
 # Function parity: worksheet functions and formulas
 
-> **Last reviewed:** 2026-10-15 · **Last updated:** 2026-10-25 · **Change:** minor (the LAMBDA row lists the recursion limit and its `#NUM!`, and the error a defined name holding an error gives when called; earlier: number text with accounting parentheses coerces like Excel 365; INDEX with one index on a 2-D reference is #REF! as in Excel; earlier: SUBTOTAL and AGGREGATE cap the cells they visit, #2175) · **Target:** Microsoft Excel (Microsoft 365), Excel for Mac 16.113.4
+> **Last reviewed:** 2026-10-31 · **Last updated:** 2026-10-31 · **Change:** minor (Student-t density uses a stable large-degrees-of-freedom gamma ratio, matching Excel at degrees through 10 billion; earlier: the LAMBDA row lists the recursion limit and its `#NUM!`, and the error a defined name holding an error gives when called; earlier: number text with accounting parentheses coerces like Excel 365; INDEX with one index on a 2-D reference is #REF! as in Excel; earlier: SUBTOTAL and AGGREGATE cap the cells they visit, #2175) · **Target:** Microsoft Excel (Microsoft 365), Excel for Mac 16.113.4
 
 Excel's worksheet functions, category by category, against GridCraft's function library. Part of
 [target-app-parity.md](target-app-parity.md); gaps feed [gaps.md](gaps.md).
@@ -123,6 +123,7 @@ workbooks; results checked in as data, not Excel files) and fixing what it finds
 
 | Date | Change | Summary |
 |---|---|---|
+| 2026-10-31 | minor | Student-t density uses an asymptotic log-gamma ratio for large degrees of freedom, avoiding cancellation while preserving bounded work; checked against Excel at 100 million and 10 billion degrees |
 | 2026-10-25 | minor | LAMBDA row: a LAMBDA that calls itself more than 140 times, and a formula nested past the depth limit, give `#NUM!` (#1809; nesting gave `#CALC!` before). `=Foo(1)` where the defined name Foo holds `#N/A` gives `#N/A`, not `#NAME?` |
 | 2026-10-23 | minor | Number text coercion (VALUE, arithmetic, typed entry): a dollar sign before accounting parentheses (`$(1,234)`, `$ (5)`) and a percent sign after them (`(5)%`) read as negatives; `(-5)`, `((5))`, `($-5)`, `$5%`, `$(5)%` and dates or times in parentheses are `#VALUE!`, as observed in Excel 365 |
 | 2026-10-23 | minor | INDEX with only a row index on a reference of several rows and columns (`INDEX(A1:C3,2)`, `INDEX(A1:C3,0)`) is `#REF!`, as observed in Excel, so it also fails as a range endpoint and inside other functions; an empty column argument (`INDEX(A1:C3,2,)`) still gives the row. Checked that a column array with one index stays a 1×1 array (`TYPE` 64), which is what Excel returns |