Merge PR #2998

# Conflicts:
#	docs/function-parity.md

crates/functions/src/stat/distributions.rs

@@ -51,6 +51,12 @@ fn f_cdf(x: f64, d1: f64, d2: f64) -> f64 {
     if x <= 0.0 {
         return 0.0;
     }
+    if x == 1.0 && d1 == d2 {
+        return 0.5;
+    }
+    if d1 >= 1e8 && d2 / d1 <= 1e-8 {
+        return reg_gamma_q(d2 / 2.0, d2 / (2.0 * (x + d2 / d1)));
+    }
     reg_inc_beta(d1 * x / (d1 * x + d2), d1 / 2.0, d2 / 2.0)
 }
 
@@ -58,6 +64,10 @@ fn f_upper(x: f64, d1: f64, d2: f64) -> f64 {
     if x <= 0.0 {
         return 1.0;
     }
+    if d1 >= 1e8 && d2 / d1 <= 1e-8 {
+        // With a much larger numerator degree, the scaled beta tail converges to a gamma tail.
+        return reg_gamma_p(d2 / 2.0, d2 / (2.0 * (x + d2 / d1)));
+    }
     reg_inc_beta(d2 / (d2 + d1 * x), d2 / 2.0, d1 / 2.0)
 }
 
@@ -347,7 +357,7 @@ fn f_args(a: &[Arg]) -> R<(f64, f64, f64)> {
     let x = num(a, 0)?;
     let d1 = num(a, 1)?.trunc();
     let d2 = num(a, 2)?.trunc();
-    if d1 < 1.0 || d2 < 1.0 || d1 >= 1e10 || d2 >= 1e10 {
+    if d1 < 1.0 || d2 < 1.0 || d1 > 1e10 || d2 > 1e10 {
         return Err(CellError::Num);
     }
     Ok((x, d1, d2))
@@ -378,7 +388,8 @@ pub(super) fn f_inv(a: &[Arg], _: C) -> R<Value> {
     if p == 0.0 {
         return num_val(0.0);
     }
-    num_val(invert(|x| f_cdf(x, d1, d2), p, 0.0, 1.0, 1e60))
+    let value = if p < 0.5 { invert(|x| f_cdf(x, d1, d2), p, 0.0, 1.0, 1e60) } else { invert(|x| f_upper(x, d1, d2), 1.0 - p, 0.0, 1.0, 1e60) };
+    num_val(value)
 }
 
 pub(super) fn f_inv_rt(a: &[Arg], _: C) -> R<Value> {

crates/functions/src/stat/tests.rs

@@ -397,6 +397,7 @@ fn t_chi_f() {
     close_tol(ev("F.DIST.RT", vec![n(15.2069), n(6.0), n(4.0)]), 0.01, 1e-6);
     close_tol(ev("FDIST", vec![n(15.2069), n(6.0), n(4.0)]), 0.01, 1e-6);
     close_tol(ev("F.INV", vec![n(0.01), n(6.0), n(4.0)]), 0.10930991, D7);
+    close_tol(ev("F.INV", vec![n(0.99), n(6.0), n(4.0)]), 15.20686, D7);
     close_tol(ev("F.INV.RT", vec![n(0.01), n(6.0), n(4.0)]), 15.20686, D7);
     close_tol(ev("FINV", vec![n(0.01), n(6.0), n(4.0)]), 15.20686, D7);
     close_tol(ev("F.TEST", vec![c(&[6.0, 7.0, 9.0, 15.0, 21.0]), c(&[20.0, 28.0, 31.0, 38.0, 40.0])]), 0.64831785, D7);
@@ -404,6 +405,19 @@ 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 f_distributions_accept_ten_billion_degrees() {
+    close_tol(ev("F.DIST", vec![n(0.0), n(10_000_000_000.0), n(1.0), b(false)]), 0.0, 0.0);
+    close_tol(ev("F.DIST.RT", vec![n(0.0), n(1.0), n(10_000_000_000.0)]), 1.0, 0.0);
+    close_tol(ev("F.DIST", vec![n(0.01), n(1_000_000_000.0), n(1.0), b(true)]), 1.52397e-23, 1e-28);
+    close_tol(ev("F.DIST", vec![n(1.0), n(10_000_000_000.0), n(10_000_000_000.0), b(true)]), 0.5, 0.0);
+    close_tol(ev("F.DIST", vec![n(1_000_000.0), n(10_000_000_000.0), n(1.0), b(true)]), 0.999202115, 1e-8);
+    close_tol(ev("F.INV", vec![n(0.5), n(10_000_000_000.0), n(1.0)]), 2.198110953542527, 2e-6);
+    close_tol(ev("F.DIST.RT", vec![n(0.0), n(9_999_999_999.0), n(1.0)]), 1.0, 0.0);
+    is_err(ev("F.DIST.RT", vec![n(0.0), n(10_000_000_001.0), n(1.0)]), CellError::Num);
+    is_err(ev("F.DIST.RT", vec![n(0.0), n(1.0), n(10_000_000_001.0)]), CellError::Num);
+}
+
 #[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:** 2026-10-31 · **Last updated:** 2026-10-31 · **Change:** minor (DOLLAR keeps the negative layout when a negative input rounds to zero at nonnegative precision; negative precision that rounds to zero retains the positive layout, as measured in Windows Excel 16.0 build 20527, LCID 1033; earlier: FIXED refuses results over 255 characters and DOLLAR refuses results over 254, matching the signed, decimal and separator boundary checks in Windows Excel 16.0 build 20527, LCID 1033; earlier: ECMA.CEILING listed with USDOLLAR as not on Microsoft's list; IMSQRT reproduces the stray real part Excel gives for negative reals, and the other IM* differences from Excel are listed; the LAMBDA row lists the recursion limit and its `#NUM!`, and the error a defined name holding an error gives when called; number text with accounting parentheses coerces like Excel 365; INDEX with one index on a 2-D reference is #REF! as in Excel; 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 (F distribution functions accept degrees of freedom through 10 billion, and the extreme numerator-degree inverse uses a stable gamma-tail limit; earlier: DOLLAR keeps the negative layout when a negative input rounds to zero at nonnegative precision; negative precision that rounds to zero retains the positive layout, as measured in Windows Excel 16.0 build 20527, LCID 1033; earlier: ECMA.CEILING listed with USDOLLAR as not on Microsoft's list; IMSQRT reproduces the stray real part Excel gives for negative reals, and the other IM* differences from Excel are listed; the LAMBDA row lists the recursion limit and its `#NUM!`, and the error a defined name holding an error gives when called; number text with accounting parentheses coerces like Excel 365; INDEX with one index on a 2-D reference is #REF! as in Excel; 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).
@@ -132,6 +132,7 @@ workbooks; results checked in as data, not Excel files) and fixing what it finds
 | 2026-10-31 | minor | FIXED and DOLLAR format the rounded number's shortest decimal representation before padding requested fractional zeroes, so 1.1 at 16 places and 1.005 at 20 places do not expose binary noise; measured in Windows Excel 16.0 build 20527, LCID 1033 |
 | 2026-10-31 | minor | FIXED accepts output through 255 characters; DOLLAR accepts output through 254. Windows Excel 16.0 build 20527 (LCID 1033) confirmed the distinct cutoffs with grouped and ungrouped values, signs, currency layout and decimal places |
 | 2026-10-31 | minor | DOLLAR uses the input sign for negative amounts that round to zero at nonnegative decimal places (`DOLLAR(-0.0001,0)` is `($0)`); when negative decimal places round to zero, Excel returns `$0`. Exact zero and negative zero stay unsigned; FIXED still returns `0` for `FIXED(-0.0001,0)` |
+| 2026-10-31 | minor | F.DIST, F.DIST.RT, F.INV and F.INV.RT accept degrees of freedom at the 10-billion boundary; F.INV uses the complementary tail, with a gamma-tail limit when numerator degrees dominate, to preserve inverse accuracy; values above the limit remain invalid |
 | 2026-10-27 | minor | ECMA.CEILING added to the functions that are in our library but not on Microsoft's list (with USDOLLAR), so the counts don't change |
 | 2026-10-26 | minor | IMSQRT uses Excel's polar route with its cosine reduction, so `IMSQRT("-4")` is `1.22514845490862E-16+2i` as in Excel (exact `2i` before); the rows list the IM* differences still open |
 | 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?` |