From 006b7962bd2a3279d7bc91b8f69c46953fe62b7d Mon Sep 17 00:00:00 2001
From: Harrison Booth <73434116+Harrison-Booth@users.noreply.github.com>
Date: Fri, 30 Oct 2026 21:14:19 -0500
Subject: [PATCH] Preserve F distribution tail accuracy

---
 crates/functions/src/stat/distributions.rs | 5 ++++-
 crates/functions/src/stat/tests.rs         | 2 ++
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/crates/functions/src/stat/distributions.rs b/crates/functions/src/stat/distributions.rs
index a697bc75a..9bd519066 100644
--- a/crates/functions/src/stat/distributions.rs
+++ b/crates/functions/src/stat/distributions.rs
@@ -51,8 +51,11 @@ 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 1.0 - f_upper(x, d1, d2);
+        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)
 }
diff --git a/crates/functions/src/stat/tests.rs b/crates/functions/src/stat/tests.rs
index 423a628e6..3e229262e 100644
--- a/crates/functions/src/stat/tests.rs
+++ b/crates/functions/src/stat/tests.rs
@@ -409,6 +409,8 @@ fn t_chi_f() {
 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);