From 5dffe285bd93a8292f399db9bee3cf7d52652e8c Mon Sep 17 00:00:00 2001
From: Konstantin Bogdanov <var1able@var1able.network>
Date: Thu, 8 Oct 2026 16:56:21 +0200
Subject: [PATCH] Fix precision loss in cagnoli for edges crossing the
 antimeridian

For an edge whose endpoints lie on opposite sides of +-180 degrees the
raw longitude difference is close to +-2*pi, and the true tiny step
between the vertices is lost to the ulp of 2*pi before sin and cos are
applied. Nothing cancels the error, so cells straddling the antimeridian
at resolutions 12 and above come out up to 7.8% too small (res 15).

Shift both longitudes to the same side of the antimeridian before
subtracting, so the difference is between two nearby values. sin and cos
are 2*pi-periodic, so the result is unchanged mathematically. Global area
sums at res 0-3 still equal 4*pi to within 5e-13.

Regression from v4.5.0 (uber/h3#1101), reported in
https://github.com/ClickHouse/ClickHouse/issues/124447

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
---
 src/apps/testapps/testH3CellArea.c | 17 +++++++++++++++++
 src/h3lib/lib/area.c               |  8 ++++++++
 2 files changed, 25 insertions(+)

diff --git a/src/apps/testapps/testH3CellArea.c b/src/apps/testapps/testH3CellArea.c
index 4189dfc7de..9b0ab6ac0e 100644
--- a/src/apps/testapps/testH3CellArea.c
+++ b/src/apps/testapps/testH3CellArea.c
@@ -47,6 +47,23 @@ SUITE(h3CellArea) {
         }
     }
 
+    TEST(cell_area_antimeridian) {
+        // Cells straddling the antimeridian at fine resolutions, paired with
+        // an adjacent cell that does not. Their areas must agree closely; a
+        // naive longitude difference across +-180 degrees loses precision
+        // and makes the straddling cell up to several percent off.
+        H3Index pairs[][2] = {{0x8d056898db628bfULL, 0x8d056898db62d7fULL},
+                              {0x8e32b605c51e067ULL, 0x8e32b605c51e15fULL},
+                              {0x8f7f809893b5b9dULL, 0x8f7f809893b5b9cULL}};
+        for (int i = 0; i < 3; i++) {
+            double a, b;
+            t_assertSuccess(H3_EXPORT(cellAreaRads2)(pairs[i][0], &a));
+            t_assertSuccess(H3_EXPORT(cellAreaRads2)(pairs[i][1], &b));
+            t_assert(fabs(a / b - 1.0) < 1e-5,
+                     "antimeridian cell area should match neighbor");
+        }
+    }
+
     TEST(cell_area_invalid) {
         H3Index invalid = 0xFFFFFFFFFFFFFFFF;
         double area;
diff --git a/src/h3lib/lib/area.c b/src/h3lib/lib/area.c
index cebd605c4f..f46e86dff6 100644
--- a/src/h3lib/lib/area.c
+++ b/src/h3lib/lib/area.c
@@ -37,7 +37,15 @@ static inline double cagnoli(LatLng x, LatLng y) {
     double sa = sin(x.lat) * sin(y.lat);
     double ca = cos(x.lat) * cos(y.lat);
 
+    // For an edge crossing the antimeridian, the raw difference is close to
+    // +-2*pi, and the true (tiny) longitude step is lost to the ulp of 2*pi.
+    // Shift both longitudes to the same side of the antimeridian first so
+    // that the subtraction is between two nearby values; sin and cos are
+    // 2*pi-periodic, so the result is mathematically unchanged.
     double d = y.lng - x.lng;
+    if (d > M_PI || d < -M_PI) {
+        d = (y.lng - copysign(M_PI, y.lng)) - (x.lng - copysign(M_PI, x.lng));
+    }
     double sd = sin(d);
     double cd = cos(d);