diff --git a/ext/rtree/rtree.c b/ext/rtree/rtree.c
index 0df13e50c6..4434bd5986 100644
--- a/ext/rtree/rtree.c
+++ b/ext/rtree/rtree.c
@@ -3029,35 +3029,81 @@ static int rtreeDeleteRowid(Rtree *pRtree, sqlite3_int64 iDelete){
   return rc;
 }
 
-/*
-** Rounding constants for float->double conversion.
-*/
-#define RNDTOWARDS  (1.0 - 1.0/8388608.0)  /* Round towards zero */
-#define RNDAWAY     (1.0 + 1.0/8388608.0)  /* Round away from zero */
-
 #if !defined(SQLITE_RTREE_INT_ONLY)
 /*
+** Convert a non-negative double d into the nearest float that is
+** less than or equal to (rtreeFloatDown) or greater than or equal
+** to (rtreeFloatUp) the input.
+*/
+static RtreeValue rtreeFloatDown(double d){
+  float f = d;
+  if( f>d ){
+    unsigned int x;
+    memcpy(&x, &f, 4);
+    x--;
+    memcpy(&f, &x, 4);
+  }
+  return f;
+}
+static RtreeValue rtreeFloatUp(double d){
+  float f = d;
+  if( f<d ){
+    unsigned int x;
+    memcpy(&x, &f, 4);
+    x++;
+    memcpy(&f, &x, 4);
+  }
+  return f;
+}
+/*
 ** Convert an sqlite3_value into an RtreeValue (presumably a float)
 ** while taking care to round toward negative or positive, respectively.
 */
 static RtreeValue rtreeValueDown(sqlite3_value *v){
-  double d = sqlite3_value_double(v);
-  float f = (float)d;
-  if( f>d ){
-    f = (float)(d*(d<0 ? RNDAWAY : RNDTOWARDS));
+  double d;
+  d = sqlite3_value_double(v);
+  if( d<0 ){
+    return -rtreeFloatUp(-d);
+  }else{
+    return rtreeFloatDown(d);
   }
-  return f;
 }
 static RtreeValue rtreeValueUp(sqlite3_value *v){
-  double d = sqlite3_value_double(v);
-  float f = (float)d;
-  if( f<d ){
-    f = (float)(d*(d<0 ? RNDTOWARDS : RNDAWAY));
+  double d;
+  d = sqlite3_value_double(v);
+  if( d<0 ){
+    return -rtreeFloatDown(-d);
+  }else{
+    return rtreeFloatUp(d);
   }
-  return f;
 }
 #endif /* !defined(SQLITE_RTREE_INT_ONLY) */
 
+#if !defined(SQLITE_RTREE_INT_ONLY) && defined(SQLITE_DEBUG)
+/*
+** SQL function:   rtree_round32(V,F)
+**
+** Convert the floating point value V to the nearest 32-bit float
+** and return that 32-bit float value.  Round up if F is true, or
+** down if F is falsed.
+**
+** Debugging and testing use only.
+*/
+static void rtreeRoundFunc(
+  sqlite3_context *ctx, 
+  int nArg, 
+  sqlite3_value **apArg
+){
+  float f;
+  if( sqlite3_value_int(apArg[1]) ){
+    f = rtreeValueUp(apArg[0]);
+  }else{
+    f = rtreeValueDown(apArg[0]);
+  }
+  sqlite3_result_double(ctx, (double)f);
+}
+#endif /* !defined(SQLITE_RTREE_INT_ONLY) && defined(SQLITE_DEBUG) */
+
 /*
 ** A constraint has failed while inserting a row into an rtree table. 
 ** Assuming no OOM error occurs, this function sets the error message 
@@ -4333,6 +4379,12 @@ int sqlite3RtreeInit(sqlite3 *db){
   if( rc==SQLITE_OK ){
     rc = sqlite3_create_function(db, "rtreecheck", -1, utf8, 0,rtreecheck, 0,0);
   }
+#if defined(SQLITE_DEBUG) && !defined(SQLITE_RTREE_INT_ONLY)
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_function(db, "rtree_round", 2, utf8, 0,
+                                 rtreeRoundFunc, 0, 0);
+  }
+#endif /* SQLITE_DEBUG && !SQLITE_RTREE_INT_ONLY */
   if( rc==SQLITE_OK ){
 #ifdef SQLITE_RTREE_INT_ONLY
     void *c = (void *)RTREE_COORD_INT32;
diff --git a/ext/rtree/rtree1.test b/ext/rtree/rtree1.test
index e596df71d5..5a5f3c7c61 100644
--- a/ext/rtree/rtree1.test
+++ b/ext/rtree/rtree1.test
@@ -815,4 +815,32 @@ do_execsql_test 24.2 {
   SELECT * FROM rt1 WHERE rid=1.005;
 } {}
 
+# Bug 2026-09-19T00:36:32Z
+#
+# Rounding double->float should work even for sub-normal or
+# near infinite values.
+#
+do_execsql_test 25.1 {
+  CREATE VIRTUAL TABLE t1 USING rtree(id,a,b);
+  INSERT INTO t1 VALUES(1,1e-39,1e-39);
+  SELECT id FROM t1 WHERE a<=1e-32 AND b>=1e-39;
+} 1
+foreach {id v} {
+  2   1e-40
+  3   -1e-39
+  4   -1e-40
+  5   3.1234e+38
+  6   -3.1234e+38
+  7   5e-324
+  8   -5e-324
+  9   3.5e+38
+  10  -3.5e+38
+} {
+  do_execsql_test 25.$id "
+    DELETE FROM t1;
+    INSERT INTO t1 VALUES(1,$v,$v);
+    SELECT id FROM t1 WHERE a<=$v AND b>=$v;
+  " 1
+}
+
 finish_test
diff --git a/manifest b/manifest
index 6015918846..9a26b92a94 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Fix\sissues\sin\ssupport\sfor\sSTDCALL\son\s32-bit\sWindows\sbuilds.\n[bugs:/info/2026-09-15T09:23:20Z|Bug\s2026-09-15T09:23:20Z]\sand\n[bugs:/info/2026-09-15T09:24:06Z|Bug\s2026-09-15T09:24:06Z].
-D 2026-09-18T16:50:49.794
+C Fix\s32-bit\sfloating\spoint\s(float)\srounding\sin\srtree\sso\sthat\sit\sworks\ncorrectly\sfor\ssubnormal\svalues\sand\sfor\svalues\snear\sinfinity.\n[bugs:/info/2026-09-19T00:36:32Z|Bug\s2026-09-19T00:36:32Z].
+D 2026-09-19T01:54:07.849
 F .fossil-settings/binary-glob 61195414528fb3ea9693577e1980230d78a1f8b0a54c78cf1b9b24d0a409ed6a x
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
@@ -496,9 +496,9 @@ F ext/recover/sqlite3recover.h 011c799f02deb70ab685916f6f538e6bb32c4e0025e79bfd0
 F ext/recover/test_recover.c 3d0fb1df7823f5bc22a0b93955034d16a2dfa2eb1e443e9a0123a77f120599a3
 F ext/rtree/README 734aa36238bcd2dee91db5dba107d5fcbdb02396612811377a8ad50f1272b1c1
 F ext/rtree/geopoly.c e389a95f88438668787f8276a00c2409545c35e2893d16c6c599f0e5310ab3be
-F ext/rtree/rtree.c a83a8ec01a413d4be98fcb845320d1e913a4e095b0371ca5bccdab4b30bb9bcf
+F ext/rtree/rtree.c 22850c718ab0f2f209d9ba00683d5264d3dd9c576aacb04b8627d71f106a929b
 F ext/rtree/rtree.h 4a690463901cb5e6127cf05eb8e642f127012fd5003830dbc974eca5802d9412
-F ext/rtree/rtree1.test e0608db762b2aadca0ecb6f97396cf66244490adc3ba88f2a292b27be3e1da3e
+F ext/rtree/rtree1.test d23c59978d3163f039c8f4a42c006fb5ad77cf705eb4203fa6bcfce7de236fb9
 F ext/rtree/rtree2.test 9d9deddbb16fd0c30c36e6b4fdc3ee3132d765567f0f9432ee71e1303d32603d
 F ext/rtree/rtree3.test 272594f88c344e973864008bbe4c71fd3a41a264c097d568593ee7886d83d409
 F ext/rtree/rtree4.test 304de65d484540111b896827e4261815e5dca4ce28eeecd58be648cd73452c4b
@@ -2221,9 +2221,8 @@ F tool/warnings-clang.sh bbf6a1e685e534c92ec2bfba5b1745f34fb6f0bc2a362850723a9ee
 F tool/warnings.sh a554d13f6e5cf3760f041b87939e3d616ec6961859c3245e8ef701d1eafc2ca2
 F tool/win/sqlite.vsix deb315d026cc8400325c5863eef847784a219a2f
 F tool/winmain.c 00c8fb88e365c9017db14c73d3c78af62194d9644feaf60e220ab0f411f3604c
-P 346c56e02c39858b4364e4c8b8e4c88237e64470066ebb2687ae06d2b0e978b8 5f8621d2f64344f4f0111f1d64cca5a71731cb037bfeea6e2e6f0368166085d1
-R 1f3d9a227a036345b1cb4381aaeb335e
-T +closed 5f8621d2f64344f4f0111f1d64cca5a71731cb037bfeea6e2e6f0368166085d1
+P 7e09ee42afab9868540875b4701cfbd55a591f8346358eebc3f54580fc2ec49d
+R 4c12ca9adf6f029967fc1bbeb793f41c
 U drh
-Z 351a347c94df48c9839f7a4395723866
+Z d467bb47df37c1a95fd8b85e3aa448d2
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 2e76df03de..c41f3f831b 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-7e09ee42afab9868540875b4701cfbd55a591f8346358eebc3f54580fc2ec49d
+3d5e1013245e1280b1f74fe09f9407f18313270847da5385a2e36c2b8eb56d74