diff --git a/changes/bug27139 b/changes/bug27139
new file mode 100644
index 0000000000..0d1e3b4329
--- /dev/null
+++ b/changes/bug27139
@@ -0,0 +1,14 @@
+  o Minor bugfixes (32-bit OSX and iOS, timing):
+    - Fix an integer overflow bug in our optimized 32-bit millisecond-
+      difference algorithm for 32-bit Apple platforms. Previously, it
+      would overflow when calculating the difference between two times
+      more than 47 days apart.  Fixes part of bug 27139; bugfix on
+      0.3.4.1-alpha.
+    - Improve the precision of our 32-bit millisecond difference
+      algorithm for 32-bit Apple platforms. Fixes part of bug 27139;
+      bugfix on 0.3.4.1-alpha.
+    - Relax the tolerance on the mainloop/update_time_jumps test
+      when running on 32-bit Apple platforms. Fixes part of bug 27139;
+      bugfix on 0.3.4.1-alpha.
+
+
diff --git a/src/common/compat_time.c b/src/common/compat_time.c
index 40847a8442..93b527def0 100644
--- a/src/common/compat_time.c
+++ b/src/common/compat_time.c
@@ -280,6 +280,7 @@ monotime_reset_ratchets_for_testing(void)
  */
 static struct mach_timebase_info mach_time_info;
 static struct mach_timebase_info mach_time_info_msec_cvt;
+static int32_t mach_time_msec_cvt_threshold;
 static int monotime_shift = 0;
 
 static void
@@ -299,11 +300,15 @@ monotime_init_internal(void)
   }
   {
     // For converting ticks to milliseconds in a 32-bit-friendly way, we
-    // will first right-shift by 20, and then multiply by 20/19, since
-    // (1<<20) * 19/20 is about 1e6.  We precompute a new numerate and
+    // will first right-shift by 20, and then multiply by 2048/1953, since
+    // (1<<20) * 1953/2048 is about 1e6.  We precompute a new numerator and
     // denominator here to avoid multiple multiplies.
-    mach_time_info_msec_cvt.numer = mach_time_info.numer * 20;
-    mach_time_info_msec_cvt.denom = mach_time_info.denom * 19;
+    mach_time_info_msec_cvt.numer = mach_time_info.numer * 2048;
+    mach_time_info_msec_cvt.denom = mach_time_info.denom * 1953;
+    // For any value above this amount, we should divide before multiplying,
+    // to avoid overflow.  For a value below this, we should multiply
+    // before dividing, to improve accuracy.
+    mach_time_msec_cvt_threshold = INT32_MAX / mach_time_info_msec_cvt.numer;
   }
 }
 
@@ -366,8 +371,13 @@ monotime_coarse_diff_msec32_(const monotime_coarse_t *start,
   /* We already require in di_ops.c that right-shift performs a sign-extend. */
   const int32_t diff_microticks = (int32_t)(diff_ticks >> 20);
 
-  return (diff_microticks * mach_time_info_msec_cvt.numer) /
-    mach_time_info_msec_cvt.denom;
+  if (diff_microticks >= mach_time_msec_cvt_threshold) {
+    return (diff_microticks / mach_time_info_msec_cvt.denom) *
+      mach_time_info_msec_cvt.numer;
+  } else {
+    return (diff_microticks * mach_time_info_msec_cvt.numer) /
+      mach_time_info_msec_cvt.denom;
+  }
 }
 
 uint32_t
diff --git a/src/common/compat_time.h b/src/common/compat_time.h
index 57ab20ab11..f241aa5eba 100644
--- a/src/common/compat_time.h
+++ b/src/common/compat_time.h
@@ -196,6 +196,7 @@ monotime_coarse_diff_msec32(const monotime_coarse_t *start,
   // on a 64-bit platform, let's assume 64/64 division is cheap.
   return (int32_t) monotime_coarse_diff_msec(start, end);
 #else
+#define USING_32BIT_MSEC_HACK
   return monotime_coarse_diff_msec32_(start, end);
 #endif
 }
diff --git a/src/test/test_circuitmux.c b/src/test/test_circuitmux.c
index 14c7598703..c81d53ae51 100644
--- a/src/test/test_circuitmux.c
+++ b/src/test/test_circuitmux.c
@@ -13,6 +13,8 @@
 #include "scheduler.h"
 #include "test.h"
 
+#include <math.h>
+
 /* XXXX duplicated function from test_circuitlist.c */
 static channel_t *
 new_fake_channel(void)
@@ -103,16 +105,19 @@ test_cmux_compute_ticks(void *arg)
   monotime_coarse_set_mock_time_nsec(now);
   tick = cell_ewma_get_current_tick_and_fraction(&rem);
   tt_uint_op(tick, OP_EQ, tick_zero);
-  tt_double_op(rem, OP_GT, .149999999);
-  tt_double_op(rem, OP_LT, .150000001);
+#ifdef USING_32BIT_MSEC_HACK
+  const double tolerance = .0005;
+#else
+  const double tolerance = .00000001;
+#endif
+  tt_double_op(fabs(rem - .15), OP_LT, tolerance);
 
   /* 25 second later and we should be in another tick. */
   now = START_NS + NS_PER_S * 25;
   monotime_coarse_set_mock_time_nsec(now);
   tick = cell_ewma_get_current_tick_and_fraction(&rem);
   tt_uint_op(tick, OP_EQ, tick_zero + 2);
-  tt_double_op(rem, OP_GT, .499999999);
-  tt_double_op(rem, OP_LT, .500000001);
+  tt_double_op(fabs(rem - .5), OP_LT, tolerance);
 
  done:
   ;