diff --git a/Doc/library/time.rst b/Doc/library/time.rst
index cff6320..143f84b 100644
--- a/Doc/library/time.rst
+++ b/Doc/library/time.rst
@@ -166,6 +166,9 @@
    Return the time of the specified clock *clk_id*.  Refer to
    :ref:`time-clock-id-constants` for a list of accepted values for *clk_id*.
 
+   Use :func:`clock_gettime_ns` to avoid the precision loss caused by the
+   :class:`float` type.
+
    .. availability:: Unix.
 
    .. versionadded:: 3.3
@@ -185,6 +188,9 @@
    Set the time of the specified clock *clk_id*.  Currently,
    :data:`CLOCK_REALTIME` is the only accepted value for *clk_id*.
 
+   Use :func:`clock_settime_ns` to avoid the precision loss caused by the
+   :class:`float` type.
+
    .. availability:: Unix.
 
    .. versionadded:: 3.3
@@ -273,10 +279,17 @@
    The reference point of the returned value is undefined, so that only the
    difference between the results of consecutive calls is valid.
 
+   Use :func:`monotonic_ns` to avoid the precision loss caused by the
+   :class:`float` type.
+
    .. versionadded:: 3.3
+
    .. versionchanged:: 3.5
       The function is now always available and always system-wide.
 
+   .. versionchanged:: 3.10
+      On macOS, the function is now system-wide.
+
 
 .. function:: monotonic_ns() -> int
 
@@ -295,8 +308,14 @@
    point of the returned value is undefined, so that only the difference between
    the results of consecutive calls is valid.
 
+   Use :func:`perf_counter_ns` to avoid the precision loss caused by the
+   :class:`float` type.
+
    .. versionadded:: 3.3
 
+   .. versionchanged:: 3.10
+      On Windows, the function is now system-wide.
+
 .. function:: perf_counter_ns() -> int
 
    Similar to :func:`perf_counter`, but return time as nanoseconds.
@@ -317,6 +336,9 @@
    returned value is undefined, so that only the difference between the results
    of consecutive calls is valid.
 
+   Use :func:`process_time_ns` to avoid the precision loss caused by the
+   :class:`float` type.
+
    .. versionadded:: 3.3
 
 .. function:: process_time_ns() -> int
@@ -581,6 +603,17 @@
    :class:`struct_time` object is returned, from which the components
    of the calendar date may be accessed as attributes.
 
+   Use :func:`time_ns` to avoid the precision loss caused by the :class:`float`
+   type.
+
+
+.. function:: time_ns() -> int
+
+   Similar to :func:`~time.time` but returns time as an integer number of nanoseconds
+   since the epoch_.
+
+   .. versionadded:: 3.7
+
 
 .. function:: thread_time() -> float
 
@@ -595,6 +628,9 @@
    returned value is undefined, so that only the difference between the results
    of consecutive calls in the same thread is valid.
 
+   Use :func:`thread_time_ns` to avoid the precision loss caused by the
+   :class:`float` type.
+
    .. availability::  Windows, Linux, Unix systems supporting
       ``CLOCK_THREAD_CPUTIME_ID``.
 
@@ -608,13 +644,6 @@
    .. versionadded:: 3.7
 
 
-.. function:: time_ns() -> int
-
-   Similar to :func:`~time.time` but returns time as an integer number of nanoseconds
-   since the epoch_.
-
-   .. versionadded:: 3.7
-
 .. function:: tzset()
 
    Reset the time conversion rules used by the library routines. The environment
diff --git a/Misc/NEWS.d/next/Library/2020-11-14-14-34-32.bpo-37205.iDbHrw.rst b/Misc/NEWS.d/next/Library/2020-11-14-14-34-32.bpo-37205.iDbHrw.rst
new file mode 100644
index 0000000..5cf325e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-11-14-14-34-32.bpo-37205.iDbHrw.rst
@@ -0,0 +1,5 @@
+:func:`time.perf_counter()` on Windows and :func:`time.monotonic()` on macOS
+are now system-wide. Previously, they used an offset computed at startup to
+reduce the precision loss caused by the float type. Use
+:func:`time.perf_counter_ns()` and :func:`time.monotonic_ns()` added in Python
+3.7 to avoid this precision loss.
diff --git a/Python/pytime.c b/Python/pytime.c
index 89d63e0..179bced 100644
--- a/Python/pytime.c
+++ b/Python/pytime.c
@@ -6,7 +6,7 @@
 #if defined(__APPLE__)
 #include <mach/mach_time.h>   /* mach_absolute_time(), mach_timebase_info() */
 
-#if defined(__APPLE__) && defined(__has_builtin) 
+#if defined(__APPLE__) && defined(__has_builtin)
 #  if __has_builtin(__builtin_available)
 #    define HAVE_CLOCK_GETTIME_RUNTIME __builtin_available(macOS 10.12, iOS 10.0, tvOS 10.0, watchOS 3.0, *)
 #  endif
@@ -730,7 +730,7 @@ pygettimeofday(_PyTime_t *tp, _Py_clock_info_t *info, int raise)
     }
 
 #ifdef HAVE_CLOCK_GETTIME_RUNTIME
-    } else { 
+    } else {
 #endif
 
 #endif
@@ -822,7 +822,6 @@ pymonotonic(_PyTime_t *tp, _Py_clock_info_t *info, int raise)
 
 #elif defined(__APPLE__)
     static mach_timebase_info_data_t timebase;
-    static uint64_t t0 = 0;
     uint64_t ticks;
 
     if (timebase.denom == 0) {
@@ -859,8 +858,6 @@ pymonotonic(_PyTime_t *tp, _Py_clock_info_t *info, int raise)
                             "mach_timebase_info is too large");
             return -1;
         }
-
-        t0 = mach_absolute_time();
     }
 
     if (info) {
@@ -871,9 +868,6 @@ pymonotonic(_PyTime_t *tp, _Py_clock_info_t *info, int raise)
     }
 
     ticks = mach_absolute_time();
-    /* Use a "time zero" to reduce precision loss when converting time
-       to floatting point number, as in time.monotonic(). */
-    ticks -= t0;
     *tp = _PyTime_MulDiv(ticks,
                          (_PyTime_t)timebase.numer,
                          (_PyTime_t)timebase.denom);
@@ -960,7 +954,6 @@ static int
 win_perf_counter(_PyTime_t *tp, _Py_clock_info_t *info)
 {
     static LONGLONG frequency = 0;
-    static LONGLONG t0 = 0;
     LARGE_INTEGER now;
     LONGLONG ticksll;
     _PyTime_t ticks;
@@ -1000,7 +993,6 @@ win_perf_counter(_PyTime_t *tp, _Py_clock_info_t *info)
         }
 
         QueryPerformanceCounter(&now);
-        t0 = now.QuadPart;
     }
 
     if (info) {
@@ -1013,10 +1005,6 @@ win_perf_counter(_PyTime_t *tp, _Py_clock_info_t *info)
     QueryPerformanceCounter(&now);
     ticksll = now.QuadPart;
 
-    /* Use a "time zero" to reduce precision loss when converting time
-       to floatting point number, as in time.perf_counter(). */
-    ticksll -= t0;
-
     /* Make sure that casting LONGLONG to _PyTime_t cannot overflow,
        both types are signed */
     Py_BUILD_ASSERT(sizeof(ticksll) <= sizeof(ticks));