Float type limited to 104 days

The clocks resolution of desktop and laptop computers is getting closer to nanosecond resolution. More and more clocks have a frequency in MHz, up to GHz for the CPU TSC clock.

The Python time.time() function returns the current time as a floating-point number which is usually a 64-bit binary floating-point number (in the IEEE 754 format).

The problem is that the float type starts to lose nanoseconds after 104 days. Converting from nanoseconds (int) to seconds (float) and then back to nanoseconds (int) to check if conversions lose precision:

# no precision loss
>>> x = 2 ** 52 + 1; int(float(x * 1e-9) * 1e9) - x
0
# precision loss! (1 nanosecond)
>>> x = 2 ** 53 + 1; int(float(x * 1e-9) * 1e9) - x
-1
>>> print(datetime.timedelta(seconds=2 ** 53 / 1e9))
104 days, 5:59:59.254741

time.time() returns seconds elapsed since the UNIX epoch: January 1st, 1970. This function hasn’t had nanosecond precision since May 1970 (47 years ago):

>>> import datetime
>>> unix_epoch = datetime.datetime(1970, 1, 1)
>>> print(unix_epoch + datetime.timedelta(seconds=2**53 / 1e9))
1970-04-15 05:59:59.254741

Previous rejected PEP

Five years ago, the PEP 410 proposed a large and complex change in all Python functions returning time to support nanosecond resolution using the decimal.Decimal type.

The PEP was rejected for different reasons:

• The idea of adding a new optional parameter to change the result type was rejected. It’s an uncommon (and bad?) programming practice in Python.
• It was not clear if hardware clocks really had a resolution of 1 nanosecond, or if that made sense at the Python level.
• The decimal.Decimal type is uncommon in Python and so requires to adapt code to handle it.

Issues caused by precision loss

CPython enhancements of the last 5 years

Since the PEP 410 was rejected:

• The os.stat_result structure got 3 new fields for timestamps as nanoseconds (Python int): st_atime_ns, st_ctime_ns and st_mtime_ns.
• The PEP 418 was accepted, Python 3.3 got 3 new clocks: time.monotonic(), time.perf_counter() and time.process_time().
• The CPython private “pytime” C API handling time now uses a new _PyTime_t type: simple 64-bit signed integer (C int64_t). The _PyTime_t unit is an implementation detail and not part of the API. The unit is currently 1 nanosecond.

Existing Python APIs using nanoseconds as int

The os.stat_result structure has 3 fields for timestamps as nanoseconds (int): st_atime_ns, st_ctime_ns and st_mtime_ns.

The ns parameter of the os.utime() function accepts a (atime_ns: int, mtime_ns: int) tuple: nanoseconds.

New functions

This PEP adds six new functions to the time module:

• time.clock_gettime_ns(clock_id)
• time.clock_settime_ns(clock_id, time: int)
• time.monotonic_ns()
• time.perf_counter_ns()
• time.process_time_ns()
• time.time_ns()

These functions are similar to the version without the _ns suffix, but return a number of nanoseconds as a Python int.

For example, time.monotonic_ns() == int(time.monotonic() * 1e9) if monotonic() value is small enough to not lose precision.

These functions are needed because they may return “large” timestamps, like time.time() which uses the UNIX epoch as reference, and so their float-returning variants are likely to lose precision at the nanosecond resolution.

Unchanged functions

Since the time.clock() function was deprecated in Python 3.3, no time.clock_ns() is added.

Python has other time-returning functions. No nanosecond variant is proposed for these other functions, either because their internal resolution is greater or equal to 1 us, or because their maximum value is small enough to not lose precision. For example, the maximum value of time.clock_getres() should be 1 second.

Examples of unchanged functions:

• os module: sched_rr_get_interval(), times(), wait3() and wait4()
• resource module: ru_utime and ru_stime fields of getrusage()
• signal module: getitimer(), setitimer()
• time module: clock_getres()

See also the Annex: Clocks Resolution in Python.

A new nanosecond-returning flavor of these functions may be added later if an operating system exposes new functions providing better resolution.

Sub-nanosecond resolution

time.time_ns() API is not theoretically future-proof: if clock resolutions continue to increase below the nanosecond level, new Python functions may be needed.

In practice, the 1 nanosecond resolution is currently enough for all structures returned by all common operating systems functions.

Hardware clocks with a resolution better than 1 nanosecond already exist. For example, the frequency of a CPU TSC clock is the CPU base frequency: the resolution is around 0.3 ns for a CPU running at 3 GHz. Users who have access to such hardware and really need sub-nanosecond resolution can however extend Python for their needs. Such a rare use case doesn’t justify to design the Python standard library to support sub-nanosecond resolution.

For the CPython implementation, nanosecond resolution is convenient: the standard and well supported int64_t type can be used to store a nanosecond-precise timestamp. It supports a timespan of -292 years to +292 years. Using the UNIX epoch as reference, it therefore supports representing times since year 1677 to year 2262:

>>> 1970 - 2 ** 63 / (10 ** 9 * 3600 * 24 * 365.25)
1677.728976954687
>>> 1970 + 2 ** 63 / (10 ** 9 * 3600 * 24 * 365.25)
2262.271023045313

Modifying time.time() result type

It was proposed to modify time.time() to return a different number type with better precision.

The PEP 410 proposed to return decimal.Decimal which already exists and supports arbitrary precision, but it was rejected. Apart from decimal.Decimal, no portable real number type with better precision is currently available in Python.

Changing the built-in Python float type is out of the scope of this PEP.

Moreover, changing existing functions to return a new type introduces a risk of breaking the backward compatibility even if the new type is designed carefully.

Different types

Many ideas of new types were proposed to support larger or arbitrary precision: fractions, structures or 2-tuple using integers, fixed-point number, etc.

See also the PEP 410 for a previous long discussion on other types.

Adding a new type requires more effort to support it, than reusing the existing int type. The standard library, third party code and applications would have to be modified to support it.

The Python int type is well known, well supported, easy to manipulate, and supports all arithmetic operations such as dt = t2 - t1.

Moreover, taking/returning an integer number of nanoseconds is not a new concept in Python, as witnessed by os.stat_result and os.utime(ns=(atime_ns, mtime_ns)).

Different API

The time.time(ns=False) API was proposed to avoid adding new functions. It’s an uncommon (and bad?) programming practice in Python to change the result type depending on a parameter.

Different options were proposed to allow the user to choose the time resolution. If each Python module uses a different resolution, it can become difficult to handle different resolutions, instead of just seconds (time.time() returning float) and nanoseconds (time.time_ns() returning int). Moreover, as written above, there is no need for resolution better than 1 nanosecond in practice in the Python standard library.

A new module

It was proposed to add a new time_ns module containing the following functions:

• time_ns.clock_gettime(clock_id)
• time_ns.clock_settime(clock_id, time: int)
• time_ns.monotonic()
• time_ns.perf_counter()
• time_ns.process_time()
• time_ns.time()

The first question is whether the time_ns module should expose exactly the same API (constants, functions, etc.) as the time module. It can be painful to maintain two flavors of the time module. How are users use supposed to make a choice between these two modules?

If tomorrow, other nanosecond variants are needed in the os module, will we have to add a new os_ns module as well? There are functions related to time in many modules: time, os, signal, resource, select, etc.

Another idea is to add a time.ns submodule or a nested-namespace to get the time.ns.time() syntax, but it suffers from the same issues.

Script

Example of script to measure the smallest difference between two time.time() and time.time_ns() reads ignoring differences of zero:

import math
import time

LOOPS = 10 ** 6

print("time.time_ns(): %s" % time.time_ns())
print("time.time(): %s" % time.time())

min_dt = [abs(time.time_ns() - time.time_ns())
          for _ in range(LOOPS)]
min_dt = min(filter(bool, min_dt))
print("min time_ns() delta: %s ns" % min_dt)

min_dt = [abs(time.time() - time.time())
          for _ in range(LOOPS)]
min_dt = min(filter(bool, min_dt))
print("min time() delta: %s ns" % math.ceil(min_dt * 1e9))

Linux

Clocks resolution measured in Python on Fedora 26 (kernel 4.12):

Notes on resolutions:

• clock() frequency is CLOCKS_PER_SECOND which is 1,000,000 Hz (1 MHz): resolution of 1 us.
• times() frequency is os.sysconf("SC_CLK_TCK") (or the HZ constant) which is equal to 100 Hz: resolution of 10 ms.
• resource.getrusage(), os.wait3() and os.wait4() use the ru_usage structure. The type of the ru_usage.ru_utime and ru_usage.ru_stime fields is the timeval structure which has a resolution of 1 us.

Windows

Clocks resolution measured in Python on Windows 8.1:

The frequency of perf_counter() and perf_counter_ns() comes from QueryPerformanceFrequency(). The frequency is usually 10 MHz: resolution of 100 ns. In old Windows versions, the frequency was sometimes 3,579,545 Hz (3.6 MHz): resolution of 279 ns.

Analysis

The resolution of time.time_ns() is much better than time.time(): 84 ns (2.8x better) vs 239 ns on Linux and 318 us (2.8x better) vs 894 us on Windows. The time.time() resolution will only become larger (worse) as years pass since every day adds 86,400,000,000,000 nanoseconds to the system clock, which increases the precision loss.

The difference between time.perf_counter(), time.monotonic(), time.process_time() and their respective nanosecond variants is not visible in this quick script since the script runs for less than 1 minute, and the uptime of the computer used to run the script was smaller than 1 week. A significant difference may be seen if uptime reaches 104 days or more.

resource.getrusage() and times() have a resolution greater or equal to 1 microsecond, and so don’t need a variant with nanosecond resolution.