Issue #26331: Implement the parsing part of PEP 515.

Thanks to Georg Brandl for the patch.

22 files changed, 742 insertions, 204 deletions

diff --git a/Doc/library/decimal.rst b/Doc/library/decimal.rst
index ee746e933de..e984edcb754 100644
--- a/Doc/library/decimal.rst
+++ b/Doc/library/decimal.rst
@@ -345,7 +345,7 @@ Decimal objects
    *value* can be an integer, string, tuple, :class:`float`, or another :class:`Decimal`
    object. If no *value* is given, returns ``Decimal('0')``.  If *value* is a
    string, it should conform to the decimal numeric string syntax after leading
-   and trailing whitespace characters are removed::
+   and trailing whitespace characters, as well as underscores throughout, are removed::
 
       sign           ::=  '+' | '-'
       digit          ::=  '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
@@ -394,6 +394,10 @@ Decimal objects
       :class:`float` arguments raise an exception if the :exc:`FloatOperation`
       trap is set. By default the trap is off.
 
+   .. versionchanged:: 3.6
+      Underscores are allowed for grouping, as with integral and floating-point
+      literals in code.
+
    Decimal floating point objects share many properties with the other built-in
    numeric types such as :class:`float` and :class:`int`.  All of the usual math
    operations and special methods apply.  Likewise, decimal objects can be
@@ -1075,8 +1079,8 @@ In addition to the three supplied contexts, new contexts can be created with the
          Decimal('4.44')
 
       This method implements the to-number operation of the IBM specification.
-      If the argument is a string, no leading or trailing whitespace is
-      permitted.
+      If the argument is a string, no leading or trailing whitespace or
+      underscores are permitted.
 
    .. method:: create_decimal_from_float(f)
 
diff --git a/Doc/library/functions.rst b/Doc/library/functions.rst
index db04b105c86..c4fcd98252e 100644
--- a/Doc/library/functions.rst
+++ b/Doc/library/functions.rst
@@ -271,6 +271,9 @@ are always available.  They are listed here in alphabetical order.
 
    The complex type is described in :ref:`typesnumeric`.
 
+   .. versionchanged:: 3.6
+      Grouping digits with underscores as in code literals is allowed.
+
 
 .. function:: delattr(object, name)
 
@@ -531,11 +534,14 @@ are always available.  They are listed here in alphabetical order.
 
    The float type is described in :ref:`typesnumeric`.
 
-   .. index::
-      single: __format__
-      single: string; format() (built-in function)
+   .. versionchanged:: 3.6
+      Grouping digits with underscores as in code literals is allowed.
 
 
+.. index::
+   single: __format__
+   single: string; format() (built-in function)
+
 .. function:: format(value[, format_spec])
 
    Convert a *value* to a "formatted" representation, as controlled by
@@ -702,6 +708,10 @@ are always available.  They are listed here in alphabetical order.
       :meth:`base.__int__ <object.__int__>` instead of :meth:`base.__index__
       <object.__index__>`.
 
+   .. versionchanged:: 3.6
+      Grouping digits with underscores as in code literals is allowed.
+
+
 .. function:: isinstance(object, classinfo)
 
    Return true if the *object* argument is an instance of the *classinfo*
diff --git a/Doc/reference/lexical_analysis.rst b/Doc/reference/lexical_analysis.rst
index 48f20434f01..a7c6a684c04 100644
--- a/Doc/reference/lexical_analysis.rst
+++ b/Doc/reference/lexical_analysis.rst
@@ -721,20 +721,24 @@ Integer literals
 Integer literals are described by the following lexical definitions:
 
 .. productionlist::
-   integer: `decimalinteger` | `octinteger` | `hexinteger` | `bininteger`
-   decimalinteger: `nonzerodigit` `digit`* | "0"+
+   integer: `decinteger` | `bininteger` | `octinteger` | `hexinteger`
+   decinteger: `nonzerodigit` (["_"] `digit`)* | "0"+ (["_"] "0")*
+   bininteger: "0" ("b" | "B") (["_"] `bindigit`)+
+   octinteger: "0" ("o" | "O") (["_"] `octdigit`)+
+   hexinteger: "0" ("x" | "X") (["_"] `hexdigit`)+
    nonzerodigit: "1"..."9"
    digit: "0"..."9"
-   octinteger: "0" ("o" | "O") `octdigit`+
-   hexinteger: "0" ("x" | "X") `hexdigit`+
-   bininteger: "0" ("b" | "B") `bindigit`+
+   bindigit: "0" | "1"
    octdigit: "0"..."7"
    hexdigit: `digit` | "a"..."f" | "A"..."F"
-   bindigit: "0" | "1"
 
 There is no limit for the length of integer literals apart from what can be
 stored in available memory.
 
+Underscores are ignored for determining the numeric value of the literal.  They
+can be used to group digits for enhanced readability.  One underscore can occur
+between digits, and after base specifiers like ``0x``.
+
 Note that leading zeros in a non-zero decimal number are not allowed. This is
 for disambiguation with C-style octal literals, which Python used before version
 3.0.
@@ -743,6 +747,10 @@ Some examples of integer literals::
 
    7     2147483647                        0o177    0b100110111
    3     79228162514264337593543950336     0o377    0xdeadbeef
+         100_000_000_000                   0b_1110_0101
+
+.. versionchanged:: 3.6
+   Underscores are now allowed for grouping purposes in literals.
 
 
 .. _floating:
@@ -754,23 +762,28 @@ Floating point literals are described by the following lexical definitions:
 
 .. productionlist::
    floatnumber: `pointfloat` | `exponentfloat`
-   pointfloat: [`intpart`] `fraction` | `intpart` "."
-   exponentfloat: (`intpart` | `pointfloat`) `exponent`
-   intpart: `digit`+
-   fraction: "." `digit`+
-   exponent: ("e" | "E") ["+" | "-"] `digit`+
+   pointfloat: [`digitpart`] `fraction` | `digitpart` "."
+   exponentfloat: (`digitpart` | `pointfloat`) `exponent`
+   digitpart: `digit` (["_"] `digit`)*
+   fraction: "." `digitpart`
+   exponent: ("e" | "E") ["+" | "-"] `digitpart`
 
 Note that the integer and exponent parts are always interpreted using radix 10.
 For example, ``077e010`` is legal, and denotes the same number as ``77e10``. The
-allowed range of floating point literals is implementation-dependent. Some
-examples of floating point literals::
+allowed range of floating point literals is implementation-dependent.  As in
+integer literals, underscores are supported for digit grouping.
+
+Some examples of floating point literals::
 
-   3.14    10.    .001    1e100    3.14e-10    0e0
+   3.14    10.    .001    1e100    3.14e-10    0e0    3.14_15_93
 
 Note that numeric literals do not include a sign; a phrase like ``-1`` is
 actually an expression composed of the unary operator ``-`` and the literal
 ``1``.
 
+.. versionchanged:: 3.6
+   Underscores are now allowed for grouping purposes in literals.
+
 
 .. _imaginary:
 
@@ -780,7 +793,7 @@ Imaginary literals
 Imaginary literals are described by the following lexical definitions:
 
 .. productionlist::
-   imagnumber: (`floatnumber` | `intpart`) ("j" | "J")
+   imagnumber: (`floatnumber` | `digitpart`) ("j" | "J")
 
 An imaginary literal yields a complex number with a real part of 0.0.  Complex
 numbers are represented as a pair of floating point numbers and have the same
@@ -788,7 +801,7 @@ restrictions on their range.  To create a complex number with a nonzero real
 part, add a floating point number to it, e.g., ``(3+4j)``.  Some examples of
 imaginary literals::
 
-   3.14j   10.j    10j     .001j   1e100j  3.14e-10j
+   3.14j   10.j    10j     .001j   1e100j   3.14e-10j   3.14_15_93j
 
 
 .. _operators:
diff --git a/Doc/whatsnew/3.6.rst b/Doc/whatsnew/3.6.rst
index f15bf4d30b2..9a1648643ac 100644
--- a/Doc/whatsnew/3.6.rst
+++ b/Doc/whatsnew/3.6.rst
@@ -124,6 +124,29 @@ Windows improvements:
 New Features
 ============
 
+.. _pep-515:
+
+PEP 515: Underscores in Numeric Literals
+========================================
+
+Prior to PEP 515, there was no support for writing long numeric
+literals with some form of separator to improve readability. For
+instance, how big is ``1000000000000000```? With :pep:`515`, though,
+you can use underscores to separate digits as desired to make numeric
+literals easier to read: ``1_000_000_000_000_000``. Underscores can be
+used with other numeric literals beyond integers, e.g.
+``0x_FF_FF_FF_FF``.
+
+Single underscores are allowed between digits and after any base
+specifier. More than a single underscore in a row, leading, or
+trailing underscores are not allowed.
+
+.. seealso::
+
+   :pep:`523` - Underscores in Numeric Literals
+   PEP written by Georg Brandl & Serhiy Storchaka.
+
+
 .. _pep-523:
 
 PEP 523: Adding a frame evaluation API to CPython
diff --git a/Include/pystrtod.h b/Include/pystrtod.h
index 23fd1c62551..c1e84de6fe5 100644
--- a/Include/pystrtod.h
+++ b/Include/pystrtod.h
@@ -19,6 +19,10 @@ PyAPI_FUNC(char *) PyOS_double_to_string(double val,
                                          int *type);
 
 #ifndef Py_LIMITED_API
+PyAPI_FUNC(PyObject *) _Py_string_to_number_with_underscores(
+    const char *str, Py_ssize_t len, const char *what, PyObject *obj, void *arg,
+    PyObject *(*innerfunc)(const char *, Py_ssize_t, void *));
+
 PyAPI_FUNC(double) _Py_parse_inf_or_nan(const char *p, char **endptr);
 #endif
 
diff --git a/Lib/_pydecimal.py b/Lib/_pydecimal.py
index 21e875c31c4..6318a49ce70 100644
--- a/Lib/_pydecimal.py
+++ b/Lib/_pydecimal.py
@@ -589,7 +589,7 @@ class Decimal(object):
         # From a string
         # REs insist on real strings, so we can too.
         if isinstance(value, str):
-            m = _parser(value.strip())
+            m = _parser(value.strip().replace("_", ""))
             if m is None:
                 if context is None:
                     context = getcontext()
@@ -4125,7 +4125,7 @@ class Context(object):
         This will make it round up for that operation.
         """
         rounding = self.rounding
-        self.rounding= type
+        self.rounding = type
         return rounding
 
     def create_decimal(self, num='0'):
@@ -4134,10 +4134,10 @@ class Context(object):
         This method implements the to-number operation of the
         IBM Decimal specification."""
 
-        if isinstance(num, str) and num != num.strip():
+        if isinstance(num, str) and (num != num.strip() or '_' in num):
             return self._raise_error(ConversionSyntax,
-                                     "no trailing or leading whitespace is "
-                                     "permitted.")
+                                     "trailing or leading whitespace and "
+                                     "underscores are not permitted.")
 
         d = Decimal(num, context=self)
         if d._isnan() and len(d._int) > self.prec - self.clamp:
diff --git a/Lib/test/test_complex.py b/Lib/test/test_complex.py
index 0ef9a7a1098..6633a7ae54b 100644
--- a/Lib/test/test_complex.py
+++ b/Lib/test/test_complex.py
@@ -1,5 +1,7 @@
 import unittest
 from test import support
+from test.test_grammar import (VALID_UNDERSCORE_LITERALS,
+                               INVALID_UNDERSCORE_LITERALS)
 
 from random import random
 from math import atan2, isnan, copysign
@@ -377,6 +379,18 @@ class ComplexTest(unittest.TestCase):
         self.assertAlmostEqual(complex(complex1(1j)), 2j)
         self.assertRaises(TypeError, complex, complex2(1j))
 
+    def test_underscores(self):
+        # check underscores
+        for lit in VALID_UNDERSCORE_LITERALS:
+            if not any(ch in lit for ch in 'xXoObB'):
+                self.assertEqual(complex(lit), eval(lit))
+                self.assertEqual(complex(lit), complex(lit.replace('_', '')))
+        for lit in INVALID_UNDERSCORE_LITERALS:
+            if lit in ('0_7', '09_99'):  # octals are not recognized here
+                continue
+            if not any(ch in lit for ch in 'xXoObB'):
+                self.assertRaises(ValueError, complex, lit)
+
     def test_hash(self):
         for x in range(-30, 30):
             self.assertEqual(hash(x), hash(complex(x, 0)))
diff --git a/Lib/test/test_decimal.py b/Lib/test/test_decimal.py
index 7492f5466f0..617a37eec82 100644
--- a/Lib/test/test_decimal.py
+++ b/Lib/test/test_decimal.py
@@ -554,6 +554,10 @@ class ExplicitConstructionTest(unittest.TestCase):
         self.assertEqual(str(Decimal('  -7.89')), '-7.89')
         self.assertEqual(str(Decimal("  3.45679  ")), '3.45679')
 
+        # underscores
+        self.assertEqual(str(Decimal('1_3.3e4_0')), '1.33E+41')
+        self.assertEqual(str(Decimal('1_0_0_0')), '1000')
+
         # unicode whitespace
         for lead in ["", ' ', '\u00a0', '\u205f']:
             for trail in ["", ' ', '\u00a0', '\u205f']:
@@ -578,6 +582,9 @@ class ExplicitConstructionTest(unittest.TestCase):
             # embedded NUL
             self.assertRaises(InvalidOperation, Decimal, "12\u00003")
 
+            # underscores don't prevent errors
+            self.assertRaises(InvalidOperation, Decimal, "1_2_\u00003")
+
     @cpython_only
     def test_from_legacy_strings(self):
         import _testcapi
@@ -772,6 +779,9 @@ class ExplicitConstructionTest(unittest.TestCase):
         self.assertRaises(InvalidOperation, nc.create_decimal, "xyz")
         self.assertRaises(ValueError, nc.create_decimal, (1, "xyz", -25))
         self.assertRaises(TypeError, nc.create_decimal, "1234", "5678")
+        # no whitespace and underscore stripping is done with this method
+        self.assertRaises(InvalidOperation, nc.create_decimal, " 1234")
+        self.assertRaises(InvalidOperation, nc.create_decimal, "12_34")
 
         # too many NaN payload digits
         nc.prec = 3
diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index 68b212e1959..ac8473db503 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -1,4 +1,3 @@
-
 import fractions
 import operator
 import os
@@ -9,6 +8,8 @@ import time
 import unittest
 
 from test import support
+from test.test_grammar import (VALID_UNDERSCORE_LITERALS,
+                               INVALID_UNDERSCORE_LITERALS)
 from math import isinf, isnan, copysign, ldexp
 
 INF = float("inf")
@@ -60,6 +61,27 @@ class GeneralFloatCases(unittest.TestCase):
         float(b'.' + b'1'*1000)
         float('.' + '1'*1000)
 
+    def test_underscores(self):
+        for lit in VALID_UNDERSCORE_LITERALS:
+            if not any(ch in lit for ch in 'jJxXoObB'):
+                self.assertEqual(float(lit), eval(lit))
+                self.assertEqual(float(lit), float(lit.replace('_', '')))
+        for lit in INVALID_UNDERSCORE_LITERALS:
+            if lit in ('0_7', '09_99'):  # octals are not recognized here
+                continue
+            if not any(ch in lit for ch in 'jJxXoObB'):
+                self.assertRaises(ValueError, float, lit)
+        # Additional test cases; nan and inf are never valid as literals,
+        # only in the float() constructor, but we don't allow underscores
+        # in or around them.
+        self.assertRaises(ValueError, float, '_NaN')
+        self.assertRaises(ValueError, float, 'Na_N')
+        self.assertRaises(ValueError, float, 'IN_F')
+        self.assertRaises(ValueError, float, '-_INF')
+        self.assertRaises(ValueError, float, '-INF_')
+        # Check that we handle bytes values correctly.
+        self.assertRaises(ValueError, float, b'0_.\xff9')
+
     def test_non_numeric_input_types(self):
         # Test possible non-numeric types for the argument x, including
         # subclasses of the explicitly documented accepted types.
diff --git a/Lib/test/test_grammar.py b/Lib/test/test_grammar.py
index 109013f5e2f..914aa679441 100644
--- a/Lib/test/test_grammar.py
+++ b/Lib/test/test_grammar.py
@@ -16,6 +16,87 @@ from collections import ChainMap
 from test import ann_module2
 import test
 
+# These are shared with test_tokenize and other test modules.
+#
+# Note: since several test cases filter out floats by looking for "e" and ".",
+# don't add hexadecimal literals that contain "e" or "E".
+VALID_UNDERSCORE_LITERALS = [
+    '0_0_0',
+    '4_2',
+    '1_0000_0000',
+    '0b1001_0100',
+    '0xffff_ffff',
+    '0o5_7_7',
+    '1_00_00.5',
+    '1_00_00.5e5',
+    '1_00_00e5_1',
+    '1e1_0',
+    '.1_4',
+    '.1_4e1',
+    '0b_0',
+    '0x_f',
+    '0o_5',
+    '1_00_00j',
+    '1_00_00.5j',
+    '1_00_00e5_1j',
+    '.1_4j',
+    '(1_2.5+3_3j)',
+    '(.5_6j)',
+]
+INVALID_UNDERSCORE_LITERALS = [
+    # Trailing underscores:
+    '0_',
+    '42_',
+    '1.4j_',
+    '0x_',
+    '0b1_',
+    '0xf_',
+    '0o5_',
+    '0 if 1_Else 1',
+    # Underscores in the base selector:
+    '0_b0',
+    '0_xf',
+    '0_o5',
+    # Old-style octal, still disallowed:
+    '0_7',
+    '09_99',
+    # Multiple consecutive underscores:
+    '4_______2',
+    '0.1__4',
+    '0.1__4j',
+    '0b1001__0100',
+    '0xffff__ffff',
+    '0x___',
+    '0o5__77',
+    '1e1__0',
+    '1e1__0j',
+    # Underscore right before a dot:
+    '1_.4',
+    '1_.4j',
+    # Underscore right after a dot:
+    '1._4',
+    '1._4j',
+    '._5',
+    '._5j',
+    # Underscore right after a sign:
+    '1.0e+_1',
+    '1.0e+_1j',
+    # Underscore right before j:
+    '1.4_j',
+    '1.4e5_j',
+    # Underscore right before e:
+    '1_e1',
+    '1.4_e1',
+    '1.4_e1j',
+    # Underscore right after e:
+    '1e_1',
+    '1.4e_1',
+    '1.4e_1j',
+    # Complex cases with parens:
+    '(1+1.5_j_)',
+    '(1+1.5_j)',
+]
+
 
 class TokenTests(unittest.TestCase):
 
@@ -95,6 +176,14 @@ class TokenTests(unittest.TestCase):
         self.assertEqual(1 if 0else 0, 0)
         self.assertRaises(SyntaxError, eval, "0 if 1Else 0")
 
+    def test_underscore_literals(self):
+        for lit in VALID_UNDERSCORE_LITERALS:
+            self.assertEqual(eval(lit), eval(lit.replace('_', '')))
+        for lit in INVALID_UNDERSCORE_LITERALS:
+            self.assertRaises(SyntaxError, eval, lit)
+        # Sanity check: no literal begins with an underscore
+        self.assertRaises(NameError, eval, "_0")
+
     def test_string_literals(self):
         x = ''; y = ""; self.assertTrue(len(x) == 0 and x == y)
         x = '\''; y = "'"; self.assertTrue(len(x) == 1 and x == y and ord(x) == 39)
diff --git a/Lib/test/test_int.py b/Lib/test/test_int.py
index 8847f4ce972..14bbd6192a0 100644
--- a/Lib/test/test_int.py
+++ b/Lib/test/test_int.py
@@ -2,6 +2,8 @@ import sys
 
 import unittest
 from test import support
+from test.test_grammar import (VALID_UNDERSCORE_LITERALS,
+                               INVALID_UNDERSCORE_LITERALS)
 
 L = [
         ('0', 0),
@@ -212,6 +214,25 @@ class IntTestCases(unittest.TestCase):
         self.assertEqual(int('2br45qc', 35), 4294967297)
         self.assertEqual(int('1z141z5', 36), 4294967297)
 
+    def test_underscores(self):
+        for lit in VALID_UNDERSCORE_LITERALS:
+            if any(ch in lit for ch in '.eEjJ'):
+                continue
+            self.assertEqual(int(lit, 0), eval(lit))
+            self.assertEqual(int(lit, 0), int(lit.replace('_', ''), 0))
+        for lit in INVALID_UNDERSCORE_LITERALS:
+            if any(ch in lit for ch in '.eEjJ'):
+                continue
+            self.assertRaises(ValueError, int, lit, 0)
+        # Additional test cases with bases != 0, only for the constructor:
+        self.assertEqual(int("1_00", 3), 9)
+        self.assertEqual(int("0_100"), 100)  # not valid as a literal!
+        self.assertEqual(int(b"1_00"), 100)  # byte underscore
+        self.assertRaises(ValueError, int, "_100")
+        self.assertRaises(ValueError, int, "+_100")
+        self.assertRaises(ValueError, int, "1__00")
+        self.assertRaises(ValueError, int, "100_")
+
     @support.cpython_only
     def test_small_ints(self):
         # Bug #3236: Return small longs from PyLong_FromString
diff --git a/Lib/test/test_tokenize.py b/Lib/test/test_tokenize.py
index 4c469a890f8..5a81a5f11a4 100644
--- a/Lib/test/test_tokenize.py
+++ b/Lib/test/test_tokenize.py
@@ -3,7 +3,9 @@ from tokenize import (tokenize, _tokenize, untokenize, NUMBER, NAME, OP,
                      STRING, ENDMARKER, ENCODING, tok_name, detect_encoding,
                      open as tokenize_open, Untokenizer)
 from io import BytesIO
-from unittest import TestCase, mock, main
+from unittest import TestCase, mock
+from test.test_grammar import (VALID_UNDERSCORE_LITERALS,
+                               INVALID_UNDERSCORE_LITERALS)
 import os
 import token
 
@@ -185,6 +187,21 @@ def k(x):
     NUMBER     '3.14e159'    (1, 4) (1, 12)
     """)
 
+    def test_underscore_literals(self):
+        def number_token(s):
+            f = BytesIO(s.encode('utf-8'))
+            for toktype, token, start, end, line in tokenize(f.readline):
+                if toktype == NUMBER:
+                    return token
+            return 'invalid token'
+        for lit in VALID_UNDERSCORE_LITERALS:
+            if '(' in lit:
+                # this won't work with compound complex inputs
+                continue
+            self.assertEqual(number_token(lit), lit)
+        for lit in INVALID_UNDERSCORE_LITERALS:
+            self.assertNotEqual(number_token(lit), lit)
+
     def test_string(self):
         # String literals
         self.check_tokenize("x = ''; y = \"\"", """\
@@ -1529,11 +1546,10 @@ class TestRoundtrip(TestCase):
         tempdir = os.path.dirname(fn) or os.curdir
         testfiles = glob.glob(os.path.join(tempdir, "test*.py"))
 
-        # Tokenize is broken on test_unicode_identifiers.py because regular
-        # expressions are broken on the obscure unicode identifiers in it.
-        # *sigh* With roundtrip extended to test the 5-tuple mode of
-        # untokenize, 7 more testfiles fail.  Remove them also until the
-        # failure is diagnosed.
+        # Tokenize is broken on test_pep3131.py because regular expressions are
+        # broken on the obscure unicode identifiers in it. *sigh*
+        # With roundtrip extended to test the 5-tuple mode of untokenize,
+        # 7 more testfiles fail.  Remove them also until the failure is diagnosed.
 
         testfiles.remove(os.path.join(tempdir, "test_unicode_identifiers.py"))
         for f in ('buffer', 'builtin', 'fileio', 'inspect', 'os', 'platform', 'sys'):
@@ -1565,4 +1581,4 @@ class TestRoundtrip(TestCase):
 
 
 if __name__ == "__main__":
-    main()
+    unittest.main()
diff --git a/Lib/test/test_types.py b/Lib/test/test_types.py
index a202196bd2f..382ca03e5ad 100644
--- a/Lib/test/test_types.py
+++ b/Lib/test/test_types.py
@@ -48,6 +48,7 @@ class TypesTests(unittest.TestCase):
     def test_float_constructor(self):
         self.assertRaises(ValueError, float, '')
         self.assertRaises(ValueError, float, '5\0')
+        self.assertRaises(ValueError, float, '5_5\0')
 
     def test_zero_division(self):
         try: 5.0 / 0.0
diff --git a/Lib/tokenize.py b/Lib/tokenize.py
index ec79ec886da..825aa906460 100644
--- a/Lib/tokenize.py
+++ b/Lib/tokenize.py
@@ -120,16 +120,17 @@ Comment = r'#[^\r\n]*'
 Ignore = Whitespace + any(r'\\\r?\n' + Whitespace) + maybe(Comment)
 Name = r'\w+'
 
-Hexnumber = r'0[xX][0-9a-fA-F]+'
-Binnumber = r'0[bB][01]+'
-Octnumber = r'0[oO][0-7]+'
-Decnumber = r'(?:0+|[1-9][0-9]*)'
+Hexnumber = r'0[xX](?:_?[0-9a-fA-F])+'
+Binnumber = r'0[bB](?:_?[01])+'
+Octnumber = r'0[oO](?:_?[0-7])+'
+Decnumber = r'(?:0(?:_?0)*|[1-9](?:_?[0-9])*)'
 Intnumber = group(Hexnumber, Binnumber, Octnumber, Decnumber)
-Exponent = r'[eE][-+]?[0-9]+'
-Pointfloat = group(r'[0-9]+\.[0-9]*', r'\.[0-9]+') + maybe(Exponent)
-Expfloat = r'[0-9]+' + Exponent
+Exponent = r'[eE][-+]?[0-9](?:_?[0-9])*'
+Pointfloat = group(r'[0-9](?:_?[0-9])*\.(?:[0-9](?:_?[0-9])*)?',
+                   r'\.[0-9](?:_?[0-9])*') + maybe(Exponent)
+Expfloat = r'[0-9](?:_?[0-9])*' + Exponent
 Floatnumber = group(Pointfloat, Expfloat)
-Imagnumber = group(r'[0-9]+[jJ]', Floatnumber + r'[jJ]')
+Imagnumber = group(r'[0-9](?:_?[0-9])*[jJ]', Floatnumber + r'[jJ]')
 Number = group(Imagnumber, Floatnumber, Intnumber)
 
 # Return the empty string, plus all of the valid string prefixes.
diff --git a/Misc/NEWS b/Misc/NEWS
index c47c4bf5b0a..dbd43a319a3 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -17,6 +17,8 @@ Core and Builtins
   efficient bytecode. Patch by Demur Rumed, design by Serhiy Storchaka,
   reviewed by Serhiy Storchaka and Victor Stinner.
 
+- Issue #26331: Implement tokenizing support for PEP 515. Patch by Georg Brandl.
+
 - Issue #27999: Make "global after use" a SyntaxError, and ditto for nonlocal.
   Patch by Ivan Levkivskyi.
 
@@ -2678,7 +2680,7 @@ Library
 - Issue #24774: Fix docstring in http.server.test. Patch from Chiu-Hsiang Hsu.
 
 - Issue #21159: Improve message in configparser.InterpolationMissingOptionError.
-  Patch from Å?ukasz Langa.
+  Patch from �?ukasz Langa.
 
 - Issue #20362: Honour TestCase.longMessage correctly in assertRegex.
   Patch from Ilia Kurenkov.
@@ -4606,7 +4608,7 @@ Library
   Based on patch by Martin Panter.
 
 - Issue #17293: uuid.getnode() now determines MAC address on AIX using netstat.
-  Based on patch by Aivars KalvÄ?ns.
+  Based on patch by Aivars Kalv�?ns.
 
 - Issue #22769: Fixed ttk.Treeview.tag_has() when called without arguments.
 
diff --git a/Modules/_decimal/_decimal.c b/Modules/_decimal/_decimal.c
index 3ba8e35ce95..fcc1f151cf5 100644
--- a/Modules/_decimal/_decimal.c
+++ b/Modules/_decimal/_decimal.c
@@ -1889,12 +1889,13 @@ is_space(enum PyUnicode_Kind kind, void *data, Py_ssize_t pos)
 /* Return the ASCII representation of a numeric Unicode string. The numeric
    string may contain ascii characters in the range [1, 127], any Unicode
    space and any unicode digit. If strip_ws is true, leading and trailing
-   whitespace is stripped.
+   whitespace is stripped. If ignore_underscores is true, underscores are
+   ignored.
 
    Return NULL if malloc fails and an empty string if invalid characters
    are found. */
 static char *
-numeric_as_ascii(const PyObject *u, int strip_ws)
+numeric_as_ascii(const PyObject *u, int strip_ws, int ignore_underscores)
 {
     enum PyUnicode_Kind kind;
     void *data;
@@ -1929,6 +1930,9 @@ numeric_as_ascii(const PyObject *u, int strip_ws)
 
     for (; j < len; j++) {
         ch = PyUnicode_READ(kind, data, j);
+        if (ignore_underscores && ch == '_') {
+            continue;
+        }
         if (0 < ch && ch <= 127) {
             *cp++ = ch;
             continue;
@@ -2011,7 +2015,7 @@ PyDecType_FromUnicode(PyTypeObject *type, const PyObject *u,
     PyObject *dec;
     char *s;
 
-    s = numeric_as_ascii(u, 0);
+    s = numeric_as_ascii(u, 0, 0);
     if (s == NULL) {
         return NULL;
     }
@@ -2031,7 +2035,7 @@ PyDecType_FromUnicodeExactWS(PyTypeObject *type, const PyObject *u,
     PyObject *dec;
     char *s;
 
-    s = numeric_as_ascii(u, 1);
+    s = numeric_as_ascii(u, 1, 1);
     if (s == NULL) {
         return NULL;
     }
diff --git a/Objects/complexobject.c b/Objects/complexobject.c
index a5bfb667c46..a9d5ec301ae 100644
--- a/Objects/complexobject.c
+++ b/Objects/complexobject.c
@@ -759,29 +759,12 @@ static PyMemberDef complex_members[] = {
 };
 
 static PyObject *
-complex_subtype_from_string(PyTypeObject *type, PyObject *v)
+complex_from_string_inner(const char *s, Py_ssize_t len, void *type)
 {
-    const char *s, *start;
-    char *end;
     double x=0.0, y=0.0, z;
     int got_bracket=0;
-    PyObject *s_buffer = NULL;
-    Py_ssize_t len;
-
-    if (PyUnicode_Check(v)) {
-        s_buffer = _PyUnicode_TransformDecimalAndSpaceToASCII(v);
-        if (s_buffer == NULL)
-            return NULL;
-        s = PyUnicode_AsUTF8AndSize(s_buffer, &len);
-        if (s == NULL)
-            goto error;
-    }
-    else {
-        PyErr_Format(PyExc_TypeError,
-            "complex() argument must be a string or a number, not '%.200s'",
-            Py_TYPE(v)->tp_name);
-        return NULL;
-    }
+    const char *start;
+    char *end;
 
     /* position on first nonblank */
     start = s;
@@ -822,7 +805,7 @@ complex_subtype_from_string(PyTypeObject *type, PyObject *v)
         if (PyErr_ExceptionMatches(PyExc_ValueError))
             PyErr_Clear();
         else
-            goto error;
+            return NULL;
     }
     if (end != s) {
         /* all 4 forms starting with <float> land here */
@@ -835,7 +818,7 @@ complex_subtype_from_string(PyTypeObject *type, PyObject *v)
                 if (PyErr_ExceptionMatches(PyExc_ValueError))
                     PyErr_Clear();
                 else
-                    goto error;
+                    return NULL;
             }
             if (end != s)
                 /* <float><signed-float>j */
@@ -890,18 +873,46 @@ complex_subtype_from_string(PyTypeObject *type, PyObject *v)
     if (s-start != len)
         goto parse_error;
 
-    Py_XDECREF(s_buffer);
-    return complex_subtype_from_doubles(type, x, y);
+    return complex_subtype_from_doubles((PyTypeObject *)type, x, y);
 
   parse_error:
     PyErr_SetString(PyExc_ValueError,
                     "complex() arg is a malformed string");
-  error:
-    Py_XDECREF(s_buffer);
     return NULL;
 }
 
 static PyObject *
+complex_subtype_from_string(PyTypeObject *type, PyObject *v)
+{
+    const char *s;
+    PyObject *s_buffer = NULL, *result = NULL;
+    Py_ssize_t len;
+
+    if (PyUnicode_Check(v)) {
+        s_buffer = _PyUnicode_TransformDecimalAndSpaceToASCII(v);
+        if (s_buffer == NULL) {
+            return NULL;
+        }
+        s = PyUnicode_AsUTF8AndSize(s_buffer, &len);
+        if (s == NULL) {
+            goto exit;
+        }
+    }
+    else {
+        PyErr_Format(PyExc_TypeError,
+            "complex() argument must be a string or a number, not '%.200s'",
+            Py_TYPE(v)->tp_name);
+        return NULL;
+    }
+
+    result = _Py_string_to_number_with_underscores(s, len, "complex", v, type,
+                                                   complex_from_string_inner);
+  exit:
+    Py_DECREF(s_buffer);
+    return result;
+}
+
+static PyObject *
 complex_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
 {
     PyObject *r, *i, *tmp;
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 0642b16ba1b..0f37618215c 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -124,11 +124,43 @@ PyFloat_FromDouble(double fval)
     return (PyObject *) op;
 }
 
+static PyObject *
+float_from_string_inner(const char *s, Py_ssize_t len, void *obj)
+{
+    double x;
+    const char *end;
+    const char *last = s + len;
+    /* strip space */
+    while (s < last && Py_ISSPACE(*s)) {
+        s++;
+    }
+
+    while (s < last - 1 && Py_ISSPACE(last[-1])) {
+        last--;
+    }
+
+    /* We don't care about overflow or underflow.  If the platform
+     * supports them, infinities and signed zeroes (on underflow) are
+     * fine. */
+    x = PyOS_string_to_double(s, (char **)&end, NULL);
+    if (end != last) {
+        PyErr_Format(PyExc_ValueError,
+                     "could not convert string to float: "
+                     "%R", obj);
+        return NULL;
+    }
+    else if (x == -1.0 && PyErr_Occurred()) {
+        return NULL;
+    }
+    else {
+        return PyFloat_FromDouble(x);
+    }
+}
+
 PyObject *
 PyFloat_FromString(PyObject *v)
 {
-    const char *s, *last, *end;
-    double x;
+    const char *s;
     PyObject *s_buffer = NULL;
     Py_ssize_t len;
     Py_buffer view = {NULL, NULL};
@@ -169,27 +201,8 @@ PyFloat_FromString(PyObject *v)
             Py_TYPE(v)->tp_name);
         return NULL;
     }
-    last = s + len;
-    /* strip space */
-    while (s < last && Py_ISSPACE(*s))
-        s++;
-    while (s < last - 1 && Py_ISSPACE(last[-1]))
-        last--;
-    /* We don't care about overflow or underflow.  If the platform
-     * supports them, infinities and signed zeroes (on underflow) are
-     * fine. */
-    x = PyOS_string_to_double(s, (char **)&end, NULL);
-    if (end != last) {
-        PyErr_Format(PyExc_ValueError,
-                     "could not convert string to float: "
-                     "%R", v);
-        result = NULL;
-    }
-    else if (x == -1.0 && PyErr_Occurred())
-        result = NULL;
-    else
-        result = PyFloat_FromDouble(x);
-
+    result = _Py_string_to_number_with_underscores(s, len, "float", v, v,
+                                                   float_from_string_inner);
     PyBuffer_Release(&view);
     Py_XDECREF(s_buffer);
     return result;
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 740b7f58861..bbf7e7183eb 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -2004,12 +2004,18 @@ unsigned char _PyLong_DigitValue[256] = {
  * non-digit (which may be *str!).  A normalized int is returned.
  * The point to this routine is that it takes time linear in the number of
  * string characters.
+ *
+ * Return values:
+ *   -1 on syntax error (exception needs to be set, *res is untouched)
+ *   0 else (exception may be set, in that case *res is set to NULL)
  */
-static PyLongObject *
-long_from_binary_base(const char **str, int base)
+static int
+long_from_binary_base(const char **str, int base, PyLongObject **res)
 {
     const char *p = *str;
     const char *start = p;
+    char prev = 0;
+    int digits = 0;
     int bits_per_char;
     Py_ssize_t n;
     PyLongObject *z;
@@ -2019,23 +2025,43 @@ long_from_binary_base(const char **str, int base)
 
     assert(base >= 2 && base <= 32 && (base & (base - 1)) == 0);
     n = base;
-    for (bits_per_char = -1; n; ++bits_per_char)
+    for (bits_per_char = -1; n; ++bits_per_char) {
         n >>= 1;
-    /* n <- total # of bits needed, while setting p to end-of-string */
-    while (_PyLong_DigitValue[Py_CHARMASK(*p)] < base)
+    }
+    /* count digits and set p to end-of-string */
+    while (_PyLong_DigitValue[Py_CHARMASK(*p)] < base || *p == '_') {
+        if (*p == '_') {
+            if (prev == '_') {
+                *str = p - 1;
+                return -1;
+            }
+        } else {
+            ++digits;
+        }
+        prev = *p;
         ++p;
+    }
+    if (prev == '_') {
+        /* Trailing underscore not allowed. */
+        *str = p - 1;
+        return -1;
+    }
+
     *str = p;
     /* n <- # of Python digits needed, = ceiling(n/PyLong_SHIFT). */
-    n = (p - start) * bits_per_char + PyLong_SHIFT - 1;
+    n = digits * bits_per_char + PyLong_SHIFT - 1;
     if (n / bits_per_char < p - start) {
         PyErr_SetString(PyExc_ValueError,
                         "int string too large to convert");
-        return NULL;
+        *res = NULL;
+        return 0;
     }
     n = n / PyLong_SHIFT;
     z = _PyLong_New(n);
-    if (z == NULL)
-        return NULL;
+    if (z == NULL) {
+        *res = NULL;
+        return 0;
+    }
     /* Read string from right, and fill in int from left; i.e.,
      * from least to most significant in both.
      */
@@ -2043,7 +2069,11 @@ long_from_binary_base(const char **str, int base)
     bits_in_accum = 0;
     pdigit = z->ob_digit;
     while (--p >= start) {
-        int k = (int)_PyLong_DigitValue[Py_CHARMASK(*p)];
+        int k;
+        if (*p == '_') {
+            continue;
+        }
+        k = (int)_PyLong_DigitValue[Py_CHARMASK(*p)];
         assert(k >= 0 && k < base);
         accum |= (twodigits)k << bits_in_accum;
         bits_in_accum += bits_per_char;
@@ -2062,7 +2092,8 @@ long_from_binary_base(const char **str, int base)
     }
     while (pdigit - z->ob_digit < n)
         *pdigit++ = 0;
-    return long_normalize(z);
+    *res = long_normalize(z);
+    return 0;
 }
 
 /* Parses an int from a bytestring. Leading and trailing whitespace will be
@@ -2087,23 +2118,29 @@ PyLong_FromString(const char *str, char **pend, int base)
                         "int() arg 2 must be >= 2 and <= 36");
         return NULL;
     }
-    while (*str != '\0' && Py_ISSPACE(Py_CHARMASK(*str)))
+    while (*str != '\0' && Py_ISSPACE(Py_CHARMASK(*str))) {
         str++;
-    if (*str == '+')
+    }
+    if (*str == '+') {
         ++str;
+    }
     else if (*str == '-') {
         ++str;
         sign = -1;
     }
     if (base == 0) {
-        if (str[0] != '0')
+        if (str[0] != '0') {
             base = 10;
-        else if (str[1] == 'x' || str[1] == 'X')
+        }
+        else if (str[1] == 'x' || str[1] == 'X') {
             base = 16;
-        else if (str[1] == 'o' || str[1] == 'O')
+        }
+        else if (str[1] == 'o' || str[1] == 'O') {
             base = 8;
-        else if (str[1] == 'b' || str[1] == 'B')
+        }
+        else if (str[1] == 'b' || str[1] == 'B') {
             base = 2;
+        }
         else {
             /* "old" (C-style) octal literal, now invalid.
                it might still be zero though */
@@ -2114,12 +2151,26 @@ PyLong_FromString(const char *str, char **pend, int base)
     if (str[0] == '0' &&
         ((base == 16 && (str[1] == 'x' || str[1] == 'X')) ||
          (base == 8  && (str[1] == 'o' || str[1] == 'O')) ||
-         (base == 2  && (str[1] == 'b' || str[1] == 'B'))))
+         (base == 2  && (str[1] == 'b' || str[1] == 'B')))) {
         str += 2;
+        /* One underscore allowed here. */
+        if (*str == '_') {
+            ++str;
+        }
+    }
+    if (str[0] == '_') {
+	    /* May not start with underscores. */
+	    goto onError;
+    }
 
     start = str;
-    if ((base & (base - 1)) == 0)
-        z = long_from_binary_base(&str, base);
+    if ((base & (base - 1)) == 0) {
+        int res = long_from_binary_base(&str, base, &z);
+        if (res < 0) {
+            /* Syntax error. */
+            goto onError;
+        }
+    }
     else {
 /***
 Binary bases can be converted in time linear in the number of digits, because
@@ -2208,11 +2259,13 @@ digit beyond the first.
 ***/
         twodigits c;           /* current input character */
         Py_ssize_t size_z;
+        int digits = 0;
         int i;
         int convwidth;
         twodigits convmultmax, convmult;
         digit *pz, *pzstop;
-        const char* scan;
+        const char *scan, *lastdigit;
+        char prev = 0;
 
         static double log_base_BASE[37] = {0.0e0,};
         static int convwidth_base[37] = {0,};
@@ -2226,8 +2279,9 @@ digit beyond the first.
                                    log((double)PyLong_BASE));
             for (;;) {
                 twodigits next = convmax * base;
-                if (next > PyLong_BASE)
+                if (next > PyLong_BASE) {
                     break;
+                }
                 convmax = next;
                 ++i;
             }
@@ -2238,21 +2292,43 @@ digit beyond the first.
 
         /* Find length of the string of numeric characters. */
         scan = str;
-        while (_PyLong_DigitValue[Py_CHARMASK(*scan)] < base)
+        lastdigit = str;
+
+        while (_PyLong_DigitValue[Py_CHARMASK(*scan)] < base || *scan == '_') {
+            if (*scan == '_') {
+                if (prev == '_') {
+                    /* Only one underscore allowed. */
+                    str = lastdigit + 1;
+                    goto onError;
+                }
+            }
+            else {
+                ++digits;
+                lastdigit = scan;
+            }
+            prev = *scan;
             ++scan;
+        }
+        if (prev == '_') {
+            /* Trailing underscore not allowed. */
+            /* Set error pointer to first underscore. */
+            str = lastdigit + 1;
+            goto onError;
+        }
 
         /* Create an int object that can contain the largest possible
          * integer with this base and length.  Note that there's no
          * need to initialize z->ob_digit -- no slot is read up before
          * being stored into.
          */
-        size_z = (Py_ssize_t)((scan - str) * log_base_BASE[base]) + 1;
+        size_z = (Py_ssize_t)(digits * log_base_BASE[base]) + 1;
         /* Uncomment next line to test exceedingly rare copy code */
         /* size_z = 1; */
         assert(size_z > 0);
         z = _PyLong_New(size_z);
-        if (z == NULL)
+        if (z == NULL) {
             return NULL;
+        }
         Py_SIZE(z) = 0;
 
         /* `convwidth` consecutive input digits are treated as a single
@@ -2263,9 +2339,17 @@ digit beyond the first.
 
         /* Work ;-) */
         while (str < scan) {
+            if (*str == '_') {
+                str++;
+                continue;
+            }
             /* grab up to convwidth digits from the input string */
             c = (digit)_PyLong_DigitValue[Py_CHARMASK(*str++)];
-            for (i = 1; i < convwidth && str != scan; ++i, ++str) {
+            for (i = 1; i < convwidth && str != scan; ++str) {
+                if (*str == '_') {
+                    continue;
+                }
+                i++;
                 c = (twodigits)(c *  base +
                                 (int)_PyLong_DigitValue[Py_CHARMASK(*str)]);
                 assert(c < PyLong_BASE);
@@ -2277,8 +2361,9 @@ digit beyond the first.
              */
             if (i != convwidth) {
                 convmult = base;
-                for ( ; i > 1; --i)
+                for ( ; i > 1; --i) {
                     convmult *= base;
+                }
             }
 
             /* Multiply z by convmult, and add c. */
@@ -2316,41 +2401,51 @@ digit beyond the first.
             }
         }
     }
-    if (z == NULL)
+    if (z == NULL) {
         return NULL;
+    }
     if (error_if_nonzero) {
         /* reset the base to 0, else the exception message
            doesn't make too much sense */
         base = 0;
-        if (Py_SIZE(z) != 0)
+        if (Py_SIZE(z) != 0) {
             goto onError;
+        }
         /* there might still be other problems, therefore base
            remains zero here for the same reason */
     }
-    if (str == start)
+    if (str == start) {
         goto onError;
-    if (sign < 0)
+    }
+    if (sign < 0) {
         Py_SIZE(z) = -(Py_SIZE(z));
-    while (*str && Py_ISSPACE(Py_CHARMASK(*str)))
+    }
+    while (*str && Py_ISSPACE(Py_CHARMASK(*str))) {
         str++;
-    if (*str != '\0')
+    }
+    if (*str != '\0') {
         goto onError;
+    }
     long_normalize(z);
     z = maybe_small_long(z);
-    if (z == NULL)
+    if (z == NULL) {
         return NULL;
-    if (pend != NULL)
+    }
+    if (pend != NULL) {
         *pend = (char *)str;
+    }
     return (PyObject *) z;
 
   onError:
-    if (pend != NULL)
+    if (pend != NULL) {
         *pend = (char *)str;
+    }
     Py_XDECREF(z);
     slen = strlen(orig_str) < 200 ? strlen(orig_str) : 200;
     strobj = PyUnicode_FromStringAndSize(orig_str, slen);
-    if (strobj == NULL)
+    if (strobj == NULL) {
         return NULL;
+    }
     PyErr_Format(PyExc_ValueError,
                  "invalid literal for int() with base %d: %.200R",
                  base, strobj);
diff --git a/Parser/tokenizer.c b/Parser/tokenizer.c
index d1e5d352692..a29ba472aa3 100644
--- a/Parser/tokenizer.c
+++ b/Parser/tokenizer.c
@@ -1333,6 +1333,28 @@ verify_identifier(struct tok_state *tok)
 }
 #endif
 
+static int
+tok_decimal_tail(struct tok_state *tok)
+{
+    int c;
+
+    while (1) {
+        do {
+            c = tok_nextc(tok);
+        } while (isdigit(c));
+        if (c != '_') {
+            break;
+        }
+        c = tok_nextc(tok);
+        if (!isdigit(c)) {
+            tok->done = E_TOKEN;
+            tok_backup(tok, c);
+            return 0;
+        }
+    }
+    return c;
+}
+
 /* Get next token, after space stripping etc. */
 
 static int
@@ -1353,17 +1375,20 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
         tok->atbol = 0;
         for (;;) {
             c = tok_nextc(tok);
-            if (c == ' ')
+            if (c == ' ') {
                 col++, altcol++;
+            }
             else if (c == '\t') {
                 col = (col/tok->tabsize + 1) * tok->tabsize;
                 altcol = (altcol/tok->alttabsize + 1)
                     * tok->alttabsize;
             }
-            else if (c == '\014') /* Control-L (formfeed) */
+            else if (c == '\014')  {/* Control-L (formfeed) */
                 col = altcol = 0; /* For Emacs users */
-            else
+            }
+            else {
                 break;
+            }
         }
         tok_backup(tok, c);
         if (c == '#' || c == '\n') {
@@ -1372,10 +1397,12 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                not passed to the parser as NEWLINE tokens,
                except *totally* empty lines in interactive
                mode, which signal the end of a command group. */
-            if (col == 0 && c == '\n' && tok->prompt != NULL)
+            if (col == 0 && c == '\n' && tok->prompt != NULL) {
                 blankline = 0; /* Let it through */
-            else
+            }
+            else {
                 blankline = 1; /* Ignore completely */
+            }
             /* We can't jump back right here since we still
                may need to skip to the end of a comment */
         }
@@ -1383,8 +1410,9 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
             if (col == tok->indstack[tok->indent]) {
                 /* No change */
                 if (altcol != tok->altindstack[tok->indent]) {
-                    if (indenterror(tok))
+                    if (indenterror(tok)) {
                         return ERRORTOKEN;
+                    }
                 }
             }
             else if (col > tok->indstack[tok->indent]) {
@@ -1395,8 +1423,9 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                     return ERRORTOKEN;
                 }
                 if (altcol <= tok->altindstack[tok->indent]) {
-                    if (indenterror(tok))
+                    if (indenterror(tok)) {
                         return ERRORTOKEN;
+                    }
                 }
                 tok->pendin++;
                 tok->indstack[++tok->indent] = col;
@@ -1415,8 +1444,9 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                     return ERRORTOKEN;
                 }
                 if (altcol != tok->altindstack[tok->indent]) {
-                    if (indenterror(tok))
+                    if (indenterror(tok)) {
                         return ERRORTOKEN;
+                    }
                 }
             }
         }
@@ -1462,9 +1492,11 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
     tok->start = tok->cur - 1;
 
     /* Skip comment */
-    if (c == '#')
-        while (c != EOF && c != '\n')
+    if (c == '#') {
+        while (c != EOF && c != '\n') {
             c = tok_nextc(tok);
+        }
+    }
 
     /* Check for EOF and errors now */
     if (c == EOF) {
@@ -1481,27 +1513,35 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                 saw_b = 1;
             /* Since this is a backwards compatibility support literal we don't
                want to support it in arbitrary order like byte literals. */
-            else if (!(saw_b || saw_u || saw_r || saw_f) && (c == 'u' || c == 'U'))
+            else if (!(saw_b || saw_u || saw_r || saw_f)
+                     && (c == 'u'|| c == 'U')) {
                 saw_u = 1;
+            }
             /* ur"" and ru"" are not supported */
-            else if (!(saw_r || saw_u) && (c == 'r' || c == 'R'))
+            else if (!(saw_r || saw_u) && (c == 'r' || c == 'R')) {
                 saw_r = 1;
-            else if (!(saw_f || saw_b || saw_u) && (c == 'f' || c == 'F'))
+            }
+            else if (!(saw_f || saw_b || saw_u) && (c == 'f' || c == 'F')) {
                 saw_f = 1;
-            else
+            }
+            else {
                 break;
+            }
             c = tok_nextc(tok);
-            if (c == '"' || c == '\'')
+            if (c == '"' || c == '\'') {
                 goto letter_quote;
+            }
         }
         while (is_potential_identifier_char(c)) {
-            if (c >= 128)
+            if (c >= 128) {
                 nonascii = 1;
+            }
             c = tok_nextc(tok);
         }
         tok_backup(tok, c);
-        if (nonascii && !verify_identifier(tok))
+        if (nonascii && !verify_identifier(tok)) {
             return ERRORTOKEN;
+        }
         *p_start = tok->start;
         *p_end = tok->cur;
 
@@ -1510,10 +1550,12 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
             /* Current token length is 5. */
             if (tok->async_def) {
                 /* We're inside an 'async def' function. */
-                if (memcmp(tok->start, "async", 5) == 0)
+                if (memcmp(tok->start, "async", 5) == 0) {
                     return ASYNC;
-                if (memcmp(tok->start, "await", 5) == 0)
+                }
+                if (memcmp(tok->start, "await", 5) == 0) {
                     return AWAIT;
+                }
             }
             else if (memcmp(tok->start, "async", 5) == 0) {
                 /* The current token is 'async'.
@@ -1546,8 +1588,9 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
     /* Newline */
     if (c == '\n') {
         tok->atbol = 1;
-        if (blankline || tok->level > 0)
+        if (blankline || tok->level > 0) {
             goto nextline;
+        }
         *p_start = tok->start;
         *p_end = tok->cur - 1; /* Leave '\n' out of the string */
         tok->cont_line = 0;
@@ -1570,11 +1613,13 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                 *p_start = tok->start;
                 *p_end = tok->cur;
                 return ELLIPSIS;
-            } else {
+            }
+            else {
                 tok_backup(tok, c);
             }
             tok_backup(tok, '.');
-        } else {
+        }
+        else {
             tok_backup(tok, c);
         }
         *p_start = tok->start;
@@ -1588,59 +1633,93 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
             /* Hex, octal or binary -- maybe. */
             c = tok_nextc(tok);
             if (c == 'x' || c == 'X') {
-
                 /* Hex */
                 c = tok_nextc(tok);
-                if (!isxdigit(c)) {
-                    tok->done = E_TOKEN;
-                    tok_backup(tok, c);
-                    return ERRORTOKEN;
-                }
                 do {
-                    c = tok_nextc(tok);
-                } while (isxdigit(c));
+                    if (c == '_') {
+                        c = tok_nextc(tok);
+                    }
+                    if (!isxdigit(c)) {
+                        tok->done = E_TOKEN;
+                        tok_backup(tok, c);
+                        return ERRORTOKEN;
+                    }
+                    do {
+                        c = tok_nextc(tok);
+                    } while (isxdigit(c));
+                } while (c == '_');
             }
             else if (c == 'o' || c == 'O') {
                 /* Octal */
                 c = tok_nextc(tok);
-                if (c < '0' || c >= '8') {
-                    tok->done = E_TOKEN;
-                    tok_backup(tok, c);
-                    return ERRORTOKEN;
-                }
                 do {
-                    c = tok_nextc(tok);
-                } while ('0' <= c && c < '8');
+                    if (c == '_') {
+                        c = tok_nextc(tok);
+                    }
+                    if (c < '0' || c >= '8') {
+                        tok->done = E_TOKEN;
+                        tok_backup(tok, c);
+                        return ERRORTOKEN;
+                    }
+                    do {
+                        c = tok_nextc(tok);
+                    } while ('0' <= c && c < '8');
+                } while (c == '_');
             }
             else if (c == 'b' || c == 'B') {
                 /* Binary */
                 c = tok_nextc(tok);
-                if (c != '0' && c != '1') {
-                    tok->done = E_TOKEN;
-                    tok_backup(tok, c);
-                    return ERRORTOKEN;
-                }
                 do {
-                    c = tok_nextc(tok);
-                } while (c == '0' || c == '1');
+                    if (c == '_') {
+                        c = tok_nextc(tok);
+                    }
+                    if (c != '0' && c != '1') {
+                        tok->done = E_TOKEN;
+                        tok_backup(tok, c);
+                        return ERRORTOKEN;
+                    }
+                    do {
+                        c = tok_nextc(tok);
+                    } while (c == '0' || c == '1');
+                } while (c == '_');
             }
             else {
                 int nonzero = 0;
                 /* maybe old-style octal; c is first char of it */
                 /* in any case, allow '0' as a literal */
-                while (c == '0')
+                while (1) {
+                    if (c == '_') {
+                        c = tok_nextc(tok);
+                        if (!isdigit(c)) {
+                            tok->done = E_TOKEN;
+                            tok_backup(tok, c);
+                            return ERRORTOKEN;
+                        }
+                    }
+                    if (c != '0') {
+                        break;
+                    }
                     c = tok_nextc(tok);
-                while (isdigit(c)) {
+                }
+                if (isdigit(c)) {
                     nonzero = 1;
-                    c = tok_nextc(tok);
+                    c = tok_decimal_tail(tok);
+                    if (c == 0) {
+                        return ERRORTOKEN;
+                    }
                 }
-                if (c == '.')
+                if (c == '.') {
+                    c = tok_nextc(tok);
                     goto fraction;
-                else if (c == 'e' || c == 'E')
+                }
+                else if (c == 'e' || c == 'E') {
                     goto exponent;
-                else if (c == 'j' || c == 'J')
+                }
+                else if (c == 'j' || c == 'J') {
                     goto imaginary;
+                }
                 else if (nonzero) {
+                    /* Old-style octal: now disallowed. */
                     tok->done = E_TOKEN;
                     tok_backup(tok, c);
                     return ERRORTOKEN;
@@ -1649,17 +1728,22 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
         }
         else {
             /* Decimal */
-            do {
-                c = tok_nextc(tok);
-            } while (isdigit(c));
+            c = tok_decimal_tail(tok);
+            if (c == 0) {
+                return ERRORTOKEN;
+            }
             {
                 /* Accept floating point numbers. */
                 if (c == '.') {
+                    c = tok_nextc(tok);
         fraction:
                     /* Fraction */
-                    do {
-                        c = tok_nextc(tok);
-                    } while (isdigit(c));
+                    if (isdigit(c)) {
+                        c = tok_decimal_tail(tok);
+                        if (c == 0) {
+                            return ERRORTOKEN;
+                        }
+                    }
                 }
                 if (c == 'e' || c == 'E') {
                     int e;
@@ -1681,14 +1765,16 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                         *p_end = tok->cur;
                         return NUMBER;
                     }
-                    do {
-                        c = tok_nextc(tok);
-                    } while (isdigit(c));
+                    c = tok_decimal_tail(tok);
+                    if (c == 0) {
+                        return ERRORTOKEN;
+                    }
                 }
-                if (c == 'j' || c == 'J')
+                if (c == 'j' || c == 'J') {
                     /* Imaginary part */
         imaginary:
                     c = tok_nextc(tok);
+                }
             }
         }
         tok_backup(tok, c);
@@ -1708,22 +1794,27 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
         c = tok_nextc(tok);
         if (c == quote) {
             c = tok_nextc(tok);
-            if (c == quote)
+            if (c == quote) {
                 quote_size = 3;
-            else
+            }
+            else {
                 end_quote_size = 1;     /* empty string found */
+            }
         }
-        if (c != quote)
+        if (c != quote) {
             tok_backup(tok, c);
+        }
 
         /* Get rest of string */
         while (end_quote_size != quote_size) {
             c = tok_nextc(tok);
             if (c == EOF) {
-                if (quote_size == 3)
+                if (quote_size == 3) {
                     tok->done = E_EOFS;
-                else
+                }
+                else {
                     tok->done = E_EOLS;
+                }
                 tok->cur = tok->inp;
                 return ERRORTOKEN;
             }
@@ -1732,12 +1823,14 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                 tok->cur = tok->inp;
                 return ERRORTOKEN;
             }
-            if (c == quote)
+            if (c == quote) {
                 end_quote_size += 1;
+            }
             else {
                 end_quote_size = 0;
-                if (c == '\\')
+                if (c == '\\') {
                     tok_nextc(tok);  /* skip escaped char */
+                }
             }
         }
 
@@ -1767,7 +1860,8 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
             int token3 = PyToken_ThreeChars(c, c2, c3);
             if (token3 != OP) {
                 token = token3;
-            } else {
+            }
+            else {
                 tok_backup(tok, c3);
             }
             *p_start = tok->start;
diff --git a/Python/ast.c b/Python/ast.c
index 37193329c86..dcaa697a38d 100644
--- a/Python/ast.c
+++ b/Python/ast.c
@@ -4018,7 +4018,7 @@ ast_for_stmt(struct compiling *c, const node *n)
 }
 
 static PyObject *
-parsenumber(struct compiling *c, const char *s)
+parsenumber_raw(struct compiling *c, const char *s)
 {
     const char *end;
     long x;
@@ -4061,6 +4061,31 @@ parsenumber(struct compiling *c, const char *s)
 }
 
 static PyObject *
+parsenumber(struct compiling *c, const char *s)
+{
+    char *dup, *end;
+    PyObject *res = NULL;
+
+    assert(s != NULL);
+
+    if (strchr(s, '_') == NULL) {
+        return parsenumber_raw(c, s);
+    }
+    /* Create a duplicate without underscores. */
+    dup = PyMem_Malloc(strlen(s) + 1);
+    end = dup;
+    for (; *s; s++) {
+        if (*s != '_') {
+            *end++ = *s;
+        }
+    }
+    *end = '\0';
+    res = parsenumber_raw(c, dup);
+    PyMem_Free(dup);
+    return res;
+}
+
+static PyObject *
 decode_utf8(struct compiling *c, const char **sPtr, const char *end)
 {
     const char *s, *t;
diff --git a/Python/pystrtod.c b/Python/pystrtod.c
index 5f3af92dca6..64d0c52e487 100644
--- a/Python/pystrtod.c
+++ b/Python/pystrtod.c
@@ -370,6 +370,72 @@ PyOS_string_to_double(const char *s,
     return result;
 }
 
+/* Remove underscores that follow the underscore placement rule from
+   the string and then call the `innerfunc` function on the result.
+   It should return a new object or NULL on exception.
+
+   `what` is used for the error message emitted when underscores are detected
+   that don't follow the rule. `arg` is an opaque pointer passed to the inner
+   function.
+
+   This is used to implement underscore-agnostic conversion for floats
+   and complex numbers.
+*/
+PyObject *
+_Py_string_to_number_with_underscores(
+    const char *s, Py_ssize_t orig_len, const char *what, PyObject *obj, void *arg,
+    PyObject *(*innerfunc)(const char *, Py_ssize_t, void *))
+{
+    char prev;
+    const char *p, *last;
+    char *dup, *end;
+    PyObject *result;
+
+    if (strchr(s, '_') == NULL) {
+        return innerfunc(s, orig_len, arg);
+    }
+
+    dup = PyMem_Malloc(orig_len + 1);
+    end = dup;
+    prev = '\0';
+    last = s + orig_len;
+    for (p = s; *p; p++) {
+        if (*p == '_') {
+            /* Underscores are only allowed after digits. */
+            if (!(prev >= '0' && prev <= '9')) {
+                goto error;
+            }
+        }
+        else {
+            *end++ = *p;
+            /* Underscores are only allowed before digits. */
+            if (prev == '_' && !(*p >= '0' && *p <= '9')) {
+                goto error;
+            }
+        }
+        prev = *p;
+    }
+    /* Underscores are not allowed at the end. */
+    if (prev == '_') {
+        goto error;
+    }
+    /* No embedded NULs allowed. */
+    if (p != last) {
+        goto error;
+    }
+    *end = '\0';
+    result = innerfunc(dup, end - dup, arg);
+    PyMem_Free(dup);
+    return result;
+
+  error:
+    PyMem_Free(dup);
+    PyErr_Format(PyExc_ValueError,
+		 "could not convert string to %s: "
+		 "%R", what, obj);
+    return NULL;
+}
+
 #ifdef PY_NO_SHORT_FLOAT_REPR
 
 /* Given a string that may have a decimal point in the current