From 8cf8d31ce701235491a0761236cd9f9dcf55146c Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 3 Dec 2022 17:05:53 +0000
Subject: [PATCH 01/31] Add '.f' formatting for Fraction objects

---
 Lib/fractions.py           |  99 +++++++++++++++++++++
 Lib/test/test_fractions.py | 177 +++++++++++++++++++++++++++++++++++++
 2 files changed, 276 insertions(+)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 75c7df14e1b9c7..1d64910724d87d 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -310,6 +310,105 @@ def __str__(self):
         else:
             return '%s/%s' % (self._numerator, self._denominator)
 
+    def __format__(self, format_spec, /):
+        """Format this fraction according to the given format specification."""
+
+        # Backwards compatiblility with existing formatting.
+        if not format_spec:
+            return str(self)
+
+        # Pattern matcher for the format spec; only supports "f" so far
+        FORMAT_SPEC_MATCHER = re.compile(r"""
+            (?:
+                (?P<fill>.)?
+                (?P<align>[<>=^])
+            )?
+            (?P<sign>[-+ ]?)
+            (?P<alt>\#)?
+            (?P<zeropad>0(?=\d))?
+            (?P<minimumwidth>\d+)?
+            (?P<thousands_sep>[,_])?
+            (?:\.(?P<precision>\d+))?
+            f
+        """, re.DOTALL | re.VERBOSE).fullmatch
+
+        # Validate and parse the format specifier.
+        match = FORMAT_SPEC_MATCHER(format_spec)
+        if match is None:
+            raise ValueError(
+                f"Invalid format specifier {format_spec!r} "
+                f"for object of type {type(self).__name__!r}"
+            )
+        elif match["align"] is not None and match["zeropad"] is not None:
+            # Avoid the temptation to guess.
+            raise ValueError(
+                f"Invalid format specifier {format_spec!r} "
+                f"for object of type {type(self).__name__!r}; "
+                "can't use explicit alignment when zero-padding"
+            )
+        else:
+            fill = match["fill"] or " "
+            align = match["align"] or ">"
+            pos_sign = "" if match["sign"] == "-" else match["sign"]
+            neg_sign = "-"
+            alternate_form = bool(match["alt"])
+            zeropad = bool(match["zeropad"])
+            minimumwidth = int(match["minimumwidth"] or "0")
+            thousands_sep = match["thousands_sep"]
+            precision = int(match["precision"] or "6")
+
+        # Get sign and output digits for the target number
+        negative = self < 0
+        digits = str(round(abs(self) * 10**precision))
+
+        # Assemble the output: before padding, it has the form
+        # f"{sign}{leading}{trailing}", where `leading` includes thousands
+        # separators if necessary, and `trailing` includes the decimal
+        # separator where appropriate.
+        digits = digits.zfill(precision + 1)
+        dot_pos = len(digits) - precision
+        sign = neg_sign if negative else pos_sign
+        separator = "." if precision or alternate_form else ""
+        trailing = separator + digits[dot_pos:]
+        leading = digits[:dot_pos]
+
+        # Do zero padding if required.
+        if zeropad:
+            min_leading = minimumwidth - len(sign) - len(trailing)
+            # When adding thousands separators, they'll be added to the
+            # zero-padded portion too, so we need to compensate.
+            leading = leading.zfill(
+                3 * min_leading // 4 + 1 if thousands_sep else min_leading
+            )
+
+        # Insert thousands separators if required.
+        if thousands_sep:
+            first_pos = 1 + (len(leading) - 1) % 3
+            leading = leading[:first_pos] + "".join(
+                thousands_sep + leading[pos:pos+3]
+                for pos in range(first_pos, len(leading), 3)
+            )
+
+        after_sign = leading + trailing
+
+        # Pad if a minimum width was given and we haven't already zero padded.
+        if zeropad or minimumwidth is None:
+            result = sign + after_sign
+        else:
+            padding = fill * (minimumwidth - len(sign) - len(after_sign))
+            if align == ">":
+                result = padding + sign + after_sign
+            elif align == "<":
+                result = sign + after_sign + padding
+            elif align == "=":
+                result = sign + padding + after_sign
+            else:
+                # Centered, with a leftwards bias when padding length is odd.
+                assert align == "^"
+                half = len(padding)//2
+                result = padding[:half] + sign + after_sign + padding[half:]
+        return result
+
     def _operator_fallbacks(monomorphic_operator, fallback_operator):
         """Generates forward and reverse operators given a purely-rational
         operator and a function from the operator module.
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 7fa9dbea905b59..f448e85a68ae74 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -830,6 +830,183 @@ def denominator(self):
         self.assertEqual(type(f.numerator), myint)
         self.assertEqual(type(f.denominator), myint)
 
+    def test_format(self):
+        # Triples (fraction, specification, expected_result)
+        testcases = [
+            # Case inherited from object - equivalent to str()
+            (F(1, 3), '', '1/3'),
+            (F(-1, 3), '', '-1/3'),
+            # Simple .f formatting
+            (F(0, 1), '.2f', '0.00'),
+            (F(1, 3), '.2f', '0.33'),
+            (F(2, 3), '.2f', '0.67'),
+            (F(4, 3), '.2f', '1.33'),
+            (F(1, 8), '.2f', '0.12'),
+            (F(3, 8), '.2f', '0.38'),
+            (F(1, 13), '.2f', '0.08'),
+            (F(1, 199), '.2f', '0.01'),
+            (F(1, 200), '.2f', '0.00'),
+            (F(22, 7), '.5f', '3.14286'),
+            (F('399024789'), '.2f', '399024789.00'),
+            # Large precision (more than float can provide)
+            (F(104348, 33215), '.50f',
+             '3.14159265392142104470871594159265392142104470871594'),
+            # Precision defaults to 6 if not given
+            (F(22, 7), 'f', '3.142857'),
+            (F(0), 'f', '0.000000'),
+            (F(-22, 7), 'f', '-3.142857'),
+            # Round-ties-to-even checks
+            (F('1.225'), '.2f', '1.22'),
+            (F('1.2250000001'), '.2f', '1.23'),
+            (F('1.2349999999'), '.2f', '1.23'),
+            (F('1.235'), '.2f', '1.24'),
+            (F('1.245'), '.2f', '1.24'),
+            (F('1.2450000001'), '.2f', '1.25'),
+            (F('1.2549999999'), '.2f', '1.25'),
+            (F('1.255'), '.2f', '1.26'),
+            (F('-1.225'), '.2f', '-1.22'),
+            (F('-1.2250000001'), '.2f', '-1.23'),
+            (F('-1.2349999999'), '.2f', '-1.23'),
+            (F('-1.235'), '.2f', '-1.24'),
+            (F('-1.245'), '.2f', '-1.24'),
+            (F('-1.2450000001'), '.2f', '-1.25'),
+            (F('-1.2549999999'), '.2f', '-1.25'),
+            (F('-1.255'), '.2f', '-1.26'),
+            # Negatives and sign handling
+            (F(2, 3), '.2f', '0.67'),
+            (F(2, 3), '-.2f', '0.67'),
+            (F(2, 3), '+.2f', '+0.67'),
+            (F(2, 3), ' .2f', ' 0.67'),
+            (F(-2, 3), '.2f', '-0.67'),
+            (F(-2, 3), '-.2f', '-0.67'),
+            (F(-2, 3), '+.2f', '-0.67'),
+            (F(-2, 3), ' .2f', '-0.67'),
+            # Formatting to zero places
+            (F(1, 2), '.0f', '0'),
+            (F(22, 7), '.0f', '3'),
+            (F(-22, 7), '.0f', '-3'),
+            # Formatting to zero places, alternate form
+            (F(1, 2), '#.0f', '0.'),
+            (F(22, 7), '#.0f', '3.'),
+            (F(-22, 7), '#.0f', '-3.'),
+            # Corner-case: leading zeros are allowed in the precision
+            (F(2, 3), '.02f', '0.67'),
+            (F(22, 7), '.000f', '3'),
+            # Specifying a minimum width
+            (F(2, 3), '6.2f', '  0.67'),
+            (F(12345), '6.2f', '12345.00'),
+            (F(12345), '12f', '12345.000000'),
+            # Fill and alignment
+            (F(2, 3), '>6.2f', '  0.67'),
+            (F(2, 3), '<6.2f', '0.67  '),
+            (F(2, 3), '^3.2f', '0.67'),
+            (F(2, 3), '^4.2f', '0.67'),
+            (F(2, 3), '^5.2f', '0.67 '),
+            (F(2, 3), '^6.2f', ' 0.67 '),
+            (F(2, 3), '^7.2f', ' 0.67  '),
+            (F(2, 3), '^8.2f', '  0.67  '),
+            # '=' alignment
+            (F(-2, 3), '=+8.2f', '-   0.67'),
+            (F(2, 3), '=+8.2f', '+   0.67'),
+            # Fill character
+            (F(-2, 3), 'X>3.2f', '-0.67'),
+            (F(-2, 3), 'X>7.2f', 'XX-0.67'),
+            (F(-2, 3), 'X<7.2f', '-0.67XX'),
+            (F(-2, 3), 'X^7.2f', 'X-0.67X'),
+            (F(-2, 3), 'X=7.2f', '-XX0.67'),
+            (F(-2, 3), ' >7.2f', '  -0.67'),
+            # Corner cases: weird fill characters
+            (F(-2, 3), '\x00>7.2f', '\x00\x00-0.67'),
+            (F(-2, 3), '\n>7.2f', '\n\n-0.67'),
+            (F(-2, 3), '\t>7.2f', '\t\t-0.67'),
+            # Zero-padding
+            (F(-2, 3), '07.2f', '-000.67'),
+            (F(-2, 3), '-07.2f', '-000.67'),
+            (F(2, 3), '+07.2f', '+000.67'),
+            (F(2, 3), ' 07.2f', ' 000.67'),
+            (F(2, 3), '0.2f', '0.67'),
+            # Thousands separator (only affects portion before the point)
+            (F(2, 3), ',.2f', '0.67'),
+            (F(2, 3), ',.7f', '0.6666667'),
+            (F('123456.789'), ',.2f', '123,456.79'),
+            (F('1234567'), ',.2f', '1,234,567.00'),
+            (F('12345678'), ',.2f', '12,345,678.00'),
+            (F('12345678'), ',f', '12,345,678.000000'),
+            # Underscore as thousands separator
+            (F(2, 3), '_.2f', '0.67'),
+            (F(2, 3), '_.7f', '0.6666667'),
+            (F('123456.789'), '_.2f', '123_456.79'),
+            (F('1234567'), '_.2f', '1_234_567.00'),
+            (F('12345678'), '_.2f', '12_345_678.00'),
+            # Thousands and zero-padding
+            (F('1234.5678'), '07,.2f', '1,234.57'),
+            (F('1234.5678'), '08,.2f', '1,234.57'),
+            (F('1234.5678'), '09,.2f', '01,234.57'),
+            (F('1234.5678'), '010,.2f', '001,234.57'),
+            (F('1234.5678'), '011,.2f', '0,001,234.57'),
+            (F('1234.5678'), '012,.2f', '0,001,234.57'),
+            (F('1234.5678'), '013,.2f', '00,001,234.57'),
+            (F('1234.5678'), '014,.2f', '000,001,234.57'),
+            (F('1234.5678'), '015,.2f', '0,000,001,234.57'),
+            (F('1234.5678'), '016,.2f', '0,000,001,234.57'),
+            (F('-1234.5678'), '07,.2f', '-1,234.57'),
+            (F('-1234.5678'), '08,.2f', '-1,234.57'),
+            (F('-1234.5678'), '09,.2f', '-1,234.57'),
+            (F('-1234.5678'), '010,.2f', '-01,234.57'),
+            (F('-1234.5678'), '011,.2f', '-001,234.57'),
+            (F('-1234.5678'), '012,.2f', '-0,001,234.57'),
+            (F('-1234.5678'), '013,.2f', '-0,001,234.57'),
+            (F('-1234.5678'), '014,.2f', '-00,001,234.57'),
+            (F('-1234.5678'), '015,.2f', '-000,001,234.57'),
+            (F('-1234.5678'), '016,.2f', '-0,000,001,234.57'),
+            # Corner case: no decimal point
+            (F('-1234.5678'), '06,.0f', '-1,235'),
+            (F('-1234.5678'), '07,.0f', '-01,235'),
+            (F('-1234.5678'), '08,.0f', '-001,235'),
+            (F('-1234.5678'), '09,.0f', '-0,001,235'),
+            # Corner-case - zero-padding specified through fill and align
+            # instead of the zero-pad character - in this case, treat '0' as a
+            # regular fill character and don't attempt to insert commas into
+            # the filled portion. This differs from the int and float
+            # behaviour.
+            (F('1234.5678'), '0=12,.2f', '00001,234.57'),
+            # Corner case where it's not clear whether the '0' indicates zero
+            # padding or gives the minimum width, but there's still an obvious
+            # answer to give. We want this to work in case the minimum width
+            # is being inserted programmatically: spec = f'{width}.2f'.
+            (F('12.34'), '0.2f', '12.34'),
+            (F('12.34'), 'X>0.2f', '12.34'),
+        ]
+        for fraction, spec, expected in testcases:
+            with self.subTest(fraction=fraction, spec=spec):
+                self.assertEqual(format(fraction, spec), expected)
+
+    def test_invalid_formats(self):
+        fraction = F(2, 3)
+        with self.assertRaises(TypeError):
+            format(fraction, None)
+
+        invalid_specs = [
+            "Q6f",  # regression test
+            # illegal to use fill or alignment when zero padding
+            "X>010f",
+            "X<010f",
+            "X^010f",
+            "X=010f",
+            "0>010f",
+            "0<010f",
+            "0^010f",
+            "0=010f",
+            ">010f",
+            "<010f",
+            "^010f",
+            "=010f",
+        ]
+        for spec in invalid_specs:
+            with self.subTest(spec=spec):
+                with self.assertRaises(ValueError):
+                    format(fraction, spec)
+
 
 if __name__ == '__main__':
     unittest.main()

From e9db69753c8793a36c9459b462c9e4cb4cf0a403 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 3 Dec 2022 19:57:16 +0000
Subject: [PATCH 02/31] Add support for % and F format specifiers

---
 Lib/fractions.py           | 14 ++++++++------
 Lib/test/test_fractions.py | 15 +++++++++++++++
 2 files changed, 23 insertions(+), 6 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 1d64910724d87d..1534af8c34880d 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -329,8 +329,8 @@ def __format__(self, format_spec, /):
             (?P<minimumwidth>\d+)?
             (?P<thousands_sep>[,_])?
             (?:\.(?P<precision>\d+))?
-            f
-        """, re.DOTALL | re.VERBOSE).fullmatch
+            (?P<specifier_type>[f%])
+        """, re.DOTALL | re.IGNORECASE | re.VERBOSE).fullmatch
 
         # Validate and parse the format specifier.
         match = FORMAT_SPEC_MATCHER(format_spec)
@@ -350,16 +350,17 @@ def __format__(self, format_spec, /):
             fill = match["fill"] or " "
             align = match["align"] or ">"
             pos_sign = "" if match["sign"] == "-" else match["sign"]
-            neg_sign = "-"
             alternate_form = bool(match["alt"])
             zeropad = bool(match["zeropad"])
             minimumwidth = int(match["minimumwidth"] or "0")
             thousands_sep = match["thousands_sep"]
             precision = int(match["precision"] or "6")
+            specifier_type = match["specifier_type"]
 
         # Get sign and output digits for the target number
         negative = self < 0
-        digits = str(round(abs(self) * 10**precision))
+        shift = precision + 2 if specifier_type == "%" else precision
+        digits = str(round(abs(self) * 10**shift))
 
         # Assemble the output: before padding, it has the form
         # f"{sign}{leading}{trailing}", where `leading` includes thousands
@@ -367,9 +368,10 @@ def __format__(self, format_spec, /):
         # separator where appropriate.
         digits = digits.zfill(precision + 1)
         dot_pos = len(digits) - precision
-        sign = neg_sign if negative else pos_sign
+        sign = "-" if negative else pos_sign
         separator = "." if precision or alternate_form else ""
-        trailing = separator + digits[dot_pos:]
+        percent = "%" if specifier_type == "%" else ""
+        trailing = separator + digits[dot_pos:] + percent
         leading = digits[:dot_pos]
 
         # Do zero padding if required.
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index f448e85a68ae74..d3598209421104 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -976,6 +976,21 @@ def test_format(self):
             # is being inserted programmatically: spec = f'{width}.2f'.
             (F('12.34'), '0.2f', '12.34'),
             (F('12.34'), 'X>0.2f', '12.34'),
+            # "F" should work identically to "f"
+            (F(22, 7), '.5F', '3.14286'),
+            # %-specifier
+            (F(22, 7), '.2%', '314.29%'),
+            (F(1, 7), '.2%', '14.29%'),
+            (F(1, 70), '.2%', '1.43%'),
+            (F(1, 700), '.2%', '0.14%'),
+            (F(1, 7000), '.2%', '0.01%'),
+            (F(1, 70000), '.2%', '0.00%'),
+            (F(1, 7), '.0%', '14%'),
+            (F(1, 7), '#.0%', '14.%'),
+            (F(100, 7), ',.2%', '1,428.57%'),
+            (F(22, 7), '7.2%', '314.29%'),
+            (F(22, 7), '8.2%', ' 314.29%'),
+            (F(22, 7), '08.2%', '0314.29%'),
         ]
         for fraction, spec, expected in testcases:
             with self.subTest(fraction=fraction, spec=spec):

From 6491b046ce875d298c0e13adbf33460cb217560e Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 4 Dec 2022 09:27:25 +0000
Subject: [PATCH 03/31] Add support for 'z' flag

---
 Lib/fractions.py           | 8 +++++---
 Lib/test/test_fractions.py | 9 +++++++++
 2 files changed, 14 insertions(+), 3 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 1534af8c34880d..0713c89bdfdca6 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -324,6 +324,7 @@ def __format__(self, format_spec, /):
                 (?P<align>[<>=^])
             )?
             (?P<sign>[-+ ]?)
+            (?P<no_neg_zero>z)?
             (?P<alt>\#)?
             (?P<zeropad>0(?=\d))?
             (?P<minimumwidth>\d+)?
@@ -350,6 +351,7 @@ def __format__(self, format_spec, /):
             fill = match["fill"] or " "
             align = match["align"] or ">"
             pos_sign = "" if match["sign"] == "-" else match["sign"]
+            neg_zero_ok = not match["no_neg_zero"]
             alternate_form = bool(match["alt"])
             zeropad = bool(match["zeropad"])
             minimumwidth = int(match["minimumwidth"] or "0")
@@ -360,15 +362,15 @@ def __format__(self, format_spec, /):
         # Get sign and output digits for the target number
         negative = self < 0
         shift = precision + 2 if specifier_type == "%" else precision
-        digits = str(round(abs(self) * 10**shift))
+        significand = round(abs(self) * 10**shift)
 
         # Assemble the output: before padding, it has the form
         # f"{sign}{leading}{trailing}", where `leading` includes thousands
         # separators if necessary, and `trailing` includes the decimal
         # separator where appropriate.
-        digits = digits.zfill(precision + 1)
+        digits = str(significand).zfill(precision + 1)
         dot_pos = len(digits) - precision
-        sign = "-" if negative else pos_sign
+        sign = "-" if negative and (significand or neg_zero_ok) else pos_sign
         separator = "." if precision or alternate_form else ""
         percent = "%" if specifier_type == "%" else ""
         trailing = separator + digits[dot_pos:] + percent
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index d3598209421104..77c3e9eaeb0ed8 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -976,6 +976,15 @@ def test_format(self):
             # is being inserted programmatically: spec = f'{width}.2f'.
             (F('12.34'), '0.2f', '12.34'),
             (F('12.34'), 'X>0.2f', '12.34'),
+            # z flag for suppressing negative zeros
+            (F('-0.001'), 'z.2f', '0.00'),
+            (F('-0.001'), '-z.2f', '0.00'),
+            (F('-0.001'), '+z.2f', '+0.00'),
+            (F('-0.001'), ' z.2f', ' 0.00'),
+            (F('0.001'), 'z.2f', '0.00'),
+            (F('0.001'), '-z.2f', '0.00'),
+            (F('0.001'), '+z.2f', '+0.00'),
+            (F('0.001'), ' z.2f', ' 0.00'),
             # "F" should work identically to "f"
             (F(22, 7), '.5F', '3.14286'),
             # %-specifier

From 455146856395dc0925d7b206ca3cd8fd0cc1bd66 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 4 Dec 2022 09:37:01 +0000
Subject: [PATCH 04/31] Tidy up of business logic

---
 Lib/fractions.py | 36 +++++++++++++++---------------------
 1 file changed, 15 insertions(+), 21 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 0713c89bdfdca6..da28c9a5afe152 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -330,7 +330,7 @@ def __format__(self, format_spec, /):
             (?P<minimumwidth>\d+)?
             (?P<thousands_sep>[,_])?
             (?:\.(?P<precision>\d+))?
-            (?P<specifier_type>[f%])
+            (?P<presentation_type>[f%])
         """, re.DOTALL | re.IGNORECASE | re.VERBOSE).fullmatch
 
         # Validate and parse the format specifier.
@@ -357,11 +357,11 @@ def __format__(self, format_spec, /):
             minimumwidth = int(match["minimumwidth"] or "0")
             thousands_sep = match["thousands_sep"]
             precision = int(match["precision"] or "6")
-            specifier_type = match["specifier_type"]
+            presentation_type = match["presentation_type"]
 
         # Get sign and output digits for the target number
         negative = self < 0
-        shift = precision + 2 if specifier_type == "%" else precision
+        shift = precision + 2 if presentation_type == "%" else precision
         significand = round(abs(self) * 10**shift)
 
         # Assemble the output: before padding, it has the form
@@ -372,7 +372,7 @@ def __format__(self, format_spec, /):
         dot_pos = len(digits) - precision
         sign = "-" if negative and (significand or neg_zero_ok) else pos_sign
         separator = "." if precision or alternate_form else ""
-        percent = "%" if specifier_type == "%" else ""
+        percent = "%" if presentation_type == "%" else ""
         trailing = separator + digits[dot_pos:] + percent
         leading = digits[:dot_pos]
 
@@ -395,23 +395,17 @@ def __format__(self, format_spec, /):
 
         after_sign = leading + trailing
 
-        # Pad if a minimum width was given and we haven't already zero padded.
-        if zeropad or minimumwidth is None:
-            result = sign + after_sign
-        else:
-            padding = fill * (minimumwidth - len(sign) - len(after_sign))
-            if align == ">":
-                result = padding + sign + after_sign
-            elif align == "<":
-                result = sign + after_sign + padding
-            elif align == "=":
-                result = sign + padding + after_sign
-            else:
-                # Centered, with a leftwards bias when padding length is odd.
-                assert align == "^"
-                half = len(padding)//2
-                result = padding[:half] + sign + after_sign + padding[half:]
-        return result
+        # Pad if necessary and return.
+        padding = fill * (minimumwidth - len(sign) - len(after_sign))
+        if align == ">":
+            return padding + sign + after_sign
+        elif align == "<":
+            return sign + after_sign + padding
+        elif align == "^":
+            half = len(padding)//2
+            return padding[:half] + sign + after_sign + padding[half:]
+        else:  # align == "="
+            return sign + padding + after_sign
 
     def _operator_fallbacks(monomorphic_operator, fallback_operator):
         """Generates forward and reverse operators given a purely-rational

From 43d34fc38d47a3aba7f25ee33820c8f07a11ddd8 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 4 Dec 2022 12:01:02 +0000
Subject: [PATCH 05/31] Add support for 'e' presentation type

---
 Lib/fractions.py           | 83 +++++++++++++++++++++++++-------------
 Lib/test/test_fractions.py | 72 ++++++++++++++++++++++++++++++++-
 2 files changed, 126 insertions(+), 29 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index da28c9a5afe152..a8c2d30084f4a3 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -68,6 +68,23 @@ def _hash_algorithm(numerator, denominator):
     \s*\Z                                 # and optional whitespace to finish
 """, re.VERBOSE | re.IGNORECASE)
 
+# Pattern for matching format specification; only supports 'e', 'E', 'f', 'F'
+# and '%' presentation types.
+_FORMAT_SPECIFICATION_MATCHER = re.compile(r"""
+    (?:
+        (?P<fill>.)?
+        (?P<align>[<>=^])
+    )?
+    (?P<sign>[-+ ]?)
+    (?P<no_neg_zero>z)?
+    (?P<alt>\#)?
+    (?P<zeropad>0(?=\d))?
+    (?P<minimumwidth>\d+)?
+    (?P<thousands_sep>[,_])?
+    (?:\.(?P<precision>\d+))?
+    (?P<presentation_type>[ef%])
+""", re.DOTALL | re.IGNORECASE | re.VERBOSE).fullmatch
+
 
 class Fraction(numbers.Rational):
     """This class implements rational numbers.
@@ -317,24 +334,8 @@ def __format__(self, format_spec, /):
         if not format_spec:
             return str(self)
 
-        # Pattern matcher for the format spec; only supports "f" so far
-        FORMAT_SPEC_MATCHER = re.compile(r"""
-            (?:
-                (?P<fill>.)?
-                (?P<align>[<>=^])
-            )?
-            (?P<sign>[-+ ]?)
-            (?P<no_neg_zero>z)?
-            (?P<alt>\#)?
-            (?P<zeropad>0(?=\d))?
-            (?P<minimumwidth>\d+)?
-            (?P<thousands_sep>[,_])?
-            (?:\.(?P<precision>\d+))?
-            (?P<presentation_type>[f%])
-        """, re.DOTALL | re.IGNORECASE | re.VERBOSE).fullmatch
-
         # Validate and parse the format specifier.
-        match = FORMAT_SPEC_MATCHER(format_spec)
+        match = _FORMAT_SPECIFICATION_MATCHER(format_spec)
         if match is None:
             raise ValueError(
                 f"Invalid format specifier {format_spec!r} "
@@ -361,8 +362,37 @@ def __format__(self, format_spec, /):
 
         # Get sign and output digits for the target number
         negative = self < 0
-        shift = precision + 2 if presentation_type == "%" else precision
-        significand = round(abs(self) * 10**shift)
+        self = abs(self)
+        if presentation_type == "f" or presentation_type == "F":
+            suffix = ""
+            significand = round(self * 10**precision)
+        elif presentation_type == "%":
+            suffix = "%"
+            significand = round(self * 10**(precision + 2))
+        elif presentation_type == "e" or presentation_type == "E":
+            if not self:
+                significand = 0
+                exponent = 0
+            else:
+                # Find integer 'exponent' satisfying the constraint
+                #   10**exponent <= self <= 10**(exponent + 1)
+                # (Either possibility for exponent is fine in the case
+                # where 'self' is an exact power of 10.)
+                str_n, str_d = str(self.numerator), str(self.denominator)
+                exponent = len(str_n) - len(str_d) - (str_n < str_d)
+
+                # Compute the necessary digits.
+                if precision >= exponent:
+                    significand = round(self * 10**(precision - exponent))
+                else:
+                    significand = round(self / 10**(exponent - precision))
+                if len(str(significand)) == precision + 2:
+                    # Can only happen when significand is a power of 10.
+                    assert significand % 10 == 0
+                    significand //= 10
+                    exponent += 1
+                assert len(str(significand)) == precision + 1
+            suffix = f"{presentation_type}{exponent:+03d}"
 
         # Assemble the output: before padding, it has the form
         # f"{sign}{leading}{trailing}", where `leading` includes thousands
@@ -372,8 +402,7 @@ def __format__(self, format_spec, /):
         dot_pos = len(digits) - precision
         sign = "-" if negative and (significand or neg_zero_ok) else pos_sign
         separator = "." if precision or alternate_form else ""
-        percent = "%" if presentation_type == "%" else ""
-        trailing = separator + digits[dot_pos:] + percent
+        trailing = separator + digits[dot_pos:] + suffix
         leading = digits[:dot_pos]
 
         # Do zero padding if required.
@@ -393,19 +422,19 @@ def __format__(self, format_spec, /):
                 for pos in range(first_pos, len(leading), 3)
             )
 
-        after_sign = leading + trailing
+        body = leading + trailing
 
         # Pad if necessary and return.
-        padding = fill * (minimumwidth - len(sign) - len(after_sign))
+        padding = fill * (minimumwidth - len(sign) - len(body))
         if align == ">":
-            return padding + sign + after_sign
+            return padding + sign + body
         elif align == "<":
-            return sign + after_sign + padding
+            return sign + body + padding
         elif align == "^":
             half = len(padding)//2
-            return padding[:half] + sign + after_sign + padding[half:]
+            return padding[:half] + sign + body + padding[half:]
         else:  # align == "="
-            return sign + padding + after_sign
+            return sign + padding + body
 
     def _operator_fallbacks(monomorphic_operator, fallback_operator):
         """Generates forward and reverse operators given a purely-rational
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 77c3e9eaeb0ed8..21a978d661bca7 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -830,12 +830,19 @@ def denominator(self):
         self.assertEqual(type(f.numerator), myint)
         self.assertEqual(type(f.denominator), myint)
 
-    def test_format(self):
+    def test_format_no_presentation_type(self):
         # Triples (fraction, specification, expected_result)
         testcases = [
-            # Case inherited from object - equivalent to str()
             (F(1, 3), '', '1/3'),
             (F(-1, 3), '', '-1/3'),
+        ]
+        for fraction, spec, expected in testcases:
+            with self.subTest(fraction=fraction, spec=spec):
+                self.assertEqual(format(fraction, spec), expected)
+
+    def test_format_f_presentation_type(self):
+        # Triples (fraction, specification, expected_result)
+        testcases = [
             # Simple .f formatting
             (F(0, 1), '.2f', '0.00'),
             (F(1, 3), '.2f', '0.33'),
@@ -1005,6 +1012,63 @@ def test_format(self):
             with self.subTest(fraction=fraction, spec=spec):
                 self.assertEqual(format(fraction, spec), expected)
 
+    def test_format_e_presentation_type(self):
+        # Triples (fraction, specification, expected_result)
+        testcases = [
+            (F(2, 3), '.6e', '6.666667e-01'),
+            (F(3, 2), '.6e', '1.500000e+00'),
+            (F(2, 13), '.6e', '1.538462e-01'),
+            (F(2, 23), '.6e', '8.695652e-02'),
+            (F(2, 33), '.6e', '6.060606e-02'),
+            (F(13, 2), '.6e', '6.500000e+00'),
+            (F(20, 2), '.6e', '1.000000e+01'),
+            (F(23, 2), '.6e', '1.150000e+01'),
+            (F(33, 2), '.6e', '1.650000e+01'),
+            (F(2, 3), '.6e', '6.666667e-01'),
+            (F(3, 2), '.6e', '1.500000e+00'),
+            # Zero
+            (F(0), '.3e', '0.000e+00'),
+            # Powers of 10, to exercise the log10 boundary logic
+            (F(1, 1000), '.3e', '1.000e-03'),
+            (F(1, 100), '.3e', '1.000e-02'),
+            (F(1, 10), '.3e', '1.000e-01'),
+            (F(1, 1), '.3e', '1.000e+00'),
+            (F(10), '.3e', '1.000e+01'),
+            (F(100), '.3e', '1.000e+02'),
+            (F(1000), '.3e', '1.000e+03'),
+            # Boundary where we round up to the next power of 10
+            (F('99.999994999999'), '.6e', '9.999999e+01'),
+            (F('99.999995'), '.6e', '1.000000e+02'),
+            (F('99.999995000001'), '.6e', '1.000000e+02'),
+            # Negatives
+            (F(-2, 3), '.6e', '-6.666667e-01'),
+            (F(-3, 2), '.6e', '-1.500000e+00'),
+            (F(-100), '.6e', '-1.000000e+02'),
+            # Large and small
+            (F('1e1000'), '.3e', '1.000e+1000'),
+            (F('1e-1000'), '.3e', '1.000e-1000'),
+            # Using 'E' instead of 'e' should give us a capital 'E'
+            (F(2, 3), '.6E', '6.666667E-01'),
+            # Tiny precision
+            (F(2, 3), '.1e', '6.7e-01'),
+            (F('0.995'), '.0e', '1e+00'),
+            # Default precision is 6
+            (F(22, 7), 'e', '3.142857e+00'),
+            # Alternate form forces a decimal point
+            (F('0.995'), '#.0e', '1.e+00'),
+            # Check that padding takes the exponent into account.
+            (F(22, 7), '11.6e', '3.142857e+00'),
+            (F(22, 7), '12.6e', '3.142857e+00'),
+            (F(22, 7), '13.6e', ' 3.142857e+00'),
+            # Legal to specify a thousands separator, but it'll have no effect
+            (F('1234567.123456'), ',.5e', '1.23457e+06'),
+            # Same with z flag: legal, but useless
+            (F(-1, 7**100), 'z.6e', '-3.091690e-85'),
+        ]
+        for fraction, spec, expected in testcases:
+            with self.subTest(fraction=fraction, spec=spec):
+                self.assertEqual(format(fraction, spec), expected)
+
     def test_invalid_formats(self):
         fraction = F(2, 3)
         with self.assertRaises(TypeError):
@@ -1025,6 +1089,10 @@ def test_invalid_formats(self):
             "<010f",
             "^010f",
             "=010f",
+            "=010e",
+            # Missing precision
+            ".f",
+            ".e",
         ]
         for spec in invalid_specs:
             with self.subTest(spec=spec):

From f8dfcb96ec2399154a3cf37518e67062e0d21c5a Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 4 Dec 2022 20:20:35 +0000
Subject: [PATCH 06/31] Add support for 'g' presentation type; tidy

---
 Lib/fractions.py           | 125 +++++++++++++++++----------
 Lib/test/test_fractions.py | 167 +++++++++++++++++++++++++------------
 2 files changed, 194 insertions(+), 98 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index a8c2d30084f4a3..70a2a9d19b485f 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -82,7 +82,7 @@ def _hash_algorithm(numerator, denominator):
     (?P<minimumwidth>\d+)?
     (?P<thousands_sep>[,_])?
     (?:\.(?P<precision>\d+))?
-    (?P<presentation_type>[ef%])
+    (?P<presentation_type>[efg%])
 """, re.DOTALL | re.IGNORECASE | re.VERBOSE).fullmatch
 
 
@@ -327,6 +327,35 @@ def __str__(self):
         else:
             return '%s/%s' % (self._numerator, self._denominator)
 
+    def _round_to_sig_figs(self, figures):
+        """Round a positive fraction to a given number of significant figures.
+
+        Returns a pair (significand, exponent) of integers such that
+        significand * 10**exponent gives a rounded approximation to self, and
+        significand lies in the range 10**(figures - 1) <= significand <
+        10**figures.
+        """
+        if not (self > 0 and figures > 0):
+            raise ValueError("Expected self and figures to be positive")
+
+        # Find integer m satisfying 10**(m - 1) <= self <= 10**m.
+        str_n, str_d = str(self.numerator), str(self.denominator)
+        m = len(str_n) - len(str_d) + (str_d <= str_n)
+
+        # Find best approximation significand * 10**exponent to self, with
+        # 10**(figures - 1) <= significand <= 10**figures.
+        exponent = m - figures
+        significand = round(
+            self / 10**exponent if exponent >= 0 else self * 10**-exponent
+        )
+
+        # Adjust in the case where significand == 10**figures.
+        if len(str(significand)) == figures + 1:
+            significand //= 10
+            exponent += 1
+
+        return significand, exponent
+
     def __format__(self, format_spec, /):
         """Format this fraction according to the given format specification."""
 
@@ -348,62 +377,67 @@ def __format__(self, format_spec, /):
                 f"for object of type {type(self).__name__!r}; "
                 "can't use explicit alignment when zero-padding"
             )
-        else:
-            fill = match["fill"] or " "
-            align = match["align"] or ">"
-            pos_sign = "" if match["sign"] == "-" else match["sign"]
-            neg_zero_ok = not match["no_neg_zero"]
-            alternate_form = bool(match["alt"])
-            zeropad = bool(match["zeropad"])
-            minimumwidth = int(match["minimumwidth"] or "0")
-            thousands_sep = match["thousands_sep"]
-            precision = int(match["precision"] or "6")
-            presentation_type = match["presentation_type"]
-
-        # Get sign and output digits for the target number
+
+        fill = match["fill"] or " "
+        align = match["align"] or ">"
+        pos_sign = "" if match["sign"] == "-" else match["sign"]
+        neg_zero_ok = not match["no_neg_zero"]
+        alternate_form = bool(match["alt"])
+        zeropad = bool(match["zeropad"])
+        minimumwidth = int(match["minimumwidth"] or "0")
+        thousands_sep = match["thousands_sep"]
+        precision = int(match["precision"] or "6")
+        presentation_type = match["presentation_type"]
+        trim_zeros = presentation_type in "gG" and not alternate_form
+        trim_dot = not alternate_form
+        exponent_indicator = "E" if presentation_type in "EFG" else "e"
+
+        # Record sign, then work with absolute value.
         negative = self < 0
         self = abs(self)
+
+        # Round to get the digits we need; also compute the suffix.
         if presentation_type == "f" or presentation_type == "F":
-            suffix = ""
             significand = round(self * 10**precision)
+            point_pos = precision
+            suffix = ""
         elif presentation_type == "%":
-            suffix = "%"
             significand = round(self * 10**(precision + 2))
-        elif presentation_type == "e" or presentation_type == "E":
-            if not self:
-                significand = 0
-                exponent = 0
+            point_pos = precision
+            suffix = "%"
+        elif presentation_type in "eEgG":
+            if presentation_type in "gG":
+                figures = max(precision, 1)
             else:
-                # Find integer 'exponent' satisfying the constraint
-                #   10**exponent <= self <= 10**(exponent + 1)
-                # (Either possibility for exponent is fine in the case
-                # where 'self' is an exact power of 10.)
-                str_n, str_d = str(self.numerator), str(self.denominator)
-                exponent = len(str_n) - len(str_d) - (str_n < str_d)
-
-                # Compute the necessary digits.
-                if precision >= exponent:
-                    significand = round(self * 10**(precision - exponent))
-                else:
-                    significand = round(self / 10**(exponent - precision))
-                if len(str(significand)) == precision + 2:
-                    # Can only happen when significand is a power of 10.
-                    assert significand % 10 == 0
-                    significand //= 10
-                    exponent += 1
-                assert len(str(significand)) == precision + 1
-            suffix = f"{presentation_type}{exponent:+03d}"
+                figures = precision + 1
+            if self:
+                significand, exponent = self._round_to_sig_figs(figures)
+            else:
+                significand, exponent = 0, 1 - figures
+            if presentation_type in "gG" and -4 - figures < exponent <= 0:
+                point_pos = -exponent
+                suffix = ""
+            else:
+                point_pos = figures - 1
+                suffix = f"{exponent_indicator}{exponent + point_pos:+03d}"
+        else:
+            # It shouldn't be possible to get here.
+            raise ValueError(
+                f"unknown presentation type {presentation_type!r}"
+            )
 
         # Assemble the output: before padding, it has the form
         # f"{sign}{leading}{trailing}", where `leading` includes thousands
         # separators if necessary, and `trailing` includes the decimal
         # separator where appropriate.
-        digits = str(significand).zfill(precision + 1)
-        dot_pos = len(digits) - precision
+        digits = f"{significand:0{point_pos + 1}d}"
         sign = "-" if negative and (significand or neg_zero_ok) else pos_sign
-        separator = "." if precision or alternate_form else ""
-        trailing = separator + digits[dot_pos:] + suffix
-        leading = digits[:dot_pos]
+        leading = digits[:len(digits) - point_pos]
+        frac_part = digits[len(digits) - point_pos:]
+        if trim_zeros:
+            frac_part = frac_part.rstrip("0")
+        separator = "" if trim_dot and not frac_part else "."
+        trailing = separator + frac_part + suffix
 
         # Do zero padding if required.
         if zeropad:
@@ -422,9 +456,8 @@ def __format__(self, format_spec, /):
                 for pos in range(first_pos, len(leading), 3)
             )
 
-        body = leading + trailing
-
         # Pad if necessary and return.
+        body = leading + trailing
         padding = fill * (minimumwidth - len(sign) - len(body))
         if align == ">":
             return padding + sign + body
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 21a978d661bca7..efb1eb23dfac38 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -840,6 +840,63 @@ def test_format_no_presentation_type(self):
             with self.subTest(fraction=fraction, spec=spec):
                 self.assertEqual(format(fraction, spec), expected)
 
+    def test_format_e_presentation_type(self):
+        # Triples (fraction, specification, expected_result)
+        testcases = [
+            (F(2, 3), '.6e', '6.666667e-01'),
+            (F(3, 2), '.6e', '1.500000e+00'),
+            (F(2, 13), '.6e', '1.538462e-01'),
+            (F(2, 23), '.6e', '8.695652e-02'),
+            (F(2, 33), '.6e', '6.060606e-02'),
+            (F(13, 2), '.6e', '6.500000e+00'),
+            (F(20, 2), '.6e', '1.000000e+01'),
+            (F(23, 2), '.6e', '1.150000e+01'),
+            (F(33, 2), '.6e', '1.650000e+01'),
+            (F(2, 3), '.6e', '6.666667e-01'),
+            (F(3, 2), '.6e', '1.500000e+00'),
+            # Zero
+            (F(0), '.3e', '0.000e+00'),
+            # Powers of 10, to exercise the log10 boundary logic
+            (F(1, 1000), '.3e', '1.000e-03'),
+            (F(1, 100), '.3e', '1.000e-02'),
+            (F(1, 10), '.3e', '1.000e-01'),
+            (F(1, 1), '.3e', '1.000e+00'),
+            (F(10), '.3e', '1.000e+01'),
+            (F(100), '.3e', '1.000e+02'),
+            (F(1000), '.3e', '1.000e+03'),
+            # Boundary where we round up to the next power of 10
+            (F('99.999994999999'), '.6e', '9.999999e+01'),
+            (F('99.999995'), '.6e', '1.000000e+02'),
+            (F('99.999995000001'), '.6e', '1.000000e+02'),
+            # Negatives
+            (F(-2, 3), '.6e', '-6.666667e-01'),
+            (F(-3, 2), '.6e', '-1.500000e+00'),
+            (F(-100), '.6e', '-1.000000e+02'),
+            # Large and small
+            (F('1e1000'), '.3e', '1.000e+1000'),
+            (F('1e-1000'), '.3e', '1.000e-1000'),
+            # Using 'E' instead of 'e' should give us a capital 'E'
+            (F(2, 3), '.6E', '6.666667E-01'),
+            # Tiny precision
+            (F(2, 3), '.1e', '6.7e-01'),
+            (F('0.995'), '.0e', '1e+00'),
+            # Default precision is 6
+            (F(22, 7), 'e', '3.142857e+00'),
+            # Alternate form forces a decimal point
+            (F('0.995'), '#.0e', '1.e+00'),
+            # Check that padding takes the exponent into account.
+            (F(22, 7), '11.6e', '3.142857e+00'),
+            (F(22, 7), '12.6e', '3.142857e+00'),
+            (F(22, 7), '13.6e', ' 3.142857e+00'),
+            # Legal to specify a thousands separator, but it'll have no effect
+            (F('1234567.123456'), ',.5e', '1.23457e+06'),
+            # Same with z flag: legal, but useless
+            (F(-1, 7**100), 'z.6e', '-3.091690e-85'),
+        ]
+        for fraction, spec, expected in testcases:
+            with self.subTest(fraction=fraction, spec=spec):
+                self.assertEqual(format(fraction, spec), expected)
+
     def test_format_f_presentation_type(self):
         # Triples (fraction, specification, expected_result)
         testcases = [
@@ -1012,58 +1069,60 @@ def test_format_f_presentation_type(self):
             with self.subTest(fraction=fraction, spec=spec):
                 self.assertEqual(format(fraction, spec), expected)
 
-    def test_format_e_presentation_type(self):
+    def test_format_g_presentation_type(self):
         # Triples (fraction, specification, expected_result)
         testcases = [
-            (F(2, 3), '.6e', '6.666667e-01'),
-            (F(3, 2), '.6e', '1.500000e+00'),
-            (F(2, 13), '.6e', '1.538462e-01'),
-            (F(2, 23), '.6e', '8.695652e-02'),
-            (F(2, 33), '.6e', '6.060606e-02'),
-            (F(13, 2), '.6e', '6.500000e+00'),
-            (F(20, 2), '.6e', '1.000000e+01'),
-            (F(23, 2), '.6e', '1.150000e+01'),
-            (F(33, 2), '.6e', '1.650000e+01'),
-            (F(2, 3), '.6e', '6.666667e-01'),
-            (F(3, 2), '.6e', '1.500000e+00'),
-            # Zero
-            (F(0), '.3e', '0.000e+00'),
-            # Powers of 10, to exercise the log10 boundary logic
-            (F(1, 1000), '.3e', '1.000e-03'),
-            (F(1, 100), '.3e', '1.000e-02'),
-            (F(1, 10), '.3e', '1.000e-01'),
-            (F(1, 1), '.3e', '1.000e+00'),
-            (F(10), '.3e', '1.000e+01'),
-            (F(100), '.3e', '1.000e+02'),
-            (F(1000), '.3e', '1.000e+03'),
-            # Boundary where we round up to the next power of 10
-            (F('99.999994999999'), '.6e', '9.999999e+01'),
-            (F('99.999995'), '.6e', '1.000000e+02'),
-            (F('99.999995000001'), '.6e', '1.000000e+02'),
-            # Negatives
-            (F(-2, 3), '.6e', '-6.666667e-01'),
-            (F(-3, 2), '.6e', '-1.500000e+00'),
-            (F(-100), '.6e', '-1.000000e+02'),
-            # Large and small
-            (F('1e1000'), '.3e', '1.000e+1000'),
-            (F('1e-1000'), '.3e', '1.000e-1000'),
-            # Using 'E' instead of 'e' should give us a capital 'E'
-            (F(2, 3), '.6E', '6.666667E-01'),
-            # Tiny precision
-            (F(2, 3), '.1e', '6.7e-01'),
-            (F('0.995'), '.0e', '1e+00'),
-            # Default precision is 6
-            (F(22, 7), 'e', '3.142857e+00'),
-            # Alternate form forces a decimal point
-            (F('0.995'), '#.0e', '1.e+00'),
-            # Check that padding takes the exponent into account.
-            (F(22, 7), '11.6e', '3.142857e+00'),
-            (F(22, 7), '12.6e', '3.142857e+00'),
-            (F(22, 7), '13.6e', ' 3.142857e+00'),
-            # Legal to specify a thousands separator, but it'll have no effect
-            (F('1234567.123456'), ',.5e', '1.23457e+06'),
-            # Same with z flag: legal, but useless
-            (F(-1, 7**100), 'z.6e', '-3.091690e-85'),
+            (F('0.000012345678'), '.6g', '1.23457e-05'),
+            (F('0.00012345678'), '.6g', '0.000123457'),
+            (F('0.0012345678'), '.6g', '0.00123457'),
+            (F('0.012345678'), '.6g', '0.0123457'),
+            (F('0.12345678'), '.6g', '0.123457'),
+            (F('1.2345678'), '.6g', '1.23457'),
+            (F('12.345678'), '.6g', '12.3457'),
+            (F('123.45678'), '.6g', '123.457'),
+            (F('1234.5678'), '.6g', '1234.57'),
+            (F('12345.678'), '.6g', '12345.7'),
+            (F('123456.78'), '.6g', '123457'),
+            (F('1234567.8'), '.6g', '1.23457e+06'),
+            # Rounding up cases
+            (F('9.99999e+2'), '.4g', '1000'),
+            (F('9.99999e-8'), '.4g', '1e-07'),
+            (F('9.99999e+8'), '.4g', '1e+09'),
+            # Trailing zeros and decimal point suppressed by default ...
+            (F(0), '.6g', '0'),
+            (F('123.400'), '.6g', '123.4'),
+            (F('123.000'), '.6g', '123'),
+            (F('120.000'), '.6g', '120'),
+            (F('12000000'), '.6g', '1.2e+07'),
+            # ... but not when alternate form is in effect
+            (F(0), '#.6g', '0.00000'),
+            (F('123.400'), '#.6g', '123.400'),
+            (F('123.000'), '#.6g', '123.000'),
+            (F('120.000'), '#.6g', '120.000'),
+            (F('12000000'), '#.6g', '1.20000e+07'),
+            # 'G' format (uses 'E' instead of 'e' for the exponent indicator)
+            (F('123.45678'), '.6G', '123.457'),
+            (F('1234567.8'), '.6G', '1.23457E+06'),
+            # Default precision is 6 significant figures
+            (F('3.1415926535'), 'g', '3.14159'),
+            # Precision 0 is treated the same as precision 1.
+            (F('0.000031415'), '.0g', '3e-05'),
+            (F('0.00031415'), '.0g', '0.0003'),
+            (F('0.31415'), '.0g', '0.3'),
+            (F('3.1415'), '.0g', '3'),
+            (F('3.1415'), '#.0g', '3.'),
+            (F('31.415'), '.0g', '3e+01'),
+            (F('31.415'), '#.0g', '3.e+01'),
+            (F('0.000031415'), '.1g', '3e-05'),
+            (F('0.00031415'), '.1g', '0.0003'),
+            (F('0.31415'), '.1g', '0.3'),
+            (F('3.1415'), '.1g', '3'),
+            (F('3.1415'), '#.1g', '3.'),
+            (F('31.415'), '.1g', '3e+01'),
+            # Thousands separator
+            (F(2**64), '_.25g', '18_446_744_073_709_551_616'),
+            # As with 'e' format, z flag is legal, but has no effect
+            (F(-1, 7**100), 'zg', '-3.09169e-85'),
         ]
         for fraction, spec, expected in testcases:
             with self.subTest(fraction=fraction, spec=spec):
@@ -1088,11 +1147,15 @@ def test_invalid_formats(self):
             ">010f",
             "<010f",
             "^010f",
-            "=010f",
             "=010e",
+            "=010f",
+            "=010g",
+            "=010%",
             # Missing precision
-            ".f",
             ".e",
+            ".f",
+            ".g",
+            ".%",
         ]
         for spec in invalid_specs:
             with self.subTest(spec=spec):

From 6bfbc6c10087b6604e884bf1f10113247ce45f76 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 14:00:55 +0000
Subject: [PATCH 07/31] Tidying

---
 Lib/fractions.py           | 180 ++++++++++++++++++++++---------------
 Lib/test/test_fractions.py |  29 ++++--
 2 files changed, 127 insertions(+), 82 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 70a2a9d19b485f..9b216e59e9f683 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -68,8 +68,76 @@ def _hash_algorithm(numerator, denominator):
     \s*\Z                                 # and optional whitespace to finish
 """, re.VERBOSE | re.IGNORECASE)
 
-# Pattern for matching format specification; only supports 'e', 'E', 'f', 'F'
-# and '%' presentation types.
+
+# Helpers for formatting
+
+def _round_to_exponent(n, d, exponent, no_neg_zero=False):
+    """Round a rational number to an integer multiple of a power of 10.
+
+    Rounds the rational number n/d to the nearest integer multiple of
+    10**exponent using the round-ties-to-even rule, and returns a
+    pair (sign, significand) representing the rounded value
+    (-1)**sign * significand.
+
+    d must be positive, but n and d need not be relatively prime.
+
+    If no_neg_zero is true, then the returned sign will always be False
+    for a zero result. Otherwise, the sign is based on the sign of the input.
+    """
+    if exponent >= 0:
+        d *= 10**exponent
+    else:
+        n *= 10**-exponent
+
+    # The divmod quotient rounds ties towards positive infinity; we then adjust
+    # as needed for round-ties-to-even behaviour.
+    q, r = divmod(n + (d >> 1), d)
+    if r == 0 and d & 1 == 0:  # Tie
+        q &= -2
+
+    sign = q < 0 if no_neg_zero else n < 0
+    return sign, abs(q)
+
+
+def _round_to_figures(n, d, figures):
+    """Round a rational number to a given number of significant figures.
+
+    Rounds the rational number n/d to the given number of significant figures
+    using the round-ties-to-even rule, and returns a triple (sign, significand,
+    exponent) representing the rounded value (-1)**sign * significand *
+    10**exponent.
+
+    d must be positive, but n and d need not be relatively prime.
+    figures must be positive.
+
+    In the special case where n = 0, returns an exponent of 1 - figures, for
+    compatibility with formatting; the significand will be zero. Otherwise,
+    the significand satisfies 10**(figures - 1) <= significand < 10**figures.
+    """
+    # Find integer m satisfying 10**(m - 1) <= abs(self) <= 10**m if self
+    # is nonzero, with m = 1 if self = 0. (The latter choice is a little
+    # arbitrary, but gives the "right" results when formatting zero.)
+    if n == 0:
+        m = 1
+    else:
+        str_n, str_d = str(abs(n)), str(d)
+        m = len(str_n) - len(str_d) + (str_d <= str_n)
+
+    # Round to a multiple of 10**(m - figures). The result will satisfy either
+    # significand == 0 or 10**(figures - 1) <= significand <= 10**figures.
+    exponent = m - figures
+    sign, significand = _round_to_exponent(n, d, exponent)
+
+    # Adjust in the case where significand == 10**figures.
+    if len(str(significand)) == figures + 1:
+        significand //= 10
+        exponent += 1
+
+    return sign, significand, exponent
+
+
+# Pattern for matching format specification; supports 'e', 'E', 'f', 'F',
+# 'g', 'G' and '%' presentation types.
 _FORMAT_SPECIFICATION_MATCHER = re.compile(r"""
     (?:
         (?P<fill>.)?
@@ -78,8 +146,8 @@ def _hash_algorithm(numerator, denominator):
     (?P<sign>[-+ ]?)
     (?P<no_neg_zero>z)?
     (?P<alt>\#)?
-    (?P<zeropad>0(?=\d))?
-    (?P<minimumwidth>\d+)?
+    (?P<zeropad>0(?=\d))?   # use lookahead so that an isolated '0' is treated
+    (?P<minimumwidth>\d+)?  # as minimum width rather than the zeropad flag
     (?P<thousands_sep>[,_])?
     (?:\.(?P<precision>\d+))?
     (?P<presentation_type>[efg%])
@@ -327,35 +395,6 @@ def __str__(self):
         else:
             return '%s/%s' % (self._numerator, self._denominator)
 
-    def _round_to_sig_figs(self, figures):
-        """Round a positive fraction to a given number of significant figures.
-
-        Returns a pair (significand, exponent) of integers such that
-        significand * 10**exponent gives a rounded approximation to self, and
-        significand lies in the range 10**(figures - 1) <= significand <
-        10**figures.
-        """
-        if not (self > 0 and figures > 0):
-            raise ValueError("Expected self and figures to be positive")
-
-        # Find integer m satisfying 10**(m - 1) <= self <= 10**m.
-        str_n, str_d = str(self.numerator), str(self.denominator)
-        m = len(str_n) - len(str_d) + (str_d <= str_n)
-
-        # Find best approximation significand * 10**exponent to self, with
-        # 10**(figures - 1) <= significand <= 10**figures.
-        exponent = m - figures
-        significand = round(
-            self / 10**exponent if exponent >= 0 else self * 10**-exponent
-        )
-
-        # Adjust in the case where significand == 10**figures.
-        if len(str(significand)) == figures + 1:
-            significand //= 10
-            exponent += 1
-
-        return significand, exponent
-
     def __format__(self, format_spec, /):
         """Format this fraction according to the given format specification."""
 
@@ -377,11 +416,10 @@ def __format__(self, format_spec, /):
                 f"for object of type {type(self).__name__!r}; "
                 "can't use explicit alignment when zero-padding"
             )
-
         fill = match["fill"] or " "
         align = match["align"] or ">"
         pos_sign = "" if match["sign"] == "-" else match["sign"]
-        neg_zero_ok = not match["no_neg_zero"]
+        no_neg_zero = bool(match["no_neg_zero"])
         alternate_form = bool(match["alt"])
         zeropad = bool(match["zeropad"])
         minimumwidth = int(match["minimumwidth"] or "0")
@@ -389,54 +427,50 @@ def __format__(self, format_spec, /):
         precision = int(match["precision"] or "6")
         presentation_type = match["presentation_type"]
         trim_zeros = presentation_type in "gG" and not alternate_form
-        trim_dot = not alternate_form
+        trim_point = not alternate_form
         exponent_indicator = "E" if presentation_type in "EFG" else "e"
 
-        # Record sign, then work with absolute value.
-        negative = self < 0
-        self = abs(self)
-
-        # Round to get the digits we need; also compute the suffix.
-        if presentation_type == "f" or presentation_type == "F":
-            significand = round(self * 10**precision)
-            point_pos = precision
-            suffix = ""
-        elif presentation_type == "%":
-            significand = round(self * 10**(precision + 2))
+        # Round to get the digits we need, figure out where to place the point,
+        # and decide whether to use scientific notation.
+        n, d = self._numerator, self._denominator
+        if presentation_type in "fF%":
+            exponent = -precision - (2 if presentation_type == "%" else 0)
+            negative, significand = _round_to_exponent(
+                n, d, exponent, no_neg_zero)
+            scientific = False
             point_pos = precision
+        else:  # presentation_type in "eEgG"
+            figures = (
+                max(precision, 1)
+                if presentation_type in "gG"
+                else precision + 1
+            )
+            negative, significand, exponent = _round_to_figures(n, d, figures)
+            scientific = (
+                presentation_type in "eE"
+                or exponent > 0 or exponent + figures <= -4
+            )
+            point_pos = figures - 1 if scientific else -exponent
+
+        # Get the suffix - the part following the digits.
+        if presentation_type == "%":
             suffix = "%"
-        elif presentation_type in "eEgG":
-            if presentation_type in "gG":
-                figures = max(precision, 1)
-            else:
-                figures = precision + 1
-            if self:
-                significand, exponent = self._round_to_sig_figs(figures)
-            else:
-                significand, exponent = 0, 1 - figures
-            if presentation_type in "gG" and -4 - figures < exponent <= 0:
-                point_pos = -exponent
-                suffix = ""
-            else:
-                point_pos = figures - 1
-                suffix = f"{exponent_indicator}{exponent + point_pos:+03d}"
+        elif scientific:
+            suffix = f"{exponent_indicator}{exponent + point_pos:+03d}"
         else:
-            # It shouldn't be possible to get here.
-            raise ValueError(
-                f"unknown presentation type {presentation_type!r}"
-            )
+            suffix = ""
 
         # Assemble the output: before padding, it has the form
         # f"{sign}{leading}{trailing}", where `leading` includes thousands
         # separators if necessary, and `trailing` includes the decimal
         # separator where appropriate.
         digits = f"{significand:0{point_pos + 1}d}"
-        sign = "-" if negative and (significand or neg_zero_ok) else pos_sign
-        leading = digits[:len(digits) - point_pos]
-        frac_part = digits[len(digits) - point_pos:]
+        sign = "-" if negative else pos_sign
+        leading = digits[: len(digits) - point_pos]
+        frac_part = digits[len(digits) - point_pos :]
         if trim_zeros:
             frac_part = frac_part.rstrip("0")
-        separator = "" if trim_dot and not frac_part else "."
+        separator = "" if trim_point and not frac_part else "."
         trailing = separator + frac_part + suffix
 
         # Do zero padding if required.
@@ -452,11 +486,11 @@ def __format__(self, format_spec, /):
         if thousands_sep:
             first_pos = 1 + (len(leading) - 1) % 3
             leading = leading[:first_pos] + "".join(
-                thousands_sep + leading[pos:pos+3]
+                thousands_sep + leading[pos : pos + 3]
                 for pos in range(first_pos, len(leading), 3)
             )
 
-        # Pad if necessary and return.
+        # Pad with fill character if necessary and return.
         body = leading + trailing
         padding = fill * (minimumwidth - len(sign) - len(body))
         if align == ">":
@@ -464,7 +498,7 @@ def __format__(self, format_spec, /):
         elif align == "<":
             return sign + body + padding
         elif align == "^":
-            half = len(padding)//2
+            half = len(padding) // 2
             return padding[:half] + sign + body + padding[half:]
         else:  # align == "="
             return sign + padding + body
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index efb1eb23dfac38..45f8f68f87a835 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -947,12 +947,23 @@ def test_format_f_presentation_type(self):
             (F(-2, 3), ' .2f', '-0.67'),
             # Formatting to zero places
             (F(1, 2), '.0f', '0'),
+            (F(-1, 2), '.0f', '-0'),
             (F(22, 7), '.0f', '3'),
             (F(-22, 7), '.0f', '-3'),
             # Formatting to zero places, alternate form
             (F(1, 2), '#.0f', '0.'),
+            (F(-1, 2), '#.0f', '-0.'),
             (F(22, 7), '#.0f', '3.'),
             (F(-22, 7), '#.0f', '-3.'),
+            # z flag for suppressing negative zeros
+            (F('-0.001'), 'z.2f', '0.00'),
+            (F('-0.001'), '-z.2f', '0.00'),
+            (F('-0.001'), '+z.2f', '+0.00'),
+            (F('-0.001'), ' z.2f', ' 0.00'),
+            (F('0.001'), 'z.2f', '0.00'),
+            (F('0.001'), '-z.2f', '0.00'),
+            (F('0.001'), '+z.2f', '+0.00'),
+            (F('0.001'), ' z.2f', ' 0.00'),
             # Corner-case: leading zeros are allowed in the precision
             (F(2, 3), '.02f', '0.67'),
             (F(22, 7), '.000f', '3'),
@@ -1040,15 +1051,6 @@ def test_format_f_presentation_type(self):
             # is being inserted programmatically: spec = f'{width}.2f'.
             (F('12.34'), '0.2f', '12.34'),
             (F('12.34'), 'X>0.2f', '12.34'),
-            # z flag for suppressing negative zeros
-            (F('-0.001'), 'z.2f', '0.00'),
-            (F('-0.001'), '-z.2f', '0.00'),
-            (F('-0.001'), '+z.2f', '+0.00'),
-            (F('-0.001'), ' z.2f', ' 0.00'),
-            (F('0.001'), 'z.2f', '0.00'),
-            (F('0.001'), '-z.2f', '0.00'),
-            (F('0.001'), '+z.2f', '+0.00'),
-            (F('0.001'), ' z.2f', ' 0.00'),
             # "F" should work identically to "f"
             (F(22, 7), '.5F', '3.14286'),
             # %-specifier
@@ -1088,6 +1090,15 @@ def test_format_g_presentation_type(self):
             (F('9.99999e+2'), '.4g', '1000'),
             (F('9.99999e-8'), '.4g', '1e-07'),
             (F('9.99999e+8'), '.4g', '1e+09'),
+            # Check round-ties-to-even behaviour
+            (F('-0.115'), '.2g', '-0.12'),
+            (F('-0.125'), '.2g', '-0.12'),
+            (F('-0.135'), '.2g', '-0.14'),
+            (F('-0.145'), '.2g', '-0.14'),
+            (F('0.115'), '.2g', '0.12'),
+            (F('0.125'), '.2g', '0.12'),
+            (F('0.135'), '.2g', '0.14'),
+            (F('0.145'), '.2g', '0.14'),
             # Trailing zeros and decimal point suppressed by default ...
             (F(0), '.6g', '0'),
             (F('123.400'), '.6g', '123.4'),

From 48629b711fb1052e73f1ce584ba2b3f75e72043e Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 15:30:31 +0000
Subject: [PATCH 08/31] Add news entry

---
 .../next/Library/2022-12-10-15-30-17.gh-issue-67790.P9YUZM.rst  | 2 ++
 1 file changed, 2 insertions(+)
 create mode 100644 Misc/NEWS.d/next/Library/2022-12-10-15-30-17.gh-issue-67790.P9YUZM.rst

diff --git a/Misc/NEWS.d/next/Library/2022-12-10-15-30-17.gh-issue-67790.P9YUZM.rst b/Misc/NEWS.d/next/Library/2022-12-10-15-30-17.gh-issue-67790.P9YUZM.rst
new file mode 100644
index 00000000000000..ba0db774f8b318
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-12-10-15-30-17.gh-issue-67790.P9YUZM.rst
@@ -0,0 +1,2 @@
+Add float-style formatting support for :class:`fractions.Fraction`
+instances.

From 3d21af2b6bb4656c603a8ef1cc6f3f1de3d0a7a1 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 16:03:24 +0000
Subject: [PATCH 09/31] Add documentation

---
 Doc/library/fractions.rst | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/Doc/library/fractions.rst b/Doc/library/fractions.rst
index c46d88b2297aa1..d8f8b47ce8b677 100644
--- a/Doc/library/fractions.rst
+++ b/Doc/library/fractions.rst
@@ -101,6 +101,10 @@ another rational number, or from a string.
    .. versionchanged:: 3.12
       Space is allowed around the slash for string inputs: ``Fraction('2 / 3')``.
 
+   .. versionchanged:: 3.12
+      :class:`Fraction` instances now support float-style formatting, with
+      presentation types `"e"`, `"E"`, `"f"`, `"F"`, `"g"`, `"G"` and `"%""`.
+
    .. attribute:: numerator
 
       Numerator of the Fraction in lowest term.
@@ -187,6 +191,31 @@ another rational number, or from a string.
       ``ndigits`` is negative), again rounding half toward even.  This
       method can also be accessed through the :func:`round` function.
 
+   .. method:: __format__(format_spec, /)
+
+      This method provides support for float-style formatting of
+      :class:`Fraction` instances via the :meth:`str.format` method, the
+      :func:`format` built-in function, or :ref:`Formatted string literals
+      <f-strings>`. The presentation types `"e"`, `"E"`, `"f"`, `"F"`, `"g"`,
+      `"G"`` and `"%"` are supported. For these presentation types, formatting
+      for a :class:`Fraction` object `x` behaves as though the object `x` were
+      first converted to :class:`float` and then formatted using the float
+      formatting rules, but avoids the loss of precision that might arise as
+      a result of that conversion.
+
+      Here are some examples::
+
+      >>> from fractions import Fraction
+      >>> format(Fraction(1, 7), '.40g')
+      '0.1428571428571428571428571428571428571429'
+      >>> format(Fraction('1234567.855'), '_.2f')
+      '1_234_567.86'
+      >>> f"{Fraction(355, 113):*>20.6e}"
+      '********3.141593e+00'
+      >>> old_price, new_price = 499, 672
+      >>> "{:.2%} price increase".format(Fraction(new_price, old_price) - 1)
+      '34.67% price increase'
+
 
 .. seealso::
 

From c86a57e8246fb41ecdc0aa246175049e031d6eee Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 16:30:26 +0000
Subject: [PATCH 10/31] Add what's new entry

---
 Doc/whatsnew/3.12.rst | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/Doc/whatsnew/3.12.rst b/Doc/whatsnew/3.12.rst
index 3f1ec0f9a3443b..80fb14fea55a73 100644
--- a/Doc/whatsnew/3.12.rst
+++ b/Doc/whatsnew/3.12.rst
@@ -249,6 +249,12 @@ dis
   :data:`~dis.hasarg` collection instead.
   (Contributed by Irit Katriel in :gh:`94216`.)
 
+fractions
+---------
+
+* Objects of type :class:`fractions.Fraction` now support float-style
+  formatting. (Contributed by Mark Dickinson in :gh:`100161`.)
+
 os
 --
 

From b521efbc863c129ef91a5bb6431e2a4981914b93 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 16:33:15 +0000
Subject: [PATCH 11/31] Fix backticks:

---
 Doc/library/fractions.rst | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/Doc/library/fractions.rst b/Doc/library/fractions.rst
index d8f8b47ce8b677..9f37e09d34301a 100644
--- a/Doc/library/fractions.rst
+++ b/Doc/library/fractions.rst
@@ -103,7 +103,8 @@ another rational number, or from a string.
 
    .. versionchanged:: 3.12
       :class:`Fraction` instances now support float-style formatting, with
-      presentation types `"e"`, `"E"`, `"f"`, `"F"`, `"g"`, `"G"` and `"%""`.
+      presentation types ``"e"``, ``"E"``, ``"f"``, ``"F"``, ``"g"``, ``"G"``
+      and ``"%""``.
 
    .. attribute:: numerator
 
@@ -196,12 +197,12 @@ another rational number, or from a string.
       This method provides support for float-style formatting of
       :class:`Fraction` instances via the :meth:`str.format` method, the
       :func:`format` built-in function, or :ref:`Formatted string literals
-      <f-strings>`. The presentation types `"e"`, `"E"`, `"f"`, `"F"`, `"g"`,
-      `"G"`` and `"%"` are supported. For these presentation types, formatting
-      for a :class:`Fraction` object `x` behaves as though the object `x` were
-      first converted to :class:`float` and then formatted using the float
-      formatting rules, but avoids the loss of precision that might arise as
-      a result of that conversion.
+      <f-strings>`. The presentation types ``"e"``, ``"E"``, ``"f"``, ``"F"``,
+      ``"g"``, ``"G"`` and ``"%"`` are supported. For these presentation types,
+      formatting for a :class:`Fraction` object `x` behaves as though the
+      object `x` were first converted to :class:`float` and then formatted
+      using the float formatting rules, but avoids the loss of precision that
+      might arise as a result of that conversion.
 
       Here are some examples::
 

From aac576efd6492815bc37e29f704bcd0114632319 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 16:36:02 +0000
Subject: [PATCH 12/31] Fix more missing backticks

---
 Doc/library/fractions.rst | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Doc/library/fractions.rst b/Doc/library/fractions.rst
index 9f37e09d34301a..fa8ae82fcd88e4 100644
--- a/Doc/library/fractions.rst
+++ b/Doc/library/fractions.rst
@@ -199,8 +199,8 @@ another rational number, or from a string.
       :func:`format` built-in function, or :ref:`Formatted string literals
       <f-strings>`. The presentation types ``"e"``, ``"E"``, ``"f"``, ``"F"``,
       ``"g"``, ``"G"`` and ``"%"`` are supported. For these presentation types,
-      formatting for a :class:`Fraction` object `x` behaves as though the
-      object `x` were first converted to :class:`float` and then formatted
+      formatting for a :class:`Fraction` object ``x`` behaves as though the
+      object ``x`` were first converted to :class:`float` and then formatted
       using the float formatting rules, but avoids the loss of precision that
       might arise as a result of that conversion.
 

From b9ee0ffcdb053647b2fd5b2304099468a783f47d Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 16:40:28 +0000
Subject: [PATCH 13/31] Fix indentation

---
 Doc/library/fractions.rst | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Doc/library/fractions.rst b/Doc/library/fractions.rst
index fa8ae82fcd88e4..6e931f8b50c4e1 100644
--- a/Doc/library/fractions.rst
+++ b/Doc/library/fractions.rst
@@ -206,16 +206,16 @@ another rational number, or from a string.
 
       Here are some examples::
 
-      >>> from fractions import Fraction
-      >>> format(Fraction(1, 7), '.40g')
-      '0.1428571428571428571428571428571428571429'
-      >>> format(Fraction('1234567.855'), '_.2f')
-      '1_234_567.86'
-      >>> f"{Fraction(355, 113):*>20.6e}"
-      '********3.141593e+00'
-      >>> old_price, new_price = 499, 672
-      >>> "{:.2%} price increase".format(Fraction(new_price, old_price) - 1)
-      '34.67% price increase'
+         >>> from fractions import Fraction
+         >>> format(Fraction(1, 7), '.40g')
+         '0.1428571428571428571428571428571428571429'
+         >>> format(Fraction('1234567.855'), '_.2f')
+         '1_234_567.86'
+         >>> f"{Fraction(355, 113):*>20.6e}"
+         '********3.141593e+00'
+         >>> old_price, new_price = 499, 672
+         >>> "{:.2%} price increase".format(Fraction(new_price, old_price) - 1)
+         '34.67% price increase'
 
 
 .. seealso::

From 1c8b8a9970bbf82132a57542a5e1be07c3056b6d Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 16:45:38 +0000
Subject: [PATCH 14/31] Wordsmithing for consistency with other method
 definitions

---
 Doc/library/fractions.rst | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Doc/library/fractions.rst b/Doc/library/fractions.rst
index 6e931f8b50c4e1..9420e36bfe8305 100644
--- a/Doc/library/fractions.rst
+++ b/Doc/library/fractions.rst
@@ -194,15 +194,15 @@ another rational number, or from a string.
 
    .. method:: __format__(format_spec, /)
 
-      This method provides support for float-style formatting of
-      :class:`Fraction` instances via the :meth:`str.format` method, the
-      :func:`format` built-in function, or :ref:`Formatted string literals
-      <f-strings>`. The presentation types ``"e"``, ``"E"``, ``"f"``, ``"F"``,
-      ``"g"``, ``"G"`` and ``"%"`` are supported. For these presentation types,
-      formatting for a :class:`Fraction` object ``x`` behaves as though the
-      object ``x`` were first converted to :class:`float` and then formatted
-      using the float formatting rules, but avoids the loss of precision that
-      might arise as a result of that conversion.
+      Provides support for float-style formatting of :class:`Fraction`
+      instances via the :meth:`str.format` method, the :func:`format` built-in
+      function, or :ref:`Formatted string literals <f-strings>`. The
+      presentation types ``"e"``, ``"E"``, ``"f"``, ``"F"``, ``"g"``, ``"G"``
+      and ``"%"`` are supported. For these presentation types, formatting for a
+      :class:`Fraction` object ``x`` behaves as though the object ``x`` were
+      first converted to :class:`float` and then formatted using the float
+      formatting rules, but avoids the loss of precision that might arise as a
+      result of that conversion.
 
       Here are some examples::
 

From 9dbde3b6088dcf223b03453411d7adb0f5f276a2 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 16:53:58 +0000
Subject: [PATCH 15/31] Add link to the format specification mini-language

---
 Doc/library/fractions.rst | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Doc/library/fractions.rst b/Doc/library/fractions.rst
index 9420e36bfe8305..128f4ce40c579c 100644
--- a/Doc/library/fractions.rst
+++ b/Doc/library/fractions.rst
@@ -199,10 +199,8 @@ another rational number, or from a string.
       function, or :ref:`Formatted string literals <f-strings>`. The
       presentation types ``"e"``, ``"E"``, ``"f"``, ``"F"``, ``"g"``, ``"G"``
       and ``"%"`` are supported. For these presentation types, formatting for a
-      :class:`Fraction` object ``x`` behaves as though the object ``x`` were
-      first converted to :class:`float` and then formatted using the float
-      formatting rules, but avoids the loss of precision that might arise as a
-      result of that conversion.
+      :class:`Fraction` object ``x`` follows the rules outlined for
+      the :class:`float` type in the :ref:`formatspec` section.
 
       Here are some examples::
 

From 2dd48bbb40a8030bc02d67678a6ed3e1c9844d92 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 17:12:52 +0000
Subject: [PATCH 16/31] Fix: not true that thousands separators cannot have an
 effect for the 'e' presentation type

---
 Lib/test/test_fractions.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 45f8f68f87a835..6f9f1082ccc5f9 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -888,9 +888,10 @@ def test_format_e_presentation_type(self):
             (F(22, 7), '11.6e', '3.142857e+00'),
             (F(22, 7), '12.6e', '3.142857e+00'),
             (F(22, 7), '13.6e', ' 3.142857e+00'),
-            # Legal to specify a thousands separator, but it'll have no effect
+            # Thousands separators
             (F('1234567.123456'), ',.5e', '1.23457e+06'),
-            # Same with z flag: legal, but useless
+            (F('123.123456'), '012_.2e', '0_001.23e+02'),
+            # z flag is legal, but never makes a different to the output
             (F(-1, 7**100), 'z.6e', '-3.091690e-85'),
         ]
         for fraction, spec, expected in testcases:

From 983726f1986ff0bb34f6d063572640118e66491f Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 10 Dec 2022 17:13:15 +0000
Subject: [PATCH 17/31] Fix typo in comment

---
 Lib/test/test_fractions.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 6f9f1082ccc5f9..6eff2445917a41 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -891,7 +891,7 @@ def test_format_e_presentation_type(self):
             # Thousands separators
             (F('1234567.123456'), ',.5e', '1.23457e+06'),
             (F('123.123456'), '012_.2e', '0_001.23e+02'),
-            # z flag is legal, but never makes a different to the output
+            # z flag is legal, but never makes a difference to the output
             (F(-1, 7**100), 'z.6e', '-3.091690e-85'),
         ]
         for fraction, spec, expected in testcases:

From b7e51298455496d2644fd345c25051ba69057cdd Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 09:21:43 +0000
Subject: [PATCH 18/31] Tweak docstring and comments for _round_to_exponent

---
 Lib/fractions.py | 21 +++++++++++----------
 1 file changed, 11 insertions(+), 10 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 9b216e59e9f683..cf82e25da589d2 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -72,27 +72,28 @@ def _hash_algorithm(numerator, denominator):
 # Helpers for formatting
 
 def _round_to_exponent(n, d, exponent, no_neg_zero=False):
-    """Round a rational number to an integer multiple of a power of 10.
+    """Round a rational number to the nearest multiple of a given power of 10.
 
     Rounds the rational number n/d to the nearest integer multiple of
-    10**exponent using the round-ties-to-even rule, and returns a
-    pair (sign, significand) representing the rounded value
-    (-1)**sign * significand.
+    10**exponent, rounding to the nearest even integer multiple in the case of
+    a tie. Returns a pair (sign: bool, significand: int) representing the
+    rounded value (-1)**sign * significand * 10**exponent.
 
-    d must be positive, but n and d need not be relatively prime.
+    If no_neg_zero is true, then the returned sign will always be False when
+    the significand is zero. Otherwise, the sign reflects the sign of the
+    input.
 
-    If no_neg_zero is true, then the returned sign will always be False
-    for a zero result. Otherwise, the sign is based on the sign of the input.
+    d must be positive, but n and d need not be relatively prime.
     """
     if exponent >= 0:
         d *= 10**exponent
     else:
         n *= 10**-exponent
 
-    # The divmod quotient rounds ties towards positive infinity; we then adjust
-    # as needed for round-ties-to-even behaviour.
+    # The divmod quotient is correct for round-ties-towards-positive-infinity;
+    # In the case of a tie, we zero out the least significant bit of q.
     q, r = divmod(n + (d >> 1), d)
-    if r == 0 and d & 1 == 0:  # Tie
+    if r == 0 and d & 1 == 0:
         q &= -2
 
     sign = q < 0 if no_neg_zero else n < 0

From cb5e23484769c5f120eaaa28bebfb6a667153156 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 09:34:26 +0000
Subject: [PATCH 19/31] Second pass on docstring and comments for
 _round_to_figures

---
 Lib/fractions.py | 36 +++++++++++++++++++-----------------
 1 file changed, 19 insertions(+), 17 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index cf82e25da589d2..f4ef50ac04ee47 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -104,32 +104,34 @@ def _round_to_figures(n, d, figures):
     """Round a rational number to a given number of significant figures.
 
     Rounds the rational number n/d to the given number of significant figures
-    using the round-ties-to-even rule, and returns a triple (sign, significand,
-    exponent) representing the rounded value (-1)**sign * significand *
-    10**exponent.
+    using the round-ties-to-even rule, and returns a triple
+    (sign: bool, significand: int, exponent: int) representing the rounded
+    value (-1)**sign * significand * 10**exponent.
+
+    In the special case where n = 0, returns a significand of zero and
+    an exponent of 1 - figures, for compatibility with formatting.
+    Otherwise, the returned significand satisfies
+    10**(figures - 1) <= significand < 10**figures.
 
     d must be positive, but n and d need not be relatively prime.
     figures must be positive.
-
-    In the special case where n = 0, returns an exponent of 1 - figures, for
-    compatibility with formatting; the significand will be zero. Otherwise,
-    the significand satisfies 10**(figures - 1) <= significand < 10**figures.
     """
-    # Find integer m satisfying 10**(m - 1) <= abs(self) <= 10**m if self
-    # is nonzero, with m = 1 if self = 0. (The latter choice is a little
-    # arbitrary, but gives the "right" results when formatting zero.)
+    # Special case for n == 0.
     if n == 0:
-        m = 1
-    else:
-        str_n, str_d = str(abs(n)), str(d)
-        m = len(str_n) - len(str_d) + (str_d <= str_n)
+        return False, 0, 1 - figures
+
+    # Find integer m satisfying 10**(m - 1) <= abs(n)/d <= 10**m. (If abs(n)/d
+    # is a power of 10, either of the two possible values for m is fine.)
+    str_n, str_d = str(abs(n)), str(d)
+    m = len(str_n) - len(str_d) + (str_d <= str_n)
 
-    # Round to a multiple of 10**(m - figures). The result will satisfy either
-    # significand == 0 or 10**(figures - 1) <= significand <= 10**figures.
+    # Round to a multiple of 10**(m - figures). The significand we get
+    # satisfies 10**(figures - 1) <= significand <= 10**figures.
     exponent = m - figures
     sign, significand = _round_to_exponent(n, d, exponent)
 
-    # Adjust in the case where significand == 10**figures.
+    # Adjust in the case where significand == 10**figures, to ensure that
+    # 10**(figures - 1) <= significand < 10**figures.
     if len(str(significand)) == figures + 1:
         significand //= 10
         exponent += 1

From 907487e6963caa61fa6be5c1774571c17c3823d7 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 09:43:11 +0000
Subject: [PATCH 20/31] Add tests for the corner case of zero minimum width +
 alignment

---
 Lib/fractions.py           | 4 ++--
 Lib/test/test_fractions.py | 6 ++++++
 2 files changed, 8 insertions(+), 2 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index f4ef50ac04ee47..ca6f19e6f2ac86 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -149,8 +149,8 @@ def _round_to_figures(n, d, figures):
     (?P<sign>[-+ ]?)
     (?P<no_neg_zero>z)?
     (?P<alt>\#)?
-    (?P<zeropad>0(?=\d))?   # use lookahead so that an isolated '0' is treated
-    (?P<minimumwidth>\d+)?  # as minimum width rather than the zeropad flag
+    (?P<zeropad>0(?=\d))?   # lookahead so that an isolated '0' is treated
+    (?P<minimumwidth>\d+)?  # as a minimum width rather than a zeropad flag
     (?P<thousands_sep>[,_])?
     (?:\.(?P<precision>\d+))?
     (?P<presentation_type>[efg%])
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 6eff2445917a41..d18fea7ece273a 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -1000,7 +1000,13 @@ def test_format_f_presentation_type(self):
             (F(-2, 3), '-07.2f', '-000.67'),
             (F(2, 3), '+07.2f', '+000.67'),
             (F(2, 3), ' 07.2f', ' 000.67'),
+            # An isolated zero is a minimum width, not a zero-pad flag.
+            # So unlike zero-padding, it's legal in combination with alignment.
             (F(2, 3), '0.2f', '0.67'),
+            (F(2, 3), '>0.2f', '0.67'),
+            (F(2, 3), '<0.2f', '0.67'),
+            (F(2, 3), '^0.2f', '0.67'),
+            (F(2, 3), '=0.2f', '0.67'),
             # Thousands separator (only affects portion before the point)
             (F(2, 3), ',.2f', '0.67'),
             (F(2, 3), ',.7f', '0.6666667'),

From aba35f37bed36c160ff3ecf1c04e1ad07d77ebcf Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 09:46:07 +0000
Subject: [PATCH 21/31] Tests for the case of zero padding _and_ a zero minimum
 width

---
 Lib/test/test_fractions.py | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index d18fea7ece273a..bf034dafb6e20b 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -1007,6 +1007,8 @@ def test_format_f_presentation_type(self):
             (F(2, 3), '<0.2f', '0.67'),
             (F(2, 3), '^0.2f', '0.67'),
             (F(2, 3), '=0.2f', '0.67'),
+            # Corner case: zero-padding _and_ a zero minimum width.
+            (F(2, 3), '00.2f', '0.67'),
             # Thousands separator (only affects portion before the point)
             (F(2, 3), ',.2f', '0.67'),
             (F(2, 3), ',.7f', '0.6666667'),
@@ -1169,6 +1171,8 @@ def test_invalid_formats(self):
             "=010f",
             "=010g",
             "=010%",
+            '>00.2f',
+            '>00f',
             # Missing precision
             ".e",
             ".f",

From fc4d3b5ef7eff79c4dabf97f8c810b375071d3ee Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 10:26:59 +0000
Subject: [PATCH 22/31] Cleanup of __format__ method

---
 Lib/fractions.py | 17 +++++++++++------
 1 file changed, 11 insertions(+), 6 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index ca6f19e6f2ac86..5fc1ccaae43d55 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -435,11 +435,12 @@ def __format__(self, format_spec, /):
 
         # Round to get the digits we need, figure out where to place the point,
         # and decide whether to use scientific notation.
-        n, d = self._numerator, self._denominator
         if presentation_type in "fF%":
-            exponent = -precision - (2 if presentation_type == "%" else 0)
+            exponent = -precision
+            if presentation_type == "%":
+                exponent -= 2
             negative, significand = _round_to_exponent(
-                n, d, exponent, no_neg_zero)
+                self._numerator, self._denominator, exponent, no_neg_zero)
             scientific = False
             point_pos = precision
         else:  # presentation_type in "eEgG"
@@ -448,10 +449,12 @@ def __format__(self, format_spec, /):
                 if presentation_type in "gG"
                 else precision + 1
             )
-            negative, significand, exponent = _round_to_figures(n, d, figures)
+            negative, significand, exponent = _round_to_figures(
+                self._numerator, self._denominator, figures)
             scientific = (
                 presentation_type in "eE"
-                or exponent > 0 or exponent + figures <= -4
+                or exponent > 0
+                or exponent + figures <= -4
             )
             point_pos = figures - 1 if scientific else -exponent
 
@@ -493,8 +496,10 @@ def __format__(self, format_spec, /):
                 for pos in range(first_pos, len(leading), 3)
             )
 
-        # Pad with fill character if necessary and return.
+        # We now have a sign and a body.
         body = leading + trailing
+
+        # Pad with fill character if necessary and return.
         padding = fill * (minimumwidth - len(sign) - len(body))
         if align == ">":
             return padding + sign + body

From 4ccdf942386277a85f9ae1f61b801048b5c4bede Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 10:37:17 +0000
Subject: [PATCH 23/31] Add test cases from original issue and discussion
 thread

---
 Lib/test/test_fractions.py | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index bf034dafb6e20b..e3de529c4a9545 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -1075,6 +1075,18 @@ def test_format_f_presentation_type(self):
             (F(22, 7), '7.2%', '314.29%'),
             (F(22, 7), '8.2%', ' 314.29%'),
             (F(22, 7), '08.2%', '0314.29%'),
+            # Test cases from #67790 and discuss.python.org Ideas thread.
+            (F(1, 3), '.2f', '0.33'),
+            (F(1, 8), '.2f', '0.12'),
+            (F(3, 8), '.2f', '0.38'),
+            (F(2545, 1000), '.2f', '2.54'),
+            (F(2549, 1000), '.2f', '2.55'),
+            (F(2635, 1000), '.2f', '2.64'),
+            (F(1, 100), '.1f', '0.0'),
+            (F(49, 1000), '.1f', '0.0'),
+            (F(51, 1000), '.1f', '0.1'),
+            (F(149, 1000), '.1f', '0.1'),
+            (F(151, 1000), '.1f', '0.2'),
         ]
         for fraction, spec, expected in testcases:
             with self.subTest(fraction=fraction, spec=spec):

From 67e020cc4ea2fbe625dc6af2151de005bc3a1d0d Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 10:49:08 +0000
Subject: [PATCH 24/31] Tighten up the regex - extra leading zeros not
 permitted

---
 Lib/fractions.py           | 8 +++++---
 Lib/test/test_fractions.py | 9 ++++++---
 2 files changed, 11 insertions(+), 6 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 5fc1ccaae43d55..a212d77312c2db 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -149,10 +149,12 @@ def _round_to_figures(n, d, figures):
     (?P<sign>[-+ ]?)
     (?P<no_neg_zero>z)?
     (?P<alt>\#)?
-    (?P<zeropad>0(?=\d))?   # lookahead so that an isolated '0' is treated
-    (?P<minimumwidth>\d+)?  # as a minimum width rather than a zeropad flag
+    # lookahead so that a single '0' is treated as a minimum width rather
+    # than a zeropad flag
+    (?P<zeropad>0(?=[0-9]))?
+    (?P<minimumwidth>0|[1-9][0-9]*)?
     (?P<thousands_sep>[,_])?
-    (?:\.(?P<precision>\d+))?
+    (?:\.(?P<precision>0|[1-9][0-9]*))?
     (?P<presentation_type>[efg%])
 """, re.DOTALL | re.IGNORECASE | re.VERBOSE).fullmatch
 
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index e3de529c4a9545..6aada43395a79b 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -965,9 +965,6 @@ def test_format_f_presentation_type(self):
             (F('0.001'), '-z.2f', '0.00'),
             (F('0.001'), '+z.2f', '+0.00'),
             (F('0.001'), ' z.2f', ' 0.00'),
-            # Corner-case: leading zeros are allowed in the precision
-            (F(2, 3), '.02f', '0.67'),
-            (F(22, 7), '.000f', '3'),
             # Specifying a minimum width
             (F(2, 3), '6.2f', '  0.67'),
             (F(12345), '6.2f', '12345.00'),
@@ -1185,6 +1182,12 @@ def test_invalid_formats(self):
             "=010%",
             '>00.2f',
             '>00f',
+            # Too many zeros - minimum width should not have leading zeros
+            '006f',
+            # Leading zeros in precision
+            '.010f',
+            '.02f',
+            '.000f',
             # Missing precision
             ".e",
             ".f",

From 111c41f3b16375ad64ced4a41ed3259a8a64ebf7 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Wed, 21 Dec 2022 10:57:05 +0000
Subject: [PATCH 25/31] Add tests for a few more fill character corner cases

---
 Lib/test/test_fractions.py | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 6aada43395a79b..ec0602d5b7929e 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -992,6 +992,9 @@ def test_format_f_presentation_type(self):
             (F(-2, 3), '\x00>7.2f', '\x00\x00-0.67'),
             (F(-2, 3), '\n>7.2f', '\n\n-0.67'),
             (F(-2, 3), '\t>7.2f', '\t\t-0.67'),
+            (F(-2, 3), '>>7.2f', '>>-0.67'),
+            (F(-2, 3), '<>7.2f', '<<-0.67'),
+            (F(-2, 3), '→>7.2f', '→→-0.67'),
             # Zero-padding
             (F(-2, 3), '07.2f', '-000.67'),
             (F(-2, 3), '-07.2f', '-000.67'),

From fff3751aa8c11be668945ff07919f80b825373ff Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 22 Jan 2023 09:56:04 +0000
Subject: [PATCH 26/31] Add testcases for no presentation type with an integral
 fraction

---
 Lib/test/test_fractions.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index ce81edf53c885e..e2c06358d8acdf 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -848,6 +848,8 @@ def test_format_no_presentation_type(self):
         testcases = [
             (F(1, 3), '', '1/3'),
             (F(-1, 3), '', '-1/3'),
+            (F(3), '', '3'),
+            (F(-3), '', '-3'),
         ]
         for fraction, spec, expected in testcases:
             with self.subTest(fraction=fraction, spec=spec):

From 0b8bfa6696c5257a41dfc567bf521475b3a009d8 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 22 Jan 2023 10:09:17 +0000
Subject: [PATCH 27/31] Rename the regex to allow for future API expansion

---
 Lib/fractions.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index e05e57f0072e8a..581cb99cc9e201 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -139,9 +139,9 @@ def _round_to_figures(n, d, figures):
     return sign, significand, exponent
 
 
-# Pattern for matching format specification; supports 'e', 'E', 'f', 'F',
-# 'g', 'G' and '%' presentation types.
-_FORMAT_SPECIFICATION_MATCHER = re.compile(r"""
+# Pattern for matching float-style format specifications;
+# supports 'e', 'E', 'f', 'F', 'g', 'G' and '%' presentation types.
+_FLOAT_FORMAT_SPECIFICATION_MATCHER = re.compile(r"""
     (?:
         (?P<fill>.)?
         (?P<align>[<>=^])
@@ -412,7 +412,7 @@ def __format__(self, format_spec, /):
             return str(self)
 
         # Validate and parse the format specifier.
-        match = _FORMAT_SPECIFICATION_MATCHER(format_spec)
+        match = _FLOAT_FORMAT_SPECIFICATION_MATCHER(format_spec)
         if match is None:
             raise ValueError(
                 f"Invalid format specifier {format_spec!r} "

From 54ed40211e5ac53b073a11ae1ca41c125dddb26d Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 22 Jan 2023 10:09:31 +0000
Subject: [PATCH 28/31] Tweak comment

---
 Lib/fractions.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 581cb99cc9e201..0db0cbcb1627af 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -149,8 +149,8 @@ def _round_to_figures(n, d, figures):
     (?P<sign>[-+ ]?)
     (?P<no_neg_zero>z)?
     (?P<alt>\#)?
-    # lookahead so that a single '0' is treated as a minimum width rather
-    # than a zeropad flag
+    # A '0' that's *not* followed by another digit is parsed as a minimum width
+    # rather than a zeropad flag.
     (?P<zeropad>0(?=[0-9]))?
     (?P<minimumwidth>0|[1-9][0-9]*)?
     (?P<thousands_sep>[,_])?

From e3a5fd2c328a63cd785bf71b92d4dc54f7d8250d Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 22 Jan 2023 10:28:24 +0000
Subject: [PATCH 29/31] Tweak algorithm comments

---
 Lib/fractions.py | 21 ++++++++++++---------
 1 file changed, 12 insertions(+), 9 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 0db0cbcb1627af..8f977ce372700e 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -440,7 +440,9 @@ def __format__(self, format_spec, /):
         exponent_indicator = "E" if presentation_type in "EFG" else "e"
 
         # Round to get the digits we need, figure out where to place the point,
-        # and decide whether to use scientific notation.
+        # and decide whether to use scientific notation. 'point_pos' is the
+        # relative to the _end_ of the digit string: that is, it's the number
+        # of digits that should follow the point.
         if presentation_type in "fF%":
             exponent = -precision
             if presentation_type == "%":
@@ -464,7 +466,7 @@ def __format__(self, format_spec, /):
             )
             point_pos = figures - 1 if scientific else -exponent
 
-        # Get the suffix - the part following the digits.
+        # Get the suffix - the part following the digits, if any.
         if presentation_type == "%":
             suffix = "%"
         elif scientific:
@@ -472,11 +474,13 @@ def __format__(self, format_spec, /):
         else:
             suffix = ""
 
-        # Assemble the output: before padding, it has the form
-        # f"{sign}{leading}{trailing}", where `leading` includes thousands
-        # separators if necessary, and `trailing` includes the decimal
-        # separator where appropriate.
+        # String of output digits, padded sufficiently with zeros on the left
+        # so that we'll have at least one digit before the decimal point.
         digits = f"{significand:0{point_pos + 1}d}"
+
+        # Before padding, the output has the form f"{sign}{leading}{trailing}",
+        # where `leading` includes thousands separators if necessary and
+        # `trailing` includes the decimal separator where appropriate.
         sign = "-" if negative else pos_sign
         leading = digits[: len(digits) - point_pos]
         frac_part = digits[len(digits) - point_pos :]
@@ -502,10 +506,9 @@ def __format__(self, format_spec, /):
                 for pos in range(first_pos, len(leading), 3)
             )
 
-        # We now have a sign and a body.
+        # We now have a sign and a body. Pad with fill character if necessary
+        # and return.
         body = leading + trailing
-
-        # Pad with fill character if necessary and return.
         padding = fill * (minimumwidth - len(sign) - len(body))
         if align == ">":
             return padding + sign + body

From 098d34c9118cbe2a880d3c204dd29d2954373440 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 22 Jan 2023 13:18:27 +0000
Subject: [PATCH 30/31] Fix incorrect acceptance of Z instead of z

---
 Lib/fractions.py           | 4 ++--
 Lib/test/test_fractions.py | 2 ++
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 8f977ce372700e..49a3f2841a2ed4 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -155,8 +155,8 @@ def _round_to_figures(n, d, figures):
     (?P<minimumwidth>0|[1-9][0-9]*)?
     (?P<thousands_sep>[,_])?
     (?:\.(?P<precision>0|[1-9][0-9]*))?
-    (?P<presentation_type>[efg%])
-""", re.DOTALL | re.IGNORECASE | re.VERBOSE).fullmatch
+    (?P<presentation_type>[eEfFgG%])
+""", re.DOTALL | re.VERBOSE).fullmatch
 
 
 class Fraction(numbers.Rational):
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index e2c06358d8acdf..90eed073a69799 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -1211,6 +1211,8 @@ def test_invalid_formats(self):
             ".f",
             ".g",
             ".%",
+            # Z instead of z for negative zero suppression
+            'Z.2f'
         ]
         for spec in invalid_specs:
             with self.subTest(spec=spec):

From 2c476a28c0b437d48b61acff558ec59f25d8158a Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sun, 22 Jan 2023 13:21:38 +0000
Subject: [PATCH 31/31] Use consistent quote style in tests

---
 Lib/test/test_fractions.py | 42 +++++++++++++++++++-------------------
 1 file changed, 21 insertions(+), 21 deletions(-)

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 90eed073a69799..3bc6b409e05dc3 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -1075,7 +1075,7 @@ def test_format_f_presentation_type(self):
             # is being inserted programmatically: spec = f'{width}.2f'.
             (F('12.34'), '0.2f', '12.34'),
             (F('12.34'), 'X>0.2f', '12.34'),
-            # "F" should work identically to "f"
+            # 'F' should work identically to 'f'
             (F(22, 7), '.5F', '3.14286'),
             # %-specifier
             (F(22, 7), '.2%', '314.29%'),
@@ -1181,23 +1181,23 @@ def test_invalid_formats(self):
             format(fraction, None)
 
         invalid_specs = [
-            "Q6f",  # regression test
+            'Q6f',  # regression test
             # illegal to use fill or alignment when zero padding
-            "X>010f",
-            "X<010f",
-            "X^010f",
-            "X=010f",
-            "0>010f",
-            "0<010f",
-            "0^010f",
-            "0=010f",
-            ">010f",
-            "<010f",
-            "^010f",
-            "=010e",
-            "=010f",
-            "=010g",
-            "=010%",
+            'X>010f',
+            'X<010f',
+            'X^010f',
+            'X=010f',
+            '0>010f',
+            '0<010f',
+            '0^010f',
+            '0=010f',
+            '>010f',
+            '<010f',
+            '^010f',
+            '=010e',
+            '=010f',
+            '=010g',
+            '=010%',
             '>00.2f',
             '>00f',
             # Too many zeros - minimum width should not have leading zeros
@@ -1207,10 +1207,10 @@ def test_invalid_formats(self):
             '.02f',
             '.000f',
             # Missing precision
-            ".e",
-            ".f",
-            ".g",
-            ".%",
+            '.e',
+            '.f',
+            '.g',
+            '.%',
             # Z instead of z for negative zero suppression
             'Z.2f'
         ]

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