From 482b1f983e466f2834c739c6247ff555f5b5cfeb Mon Sep 17 00:00:00 2001
From: Serhiy Storchaka <storchaka@gmail.com>
Date: Sun, 11 Aug 2019 16:55:59 +0300
Subject: [PATCH 1/4] bpo-37822: Add math.as_integer_ratio().

---
 Doc/library/math.rst                          | 11 +++
 Doc/whatsnew/3.9.rst                          |  8 ++
 Lib/fractions.py                              | 26 ++-----
 Lib/statistics.py                             | 18 +----
 Lib/test/test_math.py                         | 29 ++++++++
 .../2019-08-11-16-55-46.bpo-37822.7xHl1w.rst  |  1 +
 Modules/clinic/mathmodule.c.h                 | 11 ++-
 Modules/mathmodule.c                          | 74 +++++++++++++++++++
 8 files changed, 141 insertions(+), 37 deletions(-)
 create mode 100644 Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 43eaba935a164a..bbc577617a9473 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -29,6 +29,17 @@ noted otherwise, all return values are floats.
 Number-theoretic and representation functions
 ---------------------------------------------
 
+.. function:: as_integer_ratio(number)
+
+   Return integer ratio.
+
+   This function returns ``number.as_integer_ratio()`` if the argument has
+   the ``as_integer_ratio()`` method, otherwise it returns a pair
+   ``(number.numerator, number.denominator)``.
+
+   .. versionadded:: 3.9
+
+
 .. function:: ceil(x)
 
    Return the ceiling of *x*, the smallest integer greater than or equal to *x*.
diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index 61d9e745e87ccf..acdd418c08b2b7 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/Doc/whatsnew/3.9.rst
@@ -109,6 +109,14 @@ New Modules
 Improved Modules
 ================
 
+
+math
+----
+
+Added new function :func:`math.as_integer_ratio`.
+(Contributed by Serhiy Storchaka in :issue:``.)
+
+
 threading
 ---------
 
diff --git a/Lib/fractions.py b/Lib/fractions.py
index 7443bd3e0c6af9..9f1ff0a10cc4dd 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -115,22 +115,7 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
         self = super(Fraction, cls).__new__(cls)
 
         if denominator is None:
-            if type(numerator) is int:
-                self._numerator = numerator
-                self._denominator = 1
-                return self
-
-            elif isinstance(numerator, numbers.Rational):
-                self._numerator = numerator.numerator
-                self._denominator = numerator.denominator
-                return self
-
-            elif isinstance(numerator, (float, Decimal)):
-                # Exact conversion
-                self._numerator, self._denominator = numerator.as_integer_ratio()
-                return self
-
-            elif isinstance(numerator, str):
+            if isinstance(numerator, str):
                 # Handle construction from strings.
                 m = _RATIONAL_FORMAT.match(numerator)
                 if m is None:
@@ -156,10 +141,13 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
                             denominator *= 10**-exp
                 if m.group('sign') == '-':
                     numerator = -numerator
-
             else:
-                raise TypeError("argument should be a string "
-                                "or a Rational instance")
+                try:
+                    self._numerator, self._denominator = math.as_integer_ratio(numerator)
+                    return self
+                except TypeError:
+                    raise TypeError("argument should be a string "
+                                    "or a Rational instance")
 
         elif type(numerator) is int is type(denominator):
             pass # *very* normal case
diff --git a/Lib/statistics.py b/Lib/statistics.py
index 77291dd62cb90e..b11047cb703421 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -225,27 +225,11 @@ def _exact_ratio(x):
     x is expected to be an int, Fraction, Decimal or float.
     """
     try:
-        # Optimise the common case of floats. We expect that the most often
-        # used numeric type will be builtin floats, so try to make this as
-        # fast as possible.
-        if type(x) is float or type(x) is Decimal:
-            return x.as_integer_ratio()
-        try:
-            # x may be an int, Fraction, or Integral ABC.
-            return (x.numerator, x.denominator)
-        except AttributeError:
-            try:
-                # x may be a float or Decimal subclass.
-                return x.as_integer_ratio()
-            except AttributeError:
-                # Just give up?
-                pass
+        return math.as_integer_ratio(x)
     except (OverflowError, ValueError):
         # float NAN or INF.
         assert not _isfinite(x)
         return (x, None)
-    msg = "can't convert type '{}' to numerator/denominator"
-    raise TypeError(msg.format(type(x).__name__))
 
 
 def _convert(value, T):
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index c237bc1942e655..492e024250bb11 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -12,6 +12,8 @@
 import random
 import struct
 import sys
+from decimal import Decimal
+from fractions import Fraction
 
 
 eps = 1E-05
@@ -293,6 +295,33 @@ def testAcosh(self):
         self.assertRaises(ValueError, math.acosh, NINF)
         self.assertTrue(math.isnan(math.acosh(NAN)))
 
+    def testAsIntegerRatio(self):
+        as_integer_ratio = math.as_integer_ratio
+        self.assertEqual(as_integer_ratio(0), (0, 1))
+        self.assertEqual(as_integer_ratio(3), (3, 1))
+        self.assertEqual(as_integer_ratio(-3), (-3, 1))
+        self.assertEqual(as_integer_ratio(False), (0, 1))
+        self.assertEqual(as_integer_ratio(True), (1, 1))
+        self.assertEqual(as_integer_ratio(0.0), (0, 1))
+        self.assertEqual(as_integer_ratio(-0.0), (0, 1))
+        self.assertEqual(as_integer_ratio(0.875), (7, 8))
+        self.assertEqual(as_integer_ratio(-0.875), (-7, 8))
+        self.assertEqual(as_integer_ratio(Decimal('0')), (0, 1))
+        self.assertEqual(as_integer_ratio(Decimal('0.875')), (7, 8))
+        self.assertEqual(as_integer_ratio(Decimal('-0.875')), (-7, 8))
+        self.assertEqual(as_integer_ratio(Fraction(0)), (0, 1))
+        self.assertEqual(as_integer_ratio(Fraction(7, 8)), (7, 8))
+        self.assertEqual(as_integer_ratio(Fraction(-7, 8)), (-7, 8))
+
+        self.assertRaises(OverflowError, as_integer_ratio, float('inf'))
+        self.assertRaises(OverflowError, as_integer_ratio, float('-inf'))
+        self.assertRaises(ValueError, as_integer_ratio, float('nan'))
+        self.assertRaises(OverflowError, as_integer_ratio, Decimal('inf'))
+        self.assertRaises(OverflowError, as_integer_ratio, Decimal('-inf'))
+        self.assertRaises(ValueError, as_integer_ratio, Decimal('nan'))
+
+        self.assertRaises(TypeError, as_integer_ratio, '0')
+
     def testAsin(self):
         self.assertRaises(TypeError, math.asin)
         self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
diff --git a/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst b/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst
new file mode 100644
index 00000000000000..37e9c819b3bb21
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst
@@ -0,0 +1 @@
+Added :func:`math.as_integer_ratio`.
diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index 84561b955787b7..701e1c932b83f2 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -712,4 +712,13 @@ math_comb(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=f93cfe13ab2fdb4e input=a9049054013a1b77]*/
+
+PyDoc_STRVAR(math_as_integer_ratio__doc__,
+"as_integer_ratio($module, x, /)\n"
+"--\n"
+"\n"
+"greatest common divisor of x and y");
+
+#define MATH_AS_INTEGER_RATIO_METHODDEF    \
+    {"as_integer_ratio", (PyCFunction)math_as_integer_ratio, METH_O, math_as_integer_ratio__doc__},
+/*[clinic end generated code: output=f9722232fc321d17 input=a9049054013a1b77]*/
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index e1b46ec384a373..76bc1cc1c9ed4f 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -3306,9 +3306,83 @@ math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
 }
 
 
+/*[clinic input]
+math.as_integer_ratio
+    x: object
+    /
+greatest common divisor of x and y
+[clinic start generated code]*/
+
+static PyObject *
+math_as_integer_ratio(PyObject *module, PyObject *x)
+/*[clinic end generated code: output=1844868fd4efb2f1 input=d7f2e8ffd51c6599]*/
+{
+    _Py_IDENTIFIER(as_integer_ratio);
+    _Py_IDENTIFIER(numerator);
+    _Py_IDENTIFIER(denominator);
+    PyObject *ratio, *as_integer_ratio, *numerator, *denominator;
+
+    if (PyLong_CheckExact(x)) {
+        return PyTuple_Pack(2, x, _PyLong_One);
+    }
+
+    if (_PyObject_LookupAttrId(x, &PyId_as_integer_ratio, &as_integer_ratio) < 0) {
+        return NULL;
+    }
+    if (as_integer_ratio) {
+        ratio = _PyObject_CallNoArg(as_integer_ratio);
+        Py_DECREF(as_integer_ratio);
+        if (ratio == NULL) {
+            return NULL;
+        }
+        if (!PyTuple_Check(ratio)) {
+            PyErr_Format(PyExc_TypeError,
+                        "unexpected return type from as_integer_ratio(): "
+                        "expected tuple, got '%.200s'",
+                        Py_TYPE(ratio)->tp_name);
+            Py_DECREF(ratio);
+            return NULL;
+        }
+        if (PyTuple_GET_SIZE(ratio) != 2) {
+            PyErr_SetString(PyExc_ValueError,
+                            "as_integer_ratio() must return a 2-tuple");
+            Py_DECREF(ratio);
+            return NULL;
+        }
+    }
+    else {
+        if (_PyObject_LookupAttrId(x, &PyId_numerator, &numerator) < 0) {
+            return NULL;
+        }
+        if (numerator == NULL) {
+            PyErr_Format(PyExc_TypeError,
+                         "required a number, not '%.200s'",
+                         Py_TYPE(x)->tp_name);
+            return NULL;
+        }
+        if (_PyObject_LookupAttrId(x, &PyId_denominator, &denominator) < 0) {
+            Py_DECREF(numerator);
+            return NULL;
+        }
+        if (denominator == NULL) {
+            Py_DECREF(numerator);
+            PyErr_Format(PyExc_TypeError,
+                         "required a number, not '%.200s'",
+                         Py_TYPE(x)->tp_name);
+            return NULL;
+        }
+        ratio = PyTuple_Pack(2, numerator, denominator);
+        Py_DECREF(numerator);
+        Py_DECREF(denominator);
+    }
+    return ratio;
+}
+
+
 static PyMethodDef math_methods[] = {
     {"acos",            math_acos,      METH_O,         math_acos_doc},
     {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
+    MATH_AS_INTEGER_RATIO_METHODDEF
     {"asin",            math_asin,      METH_O,         math_asin_doc},
     {"asinh",           math_asinh,     METH_O,         math_asinh_doc},
     {"atan",            math_atan,      METH_O,         math_atan_doc},

From a587d7d890f137f196ea2de650d324889d5eac5d Mon Sep 17 00:00:00 2001
From: Serhiy Storchaka <storchaka@gmail.com>
Date: Sun, 11 Aug 2019 17:37:25 +0300
Subject: [PATCH 2/4] Better TypeError message.

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

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 9f1ff0a10cc4dd..05eda36b438dac 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -146,8 +146,8 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
                     self._numerator, self._denominator = math.as_integer_ratio(numerator)
                     return self
                 except TypeError:
-                    raise TypeError("argument should be a string "
-                                    "or a Rational instance")
+                    raise TypeError("argument should be a string or a number, "
+                                    "not %s" % type(numerator).__name__) from None
 
         elif type(numerator) is int is type(denominator):
             pass # *very* normal case

From e658d19083b3d5abfbbe536e3227e3781883e22a Mon Sep 17 00:00:00 2001
From: Serhiy Storchaka <storchaka@gmail.com>
Date: Mon, 19 Aug 2019 08:13:03 +0300
Subject: [PATCH 3/4] Make it a private helper math._as_integer_ratio().

---
 Doc/library/math.rst                              | 11 -----------
 Doc/whatsnew/3.9.rst                              |  8 --------
 Lib/fractions.py                                  |  2 +-
 Lib/statistics.py                                 |  2 +-
 Lib/test/test_math.py                             |  3 ++-
 .../2019-08-11-16-55-46.bpo-37822.7xHl1w.rst      |  1 -
 Modules/clinic/mathmodule.c.h                     | 15 +++++++++------
 Modules/mathmodule.c                              | 14 +++++++++-----
 8 files changed, 22 insertions(+), 34 deletions(-)
 delete mode 100644 Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index bbc577617a9473..43eaba935a164a 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -29,17 +29,6 @@ noted otherwise, all return values are floats.
 Number-theoretic and representation functions
 ---------------------------------------------
 
-.. function:: as_integer_ratio(number)
-
-   Return integer ratio.
-
-   This function returns ``number.as_integer_ratio()`` if the argument has
-   the ``as_integer_ratio()`` method, otherwise it returns a pair
-   ``(number.numerator, number.denominator)``.
-
-   .. versionadded:: 3.9
-
-
 .. function:: ceil(x)
 
    Return the ceiling of *x*, the smallest integer greater than or equal to *x*.
diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index 4dc9613f70e9fe..f09e09c2b90560 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/Doc/whatsnew/3.9.rst
@@ -109,14 +109,6 @@ New Modules
 Improved Modules
 ================
 
-
-math
-----
-
-Added new function :func:`math.as_integer_ratio`.
-(Contributed by Serhiy Storchaka in :issue:``.)
-
-
 threading
 ---------
 
diff --git a/Lib/fractions.py b/Lib/fractions.py
index 34e04cc16c5ad1..e5b16c9fe358e2 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -143,7 +143,7 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
                     numerator = -numerator
             else:
                 try:
-                    self._numerator, self._denominator = math.as_integer_ratio(numerator)
+                    self._numerator, self._denominator = math._as_integer_ratio(numerator)
                     return self
                 except TypeError:
                     raise TypeError("argument should be a string or a number, "
diff --git a/Lib/statistics.py b/Lib/statistics.py
index b11047cb703421..1831d0a36840b7 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -225,7 +225,7 @@ def _exact_ratio(x):
     x is expected to be an int, Fraction, Decimal or float.
     """
     try:
-        return math.as_integer_ratio(x)
+        return math._as_integer_ratio(x)
     except (OverflowError, ValueError):
         # float NAN or INF.
         assert not _isfinite(x)
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 492e024250bb11..1cf2e7c66ee9e9 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -295,8 +295,9 @@ def testAcosh(self):
         self.assertRaises(ValueError, math.acosh, NINF)
         self.assertTrue(math.isnan(math.acosh(NAN)))
 
+    @support.cpython_only
     def testAsIntegerRatio(self):
-        as_integer_ratio = math.as_integer_ratio
+        as_integer_ratio = math._as_integer_ratio
         self.assertEqual(as_integer_ratio(0), (0, 1))
         self.assertEqual(as_integer_ratio(3), (3, 1))
         self.assertEqual(as_integer_ratio(-3), (-3, 1))
diff --git a/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst b/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst
deleted file mode 100644
index 37e9c819b3bb21..00000000000000
--- a/Misc/NEWS.d/next/Library/2019-08-11-16-55-46.bpo-37822.7xHl1w.rst
+++ /dev/null
@@ -1 +0,0 @@
-Added :func:`math.as_integer_ratio`.
diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index 701e1c932b83f2..66e9ad2c596f70 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -713,12 +713,15 @@ math_comb(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
     return return_value;
 }
 
-PyDoc_STRVAR(math_as_integer_ratio__doc__,
-"as_integer_ratio($module, x, /)\n"
+PyDoc_STRVAR(math__as_integer_ratio__doc__,
+"_as_integer_ratio($module, x, /)\n"
 "--\n"
 "\n"
-"greatest common divisor of x and y");
+"Return integer ratio.\n"
+"\n"
+"Return a pair of integers, whose ratio is exactly equal to the original\n"
+"number and with a positive denominator.");
 
-#define MATH_AS_INTEGER_RATIO_METHODDEF    \
-    {"as_integer_ratio", (PyCFunction)math_as_integer_ratio, METH_O, math_as_integer_ratio__doc__},
-/*[clinic end generated code: output=f9722232fc321d17 input=a9049054013a1b77]*/
+#define MATH__AS_INTEGER_RATIO_METHODDEF    \
+    {"_as_integer_ratio", (PyCFunction)math__as_integer_ratio, METH_O, math__as_integer_ratio__doc__},
+/*[clinic end generated code: output=7f658f3ee1d866ba input=a9049054013a1b77]*/
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 76bc1cc1c9ed4f..026fc324b9ef0e 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -3307,15 +3307,19 @@ math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
 
 
 /*[clinic input]
-math.as_integer_ratio
+math._as_integer_ratio
     x: object
     /
-greatest common divisor of x and y
+
+Return integer ratio.
+
+Return a pair of integers, whose ratio is exactly equal to the original
+number and with a positive denominator.
 [clinic start generated code]*/
 
 static PyObject *
-math_as_integer_ratio(PyObject *module, PyObject *x)
-/*[clinic end generated code: output=1844868fd4efb2f1 input=d7f2e8ffd51c6599]*/
+math__as_integer_ratio(PyObject *module, PyObject *x)
+/*[clinic end generated code: output=2e4f43d93f6e7850 input=b54b48dd6bbe22ea]*/
 {
     _Py_IDENTIFIER(as_integer_ratio);
     _Py_IDENTIFIER(numerator);
@@ -3382,7 +3386,7 @@ math_as_integer_ratio(PyObject *module, PyObject *x)
 static PyMethodDef math_methods[] = {
     {"acos",            math_acos,      METH_O,         math_acos_doc},
     {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
-    MATH_AS_INTEGER_RATIO_METHODDEF
+    MATH__AS_INTEGER_RATIO_METHODDEF
     {"asin",            math_asin,      METH_O,         math_asin_doc},
     {"asinh",           math_asinh,     METH_O,         math_asinh_doc},
     {"atan",            math_atan,      METH_O,         math_atan_doc},

From 86f9f20a4b6ea2219475e9564be28ba7dc1ce933 Mon Sep 17 00:00:00 2001
From: Serhiy Storchaka <storchaka@gmail.com>
Date: Tue, 20 Aug 2019 09:27:04 +0300
Subject: [PATCH 4/4] Optimize.

---
 Lib/fractions.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index e5b16c9fe358e2..9787974a5ed65a 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -9,6 +9,7 @@
 import operator
 import re
 import sys
+from math import _as_integer_ratio
 
 __all__ = ['Fraction', 'gcd']
 
@@ -143,7 +144,7 @@ def __new__(cls, numerator=0, denominator=None, *, _normalize=True):
                     numerator = -numerator
             else:
                 try:
-                    self._numerator, self._denominator = math._as_integer_ratio(numerator)
+                    self._numerator, self._denominator = _as_integer_ratio(numerator)
                     return self
                 except TypeError:
                     raise TypeError("argument should be a string or a number, "