From 0a891d70ded5fa8b1e6491529a3b531f521b5ae1 Mon Sep 17 00:00:00 2001
From: Guido van Rossum <guido@dropbox.com>
Date: Mon, 15 Aug 2016 09:12:52 -0700
Subject: Issue #12345: Add mathemathcal constant tau to math and cmath.

Patch by Lisa Roach. See also PEP 628.
---
 Doc/library/cmath.rst | 6 ++++--
 Doc/library/math.rst  | 7 +++++++
 Include/pymath.h      | 6 ++++++
 Lib/test/test_math.py | 1 +
 Misc/NEWS             | 3 +++
 Modules/cmathmodule.c | 1 +
 Modules/mathmodule.c  | 1 +
 7 files changed, 23 insertions(+), 2 deletions(-)

diff --git a/Doc/library/cmath.rst b/Doc/library/cmath.rst
index 62ddb6b..f04f8d0 100644
--- a/Doc/library/cmath.rst
+++ b/Doc/library/cmath.rst
@@ -253,6 +253,10 @@ Constants
 
    The mathematical constant *e*, as a float.
 
+.. data:: tau
+
+   The mathematical constant *τ*, as a float.
+
 .. index:: module: math
 
 Note that the selection of functions is similar, but not identical, to that in
@@ -276,5 +280,3 @@ cuts for numerical purposes, a good reference should be the following:
    Kahan, W:  Branch cuts for complex elementary functions; or, Much ado about
    nothing's sign bit.  In Iserles, A., and Powell, M. (eds.), The state of the art
    in numerical analysis. Clarendon Press (1987) pp165-211.
-
-
diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 3fdea18..32e1352 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -426,6 +426,13 @@ Constants
 
    The mathematical constant e = 2.718281..., to available precision.
 
+.. data:: tau
+
+   The mathematical constant τ = 6.283185..., to available precision.
+   Tau is a circle constant equal to 2π, the ratio of a circle's circumference to
+   its radius. To learn more about Tau, check out Vi Hart's video `Pi is (still)
+   Wrong <https://www.youtube.com/watch?v=jG7vhMMXagQ>`_, and start celebrating
+   `Tau day <http://tauday.com/>`_ by eating twice as much pie!
 
 .. data:: inf
 
diff --git a/Include/pymath.h b/Include/pymath.h
index ed76053..894362e 100644
--- a/Include/pymath.h
+++ b/Include/pymath.h
@@ -55,6 +55,12 @@ extern double pow(double, double);
 #define Py_MATH_E 2.7182818284590452354
 #endif
 
+/* Tau (2pi) to 40 digits, taken from tauday.com/tau-digits. */
+#ifndef Py_MATH_TAU
+#define Py_MATH_TAU 6.2831853071795864769252867665590057683943L
+#endif
+
+
 /* On x86, Py_FORCE_DOUBLE forces a floating-point number out of an x87 FPU
    register and into a 64-bit memory location, rounding from extended
    precision to double precision in the process.  On other platforms it does
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 605adb5..48e8007 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -196,6 +196,7 @@ class MathTests(unittest.TestCase):
     def testConstants(self):
         self.ftest('pi', math.pi, 3.1415926)
         self.ftest('e', math.e, 2.7182818)
+        self.assertEqual(math.tau, 2*math.pi)
 
     def testAcos(self):
         self.assertRaises(TypeError, math.acos)
diff --git a/Misc/NEWS b/Misc/NEWS
index eabbf8c..ec86a53 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -57,6 +57,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #12345: Add mathemathcal constant tau to math and cmath. See also
+  PEP 628.
+
 - Issue #26823: traceback.StackSummary.format now abbreviates large sections of
   repeated lines as "[Previous line repeated {count} more times]" (this change
   then further affects other traceback display operations in the module). Patch
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index cba42a7..0e7d4db 100644
--- a/Modules/cmathmodule.c
+++ b/Modules/cmathmodule.c
@@ -1239,6 +1239,7 @@ PyInit_cmath(void)
     PyModule_AddObject(m, "pi",
                        PyFloat_FromDouble(Py_MATH_PI));
     PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
+    PyModule_AddObject(m, "tau", PyFloat_FromDouble(Py_MATH_TAU)); /* 2pi */
 
     /* initialize special value tables */
 
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index cf04901..43aa229 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2144,6 +2144,7 @@ PyInit_math(void)
 
     PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
     PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
+    PyModule_AddObject(m, "tau", PyFloat_FromDouble(Py_MATH_TAU));  /* 2pi */
     PyModule_AddObject(m, "inf", PyFloat_FromDouble(m_inf()));
 #if !defined(PY_NO_SHORT_FLOAT_REPR) || defined(Py_NAN)
     PyModule_AddObject(m, "nan", PyFloat_FromDouble(m_nan()));
-- 
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