From ef7597994ddb289e7b1a0003a3cad8836b8cc998 Mon Sep 17 00:00:00 2001
From: Sergey B Kirpichev <skirpichev@gmail.com>
Date: Sun, 3 Feb 2019 18:14:48 +0300
Subject: [PATCH] Return passed in function in defun* decorators

This turn on more doctests, e.g.:

$ py.test mpmath/functions/qfunctions.py
============================= test session starts ==============================
platform linux -- Python 3.7.1, pytest-4.2.0, py-1.7.0, pluggy-0.8.1
hypothesis profile 'default' -> database=DirectoryBasedExampleDatabase('/home/sk/src/mpmath/.hypothesis/examples')
rootdir: /home/sk/src/mpmath, inifile: setup.cfg
plugins: xdist-1.26.1, timeout-1.3.3, forked-1.0.1, cov-2.6.1, hypothesis-4.4.3
collected 4 items

mpmath/functions/qfunctions.py ....                                      [100%]

=========================== 4 passed in 0.49 seconds ===========================

Some doctests were adapted.
---
 mpmath/function_docs.py       | 8 ++++----
 mpmath/functions/functions.py | 3 +++
 mpmath/functions/zeta.py      | 4 ++--
 3 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/mpmath/function_docs.py b/mpmath/function_docs.py
index 1d18ccc5..6f5ad759 100644
--- a/mpmath/function_docs.py
+++ b/mpmath/function_docs.py
@@ -9770,8 +9770,8 @@ on the unit sphere::
     >>> Y1 = lambda t,p: fp.spherharm(l1,m1,t,p)
     >>> Y2 = lambda t,p: fp.conj(fp.spherharm(l2,m2,t,p))
     >>> l1 = l2 = 3; m1 = m2 = 2
-    >>> print(fp.quad(lambda t,p: Y1(t,p)*Y2(t,p)*dS(t,p), *sphere))
-    (1+0j)
+    >>> fp.chop(fp.quad(lambda t,p: Y1(t,p)*Y2(t,p)*dS(t,p), *sphere))
+    1.0000000000000007
     >>> m2 = 1    # m1 != m2
     >>> print(fp.chop(fp.quad(lambda t,p: Y1(t,p)*Y2(t,p)*dS(t,p), *sphere)))
     0.0
@@ -10011,7 +10011,7 @@ Pass ``exact=True`` to obtain exact values of Stirling numbers as integers::
 
     >>> stirling1(42, 5)
     -2.864498971768501633736628e+50
-    >>> print stirling1(42, 5, exact=True)
+    >>> print(stirling1(42, 5, exact=True))
     -286449897176850163373662803014001546235808317440000
 
 """
@@ -10045,7 +10045,7 @@ Pass ``exact=True`` to obtain exact values of Stirling numbers as integers::
 
     >>> stirling2(52, 10)
     2.641822121003543906807485e+45
-    >>> print stirling2(52, 10, exact=True)
+    >>> print(stirling2(52, 10, exact=True))
     2641822121003543906807485307053638921722527655
 
 
diff --git a/mpmath/functions/functions.py b/mpmath/functions/functions.py
index f03c5974..4cdf5dd9 100644
--- a/mpmath/functions/functions.py
+++ b/mpmath/functions/functions.py
@@ -80,12 +80,15 @@ class SpecialFunctions(object):
 
 def defun_wrapped(f):
     SpecialFunctions.defined_functions[f.__name__] = f, True
+    return f
 
 def defun(f):
     SpecialFunctions.defined_functions[f.__name__] = f, False
+    return f
 
 def defun_static(f):
     setattr(SpecialFunctions, f.__name__, f)
+    return f
 
 @defun_wrapped
 def cot(ctx, z): return ctx.one / ctx.tan(z)
diff --git a/mpmath/functions/zeta.py b/mpmath/functions/zeta.py
index a21dc99a..a81041b2 100644
--- a/mpmath/functions/zeta.py
+++ b/mpmath/functions/zeta.py
@@ -938,8 +938,8 @@ def secondzeta(ctx, s, a = 0.015, **kwargs):
         0.023104993115419
         >>> xi = lambda s: 0.5*s*(s-1)*pi**(-0.5*s)*gamma(0.5*s)*zeta(s)
         >>> Xi = lambda t: xi(0.5+t*j)
-        >>> -0.5*diff(Xi,0,n=2)/Xi(0)
-        (0.023104993115419 + 0.0j)
+        >>> chop(-0.5*diff(Xi,0,n=2)/Xi(0))
+        0.023104993115419
 
     We may ask for an approximate error value::