BUG: linalg: norm fails on longdouble, signed int

This fixes the following bug with longdouble:

>>> x = np.arange(10, dtype=np.longdouble)
>>> np.linalg.norm(x, ord=3)
Traceback (most recent call last):
  File "<ipython-input-5-7ee53a8ac142>", line 1, in <module>
    np.linalg.norm(x, ord=3)
  File "/tmp/v/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 2090, in norm
    return add.reduce(absx**ord, axis=axis)**(1.0/ord)
UnboundLocalError: local variable 'absx' referenced before assignment

As well as the handling of minimal values for signed integers:

>>> x = np.array([-2**31], dtype=np.int32)
>>> np.linalg.norm(x, ord=3)
/tmp/v/lib/python2.7/site-packages/numpy/linalg/linalg.py:2090: RuntimeWarning: invalid value encountered in double_scalars
  return add.reduce(absx**ord, axis=axis)**(1.0/ord)
nan

2 files changed, 24 insertions, 4 deletions

diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py
index 1b82c7cc0..dd586827e 100644
--- a/numpy/linalg/linalg.py
+++ b/numpy/linalg/linalg.py
@@ -22,7 +22,7 @@ from numpy.core import (
     array, asarray, zeros, empty, empty_like, transpose, intc, single, double,
     csingle, cdouble, inexact, complexfloating, newaxis, ravel, all, Inf, dot,
     add, multiply, sqrt, maximum, fastCopyAndTranspose, sum, isfinite, size,
-    finfo, errstate, geterrobj, longdouble, rollaxis, amin, amax, product,
+    finfo, errstate, geterrobj, longdouble, rollaxis, amin, amax, product, abs,
     broadcast
     )
 from numpy.lib import triu, asfarray
@@ -2082,12 +2082,20 @@ def norm(x, ord=None, axis=None):
                 ord + 1
             except TypeError:
                 raise ValueError("Invalid norm order for vectors.")
-            if x.dtype.type is not longdouble:
+            if x.dtype.type is longdouble:
                 # Convert to a float type, so integer arrays give
                 # float results.  Don't apply asfarray to longdouble arrays,
                 # because it will downcast to float64.
-                absx = asfarray(abs(x))
-            return add.reduce(absx**ord, axis=axis)**(1.0/ord)
+                absx = abs(x)
+            else:
+                absx = asfarray(x)
+                if absx.dtype is x.dtype:
+                    absx = abs(absx)
+                else:
+                    # if the type changed, we can safely overwrite absx
+                    abs(absx, out=absx)
+            absx **= ord
+            return add.reduce(absx, axis=axis) ** (1.0 / ord)
     elif len(axis) == 2:
         row_axis, col_axis = axis
         if not (-nd <= row_axis < nd and -nd <= col_axis < nd):
diff --git a/numpy/linalg/tests/test_linalg.py b/numpy/linalg/tests/test_linalg.py
index dd4cbcc4f..feb4c8224 100644
--- a/numpy/linalg/tests/test_linalg.py
+++ b/numpy/linalg/tests/test_linalg.py
@@ -909,6 +909,18 @@ class _TestNorm(object):
         assert_raises(ValueError, norm, B, None, (2, 3))
         assert_raises(ValueError, norm, B, None, (0, 1, 2))
 
+    def test_longdouble_norm(self):
+        # Non-regression test: p-norm of longdouble would previously raise
+        # UnboundLocalError.
+        x = np.arange(10, dtype=np.longdouble)
+        old_assert_almost_equal(norm(x, ord=3), 12.65, decimal=2)
+
+    def test_intmin(self):
+        # Non-regression test: p-norm of signed integer would previously do
+        # float cast and abs in the wrong order.
+        x = np.array([-2 ** 31], dtype=np.int32)
+        old_assert_almost_equal(norm(x, ord=3), 2 ** 31, decimal=5)
+
 
 class TestNormDouble(_TestNorm):
     dt = np.double