From 4e26f6de609a8e1e56e78fcabf37dbde14d6339a Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 29 Jun 2021 16:23:49 +0200
Subject: [PATCH 01/17] add sign, sgn

---
 CHANGELOG.md                     |  2 +
 heat/core/rounding.py            | 95 +++++++++++++++++++++++++++++++-
 heat/core/tests/test_rounding.py | 68 +++++++++++++++++++++++
 3 files changed, 164 insertions(+), 1 deletion(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0c26939204..fdc833bdba 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -55,6 +55,8 @@ Example on 2 processes:
 - [#768](https://github.com/helmholtz-analytics/heat/pull/768) New feature: unary positive and negative operations
 ### Manipulations
 - [#796](https://github.com/helmholtz-analytics/heat/pull/796) `DNDarray.reshape(shape)`: method now allows shape elements to be passed in as single arguments.
+### Rounding
+- [#827](https://github.com/helmholtz-analytics/heat/pull/827) New feature: `sign`, `sgn`
 ### Trigonometrics / Arithmetic
 - [#806](https://github.com/helmholtz-analytics/heat/pull/809) New feature: `square`
 - [#809](https://github.com/helmholtz-analytics/heat/pull/809) New feature: `acosh`, `asinh`, `atanh`
diff --git a/heat/core/rounding.py b/heat/core/rounding.py
index bef9a13eab..d19e9175a2 100644
--- a/heat/core/rounding.py
+++ b/heat/core/rounding.py
@@ -12,7 +12,19 @@
 from . import sanitation
 from . import types
 
-__all__ = ["abs", "absolute", "ceil", "clip", "fabs", "floor", "modf", "round", "trunc"]
+__all__ = [
+    "abs",
+    "absolute",
+    "ceil",
+    "clip",
+    "fabs",
+    "floor",
+    "modf",
+    "round",
+    "sign",
+    "sgn",
+    "trunc",
+]
 
 
 def abs(
@@ -328,6 +340,87 @@ def round(
 DNDarray.round.__doc__ = round.__doc__
 
 
+def sign(x: DNDarray, out: Optional[DNDarray] = None):
+    """
+    Returns an indication of the sign of a number, element-wise. The definition for complex values is equivalent to :math:`x / \\sqrt{x \\cdot x}`.
+
+    Parameters
+    ----------
+    x : DNDarray
+        Input array
+    out : DNDarray, optional
+        A location in which to store the results.
+
+    See Also
+    --------
+    :func:`sgn`
+        Equivalent function on non-complex arrays. The definition for complex values is equivalent to :math:`x / |x|`.
+
+    Examples
+    --------
+    >>> a = ht.array([-1, -0.5, 0, 0.5, 1])
+    >>> ht.sign(a)
+    DNDarray([-1., -1.,  0.,  1.,  1.], dtype=ht.float32, device=cpu:0, split=None)
+    >>> ht.sign(ht.array([5-2j, 3+4j]))
+    DNDarray([(1+0j), (1+0j)], dtype=ht.complex64, device=cpu:0, split=None)
+    """
+    # special case for complex values
+    if types.heat_type_is_complexfloating(x.dtype):
+        sanitation.sanitize_in(x)
+        if out is not None:
+            sanitation.sanitize_out(out, x.shape, x.split, x.device)
+            out.larray.copy_(x.larray)
+            data = out.larray
+        else:
+            data = torch.clone(x.larray)
+
+        indices = torch.nonzero(data)
+        pos = torch.split(indices, 1, 1)
+        data[pos] = x.larray[pos] / torch.sqrt(torch.square(x.larray[pos]))
+
+        if out is not None:
+            out.__dtype = types.heat_type_of(data)
+            return out
+        return DNDarray(
+            data,
+            gshape=x.shape,
+            dtype=types.heat_type_of(data),
+            split=x.split,
+            device=x.device,
+            comm=x.comm,
+            balanced=x.balanced,
+        )
+
+    return _operations.__local_op(torch.sign, x, out)
+
+
+def sgn(x: DNDarray, out: Optional[DNDarray] = None):
+    """
+    Returns an indication of the sign of a number, element-wise. The definition for complex values is equivalent to :math:`x / |x|`.
+
+    Parameters
+    ----------
+    x : DNDarray
+        Input array
+    out : DNDarray, optional
+        A location in which to store the results.
+
+    See Also
+    --------
+    :func:`sign`
+        Equivalent function on non-complex arrays. The definition for complex values is equivalent to :math:`x / \\sqrt{x \\cdot x}`
+
+    Examples
+    --------
+    >>> a = ht.array([-1, -0.5, 0, 0.5, 1])
+    >>> ht.sign(a)
+    DNDarray([-1., -1.,  0.,  1.,  1.], dtype=ht.float32, device=cpu:0, split=None)
+    >>> ht.sgn(ht.array([5-2j, 3+4j]))
+    DNDarray([(0.9284766912460327-0.3713906705379486j),  (0.6000000238418579+0.800000011920929j)], dtype=ht.complex64, device=cpu:0, split=None)
+    """
+    return _operations.__local_op(torch.sgn, x, out)
+
+
 def trunc(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
     """
     Return the trunc of the input, element-wise.
diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index 23af481e93..764f2c90b6 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -301,6 +301,74 @@ def test_round(self):
         self.assertEqual(float64_round_distrbd.dtype, ht.float64)
         self.assert_array_equal(float64_round_distrbd, comparison)
 
+    def test_sign(self):
+        # floats 1d
+        a = ht.array([-1, -0.5, 0, 0.5, 1])
+        signed = ht.sign(a)
+        comparison = ht.array([-1.0, -1, 0, 1, 1])
+
+        self.assertEqual(signed.dtype, comparison.dtype)
+        self.assertEqual(signed.shape, comparison.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertEqual(signed.split, a.split)
+        self.assertTrue(ht.equal(signed, comparison))
+
+        # complex + 2d + split
+        a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=0)
+        signed = ht.sign(a)
+        comparison = ht.array([[1 + 0j, -1 + 0j], [0 + 0j, 1 + 0j]])
+
+        self.assertEqual(signed.dtype, comparison.dtype)
+        self.assertEqual(signed.shape, comparison.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertEqual(signed.split, a.split)
+        self.assertTrue(ht.equal(signed, comparison))
+
+        # complex + split + out
+        a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=1)
+        b = ht.empty_like(a)
+        signed = ht.sign(a, b)
+        comparison = ht.array([[1 + 0j, -1 + 0j], [0 + 0j, 1 + 0j]])
+
+        self.assertIs(b, signed)
+        self.assertEqual(signed.dtype, comparison.dtype)
+        self.assertEqual(signed.shape, comparison.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertEqual(signed.split, a.split)
+        self.assertTrue(ht.equal(signed, comparison))
+
+        # zeros + 3d + complex + split
+        a = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
+        signed = ht.sign(a)
+        comparison = ht.zeros((4, 4, 4), dtype=ht.complex128)
+
+        self.assertEqual(signed.dtype, comparison.dtype)
+        self.assertEqual(signed.shape, comparison.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertEqual(signed.split, a.split)
+        self.assertTrue(ht.equal(signed, comparison))
+
+    def test_sgn(self):
+        # floats
+        a = ht.array([-1, -0.5, 0, 0.5, 1])
+        signed = ht.sgn(a)
+        comparison = ht.array([-1.0, -1, 0, 1, 1])
+
+        self.assertEqual(signed.dtype, comparison.dtype)
+        self.assertEqual(signed.shape, comparison.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertTrue(ht.equal(signed, comparison))
+
+        # complex
+        a = ht.array([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]], split=0)
+        signed = ht.sgn(a)
+        comparison = torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]]))
+
+        self.assertEqual(signed.dtype, ht.heat_type_of(comparison))
+        self.assertEqual(signed.shape, a.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertTrue(ht.equal(signed, ht.array(comparison)))
+
     def test_trunc(self):
         base_array = np.random.randn(20)
 

From 4327a57a8e8a189e67da9fd658c6469164c8b6c9 Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 29 Jun 2021 16:42:52 +0200
Subject: [PATCH 02/17] compute indices on cpu

---
 heat/core/rounding.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/heat/core/rounding.py b/heat/core/rounding.py
index d19e9175a2..34ef6e5bed 100644
--- a/heat/core/rounding.py
+++ b/heat/core/rounding.py
@@ -372,9 +372,9 @@ def sign(x: DNDarray, out: Optional[DNDarray] = None):
             out.larray.copy_(x.larray)
             data = out.larray
         else:
-            data = torch.clone(x.larray)
+            data = torch.clone(x.larray.cpu())
 
-        indices = torch.nonzero(data)
+        indices = torch.nonzero(data.cpu())  # nonzero_cuda not implemented for complex
         pos = torch.split(indices, 1, 1)
         data[pos] = x.larray[pos] / torch.sqrt(torch.square(x.larray[pos]))
 

From 82a7e401548dea5ee2cf2e02248a1afcfd28c3d6 Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 29 Jun 2021 16:46:02 +0200
Subject: [PATCH 03/17] revert

---
 heat/core/rounding.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/heat/core/rounding.py b/heat/core/rounding.py
index 34ef6e5bed..d19e9175a2 100644
--- a/heat/core/rounding.py
+++ b/heat/core/rounding.py
@@ -372,9 +372,9 @@ def sign(x: DNDarray, out: Optional[DNDarray] = None):
             out.larray.copy_(x.larray)
             data = out.larray
         else:
-            data = torch.clone(x.larray.cpu())
+            data = torch.clone(x.larray)
 
-        indices = torch.nonzero(data.cpu())  # nonzero_cuda not implemented for complex
+        indices = torch.nonzero(data)
         pos = torch.split(indices, 1, 1)
         data[pos] = x.larray[pos] / torch.sqrt(torch.square(x.larray[pos]))
 

From 9d375a2f90403edfe41ab5caebc703db2ca420fe Mon Sep 17 00:00:00 2001
From: coquelin77 <daniel.coquelin@gmail.com>
Date: Tue, 13 Jul 2021 13:52:43 +0200
Subject: [PATCH 04/17] correcting device issue in sign tests (hopefully)

---
 heat/core/tests/test_rounding.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index 764f2c90b6..de921de7f0 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -363,6 +363,7 @@ def test_sgn(self):
         a = ht.array([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]], split=0)
         signed = ht.sgn(a)
         comparison = torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]]))
+        comparison = comparison.to(a.device.torch_device)
 
         self.assertEqual(signed.dtype, ht.heat_type_of(comparison))
         self.assertEqual(signed.shape, a.shape)

From cd1816777b94ac2378c83354cd3ad76eeed94048 Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 20 Jul 2021 09:48:25 +0200
Subject: [PATCH 05/17] fix for older pytorch versions

---
 CHANGELOG.md          | 7 +++++--
 heat/core/rounding.py | 9 ++++++---
 2 files changed, 11 insertions(+), 5 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 48261e7cf1..3b51d73144 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,8 @@
+# Pending Additions
+## Feature Additions
+### Rounding
+- [#827](https://github.com/helmholtz-analytics/heat/pull/827) New feature: `sign`, `sgn`
+
 # v1.1.0
 
 ## Highlights
@@ -62,8 +67,6 @@ Example on 2 processes:
 
 ### Manipulations
 - [#796](https://github.com/helmholtz-analytics/heat/pull/796) `DNDarray.reshape(shape)`: method now allows shape elements to be passed in as single arguments.
-### Rounding
-- [#827](https://github.com/helmholtz-analytics/heat/pull/827) New feature: `sign`, `sgn`
 
 ### Trigonometrics / Arithmetic
 - [#806](https://github.com/helmholtz-analytics/heat/pull/809) New feature: `square`
diff --git a/heat/core/rounding.py b/heat/core/rounding.py
index d19e9175a2..2280a50c68 100644
--- a/heat/core/rounding.py
+++ b/heat/core/rounding.py
@@ -373,9 +373,12 @@ def sign(x: DNDarray, out: Optional[DNDarray] = None):
             data = out.larray
         else:
             data = torch.clone(x.larray)
-
-        indices = torch.nonzero(data)
-        pos = torch.split(indices, 1, 1)
+        # NOTE remove when min version >= 1.9
+        if "1.7" in torch.__version__ or "1.8" in torch.__version__:
+            pos = data != 0
+        else:
+            indices = torch.nonzero(data)
+            pos = torch.split(indices, 1, 1)
         data[pos] = x.larray[pos] / torch.sqrt(torch.square(x.larray[pos]))
 
         if out is not None:

From fa223502ca4e58333370620758372d2e8247afda Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Fri, 30 Jul 2021 09:57:23 +0200
Subject: [PATCH 06/17] update type hints

---
 heat/core/rounding.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/heat/core/rounding.py b/heat/core/rounding.py
index 2280a50c68..1b0a3421df 100644
--- a/heat/core/rounding.py
+++ b/heat/core/rounding.py
@@ -340,7 +340,7 @@ def round(
 DNDarray.round.__doc__ = round.__doc__
 
 
-def sign(x: DNDarray, out: Optional[DNDarray] = None):
+def sign(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
     """
     Returns an indication of the sign of a number, element-wise. The definition for complex values is equivalent to :math:`x / \\sqrt{x \\cdot x}`.
 
@@ -397,7 +397,7 @@ def sign(x: DNDarray, out: Optional[DNDarray] = None):
     return _operations.__local_op(torch.sign, x, out)
 
 
-def sgn(x: DNDarray, out: Optional[DNDarray] = None):
+def sgn(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
     """
     Returns an indication of the sign of a number, element-wise. The definition for complex values is equivalent to :math:`x / |x|`.
 

From b14de92b72d9c2e5057d893c9f25426c35e1c531 Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Mon, 23 Aug 2021 15:58:13 +0200
Subject: [PATCH 07/17] fix tests

---
 heat/core/tests/test_rounding.py | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index de921de7f0..7fd2b687a0 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -316,7 +316,7 @@ def test_sign(self):
         # complex + 2d + split
         a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=0)
         signed = ht.sign(a)
-        comparison = ht.array([[1 + 0j, -1 + 0j], [0 + 0j, 1 + 0j]])
+        comparison = ht.array([[1 + 0j, -1 + 0j], [0 + 0j, 1 + 0j]], split=0)
 
         self.assertEqual(signed.dtype, comparison.dtype)
         self.assertEqual(signed.shape, comparison.shape)
@@ -328,7 +328,7 @@ def test_sign(self):
         a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=1)
         b = ht.empty_like(a)
         signed = ht.sign(a, b)
-        comparison = ht.array([[1 + 0j, -1 + 0j], [0 + 0j, 1 + 0j]])
+        comparison = ht.array([[1 + 0j, -1 + 0j], [0 + 0j, 1 + 0j]], split=1)
 
         self.assertIs(b, signed)
         self.assertEqual(signed.dtype, comparison.dtype)
@@ -340,7 +340,7 @@ def test_sign(self):
         # zeros + 3d + complex + split
         a = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
         signed = ht.sign(a)
-        comparison = ht.zeros((4, 4, 4), dtype=ht.complex128)
+        comparison = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
 
         self.assertEqual(signed.dtype, comparison.dtype)
         self.assertEqual(signed.shape, comparison.shape)
@@ -362,13 +362,14 @@ def test_sgn(self):
         # complex
         a = ht.array([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]], split=0)
         signed = ht.sgn(a)
-        comparison = torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]]))
-        comparison = comparison.to(a.device.torch_device)
+        comparison = ht.array(
+            torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]])), split=0
+        )
 
-        self.assertEqual(signed.dtype, ht.heat_type_of(comparison))
+        self.assertEqual(signed.dtype, comparison.dtype)
         self.assertEqual(signed.shape, a.shape)
         self.assertEqual(signed.device, a.device)
-        self.assertTrue(ht.equal(signed, ht.array(comparison)))
+        self.assertTrue(ht.equal(signed, comparison))
 
     def test_trunc(self):
         base_array = np.random.randn(20)

From 1c49a3c8a27f251d613e78c6d9bcc4d3f080410e Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Mon, 23 Aug 2021 16:39:12 +0200
Subject: [PATCH 08/17] seperate complex tests

---
 heat/core/tests/test_rounding.py | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index 7fd2b687a0..d8c9c06f93 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -322,7 +322,8 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
-        self.assertTrue(ht.equal(signed, comparison))
+        self.assertTrue(ht.equal(signed.real, comparison.real))
+        self.assertTrue(ht.equal(signed.imag, comparison.imag))
 
         # complex + split + out
         a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=1)
@@ -335,7 +336,8 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
-        self.assertTrue(ht.equal(signed, comparison))
+        self.assertTrue(ht.equal(signed.real, comparison.real))
+        self.assertTrue(ht.equal(signed.imag, comparison.imag))
 
         # zeros + 3d + complex + split
         a = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
@@ -346,7 +348,8 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
-        self.assertTrue(ht.equal(signed, comparison))
+        self.assertTrue(ht.equal(signed.real, comparison.real))
+        self.assertTrue(ht.equal(signed.imag, comparison.imag))
 
     def test_sgn(self):
         # floats
@@ -369,7 +372,8 @@ def test_sgn(self):
         self.assertEqual(signed.dtype, comparison.dtype)
         self.assertEqual(signed.shape, a.shape)
         self.assertEqual(signed.device, a.device)
-        self.assertTrue(ht.equal(signed, comparison))
+        self.assertTrue(ht.equal(signed.real, comparison.real))
+        self.assertTrue(ht.equal(signed.imag, comparison.imag))
 
     def test_trunc(self):
         base_array = np.random.randn(20)

From 71a2b136bd8bbd25e0d5207e95973b8bb70f174d Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Mon, 23 Aug 2021 16:52:19 +0200
Subject: [PATCH 09/17] use allclose comparison

---
 heat/core/tests/test_rounding.py | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index d8c9c06f93..a3b9c1e5e9 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -322,8 +322,8 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
-        self.assertTrue(ht.equal(signed.real, comparison.real))
-        self.assertTrue(ht.equal(signed.imag, comparison.imag))
+        self.assertTrue(ht.allclose(signed.real, comparison.real))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
 
         # complex + split + out
         a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=1)
@@ -336,8 +336,8 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
-        self.assertTrue(ht.equal(signed.real, comparison.real))
-        self.assertTrue(ht.equal(signed.imag, comparison.imag))
+        self.assertTrue(ht.allclose(signed.real, comparison.real))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
 
         # zeros + 3d + complex + split
         a = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
@@ -348,8 +348,8 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
-        self.assertTrue(ht.equal(signed.real, comparison.real))
-        self.assertTrue(ht.equal(signed.imag, comparison.imag))
+        self.assertTrue(ht.allclose(signed.real, comparison.real))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
 
     def test_sgn(self):
         # floats
@@ -372,8 +372,8 @@ def test_sgn(self):
         self.assertEqual(signed.dtype, comparison.dtype)
         self.assertEqual(signed.shape, a.shape)
         self.assertEqual(signed.device, a.device)
-        self.assertTrue(ht.equal(signed.real, comparison.real))
-        self.assertTrue(ht.equal(signed.imag, comparison.imag))
+        self.assertTrue(ht.allclose(signed.real, comparison.real))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
 
     def test_trunc(self):
         base_array = np.random.randn(20)

From cbc3f8c788f7ce1f163301b0627d9e7f90da6ce5 Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Mon, 23 Aug 2021 17:05:23 +0200
Subject: [PATCH 10/17] test sgn device

---
 heat/core/tests/test_rounding.py | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index a3b9c1e5e9..eaa374fd7f 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -365,15 +365,13 @@ def test_sgn(self):
         # complex
         a = ht.array([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]], split=0)
         signed = ht.sgn(a)
-        comparison = ht.array(
-            torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]])), split=0
-        )
+        comparison = torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]]))
+        comparison = comparison.to(a.device.torch_device)
 
-        self.assertEqual(signed.dtype, comparison.dtype)
+        self.assertEqual(signed.dtype, ht.heat_type_of(comparison))
         self.assertEqual(signed.shape, a.shape)
         self.assertEqual(signed.device, a.device)
-        self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
+        self.assertTrue(ht.equal(signed, ht.array(comparison, split=0)))
 
     def test_trunc(self):
         base_array = np.random.randn(20)

From a8e7cc636e5cd5fd5f4f7a04fff2d023e56c15ec Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 24 Aug 2021 09:23:33 +0200
Subject: [PATCH 11/17] debug

---
 heat/core/tests/test_rounding.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index eaa374fd7f..14fd835ae6 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -1,3 +1,4 @@
+from heat.core.rounding import sign
 import numpy as np
 import torch
 
@@ -322,6 +323,7 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
+        print(signed, comparison)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
         self.assertTrue(ht.allclose(signed.imag, comparison.imag))
 

From 911be2e4b27030f5571571b4f0d4df6182aed81b Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 24 Aug 2021 09:29:15 +0200
Subject: [PATCH 12/17] higher tolerance

---
 heat/core/tests/test_rounding.py | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index 14fd835ae6..3d52de6402 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -1,4 +1,3 @@
-from heat.core.rounding import sign
 import numpy as np
 import torch
 
@@ -323,9 +322,8 @@ def test_sign(self):
         self.assertEqual(signed.shape, comparison.shape)
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
-        print(signed, comparison)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=2e-5))
 
         # complex + split + out
         a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=1)
@@ -339,7 +337,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=2e-5))
 
         # zeros + 3d + complex + split
         a = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
@@ -351,7 +349,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=2e-5))
 
     def test_sgn(self):
         # floats

From 7ab3781d22ee4b9553fbb79aa387840f36af9aec Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 24 Aug 2021 09:58:02 +0200
Subject: [PATCH 13/17] higher tolerance

---
 heat/core/tests/test_rounding.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index 3d52de6402..0b269cc8e0 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -323,7 +323,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=2e-5))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=1e-4))
 
         # complex + split + out
         a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=1)
@@ -337,7 +337,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=2e-5))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=1e-4))
 
         # zeros + 3d + complex + split
         a = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
@@ -349,7 +349,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=2e-5))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=1e-4))
 
     def test_sgn(self):
         # floats

From cde6fa0f40980823cfd8490fcabc933335ec40cf Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Tue, 24 Aug 2021 10:03:43 +0200
Subject: [PATCH 14/17] use atol

---
 heat/core/tests/test_rounding.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index 0b269cc8e0..88f86482cd 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -323,7 +323,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=1e-4))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, atol=2e-5))
 
         # complex + split + out
         a = ht.array([[1 - 2j, -0.5 + 1j], [0, 4 + 6j]], split=1)
@@ -337,7 +337,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=1e-4))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, atol=2e-5))
 
         # zeros + 3d + complex + split
         a = ht.zeros((4, 4, 4), dtype=ht.complex128, split=2)
@@ -349,7 +349,7 @@ def test_sign(self):
         self.assertEqual(signed.device, a.device)
         self.assertEqual(signed.split, a.split)
         self.assertTrue(ht.allclose(signed.real, comparison.real))
-        self.assertTrue(ht.allclose(signed.imag, comparison.imag, rtol=1e-4))
+        self.assertTrue(ht.allclose(signed.imag, comparison.imag, atol=2e-5))
 
     def test_sgn(self):
         # floats

From ef780abd93ab4e58a130ad2b82cd86dfc705227f Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Thu, 26 Aug 2021 07:50:04 +0200
Subject: [PATCH 15/17] ignore code for pytorch>1.8 in coverage

---
 heat/core/rounding.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/heat/core/rounding.py b/heat/core/rounding.py
index 1b0a3421df..f99f9a2883 100644
--- a/heat/core/rounding.py
+++ b/heat/core/rounding.py
@@ -376,7 +376,7 @@ def sign(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
         # NOTE remove when min version >= 1.9
         if "1.7" in torch.__version__ or "1.8" in torch.__version__:
             pos = data != 0
-        else:
+        else:  # pragma: no cover
             indices = torch.nonzero(data)
             pos = torch.split(indices, 1, 1)
         data[pos] = x.larray[pos] / torch.sqrt(torch.square(x.larray[pos]))

From 0dbdac093aa868a167a00699bb9c2efb2653b7ce Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Fri, 17 Sep 2021 10:00:58 +0200
Subject: [PATCH 16/17] alphabetical order

---
 heat/core/rounding.py            | 56 ++++++++++++++++----------------
 heat/core/tests/test_rounding.py | 44 ++++++++++++-------------
 2 files changed, 50 insertions(+), 50 deletions(-)

diff --git a/heat/core/rounding.py b/heat/core/rounding.py
index f99f9a2883..f9fa6b005d 100644
--- a/heat/core/rounding.py
+++ b/heat/core/rounding.py
@@ -21,8 +21,8 @@
     "floor",
     "modf",
     "round",
-    "sign",
     "sgn",
+    "sign",
     "trunc",
 ]
 
@@ -340,6 +340,33 @@ def round(
 DNDarray.round.__doc__ = round.__doc__
 
 
+def sgn(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
+    """
+    Returns an indication of the sign of a number, element-wise. The definition for complex values is equivalent to :math:`x / |x|`.
+
+    Parameters
+    ----------
+    x : DNDarray
+        Input array
+    out : DNDarray, optional
+        A location in which to store the results.
+
+    See Also
+    --------
+    :func:`sign`
+        Equivalent function on non-complex arrays. The definition for complex values is equivalent to :math:`x / \\sqrt{x \\cdot x}`
+
+    Examples
+    --------
+    >>> a = ht.array([-1, -0.5, 0, 0.5, 1])
+    >>> ht.sign(a)
+    DNDarray([-1., -1.,  0.,  1.,  1.], dtype=ht.float32, device=cpu:0, split=None)
+    >>> ht.sgn(ht.array([5-2j, 3+4j]))
+    DNDarray([(0.9284766912460327-0.3713906705379486j),  (0.6000000238418579+0.800000011920929j)], dtype=ht.complex64, device=cpu:0, split=None)
+    """
+    return _operations.__local_op(torch.sgn, x, out)
+
+
 def sign(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
     """
     Returns an indication of the sign of a number, element-wise. The definition for complex values is equivalent to :math:`x / \\sqrt{x \\cdot x}`.
@@ -397,33 +424,6 @@ def sign(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
     return _operations.__local_op(torch.sign, x, out)
 
 
-def sgn(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
-    """
-    Returns an indication of the sign of a number, element-wise. The definition for complex values is equivalent to :math:`x / |x|`.
-
-    Parameters
-    ----------
-    x : DNDarray
-        Input array
-    out : DNDarray, optional
-        A location in which to store the results.
-
-    See Also
-    --------
-    :func:`sign`
-        Equivalent function on non-complex arrays. The definition for complex values is equivalent to :math:`x / \\sqrt{x \\cdot x}`
-
-    Examples
-    --------
-    >>> a = ht.array([-1, -0.5, 0, 0.5, 1])
-    >>> ht.sign(a)
-    DNDarray([-1., -1.,  0.,  1.,  1.], dtype=ht.float32, device=cpu:0, split=None)
-    >>> ht.sgn(ht.array([5-2j, 3+4j]))
-    DNDarray([(0.9284766912460327-0.3713906705379486j),  (0.6000000238418579+0.800000011920929j)], dtype=ht.complex64, device=cpu:0, split=None)
-    """
-    return _operations.__local_op(torch.sgn, x, out)
-
-
 def trunc(x: DNDarray, out: Optional[DNDarray] = None) -> DNDarray:
     """
     Return the trunc of the input, element-wise.
diff --git a/heat/core/tests/test_rounding.py b/heat/core/tests/test_rounding.py
index 88f86482cd..379c0e0ca4 100644
--- a/heat/core/tests/test_rounding.py
+++ b/heat/core/tests/test_rounding.py
@@ -301,6 +301,28 @@ def test_round(self):
         self.assertEqual(float64_round_distrbd.dtype, ht.float64)
         self.assert_array_equal(float64_round_distrbd, comparison)
 
+    def test_sgn(self):
+        # floats
+        a = ht.array([-1, -0.5, 0, 0.5, 1])
+        signed = ht.sgn(a)
+        comparison = ht.array([-1.0, -1, 0, 1, 1])
+
+        self.assertEqual(signed.dtype, comparison.dtype)
+        self.assertEqual(signed.shape, comparison.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertTrue(ht.equal(signed, comparison))
+
+        # complex
+        a = ht.array([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]], split=0)
+        signed = ht.sgn(a)
+        comparison = torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]]))
+        comparison = comparison.to(a.device.torch_device)
+
+        self.assertEqual(signed.dtype, ht.heat_type_of(comparison))
+        self.assertEqual(signed.shape, a.shape)
+        self.assertEqual(signed.device, a.device)
+        self.assertTrue(ht.equal(signed, ht.array(comparison, split=0)))
+
     def test_sign(self):
         # floats 1d
         a = ht.array([-1, -0.5, 0, 0.5, 1])
@@ -351,28 +373,6 @@ def test_sign(self):
         self.assertTrue(ht.allclose(signed.real, comparison.real))
         self.assertTrue(ht.allclose(signed.imag, comparison.imag, atol=2e-5))
 
-    def test_sgn(self):
-        # floats
-        a = ht.array([-1, -0.5, 0, 0.5, 1])
-        signed = ht.sgn(a)
-        comparison = ht.array([-1.0, -1, 0, 1, 1])
-
-        self.assertEqual(signed.dtype, comparison.dtype)
-        self.assertEqual(signed.shape, comparison.shape)
-        self.assertEqual(signed.device, a.device)
-        self.assertTrue(ht.equal(signed, comparison))
-
-        # complex
-        a = ht.array([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]], split=0)
-        signed = ht.sgn(a)
-        comparison = torch.sgn(torch.tensor([[1 - 2j, -0.5 + 1j], [0 - 3j, 4 + 6j]]))
-        comparison = comparison.to(a.device.torch_device)
-
-        self.assertEqual(signed.dtype, ht.heat_type_of(comparison))
-        self.assertEqual(signed.shape, a.shape)
-        self.assertEqual(signed.device, a.device)
-        self.assertTrue(ht.equal(signed, ht.array(comparison, split=0)))
-
     def test_trunc(self):
         base_array = np.random.randn(20)
 

From b6fa52f84f0a4a4cc2744cffe08112a9b5f35b36 Mon Sep 17 00:00:00 2001
From: Michael Tarnawa <m.tarnawa@fz-juelich.de>
Date: Fri, 17 Sep 2021 10:30:32 +0200
Subject: [PATCH 17/17] fix changelog

---
 CHANGELOG.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index b62857575f..c6d15776e7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -18,10 +18,10 @@
 - [#829](https://github.com/helmholtz-analytics/heat/pull/829) New feature: `roll`
 - [#853](https://github.com/helmholtz-analytics/heat/pull/853) New Feature: `swapaxes`
 - [#854](https://github.com/helmholtz-analytics/heat/pull/854) New Feature: `moveaxis`
-### Rounding
-- [#827](https://github.com/helmholtz-analytics/heat/pull/827) New feature: `sign`, `sgn`
 ### Random
 - [#858](https://github.com/helmholtz-analytics/heat/pull/858) New Feature: `standard_normal`, `normal`
+### Rounding
+- [#827](https://github.com/helmholtz-analytics/heat/pull/827) New feature: `sign`, `sgn`
 
 # v1.1.1
 - [#864](https://github.com/helmholtz-analytics/heat/pull/864) Dependencies: constrain `torchvision` version range to match supported `pytorch` version range.