From a8aa65bc89cbc643fa1fa7f94c3fce1d8e1a45d6 Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Thu, 25 Sep 2025 12:43:24 -0700
Subject: [PATCH 01/12] Add VM implementation

---
 dpnp/backend/extensions/vm/erf_funcs.cpp | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/dpnp/backend/extensions/vm/erf_funcs.cpp b/dpnp/backend/extensions/vm/erf_funcs.cpp
index 199ed0e7d55..6fa99eeb61a 100644
--- a/dpnp/backend/extensions/vm/erf_funcs.cpp
+++ b/dpnp/backend/extensions/vm/erf_funcs.cpp
@@ -133,6 +133,7 @@ using ew_cmn_ns::unary_contig_impl_fn_ptr_t;
 
 MACRO_DEFINE_IMPL(erf, Erf);
 MACRO_DEFINE_IMPL(erfc, Erfc);
+MACRO_DEFINE_IMPL(erfcx, Erfcx);
 
 template <template <typename fnT, typename T> typename factoryT>
 static void populate(py::module_ m,
@@ -187,5 +188,11 @@ void init_erf_funcs(py::module_ m)
         "Call `erfc` function from OneMKL VM library to compute the "
         "complementary error function value of vector elements",
         impl::erfc_contig_dispatch_vector);
+
+    impl::populate<impl::ErfcxContigFactory>(
+        m, "_erfcx",
+        "Call `erfcx` function from OneMKL VM library to compute the scaled "
+        "complementary error function value of vector elements",
+        impl::erfc_contig_dispatch_vector);
 }
 } // namespace dpnp::extensions::vm

From 6eb1b9a989c2ba7fc87d306bb0099ee915a3a7d0 Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Thu, 25 Sep 2025 12:46:17 -0700
Subject: [PATCH 02/12] Add ufunc implementation

---
 .../ufunc/elementwise_functions/erf_funcs.cpp |  5 ++++
 .../kernels/elementwise_functions/erf.hpp     | 26 ++++++++++++++++---
 2 files changed, 28 insertions(+), 3 deletions(-)

diff --git a/dpnp/backend/extensions/ufunc/elementwise_functions/erf_funcs.cpp b/dpnp/backend/extensions/ufunc/elementwise_functions/erf_funcs.cpp
index 29fe5e773ed..fbd2ac21198 100644
--- a/dpnp/backend/extensions/ufunc/elementwise_functions/erf_funcs.cpp
+++ b/dpnp/backend/extensions/ufunc/elementwise_functions/erf_funcs.cpp
@@ -212,6 +212,7 @@ static void populate(py::module_ m,
 
 MACRO_DEFINE_IMPL(erf, Erf);
 MACRO_DEFINE_IMPL(erfc, Erfc);
+MACRO_DEFINE_IMPL(erfcx, Erfcx);
 } // namespace impl
 
 void init_erf_funcs(py::module_ m)
@@ -231,5 +232,9 @@ void init_erf_funcs(py::module_ m)
     impl::populate<impl::ErfcContigFactory, impl::ErfcStridedFactory>(
         m, "_erfc", "", impl::erfc_contig_dispatch_vector,
         impl::erfc_strided_dispatch_vector);
+
+    impl::populate<impl::ErfcxContigFactory, impl::ErfcxStridedFactory>(
+        m, "_erfcx", "", impl::erfcx_contig_dispatch_vector,
+        impl::erfcx_strided_dispatch_vector);
 }
 } // namespace dpnp::extensions::ufunc
diff --git a/dpnp/backend/kernels/elementwise_functions/erf.hpp b/dpnp/backend/kernels/elementwise_functions/erf.hpp
index f3d7bbc4130..f42c43c1553 100644
--- a/dpnp/backend/kernels/elementwise_functions/erf.hpp
+++ b/dpnp/backend/kernels/elementwise_functions/erf.hpp
@@ -32,6 +32,19 @@
 
 #include <sycl/sycl.hpp>
 
+/**
+ * Include <sycl/ext/intel/math.hpp> only when targeting to Intel devices.
+ */
+#if defined(__INTEL_LLVM_COMPILER)
+#define __SYCL_EXT_INTEL_MATH_SUPPORT
+#endif
+
+#if defined(__SYCL_EXT_INTEL_MATH_SUPPORT)
+#include <sycl/ext/intel/math.hpp>
+#else
+#include <cmath>
+#endif
+
 namespace dpnp::kernels::erfs
 {
 template <typename OpT, typename ArgT, typename ResT>
@@ -65,13 +78,20 @@ struct BaseFunctor
         template <typename Tp>                                                 \
         static Tp apply(const Tp &x)                                           \
         {                                                                      \
-            return sycl::__name__(x);                                          \
+            return __name__(x);                                                \
         }                                                                      \
     };                                                                         \
                                                                                \
     template <typename ArgT, typename ResT>                                    \
     using __f_name__##Functor = BaseFunctor<__f_name__##Op, ArgT, ResT>;
 
-MACRO_DEFINE_FUNCTOR(erf, Erf);
-MACRO_DEFINE_FUNCTOR(erfc, Erfc);
+MACRO_DEFINE_FUNCTOR(sycl::erf, Erf);
+MACRO_DEFINE_FUNCTOR(sycl::erfc, Erfc);
+MACRO_DEFINE_FUNCTOR(
+#if defined(__SYCL_EXT_INTEL_MATH_SUPPORT)
+    sycl::ext::intel::math::erfcx,
+#else
+    std::erfc,
+#endif
+    Erfcx);
 } // namespace dpnp::kernels::erfs

From 206248c6172abeb2edb558f5aefea8a3001edd90 Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Thu, 25 Sep 2025 12:46:59 -0700
Subject: [PATCH 03/12] Add python implementation

---
 doc/reference/scipy_special.rst | 1 -
 dpnp/scipy/special/__init__.py  | 2 ++
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/doc/reference/scipy_special.rst b/doc/reference/scipy_special.rst
index 0df23dbd6ce..603f7bfebb0 100644
--- a/doc/reference/scipy_special.rst
+++ b/doc/reference/scipy_special.rst
@@ -15,6 +15,5 @@ Error function and Fresnel integrals
    erf
    erfc
    erfcx
-   erfi
    erfinv
    erfcinv
diff --git a/dpnp/scipy/special/__init__.py b/dpnp/scipy/special/__init__.py
index 2b9a1e04db6..50c72d5ace3 100644
--- a/dpnp/scipy/special/__init__.py
+++ b/dpnp/scipy/special/__init__.py
@@ -45,9 +45,11 @@
 from ._erf import (
     erf,
     erfc,
+    erfcx,
 )
 
 __all__ = [
     "erf",
     "erfc",
+    "erfcx",
 ]

From 233c5af579f33a9bbae1887dc6b165bb5480af08 Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Thu, 25 Sep 2025 12:47:18 -0700
Subject: [PATCH 04/12] Add tests

---
 dpnp/backend/extensions/vm/erf_funcs.cpp      |  2 +-
 dpnp/tests/test_special.py                    | 26 ++++++++++++++-----
 dpnp/tests/test_strides.py                    |  2 +-
 dpnp/tests/test_sycl_queue.py                 |  2 +-
 dpnp/tests/test_usm_type.py                   |  2 +-
 .../scipy_tests/special_tests/test_erf.py     |  1 -
 6 files changed, 23 insertions(+), 12 deletions(-)

diff --git a/dpnp/backend/extensions/vm/erf_funcs.cpp b/dpnp/backend/extensions/vm/erf_funcs.cpp
index 6fa99eeb61a..c443a773775 100644
--- a/dpnp/backend/extensions/vm/erf_funcs.cpp
+++ b/dpnp/backend/extensions/vm/erf_funcs.cpp
@@ -193,6 +193,6 @@ void init_erf_funcs(py::module_ m)
         m, "_erfcx",
         "Call `erfcx` function from OneMKL VM library to compute the scaled "
         "complementary error function value of vector elements",
-        impl::erfc_contig_dispatch_vector);
+        impl::erfcx_contig_dispatch_vector);
 }
 } // namespace dpnp::extensions::vm
diff --git a/dpnp/tests/test_special.py b/dpnp/tests/test_special.py
index e55fa001786..2922dedb357 100644
--- a/dpnp/tests/test_special.py
+++ b/dpnp/tests/test_special.py
@@ -14,7 +14,7 @@
 
 
 @with_requires("scipy")
-@pytest.mark.parametrize("func", ["erf", "erfc"])
+@pytest.mark.parametrize("func", ["erf", "erfc", "erfcx"])
 class TestCommon:
     @pytest.mark.parametrize(
         "dt", get_all_dtypes(no_none=True, no_float16=False, no_complex=True)
@@ -65,19 +65,31 @@ def test_complex(self, func, dt):
 
 class TestConsistency:
 
-    @pytest.mark.filterwarnings("ignore::RuntimeWarning")
-    def test_erfc(self):
+    def _check_variant_func(self, func, other_func, rtol, atol=0):
         # TODO: replace with dpnp.random.RandomState, once pareto is added
         rng = numpy.random.RandomState(1234)
         n = 10000
         a = rng.pareto(0.02, n) * (2 * rng.randint(0, 2, n) - 1)
         a = dpnp.array(a)
+        a = a[::-1]
 
-        res = 1 - dpnp.scipy.special.erf(a)
+        res = other_func(a)
         mask = dpnp.isfinite(res)
         a = a[mask]
 
-        tol = 8 * dpnp.finfo(a).resolution
-        assert dpnp.allclose(
-            dpnp.scipy.special.erfc(a), res[mask], rtol=tol, atol=tol
+        assert dpnp.allclose(func(a), res[mask], rtol=rtol, atol=atol)
+
+    def test_erfc(self):
+        self._check_variant_func(
+            dpnp.special.erfc,
+            lambda z: 1 - dpnp.special.erf(z),
+            rtol=1e-12,
+            atol=1e-14,
+        )
+
+    def test_erfcx(self):
+        self._check_variant_func(
+            dpnp.special.erfcx,
+            lambda z: dpnp.exp(z * z) * dpnp.special.erfc(z),
+            rtol=1e-12,
         )
diff --git a/dpnp/tests/test_strides.py b/dpnp/tests/test_strides.py
index 3d91231bcb7..3690ff61ec0 100644
--- a/dpnp/tests/test_strides.py
+++ b/dpnp/tests/test_strides.py
@@ -167,7 +167,7 @@ def test_reduce_hypot(dtype, stride):
 
 
 @with_requires("scipy")
-@pytest.mark.parametrize("func", ["erf", "erfc"])
+@pytest.mark.parametrize("func", ["erf", "erfc", "erfcx"])
 @pytest.mark.parametrize("stride", [2, -1, -3])
 def test_erf_funcs(func, stride):
     import scipy.special
diff --git a/dpnp/tests/test_sycl_queue.py b/dpnp/tests/test_sycl_queue.py
index 8a034bc8174..3ed3ef17f96 100644
--- a/dpnp/tests/test_sycl_queue.py
+++ b/dpnp/tests/test_sycl_queue.py
@@ -1488,7 +1488,7 @@ def test_interp(device, left, right, period):
     assert_sycl_queue_equal(result.sycl_queue, x.sycl_queue)
 
 
-@pytest.mark.parametrize("func", ["erf", "erfc"])
+@pytest.mark.parametrize("func", ["erf", "erfc", "erfcx"])
 @pytest.mark.parametrize("device", valid_dev, ids=dev_ids)
 def test_erf_funcs(func, device):
     x = dpnp.linspace(-3, 3, num=5, device=device)
diff --git a/dpnp/tests/test_usm_type.py b/dpnp/tests/test_usm_type.py
index da1b575166d..97ceb0220e5 100644
--- a/dpnp/tests/test_usm_type.py
+++ b/dpnp/tests/test_usm_type.py
@@ -1296,7 +1296,7 @@ def test_choose(usm_type_x, usm_type_ind):
     assert z.usm_type == du.get_coerced_usm_type([usm_type_x, usm_type_ind])
 
 
-@pytest.mark.parametrize("func", ["erf", "erfc"])
+@pytest.mark.parametrize("func", ["erf", "erfc", "erfcx"])
 @pytest.mark.parametrize("usm_type", list_of_usm_types)
 def test_erf_funcs(func, usm_type):
     x = dpnp.linspace(-3, 3, num=5, usm_type=usm_type)
diff --git a/dpnp/tests/third_party/cupyx/scipy_tests/special_tests/test_erf.py b/dpnp/tests/third_party/cupyx/scipy_tests/special_tests/test_erf.py
index 02e505a51ed..13d1523ff78 100644
--- a/dpnp/tests/third_party/cupyx/scipy_tests/special_tests/test_erf.py
+++ b/dpnp/tests/third_party/cupyx/scipy_tests/special_tests/test_erf.py
@@ -27,7 +27,6 @@ def test_erf(self):
     def test_erfc(self):
         self.check_unary("erfc")
 
-    @pytest.mark.skip("erfcx() is not supported yet")
     @testing.with_requires("scipy>=1.16.0")
     def test_erfcx(self):
         self.check_unary("erfcx")

From 699b156ee342b173f1946d7f7914e9662bd63a45 Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Thu, 25 Sep 2025 13:16:46 -0700
Subject: [PATCH 05/12] Add PR to the changelog

---
 CHANGELOG.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3e5bc60b80d..84a2e49a3ef 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,7 @@ This release changes the license from `BSD-2-Clause` to `BSD-3-Clause`.
 
 * Added the docstrings to `dpnp.linalg.LinAlgError` exception [#2613](https://github.com/IntelPython/dpnp/pull/2613)
 * Added implementation of `dpnp.linalg.lu_solve` for batch inputs (SciPy-compatible) [#2619](https://github.com/IntelPython/dpnp/pull/2619)
+* Added implementation of `dpnp.special.erfcx` [#2596](https://github.com/IntelPython/dpnp/pull/2596)
 
 ### Changed
 

From a84a5a478c6dd121078f69b874e5bc6fa06361ac Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Fri, 26 Sep 2025 04:33:31 -0700
Subject: [PATCH 06/12] Tune a tolerance in ercx consistency tests

---
 dpnp/tests/test_special.py | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/dpnp/tests/test_special.py b/dpnp/tests/test_special.py
index 2922dedb357..583b72e2af5 100644
--- a/dpnp/tests/test_special.py
+++ b/dpnp/tests/test_special.py
@@ -65,6 +65,8 @@ def test_complex(self, func, dt):
 
 class TestConsistency:
 
+    tol = 8 * dpnp.finfo(dpnp.default_float_type()).resolution
+
     def _check_variant_func(self, func, other_func, rtol, atol=0):
         # TODO: replace with dpnp.random.RandomState, once pareto is added
         rng = numpy.random.RandomState(1234)
@@ -77,19 +79,22 @@ def _check_variant_func(self, func, other_func, rtol, atol=0):
         mask = dpnp.isfinite(res)
         a = a[mask]
 
-        assert dpnp.allclose(func(a), res[mask], rtol=rtol, atol=atol)
+        x, y = func(a), res[mask]
+        if not dpnp.allclose(x, y, rtol=rtol, atol=atol):
+            # calling numpy testing func, because it's more verbose
+            assert_allclose(x.asnumpy(), y.asnumpy(), rtol=rtol, atol=atol)
 
     def test_erfc(self):
         self._check_variant_func(
             dpnp.special.erfc,
             lambda z: 1 - dpnp.special.erf(z),
-            rtol=1e-12,
-            atol=1e-14,
+            rtol=self.tol,
+            atol=self.tol,
         )
 
     def test_erfcx(self):
         self._check_variant_func(
             dpnp.special.erfcx,
             lambda z: dpnp.exp(z * z) * dpnp.special.erfc(z),
-            rtol=1e-12,
+            rtol=10 * self.tol,
         )

From a4f86b5986e399c3b708d9eb3da65179387f38e0 Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Tue, 14 Oct 2025 15:52:01 +0200
Subject: [PATCH 07/12] Add erfcx implementation for non-Intel devices

---
 .../kernels/elementwise_functions/erf.hpp     |    6 +-
 .../kernels/elementwise_functions/erfcx.hpp   | 1653 +++++++++++++++++
 .../kernels/elementwise_functions/i0.hpp      |    2 +-
 dpnp/scipy/special/_erf.py                    |   46 +-
 4 files changed, 1702 insertions(+), 5 deletions(-)
 create mode 100644 dpnp/backend/kernels/elementwise_functions/erfcx.hpp

diff --git a/dpnp/backend/kernels/elementwise_functions/erf.hpp b/dpnp/backend/kernels/elementwise_functions/erf.hpp
index f42c43c1553..70a763ff396 100644
--- a/dpnp/backend/kernels/elementwise_functions/erf.hpp
+++ b/dpnp/backend/kernels/elementwise_functions/erf.hpp
@@ -35,14 +35,14 @@
 /**
  * Include <sycl/ext/intel/math.hpp> only when targeting to Intel devices.
  */
-#if defined(__INTEL_LLVM_COMPILER)
+#if (defined(__SPIR__) || defined(__SPIRV__)) && defined(__INTEL_LLVM_COMPILER)
 #define __SYCL_EXT_INTEL_MATH_SUPPORT
 #endif
 
 #if defined(__SYCL_EXT_INTEL_MATH_SUPPORT)
 #include <sycl/ext/intel/math.hpp>
 #else
-#include <cmath>
+#include "erfcx.hpp"
 #endif
 
 namespace dpnp::kernels::erfs
@@ -91,7 +91,7 @@ MACRO_DEFINE_FUNCTOR(
 #if defined(__SYCL_EXT_INTEL_MATH_SUPPORT)
     sycl::ext::intel::math::erfcx,
 #else
-    std::erfc,
+    impl::erfcx,
 #endif
     Erfcx);
 } // namespace dpnp::kernels::erfs
diff --git a/dpnp/backend/kernels/elementwise_functions/erfcx.hpp b/dpnp/backend/kernels/elementwise_functions/erfcx.hpp
new file mode 100644
index 00000000000..13ffd11e47e
--- /dev/null
+++ b/dpnp/backend/kernels/elementwise_functions/erfcx.hpp
@@ -0,0 +1,1653 @@
+//*****************************************************************************
+// Copyright (c) 2025, Intel Corporation
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+// - Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// - Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// - Neither the name of the copyright holder nor the names of its contributors
+//   may be used to endorse or promote products derived from this software
+//   without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
+// THE POSSIBILITY OF SUCH DAMAGE.
+//*****************************************************************************
+
+#pragma once
+
+#include <cmath>
+#include <sycl/sycl.hpp>
+
+namespace dpnp::kernels::erfs::impl
+{
+/**
+Steven G. Johnson, October 2012.
+
+Given y100=100*y, where y = 4/(4+x) for x >= 0, compute erfc(x).
+
+Uses a look-up table of 100 different Chebyshev polynomials for y intervals
+[0,0.01], [0.01,0.02], ...., [0.99,1], generated with the help of Maple and
+a little shell script.
+This allows the Chebyshev polynomials to be of significantly lower degree
+(about 1/4) compared to fitting the whole [0,1] interval with a single
+polynomial.
+*/
+template <typename Tp>
+inline Tp erfcx_y100(Tp y100)
+{
+    switch ((int)y100) {
+    case 0:
+    {
+        Tp t = 2 * y100 - 1;
+        return 0.70878032454106438663e-3 +
+               (0.71234091047026302958e-3 +
+                (0.35779077297597742384e-5 +
+                 (0.17403143962587937815e-7 +
+                  (0.81710660047307788845e-10 +
+                   (0.36885022360434957634e-12 +
+                    0.15917038551111111111e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 1:
+    {
+        Tp t = 2 * y100 - 3;
+        return 0.21479143208285144230e-2 +
+               (0.72686402367379996033e-3 +
+                (0.36843175430938995552e-5 +
+                 (0.18071841272149201685e-7 +
+                  (0.85496449296040325555e-10 +
+                   (0.38852037518534291510e-12 +
+                    0.16868473576888888889e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 2:
+    {
+        Tp t = 2 * y100 - 5;
+        return 0.36165255935630175090e-2 +
+               (0.74182092323555510862e-3 +
+                (0.37948319957528242260e-5 +
+                 (0.18771627021793087350e-7 +
+                  (0.89484715122415089123e-10 +
+                   (0.40935858517772440862e-12 +
+                    0.17872061464888888889e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 3:
+    {
+        Tp t = 2 * y100 - 7;
+        return 0.51154983860031979264e-2 +
+               (0.75722840734791660540e-3 +
+                (0.39096425726735703941e-5 +
+                 (0.19504168704300468210e-7 +
+                  (0.93687503063178993915e-10 +
+                   (0.43143925959079664747e-12 +
+                    0.18939926435555555556e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 4:
+    {
+        Tp t = 2 * y100 - 9;
+        return 0.66457513172673049824e-2 +
+               (0.77310406054447454920e-3 +
+                (0.40289510589399439385e-5 +
+                 (0.20271233238288381092e-7 +
+                  (0.98117631321709100264e-10 +
+                   (0.45484207406017752971e-12 +
+                    0.20076352213333333333e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 5:
+    {
+        Tp t = 2 * y100 - 11;
+        return 0.82082389970241207883e-2 +
+               (0.78946629611881710721e-3 +
+                (0.41529701552622656574e-5 +
+                 (0.21074693344544655714e-7 +
+                  (0.10278874108587317989e-9 +
+                   (0.47965201390613339638e-12 +
+                    0.21285907413333333333e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 6:
+    {
+        Tp t = 2 * y100 - 13;
+        return 0.98039537275352193165e-2 +
+               (0.80633440108342840956e-3 +
+                (0.42819241329736982942e-5 +
+                 (0.21916534346907168612e-7 +
+                  (0.10771535136565470914e-9 +
+                   (0.50595972623692822410e-12 +
+                    0.22573462684444444444e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 7:
+    {
+        Tp t = 2 * y100 - 15;
+        return 0.11433927298290302370e-1 +
+               (0.82372858383196561209e-3 +
+                (0.44160495311765438816e-5 +
+                 (0.22798861426211986056e-7 +
+                  (0.11291291745879239736e-9 +
+                   (0.53386189365816880454e-12 +
+                    0.23944209546666666667e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 8:
+    {
+        Tp t = 2 * y100 - 17;
+        return 0.13099232878814653979e-1 +
+               (0.84167002467906968214e-3 +
+                (0.45555958988457506002e-5 +
+                 (0.23723907357214175198e-7 +
+                  (0.11839789326602695603e-9 +
+                   (0.56346163067550237877e-12 +
+                    0.25403679644444444444e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 9:
+    {
+        Tp t = 2 * y100 - 19;
+        return 0.14800987015587535621e-1 +
+               (0.86018092946345943214e-3 +
+                (0.47008265848816866105e-5 +
+                 (0.24694040760197315333e-7 +
+                  (0.12418779768752299093e-9 +
+                   (0.59486890370320261949e-12 +
+                    0.26957764568888888889e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 10:
+    {
+        Tp t = 2 * y100 - 21;
+        return 0.16540351739394069380e-1 +
+               (0.87928458641241463952e-3 +
+                (0.48520195793001753903e-5 +
+                 (0.25711774900881709176e-7 +
+                  (0.13030128534230822419e-9 +
+                   (0.62820097586874779402e-12 +
+                    0.28612737351111111111e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 11:
+    {
+        Tp t = 2 * y100 - 23;
+        return 0.18318536789842392647e-1 +
+               (0.89900542647891721692e-3 +
+                (0.50094684089553365810e-5 +
+                 (0.26779777074218070482e-7 +
+                  (0.13675822186304615566e-9 +
+                   (0.66358287745352705725e-12 +
+                    0.30375273884444444444e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 12:
+    {
+        Tp t = 2 * y100 - 25;
+        return 0.20136801964214276775e-1 +
+               (0.91936908737673676012e-3 +
+                (0.51734830914104276820e-5 +
+                 (0.27900878609710432673e-7 +
+                  (0.14357976402809042257e-9 +
+                   (0.70114790311043728387e-12 +
+                    0.32252476000000000000e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 13:
+    {
+        Tp t = 2 * y100 - 27;
+        return 0.21996459598282740954e-1 +
+               (0.94040248155366777784e-3 +
+                (0.53443911508041164739e-5 +
+                 (0.29078085538049374673e-7 +
+                  (0.15078844500329731137e-9 +
+                   (0.74103813647499204269e-12 +
+                    0.34251892320000000000e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 14:
+    {
+        Tp t = 2 * y100 - 29;
+        return 0.23898877187226319502e-1 +
+               (0.96213386835900177540e-3 +
+                (0.55225386998049012752e-5 +
+                 (0.30314589961047687059e-7 +
+                  (0.15840826497296335264e-9 +
+                   (0.78340500472414454395e-12 +
+                    0.36381553564444444445e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 15:
+    {
+        Tp t = 2 * y100 - 31;
+        return 0.25845480155298518485e-1 +
+               (0.98459293067820123389e-3 +
+                (0.57082915920051843672e-5 +
+                 (0.31613782169164830118e-7 +
+                  (0.16646478745529630813e-9 +
+                   (0.82840985928785407942e-12 +
+                    0.38649975768888888890e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 16:
+    {
+        Tp t = 2 * y100 - 33;
+        return 0.27837754783474696598e-1 +
+               (0.10078108563256892757e-2 +
+                (0.59020366493792212221e-5 +
+                 (0.32979263553246520417e-7 +
+                  (0.17498524159268458073e-9 +
+                   (0.87622459124842525110e-12 +
+                    0.41066206488888888890e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 17:
+    {
+        Tp t = 2 * y100 - 35;
+        return 0.29877251304899307550e-1 +
+               (0.10318204245057349310e-2 +
+                (0.61041829697162055093e-5 +
+                 (0.34414860359542720579e-7 +
+                  (0.18399863072934089607e-9 +
+                   (0.92703227366365046533e-12 +
+                    0.43639844053333333334e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 18:
+    {
+        Tp t = 2 * y100 - 37;
+        return 0.31965587178596443475e-1 +
+               (0.10566560976716574401e-2 +
+                (0.63151633192414586770e-5 +
+                 (0.35924638339521924242e-7 +
+                  (0.19353584758781174038e-9 +
+                   (0.98102783859889264382e-12 +
+                    0.46381060817777777779e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 19:
+    {
+        Tp t = 2 * y100 - 39;
+        return 0.34104450552588334840e-1 +
+               (0.10823541191350532574e-2 +
+                (0.65354356159553934436e-5 +
+                 (0.37512918348533521149e-7 +
+                  (0.20362979635817883229e-9 +
+                   (0.10384187833037282363e-11 +
+                    0.49300625262222222221e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 20:
+    {
+        Tp t = 2 * y100 - 41;
+        return 0.36295603928292425716e-1 +
+               (0.11089526167995268200e-2 +
+                (0.67654845095518363577e-5 +
+                 (0.39184292949913591646e-7 +
+                  (0.21431552202133775150e-9 +
+                   (0.10994259106646731797e-11 +
+                    0.52409949102222222221e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 21:
+    {
+        Tp t = 2 * y100 - 43;
+        return 0.38540888038840509795e-1 +
+               (0.11364917134175420009e-2 +
+                (0.70058230641246312003e-5 +
+                 (0.40943644083718586939e-7 +
+                  (0.22563034723692881631e-9 +
+                   (0.11642841011361992885e-11 +
+                    0.55721092871111111110e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 22:
+    {
+        Tp t = 2 * y100 - 45;
+        return 0.40842225954785960651e-1 +
+               (0.11650136437945673891e-2 +
+                (0.72569945502343006619e-5 +
+                 (0.42796161861855042273e-7 +
+                  (0.23761401711005024162e-9 +
+                   (0.12332431172381557035e-11 +
+                    0.59246802364444444445e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 23:
+    {
+        Tp t = 2 * y100 - 47;
+        return 0.43201627431540222422e-1 +
+               (0.11945628793917272199e-2 +
+                (0.75195743532849206263e-5 +
+                 (0.44747364553960993492e-7 +
+                  (0.25030885216472953674e-9 +
+                   (0.13065684400300476484e-11 +
+                    0.63000532853333333334e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 24:
+    {
+        Tp t = 2 * y100 - 49;
+        return 0.45621193513810471438e-1 +
+               (0.12251862608067529503e-2 +
+                (0.77941720055551920319e-5 +
+                 (0.46803119830954460212e-7 +
+                  (0.26375990983978426273e-9 +
+                   (0.13845421370977119765e-11 +
+                    0.66996477404444444445e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 25:
+    {
+        Tp t = 2 * y100 - 51;
+        return 0.48103121413299865517e-1 +
+               (0.12569331386432195113e-2 +
+                (0.80814333496367673980e-5 +
+                 (0.48969667335682018324e-7 +
+                  (0.27801515481905748484e-9 +
+                   (0.14674637611609884208e-11 +
+                    0.71249589351111111110e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 26:
+    {
+        Tp t = 2 * y100 - 53;
+        return 0.50649709676983338501e-1 +
+               (0.12898555233099055810e-2 +
+                (0.83820428414568799654e-5 +
+                 (0.51253642652551838659e-7 +
+                  (0.29312563849675507232e-9 +
+                   (0.15556512782814827846e-11 +
+                    0.75775607822222222221e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 27:
+    {
+        Tp t = 2 * y100 - 55;
+        return 0.53263363664388864181e-1 +
+               (0.13240082443256975769e-2 +
+                (0.86967260015007658418e-5 +
+                 (0.53662102750396795566e-7 +
+                  (0.30914568786634796807e-9 +
+                   (0.16494420240828493176e-11 +
+                    0.80591079644444444445e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 28:
+    {
+        Tp t = 2 * y100 - 57;
+        return 0.55946601353500013794e-1 +
+               (0.13594491197408190706e-2 +
+                (0.90262520233016380987e-5 +
+                 (0.56202552975056695376e-7 +
+                  (0.32613310410503135996e-9 +
+                   (0.17491936862246367398e-11 +
+                    0.85713381688888888890e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 29:
+    {
+        Tp t = 2 * y100 - 59;
+        return 0.58702059496154081813e-1 +
+               (0.13962391363223647892e-2 +
+                (0.93714365487312784270e-5 +
+                 (0.58882975670265286526e-7 +
+                  (0.34414937110591753387e-9 +
+                   (0.18552853109751857859e-11 +
+                    0.91160736711111111110e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 30:
+    {
+        Tp t = 2 * y100 - 61;
+        return 0.61532500145144778048e-1 +
+               (0.14344426411912015247e-2 +
+                (0.97331446201016809696e-5 +
+                 (0.61711860507347175097e-7 +
+                  (0.36325987418295300221e-9 +
+                   (0.19681183310134518232e-11 +
+                    0.96952238400000000000e-14 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 31:
+    {
+        Tp t = 2 * y100 - 63;
+        return 0.64440817576653297993e-1 +
+               (0.14741275456383131151e-2 +
+                (0.10112293819576437838e-4 +
+                 (0.64698236605933246196e-7 +
+                  (0.38353412915303665586e-9 +
+                   (0.20881176114385120186e-11 +
+                    0.10310784480000000000e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 32:
+    {
+        Tp t = 2 * y100 - 65;
+        return 0.67430045633130393282e-1 +
+               (0.15153655418916540370e-2 +
+                (0.10509857606888328667e-4 +
+                 (0.67851706529363332855e-7 +
+                  (0.40504602194811140006e-9 +
+                   (0.22157325110542534469e-11 +
+                    0.10964842115555555556e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 33:
+    {
+        Tp t = 2 * y100 - 67;
+        return 0.70503365513338850709e-1 +
+               (0.15582323336495709827e-2 +
+                (0.10926868866865231089e-4 +
+                 (0.71182482239613507542e-7 +
+                  (0.42787405890153386710e-9 +
+                   (0.23514379522274416437e-11 +
+                    0.11659571751111111111e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 34:
+    {
+        Tp t = 2 * y100 - 69;
+        return 0.73664114037944596353e-1 +
+               (0.16028078812438820413e-2 +
+                (0.11364423678778207991e-4 +
+                 (0.74701423097423182009e-7 +
+                  (0.45210162777476488324e-9 +
+                   (0.24957355004088569134e-11 +
+                    0.12397238257777777778e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 35:
+    {
+        Tp t = 2 * y100 - 71;
+        return 0.76915792420819562379e-1 +
+               (0.16491766623447889354e-2 +
+                (0.11823685320041302169e-4 +
+                 (0.78420075993781544386e-7 +
+                  (0.47781726956916478925e-9 +
+                   (0.26491544403815724749e-11 +
+                    0.13180196462222222222e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 36:
+    {
+        Tp t = 2 * y100 - 73;
+        return 0.80262075578094612819e-1 +
+               (0.16974279491709504117e-2 +
+                (0.12305888517309891674e-4 +
+                 (0.82350717698979042290e-7 +
+                  (0.50511496109857113929e-9 +
+                   (0.28122528497626897696e-11 +
+                    0.14010889635555555556e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 37:
+    {
+        Tp t = 2 * y100 - 75;
+        return 0.83706822008980357446e-1 +
+               (0.17476561032212656962e-2 +
+                (0.12812343958540763368e-4 +
+                 (0.86506399515036435592e-7 +
+                  (0.53409440823869467453e-9 +
+                   (0.29856186620887555043e-11 +
+                    0.14891851591111111111e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 38:
+    {
+        Tp t = 2 * y100 - 77;
+        return 0.87254084284461718231e-1 +
+               (0.17999608886001962327e-2 +
+                (0.13344443080089492218e-4 +
+                 (0.90900994316429008631e-7 +
+                  (0.56486134972616465316e-9 +
+                   (0.31698707080033956934e-11 +
+                    0.15825697795555555556e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 39:
+    {
+        Tp t = 2 * y100 - 79;
+        return 0.90908120182172748487e-1 +
+               (0.18544478050657699758e-2 +
+                (0.13903663143426120077e-4 +
+                 (0.95549246062549906177e-7 +
+                  (0.59752787125242054315e-9 +
+                   (0.33656597366099099413e-11 +
+                    0.16815130613333333333e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 40:
+    {
+        Tp t = 2 * y100 - 81;
+        return 0.94673404508075481121e-1 +
+               (0.19112284419887303347e-2 +
+                (0.14491572616545004930e-4 +
+                 (0.10046682186333613697e-6 +
+                  (0.63221272959791000515e-9 +
+                   (0.35736693975589130818e-11 +
+                    0.17862931591111111111e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 41:
+    {
+        Tp t = 2 * y100 - 83;
+        return 0.98554641648004456555e-1 +
+               (0.19704208544725622126e-2 +
+                (0.15109836875625443935e-4 +
+                 (0.10567036667675984067e-6 +
+                  (0.66904168640019354565e-9 +
+                   (0.37946171850824333014e-11 +
+                    0.18971959040000000000e-13 * t) *
+                       t) *
+                      t) *
+                     t) *
+                    t) *
+                   t;
+    }
+    case 42:
+    {
+        Tp t = 2 * y100 - 85;
+        return 0.10255677889470089531e0 + (0.20321499629472857418e-2 +
+                                           (0.15760224242962179564e-4 +
+                                            (0.11117756071353507391e-6 +
+                                             (0.70814785110097658502e-9 +
+                                              (0.40292553276632563925e-11 +
+                                               0.20145143075555555556e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 43:
+    {
+        Tp t = 2 * y100 - 87;
+        return 0.10668502059865093318e0 + (0.20965479776148731610e-2 +
+                                           (0.16444612377624983565e-4 +
+                                            (0.11700717962026152749e-6 +
+                                             (0.74967203250938418991e-9 +
+                                              (0.42783716186085922176e-11 +
+                                               0.21385479360000000000e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 44:
+    {
+        Tp t = 2 * y100 - 89;
+        return 0.11094484319386444474e0 + (0.21637548491908170841e-2 +
+                                           (0.17164995035719657111e-4 +
+                                            (0.12317915750735938089e-6 +
+                                             (0.79376309831499633734e-9 +
+                                              (0.45427901763106353914e-11 +
+                                               0.22696025653333333333e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 45:
+    {
+        Tp t = 2 * y100 - 91;
+        return 0.11534201115268804714e0 + (0.22339187474546420375e-2 +
+                                           (0.17923489217504226813e-4 +
+                                            (0.12971465288245997681e-6 +
+                                             (0.84057834180389073587e-9 +
+                                              (0.48233721206418027227e-11 +
+                                               0.24079890062222222222e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 46:
+    {
+        Tp t = 2 * y100 - 93;
+        return 0.11988259392684094740e0 + (0.23071965691918689601e-2 +
+                                           (0.18722342718958935446e-4 +
+                                            (0.13663611754337957520e-6 +
+                                             (0.89028385488493287005e-9 +
+                                              (0.51210161569225846701e-11 +
+                                               0.25540227111111111111e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 47:
+    {
+        Tp t = 2 * y100 - 95;
+        return 0.12457298393509812907e0 + (0.23837544771809575380e-2 +
+                                           (0.19563942105711612475e-4 +
+                                            (0.14396736847739470782e-6 +
+                                             (0.94305490646459247016e-9 +
+                                              (0.54366590583134218096e-11 +
+                                               0.27080225920000000000e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 48:
+    {
+        Tp t = 2 * y100 - 97;
+        return 0.12941991566142438816e0 + (0.24637684719508859484e-2 +
+                                           (0.20450821127475879816e-4 +
+                                            (0.15173366280523906622e-6 +
+                                             (0.99907632506389027739e-9 +
+                                              (0.57712760311351625221e-11 +
+                                               0.28703099555555555556e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 49:
+    {
+        Tp t = 2 * y100 - 99;
+        return 0.13443048593088696613e0 + (0.25474249981080823877e-2 +
+                                           (0.21385669591362915223e-4 +
+                                            (0.15996177579900443030e-6 +
+                                             (0.10585428844575134013e-8 +
+                                              (0.61258809536787882989e-11 +
+                                               0.30412080142222222222e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 50:
+    {
+        Tp t = 2 * y100 - 101;
+        return 0.13961217543434561353e0 + (0.26349215871051761416e-2 +
+                                           (0.22371342712572567744e-4 +
+                                            (0.16868008199296822247e-6 +
+                                             (0.11216596910444996246e-8 +
+                                              (0.65015264753090890662e-11 +
+                                               0.32210394506666666666e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 51:
+    {
+        Tp t = 2 * y100 - 103;
+        return 0.14497287157673800690e0 + (0.27264675383982439814e-2 +
+                                           (0.23410870961050950197e-4 +
+                                            (0.17791863939526376477e-6 +
+                                             (0.11886425714330958106e-8 +
+                                              (0.68993039665054288034e-11 +
+                                               0.34101266222222222221e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 52:
+    {
+        Tp t = 2 * y100 - 105;
+        return 0.15052089272774618151e0 + (0.28222846410136238008e-2 +
+                                           (0.24507470422713397006e-4 +
+                                            (0.18770927679626136909e-6 +
+                                             (0.12597184587583370712e-8 +
+                                              (0.73203433049229821618e-11 +
+                                               0.36087889048888888890e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 53:
+    {
+        Tp t = 2 * y100 - 107;
+        return 0.15626501395774612325e0 + (0.29226079376196624949e-2 +
+                                           (0.25664553693768450545e-4 +
+                                            (0.19808568415654461964e-6 +
+                                             (0.13351257759815557897e-8 +
+                                              (0.77658124891046760667e-11 +
+                                               0.38173420035555555555e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 54:
+    {
+        Tp t = 2 * y100 - 109;
+        return 0.16221449434620737567e0 + (0.30276865332726475672e-2 +
+                                           (0.26885741326534564336e-4 +
+                                            (0.20908350604346384143e-6 +
+                                             (0.14151148144240728728e-8 +
+                                              (0.82369170665974313027e-11 +
+                                               0.40360957457777777779e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 55:
+    {
+        Tp t = 2 * y100 - 111;
+        return 0.16837910595412130659e0 + (0.31377844510793082301e-2 +
+                                           (0.28174873844911175026e-4 +
+                                            (0.22074043807045782387e-6 +
+                                             (0.14999481055996090039e-8 +
+                                              (0.87348993661930809254e-11 +
+                                               0.42653528977777777779e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 56:
+    {
+        Tp t = 2 * y100 - 113;
+        return 0.17476916455659369953e0 + (0.32531815370903068316e-2 +
+                                           (0.29536024347344364074e-4 +
+                                            (0.23309632627767074202e-6 +
+                                             (0.15899007843582444846e-8 +
+                                              (0.92610375235427359475e-11 +
+                                               0.45054073102222222221e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 57:
+    {
+        Tp t = 2 * y100 - 115;
+        return 0.18139556223643701364e0 + (0.33741744168096996041e-2 +
+                                           (0.30973511714709500836e-4 +
+                                            (0.24619326937592290996e-6 +
+                                             (0.16852609412267750744e-8 +
+                                              (0.98166442942854895573e-11 +
+                                               0.47565418097777777779e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 58:
+    {
+        Tp t = 2 * y100 - 117;
+        return 0.18826980194443664549e0 + (0.35010775057740317997e-2 +
+                                           (0.32491914440014267480e-4 +
+                                            (0.26007572375886319028e-6 +
+                                             (0.17863299617388376116e-8 +
+                                              (0.10403065638343878679e-10 +
+                                               0.50190265831111111110e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 59:
+    {
+        Tp t = 2 * y100 - 119;
+        return 0.19540403413693967350e0 + (0.36342240767211326315e-2 +
+                                           (0.34096085096200907289e-4 +
+                                            (0.27479061117017637474e-6 +
+                                             (0.18934228504790032826e-8 +
+                                              (0.11021679075323598664e-10 +
+                                               0.52931171733333333334e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 60:
+    {
+        Tp t = 2 * y100 - 121;
+        return 0.20281109560651886959e0 + (0.37739673859323597060e-2 +
+                                           (0.35791165457592409054e-4 +
+                                            (0.29038742889416172404e-6 +
+                                             (0.20068685374849001770e-8 +
+                                              (0.11673891799578381999e-10 +
+                                               0.55790523093333333334e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 61:
+    {
+        Tp t = 2 * y100 - 123;
+        return 0.21050455062669334978e0 + (0.39206818613925652425e-2 +
+                                           (0.37582602289680101704e-4 +
+                                            (0.30691836231886877385e-6 +
+                                             (0.21270101645763677824e-8 +
+                                              (0.12361138551062899455e-10 +
+                                               0.58770520160000000000e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 62:
+    {
+        Tp t = 2 * y100 - 125;
+        return 0.21849873453703332479e0 + (0.40747643554689586041e-2 +
+                                           (0.39476163820986711501e-4 +
+                                            (0.32443839970139918836e-6 +
+                                             (0.22542053491518680200e-8 +
+                                              (0.13084879235290858490e-10 +
+                                               0.61873153262222222221e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 63:
+    {
+        Tp t = 2 * y100 - 127;
+        return 0.22680879990043229327e0 + (0.42366354648628516935e-2 +
+                                           (0.41477956909656896779e-4 +
+                                            (0.34300544894502810002e-6 +
+                                             (0.23888264229264067658e-8 +
+                                              (0.13846596292818514601e-10 +
+                                               0.65100183751111111110e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 64:
+    {
+        Tp t = 2 * y100 - 129;
+        return 0.23545076536988703937e0 + (0.44067409206365170888e-2 +
+                                           (0.43594444916224700881e-4 +
+                                            (0.36268045617760415178e-6 +
+                                             (0.25312606430853202748e-8 +
+                                              (0.14647791812837903061e-10 +
+                                               0.68453122631111111110e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 65:
+    {
+        Tp t = 2 * y100 - 131;
+        return 0.24444156740777432838e0 + (0.45855530511605787178e-2 +
+                                           (0.45832466292683085475e-4 +
+                                            (0.38352752590033030472e-6 +
+                                             (0.26819103733055603460e-8 +
+                                              (0.15489984390884756993e-10 +
+                                               0.71933206364444444445e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 66:
+    {
+        Tp t = 2 * y100 - 133;
+        return 0.25379911500634264643e0 + (0.47735723208650032167e-2 +
+                                           (0.48199253896534185372e-4 +
+                                            (0.40561404245564732314e-6 +
+                                             (0.28411932320871165585e-8 +
+                                              (0.16374705736458320149e-10 +
+                                               0.75541379822222222221e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 67:
+    {
+        Tp t = 2 * y100 - 135;
+        return 0.26354234756393613032e0 + (0.49713289477083781266e-2 +
+                                           (0.50702455036930367504e-4 +
+                                            (0.42901079254268185722e-6 +
+                                             (0.30095422058900481753e-8 +
+                                              (0.17303497025347342498e-10 +
+                                               0.79278273368888888890e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 68:
+    {
+        Tp t = 2 * y100 - 137;
+        return 0.27369129607732343398e0 + (0.51793846023052643767e-2 +
+                                           (0.53350152258326602629e-4 +
+                                            (0.45379208848865015485e-6 +
+                                             (0.31874057245814381257e-8 +
+                                              (0.18277905010245111046e-10 +
+                                               0.83144182364444444445e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 69:
+    {
+        Tp t = 2 * y100 - 139;
+        return 0.28426714781640316172e0 + (0.53983341916695141966e-2 +
+                                           (0.56150884865255810638e-4 +
+                                            (0.48003589196494734238e-6 +
+                                             (0.33752476967570796349e-8 +
+                                              (0.19299477888083469086e-10 +
+                                               0.87139049137777777779e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 70:
+    {
+        Tp t = 2 * y100 - 141;
+        return 0.29529231465348519920e0 + (0.56288077305420795663e-2 +
+                                           (0.59113671189913307427e-4 +
+                                            (0.50782393781744840482e-6 +
+                                             (0.35735475025851713168e-8 +
+                                              (0.20369760937017070382e-10 +
+                                               0.91262442613333333334e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 71:
+    {
+        Tp t = 2 * y100 - 143;
+        return 0.30679050522528838613e0 + (0.58714723032745403331e-2 +
+                                           (0.62248031602197686791e-4 +
+                                            (0.53724185766200945789e-6 +
+                                             (0.37827999418960232678e-8 +
+                                              (0.21490291930444538307e-10 +
+                                               0.95513539182222222221e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 72:
+    {
+        Tp t = 2 * y100 - 145;
+        return 0.31878680111173319425e0 + (0.61270341192339103514e-2 +
+                                           (0.65564012259707640976e-4 +
+                                            (0.56837930287837738996e-6 +
+                                             (0.40035151353392378882e-8 +
+                                              (0.22662596341239294792e-10 +
+                                               0.99891109760000000000e-13 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 73:
+    {
+        Tp t = 2 * y100 - 147;
+        return 0.33130773722152622027e0 + (0.63962406646798080903e-2 +
+                                           (0.69072209592942396666e-4 +
+                                            (0.60133006661885941812e-6 +
+                                             (0.42362183765883466691e-8 +
+                                              (0.23888182347073698382e-10 +
+                                               0.10439349811555555556e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 74:
+    {
+        Tp t = 2 * y100 - 149;
+        return 0.34438138658041336523e0 + (0.66798829540414007258e-2 +
+                                           (0.72783795518603561144e-4 +
+                                            (0.63619220443228800680e-6 +
+                                             (0.44814499336514453364e-8 +
+                                              (0.25168535651285475274e-10 +
+                                               0.10901861383111111111e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 75:
+    {
+        Tp t = 2 * y100 - 151;
+        return 0.35803744972380175583e0 + (0.69787978834882685031e-2 +
+                                           (0.76710543371454822497e-4 +
+                                            (0.67306815308917386747e-6 +
+                                             (0.47397647975845228205e-8 +
+                                              (0.26505114141143050509e-10 +
+                                               0.11376390933333333333e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 76:
+    {
+        Tp t = 2 * y100 - 153;
+        return 0.37230734890119724188e0 + (0.72938706896461381003e-2 +
+                                           (0.80864854542670714092e-4 +
+                                            (0.71206484718062688779e-6 +
+                                             (0.50117323769745883805e-8 +
+                                              (0.27899342394100074165e-10 +
+                                               0.11862637614222222222e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 77:
+    {
+        Tp t = 2 * y100 - 155;
+        return 0.38722432730555448223e0 + (0.76260375162549802745e-2 +
+                                           (0.85259785810004603848e-4 +
+                                            (0.75329383305171327677e-6 +
+                                             (0.52979361368388119355e-8 +
+                                              (0.29352606054164086709e-10 +
+                                               0.12360253370666666667e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 78:
+    {
+        Tp t = 2 * y100 - 157;
+        return 0.40282355354616940667e0 + (0.79762880915029728079e-2 +
+                                           (0.89909077342438246452e-4 +
+                                            (0.79687137961956194579e-6 +
+                                             (0.55989731807360403195e-8 +
+                                              (0.30866246101464869050e-10 +
+                                               0.12868841946666666667e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 79:
+    {
+        Tp t = 2 * y100 - 159;
+        return 0.41914223158913787649e0 + (0.83456685186950463538e-2 +
+                                           (0.94827181359250161335e-4 +
+                                            (0.84291858561783141014e-6 +
+                                             (0.59154537751083485684e-8 +
+                                              (0.32441553034347469291e-10 +
+                                               0.13387957943111111111e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 80:
+    {
+        Tp t = 2 * y100 - 161;
+        return 0.43621971639463786896e0 + (0.87352841828289495773e-2 +
+                                           (0.10002929142066799966e-3 +
+                                            (0.89156148280219880024e-6 +
+                                             (0.62480008150788597147e-8 +
+                                              (0.34079760983458878910e-10 +
+                                               0.13917107176888888889e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 81:
+    {
+        Tp t = 2 * y100 - 163;
+        return 0.45409763548534330981e0 + (0.91463027755548240654e-2 +
+                                           (0.10553137232446167258e-3 +
+                                            (0.94293113464638623798e-6 +
+                                             (0.65972492312219959885e-8 +
+                                              (0.35782041795476563662e-10 +
+                                               0.14455745872000000000e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 82:
+    {
+        Tp t = 2 * y100 - 165;
+        return 0.47282001668512331468e0 + (0.95799574408860463394e-2 +
+                                           (0.11135019058000067469e-3 +
+                                            (0.99716373005509038080e-6 +
+                                             (0.69638453369956970347e-8 +
+                                              (0.37549499088161345850e-10 +
+                                               0.15003280712888888889e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 83:
+    {
+        Tp t = 2 * y100 - 167;
+        return 0.49243342227179841649e0 + (0.10037550043909497071e-1 +
+                                           (0.11750334542845234952e-3 +
+                                            (0.10544006716188967172e-5 +
+                                             (0.73484461168242224872e-8 +
+                                              (0.39383162326435752965e-10 +
+                                               0.15559069118222222222e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 84:
+    {
+        Tp t = 2 * y100 - 169;
+        return 0.51298708979209258326e0 + (0.10520454564612427224e-1 +
+                                           (0.12400930037494996655e-3 +
+                                            (0.11147886579371265246e-5 +
+                                             (0.77517184550568711454e-8 +
+                                              (0.41283980931872622611e-10 +
+                                               0.16122419680000000000e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 85:
+    {
+        Tp t = 2 * y100 - 171;
+        return 0.53453307979101369843e0 + (0.11030120618800726938e-1 +
+                                           (0.13088741519572269581e-3 +
+                                            (0.11784797595374515432e-5 +
+                                             (0.81743383063044825400e-8 +
+                                              (0.43252818449517081051e-10 +
+                                               0.16692592640000000000e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 86:
+    {
+        Tp t = 2 * y100 - 173;
+        return 0.55712643071169299478e0 + (0.11568077107929735233e-1 +
+                                           (0.13815797838036651289e-3 +
+                                            (0.12456314879260904558e-5 +
+                                             (0.86169898078969313597e-8 +
+                                              (0.45290446811539652525e-10 +
+                                               0.17268801084444444444e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 87:
+    {
+        Tp t = 2 * y100 - 175;
+        return 0.58082532122519320968e0 + (0.12135935999503877077e-1 +
+                                           (0.14584223996665838559e-3 +
+                                            (0.13164068573095710742e-5 +
+                                             (0.90803643355106020163e-8 +
+                                              (0.47397540713124619155e-10 +
+                                               0.17850211608888888889e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 88:
+    {
+        Tp t = 2 * y100 - 177;
+        return 0.60569124025293375554e0 + (0.12735396239525550361e-1 +
+                                           (0.15396244472258863344e-3 +
+                                            (0.13909744385382818253e-5 +
+                                             (0.95651595032306228245e-8 +
+                                              (0.49574672127669041550e-10 +
+                                               0.18435945564444444444e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 89:
+    {
+        Tp t = 2 * y100 - 179;
+        return 0.63178916494715716894e0 + (0.13368247798287030927e-1 +
+                                           (0.16254186562762076141e-3 +
+                                            (0.14695084048334056083e-5 +
+                                             (0.10072078109604152350e-7 +
+                                              (0.51822304995680707483e-10 +
+                                               0.19025081422222222222e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 90:
+    {
+        Tp t = 2 * y100 - 181;
+        return 0.65918774689725319200e0 + (0.14036375850601992063e-1 +
+                                           (0.17160483760259706354e-3 +
+                                            (0.15521885688723188371e-5 +
+                                             (0.10601827031535280590e-7 +
+                                              (0.54140790105837520499e-10 +
+                                               0.19616655146666666667e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 91:
+    {
+        Tp t = 2 * y100 - 183;
+        return 0.68795950683174433822e0 + (0.14741765091365869084e-1 +
+                                           (0.18117679143520433835e-3 +
+                                            (0.16392004108230585213e-5 +
+                                             (0.11155116068018043001e-7 +
+                                              (0.56530360194925690374e-10 +
+                                               0.20209663662222222222e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 92:
+    {
+        Tp t = 2 * y100 - 185;
+        return 0.71818103808729967036e0 + (0.15486504187117112279e-1 +
+                                           (0.19128428784550923217e-3 +
+                                            (0.17307350969359975848e-5 +
+                                             (0.11732656736113607751e-7 +
+                                              (0.58991125287563833603e-10 +
+                                               0.20803065333333333333e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 93:
+    {
+        Tp t = 2 * y100 - 187;
+        return 0.74993321911726254661e0 + (0.16272790364044783382e-1 +
+                                           (0.20195505163377912645e-3 +
+                                            (0.18269894883203346953e-5 +
+                                             (0.12335161021630225535e-7 +
+                                              (0.61523068312169087227e-10 +
+                                               0.21395783431111111111e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 94:
+    {
+        Tp t = 2 * y100 - 189;
+        return 0.78330143531283492729e0 + (0.17102934132652429240e-1 +
+                                           (0.21321800585063327041e-3 +
+                                            (0.19281661395543913713e-5 +
+                                             (0.12963340087354341574e-7 +
+                                              (0.64126040998066348872e-10 +
+                                               0.21986708942222222222e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 95:
+    {
+        Tp t = 2 * y100 - 191;
+        return 0.81837581041023811832e0 + (0.17979364149044223802e-1 +
+                                           (0.22510330592753129006e-3 +
+                                            (0.20344732868018175389e-5 +
+                                             (0.13617902941839949718e-7 +
+                                              (0.66799760083972474642e-10 +
+                                               0.22574701262222222222e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 96:
+    {
+        Tp t = 2 * y100 - 193;
+        return 0.85525144775685126237e0 + (0.18904632212547561026e-1 +
+                                           (0.23764237370371255638e-3 +
+                                            (0.21461248251306387979e-5 +
+                                             (0.14299555071870523786e-7 +
+                                              (0.69543803864694171934e-10 +
+                                               0.23158593688888888889e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 97:
+    {
+        Tp t = 2 * y100 - 195;
+        return 0.89402868170849933734e0 + (0.19881418399127202569e-1 +
+                                           (0.25086793128395995798e-3 +
+                                            (0.22633402747585233180e-5 +
+                                             (0.15008997042116532283e-7 +
+                                              (0.72357609075043941261e-10 +
+                                               0.23737194737777777778e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 98:
+    {
+        Tp t = 2 * y100 - 197;
+        return 0.93481333942870796363e0 + (0.20912536329780368893e-1 +
+                                           (0.26481403465998477969e-3 +
+                                            (0.23863447359754921676e-5 +
+                                             (0.15746923065472184451e-7 +
+                                              (0.75240468141720143653e-10 +
+                                               0.24309291271111111111e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    case 99:
+    {
+        Tp t = 2 * y100 - 199;
+        return 0.97771701335885035464e0 + (0.22000938572830479551e-1 +
+                                           (0.27951610702682383001e-3 +
+                                            (0.25153688325245314530e-5 +
+                                             (0.16514019547822821453e-7 +
+                                              (0.78191526829368231251e-10 +
+                                               0.24873652355555555556e-12 * t) *
+                                                  t) *
+                                                 t) *
+                                                t) *
+                                               t) *
+                                              t;
+    }
+    }
+    // we only get here if y = 1, i.e. |x| < 4*eps, in which case
+    // erfcx is within 1e-15 of 1..
+    return Tp(1.0);
+}
+
+/**
+Steven G. Johnson, October 2012.
+
+This function combines a few different ideas.
+
+First, for x > 50, it uses a continued-fraction expansion (same as for the
+Faddeeva function, but with algebraic simplifications for z=i*x).
+
+Second, for 0 <= x <= 50, it uses Chebyshev polynomial approximations, but with
+two twists:
+
+    a) It maps x to y = 4 / (4+x) in [0,1].  This simple transformation,
+       inspired by a similar transformation in the octave-forge/specfun erfcx
+       by Soren Hauberg, results in much faster Chebyshev convergence than
+       other simple transformations I have examined.
+
+    b) Instead of using a single Chebyshev polynomial for the entire [0,1] y
+       interval, we break the interval up into 100 equal subintervals, with a
+       switch/lookup table, and use much lower degree Chebyshev polynomials in
+       each subinterval. This greatly improves performance in my tests.
+
+For x < 0, we use the relationship erfcx(-x) = 2 exp(x^2) - erfc(x), with the
+usual checks for overflow etcetera.
+*/
+template <typename Tp>
+Tp erfcx(Tp x)
+{
+    static_assert(std::is_floating_point_v<Tp>,
+                  "erfcx requires a floating-point type");
+
+    if (x >= 0) {
+        if (x > 50) // continued-fraction expansion is faster
+        {
+            // 1/sqrt(pi)
+            constexpr Tp inv_sqrtpi = 0.564189583547756286948079451560772586L;
+
+            if (x > 5e7) // 1-term expansion, important to avoid overflow
+            {
+                return inv_sqrtpi / x;
+            }
+
+            // 5-term expansion (rely on compiler for CSE)
+            return inv_sqrtpi * ((x * x) * (x * x + 4.5) + 2) /
+                   (x * ((x * x) * (x * x + 5) + 3.75));
+        }
+        return erfcx_y100(400 / (4 + x));
+    }
+
+    return x < -26.7
+               ? std::HUGE_VAL
+               : (x < -6.1 ? 2 * sycl::exp(x * x)
+                           : 2 * sycl::exp(x * x) - erfcx_y100(400 / (4 - x)));
+}
+} // namespace dpnp::kernels::erfs::impl
diff --git a/dpnp/backend/kernels/elementwise_functions/i0.hpp b/dpnp/backend/kernels/elementwise_functions/i0.hpp
index 90629adcec5..a634b74b9da 100644
--- a/dpnp/backend/kernels/elementwise_functions/i0.hpp
+++ b/dpnp/backend/kernels/elementwise_functions/i0.hpp
@@ -43,7 +43,7 @@
  * This header relies on intel-specific types like _iml_half_internal,
  * which are not suppose to work with other targets (e.g., CUDA, AMD).
  */
-#if defined(__SPIR__) && defined(__INTEL_LLVM_COMPILER)
+#if (defined(__SPIR__) || defined(__SPIRV__)) && defined(__INTEL_LLVM_COMPILER)
 #define __SYCL_EXT_INTEL_MATH_SUPPORT
 #endif
 
diff --git a/dpnp/scipy/special/_erf.py b/dpnp/scipy/special/_erf.py
index ff7128274a0..2148f1f63bc 100644
--- a/dpnp/scipy/special/_erf.py
+++ b/dpnp/scipy/special/_erf.py
@@ -45,7 +45,7 @@
 import dpnp.backend.extensions.ufunc._ufunc_impl as ufi
 from dpnp.dpnp_algo.dpnp_elementwise_common import DPNPUnaryFunc
 
-__all__ = ["erf", "erfc"]
+__all__ = ["erf", "erfc", "erfcx"]
 
 
 # pylint: disable=too-few-public-methods
@@ -174,3 +174,47 @@ def __call__(self, x, out=None):  # pylint: disable=signature-differs
     mkl_fn_to_call="_mkl_erf_to_call",
     mkl_impl_fn="_erfc",
 )
+
+_ERFCX_DOCSTRING = r"""
+Calculates the scaled complementary error function of a given input array.
+It is defined as :math:`\exp(x^2) * \operatorname{erfc}(x)`.
+
+For full documentation refer to :obj:`scipy.special.erfcx`.
+
+Parameters
+----------
+x : {dpnp.ndarray, usm_ndarray}
+    Input array, expected to have a real-valued floating-point data type.
+out : {dpnp.ndarray, usm_ndarray}, optional
+    Optional output array for the function values.
+
+Returns
+-------
+out : dpnp.ndarray
+    The values of the scaled complementary error function at the given points
+    `x`.
+
+See Also
+--------
+:obj:`dpnp.special.erf` : Gauss error function.
+:obj:`dpnp.special.erfc` : Complementary error function.
+:obj:`dpnp.special.erfinv` : Inverse of the error function.
+:obj:`dpnp.special.erfcinv` : Inverse of the complementary error function.
+
+Examples
+--------
+>>> import dpnp as np
+>>> x = np.linspace(-3, 3, num=4)
+>>> np.special.erfcx(x)
+array([1.62059889e+04, 5.00898008e+00, 4.27583576e-01, 1.79001151e-01])
+
+"""
+
+erfcx = DPNPErf(
+    "erfcx",
+    ufi._erf_result_type,
+    ufi._erfcx,
+    _ERFCX_DOCSTRING,
+    mkl_fn_to_call="_mkl_erf_to_call",
+    mkl_impl_fn="_erfcx",
+)

From 5a5f2e60cd81bcaeac8738c8574d877a177ecf94 Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Tue, 14 Oct 2025 07:02:16 -0700
Subject: [PATCH 08/12] Use std::numeric_limits<Tp>::infinity() instead of
 HUGE_VAL

---
 dpnp/backend/kernels/elementwise_functions/erfcx.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/dpnp/backend/kernels/elementwise_functions/erfcx.hpp b/dpnp/backend/kernels/elementwise_functions/erfcx.hpp
index 13ffd11e47e..9fbb8aeac56 100644
--- a/dpnp/backend/kernels/elementwise_functions/erfcx.hpp
+++ b/dpnp/backend/kernels/elementwise_functions/erfcx.hpp
@@ -28,7 +28,7 @@
 
 #pragma once
 
-#include <cmath>
+#include <limits>
 #include <sycl/sycl.hpp>
 
 namespace dpnp::kernels::erfs::impl
@@ -1646,7 +1646,7 @@ Tp erfcx(Tp x)
     }
 
     return x < -26.7
-               ? std::HUGE_VAL
+               ? std::numeric_limits<Tp>::infinity()
                : (x < -6.1 ? 2 * sycl::exp(x * x)
                            : 2 * sycl::exp(x * x) - erfcx_y100(400 / (4 - x)));
 }

From 2c25c169f486b45f22f40b75d94ecf1d1d741ada Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Tue, 14 Oct 2025 07:07:48 -0700
Subject: [PATCH 09/12] Update consistency tests with correct path to erf
 submodule

---
 dpnp/tests/test_special.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/dpnp/tests/test_special.py b/dpnp/tests/test_special.py
index 583b72e2af5..66b62aad65a 100644
--- a/dpnp/tests/test_special.py
+++ b/dpnp/tests/test_special.py
@@ -86,15 +86,15 @@ def _check_variant_func(self, func, other_func, rtol, atol=0):
 
     def test_erfc(self):
         self._check_variant_func(
-            dpnp.special.erfc,
-            lambda z: 1 - dpnp.special.erf(z),
+            dpnp.scipy.special.erfc,
+            lambda z: 1 - dpnp.scipy.special.erf(z),
             rtol=self.tol,
             atol=self.tol,
         )
 
     def test_erfcx(self):
         self._check_variant_func(
-            dpnp.special.erfcx,
-            lambda z: dpnp.exp(z * z) * dpnp.special.erfc(z),
+            dpnp.scipy.special.erfcx,
+            lambda z: dpnp.exp(z * z) * dpnp.scipy.special.erfc(z),
             rtol=10 * self.tol,
         )

From 35ddd918d3057461e0171597380ab16562f8c98e Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Tue, 14 Oct 2025 07:11:30 -0700
Subject: [PATCH 10/12] Update the docstring of erfcx with correct path to the
 erf functions

---
 dpnp/scipy/special/_erf.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/dpnp/scipy/special/_erf.py b/dpnp/scipy/special/_erf.py
index 2148f1f63bc..1e817e46a82 100644
--- a/dpnp/scipy/special/_erf.py
+++ b/dpnp/scipy/special/_erf.py
@@ -196,16 +196,16 @@ def __call__(self, x, out=None):  # pylint: disable=signature-differs
 
 See Also
 --------
-:obj:`dpnp.special.erf` : Gauss error function.
-:obj:`dpnp.special.erfc` : Complementary error function.
-:obj:`dpnp.special.erfinv` : Inverse of the error function.
-:obj:`dpnp.special.erfcinv` : Inverse of the complementary error function.
+:obj:`dpnp.scipy.special.erf` : Gauss error function.
+:obj:`dpnp.scipy.special.erfc` : Complementary error function.
+:obj:`dpnp.scipy.special.erfinv` : Inverse of the error function.
+:obj:`dpnp.scipy.special.erfcinv` : Inverse of the complementary error function.
 
 Examples
 --------
 >>> import dpnp as np
 >>> x = np.linspace(-3, 3, num=4)
->>> np.special.erfcx(x)
+>>> np.scipy.special.erfcx(x)
 array([1.62059889e+04, 5.00898008e+00, 4.27583576e-01, 1.79001151e-01])
 
 """

From 81f1cdce89911442af1b9baa58bad657ff396b6b Mon Sep 17 00:00:00 2001
From: Anton Volkov <antonwolfy@gmail.com>
Date: Wed, 15 Oct 2025 13:03:11 +0200
Subject: [PATCH 11/12] Correct namespace path for erf-like functions in the
 changelog

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

diff --git a/CHANGELOG.md b/CHANGELOG.md
index a8957d66b6c..52149408a25 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -13,7 +13,7 @@ This release changes the license from `BSD-2-Clause` to `BSD-3-Clause`.
 * Added the docstrings to `dpnp.linalg.LinAlgError` exception [#2613](https://github.com/IntelPython/dpnp/pull/2613)
 * Added implementation of `dpnp.linalg.lu_solve` for batch inputs (SciPy-compatible) [#2619](https://github.com/IntelPython/dpnp/pull/2619)
 * Added `dpnp.exceptions` submodule to aggregate the generic exceptions used by dpnp [#2616](https://github.com/IntelPython/dpnp/pull/2616)
-* Added implementation of `dpnp.special.erfcx` [#2596](https://github.com/IntelPython/dpnp/pull/2596)
+* Added implementation of `dpnp.scipy.special.erfcx` [#2596](https://github.com/IntelPython/dpnp/pull/2596)
 
 ### Changed
 
@@ -48,7 +48,7 @@ This release is compatible with NumPy 2.3.3.
 * Added implementation of `dpnp.linalg.lu_factor` (SciPy-compatible) [#2557](https://github.com/IntelPython/dpnp/pull/2557), [#2565](https://github.com/IntelPython/dpnp/pull/2565)
 * Added implementation of `dpnp.piecewise` [#2550](https://github.com/IntelPython/dpnp/pull/2550)
 * Added implementation of `dpnp.linalg.lu_solve` for 2D inputs (SciPy-compatible) [#2575](https://github.com/IntelPython/dpnp/pull/2575)
-* Added implementation of `dpnp.special.erfc` [#2588](https://github.com/IntelPython/dpnp/pull/2588)
+* Added implementation of `dpnp.scipy.special.erfc` [#2588](https://github.com/IntelPython/dpnp/pull/2588)
 * Added `dpnp.scipy` submodule to aggregate new SciPy-compatible functions from `linalg` and `special` namespaces [#2603](https://github.com/IntelPython/dpnp/pull/2603)
 
 ### Changed

From f86496a3faafc26cabcf85fb5235b5cbfe68530d Mon Sep 17 00:00:00 2001
From: Anton <100830759+antonwolfy@users.noreply.github.com>
Date: Wed, 15 Oct 2025 14:59:26 +0200
Subject: [PATCH 12/12] Apply suggestions from code review

Co-authored-by: vlad-perevezentsev <vladislav.perevezentsev@intel.com>
---
 CHANGELOG.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 52149408a25..7ab65f4381e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -45,9 +45,9 @@ This release is compatible with NumPy 2.3.3.
 * Added `timeout-minutes` property to GitHub jobs [#2526](https://github.com/IntelPython/dpnp/pull/2526)
 * Added implementation of `dpnp.ndarray.data` and `dpnp.ndarray.data.ptr` attributes [#2521](https://github.com/IntelPython/dpnp/pull/2521)
 * Added `dpnp.ndarray.__contains__` method [#2534](https://github.com/IntelPython/dpnp/pull/2534)
-* Added implementation of `dpnp.linalg.lu_factor` (SciPy-compatible) [#2557](https://github.com/IntelPython/dpnp/pull/2557), [#2565](https://github.com/IntelPython/dpnp/pull/2565)
+* Added implementation of `dpnp.scipy.linalg.lu_factor` (SciPy-compatible) [#2557](https://github.com/IntelPython/dpnp/pull/2557), [#2565](https://github.com/IntelPython/dpnp/pull/2565)
 * Added implementation of `dpnp.piecewise` [#2550](https://github.com/IntelPython/dpnp/pull/2550)
-* Added implementation of `dpnp.linalg.lu_solve` for 2D inputs (SciPy-compatible) [#2575](https://github.com/IntelPython/dpnp/pull/2575)
+* Added implementation of `dpnp.scipy.linalg.lu_solve` for 2D inputs (SciPy-compatible) [#2575](https://github.com/IntelPython/dpnp/pull/2575)
 * Added implementation of `dpnp.scipy.special.erfc` [#2588](https://github.com/IntelPython/dpnp/pull/2588)
 * Added `dpnp.scipy` submodule to aggregate new SciPy-compatible functions from `linalg` and `special` namespaces [#2603](https://github.com/IntelPython/dpnp/pull/2603)