From 8fd88b217c9f40b39f5ae72a94e956873d57e403 Mon Sep 17 00:00:00 2001
From: Felix Hekhorn <felix.hekhorn@uni-tuebingen.de>
Date: Fri, 18 Mar 2022 16:46:50 +0100
Subject: [PATCH 1/5] Remove all numba signatures

---
 benchmarks/lha_paper_bench.py                 | 14 +++---
 pyproject.toml                                |  1 +
 src/eko/anomalous_dimensions/__init__.py      |  6 +--
 src/eko/anomalous_dimensions/aem1.py          |  8 ++--
 src/eko/anomalous_dimensions/as1.py           | 10 ++--
 src/eko/anomalous_dimensions/as2.py           | 14 +++---
 src/eko/anomalous_dimensions/as3.py           | 16 +++----
 src/eko/anomalous_dimensions/harmonics.py     | 14 +++---
 src/eko/beta.py                               | 12 ++---
 src/eko/evolution_operator/__init__.py        |  4 +-
 src/eko/gamma.py                              | 10 ++--
 src/eko/interpolation.py                      | 10 ++--
 src/eko/kernels/evolution_integrals.py        | 22 ++++-----
 src/eko/kernels/non_singlet.py                | 20 ++++----
 src/eko/kernels/singlet.py                    | 28 +++++------
 src/eko/kernels/utils.py                      |  2 +-
 src/eko/matching_conditions/as1.py            | 12 ++---
 src/eko/matching_conditions/as2.py            | 14 +++---
 src/eko/matching_conditions/as3/__init__.py   |  4 +-
 src/eko/matching_conditions/as3/aHg.py        |  2 +-
 src/eko/matching_conditions/as3/aHgstfac.py   |  2 +-
 src/eko/matching_conditions/as3/aHq.py        |  2 +-
 src/eko/matching_conditions/as3/agg.py        |  2 +-
 src/eko/matching_conditions/as3/aggTF2.py     |  2 +-
 src/eko/matching_conditions/as3/agq.py        |  2 +-
 src/eko/matching_conditions/as3/aqg.py        |  2 +-
 src/eko/matching_conditions/as3/aqqNS.py      |  2 +-
 src/eko/matching_conditions/as3/aqqPS.py      |  2 +-
 .../as3/f_functions/f11.py                    |  2 +-
 .../as3/f_functions/f13.py                    |  2 +-
 .../as3/f_functions/f14_f12.py                |  2 +-
 .../as3/f_functions/f16.py                    |  2 +-
 .../as3/f_functions/f17.py                    |  2 +-
 .../as3/f_functions/f18.py                    |  2 +-
 .../as3/f_functions/f19.py                    |  2 +-
 .../as3/f_functions/f20.py                    |  2 +-
 .../as3/f_functions/f21.py                    |  2 +-
 .../matching_conditions/as3/f_functions/f9.py |  2 +-
 .../matching_conditions/as3/g_functions.py    | 16 +++----
 .../matching_conditions/as3/s_functions.py    | 48 +++++++++----------
 .../operator_matrix_element.py                | 14 +++---
 src/eko/mellin.py                             | 12 ++---
 src/eko/msbar_masses.py                       |  2 +-
 src/eko/scale_variations/expanded.py          | 16 ++-----
 src/eko/scale_variations/exponentiated.py     |  2 +-
 src/eko/strong_coupling.py                    |  2 +-
 46 files changed, 183 insertions(+), 188 deletions(-)

diff --git a/benchmarks/lha_paper_bench.py b/benchmarks/lha_paper_bench.py
index 415ed665d..b43ec8b2d 100644
--- a/benchmarks/lha_paper_bench.py
+++ b/benchmarks/lha_paper_bench.py
@@ -222,14 +222,14 @@ def benchmark_sv(self, pto):
 
     # Benchmark to LHA
     # obj = BenchmarkVFNS()
-    # obj = BenchmarkFFNS()
+    obj = BenchmarkFFNS()
 
-    # obj.benchmark_plain(2)
+    obj.benchmark_plain(0)
     # obj.benchmark_sv(2)
 
     # # VFNS benchmarks with LHA settings
-    programs = ["LHA", "pegasus", "apfel"]
-    for p in programs:
-        obj = BenchmarkRunner(p)
-        # obj.benchmark_plain(2)
-        obj.benchmark_sv(2)
+    # programs = ["LHA", "pegasus", "apfel"]
+    # for p in programs:
+    #     obj = BenchmarkRunner(p)
+    #     # obj.benchmark_plain(2)
+    #     obj.benchmark_sv(2)
diff --git a/pyproject.toml b/pyproject.toml
index 97429f93e..054e83b27 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -84,6 +84,7 @@ bench-run.env.NUMBA_DISABLE_JIT.default = "0"
 lint = "pylint src/**/*.py -E"
 lint-warnings = "pylint src/**/*.py --exit-zero"
 sandbox = "python benchmarks/sandbox.py"
+lha = "python benchmarks/lha_paper_bench.py"
 nav = "ekonav --config benchmarks/banana.yaml"
 navigator = "ekonav --config benchmarks/banana.yaml"
 docs = { "shell" = "cd doc; make html" }
diff --git a/src/eko/anomalous_dimensions/__init__.py b/src/eko/anomalous_dimensions/__init__.py
index 438966249..a02322360 100644
--- a/src/eko/anomalous_dimensions/__init__.py
+++ b/src/eko/anomalous_dimensions/__init__.py
@@ -23,7 +23,7 @@
 from . import as1, as2, as3, harmonics
 
 
-@nb.njit("Tuple((c16[:,:],c16,c16,c16[:,:],c16[:,:]))(c16[:,:])", cache=True)
+@nb.njit(cache=True)
 def exp_singlet(gamma_S):
     r"""
     Computes the exponential and the eigensystem of the singlet anomalous dimension matrix
@@ -71,7 +71,7 @@ def exp_singlet(gamma_S):
     return exp, lambda_p, lambda_m, e_p, e_m
 
 
-@nb.njit("c16[:](u1,u2,c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_ns(order, mode, n, nf):
     r"""
     Computes the tower of the non-singlet anomalous dimensions
@@ -131,7 +131,7 @@ def gamma_ns(order, mode, n, nf):
     return gamma_ns
 
 
-@nb.njit("c16[:,:,:](u1,c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_singlet(order, n, nf):
     r"""
     Computes the tower of the singlet anomalous dimensions matrices
diff --git a/src/eko/anomalous_dimensions/aem1.py b/src/eko/anomalous_dimensions/aem1.py
index de620655a..9b125a7f5 100644
--- a/src/eko/anomalous_dimensions/aem1.py
+++ b/src/eko/anomalous_dimensions/aem1.py
@@ -5,7 +5,7 @@
 from . import as1
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def gamma_phq(N):
     """
     Computes the leading-order photon-quark anomalous dimension
@@ -26,7 +26,7 @@ def gamma_phq(N):
     return as1.gamma_gq(N) / constants.CF
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_qph(N, nf):
     """
     Computes the leading-order quark-photon anomalous dimension
@@ -50,7 +50,7 @@ def gamma_qph(N, nf):
     return as1.gamma_qg(N, nf) / constants.TR * constants.NC
 
 
-@nb.njit("c16(u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_phph(nf):
     """
     Computes the leading-order photon-photon anomalous dimension
@@ -71,7 +71,7 @@ def gamma_phph(nf):
     return 2 / 3 * constants.NC * 2 * nf
 
 
-@nb.njit("c16(c16,c16)", cache=True)
+@nb.njit(cache=True)
 def gamma_ns(N, s1):
     """
     Computes the leading-order non-singlet QED anomalous dimension.
diff --git a/src/eko/anomalous_dimensions/as1.py b/src/eko/anomalous_dimensions/as1.py
index 2efc0cae5..0c94d61d3 100644
--- a/src/eko/anomalous_dimensions/as1.py
+++ b/src/eko/anomalous_dimensions/as1.py
@@ -7,7 +7,7 @@
 from .. import constants
 
 
-@nb.njit("c16(c16,c16)", cache=True)
+@nb.njit(cache=True)
 def gamma_ns(N, s1):
     """
     Computes the leading-order non-singlet anomalous dimension.
@@ -31,7 +31,7 @@ def gamma_ns(N, s1):
     return result
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_qg(N, nf):
     """
     Computes the leading-order quark-gluon anomalous dimension
@@ -55,7 +55,7 @@ def gamma_qg(N, nf):
     return result
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def gamma_gq(N):
     """
     Computes the leading-order gluon-quark anomalous dimension
@@ -77,7 +77,7 @@ def gamma_gq(N):
     return result
 
 
-@nb.njit("c16(c16,c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_gg(N, s1, nf):
     """
     Computes the leading-order gluon-gluon anomalous dimension
@@ -103,7 +103,7 @@ def gamma_gg(N, s1, nf):
     return result
 
 
-@nb.njit("c16[:,:](c16,c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_singlet(N, s1, nf):
     r"""
       Computes the leading-order singlet anomalous dimension matrix
diff --git a/src/eko/anomalous_dimensions/as2.py b/src/eko/anomalous_dimensions/as2.py
index 7c477c591..07249ef31 100644
--- a/src/eko/anomalous_dimensions/as2.py
+++ b/src/eko/anomalous_dimensions/as2.py
@@ -14,7 +14,7 @@
 from . import harmonics
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_nsm(n, nf):
     """
     Computes the |NLO| valence-like non-singlet anomalous dimension.
@@ -57,7 +57,7 @@ def gamma_nsm(n, nf):
     return result
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_nsp(n, nf):
     """
     Computes the |NLO| singlet-like non-singlet anomalous dimension.
@@ -98,7 +98,7 @@ def gamma_nsp(n, nf):
     return result
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_ps(n, nf):
     """
     Computes the |NLO| pure-singlet quark-quark anomalous dimension.
@@ -125,7 +125,7 @@ def gamma_ps(n, nf):
     return result
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_qg(n, nf):
     """
     Computes the |NLO| quark-gluon singlet anomalous dimension.
@@ -158,7 +158,7 @@ def gamma_qg(n, nf):
     return result
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_gq(n, nf):
     """
     Computes the |NLO| gluon-quark singlet anomalous dimension.
@@ -194,7 +194,7 @@ def gamma_gq(n, nf):
     return result
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_gg(n, nf):
     """
     Computes the |NLO| gluon-gluon singlet anomalous dimension.
@@ -232,7 +232,7 @@ def gamma_gg(n, nf):
     return result
 
 
-@nb.njit("c16[:,:](c16,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_singlet(N, nf):
     r"""
       Computes the next-leading-order singlet anomalous dimension matrix
diff --git a/src/eko/anomalous_dimensions/as3.py b/src/eko/anomalous_dimensions/as3.py
index c0864d2ff..1868a7604 100644
--- a/src/eko/anomalous_dimensions/as3.py
+++ b/src/eko/anomalous_dimensions/as3.py
@@ -16,7 +16,7 @@
 zeta3 = harmonics.zeta3
 
 
-@nb.njit("c16(c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_nsm(n, nf, sx):
     """
     Computes the |NNLO| valence-like non-singlet anomalous dimension.
@@ -93,7 +93,7 @@ def gamma_nsm(n, nf, sx):
     return result
 
 
-@nb.njit("c16(c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_nsp(n, nf, sx):
     """
     Computes the |NNLO| singlet-like non-singlet anomalous dimension.
@@ -170,7 +170,7 @@ def gamma_nsp(n, nf, sx):
     return result
 
 
-@nb.njit("c16(c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_nsv(n, nf, sx):
     """
     Computes the |NNLO| valence non-singlet anomalous dimension.
@@ -225,7 +225,7 @@ def gamma_nsv(n, nf, sx):
     return result
 
 
-@nb.njit("c16(c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_ps(n, nf, sx):
     """
     Computes the |NNLO| pure-singlet quark-quark anomalous dimension.
@@ -297,7 +297,7 @@ def gamma_ps(n, nf, sx):
     return result
 
 
-@nb.njit("c16(c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_qg(n, nf, sx):
     """
     Computes the |NNLO| quark-gluon singlet anomalous dimension.
@@ -371,7 +371,7 @@ def gamma_qg(n, nf, sx):
     return result
 
 
-@nb.njit("c16(c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_gq(n, nf, sx):
     """
     Computes the |NNLO| gluon-quark singlet anomalous dimension.
@@ -461,7 +461,7 @@ def gamma_gq(n, nf, sx):
     return result
 
 
-@nb.njit("c16(c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_gg(n, nf, sx):
     """
     Computes the |NNLO| gluon-gluon singlet anomalous dimension.
@@ -549,7 +549,7 @@ def gamma_gg(n, nf, sx):
     return result
 
 
-@nb.njit("c16[:,:](c16,u1,c16[:])", cache=True)
+@nb.njit(cache=True)
 def gamma_singlet(N, nf, sx):
     r"""
       Computes the |NNLO| singlet anomalous dimension matrix
diff --git a/src/eko/anomalous_dimensions/harmonics.py b/src/eko/anomalous_dimensions/harmonics.py
index 9a7763c91..ac50d4e9a 100644
--- a/src/eko/anomalous_dimensions/harmonics.py
+++ b/src/eko/anomalous_dimensions/harmonics.py
@@ -16,7 +16,7 @@
 zeta5 = scipy.special.zeta(5)
 
 
-@nb.njit("c16(c16,u1)", cache=True)
+@nb.njit(cache=True)
 def cern_polygamma(Z, K):  # pylint: disable=all
     """
     Computes the polygamma functions :math:`\\psi_k(z)`.
@@ -133,7 +133,7 @@ def cern_polygamma(Z, K):  # pylint: disable=all
     # fmt: on
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S1(N):
     r"""
     Computes the harmonic sum :math:`S_1(N)`.
@@ -161,7 +161,7 @@ def harmonic_S1(N):
     return cern_polygamma(N + 1.0, 0) + np.euler_gamma
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S2(N):
     r"""
     Computes the harmonic sum :math:`S_2(N)`.
@@ -189,7 +189,7 @@ def harmonic_S2(N):
     return -cern_polygamma(N + 1.0, 1) + zeta2
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S3(N):
     r"""
     Computes the harmonic sum :math:`S_3(N)`.
@@ -217,7 +217,7 @@ def harmonic_S3(N):
     return 0.5 * cern_polygamma(N + 1.0, 2) + zeta3
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S4(N):
     r"""
     Computes the harmonic sum :math:`S_4(N)`.
@@ -245,7 +245,7 @@ def harmonic_S4(N):
     return zeta4 - 1.0 / 6.0 * cern_polygamma(N + 1.0, 3)
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S5(N):
     r"""
     Computes the harmonic sum :math:`S_5(N)`.
@@ -273,7 +273,7 @@ def harmonic_S5(N):
     return zeta5 + 1.0 / 24.0 * cern_polygamma(N + 1.0, 4)
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g3(N):
     r"""
     Computes the Mellin transform of :math:`\text{Li}_2(x)/(1+x)`.
diff --git a/src/eko/beta.py b/src/eko/beta.py
index f7d9af05d..2254cad86 100644
--- a/src/eko/beta.py
+++ b/src/eko/beta.py
@@ -11,7 +11,7 @@
 from .anomalous_dimensions.harmonics import zeta3
 
 
-@nb.njit("f8(u1)", cache=True)
+@nb.njit(cache=True)
 def beta_0(nf):
     """
     Computes the first coefficient of the QCD beta function.
@@ -32,7 +32,7 @@ def beta_0(nf):
     return beta_0
 
 
-@nb.njit("f8(u1)", cache=True)
+@nb.njit(cache=True)
 def beta_1(nf):
     """
     Computes the second coefficient of the QCD beta function.
@@ -57,7 +57,7 @@ def beta_1(nf):
     return beta_1
 
 
-@nb.njit("f8(u1)", cache=True)
+@nb.njit(cache=True)
 def beta_2(nf):
     """
     Computes the third coefficient of the QCD beta function
@@ -86,7 +86,7 @@ def beta_2(nf):
     return beta_2
 
 
-@nb.njit("f8(u1)", cache=True)
+@nb.njit(cache=True)
 def beta_3(nf):
     """
     Computes the fourth coefficient of the QCD beta function
@@ -113,7 +113,7 @@ def beta_3(nf):
     return beta_3
 
 
-@nb.njit("f8(u1,u1)", cache=True)
+@nb.njit(cache=True)
 def beta(k, nf):
     """
     Compute value of a beta coefficients
@@ -144,7 +144,7 @@ def beta(k, nf):
     return beta_
 
 
-@nb.njit("f8(u1,u1)", cache=True)
+@nb.njit(cache=True)
 def b(k, nf):
     """
     Compute b coefficient.
diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 830c2c39f..813d77fc2 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -26,7 +26,7 @@
 logger = logging.getLogger(__name__)
 
 
-@nb.njit("c16(c16[:,:],u2,u2)")
+@nb.njit(cache=True)
 def select_singlet_element(ker, mode0, mode1):
     """
     Select element of the singlet matrix
@@ -116,7 +116,7 @@ def integrand(
         return self.path.prefactor * pj * self.path.jac
 
 
-@nb.njit("f8(f8,u1,u2,u2,string,b1,f8,f8[:,:],f8,f8,f8,f8,u4,u1,u1)", cache=True)
+@nb.njit(cache=True)
 def quad_ker(
     u,
     order,
diff --git a/src/eko/gamma.py b/src/eko/gamma.py
index 15fc1b53b..a9379d83d 100644
--- a/src/eko/gamma.py
+++ b/src/eko/gamma.py
@@ -9,7 +9,7 @@
 from .anomalous_dimensions.harmonics import zeta3, zeta4, zeta5
 
 
-@nb.njit("f8()", cache=True)
+@nb.njit(cache=True)
 def gamma_0():
     """
     Computes the first coefficient of the QCD gamma function.
@@ -24,7 +24,7 @@ def gamma_0():
     return 4.0
 
 
-@nb.njit("f8(u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_1(nf):
     """
     Computes the second coefficient of the QCD gamma function.
@@ -44,7 +44,7 @@ def gamma_1(nf):
     return 202.0 / 3.0 - 20.0 / 9.0 * nf
 
 
-@nb.njit("f8(u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_2(nf):
     """
     Computes the third coefficient of the QCD gamma function.
@@ -64,7 +64,7 @@ def gamma_2(nf):
     return 1249.0 - (2216.0 / 27.0 + 160.0 / 3.0 * zeta3) * nf - 140.0 / 81.0 * nf**2
 
 
-@nb.njit("f8(u1)", cache=True)
+@nb.njit(cache=True)
 def gamma_3(nf):
     """
     Computes the fourth coefficient of the QCD gamma function.
@@ -97,7 +97,7 @@ def gamma_3(nf):
     )
 
 
-@nb.njit("f8(u1,u1)", cache=True)
+@nb.njit(cache=True)
 def gamma(order, nf):
     """
     Compute the value of a gamma coefficient
diff --git a/src/eko/interpolation.py b/src/eko/interpolation.py
index bb0ade7b0..08d37f771 100644
--- a/src/eko/interpolation.py
+++ b/src/eko/interpolation.py
@@ -76,7 +76,7 @@ def __iter__(self):
             yield coef
 
 
-@nb.njit("c16(c16,f8,f8[:,:])", cache=True)
+@nb.njit(cache=True)
 def log_evaluate_Nx(N, logx, area_list):
     r"""
     Evaluates a single logarithmic Lagrange interpolator in N-space multiplied
@@ -133,7 +133,7 @@ def log_evaluate_Nx(N, logx, area_list):
     return res
 
 
-@nb.njit("c16(c16,f8,f8[:,:])", cache=True)
+@nb.njit(cache=True)
 def evaluate_Nx(N, logx, area_list):
     r"""
     Evaluates a single linear Lagrange interpolator in N-space multiplied
@@ -176,7 +176,7 @@ def evaluate_Nx(N, logx, area_list):
     return res
 
 
-@nb.njit("c16(c16,b1,f8,f8[:,:])", cache=True)
+@nb.njit(cache=True)
 def evaluate_grid(N, is_log, logx, area_list):
     """
     Evaluate interpolator in N-space
@@ -208,7 +208,7 @@ def evaluate_grid(N, is_log, logx, area_list):
 _atol_eps = 10 * np.finfo(float).eps
 
 
-@nb.njit("f8(f8,f8[:,:])", cache=True)
+@nb.njit(cache=True)
 def evaluate_x(x, area_list):
     """
     Get a single linear Lagrange interpolator in x-space
@@ -241,7 +241,7 @@ def evaluate_x(x, area_list):
     return res
 
 
-@nb.njit("f8(f8,f8[:,:])", cache=True)
+@nb.njit(cache=True)
 def log_evaluate_x(x, area_list):
     """
     Get a single logarithmic Lagrange interpolator in x-space
diff --git a/src/eko/kernels/evolution_integrals.py b/src/eko/kernels/evolution_integrals.py
index 148990d4f..3c764d0c3 100644
--- a/src/eko/kernels/evolution_integrals.py
+++ b/src/eko/kernels/evolution_integrals.py
@@ -15,7 +15,7 @@
 from .. import beta
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j00(a1, a0, nf):
     r"""
     LO-LO exact evolution integral.
@@ -41,7 +41,7 @@ def j00(a1, a0, nf):
     return np.log(a1 / a0) / beta.beta(0, nf)
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j11_exact(a1, a0, nf):
     r"""
     NLO-NLO exact evolution integral.
@@ -70,7 +70,7 @@ def j11_exact(a1, a0, nf):
     return (1.0 / beta_1) * np.log((1.0 + a1 * b1) / (1.0 + a0 * b1))
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j11_expanded(a1, a0, nf):
     r"""
     NLO-NLO expanded evolution integral.
@@ -95,7 +95,7 @@ def j11_expanded(a1, a0, nf):
     return 1.0 / beta.beta(0, nf) * (a1 - a0)
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j01_exact(a1, a0, nf):
     r"""
     LO-NLO exact evolution integral.
@@ -122,7 +122,7 @@ def j01_exact(a1, a0, nf):
     return j00(a1, a0, nf) - beta.b(1, nf) * j11_exact(a1, a0, nf)
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j01_expanded(a1, a0, nf):
     r"""
     LO-NLO expanded evolution integral.
@@ -147,7 +147,7 @@ def j01_expanded(a1, a0, nf):
     return j00(a1, a0, nf) - beta.b(1, nf) * j11_expanded(a1, a0, nf)
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j22_exact(a1, a0, nf):
     r"""
     NNLO-NNLO exact evolution integral.
@@ -190,7 +190,7 @@ def j22_exact(a1, a0, nf):
     )
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j12_exact(a1, a0, nf):
     r"""
     NLO-NNLO exact evolution integral.
@@ -225,7 +225,7 @@ def j12_exact(a1, a0, nf):
     return 2.0 / (beta.beta(0, nf)) * np.real(delta / Delta)
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j02_exact(a1, a0, nf):
     r"""
     LO-NNLO exact evolution integral.
@@ -256,7 +256,7 @@ def j02_exact(a1, a0, nf):
     )
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j22_expanded(a1, a0, nf):
     r"""
     NNLO-NNLO expanded evolution integral.
@@ -281,7 +281,7 @@ def j22_expanded(a1, a0, nf):
     return 1 / (2 * beta.beta(0, nf)) * (a1**2 - a0**2)
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j12_expanded(a1, a0, nf):
     r"""
     NLO-NNLO expanded evolution integral.
@@ -308,7 +308,7 @@ def j12_expanded(a1, a0, nf):
     return 1 / beta.beta(0, nf) * (a1 - a0 - b1 / 2 * (a1**2 - a0**2))
 
 
-@nb.njit("f8(f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def j02_expanded(a1, a0, nf):
     r"""
     LO-NNLO expanded evolution integral.
diff --git a/src/eko/kernels/non_singlet.py b/src/eko/kernels/non_singlet.py
index 0229e75df..72ac438d2 100644
--- a/src/eko/kernels/non_singlet.py
+++ b/src/eko/kernels/non_singlet.py
@@ -11,7 +11,7 @@
 from . import utils
 
 
-@nb.njit("c16(c16[:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def lo_exact(gamma_ns, a1, a0, nf):
     """
     |LO| non-singlet exact EKO
@@ -35,7 +35,7 @@ def lo_exact(gamma_ns, a1, a0, nf):
     return np.exp(gamma_ns[0] * ei.j00(a1, a0, nf))
 
 
-@nb.njit("c16(c16[:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nlo_exact(gamma_ns, a1, a0, nf):
     """
     |NLO| non-singlet exact EKO
@@ -61,7 +61,7 @@ def nlo_exact(gamma_ns, a1, a0, nf):
     )
 
 
-@nb.njit("c16(c16[:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nlo_expanded(gamma_ns, a1, a0, nf):
     """
     |NLO| non-singlet expanded EKO
@@ -88,7 +88,7 @@ def nlo_expanded(gamma_ns, a1, a0, nf):
     )
 
 
-@nb.njit("c16(c16[:],f8,f8,u1,u4)", cache=True)
+@nb.njit(cache=True)
 def nlo_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     """
     |NLO| non-singlet truncated EKO
@@ -122,7 +122,7 @@ def nlo_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     return e
 
 
-@nb.njit("c16(c16[:],f8,f8,u1,u4)", cache=True)
+@nb.njit(cache=True)
 def nlo_ordered_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     """
     |NLO| non-singlet ordered-truncated EKO
@@ -161,7 +161,7 @@ def nlo_ordered_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     return e
 
 
-@nb.njit("c16(c16[:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nnlo_exact(gamma_ns, a1, a0, nf):
     """
     |NNLO| non-singlet exact EKO
@@ -189,7 +189,7 @@ def nnlo_exact(gamma_ns, a1, a0, nf):
     )
 
 
-@nb.njit("c16(c16[:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nnlo_expanded(gamma_ns, a1, a0, nf):
     """
     |NNLO| non-singlet expanded EKO
@@ -217,7 +217,7 @@ def nnlo_expanded(gamma_ns, a1, a0, nf):
     )
 
 
-@nb.njit("c16(c16[:],f8,f8,u1,u4)", cache=True)
+@nb.njit(cache=True)
 def nnlo_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     """
     |NNLO| non-singlet truncated EKO
@@ -263,7 +263,7 @@ def nnlo_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     return e
 
 
-@nb.njit("c16(c16[:],f8,f8,u1,u4)", cache=True)
+@nb.njit(cache=True)
 def nnlo_ordered_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     """
     |NNLO| non-singlet ordered truncated EKO
@@ -303,7 +303,7 @@ def nnlo_ordered_truncated(gamma_ns, a1, a0, nf, ev_op_iterations):
     return e
 
 
-@nb.njit("c16(u1,string,c16[:],f8,f8,u1,u4)", cache=True)
+@nb.njit(cache=True)
 def dispatcher(
     order, method, gamma_ns, a1, a0, nf, ev_op_iterations
 ):  # pylint: disable=too-many-return-statements
diff --git a/src/eko/kernels/singlet.py b/src/eko/kernels/singlet.py
index 40ac12e0b..1a4b536ed 100644
--- a/src/eko/kernels/singlet.py
+++ b/src/eko/kernels/singlet.py
@@ -12,7 +12,7 @@
 from . import utils
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def lo_exact(gamma_singlet, a1, a0, nf):
     """
     Singlet leading order exact EKO
@@ -36,7 +36,7 @@ def lo_exact(gamma_singlet, a1, a0, nf):
     return ad.exp_singlet(gamma_singlet[0] * ei.j00(a1, a0, nf))[0]
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8)", cache=True)
+@nb.njit(cache=True)
 def nlo_decompose(gamma_singlet, j01, j11):
     """
     Singlet next-to-leading order decompose EKO
@@ -64,7 +64,7 @@ def nlo_decompose(gamma_singlet, j01, j11):
     return ad.exp_singlet(gamma_singlet[0] * j01 + gamma_singlet[1] * j11)[0]
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nlo_decompose_exact(gamma_singlet, a1, a0, nf):
     """
     Singlet next-to-leading order decompose-exact EKO
@@ -90,7 +90,7 @@ def nlo_decompose_exact(gamma_singlet, a1, a0, nf):
     )
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nlo_decompose_expanded(gamma_singlet, a1, a0, nf):
     """
     Singlet next-to-leading order decompose-expanded EKO
@@ -116,7 +116,7 @@ def nlo_decompose_expanded(gamma_singlet, a1, a0, nf):
     )
 
 
-@nb.njit("c16[:,:](c16[:,:,:],c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def nnlo_decompose(gamma_singlet, j02, j12, j22):
     """
     Singlet next-to-next-to-leading order decompose EKO
@@ -147,7 +147,7 @@ def nnlo_decompose(gamma_singlet, j02, j12, j22):
     )[0]
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nnlo_decompose_exact(gamma_singlet, a1, a0, nf):
     """
     Singlet next-to-next-to-leading order decompose-exact EKO
@@ -176,7 +176,7 @@ def nnlo_decompose_exact(gamma_singlet, a1, a0, nf):
     )
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1)", cache=True)
+@nb.njit(cache=True)
 def nnlo_decompose_expanded(gamma_singlet, a1, a0, nf):
     """
     Singlet next-to-next-to-leading order decompose-expanded EKO
@@ -205,7 +205,7 @@ def nnlo_decompose_expanded(gamma_singlet, a1, a0, nf):
     )
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1, u1, u4)", cache=True)
+@nb.njit(cache=True)
 def eko_iterate(gamma_singlet, a1, a0, nf, order, ev_op_iterations):
     """
     Singlet NLO or NNLO iterated (exact) EKO
@@ -262,7 +262,7 @@ def eko_iterate(gamma_singlet, a1, a0, nf, order, ev_op_iterations):
     return e
 
 
-@nb.njit("c16[:,:,:](c16[:,:,:],u1,u1,u1,b1)", cache=True)
+@nb.njit(cache=True)
 def r_vec(gamma_singlet, nf, ev_op_max_order, order, is_exact):
     r"""
     Compute singlet R vector for perturbative mode.
@@ -310,7 +310,7 @@ def r_vec(gamma_singlet, nf, ev_op_max_order, order, is_exact):
     return r
 
 
-@nb.njit("c16[:,:,:](c16[:,:,:],u1)", cache=True)
+@nb.njit(cache=True)
 def u_vec(r, ev_op_max_order):
     r"""
     Compute the elements of the singlet U vector.
@@ -351,7 +351,7 @@ def u_vec(r, ev_op_max_order):
     return u
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8)", cache=True)
+@nb.njit(cache=True)
 def sum_u(uvec, a):
     r"""
     Sums up the actual U operator.
@@ -383,7 +383,7 @@ def sum_u(uvec, a):
     return res
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1,u1,u4,u1,b1)", cache=True)
+@nb.njit(cache=True)
 def eko_perturbative(
     gamma_singlet, a1, a0, nf, order, ev_op_iterations, ev_op_max_order, is_exact
 ):
@@ -431,7 +431,7 @@ def eko_perturbative(
     return e
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,f8,u1,u1,u4)", cache=True)
+@nb.njit(cache=True)
 def eko_truncated(gamma_singlet, a1, a0, nf, order, ev_op_iterations):
     """
     Singlet NLO or NNLO truncated EKO
@@ -480,7 +480,7 @@ def eko_truncated(gamma_singlet, a1, a0, nf, order, ev_op_iterations):
     return e
 
 
-@nb.njit("c16[:,:](u1,string,c16[:,:,:],f8,f8,u1,u4,u1)", cache=True)
+@nb.njit(cache=True)
 def dispatcher(  # pylint: disable=too-many-return-statements
     order, method, gamma_singlet, a1, a0, nf, ev_op_iterations, ev_op_max_order
 ):
diff --git a/src/eko/kernels/utils.py b/src/eko/kernels/utils.py
index 474686aac..083c40edb 100644
--- a/src/eko/kernels/utils.py
+++ b/src/eko/kernels/utils.py
@@ -5,7 +5,7 @@
 import numpy as np
 
 
-@nb.njit("f8[:](f8,f8,u4)", cache=True)
+@nb.njit(cache=True)
 def geomspace(start, end, num):
     """
     Numba port of :func:`numpy.geomspace`.
diff --git a/src/eko/matching_conditions/as1.py b/src/eko/matching_conditions/as1.py
index 9d04061bc..ee31f565c 100644
--- a/src/eko/matching_conditions/as1.py
+++ b/src/eko/matching_conditions/as1.py
@@ -13,7 +13,7 @@
 from ..constants import CF
 
 
-@nb.njit("c16(c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_hh(n, sx, L):
     r"""
     |NLO| heavy-heavy |OME| :math:`A_{HH}^{(1)}` defined as the
@@ -47,7 +47,7 @@ def A_hh(n, sx, L):
     return -CF * (ahh_l * L + ahh)
 
 
-@nb.njit("c16(c16,f8)", cache=True)
+@nb.njit(cache=True)
 def A_gh(n, L):
     r"""
     |NLO| gluon-heavy |OME| :math:`A_{gH}^{(1)}` defined as the
@@ -73,7 +73,7 @@ def A_gh(n, L):
     return 2 * CF * (agh_l0 + agh_l1 * L)
 
 
-@nb.njit("c16(c16,f8)", cache=True)
+@nb.njit(cache=True)
 def A_hg(n, L):
     r"""
     |NLO| heavy-gluon |OME| :math:`A_{Hg}^{S,(1)}` defined as the
@@ -96,7 +96,7 @@ def A_hg(n, L):
     return num * den * L
 
 
-@nb.njit("c16(f8)", cache=True)
+@nb.njit(cache=True)
 def A_gg(L):
     r"""
     |NLO| gluon-gluon |OME| :math:`A_{gg,H}^{S,(1)}` defined as the
@@ -115,7 +115,7 @@ def A_gg(L):
     return -2.0 / 3.0 * L
 
 
-@nb.njit("c16[:,:](c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_singlet(n, sx, L):
     r"""
       Computes the |NLO| singlet |OME|.
@@ -157,7 +157,7 @@ def A_singlet(n, sx, L):
     return A_S
 
 
-@nb.njit("c16[:,:](c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_ns(n, sx, L):
     r"""
       Computes the |NLO| non-singlet |OME| with intrinsic contributions.
diff --git a/src/eko/matching_conditions/as2.py b/src/eko/matching_conditions/as2.py
index 0b9f0257b..421b40844 100644
--- a/src/eko/matching_conditions/as2.py
+++ b/src/eko/matching_conditions/as2.py
@@ -22,7 +22,7 @@
 zeta3 = harmonics.zeta3
 
 
-@nb.njit("c16(c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_qq_ns(n, sx, L):
     r"""
     |NNLO| light-light non-singlet |OME| :math:`A_{qq,H}^{NS,(2)}` given in
@@ -77,7 +77,7 @@ def A_qq_ns(n, sx, L):
     return constants.CF * constants.TR * (a_qq_l2 * L**2 + a_qq_l1 * L + a_qq_l0)
 
 
-@nb.njit("c16(c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_hq_ps(n, sx, L):
     r"""
     |NNLO| heavy-light pure-singlet |OME| :math:`A_{Hq}^{PS,(2)}` given in
@@ -140,7 +140,7 @@ def A_hq_ps(n, sx, L):
     return constants.CF * constants.TR * (a_hq_l2 * L**2 + a_hq_l1 * L + a_hq_l0)
 
 
-@nb.njit("c16(c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_hg(n, sx, L):
     r"""
     |NNLO| heavy-gluon |OME| :math:`A_{Hg}^{S,(2)}` given in
@@ -288,7 +288,7 @@ def A_hg(n, sx, L):
     return a_hg_l2 * L**2 + a_hg_l1 * L + a_hg_l0
 
 
-@nb.njit("c16(c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_gq(n, sx, L):
     r"""
     |NNLO| gluon-quark |OME| :math:`A_{gq,H}^{S,(2)}` given in
@@ -338,7 +338,7 @@ def A_gq(n, sx, L):
     return constants.CF * constants.TR * (a_gq_l2 * L**2 + a_gq_l1 * L + a_gq_l0)
 
 
-@nb.njit("c16(c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_gg(n, sx, L):
     r"""
     |NNLO| gluon-gluon |OME| :math:`A_{gg,H}^{S,(2)} ` given in
@@ -425,7 +425,7 @@ def A_gg(n, sx, L):
     return a_gg_l2 * L**2 + a_gg_l1 * L + a_gg_l0
 
 
-@nb.njit("c16[:,:](c16,c16[:],f8,b1)", cache=True)
+@nb.njit(cache=True)
 def A_singlet(n, sx, L, is_msbar=False):
     r"""
       Computes the |NNLO| singlet |OME|.
@@ -475,7 +475,7 @@ def A_singlet(n, sx, L, is_msbar=False):
     return A_S
 
 
-@nb.njit("c16[:,:](c16,c16[:],f8)", cache=True)
+@nb.njit(cache=True)
 def A_ns(n, sx, L):
     r"""
       Computes the |NNLO| non-singlet |OME|.
diff --git a/src/eko/matching_conditions/as3/__init__.py b/src/eko/matching_conditions/as3/__init__.py
index 6949a3fc1..e8e5c2f66 100644
--- a/src/eko/matching_conditions/as3/__init__.py
+++ b/src/eko/matching_conditions/as3/__init__.py
@@ -36,7 +36,7 @@
 from .aqqPS import A_qqPS
 
 
-@nb.njit("c16[:,:](c16,c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_singlet(n, sx_all, nf, L):
     r"""
     Computes the |N3LO| singlet |OME|.
@@ -93,7 +93,7 @@ def A_singlet(n, sx_all, nf, L):
     return A_S
 
 
-@nb.njit("c16[:,:](c16,c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_ns(n, sx_all, nf, L):
     r"""
     Computes the |N3LO| non-singlet |OME|.
diff --git a/src/eko/matching_conditions/as3/aHg.py b/src/eko/matching_conditions/as3/aHg.py
index 7a9ebc7cd..a95bb60c4 100644
--- a/src/eko/matching_conditions/as3/aHg.py
+++ b/src/eko/matching_conditions/as3/aHg.py
@@ -6,7 +6,7 @@
 from .aHgstfac import A_Hgstfac
 
 
-@nb.njit("c16(c16,c16[:],c16[:],c16[:],c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_Hg(n, sx, smx, s3x, s4x, nf, L):  # pylint: disable=too-many-locals
     r"""
     Computes the |N3LO| singlet |OME| :math:`A_{Hg}^{S,(3)}(N)`.
diff --git a/src/eko/matching_conditions/as3/aHgstfac.py b/src/eko/matching_conditions/as3/aHgstfac.py
index 54f4679f2..8c4b2f05b 100644
--- a/src/eko/matching_conditions/as3/aHgstfac.py
+++ b/src/eko/matching_conditions/as3/aHgstfac.py
@@ -3,7 +3,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16[:],c16[:],c16[:],c16[:],u4)", cache=True)
+@nb.njit(cache=True)
 def A_Hgstfac(n, sx, smx, s3x, s4x, nf):
     r"""
     Computes the approximate incomplete part of :math:`A_{Hg}^{S,(3)}(N)`
diff --git a/src/eko/matching_conditions/as3/aHq.py b/src/eko/matching_conditions/as3/aHq.py
index bd0d1d9ed..675e4ab53 100644
--- a/src/eko/matching_conditions/as3/aHq.py
+++ b/src/eko/matching_conditions/as3/aHq.py
@@ -4,7 +4,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16[:],c16[:],c16[:],c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_Hq(n, sx, smx, s3x, s4x, nf, L):  # pylint: disable=too-many-locals
     r"""
     Computes the |N3LO| singlet |OME| :math:`A_{Hq}^{S,(3)}(N)`.
diff --git a/src/eko/matching_conditions/as3/agg.py b/src/eko/matching_conditions/as3/agg.py
index 8b45450b5..1f537e0fc 100644
--- a/src/eko/matching_conditions/as3/agg.py
+++ b/src/eko/matching_conditions/as3/agg.py
@@ -6,7 +6,7 @@
 from .aggTF2 import A_ggTF2
 
 
-@nb.njit("c16(c16,c16[:],c16[:],c16[:],c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_gg(n, sx, smx, s3x, s4x, nf, L):  # pylint: disable=too-many-locals
     r"""
     Computes the |N3LO| singlet |OME| :math:`A_{gg}^{S,(3)}(N)`.
diff --git a/src/eko/matching_conditions/as3/aggTF2.py b/src/eko/matching_conditions/as3/aggTF2.py
index 40d79a169..f2eb5ed75 100644
--- a/src/eko/matching_conditions/as3/aggTF2.py
+++ b/src/eko/matching_conditions/as3/aggTF2.py
@@ -3,7 +3,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16[:],c16[:])", cache=True)
+@nb.njit(cache=True)
 def A_ggTF2(n, sx, s3x):
     r"""
     Computes the approximate incomplete part of :math:`A_{gg}^{S,(3)}(N)`
diff --git a/src/eko/matching_conditions/as3/agq.py b/src/eko/matching_conditions/as3/agq.py
index 7bda36516..d7d668faa 100644
--- a/src/eko/matching_conditions/as3/agq.py
+++ b/src/eko/matching_conditions/as3/agq.py
@@ -3,7 +3,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16[:],c16[:],c16[:],c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_gq(n, sx, smx, s3x, s4x, nf, L):  # pylint: disable=too-many-locals
     r"""
     Computes the |N3LO| singlet |OME| :math:`A_{gq}^{S,(3)}(N)`.
diff --git a/src/eko/matching_conditions/as3/aqg.py b/src/eko/matching_conditions/as3/aqg.py
index 3b347e939..577396c08 100644
--- a/src/eko/matching_conditions/as3/aqg.py
+++ b/src/eko/matching_conditions/as3/aqg.py
@@ -3,7 +3,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16[:],c16[:],c16[:],c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_qg(n, sx, smx, s3x, s4x, nf, L):
     r"""
     Computes the |N3LO| singlet |OME| :math:`A_{qg}^{S,(3)}(N)`.
diff --git a/src/eko/matching_conditions/as3/aqqNS.py b/src/eko/matching_conditions/as3/aqqNS.py
index 39a7f7604..fa8079cb8 100644
--- a/src/eko/matching_conditions/as3/aqqNS.py
+++ b/src/eko/matching_conditions/as3/aqqNS.py
@@ -5,7 +5,7 @@
 from . import s_functions as sf
 
 
-@nb.njit("c16(c16,c16[:],c16[:],c16[:],c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_qqNS(n, sx, smx, s3x, s4x, nf, L):  # pylint: disable=too-many-locals
     r"""
     Computes the |N3LO| singlet |OME| :math:`A_{qq}^{NS,(3)}(N)`.
diff --git a/src/eko/matching_conditions/as3/aqqPS.py b/src/eko/matching_conditions/as3/aqqPS.py
index b10fb72d2..7846c0111 100644
--- a/src/eko/matching_conditions/as3/aqqPS.py
+++ b/src/eko/matching_conditions/as3/aqqPS.py
@@ -3,7 +3,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_qqPS(n, sx, nf, L):
     r"""
     Computes the |N3LO| singlet |OME| :math:`A_{qq}^{PS,(3)}(N)`.
diff --git a/src/eko/matching_conditions/as3/f_functions/f11.py b/src/eko/matching_conditions/as3/f_functions/f11.py
index b5ad27023..cdeb80587 100644
--- a/src/eko/matching_conditions/as3/f_functions/f11.py
+++ b/src/eko/matching_conditions/as3/f_functions/f11.py
@@ -8,7 +8,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F11(n, S1, S2):
     """Implements eq 9.27 of :cite:`Blumlein:2009ta`"""
     return (
diff --git a/src/eko/matching_conditions/as3/f_functions/f13.py b/src/eko/matching_conditions/as3/f_functions/f13.py
index 7f97d50a2..dea80341e 100644
--- a/src/eko/matching_conditions/as3/f_functions/f13.py
+++ b/src/eko/matching_conditions/as3/f_functions/f13.py
@@ -8,7 +8,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F13(n, S1, S2):
     """Implements eq 9.29 of :cite:`Blumlein:2009ta`"""
     return (
diff --git a/src/eko/matching_conditions/as3/f_functions/f14_f12.py b/src/eko/matching_conditions/as3/f_functions/f14_f12.py
index 37a7cb91f..0041af6d9 100644
--- a/src/eko/matching_conditions/as3/f_functions/f14_f12.py
+++ b/src/eko/matching_conditions/as3/f_functions/f14_f12.py
@@ -9,7 +9,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F14F12(n, S1, S21):
     """Linear combination of :math:`M[( 2 S_{2,2}(x)- Li_2(x)^2/2)/(1+x)](N)`"""
     return (
diff --git a/src/eko/matching_conditions/as3/f_functions/f16.py b/src/eko/matching_conditions/as3/f_functions/f16.py
index 741139f19..fed342e0b 100644
--- a/src/eko/matching_conditions/as3/f_functions/f16.py
+++ b/src/eko/matching_conditions/as3/f_functions/f16.py
@@ -9,7 +9,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F16(n, S1, Sm1, Sm2, Sm3, Sm21):
     """Implements eq 9.32 of :cite:`Blumlein:2009ta`"""
     return (
diff --git a/src/eko/matching_conditions/as3/f_functions/f17.py b/src/eko/matching_conditions/as3/f_functions/f17.py
index 5396c127d..2411a1ff1 100644
--- a/src/eko/matching_conditions/as3/f_functions/f17.py
+++ b/src/eko/matching_conditions/as3/f_functions/f17.py
@@ -8,7 +8,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F17(n, S1, S2, S3):
     """Implements eq 9.35 of :cite:`Blumlein:2009ta`"""
     return (
diff --git a/src/eko/matching_conditions/as3/f_functions/f18.py b/src/eko/matching_conditions/as3/f_functions/f18.py
index 03d6bd0a5..23b252d4d 100644
--- a/src/eko/matching_conditions/as3/f_functions/f18.py
+++ b/src/eko/matching_conditions/as3/f_functions/f18.py
@@ -9,7 +9,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F18(n, S1, S2, S3):
     """Implements eq 9.36 of :cite:`Blumlein:2009ta`"""
     return (
diff --git a/src/eko/matching_conditions/as3/f_functions/f19.py b/src/eko/matching_conditions/as3/f_functions/f19.py
index d2db32520..95f3e506d 100644
--- a/src/eko/matching_conditions/as3/f_functions/f19.py
+++ b/src/eko/matching_conditions/as3/f_functions/f19.py
@@ -8,7 +8,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F19(n, S1, S2, S3):
     """Mellin tranfrom of eq 9.3 of :cite:`Blumlein:2009ta`"""
     return (
diff --git a/src/eko/matching_conditions/as3/f_functions/f20.py b/src/eko/matching_conditions/as3/f_functions/f20.py
index e5b2d1def..53640efcb 100644
--- a/src/eko/matching_conditions/as3/f_functions/f20.py
+++ b/src/eko/matching_conditions/as3/f_functions/f20.py
@@ -8,7 +8,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F20(n, Sm1, Sm2, Sm3):
     """Mellin transform of eq 9.5 :cite:`Blumlein:2009ta`"""
     return 2.3148148148148148e-7 * (
diff --git a/src/eko/matching_conditions/as3/f_functions/f21.py b/src/eko/matching_conditions/as3/f_functions/f21.py
index 44e51c334..f46d4b539 100644
--- a/src/eko/matching_conditions/as3/f_functions/f21.py
+++ b/src/eko/matching_conditions/as3/f_functions/f21.py
@@ -8,7 +8,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F21(n, Sm1, Sm2, Sm3):
     """Mellin transform of eq 9.4 of :cite:`Blumlein:2009ta`"""
     return 2.3148148148148148e-7 * (
diff --git a/src/eko/matching_conditions/as3/f_functions/f9.py b/src/eko/matching_conditions/as3/f_functions/f9.py
index 475d0bcaa..ab9340a44 100644
--- a/src/eko/matching_conditions/as3/f_functions/f9.py
+++ b/src/eko/matching_conditions/as3/f_functions/f9.py
@@ -8,7 +8,7 @@
 import numpy as np
 
 
-@nb.njit("c16(c16,c16)", cache=True)
+@nb.njit(cache=True)
 def F9(n, S1):
     """Implements eq 9.19 of :cite:`Blumlein:2009ta`"""
     return (
diff --git a/src/eko/matching_conditions/as3/g_functions.py b/src/eko/matching_conditions/as3/g_functions.py
index 043d90bb0..aff3b8a9f 100644
--- a/src/eko/matching_conditions/as3/g_functions.py
+++ b/src/eko/matching_conditions/as3/g_functions.py
@@ -63,7 +63,7 @@
 p31 = np.array([205.0 / 144.0, -25.0 / 12.0, 23.0 / 24.0, -13.0 / 36.0, 1.0 / 16])
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g4(N):
     r"""
     Computes the Mellin transform of :math:`\text{Li}_2(-x)/(1+x)`.
@@ -90,7 +90,7 @@ def mellin_g4(N):
     return g4
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g5(N):
     r"""
     Computes the Mellin transform of :math:`(\text{Li}_2(x)ln(x))/(1+x)`.
@@ -119,7 +119,7 @@ def mellin_g5(N):
     return g5
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g6(N):
     r"""
     Computes the Mellin transform of :math:`\text{Li}_3(x)/(1+x)`.
@@ -146,7 +146,7 @@ def mellin_g6(N):
     return g6
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g8(N):
     r"""
     Computes the Mellin transform of :math:`S_{1,2}(x)/(1+x)`.
@@ -174,7 +174,7 @@ def mellin_g8(N):
     return g8
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g18(N, S1, S2):
     r"""
     Computes the Mellin transform of :math:`-(\text{Li}_2(x) - \zeta_2)/(1-x)`.
@@ -209,7 +209,7 @@ def mellin_g18(N, S1, S2):
     return g18
 
 
-@nb.njit("c16(c16,c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g19(N, S1):
     r"""
     Computes the Mellin transform of :math:`-(\text{Li}_2(-x) + \zeta_2/2)/(1-x)`.
@@ -236,7 +236,7 @@ def mellin_g19(N, S1):
     return g19
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g21(N, S1, S2, S3):
     r"""
     Computes the Mellin transform of :math:`-(S_{1,2}(x) - \zeta_3)/(1-x)`.
@@ -287,7 +287,7 @@ def mellin_g21(N, S1, S2, S3):
     return g21
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def mellin_g22(N):
     r"""
     Computes the Mellin transform of :math:`-(\text{Li}_2(x) ln(x))/(1-x)`.
diff --git a/src/eko/matching_conditions/as3/s_functions.py b/src/eko/matching_conditions/as3/s_functions.py
index 409333757..bf243742c 100644
--- a/src/eko/matching_conditions/as3/s_functions.py
+++ b/src/eko/matching_conditions/as3/s_functions.py
@@ -20,7 +20,7 @@
 log2 = np.log(2)
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm1(N):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-1}(N)`.
@@ -47,7 +47,7 @@ def harmonic_Sm1(N):
     ) - log2
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm2(N):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2}(N)`.
@@ -74,7 +74,7 @@ def harmonic_Sm2(N):
     ) - zeta2 / 2
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm3(N):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-3}(N)`.
@@ -101,7 +101,7 @@ def harmonic_Sm3(N):
     ) - 3 / 4 * zeta3
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm4(N):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-4}(N)`.
@@ -128,7 +128,7 @@ def harmonic_Sm4(N):
     ) - 7 / 8 * zeta4
 
 
-@nb.njit("c16(c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm5(N):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-5}(N)`.
@@ -155,7 +155,7 @@ def harmonic_Sm5(N):
     ) - 15 / 16 * zeta5
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S21(N, S1, S2):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,1}(N)`
@@ -182,7 +182,7 @@ def harmonic_S21(N, S1, S2):
     return -gf.mellin_g18(N, S1, S2) + 2 * zeta3
 
 
-@nb.njit("c16(c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm21(N, Sm1):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2,1}(N)`
@@ -213,7 +213,7 @@ def harmonic_Sm21(N, Sm1):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S2m1(N, S2, Sm1, Sm2):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,-1}(N)`
@@ -248,7 +248,7 @@ def harmonic_S2m1(N, S2, Sm1, Sm2):
     )
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm31(N, Sm1, Sm2):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-3,1}(N)`
@@ -284,7 +284,7 @@ def harmonic_Sm31(N, Sm1, Sm2):
     )
 
 
-@nb.njit("c16(c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm22(N, Sm31):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2,2}(N)`
@@ -313,7 +313,7 @@ def harmonic_Sm22(N, Sm31):
     )
 
 
-@nb.njit("c16(c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm211(N, Sm1):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2,1,1}(N)`
@@ -346,7 +346,7 @@ def harmonic_Sm211(N, Sm1):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm2m1(N, S1, S2, Sm2):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2,-1}(N)`
@@ -375,7 +375,7 @@ def harmonic_Sm2m1(N, S1, S2, Sm2):
     return -gf.mellin_g19(N, S1) + log2 * (S2 - Sm2) - 5 / 8 * zeta3
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S211(N, S1, S2, S3):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,1,1}(N)`
@@ -404,7 +404,7 @@ def harmonic_S211(N, S1, S2, S3):
     return -gf.mellin_g21(N, S1, S2, S3) + 6 / 5 * zeta2**2
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S31(N, S2, S4):
     r"""
     Analytic continuation of harmonic sum :math:`S_{3,1}(N)`
@@ -437,7 +437,7 @@ def harmonic_S31(N, S2, S4):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S41(N, S1, S2, S3):
     r"""
     Analytic continuation of harmonic sum :math:`S_{4,1}(N)`
@@ -467,7 +467,7 @@ def harmonic_S41(N, S1, S2, S3):
     return -f.F9(N, S1) + S1 * zeta4 - S2 * zeta3 + S3 * zeta2
 
 
-@nb.njit("c16(c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S311(N, S1, S2):
     r"""
     Analytic continuation of harmonic sum :math:`S_{3,1,1}(N)`
@@ -495,7 +495,7 @@ def harmonic_S311(N, S1, S2):
     return f.F11(N, S1, S2) + zeta3 * S2 - zeta4 / 4 * S1
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S221(N, S1, S2, S21):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,2,1}(N)`
@@ -532,7 +532,7 @@ def harmonic_S221(N, S1, S2, S21):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm221(N, S1, Sm1, S21, Sm21):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2,2,1}(N)`
@@ -570,7 +570,7 @@ def harmonic_Sm221(N, S1, Sm1, S21, Sm21):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16,c16,c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S21m2(N, S1, S2, Sm1, Sm2, Sm3, S21, Sm21, S2m1):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,1,-2}(N)`
@@ -618,7 +618,7 @@ def harmonic_S21m2(N, S1, S2, Sm1, Sm2, Sm3, S21, Sm21, S2m1):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S2111(N, S1, S2, S3):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,1,1,1}(N)`
@@ -648,7 +648,7 @@ def harmonic_S2111(N, S1, S2, S3):
     return -f.F17(N, S1, S2, S3) + zeta4 * S1
 
 
-@nb.njit("c16(c16,c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm2111(N, S1, S2, S3, Sm1):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2,1,1,1}(N)`
@@ -685,7 +685,7 @@ def harmonic_Sm2111(N, S1, S2, S3, Sm1):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S23(N, S1, S2, S3):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,3}(N)`
@@ -719,7 +719,7 @@ def harmonic_S23(N, S1, S2, S3):
     return f.F19(N, S1, S2, S3) + 3 * zeta4 * S1
 
 
-@nb.njit("c16(c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_Sm23(N, Sm1, Sm2, Sm3):
     r"""
     Analytic continuation of harmonic sum :math:`S_{-2,3}(N)`
@@ -759,7 +759,7 @@ def harmonic_Sm23(N, Sm1, Sm2, Sm3):
     )
 
 
-@nb.njit("c16(c16,c16,c16,c16,c16)", cache=True)
+@nb.njit(cache=True)
 def harmonic_S2m3(N, S2, Sm1, Sm2, Sm3):
     r"""
     Analytic continuation of harmonic sum :math:`S_{2,-3}(N)`
diff --git a/src/eko/matching_conditions/operator_matrix_element.py b/src/eko/matching_conditions/operator_matrix_element.py
index 22f217edb..2ec0fae4c 100644
--- a/src/eko/matching_conditions/operator_matrix_element.py
+++ b/src/eko/matching_conditions/operator_matrix_element.py
@@ -19,7 +19,7 @@
 logger = logging.getLogger(__name__)
 
 
-@nb.njit("c16[:](c16)", cache=True)
+@nb.njit(cache=True)
 def get_smx(n):
     """Get the S-minus cache"""
     return np.array(
@@ -33,7 +33,7 @@ def get_smx(n):
     )
 
 
-@nb.njit("c16[:](c16,c16[:],c16[:])", cache=True)
+@nb.njit(cache=True)
 def get_s3x(n, sx, smx):
     """Get the S-w3 cache"""
     return np.array(
@@ -46,7 +46,7 @@ def get_s3x(n, sx, smx):
     )
 
 
-@nb.njit("c16[:](c16,c16[:],c16[:])", cache=True)
+@nb.njit(cache=True)
 def get_s4x(n, sx, smx):
     """Get the S-w4 cache"""
     Sm31 = s_functions.harmonic_Sm31(n, smx[0], smx[1])
@@ -61,7 +61,7 @@ def get_s4x(n, sx, smx):
     )
 
 
-@nb.njit("c16[:,:,:](u1,c16,c16[:],u4,f8,b1)", cache=True)
+@nb.njit(cache=True)
 def A_singlet(order, n, sx, nf, L, is_msbar):
     r"""
     Computes the tower of the singlet |OME|.
@@ -105,7 +105,7 @@ def A_singlet(order, n, sx, nf, L, is_msbar):
     return A_s
 
 
-@nb.njit("c16[:,:,:](u1,c16,c16[:],u4,f8)", cache=True)
+@nb.njit(cache=True)
 def A_non_singlet(order, n, sx, nf, L):
     r"""
     Computes the tower of the non-singlet |OME|
@@ -145,7 +145,7 @@ def A_non_singlet(order, n, sx, nf, L):
     return A_ns
 
 
-@nb.njit("c16[:,:](c16[:,:,:],u4,f8,string)", cache=True)
+@nb.njit(cache=True)
 def build_ome(A, order, a_s, backward_method):
     r"""
     Construct the matching expansion in :math:`a_s` with the appropriate method.
@@ -197,7 +197,7 @@ def build_ome(A, order, a_s, backward_method):
     return ome
 
 
-@nb.njit("f8(f8,u1,u2,u2,b1,f8,f8[:,:],f8,u1,f8,string,b1)", cache=True)
+@nb.njit(cache=True)
 def quad_ker(
     u, order, mode0, mode1, is_log, logx, areas, a_s, nf, L, backward_method, is_msbar
 ):
diff --git a/src/eko/mellin.py b/src/eko/mellin.py
index 055276c0e..e0b9c637a 100644
--- a/src/eko/mellin.py
+++ b/src/eko/mellin.py
@@ -22,7 +22,7 @@
 import numpy as np
 
 
-@nb.njit("c16(f8,f8,f8)", cache=True)
+@nb.njit(cache=True)
 def Talbot_path(t, r, o):
     r"""
     Talbot path.
@@ -56,7 +56,7 @@ def Talbot_path(t, r, o):
     return o + r * complex(re, im)
 
 
-@nb.njit("c16(f8,f8,f8)", cache=True)
+@nb.njit(cache=True)
 def Talbot_jac(t, r, o):  # pylint: disable=unused-argument
     r"""
     Derivative of Talbot path.
@@ -90,7 +90,7 @@ def Talbot_jac(t, r, o):  # pylint: disable=unused-argument
     return r * np.pi * 2.0 * complex(re, im)
 
 
-@nb.njit("c16(f8,f8,f8)", cache=True)
+@nb.njit(cache=True)
 def line_path(t, m, c):
     r"""
     Textbook path, i.e. a straight line parallel to the imaginary axis.
@@ -115,7 +115,7 @@ def line_path(t, m, c):
     return complex(c, m * (2 * t - 1))
 
 
-@nb.njit("c16(f8,f8,f8)", cache=True)
+@nb.njit(cache=True)
 def line_jac(_t, m, _c):
     r"""
     Derivative of Textbook path.
@@ -140,7 +140,7 @@ def line_jac(_t, m, _c):
     return complex(0, m * 2)
 
 
-@nb.njit("c16(f8,f8,f8,f8)", cache=True)
+@nb.njit(cache=True)
 def edge_path(t, m, c, phi):
     r"""
     Edged path with a given angle.
@@ -169,7 +169,7 @@ def edge_path(t, m, c, phi):
     return c + (t - 0.5) * m * np.exp(complex(0, +phi))
 
 
-@nb.njit("c16(f8,f8,f8,f8)", cache=True)
+@nb.njit(cache=True)
 def edge_jac(t, m, _c, phi):
     r"""
     Derivative of edged path
diff --git a/src/eko/msbar_masses.py b/src/eko/msbar_masses.py
index 9b984704d..c793010c9 100644
--- a/src/eko/msbar_masses.py
+++ b/src/eko/msbar_masses.py
@@ -69,7 +69,7 @@ def integrand(a, b_vec, g_vec):
     return np.exp(val)
 
 
-@nb.njit("f8(f8,f8,u1,u1)", cache=True)
+@nb.njit(cache=True)
 def ker_expanded(a0, a1, order, nf):
     r"""
     Expanded |MSbar| |RGE| kernel
diff --git a/src/eko/scale_variations/expanded.py b/src/eko/scale_variations/expanded.py
index 610f2f225..a739df5c0 100644
--- a/src/eko/scale_variations/expanded.py
+++ b/src/eko/scale_variations/expanded.py
@@ -10,7 +10,7 @@
 from .. import beta
 
 
-@nb.njit(["c16(c16[:],f8)", "c16[:,:](c16[:,:,:],f8)"], cache=True)
+@nb.njit(cache=True)
 def gamma_1_variation(gamma, L):
     r"""
     Computes the |NLO| anomalous dimension variation.
@@ -30,7 +30,7 @@ def gamma_1_variation(gamma, L):
     return -L * gamma[0]
 
 
-@nb.njit(["c16(c16[:],f8,f8,c16)", "c16[:,:](c16[:,:,:],f8,f8,c16[:,:])"], cache=True)
+@nb.njit(cache=True)
 def gamma_2_variation(gamma, L, beta0, g0e2):
     r"""
     Computes the |NNLO| anomalous dimension variation.
@@ -54,13 +54,7 @@ def gamma_2_variation(gamma, L, beta0, g0e2):
     return -gamma[1] * L + 1 / 2 * (beta0 * gamma[0] + g0e2) * L**2
 
 
-@nb.njit(
-    [
-        "c16(c16[:],f8,f8,f8,c16,c16,c16)",
-        "c16[:,:](c16[:,:,:],f8,f8,f8,c16[:,:],c16[:,:],c16[:,:])",
-    ],
-    cache=True,
-)
+@nb.njit(cache=True)
 def gamma_3_variation(gamma, L, beta0, beta1, g0e2, g0e3, g1g0):
     r"""
     Computes the |N3LO| anomalous dimension variation.
@@ -94,7 +88,7 @@ def gamma_3_variation(gamma, L, beta0, beta1, g0e2, g0e3, g1g0):
     )
 
 
-@nb.njit("c16(c16[:],f8,u1,u1,f8)", cache=True)
+@nb.njit(cache=True)
 def non_singlet_variation(gamma, a_s, order, nf, L):
     """
     Scale Variation non singlet dispatcher
@@ -131,7 +125,7 @@ def non_singlet_variation(gamma, a_s, order, nf, L):
     return sv_ker
 
 
-@nb.njit("c16[:,:](c16[:,:,:],f8,u1,u1,f8)", cache=True)
+@nb.njit(cache=True)
 def singlet_variation(gamma, a_s, order, nf, L):
     """
     Scale Variation singlet dispatcher
diff --git a/src/eko/scale_variations/exponentiated.py b/src/eko/scale_variations/exponentiated.py
index d0657de12..77608bbda 100644
--- a/src/eko/scale_variations/exponentiated.py
+++ b/src/eko/scale_variations/exponentiated.py
@@ -7,7 +7,7 @@
 from .. import beta
 
 
-@nb.njit(["c16[:,:,:](c16[:,:,:],u1,u1,f8)", "c16[:](c16[:],u1,u1,f8)"], cache=True)
+@nb.njit(cache=True)
 def gamma_variation(gamma, order, nf, L):
     """
     Adjust the anomalous dimensions with the scale variations.
diff --git a/src/eko/strong_coupling.py b/src/eko/strong_coupling.py
index 1aa8c5a8d..29a56675d 100644
--- a/src/eko/strong_coupling.py
+++ b/src/eko/strong_coupling.py
@@ -36,7 +36,7 @@ def strong_coupling_mod_ev(mod_ev):
     raise ValueError(f"Unknown evolution mode {mod_ev}")
 
 
-@nb.njit("f8(u1,f8,u1,f8,f8)", cache=True)
+@nb.njit(cache=True)
 def as_expanded(order, as_ref, nf, scale_from, scale_to):
     """
     Compute expanded expression.

From e18e72bd70e72be7af7198c76a62847dcbed5753 Mon Sep 17 00:00:00 2001
From: giacomomagni <giac.magni@gmail.com>
Date: Mon, 28 Mar 2022 16:41:20 +0200
Subject: [PATCH 2/5] Adding n_core_parallel option

---
 src/eko/evolution_operator/__init__.py | 22 +++++++++++++++++-----
 src/eko/evolution_operator/grid.py     |  1 +
 src/ekomark/data/db.py                 |  1 +
 src/ekomark/data/operators.py          |  2 ++
 4 files changed, 21 insertions(+), 5 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 813d77fc2..205d84b7e 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -240,7 +240,6 @@ class Operator:
     """
 
     log_label = "Evolution"
-    n_pools = os.cpu_count()
     # complete list of possible evolution operators labels
     full_labels = br.full_labels
 
@@ -254,6 +253,13 @@ def __init__(self, config, managers, nf, q2_from, q2_to=None, mellin_cut=5e-2):
         self._mellin_cut = mellin_cut
         self.op_members = {}
 
+    @property
+    def n_pools(self):
+        n_pools = self.config["n_integration_cores"]
+        if n_pools > 0:
+            return n_pools
+        return os.cpu_count() + n_pools
+
     @property
     def fact_to_ren(self):
         r"""Returns the factor :math:`(\mu_F/\mu_R)^2`"""
@@ -264,8 +270,7 @@ def sv_mode(self):
         """Returns the scale variation mode"""
         if self.config["ModSV"] is not None:
             return sv.Modes[self.config["ModSV"]]
-        else:
-            return sv.Modes.unvaried
+        return sv.Modes.unvaried
 
     @property
     def int_disp(self):
@@ -466,11 +471,18 @@ def integrate(
         tot_start_time = time.perf_counter()
 
         # run integration in parallel for each grid point
-        with Pool(self.n_pools) as pool:
-            res = pool.map(
+        # or avoid opening a single pool
+        if self.n_pools == 1:
+            res = map(
                 self.run_op_integration,
                 enumerate(np.log(self.int_disp.xgrid_raw)),
             )
+        else:
+            with Pool(self.n_pools) as pool:
+                res = pool.map(
+                    self.run_op_integration,
+                    enumerate(np.log(self.int_disp.xgrid_raw)),
+                )
 
         # collect results
         for k, row in enumerate(res):
diff --git a/src/eko/evolution_operator/grid.py b/src/eko/evolution_operator/grid.py
index 50121673e..0a28802f7 100644
--- a/src/eko/evolution_operator/grid.py
+++ b/src/eko/evolution_operator/grid.py
@@ -126,6 +126,7 @@ def from_dict(
         config["ev_op_iterations"] = operators_card["ev_op_iterations"]
         config["debug_skip_singlet"] = operators_card["debug_skip_singlet"]
         config["debug_skip_non_singlet"] = operators_card["debug_skip_non_singlet"]
+        config["n_integration_cores"] = operators_card["n_integration_cores"]
         config["HQ"] = theory_card["HQ"]
         config["ModSV"] = theory_card["ModSV"]
         q2_grid = np.array(operators_card["Q2grid"], np.float_)
diff --git a/src/ekomark/data/db.py b/src/ekomark/data/db.py
index 02908c9a8..94252fac5 100644
--- a/src/ekomark/data/db.py
+++ b/src/ekomark/data/db.py
@@ -22,3 +22,4 @@ class Operator(Base):  # pylint: disable=too-few-public-methods
     ev_op_max_order = Column(Integer)
     ev_op_iterations = Column(Integer)
     Q2grid = Column(Text)
+    n_integration_cores = Column(Integer)
diff --git a/src/ekomark/data/operators.py b/src/ekomark/data/operators.py
index 12bd14309..84d3c3eff 100644
--- a/src/ekomark/data/operators.py
+++ b/src/ekomark/data/operators.py
@@ -2,6 +2,7 @@
 """
 Operator card configurations.
 """
+import os
 
 from banana.data import cartesian_product, sql
 
@@ -18,6 +19,7 @@
     ev_op_max_order=10,
     ev_op_iterations=10,
     backward_inversion="expanded",
+    n_integration_cores=os.cpu_count(),
     Q2grid=[100],
 )
 

From 80082693b85e4d6495d637a1f16dcd6768760a04 Mon Sep 17 00:00:00 2001
From: giacomomagni <giac.magni@gmail.com>
Date: Mon, 28 Mar 2022 16:42:08 +0200
Subject: [PATCH 3/5] remove parallel computation in tests

---
 tests/eko/test_ev_op_grid.py  |  1 +
 tests/eko/test_ev_operator.py | 31 +++++++++++++++++++++++++++++--
 tests/eko/test_ome.py         |  3 +++
 tests/eko/test_runner.py      |  1 +
 4 files changed, 34 insertions(+), 2 deletions(-)

diff --git a/tests/eko/test_ev_op_grid.py b/tests/eko/test_ev_op_grid.py
index 4354346a7..d505bb033 100644
--- a/tests/eko/test_ev_op_grid.py
+++ b/tests/eko/test_ev_op_grid.py
@@ -48,6 +48,7 @@ def _get_setup(self, use_FFNS):
             "ev_op_max_order": 1,
             "ev_op_iterations": 1,
             "backward_inversion": "exact",
+            "n_integration_cores": 1,
         }
         if use_FFNS:
             theory_card["FNS"] = "FFNS"
diff --git a/tests/eko/test_ev_operator.py b/tests/eko/test_ev_operator.py
index 7e806b73a..ba7cfc807 100644
--- a/tests/eko/test_ev_operator.py
+++ b/tests/eko/test_ev_operator.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+import os
 
 import numpy as np
 import scipy.integrate
@@ -126,7 +127,12 @@ def test_quad_ker(monkeypatch):
 class TestOperator:
     def test_labels(self):
         o = Operator(
-            dict(order=2, debug_skip_non_singlet=False, debug_skip_singlet=False),
+            dict(
+                order=2,
+                debug_skip_non_singlet=False,
+                debug_skip_singlet=False,
+                n_integration_cores=1,
+            ),
             {},
             3,
             1,
@@ -134,7 +140,12 @@ def test_labels(self):
         )
         assert sorted(o.labels) == sorted(br.full_labels)
         o = Operator(
-            dict(order=1, debug_skip_non_singlet=True, debug_skip_singlet=True),
+            dict(
+                order=1,
+                debug_skip_non_singlet=True,
+                debug_skip_singlet=True,
+                n_integration_cores=1,
+            ),
             {},
             3,
             1,
@@ -142,6 +153,21 @@ def test_labels(self):
         )
         assert sorted(o.labels) == []
 
+    def test_n_pools(self):
+        excluded_cores = 3
+        o = Operator(
+            dict(
+                order=1,
+                debug_skip_non_singlet=True,
+                debug_skip_singlet=True,
+                n_integration_cores=-excluded_cores,
+            ),
+            {},
+            3,
+            1,
+        )
+        assert o.n_pools == os.cpu_count() - excluded_cores
+
     def test_compute(self, monkeypatch):
         # setup objs
         theory_card = {
@@ -178,6 +204,7 @@ def test_compute(self, monkeypatch):
             "ev_op_max_order": 1,
             "ev_op_iterations": 1,
             "backward_inversion": "exact",
+            "n_integration_cores": 1,
         }
         g = OperatorGrid.from_dict(
             theory_card,
diff --git a/tests/eko/test_ome.py b/tests/eko/test_ome.py
index 40f32b119..dc14e08e0 100644
--- a/tests/eko/test_ome.py
+++ b/tests/eko/test_ome.py
@@ -369,6 +369,7 @@ class TestOperatorMatrixElement:
         "ev_op_max_order": 1,
         "ev_op_iterations": 1,
         "backward_inversion": "exact",
+        "n_integration_cores": 1,
     }
 
     def test_labels(self):
@@ -384,6 +385,7 @@ def test_labels(self):
                     "ev_op_max_order": 1,
                     "ev_op_iterations": 1,
                     "backward_inversion": "exact",
+                    "n_integration_cores": 1,
                 }
                 g = OperatorGrid.from_dict(
                     self.theory_card,
@@ -516,6 +518,7 @@ def test_compute_nlo(self):
             "ev_op_max_order": 1,
             "ev_op_iterations": 1,
             "backward_inversion": "exact",
+            "n_integration_cores": 1,
         }
         t = copy.deepcopy(self.theory_card)
         t["PTO"] = 1
diff --git a/tests/eko/test_runner.py b/tests/eko/test_runner.py
index e74cae619..75a871095 100644
--- a/tests/eko/test_runner.py
+++ b/tests/eko/test_runner.py
@@ -42,6 +42,7 @@
     "ev_op_max_order": 1,
     "ev_op_iterations": 1,
     "backward_inversion": "exact",
+    "n_integration_cores": 1,
 }
 
 

From 598613494150dcb778858f3e0dd7028e17abf2c9 Mon Sep 17 00:00:00 2001
From: giacomomagni <giac.magni@gmail.com>
Date: Mon, 28 Mar 2022 17:07:36 +0200
Subject: [PATCH 4/5] restore benchmarks

---
 benchmarks/eko/benchmark_evol_to_unity.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/benchmarks/eko/benchmark_evol_to_unity.py b/benchmarks/eko/benchmark_evol_to_unity.py
index 047ef9148..376c76c18 100644
--- a/benchmarks/eko/benchmark_evol_to_unity.py
+++ b/benchmarks/eko/benchmark_evol_to_unity.py
@@ -49,6 +49,7 @@ class BenchmarkBackwardForward:
         "ev_op_max_order": 1,
         "ev_op_iterations": 1,
         "backward_inversion": "exact",
+        "n_integration_cores": 1,
     }
     g = OperatorGrid.from_dict(
         theory_card,

From d5f8bba887ade989eca7a6cc879541c4db3c32ce Mon Sep 17 00:00:00 2001
From: giacomomagni <giac.magni@gmail.com>
Date: Tue, 29 Mar 2022 14:56:22 +0200
Subject: [PATCH 5/5] minor fixes on data db

---
 src/eko/evolution_operator/__init__.py | 11 +++--------
 src/ekomark/data/db.py                 |  2 +-
 src/ekomark/data/operators.py          |  4 +---
 3 files changed, 5 insertions(+), 12 deletions(-)

diff --git a/src/eko/evolution_operator/__init__.py b/src/eko/evolution_operator/__init__.py
index 205d84b7e..0fadfbedc 100644
--- a/src/eko/evolution_operator/__init__.py
+++ b/src/eko/evolution_operator/__init__.py
@@ -472,17 +472,12 @@ def integrate(
 
         # run integration in parallel for each grid point
         # or avoid opening a single pool
+        args = (self.run_op_integration, enumerate(np.log(self.int_disp.xgrid_raw)))
         if self.n_pools == 1:
-            res = map(
-                self.run_op_integration,
-                enumerate(np.log(self.int_disp.xgrid_raw)),
-            )
+            res = map(*args)
         else:
             with Pool(self.n_pools) as pool:
-                res = pool.map(
-                    self.run_op_integration,
-                    enumerate(np.log(self.int_disp.xgrid_raw)),
-                )
+                res = pool.map(*args)
 
         # collect results
         for k, row in enumerate(res):
diff --git a/src/ekomark/data/db.py b/src/ekomark/data/db.py
index 94252fac5..67328c522 100644
--- a/src/ekomark/data/db.py
+++ b/src/ekomark/data/db.py
@@ -22,4 +22,4 @@ class Operator(Base):  # pylint: disable=too-few-public-methods
     ev_op_max_order = Column(Integer)
     ev_op_iterations = Column(Integer)
     Q2grid = Column(Text)
-    n_integration_cores = Column(Integer)
+    backward_inversion = Column(Text)
diff --git a/src/ekomark/data/operators.py b/src/ekomark/data/operators.py
index 84d3c3eff..1a532e5e5 100644
--- a/src/ekomark/data/operators.py
+++ b/src/ekomark/data/operators.py
@@ -2,8 +2,6 @@
 """
 Operator card configurations.
 """
-import os
-
 from banana.data import cartesian_product, sql
 
 from eko import interpolation
@@ -19,7 +17,7 @@
     ev_op_max_order=10,
     ev_op_iterations=10,
     backward_inversion="expanded",
-    n_integration_cores=os.cpu_count(),
+    n_integration_cores=0,
     Q2grid=[100],
 )