Add python-gmp as optional backend (gmpy2 alternative)

Closes #895

.github/workflows/coverage.yml

@@ -17,7 +17,7 @@ jobs:
       - name: Install dependencies
         run: |
           pip install --upgrade setuptools pip
-          pip install --upgrade .[develop,gmpy2,ci]
+          pip install --upgrade .[develop,gmpy2,gmp,ci]
       - name: Run coverage tests
         run: |
           pytest
@@ -27,6 +27,10 @@ jobs:
           pytest mpmath/tests/test_basic_ops.py mpmath/tests/test_convert.py \
             mpmath/tests/test_functions.py mpmath/tests/test_gammazeta.py \
             mpmath/tests/test_bitwise.py
+          pip uninstall -y python-gmp
+          pytest mpmath/tests/test_basic_ops.py mpmath/tests/test_convert.py \
+            mpmath/tests/test_functions.py mpmath/tests/test_gammazeta.py \
+            mpmath/tests/test_bitwise.py
       - name: Generate coverage reports
         run: |
           coverage xml

.github/workflows/test.yml

@@ -16,6 +16,10 @@ jobs:
       fail-fast: false
       matrix:
         python-version: [3.9, '3.10', 3.11, 3.12, 3.13, 3.14, 'pypy3.10', pypy3.11]
+        nogmpy: [false]
+        include:
+          - python-version: 3.13
+            nogmpy: true
     env:
       PYTEST_ADDOPTS: -n auto
     steps:
@@ -33,5 +37,7 @@ jobs:
     - name: Install dependencies
       run: |
         pip install --upgrade setuptools pip
-        pip install --upgrade .[develop,gmpy2,ci]
+        pip install --upgrade .[develop,gmpy2,gmp,ci]
+    - run: pip uninstall -y gmpy2
+      if: matrix.nogmpy
     - run: pytest

mpmath/libmp/backend.py

@@ -27,7 +27,11 @@ if 'MPMATH_NOGMPY' not in os.environ:
         import gmpy2 as gmpy
         BACKEND = 'gmpy'
     except ImportError:
-        pass
+        try:
+            import gmp as gmpy
+            BACKEND = 'gmp'
+        except ImportError:
+            pass
 
     if gmpy:
         MPZ = gmpy.mpz

pyproject.toml

@@ -37,6 +37,7 @@ develop = ['mpmath[tests]', 'flake518>=1.5; python_version>="3.9"',
            'pytest-cov', 'wheel', 'build']
 gmpy2 = ['gmpy2>=2.2; platform_python_implementation!="PyPy"']
 gmpy = ['mpmath[gmpy2]']
+gmp = ['python-gmp>=0.4.0a1']
 docs = ['sphinx',
         'matplotlib; platform_python_implementation!="PyPy" and python_version<"3.14"',
         'sphinxcontrib-autoprogram']