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backend.py

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+import os
+import sys
+
+#----------------------------------------------------------------------------#
+# Support GMPY for high-speed large integer arithmetic.                      #
+#                                                                            #
+# To allow an external module to handle arithmetic, we need to make sure     #
+# that all high-precision variables are declared of the correct type. MPZ    #
+# is the constructor for the high-precision type. It defaults to Python's    #
+# long type but can be assinged another type, typically gmpy.mpz.            #
+#                                                                            #
+# MPZ must be used for the mantissa component of an mpf and must be used     #
+# for internal fixed-point operations.                                       #
+#                                                                            #
+# Side-effects                                                               #
+# 1) "is" cannot be used to test for special values. Must use "==".          #
+# 2) There are bugs in GMPY prior to v1.02 so we must use v1.03 or later.    #
+#----------------------------------------------------------------------------#
+
+# So we can import it from this module
+gmpy = None
+sage = None
+sage_utils = None
+
+if sys.version_info[0] < 3:
+    python3 = False
+else:
+    python3 = True
+
+BACKEND = 'python'
+
+if not python3:
+    MPZ = long
+    xrange = xrange
+    basestring = basestring
+
+    def exec_(_code_, _globs_=None, _locs_=None):
+        """Execute code in a namespace."""
+        if _globs_ is None:
+            frame = sys._getframe(1)
+            _globs_ = frame.f_globals
+            if _locs_ is None:
+                _locs_ = frame.f_locals
+            del frame
+        elif _locs_ is None:
+            _locs_ = _globs_
+        exec("""exec _code_ in _globs_, _locs_""")
+else:
+    MPZ = int
+    xrange = range
+    basestring = str
+
+    import builtins
+    exec_ = getattr(builtins, "exec")
+
+# Define constants for calculating hash on Python 3.2.
+if sys.version_info >= (3, 2):
+    HASH_MODULUS = sys.hash_info.modulus
+    if sys.hash_info.width == 32:
+        HASH_BITS = 31
+    else:
+        HASH_BITS = 61
+else:
+    HASH_MODULUS = None
+    HASH_BITS = None
+
+if 'MPMATH_NOGMPY' not in os.environ:
+    try:
+        try:
+            import gmpy2 as gmpy
+        except ImportError:
+            try:
+                import gmpy
+            except ImportError:
+                raise ImportError
+        if gmpy.version() >= '1.03':
+            BACKEND = 'gmpy'
+            MPZ = gmpy.mpz
+    except:
+        pass
+
+if ('MPMATH_NOSAGE' not in os.environ and 'SAGE_ROOT' in os.environ or
+        'MPMATH_SAGE' in os.environ):
+    try:
+        import sage.all
+        import sage.libs.mpmath.utils as _sage_utils
+        sage = sage.all
+        sage_utils = _sage_utils
+        BACKEND = 'sage'
+        MPZ = sage.Integer
+    except:
+        pass
+
+if 'MPMATH_STRICT' in os.environ:
+    STRICT = True
+else:
+    STRICT = False
+
+MPZ_TYPE = type(MPZ(0))
+MPZ_ZERO = MPZ(0)
+MPZ_ONE = MPZ(1)
+MPZ_TWO = MPZ(2)
+MPZ_THREE = MPZ(3)
+MPZ_FIVE = MPZ(5)
+
+try:
+    if BACKEND == 'python':
+        int_types = (int, long)
+    else:
+        int_types = (int, long, MPZ_TYPE)
+except NameError:
+    if BACKEND == 'python':
+        int_types = (int,)
+    else:
+        int_types = (int, MPZ_TYPE)