diff -r c61d2c43d22e Lib/_pydecimal.py
--- a/Lib/_pydecimal.py	Sun May 08 14:02:35 2016 +0000
+++ b/Lib/_pydecimal.py	Sun May 08 18:42:58 2016 +0300
@@ -743,7 +743,7 @@ class Decimal(object):
             sign = 0
         else:
             sign = 1
-        n, d = abs(f).as_integer_ratio()
+        n, d = abs(float(f)).as_integer_ratio()
         k = d.bit_length() - 1
         result = _dec_from_triple(sign, str(n*5**k), -k)
         if cls is Decimal:
diff -r c61d2c43d22e Lib/test/test_decimal.py
--- a/Lib/test/test_decimal.py	Sun May 08 14:02:35 2016 +0000
+++ b/Lib/test/test_decimal.py	Sun May 08 18:42:58 2016 +0300
@@ -2548,6 +2548,16 @@ class PythonAPItests(unittest.TestCase):
             x = random.expovariate(0.01) * (random.random() * 2.0 - 1.0)
             self.assertEqual(x, float(MyDecimal.from_float(x))) # roundtrip
 
+        # Issue #26974: Crash when as_integer_ratio() returns insane value.
+        class BadFloat(float):
+            def as_integer_ratio(self):
+                raise AssertionError
+        self.assertEqual(Decimal.from_float(BadFloat(1.25)), Decimal('1.25'))
+        class BadFloat(float):
+            def __abs__(self):
+                raise AssertionError
+        self.assertEqual(Decimal.from_float(BadFloat(1.25)), Decimal('1.25'))
+
     def test_create_decimal_from_float(self):
         Decimal = self.decimal.Decimal
         Context = self.decimal.Context
diff -r c61d2c43d22e Modules/_decimal/_decimal.c
--- a/Modules/_decimal/_decimal.c	Sun May 08 14:02:35 2016 +0000
+++ b/Modules/_decimal/_decimal.c	Sun May 08 18:42:58 2016 +0300
@@ -2213,7 +2213,7 @@ static PyObject *
 PyDecType_FromFloatExact(PyTypeObject *type, PyObject *v,
                          PyObject *context)
 {
-    PyObject *dec, *tmp;
+    PyObject *dec, *tmp = NULL;
     PyObject *n, *d, *n_d;
     mpd_ssize_t k;
     double x;
@@ -2256,18 +2256,22 @@ PyDecType_FromFloatExact(PyTypeObject *t
         return dec;
     }
 
-    /* absolute value of the float */
-    tmp = PyObject_CallMethod(v, "__abs__", NULL);
-    if (tmp == NULL) {
-        return NULL;
+    /* absolute value of the float as exact float */
+    if (!PyFloat_CheckExact(v) || x < 0) {
+        tmp = v = PyFloat_FromDouble(x < 0 ? -x : x);
+        if (tmp == NULL) {
+            return NULL;
+        }
     }
 
     /* float as integer ratio: numerator/denominator */
-    n_d = PyObject_CallMethod(tmp, "as_integer_ratio", NULL);
-    Py_DECREF(tmp);
+    n_d = PyObject_CallMethod(v, "as_integer_ratio", NULL);
+    Py_XDECREF(tmp);
     if (n_d == NULL) {
         return NULL;
     }
+    assert(PyTuple_Check(n_d));
+    assert(PyTuple_GET_SIZE(n_d) == 2);
     n = PyTuple_GET_ITEM(n_d, 0);
     d = PyTuple_GET_ITEM(n_d, 1);