Set dynamic maxsteps value for the bisect method

Closes #285
Closes #339

mpmath/calculus/optimization.py

@@ -306,8 +306,8 @@ class Bisection:
         if len(x0) != 2:
             raise ValueError('expected interval of 2 points, got %i' % len(x0))
         self.f = f
-        self.a = x0[0]
-        self.b = x0[1]
+        self.a, self.b = x0
+        self.maxsteps = 2*ctx.prec + ctx.ceil(ctx.log2(abs(self.a - self.b)))
 
     def __iter__(self):
         ctx = self.ctx

mpmath/tests/test_rootfinding.py

@@ -53,6 +53,21 @@ def test_bisection():
     with pytest.raises(ValueError):
         findroot(lambda x: x**2-1, (4, 2), solver='bisect') == 1
 
+    # issue 285
+    mp.dps = 240
+    sol = -mp.ceil(mp.log(abs(findroot(lambda x: mp.sign(x - 3), (1, 4),
+                                       solver='bisect', verify=False,
+                                       tol=1e-200) - 3))/mp.log(10))
+    assert sol.ae(200)
+
+    # issue 339
+    mp.dps = 15
+    res = mpf('0.73908513321516064')
+    for dps in [100, 200, 300, 1000]:
+        with mp.workdps(dps):
+            sol = findroot(lambda x: cos(x) - x, [0, 1], solver='bisect')
+        assert (+sol).ae(res)
+
 def test_mnewton():
     f = lambda x: polyval([1, 3, 3, 1], x)
     x = findroot(f, -0.9, solver='mnewton')