Add PrecisionManager to flint context

This allows temporarily changing the working precision using python
context managers.

Related: #5

Author: Tom-Hubrecht

doc/source/general.rst

@@ -55,6 +55,28 @@ The special method ``ctx.cleanup()`` frees up internal caches
 used by MPFR, FLINT and Arb. The user does normally not have to
 worry about this.
 
+The context object ``flint.ctx`` can be controlled locally to increase the
+working precision using python context managers::
+
+    >>> arb(2).sqrt()
+    [1.41421356237309 +/- 5.15e-15]
+    >>> with ctx.extraprec(15):
+    ...     arb(2).sqrt()
+    ...
+    [1.414213562373095049 +/- 2.10e-19]
+
+In the same manner, it is possible to exactly set the working precision,
+or to update it in terms of digits::
+
+    >>> with ctx.extradps(15):
+    ...     arb(2).sqrt()
+    ...
+    [1.41421356237309504880168872421 +/- 6.27e-31]
+    >>> with ctx.workprec(15):
+    ...     arb(2).sqrt()
+    ...
+    [1.414 +/- 2.46e-4]
+
 Types and methods
 -----------------
 

src/flint/flint_base/flint_context.pyx

@@ -57,6 +57,18 @@ cdef class FlintContext:
         assert num >= 1 and num <= 64
         flint_set_num_threads(num)
 
+    def extraprec(self, n):
+        return self.workprec(n + self.prec)
+
+    def extradps(self, n):
+        return self.workdps(n + self.dps)
+
+    def workprec(self, n):
+        return PrecisionManager(self, eprec=n)
+
+    def workdps(self, n):
+        return PrecisionManager(self, edps=n)
+
     def __repr__(self):
         return "pretty = %-8s  # pretty-print repr() output\n" \
                "unicode = %-8s # use unicode characters in output\n" \
@@ -69,4 +81,28 @@ cdef class FlintContext:
     def cleanup(self):
         flint_cleanup()
 
+
+class PrecisionManager:
+    def __init__(self, ctx, eprec=None, edps=None):
+        if eprec is not None and edps is not None:
+            raise ValueError("two different precisions requested")
+
+        self.ctx = ctx
+
+        self.eprec = eprec
+        self.edps = edps
+
+    def __enter__(self):
+        self._oldprec = self.ctx.prec
+
+        if self.eprec is not None:
+            self.ctx.prec = self.eprec
+
+        if self.edps is not None:
+            self.ctx.dps = self.edps
+
+    def __exit__(self, type, value, traceback):
+        self.ctx.prec = self._oldprec
+
+
 cdef FlintContext thectx = FlintContext()