Merge pull request #130 from malb/TUniform

Add TUniform distribution

estimator/nd.py

@@ -401,6 +401,58 @@ def UniformMod(q, n=None):
     return Uniform(a, b, n=n)
 
 
+class TUniform(NoiseDistribution):
+    """
+    TUniform distribution ∈ ``ZZ ∩ [-2**b, 2**b]``, endpoints inclusive.
+    This distribution samples the two end-points with probability 1/2**(b+2) and the
+    intermediate points with probability 1/2**(b+1).
+
+    As an example, with b=0 this distribution samples ±1 each with probability 1/4 and
+    0 with probability 1/2.
+
+    EXAMPLE::
+
+        >>> from estimator import *
+        >>> ND.TUniform(0)
+        D(σ=0.71)
+        >>> ND.TUniform(10)
+        D(σ=591.21)
+    """
+    def __init__(self, b, n=None):
+        b = int(ceil(b))
+
+        super().__init__(
+            n=n,
+            mean=RR(0),
+            stddev=RR(sqrt((2**(2*b+1) + 1)/6)),
+            bounds=(-2**b, 2**b),
+            _density=(1 - 1 / 2**(b+1)),
+        )
+
+    def __hash__(self):
+        """
+        EXAMPLE::
+
+            >>> from estimator import *
+            >>> hash(ND.TUniform(2)) == hash(("TUniform", (-4, 4), None))
+            True
+        """
+        return hash(("TUniform", self.bounds, self.n))
+
+    def support_size(self, fraction=1.0):
+        """
+        Compute the size of the support covering the probability given as fraction.
+
+        EXAMPLE::
+
+            >>> from estimator import *
+            >>> ND.TUniform(0, 64).support_size(0.99)
+            3399346982089587232319333203968
+        """
+        a, b = self.bounds
+        return ceil(RR(fraction) * (b - a + 1)**len(self))
+
+
 class SparseTernary(NoiseDistribution):
     """
     Distribution of vectors of length ``n`` with ``p`` entries of 1 and ``m`` entries of -1, rest 0.