Limit the amount of entropy we use for generating float16 numbers to avoid oversampling 0.0.

theano/sandbox/rng_mrg.py

@@ -788,15 +788,20 @@ class GPUA_mrg_uniform(GpuKernelBase, mrg_uniform_base):
         write = write_w(self.output_type.dtype)
         if self.output_type.dtype == 'float16':
             otype = 'ga_half'
-            # Same as for float32
-            NORM = '4.6566126e-10f'  # numpy.float32(1.0/(2**31+65))
+            # limit the values of the state that we use.
+            mask = '& 0xffff'
+            NORM = '1.5199e-05f'  # numpy.float16(1.0/(2**16+130))
+            # this was determined by finding the biggest number such that
+            # numpy.float16(number * (M1 & 0xffff)) < 1.0
         elif self.output_type.dtype == 'float32':
             otype = 'float'
+            mask = ''
             NORM = '4.6566126e-10f'  # numpy.float32(1.0/(2**31+65))
             # this was determined by finding the biggest number such that
             # numpy.float32(number * M1) < 1.0
         elif self.output_type.dtype == 'float64':
             otype = 'double'
+            mask = ''
             NORM = '4.656612873077392578125e-10'
         else:
             raise ValueError('Unsupported data type for output',
@@ -863,11 +868,11 @@ class GPUA_mrg_uniform(GpuKernelBase, mrg_uniform_base):
                 x21 = y2;
 
                 if (x11 <= x21) {
-                    sample_data[i] = %(write)s((x11 - x21 + M1) * %(NORM)s);
+                    sample_data[i] = %(write)s(((x11 - x21 + M1) %(mask)s) * %(NORM)s);
                 }
                 else
                 {
-                    sample_data[i] = %(write)s((x11 - x21) * %(NORM)s);
+                    sample_data[i] = %(write)s(((x11 - x21) %(mask)s) * %(NORM)s);
                 }
             }
 
@@ -1001,7 +1006,7 @@ class GPUA_mrg_uniform(GpuKernelBase, mrg_uniform_base):
         """ % locals()
 
     def c_code_cache_version(self):
-        return (5, self.GpuKernelBase_version)
+        return (6, self.GpuKernelBase_version)
 
 
 def guess_n_streams(size, warn=False):