Try wrapping in a summator.

libraries/base/common/python/try_wrap.py

+#! /usr/bin/env python3
+###############################################################################
+#
+# Copyright 2022
+# ASTRON (Netherlands Institute for Radio Astronomy) <http://www.astron.nl/>
+# P.O.Box 2, 7990 AA Dwingeloo, The Netherlands
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+###############################################################################
+
+# Author: Eric Kooistra
+# Date: jan 2023
+# Purpose:
+#   Try wrapping in a summator
+# Description:
+#   Usage:
+#   > python3 try_wrap.py -N 10
+#
+
+import argparse
+import textwrap
+
+import numpy as np
+import matplotlib
+matplotlib.use('tkagg')  # to make X11 forwarding work
+import matplotlib.pyplot as plt
+
+import random
+
+import common as cm
+
+# Parse arguments to derive user parameters
+_parser = argparse.ArgumentParser(
+    description="".join(textwrap.dedent("""\
+        The int_wrap function keeps w LSbits and remove MSbits from an integer,
+        so that the result is in range range -2**(w-1) to + 2**(w-1)-1. This
+        try_wrap.py show that wrap(sum) = wrap(sum(wrap)), so intermediate
+        wrapping in a summator does not change the final sum.
+
+        The wrap function is distributive, similar to modulo [1]:
+
+            (a + b) mod n = [(a mod n) + (b mod n)] mod n
+                 ab mod n = [(a mod n)(b mod n)] mod n
+
+        > python try_wrap.py -N 10 --w_inp 10 --w_sum 4
+
+        References:
+        [1] https://en.wikipedia.org/wiki/Modulo_operation
+        \n""")),
+    formatter_class=argparse.RawTextHelpFormatter)
+_parser.add_argument('-N', default=1000, type=int, help='Number of input samples')
+_parser.add_argument('--w_inp', default=10, type=int, help='Number bits of input samples')
+_parser.add_argument('--w_sum', default=4, type=int, help='Number bits of output sum')
+args = _parser.parse_args()
+
+N_samples = args.N
+W_input = args.w_inp
+W_sum = args.w_sum
+
+lo = -1 * 2**(W_input - 1)
+hi = 2**(W_input - 1) - 1
+x = [random.randint(lo, hi) for i in range(N_samples)]
+x_wrap = [cm.int_wrap(i, W_sum) for i in x]
+x_wrap_sum_wrap = cm.int_wrap(cm.add_list_elements(x_wrap), W_sum)
+x_wrap_sum      = cm.int_wrap(cm.add_list_elements(x), W_sum)
+
+print(x)
+print()
+print(x_wrap)
+print()
+
+if x_wrap_sum_wrap == x_wrap_sum:
+    print('OK')
+else:
+    print('Error:')
+    print(x_wrap_sum_wrap)
+    print(x_wrap_sum)
+