mcs: Add reciprocal.py

Used for calculating constants for reciprocal division.

tools/reciprocal.py

@@ -0,0 +1,65 @@
+#!/usr/bin/env python3
+#
+# Copyright 2019, Data61
+# Commonwealth Scientific and Industrial Research Organisation (CSIRO)
+# ABN 41 687 119 230.
+#
+# This software may be distributed and modified according to the terms of
+# the GNU General Public License version 2. Note that NO WARRANTY is provided.
+# See "LICENSE_GPLv2.txt" for details.
+#
+# @TAG(DATA61_GPL)
+#
+
+# this script can be used to calculate the reciprocal for
+# unsigned division of an unknown 64 bit value by a known 64bit
+# constant. It is used to calculate the correct magic numbers
+# for fixed cpu times on arm in order to do 64 bit division to calculate
+# ticks -> microseconds.
+
+# for details on how this script works,
+# see Hacker's delight, Chapter 10, unsigned division.
+from math import floor, ceil
+import argparse
+import sys
+from past.builtins import xrange
+
+# now unsigned
+
+
+def magicgu(nmax, d):
+    nc = ((nmax + 1)//d)*d - 1
+    nbits = len(bin(nmax)) - 2
+    for p in range(0, 2*nbits + 1):
+        if 2**p > nc*(d - 1 - (2**p - 1) % d):
+            m = (2**p + d - 1 - (2**p - 1) % d)//d
+            return (m, p)
+    print("Can't find p, something is wrong.")
+    sys.exit(1)
+
+
+def do_div(n):
+    return ((n + add_ind) * magic) >> shift_amt
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(
+        description="Generate magic numbers for emulating 64-bit division with multiplication by reciprocal using algorithm from Hacker's Delight, chapter 10.")
+    parser.add_argument("--divisor", type=int, required=True,
+                        help="Devisor to calculate magic numbers for")
+    args = parser.parse_args()
+
+    magic, shift_amt = magicgu(2**32 - 1, args.divisor)
+    print("magic number is: %d, shift amount is %d" % (magic, shift_amt))
+    add_ind = 0
+
+    print("Doing sanity check")
+    # sanity check
+    for i in xrange(2**32-1):
+        q1, q2 = (i / args.divisor, do_div(i))
+        if int(q1) != q2:
+            print("Combination failed %d %d %d" % i, q1, q2)
+            sys.exit(-1)
+
+    print("Success! Use (n * %d) >> %d to calculate n / %d" % (magic, shift_amt, args.divisor))
+    print("magic number is: %d, shift amount is %d" % (magic, shift_amt))