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e9b9f821b6
- add type annotations for pylance/strict - replace xrange by range for python3 - point out that you need 128-bit intermediate for 64-bit division by multiplication There should be no behaviour change. Signed-off-by: Gerwin Klein <gerwin.klein@proofcraft.systems>
63 lines
2.0 KiB
Python
Executable File
63 lines
2.0 KiB
Python
Executable File
#!/usr/bin/env python3
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#
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# Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
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#
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# SPDX-License-Identifier: GPL-2.0-only
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#
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# this script can be used to calculate the reciprocal for
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# unsigned division of an unknown 64 bit value by a known 64bit
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# constant. It is used to calculate the correct magic numbers
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# for fixed cpu times on arm in order to do 64 bit division to calculate
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# ticks -> microseconds.
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# for details on how this script works,
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# see Hacker's delight, Chapter 10, unsigned division.
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# Note that you need an intermediate value that is 128 bits wide for the
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# multiplication if want to guarantee absence of overflow when you have a 64 bit
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# divisor.
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from __future__ import annotations
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import argparse
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import sys
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def magicgu(nmax: int, d: int) -> tuple[int, int]:
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nc = ((nmax + 1)//d)*d - 1
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nbits = len(bin(nmax)) - 2
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for p in range(0, 2*nbits + 1):
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if 2**p > nc*(d - 1 - (2**p - 1) % d):
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m = (2**p + d - 1 - (2**p - 1) % d)//d
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return (m, p)
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print("Can't find p, something is wrong.")
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sys.exit(1)
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def do_div(n: int) -> int:
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return ((n + add_ind) * magic) >> shift_amt
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if __name__ == "__main__":
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parser = argparse.ArgumentParser(
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description="Generate magic numbers for emulating 64-bit division with multiplication by reciprocal using algorithm from Hacker's Delight, chapter 10.")
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parser.add_argument("--divisor", type=int, required=True,
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help="Devisor to calculate magic numbers for")
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args = parser.parse_args()
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magic, shift_amt = magicgu(2**32 - 1, args.divisor)
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print("magic number is: %d, shift amount is %d" % (magic, shift_amt))
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add_ind = 0
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print("Doing sanity check")
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# sanity check
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for i in range(2**32-1):
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q1, q2 = (i / args.divisor, do_div(i))
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if int(q1) != q2:
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print("Combination failed %d %d %d" % i, q1, q2)
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sys.exit(-1)
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print("Success! Use (n * %d) >> %d to calculate n / %d" % (magic, shift_amt, args.divisor))
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print("magic number is: %d, shift amount is %d" % (magic, shift_amt))
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