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Path: utzoo!watmath!kpmartin
From: kpmartin@watmath.UUCP (Kevin Martin)
Newsgroups: net.lang.c
Subject: Non-zero lower bounds
Message-ID: <8769@watmath.UUCP>
Date: Sun, 26-Aug-84 15:03:11 EDT
Article-I.D.: watmath.8769
Posted: Sun Aug 26 15:03:11 1984
Date-Received: Mon, 27-Aug-84 00:29:55 EDT
References: <8131@umcp-cs.UUCP>
Reply-To: kpmartin@watmath.UUCP (Kevin Martin)
Organization: U of Waterloo, Ontario
Lines: 17


With non-zero lower bounds, but no bounds checking, there is no need for
subtracting each lower subscript bound from the corresponding subscript.
Since the lower bounds and multipliers are constants, all the constant
terms can be pulled out, to form one constant, e.g. for a zero-origin
10 by 20 by 30 array,
  z_offset(i, j, k) = 20 * (30 * i + j) + k
For one-origin,
  general_offset(i, j, k) = 20 * (30 * (i-1) + (j-1)) + (k-1)
                          = 20 * (30 * i - 30 + j - 1) + (k-1)
                          = 20 * (30 * i + j - 31) + (k-1)
                          = 20 * (30 * i + j) - 620 + k - 1
                          = 20 * (30 * i + j) + k - 621
                          = z_offset(i, j, k) - z_offset(1, 1, 1)

Note that the second term is a compile-time constant.
                    Kevin Martin, UofW Software Development Group