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65 lines
1.5 KiB
Plaintext
65 lines
1.5 KiB
Plaintext
Division
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This describes the division algorithm used by the MPI library.
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Input: a, b; a > b
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Compute: Q, R; a = Qb + R
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The input numbers are normalized so that the high-order digit of b is
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at least half the radix. This guarantees that we have a reasonable
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way to guess at the digits of the quotient (this method was taken from
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Knuth, vol. 2, with adaptations).
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To normalize, test the high-order digit of b. If it is less than half
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the radix, multiply both a and b by d, where:
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radix - 1
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d = -----------
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bmax + 1
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...where bmax is the high-order digit of b. Otherwise, set d = 1.
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Given normalize values for a and b, let the notation a[n] denote the
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nth digit of a. Let #a be the number of significant figures of a (not
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including any leading zeroes).
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Let R = 0
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Let p = #a - 1
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while(p >= 0)
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do
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R = (R * radix) + a[p]
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p = p - 1
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while(R < b and p >= 0)
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if(R < b)
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break
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q = (R[#R - 1] * radix) + R[#R - 2]
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q = q / b[#b - 1]
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T = b * q
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while(T > L)
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q = q - 1
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T = T - b
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endwhile
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L = L - T
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Q = (Q * radix) + q
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endwhile
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At this point, Q is the quotient, and R is the normalized remainder.
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To denormalize R, compute:
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R = (R / d)
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At this point, you are finished.
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------------------------------------------------------------------
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This Source Code Form is subject to the terms of the Mozilla Public
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# License, v. 2.0. If a copy of the MPL was not distributed with this
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# file, You can obtain one at http://mozilla.org/MPL/2.0/.
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