27 lines
1.8 KiB
Plaintext
27 lines
1.8 KiB
Plaintext
[[wp:Balanced ternary|Balanced ternary]] is a way of representing numbers. Unlike the prevailing binary representation, a balanced ternary integer is in base 3, and each digit can have the values 1, 0, or −1.
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;Examples:
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Decimal 11 = 3<sup>2</sup> + 3<sup>1</sup> − 3<sup>0</sup>, thus it can be written as "++−"
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Decimal 6 = 3<sup>2</sup> − 3<sup>1</sup> + 0 × 3<sup>0</sup>, thus it can be written as "+−0"
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;Task:
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Implement balanced ternary representation of integers with the following:
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# Support arbitrarily large integers, both positive and negative;
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# Provide ways to convert to and from text strings, using digits '+', '−' and '0' (unless you are already using strings to represent balanced ternary; but see requirement 5).
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# Provide ways to convert to and from native integer type (unless, improbably, your platform's native integer type ''is'' balanced ternary). If your native integers can't support arbitrary length, overflows during conversion must be indicated.
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# Provide ways to perform addition, negation and multiplication directly on balanced ternary integers; do ''not'' convert to native integers first.
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# Make your implementation efficient, with a reasonable definition of "efficient" (and with a reasonable definition of "reasonable").
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'''Test case''' With balanced ternaries ''a'' from string "+−0++0+", ''b'' from native integer −436, ''c'' "+−++−":
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* write out ''a'', ''b'' and ''c'' in decimal notation;
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* calculate ''a'' × (''b'' − ''c''), write out the result in both ternary and decimal notations.
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'''Note:''' The pages [[generalised floating point addition]] and [[generalised floating point multiplication]] have code implementing [[wp:arbitrary precision|arbitrary precision]] [[wp:floating point|floating point]] balanced ternary.
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<br><br>
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