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==Implementation issues==
Arbitrary-precision arithmetic is considerably slower than arithmetic using numbers that fit entirely within processor registers, since the latter are usually implemented in [[Arithmetic logic unit|hardware arithmetic]] whereas the former must be implemented in software. Even if the [[computer]] lacks hardware for certain operations (such as integer division, or all floating-point operations) and software is provided instead, it will use number sizes closely related to the available hardware registers: one or two words only and definitely not N words. There are exceptions, as certain ''[[variable word length machine|variable word length]]'' machines of the 1950s and 1960s, notably the [[IBM 1620]], [[IBM 1401]] and the Honeywell ''Liberator'' series, could manipulate numbers bound only by available storage, with an extra bit that delimited the value.
Numbers can be stored in a [[fixed-point arithmetic|fixed-point]] format, or in a [[floating-point]] format as a [[significand]] multiplied by an arbitrary exponent. However, since division almost immediately introduces infinitely repeating sequences of digits (such as 4/7 in decimal, or 1/10 in binary), should this possibility arise then either the representation would be truncated at some satisfactory size or else rational numbers would be used: a large integer for the [[numerator]] and for the [[denominator]]. But even with the [[greatest common divisor]] divided out, arithmetic with rational numbers can become unwieldy very swiftly: 1/99 – 1/100 = 1/9900, and if 1/101 is then added the result is 10001/999900.
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