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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク guard digit ： ウィキペディア英語版 guard digit In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. For example, suppose that the final result of a long, multi-step calculation can be safely rounded off to ''N'' decimal places. That is to say, the roundoff error introduced by this final roundoff makes a negligible contribution to the overall uncertainty. However, it is quite likely that it is ''not'' safe to round off the intermediate steps in the calculation to the same number of digits. Be aware that roundoff errors can accumulate. If ''M'' decimal places are used in the intermediate calculation, we say there are ''M−N'' guard digits. Guard digits are also used in floating point operations in most computer systems. Given $2^1\; \backslash times\; 0.100\_2\; -\; 2^0\; \backslash times\; 0.111\_2$ we have to line up the binary points. This means we must add an extra digit to the first operand—a guard digit. This gives us $2^1\; \backslash times\; 0.1000\_2\; -\; 2^1\; \backslash times\; 0.0111\_2$. Performing this operation gives us $2^1\; \backslash times\; 0.0001\_2$ or $2^\; \backslash times\; 0.100\_2$. Without using a guard digit we have $2^1\; \backslash times\; 0.100\_2\; -\; 2^1\; \backslash times\; 0.011\_2$, yielding $2^1\; \backslash times\; 0.001\_2=$ or $2^\; \backslash times\; 0.100\_2$. This gives us a relative error of 1. Therefore we can see how important guard digits can be. An example of the error caused by floating point roundoff is illustrated in the following C code. int main() It appears that the program should not terminate. Yet the output is : i=54 a=1.000000 Another example is: Take 2 numbers: 2.56 *10^0 and 2.34 *10^2 we bring the first number to the same power of 10 as the second one: 0.0256 *10^2 The addition of the 2 numbers is: 0.0256 *10^2 + 2.3400 *10^2 ____________ 2.3656 *10^2 After padding the second number with 0, the bit after 4 is the guard digit and the bit after is the round digit. The result after rounding is 2.37 as opposed to 2.36 without the extra bits (guard and round bits), i.e. by considering only 0.02+2.34 = 2.36. The error therefore is 0.01. ==References== * Forman S. Acton. ''Numerical Methods that Work'', The Mathematical Association of America (August 1997). * Higham, Nicholas J. ''Accuracy and Stability of Numerical Algorithms'', Washington D.C.: Society for Industrial & Applied Mathematics, 2002. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「guard digit」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.