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In der Informatik ist vierfache Genauigkeit (englisch quad precision) eine Bezeichnung für ein Zahlenformat, das vier Speichereinheiten im Rechner belegt. Damit sind die genauen Details abhängig vom Rechnerhersteller und dessen Speicherarchitektur. Der im folgenden Bild gezeigte 128-Bit-Datentyp ist in der aktuellen Fassung des IEEE 754-2008 Standard beschrieben: Die Bezeichnung ist nicht nur für Gleitkommazahlen vorbehalten, sondern auch für Ganzzahlformate anwendbar (Double Quadword). (de) In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision. This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision, but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables. William Kahan, primary architect of the original IEEE-754 floating point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Point Arithmetic was framed." In IEEE 754-2008 the 128-bit base-2 format is officially referred to as binary128. (en) 四倍精度浮動小数点形式（よんばいせいどふどうしょうすうてん、英語: quadruple-precision floating-point format）は、浮動小数点数の形式の1つで、よく使われている通常の倍精度形式と比して、仮数部の長さが約2倍である。 Nicholas J. Higham『Accuracy and Stability of Numerical Algorithms』（2nd.e）が、カハンの言として引用している文によれば、 For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Point Arithmetic was framed. （訳）これまでのところは、10バイトの拡張倍精度は、高精度演算の価値と高速に動作させるための実装コストとの間の妥協点としては許容できるものです。そうしてすぐにさらに2バイト分長い精度が妥当になるでしょう。そうして究極的には16バイトフォーマットもが…。この種の、より広い精度への段階的な進化はIEEE 754の規格が形成された時には既に想定されていました。 とのことである。（編注: 英語版Wikipediaが孫引きしている。英語版Wikipediaの引用元が示している引用元は「W. Kahan. Computer benchmarks versus accuracy. Draft manuscript, June 1994.」となっている） IEEE 754-2008では、128ビットの二進フォーマットが公式にbinary128として定義された。次に示す。 (ja) Число́ четверно́й то́чности (англ. Quadruple precision) — компьютерный формат представления чисел с плавающей запятой, занимающий в памяти четыре последовательных ячейки (компьютерных слова; в случае 32-битного компьютера — 128 бит или 16 байт). Как правило, обозначает формат числа с плавающей запятой binary128 стандарта IEEE 754. (ru) |
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In der Informatik ist vierfache Genauigkeit (englisch quad precision) eine Bezeichnung für ein Zahlenformat, das vier Speichereinheiten im Rechner belegt. Damit sind die genauen Details abhängig vom Rechnerhersteller und dessen Speicherarchitektur. Der im folgenden Bild gezeigte 128-Bit-Datentyp ist in der aktuellen Fassung des IEEE 754-2008 Standard beschrieben: Die Bezeichnung ist nicht nur für Gleitkommazahlen vorbehalten, sondern auch für Ganzzahlformate anwendbar (Double Quadword). (de) Число́ четверно́й то́чности (англ. Quadruple precision) — компьютерный формат представления чисел с плавающей запятой, занимающий в памяти четыре последовательных ячейки (компьютерных слова; в случае 32-битного компьютера — 128 бит или 16 байт). Как правило, обозначает формат числа с плавающей запятой binary128 стандарта IEEE 754. (ru) In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision. In IEEE 754-2008 the 128-bit base-2 format is officially referred to as binary128. (en) 四倍精度浮動小数点形式（よんばいせいどふどうしょうすうてん、英語: quadruple-precision floating-point format）は、浮動小数点数の形式の1つで、よく使われている通常の倍精度形式と比して、仮数部の長さが約2倍である。 Nicholas J. Higham『Accuracy and Stability of Numerical Algorithms』（2nd.e）が、カハンの言として引用している文によれば、 （訳）これまでのところは、10バイトの拡張倍精度は、高精度演算の価値と高速に動作させるための実装コストとの間の妥協点としては許容できるものです。そうしてすぐにさらに2バイト分長い精度が妥当になるでしょう。そうして究極的には16バイトフォーマットもが…。この種の、より広い精度への段階的な進化はIEEE 754の規格が形成された時には既に想定されていました。 とのことである。（編注: 英語版Wikipediaが孫引きしている。英語版Wikipediaの引用元が示している引用元は「W. Kahan. Computer benchmarks versus accuracy. Draft manuscript, June 1994.」となっている） (ja) |
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