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In computing, quadruple precision (also commonly shortened to quad precision) is a binary floating-point-based computer number format that occupies 16 bytes (128 bits) in computer memory and whose precision is about twice the 53-bit double precision. This 128 bit quadruple precision is designed not only for applications requiring results in higher than double precision,〔(【引用サイトリンク】title=High-Precision Computation and Mathematical Physics )〕 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: as 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. == IEEE 754 quadruple-precision binary floating-point format: binary128 == The IEEE 754 standard specifies a binary128 as having: * Sign bit: 1 bit * Exponent width: 15 bits * Significand precision: 113 bits (112 explicitly stored) This gives from 33 to 36 significant decimal digits precision (if a decimal string with at most 33 significant decimal is converted to IEEE 754 quadruple precision and then converted back to the same number of significant decimal, then the final string should match the original; and if an IEEE 754 quadruple precision is converted to a decimal string with at least 36 significant decimal and then converted back to quadruple, then the final number must match the original 〔(【引用サイトリンク】title=Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic )〕). The format is written with an implicit lead bit with value 1 unless the exponent is stored with all zeros. Thus only 112 bits of the significand appear in the memory format, but the total precision is 113 bits (approximately 34 decimal digits: ). The bits are laid out as: A binary256 would have a significand precision of 237 bits (approximately 71 decimal digits) and exponent bias 262143. 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「Quadruple-precision floating-point format」の詳細全文を読む スポンサード リンク
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