Quadruple-precision floating-point format

In <a href="/facts/Computing/Kghtm9fX">computing</a>, quadruple precision (or quad precision) is a binary <a href="/facts/Floating-point_arithmetic/eIckahxe">floating-point</a>–based <a href="/facts/Computer_number_format/fmLUI4hh">computer number format</a> that occupies 16 bytes (<a href="/facts/128-bit_computing/fo1QpdNj">128 bits</a>) with precision at least twice the 53-bit <a href="/facts/Double-precision_floating-point_format/JYyXXYFM">double precision</a>.
This 128-bit quadruple precision is designed for applications needing results in higher than double precision, and as a primary function, to allow computing double precision results more reliably and accurately by minimising overflow and <a href="/facts/Round-off_error/aF9N8X4I">round-off errors</a> in intermediate calculations and scratch variables. <a href="/facts/William_Kahan/J1GNQDyN">William Kahan</a>, primary architect of the original IEEE 754 floating-point standard noted, "For now the <a href="/facts/Extended_precision/CVpdQYeC">10-byte Extended format</a> 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 <a href="/facts/IEEE_754/dD3e7zAl">IEEE Standard 754 for Floating-Point Arithmetic</a> was framed."
In <a href="/facts/IEEE_754-2008/gqqJPoYC">IEEE 754-2008</a> the 128-bit base-2 format is officially referred to as binary128.

Quadruple-precision floating-point format open-in-new

Quadruple-precision floating-point format