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Here the 'IEEE 754 double value' resulting of the 15 bit figure is 3.330560653658221E-15, which is rounded by Excel for the 'user interface' to 15 digits 3.33056065365822E-15, and then displayed with 30 decimals digits gets one 'fake zero' added, thus the 'binary' and 'decimal' values in the sample are identical only in display, the values ...
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).
OpenCL also supports half-precision floating point numbers with the half datatype on IEEE 754-2008 half-precision storage format. [21] As of 2024, Rust is currently working on adding a new f16 type for IEEE half-precision 16-bit floats. [22] Julia provides support for half-precision floating point numbers with the Float16 type. [23]
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The new IEEE 754 (formally IEEE Std 754-2008, the IEEE Standard for Floating-Point Arithmetic) was published by the IEEE Computer Society on 29 August 2008, and is available from the IEEE Xplore website [4] This standard replaces IEEE 754-1985. IEEE 854, the Radix-Independent floating-point standard was withdrawn in December 2008.
That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Point Arithmetic was framed." [19] This 80-bit format uses one bit for the sign of the significand, 15 bits for the exponent field (i.e. the same range as the 128-bit quadruple precision IEEE 754 format) and
On Java before version 1.2, every implementation had to be IEEE 754 compliant. Version 1.2 allowed implementations to bring extra precision in intermediate computations for platforms like x87. Thus a modifier strictfp was introduced to enforce strict IEEE 754 computations. Strict floating point has been restored in Java 17.
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