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For the binary interchange formats whose encoding follows the IEEE 754-2008 recommendation on placement of the NaN signaling bit, the comparison is identical to one that type puns the floating-point numbers to a sign–magnitude integer (assuming a payload ordering consistent with this comparison), an old trick for FP comparison without an FPU.
The binary interchange formats have the "half precision" (16-bit storage format) and "quad precision" (128-bit format) added, together with generalized formulae for some wider formats; the basic formats have 32-bit, 64-bit, and 128-bit encodings. Three new decimal formats are described, matching the lengths of the 32–128-bit binary formats.
The VAX processor implemented non-IEEE quadruple-precision floating point as its "H Floating-point" format. It had one sign bit, a 15-bit exponent and 112-fraction bits, however the layout in memory was significantly different from IEEE quadruple precision and the exponent bias also differed.
In its 2008 revision, the IEEE 754 standard specifies a binary256 format among the interchange formats (it is not a basic format), as having: Sign bit: 1 bit; Exponent width: 19 bits; Significand precision: 237 bits (236 explicitly stored) The format is written with an implicit lead bit with value 1 unless the exponent is all zeros.
The 2008 and 2019 revisions of the IEEE 754 standard make formal requirements and recommendations for the encoding of the signaling/quiet state. For binary interchange formats, the most significant bit of the trailing significand field is exclusively used to distinguish between quiet and signaling NaNs. [14] (This requirement has been added in ...
IEEE 754-1985 [1] is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. [2] During its 23 years, it was the most widely used format for floating-point computation.
In IEEE 754-2008, denormal numbers are renamed subnormal numbers and are supported in both binary and decimal formats. In binary interchange formats, subnormal numbers are encoded with a biased exponent of 0, but are interpreted with the value of the smallest allowed exponent, which is one greater (i.e., as if it were encoded as a 1). In ...
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.