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Extended precision refers to floating-point number formats that provide greater precision than the basic floating-point formats. [1] Extended precision formats support a basic format by minimizing roundoff and overflow errors in intermediate values of expressions on the base format. In contrast to extended precision, arbitrary-precision arithmetic refers to implementations of much larger numeric types (with a storage count that usually is not a power of two) using special software (or, rarely, hardware). And since it's a "legacy" instruction set, modern CPUs don't tend to optimize x87 instructions very well. If you don't need float80, then you have the option to do all your x86 floating point with SSE, which is a much more "normal" architecture with a random-access register file ( xmm), and ignore the x87 altogether. SSE is supported by all x86-64 CPUs, and by all 32-bit x86 CPUs from the last 20 years or so. The FPA10 math coprocessor for early ARM processors also supports this extended precision type (similar to the Intel format although padded to a 96-bit format with 16zero bits inserted between the sign and the exponent fields), but without correct rounding. [11]
Writing for Legacy is a thing. There are industries still using Windows XP for their QA software/hardware and some banks still run SW written in COBOL for Mainframes in the 70's.log 2 ( 2 ( − 1 ) s ⋅ E ⋅ M ) = ( − 1 ) s ⋅ E ⋅ log 2 ( 2 ) + log 2 ( M ) = ± E + log 2 ( M ) {\displaystyle \log _{2}(2 In contrast to the single and double-precision formats, this format does not utilize an implicit/ hidden bit. Rather, bit 63 contains the integer part of the significand and bits 62-0 hold the fractional part. Bit 63 will be 1 on all normalized numbers. There were several advantages to this design when the 8087 was being developed: Pseudo-Infinity. The sign bit gives the sign of the infinity. The 8087 and 80287 treat this as Infinity. The 80387 and later treat this as an invalid operand.
long float: type to which float values are promoted for computations (and might be as small as float or as big as long double. Quiet Not a Number, the sign bit is meaningless. The 8087 and 80287 treat this as a Signaling Not a Number. I would then suggest having a means of explicitly passing types other than double to functions, but say that expressions that don't explicitly force the type of a floating-point value passed to a variadic function would by default be converted to double.
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Extra digits make it easier for ordinary mortals to write floating-point calculations that won't go wrong for hard-to-analyze reasons. The more extra precision you have, the more you can imagine that your custom formulas (a + bx + cyz) will behave similarly to library functions (sin x) that were designed by experts to have a error of no more than 1 ulp over their whole domain. You don't get guaranteed accuracy, but you do get more reliable accuracy. It's too expensive to migrate everything, so we paid someone to add functionality we needed to our current compiler" It is also worth remembering that the x87 FPU had no ability to store the 80 bits into memory. Those extra 16 bits only lived in registers and were lost once they spill into memory. Its usefulness has always been limited. where s is the sign of the exponent (either 0 or 1), E is the unbiased exponent, which is an integer that ranges from 0 to 1023, and M is the significand which is a 53-bit value that falls in the range 1 ≤ M< 2. Negative numbers and zero can be ignored because the logarithm of these values is undefined. For purposes of this discussion M does not have 53bits of precision because it is constrained to be greater than or equal to one i.e. the hidden bit does not count towards the precision (Note that in situations where M is less than 1, the value is actually a de-normal and therefore may have already suffered precision loss. This situation is beyond the scope of this article).
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