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Quiet Not a Number, the sign bit is meaningless. The 8087 and 80287 treat this as a Signaling Not a Number. The IBM System/360 supports a 32-bit "short" floating-point format and a 64-bit "long" floating-point format. [4] The 360/85 and follow-on System/370 add support for a 128-bit "extended" format. [5] These formats are still supported in the current design, where they are now called the " hexadecimal floating-point" (HFP) formats. 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 64 bits for the significand. The exponent field is biased by 16383, meaning that 16383 has to be subtracted from the value in the exponent field to compute the actual power of 2. [20] An exponent field value of 32767 (all fifteen bits 1) is reserved so as to enable the representation of special states such as infinity and Not a Number. If the exponent field is zero, the value is a denormal number and the exponent of 2 is −16382. [21] It's too expensive to migrate everything, so we paid someone to add functionality we needed to our current compiler" 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.
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.The 8087 had 80-bit registers so that if the inputs to your computation had 64-bit accuracy, the outputs would also have 64-bit accuracy. The IEEE 754 floating-point standard recommends that implementations provide extended precision formats. The standard specifies the minimum requirements for an extended format but does not specify an encoding. [7] The encoding is the implementor's choice. [8] In addition to supporting IEEE single and double precision numbers, it also supported an 80-bit extended precision number. Some C compilers (e.g. clang) mapped this to the long double type in C The Microsoft BASIC port for the 6502 CPU, such as in adaptations like Commodore BASIC, AppleSoft BASIC, KIM-1 BASIC or MicroTAN BASIC, supports an extended 40-bit variant of the floating-point format Microsoft Binary Format (MBF) since 1977. [6] IEEE 754 extended precision formats [ edit ] Taking the log of this representation of a double-precision number and simplifying results in the following:
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. A notable example of the need for a minimum of 64bits of precision in the significand of the extended precision format is the need to avoid precision loss when performing exponentiation on double-precision values. [26] [27] [28] [c] The x86 floating-point units do not provide an instruction that directly performs exponentiation. Instead they provide a set of instructions that a program can use in sequence to perform exponentiation using the equation:
Further fun facts:
The x87 and Motorola68881 80-bit formats meet the requirements of the IEEE 754 double extended format, [12] as does the IEEE754 128-bit format. Pseudo Denormal. The 80387 and later properly interpret this value but will not generate it. The value is (−1) s × m × 2 −16382 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]
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