Octuple-precision floating-point format

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In computing, octuple precision is a binary floating-point-based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256-bit octuple precision is for applications requiring results in higher than quadruple precision. The range greatly exceeds what is needed to describe the size of the observable universe, precise to the Planck length. However, some problems in experimental mathematics do require octuple (or higher) precision. In its 2008 revision, the IEEE 754 standard specifies a binary256 format among the interchange formats (it is not a basic format), as having: The format is written with an implicit lead bit with value 1 unless the exponent is all zeros. Thus only 236 bits of the significand appear in the memory format, but the total precision is 237 bits (approximately 71 decimal digits: log10(2) ≈ 71.344). The bits are laid out as follows: The octuple-precision binary floating-point exponent is encoded using an offset binary representation, with the zero offset being 262143; also known as exponent bias in the IEEE 754 standard. Thus, as defined by the offset binary representation, in order to get the true exponent the offset of 262143 has to be subtracted from the stored exponent. The stored exponents 0000016 and 7FFFF16 are interpreted specially. The minimum strictly positive (subnormal) value is 2 ≈ 10 and has a precision of only one bit.