3.8 Quadruple-precision Floating-point

The standard defines the encoding for the quadruple-precision floating-point data type "quadruple" (128 bits or 16 bytes). The encoding used is designed to be a simple analog of of the encoding used for single and double-precision floating-point numbers using one form of IEEE double extended precision. The standard encodes the following three fields, which describe the quadruple-precision floating-point number:

      S: The sign of the number.  Values 0 and 1 represent positive and
         negative, respectively.  One bit.

      E: The exponent of the number, base 2.  15 bits are devoted to
         this field.  The exponent is biased by 16383.

      F: The fractional part of the number's mantissa, base 2.  112 bits
         are devoted to this field.

Therefore, the floating-point number is described by:

         (-1)**S * 2**(E-Bias) * 1.F

It is declared as follows:

         quadruple identifier;

         +------+------+------+------+------+------+-...--+------+
         |byte 0|byte 1|byte 2|byte 3|byte 4|byte 5| ...  |byte15|
         S|    E       |                  F                      |
         +------+------+------+------+------+------+-...--+------+
         1|<----15---->|<-------------112 bits------------------>|
         <-----------------------128 bits------------------------>
                                      QUADRUPLE-PRECISION FLOATING-POINT

Just as the most and least significant bytes of a number are 0 and 3, the most and least significant bits of a quadruple-precision floating-point number are 0 and 127. The beginning bit (and most significant bit) offsets of S, E , and F are 0, 1, and 16, respectively. Note that these numbers refer to the mathematical positions of the bits, and NOT to their actual physical locations (which vary from medium to medium).

The encoding for signed zero, signed infinity (overflow), and denormalized numbers are analogs of the corresponding encodings for single and double-precision floating-point numbers [5], [6]. The "NaN" encoding as it applies to quadruple-precision floating-point numbers is system dependent and should not be interpreted within XDR as anything other than "NaN".