Quadruple-Precision Floating Point

Description

The standard defines the encoding for the quadruple-precision floating-point data type quadruple (128 bits or 16 bytes). The encoding used is the IEEE standard for normalized quadruple-precision floating-point numbers [1]. 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. There are 15 bits in this field. The exponent is biased by 16383.

F: The fractional part of the number's mantissa, base 2. There are 111 bits in this field.

Therefore, the floating-point number is described by:

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

Declaration

quadruple identifier; 

Encoding

Quadruple-Precision Floating Point

Just as the most and least significant bytes of an integer 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. These offsets refer to the logical positions of the bits, not to their physical locations (which vary from medium to medium).

The IEEE specifications should be consulted about the encoding for signed zero, signed infinity (overflow), and de-normalized numbers (underflow) [1]. According to IEEE specifications, the NaN (not a number) is system dependent and should not be used externally.