Single-Precision Floating Point

XDR defines the single-precision floating-point data type as a float.

The length of a float is 32 bits, or 4 bytes. Floats are encoded using the IEEE standard for normalized single-precision floating-point numbers.

The single-precision floating-point number is declared as follows:


(-1)**S * 2**(E-Bias) * 1.F

Item	Description
`S`	Sign of the number. This 1-bit field specifies either 0 for positive or 1 for negative.
`E`	Exponent of the number in base 2. This field contains 8 bits. The exponent is biased by 127.
`F`	Fractional part of the number's mantissa in base 2. This field contains 23 bits.

See the Single-Precision Floating-Point figure (Figure 1).

The first line of this diagram lists bytes 0 through 3, with the most significant byte 0 first, and the least significant byte 3 last. The second line of the diagram shows the corresponding fields and their respective lengths: S (1 bit) and E (8 bits) extend under byte 0 and byte 1, while F (23 bits) extends from byte 1 to byte 3. The third line shows the total length of bytes 0 through 3, which is 32 bits. — Figure 1. Single-Precision Floating-Point

The most and least significant bytes of an integer are 0 and 3. The most and least significant bits of a single-precision floating-point number are 0 and 31. The beginning (and most significant) bit offsets of S, E, and F are 0, 1, and 9, respectively. These numbers refer to the mathematical positions of the bits but not to their physical locations, which vary from medium to medium.

The IEEE specifications should be considered when encoding signed zero, signed infinity (overflow), and denormalized numbers (underflow). According to IEEE specifications, the NaN (not-a-number) is system-dependent and should not be used externally.