Intel 64 and IA-32 Architectures Software Developers Manual Volume 1, Basic Architecture

Vol. 1 4-7

DATA TYPES

NOTE

Section 4.8, “Real Numbers and Floating-Point Formats,” gives an

overview of the IEEE Standard 754 floating-point formats and defines

the terms integer bit, QNaN, SNaN, and denormal value.

Table 4-3 shows the floating-point encodings for zeros, denormalized finite numbers,

normalized finite numbers, infinites, and NaNs for each of the three floating-point

data types. It also gives the format for the QNaN floating-point indefinite value. (See

Section 4.8.3.7, “QNaN Floating-Point Indefinite,” for a discussion of the use of the

QNaN floating-point indefinite value.)

For the single-precision and double-precision formats, only the fraction part of the

significand is encoded. The integer is assumed to be 1 for all numbers except 0 and

denormalized finite numbers. For the double extended-precision format, the integer

is contained in bit 63, and the most-significant fraction bit is bit 62. Here, the integer

is explicitly set to 1 for normalized numbers, infinities, and NaNs, and to 0 for zero

and denormalized numbers.

Table 4-2. Length, Precision, and Range of Floating-Point Data Types

Data Type Length Precision

(Bits)

Approximate Normalized Range

Binary Decimal

Single Precision 32 24 2

–126

to 2

127

1.18 × 10

–38

to 3.40 × 10

Double Precision 64 53 2

–1022

to 2

1023

2.23 × 10

–308

to 1.79 ×

308

Double Extended

Precision

80 64 2

–16382

16383

3.37 × 10

–4932

to 1.18 ×

4932