Intel ITANIUM ARCHITECTURE - SOFTWARE DEVELOPERS VOLUME 3 REV 2.3, Manual

Page: 1777 / 1898

Volume 4: IA-32 SSE Instruction Reference 4:475
Because the size and number of registers that any computer can have is limited, only a
subset of the real-number continuum can be used in real-number calculations. As
shown at the bottom of
Figure 4-1 , the subset of real numbers that a particular
processor supports represents an approximation of the real number system. The range
and precision of this real-number subset is determined by the format that the processor
uses to represent real numbers.
4.7.1.1 Floating-point Format
To increase the speed and efficiency of real-number computations, computers typically
represent real numbers in a binary floating-point format. In this format, a real number
has three parts: a sign, a significand, and an exponent.
Figure 4-9 shows the binary
floating-point format that SSE data uses. This format conforms to the IEEE standard.
The sign is a binary value that indicates whether the number is positive (0) or negative
(1). The significand has two parts: a 1-bit binary integer (also referred to as the J-bit)
and a binary fraction. The J-bit is often not represented, but instead is an implied value.
The exponent is a binary integer that represents the base-2 power that the significand
is raised to.
Figure 4-8. Binary Real Number System
Binary Real Number System
Subset of binary real-numbers that can be represented with
IEEE single-precision (32-bit) floating-point format.
+10
10.0000000000000000000000
1.11111111111111111111111
Precision 24 Binary Digits
Numbers within this range
cannot be represented.
VV VV
-100 -10 -1 0 1 10 100
VV VV
-100 -10 -1 0 1 10 100