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4:476
Volume 4: IA-32 SSE Instruction Reference
shows how the real number 178.125 (in ordinary decimal format) is stored in
floating-point format. The table lists a progression of real number notations that leads
to the format that the processor uses. In this format, the binary real number is
normalized and the exponent is biased.
4.7.1.2
Normalized Numbers
In most cases, the processor represents real numbers in normalized form. This means
that except for zero, the significand is always made up of an integer of 1 and the
following fraction:
1.fff...ff
For values less than 1, leading zeros are eliminated. (For each leading zero eliminated,
the exponent is decremented by one.)
Representing numbers in normalized form maximizes the number of significant digits
that can be accommodated in a significand of a given width. To summarize, a
normalized real number consists of a normalized significand that represents a real
number between 1 and 2 and an exponent that specifies the number’s binary point.
4.7.1.3
Biased Exponent
The processor represents exponents in a biased form. This means that a constant is
added to the actual exponent so that the biased exponent is always a positive number.
The value of the biasing constant depends on the number of bits available for
representing exponents in the floating-point format being used. The biasing constant is
chosen so that the smallest normalized number can be reciprocated without overflow.
Figure 4-9.
Binary Floating-point Format
Table 4-1.
Real Number Notation
Notation
Value
Ordinary Decimal
178.125
Scientific Decimal
1
.
78125E
10
2
Scientific Binary
1
.
0110010001E
2
111
Scientific Binary
(Biased Exponent)
1
0110010001E
2
10000110
Single Format (Normalized)
Sign
Biased Exponent
Significand
0
10000110
01100100010000000000000
1
(Implied)
Sign
Integer or J-Bit
Exponent
Significand
Fraction
Summary of Contents for ITANIUM ARCHITECTURE - SOFTWARE DEVELOPERS VOLUME 3 REV 2.3
Page 1: ......
Page 11: ...x Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 13: ...1 2 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 33: ...1 22 Volume 1 Part 1 Introduction to the Intel Itanium Architecture ...
Page 57: ...1 46 Volume 1 Part 1 Execution Environment ...
Page 147: ...1 136 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 149: ...1 138 Volume 1 Part 2 About the Optimization Guide ...
Page 191: ...1 180 Volume 1 Part 2 Predication Control Flow and Instruction Stream ...
Page 230: ......
Page 248: ...236 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 250: ...2 2 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 264: ...2 16 Volume 2 Part 1 Intel Itanium System Environment ...
Page 380: ...2 132 Volume 2 Part 1 Interruptions ...
Page 398: ...2 150 Volume 2 Part 1 Register Stack Engine ...
Page 486: ...2 238 Volume 2 Part 1 IA 32 Interruption Vector Descriptions ...
Page 750: ...2 502 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 754: ...2 506 Volume 2 Part 2 About the System Programmer s Guide ...
Page 796: ...2 548 Volume 2 Part 2 Interruptions and Serialization ...
Page 808: ...2 560 Volume 2 Part 2 Context Management ...
Page 842: ...2 594 Volume 2 Part 2 Floating point System Software ...
Page 850: ...2 602 Volume 2 Part 2 IA 32 Application Support ...
Page 862: ...2 614 Volume 2 Part 2 External Interrupt Architecture ...
Page 870: ...2 622 Volume 2 Part 2 Performance Monitoring Support ...
Page 891: ......
Page 1099: ...3 200 Volume 3 Instruction Reference padd Interruptions Illegal Operation fault ...
Page 1295: ...3 396 Volume 3 Resource and Dependency Semantics ...
Page 1296: ......
Page 1302: ...402 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 1494: ...4 192 Volume 4 Base IA 32 Instruction Reference FWAIT Wait See entry for WAIT ...
Page 1647: ...Volume 4 Base IA 32 Instruction Reference 4 345 ROL ROR Rotate See entry for RCL RCR ROL ROR ...
Page 1884: ...4 582 Volume 4 IA 32 SSE Instruction Reference ...
Page 1885: ...Index Intel Itanium Architecture Software Developer s Manual Rev 2 3 Index ...
Page 1886: ...Index Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Page 1898: ...INDEX Index 12 Index for Volumes 1 2 3 and 4 ...