4:478
Volume 4: IA-32 SSE Instruction Reference
When real numbers become very close to zero, the normalized-number format can no
longer be used to represent the numbers. This is because the range of the exponent is
not large enough to compensate for shifting the binary point to the right to eliminate
leading zeros.
When the biased exponent is zero, smaller numbers can only be represented by making
the integer bit (and perhaps other leading bits) of the significand zero. The numbers in
this range are called
denormalized
(or
tiny
) numbers. The use of leading zeros with
denormalized numbers allows smaller numbers to be represented. However, this
denormalization causes a loss of precision (the number of significant bits in the fraction
is reduced by the leading zeros).
When performing normalized floating-point computations, a processor normally
operates on normalized numbers and produces normalized numbers as results.
Denormalized numbers represent an
underflow
condition.
A denormalized number is computed through a technique called gradual underflow.
gives an example of gradual underflow in the denormalization process. Here
the single-real format is being used, so the minimum exponent (unbiased) is
126
10
.
The true result in this example requires an exponent of
129
10
in order to have a
normalized number. Since
129
10
is beyond the allowable exponent range, the result
is denormalized by inserting leading zeros until the minimum exponent of
126
10
is
reached.
Figure 4-10. Real Numbers and NaNs
Table 4-2.
Denormalization Process
Operation
Sign
Exponent
a
Significand
True Result
0
129
1.01011100000...00
Denormalize
0
128
0.10101110000...00
Denormalize
0
127
0.01010111000...00
1
0
0
S
E
F
-0
1
0
-Denormalized
Finite
NaN
1 1...254
Any Value
-Normalized
Finite
1
255
0
-
255
1.0XX
2
-SNaN
255
1.1XX
-QNaN
Notes
1. Sign bit ignored
2. Fractions must be non-zero
0
0
0
S
E
F
0
0
NaN
0 1...254
Any Value
0
255
0
X
1
255
1.0XX
2
255
1.1XX
+0
+Denormalized
Finite
+Normalized
Finite
+
+SNaN
+QNaN X
1
X
1
X
1
Real Number and NaN Encodings For 32-bit Floating-point Format
-Denormalized Finite
-
Normalized Finite
-0
-
+
+Denormalized Finite
+Normalized Finite
+0
0.XXX
2
0.XXX
2
Содержание ITANIUM ARCHITECTURE - SOFTWARE DEVELOPERS VOLUME 3 REV 2.3
Страница 1: ......
Страница 11: ...x Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 12: ...1 1 Intel Itanium Architecture Software Developer s Manual Rev 2 3 Part I Application Architecture Guide ...
Страница 13: ...1 2 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 33: ...1 22 Volume 1 Part 1 Introduction to the Intel Itanium Architecture ...
Страница 57: ...1 46 Volume 1 Part 1 Execution Environment ...
Страница 147: ...1 136 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 149: ...1 138 Volume 1 Part 2 About the Optimization Guide ...
Страница 191: ...1 180 Volume 1 Part 2 Predication Control Flow and Instruction Stream ...
Страница 230: ......
Страница 248: ...236 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 249: ...2 1 Intel Itanium Architecture Software Developer s Manual Rev 2 3 Part I System Architecture Guide ...
Страница 250: ...2 2 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 264: ...2 16 Volume 2 Part 1 Intel Itanium System Environment ...
Страница 380: ...2 132 Volume 2 Part 1 Interruptions ...
Страница 398: ...2 150 Volume 2 Part 1 Register Stack Engine ...
Страница 486: ...2 238 Volume 2 Part 1 IA 32 Interruption Vector Descriptions ...
Страница 749: ...2 501 Intel Itanium Architecture Software Developer s Manual Rev 2 3 Part II System Programmer s Guide ...
Страница 750: ...2 502 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 754: ...2 506 Volume 2 Part 2 About the System Programmer s Guide ...
Страница 796: ...2 548 Volume 2 Part 2 Interruptions and Serialization ...
Страница 808: ...2 560 Volume 2 Part 2 Context Management ...
Страница 842: ...2 594 Volume 2 Part 2 Floating point System Software ...
Страница 850: ...2 602 Volume 2 Part 2 IA 32 Application Support ...
Страница 862: ...2 614 Volume 2 Part 2 External Interrupt Architecture ...
Страница 870: ...2 622 Volume 2 Part 2 Performance Monitoring Support ...
Страница 891: ......
Страница 941: ...3 42 Volume 3 Instruction Reference cmp illegal_operation_fault PR p1 0 PR p2 0 Interruptions Illegal Operation fault ...
Страница 1099: ...3 200 Volume 3 Instruction Reference padd Interruptions Illegal Operation fault ...
Страница 1191: ...3 292 Volume 3 Pseudo Code Functions Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 1295: ...3 396 Volume 3 Resource and Dependency Semantics ...
Страница 1296: ......
Страница 1302: ...402 Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 1494: ...4 192 Volume 4 Base IA 32 Instruction Reference FWAIT Wait See entry for WAIT ...
Страница 1564: ...4 262 Volume 4 Base IA 32 Instruction Reference LES Load Full Pointer See entry for LDS LES LFS LGS LSS ...
Страница 1565: ...Volume 4 Base IA 32 Instruction Reference 4 263 LFS Load Full Pointer See entry for LDS LES LFS LGS LSS ...
Страница 1568: ...4 266 Volume 4 Base IA 32 Instruction Reference LGS Load Full Pointer See entry for LDS LES LFS LGS LSS ...
Страница 1583: ...Volume 4 Base IA 32 Instruction Reference 4 281 LSS Load Full Pointer See entry for LDS LES LFS LGS LSS ...
Страница 1647: ...Volume 4 Base IA 32 Instruction Reference 4 345 ROL ROR Rotate See entry for RCL RCR ROL ROR ...
Страница 1663: ...Volume 4 Base IA 32 Instruction Reference 4 361 SHL SHR Shift Instructions See entry for SAL SAR SHL SHR ...
Страница 1668: ...4 366 Volume 4 Base IA 32 Instruction Reference SIDT Store Interrupt Descriptor Table Register See entry for SGDT SIDT ...
Страница 1884: ...4 582 Volume 4 IA 32 SSE Instruction Reference ...
Страница 1885: ...Index Intel Itanium Architecture Software Developer s Manual Rev 2 3 Index ...
Страница 1886: ...Index Intel Itanium Architecture Software Developer s Manual Rev 2 3 ...
Страница 1898: ...INDEX Index 12 Index for Volumes 1 2 3 and 4 ...