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Extended Floating-Point Number
High-Order Part
rlr-------------------r-------------/------------
High-Order
S Characteristic
Leftmost 14 Digits
of 28-Digit Fraction
~------------~---------/----------~
o
8
63
Low-Order Part
Low-Order
Rightmost 14 Digits
I
r.-------------~--------/----------~
S Characteristic
of 28-Digit Fraction
~------------~---------/----------~
64
72
127
In all formats, the first bit (bit 0) is the sign bit
(S). The next seven bits are the characteristic. In
the short and long formats, the remaining bits
constitute the fraction, which consists of six or 14
hexadecimal digits, respectively.
A short floating-point number occupies only the
leftmost 32 bit positions of a floating-point register.
The rightmost 32 bit positions of the register are
ignored when used as an operand in the short
format and remain unchanged when a short result
is placed in the register.
An extended floating-point number has a
28-digit fraction and consists of two long
floating-point numbers which are called the
high-order and low-order parts. The high-order
part may be any long floating-point number. The
fraction of the high-order part contains the leftmost
14 hexadecimal digits of the 28-digit fraction. The
characteristic and sign of the high -order part are
the characteristic and sign of the extended
floating-point number.
If
the high-order part is
normalized, the extended number is considered
normalized. The fraction of the low-order part
contains the rightmost 14 digits of the 28-digit
fraction. The sign and characteristic of the
low-order part of an extended'operand are ignored.
When a result in the extended format is placed
in a register pair, the sign of the low-order part is
made the same as that of the high-order part, and,
unless the result is a true zero, the low-order
characteristic is made 14 less than the high-order
characteristic. When the subtraction of 14 would
cause the low-order characteristic to become less
than zero, the characteristic is made 128 greater
than its correct value. Exponent underflow is
indicated only when the high-order characteristic
underflows.
When an extended result is made a true zero,
both the high-order and low-order parts are made a
true zero.
The range covered by the magnitude (M) of a
normalized floating-point number depends on the
format.
In the short format:
16
65 ~
M
~
(1 - 16
6)
x 16
63
In the long format:
16
65 ~
M
~
(1 - 16
14)
x 16
63
In the extended format:
16
65 ~
M
~
(1-16
28)
x 16
63
In all formats, approximately:
5.4
x
10
79 ~
M
~
7.2
x
10
75
Although the final result of a floating-point
operation has six hexadecimal fraction digits in the
short format, 14 fraction digits in the long format,
and 28 fraction digits in the extended format
intermediate results have one additional
'
hexadecimal digit on the right. This digit is called
the guard digit. The guard digit may increase the
precision of the final result because it participates
. in addition, subtraction, and comparison operations
and in the left shift that occurs during
normalization.
The entire set of floating-point operations is
available for both short and long operands. These
instructions generate a result that has the same
format as the operands, except that for
MUL TIPL Y, a long product is produced from a
short multiplier and multiplicand. Extended
floating-point instructions are provided only for
normalized addition, subtraction, and
I
?Iultipli~ation.
Two additional multiplication
InstructIOns generate an extended product from a
long multiplier and multiplicand. The rounding
instructions provide for rounding from extended to
long format and from long to short format.
Programming Notes
1.
A long floating-point number can be converted
to the extended format by appending any long
floating-point number having a zero fraction,
ihcluding a true zero. Conversion from the
extended to the long format can be
accomplished by truncation or by means of
LOAD ROUNDED.
Chapter 9. Floating-Point Instructions
9-3
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