Floating-Point Numbers - Xerox 560 Reference Manual

Instruction Name Mnemonic
Floating Subtract Long
FSL
Floating Multiply Short
FMS
Floating Multiply Long
FML
Floating Divide Short
FDS
Floating Divide Long FDL
FLOATING-POINT NUMBERS
Two number formats are accommodated for floating-point
arithmetic: short and long. A short-format floating-point
number consists of a sign (bit 0), a biased t , base 16 expo-
nent, which is called a characteristic (bits 1-7), and a
six-digit hexadecimal fraction (bits
8-31).
A long-format
floating-point number consists of a short-format floating-
point number followed by an additional eight hexadecimal
digits of fractional significance, and occupies a double-
word memory location or an even-odd pair of general
registers.
A floating-point number (N) has the following format:
A floating-point number (N) has the following formal
definition:
1.
C-64
N = F x 16 where F
=
0 or
-6
16
s
IFI
s
1 (short format) or
-14
16 S IFI
$
1 {long format)
and 0
$
C
$
127.
2. A positive floating-point number with a fraction of
zero and a characteristic of zero is a "true" zero.
A positive floating-point number with a fraction of
zero and a nonzero characteristic is an "abnorma
I"
zero. For floating-point multiplication and division,
an abnormal zero is treated as a true zero. However,
t
The bias value of 4016 is added to the exponent for the
purpose of making it possible to compare the absolute mag-
nitude of two numbers,
i.
e.,
without reference to a sign
bit. This manipulation effectively removes the sign bit,
making each characteristic a 7-bit positive number.
for addition and subtraction, an abnormal zero is
treated the same as any nonzero operand.
3. A positive floating-point number is normalized if and
only if the fraction is contained in the interval
1/16
$
F
<
1
4. A negative floating-point number is the two1s comple-
ment of its positive representation.
5.
A negative floating-point number is normalized if and
only if its two1s complement is a normalized positive
number.
By this definition, a floating-point number of the form
1 xxx xxxx
1111
0000 . .• 0000
is normalized, and a floating-point number of the form
1 xxx xxxx 0000 0000 . .. 0000
is illegal and, whenever generated by floating-point in-
structions, is converted to the form
1 yyy yyyy
1111
0000 . .. 0000
where yy ...
Y
is 1 less than xx ... x. Table 7 contains
examples of floating-point numbers.
Modes of Operation
There are four mode control bits that are used to qual ify
£"1 __ .
.L- __ . • .L ____ .I..- _ _
TI _ _ _ _ _ I. __
L..
I I
-.1. _ _ _
IIUUIIII~-PUIIII Upt::IUIIUII:>. 1111::::>1::: IIIUUI::: ,",UIIIIUI Uti:> utI:::
identified as FR (floating round), FS (floating significance),
FZ (floating zero), and FN (floating normalize); they are
contained in bit positions 4,
5,
6, and 7, respectively, of
the program status words (PSWs4_7).
The floating-point mode is established by setting the four
floating-point mode control bits. This can be performed by
any of the following instructions:
Instruction Name
Load Conditions and Floating Control
Load Conditions and Floating Control
Immediate
Load Program Status Words
Exchange Program Status Words
Mnemonic
LCF
LCFI
LPSD
XPSD
The floating-point mode control bits are stored by execut-
ing either of the following instructions:
Instruction Name Mnemonic
Store Conditions and Floating Control STCF
Exchange Program Status Words XPSD
Floating-Point Arithmetic Instructions 75