Control Data Cyber 170 State Hardware Reference Manual page 131

CP Normalize Instructions
Round Normalize
Round normalize (Xk)
t o X i and B j Z X i B j ,
This i n s t r u c t i o n reads one operand from Xk, performs a rounding and then
a
normalizing o p e r a t i o n i n floating-point format, and d e l i v e r s t h e round
normalized r e s u l t t o X i .
I n a d d i t i o n , a p o s i t i v e i n t e g e r s h i f t count i s s e n t
t o B j . This s h i f t count i s t h e number of b i t p o s i t i o n s of s h i f t required t o
normalize t h e o r i g i n a l operand c o e f f i c i e n t .
The rounding o p e r a t i o n c o n s i s t s of adding a b i t t o t h e c o e f f i c i e n t p o r t i o n of
t h e operand i n a b i t p o s i t i o n immediately below the l e a s t - s i g n i f i c a n t b i t
p o s i t i o n .
This round b i t h a s a value equal t o t h e complement of the operand
s i g n b i t . The r e s u l t i n c r e a s e s t h e magnitude of t h e c o e f f i c i e n t by one-half
t h e value of t h e l e a s t - s i g n i f i c a n t b i t .
The normalizing operation c o n s i s t s of r e p o s i t i o n i n g t h e c o e f f i c i e n t and
a d j u s t i n g t h e exponent t o l e a v e t h e v a l u e of t h e r e s u l t i n g f l o a t i n g - p o i n t
q u a n t i t y unaltered. The c o e f f i c i e n t
i s
s h i f t e d towards t h e higher-order b i t
p o s i t i o n s . The round b i t i s s h i f t e d along with t h e c o e f f i c i e n t .
The
displacement
i s the minimum number of b i t p o s i t i o n s r e q u i r e d t o make b i t 47
d i f f e r e n t from s i g n b i t
59.
This places t h e most-significant b i t of the
c o e f f i c i e n t i n t h e highest-order b i t p o s i t i o n . The exponent i s decreased by
t h e number of b i t p o s i t i o n s s h i f t e d .
Two sample computations a r e l i s t e d i n o c t a l n o t a t i o n t o i l l u s t r a t e the
normalizing o p e r a t i o n performed.
An example t h a t involves
a
p o s i t i v e floating-point number i s a s follows.
The following example involves a negative number.
( x i ) = 5751 3012 7777 7755 1537
If Xk contains e i t h e r an i n f i n i t e q u a n t i t y (3777mrx
...
x o r 4000xxx
...
x )
o r an
i n d e f i n i t e q u a n t i t y (1777xxx
...
x
o r 6OOOx
n . . .
x ) , no s h i f t t a k e s place.
The
content of Xk i s copied t o X i , and B j i s
s e t
t o 0. Corresponding i n f i n i t e and
i n d e f i n i t e e x i t conditions a r e a l s o s e t i n t h e C P f o r e x i t mode a c t i o n .
Refer t o Floating-Point Arithmetic under CP Programming i n chapter 5.