Cray CRAY-1 - Multiplication Algorithm

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I

Multiplication

algorithm

The

floating-point

multiply

unit

in the

CPU

has

an

input

of

48

bits

of

coefficient

into

a

multiply

pyramid

(figure

3-5).

The

pyramid

truncates

part

of

the

lower

bits

of

the

96-bit

product.

To

adjust

for

this

trun-

cation,

a

constant

is

unconditionally

added above

the

truncation.

The

value determined

by

summing

all

carries

produced

by

all

possible

com-

binations

that

could

be

truncated,

and

dividing

the

sum

by

the

number

of

possible

combinations. This averages to nine

carries

which

are

injected

at

the

2-

56

positton.

The

errors

due

to

this

truncation

and

rounding

are

in the range:

-48 -48

-0.23

x 2 to +0.57 x 2

or

-16 -16

-8.17 x

10

to +20.25 x

10

.

The

effect

of

this

error

is

at

most

a round

up

of

bit

2-

48

of

the

result.

2240004

3-25

E-01

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