Texas Instruments TMS320C3x 사용자 설명서

Floating-Point Multiplication

5-26

5.5

Floating-Point Multiplication

A floating-point number

can be written in floating-point format as in the following

formula, where

(

man) is the mantissa and

(

exp) is the exponent:

(

man)

(

exp)

The product of

and

b is c, defined as:

c =

b =

(

man)

b(man)

(

exp) + b (exp))

thus:

c(man) =

(

man)

b(man)

c(exp) =

(

exp) + b(exp)

During floating-point multiplication, source operands are in the single-precision
floating-point format. If the source operands are in short floating-point format,
they are converted to single-precision floating-point format. If the source oper-
ands are in extended-precision floating-point format, they are truncated to
single-precision format. These conversions occur automatically in hardware
with no overhead. All results of floating-point multiplications are in the extended-
precision format. These multiplications occur in a single cycle.

Figure 5–16 is a flowchart that shows the steps involved in floating-point multi-
plication. Each step is labelled with a number in parenthesis.

In step 1, the 24-bit source operand mantissas are multiplied, producing
a 50-bit result

c(man). (Input and output data are always represented as

normalized numbers.)

In step 2, the exponents,

(

exp) and b(exp), are added, yielding c(exp).

Step 3 checks for whether

c(man) in extended-precision format is equal to

0. If

c(man) is 0, step 7 sets c(exp) to –128, thus yielding the representation

for 0.

Steps 4 and 5 normalize the result.

If a right shift of 1 is necessary, then in step 8,

c(man) is right-shifted one

bit, thus adding 1 to

c(exp).

If a right shift of 2 is necessary, then in step 9,

c(man) is right-shifted two

bits, thus adding 2 to

c(exp). Step 6 occurs when the result is normalized.

In step 10,

c(man) is set in the extended-precision floating-point format.

Steps 11 through 16 check for special cases of

c(exp).