GPGPU Programming for Games and Science

30 GPGPU Programming for Games and Science

You are more familiar with the notation using fractions,

r

0

+ r

1

=

x

0

y

0

+

x

1

y

1

=

x

0

y

1

+ x

1

y

0

y

0

y

1

(2.31)

where the sum is computed by constructing the common denominator of the

two fractions. Observe that the components of the 2-tuple are computed us-

ing multiplication and addition of binary scientific numbers, something we

already know how to do with a computer implementation (class

BSNumber).

Subtraction is defined similarly:

r

0

− r

1

=(x

0

∗ y

1

− x

1

∗ y

0

,y

0

∗ y

1

) (2.32)

Multiplication of two ratios is defined as

r

0

∗ r

1

=(x

0

∗ x

1

,y

0

∗ y

1

) (2.33)

where in fraction notation,

r

0

r

1

=

x

0

y

0

x

1

y

1

=

x

0

x

1

y

0

y

1

(2.34)

Division is similarly defined a