In order to analyze the security and universality of the arithmetic proposed by Sheng et al

the concept of information loss in single iteration and average speed of information loss in dynamic system is proposed based on information theory.It is shown that the information loss of the 2nd bit-operation transformation is 12 bits

and which of the standard 2nd bit-operation transformation is related to the exponent

e

.It is possible that the information loss of the 2nd bit-operation transformation is so small.Not all of the float number in[-1

1

]

can be traversed by the standard 2nd bit-opera

tion transformation just because the 1023-

e

is used as the shift number.The concept of transient data and 1st transient transformation is proposed further

and the arithmetic proposed in literature[14

]

is improved as well.The output sequence of random digital chaotic system can be transformed as float number in[0

1

]

by the improved arithmetic.The information loss of this transformation is

L

-1 bits

which is approached to the maximum speed of information loss

I

max

=

L

under the computing precision

L

.The transformed sequence is uniform distributed which can be proved by

-verification.