Exponential calculation device and decoding device

Details Exponential calculation device and decoding device Exponential calculation device and decoding device

1999-02-03

2001-10-16

Mai, Tan V. (Department: 2121)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

06304890

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an exponential calculation device and a decoding device for performing a predetermined calculation for a given encoded bit stream. More particularly, the present invention relates to an exponential calculation device for calculating x{circumflex over ( )}(a/b) and a decoding device for calculating x{circumflex over ( )}(a/b)*2{circumflex over ( )}(y/c) for given integer values x and y contained in a bit stream which has been encoded based on the MPEG (moving picture experts group) 2 audio encoding standard “AAC”.
2. Description of the Related Art
Conventionally, in order to calculate z=x{circumflex over ( )}(a/b) for a given value of x (where a and b are constant values), values of x{circumflex over ( )}(a/b) for all the possible values of x are stored in a table whose addresses are associated with the respective values of x. The value of z for a given value of x is obtained by reading out the value stored in the table.
In this specification, “x to a power of (a/b)” is represented as “x{circumflex over ( )}(a/b)”, where the symbol “{circumflex over ( )}” denotes the use of an exponential function, and the symbol “/” denotes a division function. The symbol“*” will also be used herein to denote a multiplication function.
FIG. 27
illustrates a table containing values of x{circumflex over ( )}(4/3) for values of x in a range of
0≦x≦8191
. A decoding operation based on the MPEG 2 audio encoding standard AAC requires calculation of x{circumflex over ( )}(4/3) for a value of x in the range from 0 to 8191. When the conventional method of obtaining the value of x{circumflex over ( )}(a/b) is employed in the exponential calculation involved in decoding data encoded based on the MPEG 2 audio encoding standard AAC, an input value of x is used as an address for reading out the corresponding value from a table provided in advance, as illustrated in
FIG. 27
, to obtain the value of x{circumflex over ( )}(4/3) an output value z.
In order to decode an encoded bit stream so as to obtain the intended data, it is necessary to perform a predetermined calculation process. A bit stream encoded based on the MPEG 2 audio encoding standard AAC contains a quantization code “x” and a scaling factor “y”. The quantization code “x” and the scaling factor “y” are both integers. In the case of the MPEG 2 audio encoding standard AAC, the decoding device calculates x{circumflex over ( )}(a/b)*2{circumflex over ( )}(y/c) (where a,b and c are constants) for given values of x and y. Details of the MPEG 2 audio encoding standard AAC are disclosed in ISO/IEC 13818-7:1997, pp.57-59.
Conventionally, an operation of calculating x{circumflex over ( )}(a/b)*2{circumflex over ( )}(y/c) for given values of x and y has been performed as follows with a DSP (digital signal processor) of a fixed point format.
FIG. 28
illustrates an exemplary 32-bit fixed point format. Referring to
FIG. 28
, where the bit
0
is the least significant bit and the bit
31
is the most significant bit, the decimal point is fixed between the bit
30
and the bit
29
. In particular, bit
30
represents the integral portion of a value, while the bits
29
-
0
represent the fractional portion of the value. Bit
31
is the sign bit indicating whether the value is positive or negative. Such a numeric representation with a fixed decimal point is called a “fixed point format”.
For example, a value “f” represented in the 32-bit fixed point format, as illustrated in
FIG. 28
, can vary in the range of −2≦f<2. Then, in order to perform a calculation with a fixed-point-format processing unit, such as a DSP, values involved in the calculation are adjusted so that they are each in the range of ±2.0 before performing the intended calculation.
In the MPEG 2 audio encoding standard AAC, x can vary in the range of 0≦x<8192, whereas y can vary in the range of −100≦y<156. Consider a calculation of Expression (1) below for x and y having such ranges.
x{circumflex over ( )}(4/3)*2{circumflex over ( )}(y/4)  (1)
Expression (1) may be calculated as follows based on the prior art technique with a fixed-point-format processing unit. First, Expression (1) is converted to Expression (2) below.
x{circumflex over ( )}(4/3)*2{circumflex over ( )}((y%4)/4)*2{circumflex over ( )}int(y/4)  (2)
In Expression (2), “(y%4)” represents a remainder of a division y/4, and “int(y/4)” represents a quotient (integer) of the division y/4. In the calculation of Expression (2), x{circumflex over ( )}(4/3) is first calculated. The calculation x{circumflex over ( )}(4/3) is typically performed using a ROM table. In particular, values of x{circumflex over ( )}(4/3) for various values of x are calculated and stored in a table in advance. Then, the value of x{circumflex over ( )}(4/3) for a given value of x is obtained by referencing the ROM table using the value of x as the address of the table.
The calculation of Expression (1) or (2) assumes the use of a fixed-point-format processing unit. In particular, different values of x{circumflex over ( )}(4/3) are normalized and stored in a table in advance, with the maximum value thereof being normalized to a value which does not exceed 1.0.
FIG. 29
illustrates the contents of a first table for use with a conventional decoding device. The table illustrated in
FIG. 29
contains values of f(x) for the range of 0≦x<8192 at addresses which correspond to the respective values of x. The values of f(x) are obtained by first calculating x{circumflex over ( )}(4/3) for various values of x, and then dividing the calculated values by 2{circumflex over ( )}18 to normalize the values so that none of them exceeds 1.0.
In the calculation of Expression (2), 2{circumflex over ( )}((y%4)/4) is then calculated. Typically, 2{circumflex over ( )}((y%4)/4) is also calculated using a ROM table. In particular, different values of 2{circumflex over ( )}((y%4)/4) for various integers (y%4) are calculated and stored in a table in advance. Then, an integer (y%4) is used as an address for referencing the table so as to obtain the value of 2{circumflex over ( )}((y%4)/4) for the integer (y%4).
FIG. 30
illustrates the contents of a second table for use with a conventional decoding device. The second table illustrated in
FIG. 30
contains values of g(y) for the address values (y%4) in the range from 0 to 3. The values of g(y) are obtained by normalizing values of 2{circumflex over ( )}((y%4)/4) so that none of them exceeds 2.0.
After such a table is provided, the value of Expression (2) can be obtained. First, the first table illustrated in
FIG. 29
is referenced using an input integer x as an address so as to obtain the normalized value f(x) for x{circumflex over ( )}(4/3). Then, (y%4) is calculated for a given integer of y. Subsequently, the calculated value of (y%4) is used as an address to obtain a value of g(y)=2{circumflex over ( )}((y%4)/4) from the second table illustrated in FIG.
30
. Then, a multiplier is used to calculate f(x)*g(y) so as to obtain a multiplied value f(x)*g(y)=h(x,y). Since the obtained value f(x) is within the range of ±1 while the obtained value g(y) is within the range of ±2, the multiplication result h(x,y) should always has a value in the range of ±2.
Then, h(x,y) is multiplied by 2{circumflex over ( )}int(y/4) so as to obtain a multiplied value i(x,y) as a calculation result of Expression (2). The multiplication can be performed by a bit shift operation. In the bit shift operation, it is assumed that a limit operation (so called a “clipping operation”) is performed when the final calculation result exceeds the range of ±2. Thus, in the prior art, the calculation i(x,y)=x{circumflex over ( )}(4/3)*2{circumflex over ( )}(y/4) is performed using a large-capacity table.
Use of the above conventional method for obtaining a value of x{circumflex over ( )}(a/b) requires a large memory area for the table containing different values of x{ci

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