JP2010032762A - Arithmetic processing unit and method, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To precisely and easily compute an exponential. <P>SOLUTION: A mantissa/exponent separation part 101 separates an input value X=(1+X<SB>1</SB>/2<SP>23</SP>)×(2^X<SB>2</SB>) into a mantissa X<SB>1</SB>in a mantissa of a floating point, and an exponent X<SB>2</SB>in an exponential part. An integer/decimal separation part 102 separates a product (X<SB>2</SB>×Y)=X<SB>int</SB>×X<SB>amari</SB>of the exponent X<SB>2</SB>and an exponent Y into an integer X<SB>int</SB>and a decimal X<SB>amari</SB>. An exponential computing part 105 finds a computation value P=X<SP>Y</SP>=(1+X<SB>1</SB>/2<SP>23</SP>)<SP>Y</SP>×(2^X<SB>amari</SB>)×(2^X<SB>int</SB>), based on the mantissa X<SB>1</SB>, the integer X<SB>int</SB>and the decimal X<SB>amari</SB>. The exponential computing part 105 acquires therein an exponential value (1+X<SB>1</SB>/2<SP>23</SP>)<SP>Y</SP>of the mantissa of the input value X, and an exponential value (2^X<SB>amari</SB>) of a base of the input value, from a table, using the mantissa X<SB>1</SB>and the decimal X<SB>amari</SB>. The present invention is applicable for a quantization device. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to an arithmetic processing device and method, and a program, and more particularly, to an arithmetic processing device and method, and a program that can perform a power operation with higher accuracy.

  The MPEG (Moving Picture Expert Group) audio standard is known as a method for encoding an audio signal. The MPEG audio standard has multiple encoding methods, but the ISO / IEC (International Organization for Standardization / International Electrotechnical Commission) 13818-7 standardized the MPEG-2 audio standard AAC (Advanced Audio Coding). ing.

  Further, an expanded ISO / IEC 14496-3 standardizes an MPEG-4 audio standard AAC encoding method. Hereinafter, the MPEG-2 audio standard AAC and the MPEG-4 audio standard AAC are collectively referred to as the AAC standard.

  FIG. 1 shows a configuration of a conventional encoding device compliant with the AAC standard.

  The encoding device includes an auditory psychological model holding unit 11, a gain control unit 12, a spectrum processing unit 13, a quantization / encoding unit 14, and a multiplexer unit 15.

  The audio signal input to the encoding device is supplied to the psychoacoustic model holding unit 11 and the gain control unit 12. The psychoacoustic model holding unit 11 blocks the supplied audio signal along the time axis, analyzes the blocked audio signal for each divided band according to human auditory characteristics, and determines the allowable error intensity of each divided band. calculate.

  The gain control unit 12 is used only for an SSR (Scalable Sampling Rate) profile, divides the supplied audio signal into four equally spaced frequency bands, and performs gain adjustment for bands other than the lowest band.

  The spectrum processing unit 13 converts the audio signal whose gain has been adjusted by the gain control unit 12 into spectrum data in the frequency domain. Further, the spectrum processing unit 13 controls each part of the spectrum processing unit 13 based on the allowable error intensity supplied from the auditory psychological model holding unit 11 and performs predetermined processing on the spectrum data.

  The spectrum processing unit 13 includes an MDCT (Modified Discrete Cosine Transform) unit 21, a TNS (Temporal Noise Shaping) processing unit 22, an intensity / coupling unit 23, a prediction unit 24, and an M / S (Middle / Side Stereo) stereo unit. 25.

  The MDCT unit 21 converts the time-domain audio signal supplied from the gain control unit 12 into spectrum data in the frequency domain. The TNS processing unit 22 processes the audio signal converted into the spectrum data by the MDCT unit 21 and adjusts the temporal shape of the quantization noise. The intensity / coupling unit 23 performs a stereo correlation encoding process on the audio signal processed by the TNS processing unit 22.

  The prediction unit 24 performs prediction encoding using the audio signal that has been stereo correlation encoded in the intensity / coupling unit 23 and the audio signal supplied from the quantization unit 27, and the audio signal obtained as a result thereof Is supplied to the M / S stereo unit 25. The M / S stereo unit 25 stereo-encodes the audio signal from the prediction unit 24 and supplies the audio signal to the quantization / encoding unit 14.

  The quantization / encoding unit 14 converts the audio signal from the M / S stereo unit 25 into a code string and supplies it to the multiplexer unit 15. The quantization / encoding unit 14 includes a normalization coefficient unit 26, a quantization unit 27, and a Huffman encoding unit 28.

  The normalization coefficient unit 26 supplies the audio signal from the M / S stereo unit 25 to the quantization unit 27, calculates a normalization coefficient used for quantization of the audio signal based on the audio signal, and performs quantization. To the unit 27 and the Huffman encoding unit 28. For example, the allowable error intensity from the psychoacoustic model holding unit 11 is used, and the quantization step parameter is calculated as a normalization coefficient for each divided band.

  The quantization unit 27 nonlinearly quantizes the audio signal supplied from the normalization coefficient unit 26 using the normalization coefficient from the normalization coefficient unit 26, and the audio signal (quantization value) obtained as a result is Huffman. The data is supplied to the encoding unit 28 and the prediction unit 24. The Huffman encoding unit 28 performs normalization by giving a Huffman code to each of the normalization coefficient from the normalization coefficient unit 26 and the quantization value from the quantization unit 27 based on a predetermined Huffman code table. The quantization coefficient and the quantized value are Huffman encoded and supplied to the multiplexer unit 15.

  The multiplexer unit 15 is supplied with the gain control unit 12 and the MDCT unit 21 through the normalization coefficient unit 26, and various information generated in the process of encoding the audio signal, and the Huffman code from the Huffman encoding unit 28. Are multiplexed to generate and output a bit stream of the encoded audio signal.

  In addition, the non-linear quantization of the audio signal in the quantization unit 27 is performed by using the value of the audio signal from the normalization coefficient unit 26 as the input value AX and the quantization step parameter as the normalization coefficient from the normalization coefficient unit 26 as q. Then, the calculation is performed by calculating the following equation (1). That is, Equation (1) is calculated, and the quantized value Z is obtained from the input value AX of the audio signal.

  In Expression (1), (int) (A) indicates an operation for obtaining an integer part by truncating the decimal part of the floating-point number A.

In the encoding of the AAC standard, the quantized value Z is defined as 14 bits. Therefore, the value AY = AX / 2 ^{q / 4} before quantization is calculated as 0 ≦ AY <8191.5943 ^(4/3) A value in the range of Therefore, the quantized value Z is an integer in the range of 0 ≦ Z ≦ 8191, and the quantization step parameter q is determined so that the quantized value Z is a value within this range.

  Further, when the audio signal is quantized, the quantizing unit 27 inversely quantizes the quantized values Z for all the input values AX, and confirms whether the quantization error is within a predetermined range. For example, the inverse quantization is performed by the calculation of the following equation (2), and the inverse quantization value W is obtained.

  Further, the quantization error is obtained by obtaining a difference between the inverse quantized value W and the input value AX, and it is determined whether or not the difference is a value within a predetermined range.

  By the way, conventionally, there has been proposed a method for efficiently obtaining a power calculation result such as the third power in Equation (1) and the fourth power in Equation (2) (for example, Patent Document 1). reference). Patent Document 1 discloses that a constant exponent, Y = A / B (where A = 3, B = 4), is used to calculate an arbitrary variable X to the Y power using a table. Has been. That is, the paragraph of number 63 of Patent Document 1 describes that “the mantissa part is obtained by searching the ROM table for the decimal part u”, and the u powers of the variable X are obtained using u tables. Desired.

  Specifically, in Japanese Patent Application Laid-Open No. 2004-228620, power calculation is performed according to the procedure described below.

  First, when an operation value obtained as an operation result of the variable X raised to the power Y is P, the relationship of the following equation (3) is established.

Next, the input variable X is separated into a mantissa X ₁ and an exponent X ₂ based on the specifications of the C language functions frexp and ldexp as shown in Expression (4). Here, the range of possible values of the mantissa X ₁ is 0.5 or more and less than 1.0.

  Substituting this equation (4) into equation (3) yields the following equation (5).

Furthermore, when the integer part of X ₂ × A / B in the formula (5) is X _int and the decimal part is X _amari , the formula (5) is expressed by the formula (6), and the integer part X _int and the decimal part X _amari is represented by formula (7) and formula (8), respectively.

Note that (int) (A) in equation (7) indicates an operation to obtain an integer part by truncating the decimal part of the floating-point number A (the same applies to the following description). Moreover, in Formula (8),% means modulo and has shown the process which calculates | requires the remainder which divided (X < ₂ > * (BA)) by B. FIG.

Further, a table for obtaining (X ₁ ^ (A / B)) × (2 ^ X _amari ) in the equation (6) from the mantissa X ₁ and the decimal part X _amari and the mantissa X ₁ is 0.5 or more and less than 1.0. Tables for adjusting the index X ₂ are prepared, and the calculation value P is obtained as the calculation result of the variable X to the Y power by performing the calculation of Expression (6) using these tables. Note that “^” represents a power, and for example, “2 ^ X _amari ” represents 2 to the power of X _amari . The same applies to “^” in the following description.

  The quantizing device that performs exponentiation and quantizes the audio signal as described above is configured as shown in FIG.

  The quantizing device 51 corresponds to the quantizing unit 27 in FIG. 1, and the quantizing device 51 is supplied with the value AY before quantization in the equation (1) as a variable X and with a power exponent Y. The

The mantissa / exponent separator 61 separates the supplied variable X into a mantissa X ₁ and an exponent X ₂ , supplies the exponent X ₂ to the integer / decimal separator 62, and supplies the mantissa X ₁ to the power calculator 63. To do. The integer / decimal separator 62 obtains the integer part X _int and the decimal part X _amari of the product of the exponent X ₂ from the mantissa / exponent separator 61 and the supplied exponent Y and supplies the integer part X _int to the power calculator 63. .

The power table holding unit 64 holds a power table for obtaining a mantissa P _amari when a calculation value P to be obtained is expressed as a floating point from the mantissa X ₁ and the decimal part X _amari . Also, index adjustment table holding section 65, the integer part X _int and fractional part X _amari, holds the adjustment table for obtaining an adjustment value of the exponent P _int when the calculated value P and the floating-point representation.

The exponent operation unit 63 uses the mantissa X ₁ from the mantissa / exponent separator 61 and the integer part X _int and the fraction part X _amari from the integer / decimal separator 62 to calculate the mantissa P _amari and exponent of the operation value P by obtaining the P _int, it performs calculation of the variable X Y th power of. At this time, the power calculation unit 63 obtains the mantissa P _amari and the adjustment value using the power table of the power table holding unit 64 and the exponent adjustment table of the exponent adjustment table holding unit 65. The index P _int is obtained from the integer part X _int and the adjustment value.

  The integer conversion unit 66 extracts an integer part of a number obtained by adding a predetermined constant α to the operation value P obtained by the power operation unit 63, and the extracted integer part is quantized to the input variable X Output as value Z. In this case, the constant α is set to “−0.0946 + 0.5” in Expression (1).

  Next, the quantization processing by the quantization device 51 will be described with reference to the flowchart of FIG.

  In step S11, the power table holding unit 64 and the exponent adjustment table holding unit 65 generate a power table and an exponent adjustment table.

That is, when the table size is 2 ^N = SIZE, the power table holding unit 64 generates a power table made up of the value frc [i] [j] of the mantissa P _amari shown in the following equation (9).

In the expression (9), the variable i values of the mantissa _{P amari frc [i] [j} ] indicates the value of the index index1 obtained from mantissa X _1, variable i = 0, · · ·, (SIZE -1). Further, the variable j of frc [i] [j] indicates the value of the decimal part X _amari , and variables j = 1,..., (B-1). “B” in the variable j is B in the power index Y = A / B.

  Furthermore, frctmp in equation (9) is a value obtained from equation (10).

  Note that the value frc [i] [0] in equation (10) is a value obtained from equation (11).

  Here, “A” and “B” in the equations (10) and (11) are also A and B in the power index Y = A / B.

In this way, the power table holding unit 64 generates and holds a power table made up of each value frc [i] [j] of the mantissa P _amari determined by the index index1 and the decimal part X _amari .

Also, index adjustment table holding section 65, the table size as the 2 ^N = SIZE, and generates an exponent adjustment table of adjustment values of the exponent _{P int exp [i] [j} ] shown in the following equation (12).

  Here, the variables i and j of the adjustment value exp [i] [j] are the same as the variables i and j in frc [i] [j], and frctmp in the equation (12) is the above-described equation (10). It is obtained by. The adjustment value exp [i] [0] is set to 0.

The exponent adjustment table holding unit 65 generates and holds an exponent adjustment table including adjustment values exp [i] [j] determined by the index index1 and the decimal part X _amari .

Note that the value frc [i] [j] of the mantissa P _amari described above and the adjustment value exp [i] [j] are values when a power exponent Y = A / B = 3/4 is assumed. Yes, in order to make the numerator “A” and denominator “B” of the power exponent Y arbitrary values, frc [i] [j] so that 0.5 ≦ frc [i] [j] <1.0 ] And the adjustment value exp [i] [j] must be obtained.

When power table and index adjustment table is created, in step S12, mantissa / exponent separation unit 61, using the C language function frexp, obtains the mantissa X ₁ and exponent X ₂ of the supplied variable X. Here, the mantissa X ₁ is a value not less than 0.5 and less than 1.0.

The mantissa / exponent separation unit 61 supplies the obtained mantissa X ₁ to the power operation unit 63 and supplies the exponent X ₂ to the integer / decimal separation unit 62.

In step S13, integer / fraction separation unit 62, an exponent X ₂ from mantissa / exponent separation unit 61 performs the calculation of Equation (7) and (8) by using the index Y should have been supplied, exponent The integer part X _int and the fractional part X _amari of the product of X ₂ and the exponent Y = A / B are obtained.

In step S14, the power calculation unit 63 includes a mantissa X ₁ from mantissa / exponent separator unit 61, by using the integer part X _int and fractional part X _amari from integer / fraction separator 62, a variable X-th power Y The operation value P obtained in this way is obtained.

  That is, the power calculation unit 63 calculates the following equation (13) to subtract the desired values of frc [i] [j] and exp [i] [j] from the power table and the exponent adjustment table. Find the index index1 to be used.

Then, the power calculation unit 63 calculates the mantissa P _amari of the calculation value P shown in Expression (14) using the obtained index index1 and the decimal part X _amari from the integer / decimal number separation unit 62.

That is, the power calculation unit 63 acquires frc [index1] [X _amari ] from the power table of the power table holding unit 64, and sets the value of this frc [index1] [X _amari ] as the mantissa P _amari .

Further, the power calculation unit 63 acquires the adjustment value exp [index1] [X _amari ] specified from the index index1 and the decimal part X _amari from the exponent adjustment table of the exponent adjustment table holding unit 65. Further, the power calculation unit 63 calculates the following expression (15) using the acquired adjustment value exp [index1] [X _amari ] and the integer part X _int from the integer / decimal separator 62, and calculates the calculated value P The index P _int is obtained.

The exponent operation unit 63 obtains the mantissa P _amari and the exponent P _int of the operation value P, synthesizes the mantissa P _amari and the exponent P _int using the C language function ldexp, and obtains the result of the exponentiation of the floating-point number. The calculated value P is obtained and supplied to the integer conversion unit 66.

  In step S15, the integer conversion unit 66 obtains and outputs the quantized value Z of the variable X using the calculated value P from the power calculating unit 63, and the quantization process ends.

  That is, the integer conversion unit 66 calculates the following equation (16) from the calculated value P and a predetermined constant α to obtain the quantized value Z.

  As described above, the quantizing device 51 calculates the power of the input variable X to obtain the quantized value Z.

JP 2002-344316 A

  However, with the above-described technique, it has been difficult to perform power calculations easily and accurately with a small amount of memory.

  For example, in the technique described in Patent Document 1, calculation using the numerator A and the denominator B of power exponent Y = A / B is performed individually. Therefore, the technique described in Patent Document 1 uses power index Y as a fraction. It can only be applied to exponentiation when expressed.

Also, the number of mantissa P _amari values frc [i] [j] for variables i and j, that is, the number of power tables is required to be SIZE × B, and an index for adjusting variable X to the specifications of functions frexp and ldexp. The number of adjustment values, that is, the number of index adjustment tables is required to be SIZE × B. Therefore, depending on the value of the denominator B of the power exponent Y, a huge amount of memory is required to record the power table and the exponent adjustment table.

  Furthermore, even if an attempt is made to directly calculate a power without using a power table or an exponent adjustment table, the mantissa and exponent of the variable X are based on the specifications of the C language functions frexp and ldexp. It is different from the mantissa and exponent of numbers. Therefore, it is not easy to replace a part of the quantization device 51 with an arithmetic unit that performs a floating point number operation.

  Furthermore, if the power calculation accuracy is to be increased, it is necessary to increase the size of the power table and the exponent adjustment table. Conversely, if the size of these tables is reduced, the power calculation accuracy is reduced.

  Specifically, the following equation (17) is calculated using a set of L data composed of the power value P calculated by the quantization device 51 and the power value Q calculated using a mathematical library. Then, consider calculating the relative error average T to evaluate the calculation accuracy.

In Equation (17), P _i indicates the i-th sample of the power value P (calculated value P) calculated by the quantization device 51, and Q _i is the Q obtained by the mathematical library. The corresponding number is shown.

The applicant calculated exponent (Y) with exponent Y = 3/4 and L = 8192, and evaluated the calculation accuracy of the power value P (calculation value P) by the quantization device 51. The table size When ^N in 2 ^N is 8, that is, when SIZE = 256, the relative error average T = 8.25 × 10 ⁻⁴ , and so high accuracy could not be obtained. Further, when ^N in the table size 2 ^N is 16, that is, when SIZE = 65536, the relative error average T = 2.56 × 10 ⁻⁸ , which is higher than in the case of N = 8.

  However, in order to increase the calculation accuracy of the power calculation value P, if the size of the power table and the exponent adjustment table is SIZE = 65536, a total of 524288 (= 65536 × 4 × 2) tables are required. The memory capacity for recording the table becomes tight.

  Further, for example, as shown in the equation (1), when an audio signal is quantized, an arithmetic value P must be obtained by a power operation, and a constant α must be added before integerization. I couldn't easily find a power integer.

  The present invention has been made in view of such a situation, and makes it possible to perform a power operation more easily and accurately with a small amount of memory. Further, the present invention makes it possible to obtain a power integer more easily.

  An arithmetic processing apparatus according to a first aspect of the present invention is an arithmetic processing apparatus that performs a power operation of a predetermined input value X with a constant Y as a power exponent, and the input value X in floating-point type data Is expressed as a mantissa part X1 representing a mantissa when the input value X is represented by a floating point number, and an exponent X2 representing an exponent part representing the exponent when the input value X is represented by a floating point number. A mantissa / exponent separating means for separating, and an integer / decimal separating means for separating a product of the exponent X2 and the constant Y into an integer Xint that is an integer part of the product and a decimal Xamari that is a decimal part of the product A first recording means for recording a power value of the mantissa of the input value X with the constant Y as a power exponent, which is determined with respect to the mantissa X1, and the decimal number Xamari determined with respect to the decimal number Xamari. Finger A second recording means for recording a power value of a base when the input value X is expressed by a floating-point number; and the power of the mantissa acquired from the first recording means using the mantissa X1 A power operation for calculating a power of the input value X using the constant Y as a power exponent from the value, the power value of the base obtained from the second recording means using the decimal number Xamari, and the integer Xint Means.

  The arithmetic processing device further includes an interpolating unit that performs interpolation using a plurality of power values obtained from the first recording unit using the mantissa X1 and obtains the power value of the final mantissa. The power calculation means includes the input value X with the constant Y as a power exponent from the power value of the base, the integer Xint, and the power value of the mantissa obtained by the interpolation means. The power of can be calculated.

  The arithmetic processing device further includes an interpolation unit that performs interpolation processing using a plurality of power values acquired from the second recording unit using the decimal number Xamari, and obtains the final power value of the base. The power calculation means includes the input value X with the constant Y as a power exponent from the power value of the mantissa, the integer Xint, and the power value of the base obtained by the interpolation means. The power of can be calculated.

  The arithmetic processing method or program according to the first aspect of the present invention floats the input value X in floating-point type data when performing a power operation of a predetermined input value X with a constant Y as a power exponent. The input value X is separated into a mantissa X1 which is a mantissa part representing a mantissa when expressed in a decimal number and an exponent X2 which is an exponent part representing an exponent when the input value X is represented as a floating point number. , The product of the exponent X2 and the constant Y is separated into an integer Xint that is an integer part of the product and a fraction Xamari that is a fractional part of the product, and the mantissa X1 obtained using the mantissa X1 The input value X is a floating-point number that is determined with respect to the decimal number Xamari obtained by using the mantissa power value of the input value X with the constant Y as an exponent and the decimal number Xamari. Exponential value to the fractional Xamari to the index of the bottom when revealed, and the integer Xint, and with the constant Y the exponent comprises the step of calculating the power of the input value X.

In the first aspect of the present invention, when performing a power operation of a predetermined input value X with a constant Y as a power exponent, the input value X in floating point type data is expressed by a floating point number. The input value X is separated into a mantissa X ₁ which is a mantissa part representing the mantissa of the hour and an exponent X ₂ which is an exponent part representing an exponent when the input value X is represented by a floating-point number, and the exponent The constant Y, wherein the product of X ₂ and the constant Y is separated into an integer X _int that is an integer part of the product and a decimal number X _amari that is a decimal part of the product, and is determined with respect to the mantissa X ₁ is recorded exponential value of the mantissa of the input value X to the exponent determined with respect to the fractional X _amari, wherein the fractional X _amari to the index, when representing said input values X in the floating-point number the exponential value of the bottom recording, said mantissa X ₁ are used Obtained by said power value of the mantissa, the exponent value of the said bottom fraction X _amari is acquired is used, and from the integer X _int, and the exponent of the constant Y, a power of the input value X Is calculated.

  An arithmetic processing unit according to a second aspect of the present invention is an arithmetic processing unit that obtains an integer of a power value of a predetermined input value X with a constant Y as a power exponent, and the input value in floating-point type data The input value X1 is a mantissa X1 that is a mantissa representing a mantissa when X is represented by a floating-point number, and an exponent X2 that is an exponent representing an exponent when the input value X is represented by a floating-point number. An integer / decimal separator that separates a product of the exponent X2 and the constant Y into an integer Xint that is an integer part of the product and a decimal Xamari that is a decimal part of the product A power value of the mantissa of the input value X with the constant Y as a power exponent, and the input value X with a power of the decimal number Xamari, which is determined with respect to the mantissa X1 When the bottom of Indicates the number obtained by subtracting the integer Xint from the number of bits from the least significant bit of the fixed-point data to the decimal point position with respect to the fixed-point data that indicates the product with the raised value Power integer conversion means for performing a right shift operation by the number of bits and obtaining the integer of the power value of the input value X.

  The arithmetic processing unit includes a first recording unit that records the power value of the mantissa of the input value X, which is determined with respect to the mantissa X1, and the power value of the base that is determined with respect to the decimal number Xamari. A second recording means for recording, wherein the power integer conversion means uses the power value of the mantissa obtained from the first recording means using the mantissa X1 and the decimal number Xamari. The integer of the power value of the input value X can be obtained using the power value of the base acquired from the second recording means.

  The arithmetic processing device further includes an interpolating unit that performs interpolation using a plurality of power values obtained from the first recording unit using the mantissa X1 and obtains the power value of the final mantissa. The power integer converting means may be configured to obtain the integer of the power value of the input value X using the power value of the mantissa obtained by the interpolation means.

  The arithmetic processing device further includes an interpolation unit that performs interpolation processing using a plurality of power values acquired from the second recording unit using the decimal number Xamari, and obtains the final power value of the base. The power integer converting means may be configured to obtain the integer of the power value of the input value X using the power value of the base obtained by the interpolation means.

  When the arithmetic processing method or program according to the second aspect of the present invention obtains an integer that is a power value of a predetermined input value X with a constant Y as a power exponent, the input value X in the floating-point data is calculated. The input value X is separated into a mantissa X1 which is a mantissa part representing a mantissa when expressed in a floating-point number and an exponent X2 which is an exponent part representing an exponent when the input value X is represented as a floating-point number. The constant Y, which is determined by dividing the product of the exponent X2 and the constant Y into an integer Xint that is an integer part of the product and a decimal number Xamari that is a fractional part of the product, is determined with respect to the mantissa X1 A fixed-point indicating a product of the exponent value of the mantissa of the input value X having a power exponent and the power value of the base when the input value X is expressed as a floating-point number with the decimal number Xamari as a power exponent Day On the other hand, a right shift operation is performed by the number of bits indicating the number obtained by subtracting the integer Xint from the number of bits from the least significant bit of the fixed-point data to the decimal point position, and the input value Determining the integer value of the power of X.

  In the second aspect of the present invention, when obtaining an integer of a power value of a predetermined input value X with a constant Y as a power exponent, the input value X in floating point type data is expressed by a floating point number. The input value X is separated into a mantissa X1 which is a mantissa part representing a mantissa when the input value X and an exponent X2 which is an exponent part representing an exponent when the input value X is represented by a floating-point number, and the exponent X2 And the constant Y are separated into an integer Xint that is an integer part of the product and a decimal Xamari that is a fractional part of the product, and the constant Y determined for the mantissa X1 is a power exponent Fixed-point data indicating the product of the exponent value of the mantissa of the input value X and the power value of the base when the input value X is expressed as a floating-point number with the decimal number Xamari as a power exponent On the other hand, A right shift operation is performed by the number of bits indicating the number obtained by subtracting the integer Xint from the number of bits from the least significant bit of the decimal point data to the decimal point position, and the power value of the input value X is calculated. The integer is determined.

  According to the first aspect of the present invention, a power can be calculated. In particular, according to the first aspect of the present invention, it is possible to perform power calculation more easily and accurately with a small amount of memory.

  Further, according to the second aspect of the present invention, it is possible to perform an operation for obtaining a power integer. In particular, according to the second aspect of the present invention, it is possible to perform an operation for obtaining a power integer in a simpler and more accurate manner.

  Embodiments to which the present invention is applied will be described below with reference to the drawings.

[First Embodiment]
First, an outline of processing performed by the arithmetic processing device to which the present invention is applied will be described.

  The arithmetic processing apparatus to which the present invention is applied performs an operation for obtaining the Y power of the input value X. At this time, the arithmetic processing unit may use an IEEE (Institute) so that the exponent Y, which should be a constant, can perform a power operation regardless of any value such as a floating point number such as Y = 3.141592. for electrical and electronics engineering), using floating point mantissa and exponent based on 754.

For example, as shown in FIG. 4, the floating-point type data indicating a single-precision floating-point number based on the IEEE754 standard is composed of a 32-bit bit string. That is, the portion from bit 0 is the least significant bit of the data of the floating-point number to a 22 th bit is a mantissa X ₁ is a mantissa representing the mantissa of the floating-point number, up to 30 bit from 23 bit Is the exponent X ₂ which is the exponent part representing the exponent of the floating-point number, and the most significant 31st bit is the sign bit S.

Here, the sign bit S is “0” when the mantissa part is positive, and is “1” when the mantissa part is negative. The bit structure of the exponent part is “exponent + bias”. Therefore, the exponent X _{2 of the} exponent part is a value obtained by adding a bias to the actual exponent value. For example, in the IEEE754 standard, 127 is used as a single precision bias. Therefore, when the exponent value is “0”, the value of the exponent X ₂ is “127” (= 0 + 127), and the exponent part is 127. (0x7f) indicates that “7f” is a hexadecimal number.

  In addition, when the exponent part is 0 and 255, there is a special meaning, but the explanation is omitted.

  Thus, when the input value X represented by the floating-point type data is represented in a numerical expression format, the input value X is represented as shown in the following equation (18).

In Expression (18), “.X ₁ ” indicates that the mantissa part is expressed as a decimal point, assuming that the decimal point is located before the upper bits of the mantissa X ₁ . Further, “B” in Expression (18) indicates a bias component, and “S” indicates a sign bit.

The arithmetic processing unit performs an exponentiation operation by separating the input value X, which is a floating point number as described above, into a mantissa X ₁ and an exponent X ₂ . When the input value X is expressed by a floating-point number based on IEEE754, the input value X is expressed as shown in Expression (19).

In the formula (19), (1 + X 1/2 23) is a mantissa when representing the input value X in the floating-point number, X ₁ in the mantissa is in the floating-point data, the mantissa of the input value X Is a mantissa part (a mantissa X ₁ ). In Expression (19), X ₂ is an exponent part (exponent X ₂ ) representing the exponent of the input value X in the floating-point data. Further, in the equation (19), the radix (base) of the input value X expressed by a floating point number is 2.

Now, considering the calculation of the input value X to the Y power, the calculated value P = X ^Y obtained by this power calculation is expressed by the following equation (20).

Also, assuming that the integer part of “X ₂ × Y” in the expression (20) is an integer X _int and the decimal part is a decimal X _amari , the calculated value P, the integer X _int , and the decimal X _amari are respectively expressed by the expression (21) Thru | or Formula (23).

  Note that (int) (A) in the equation (22) indicates an operation for rounding off the decimal part of the floating-point number A to obtain an integer part, and is the same in the following description.

The arithmetic processing unit finally obtains a calculation value P obtained by raising the power of the input value X by a power exponent Y by obtaining the value of each term of Expression (21). Note that the case where the input value X = 0.0 is a special case as a floating-point number, and therefore it is separately obtained as the calculation value P = 0.0 ^Y = 0.

  Next, FIG. 5 shows a configuration example of an embodiment of an arithmetic processing apparatus to which the present invention is applied.

  The arithmetic processing unit 91 includes a mantissa / exponent separator 101, an integer / decimal separator 102, a mantissa power table holding unit 103, a decimal power table holding unit 104, a power operator 105, and an integer converter 106. . In the arithmetic processing unit 91, the input value X is supplied to the mantissa / exponent separator 101 and the exponent Y, which should be a constant, is supplied to the integer / decimal separator 102.

The mantissa / exponent separation unit 101 separates the supplied input value X into a floating-point number mantissa X ₁ and an exponent X ₂ based on IEEE 754, supplies the mantissa X ₁ to the power operation unit 105, and uses the exponent X _2. Is supplied to the integer / decimal separator 102. The integer / decimal separator 102 obtains an integer X _int and a decimal X _amari of the product of the exponent X ₂ from the mantissa / exponent separator 101 and the supplied exponent Y, and supplies them to the power calculator 105.

Power table holding unit 103 of the mantissa is determined by the value of the mantissa X _1, it holds the power table of mantissa that includes power value of the mantissa part of the input value X. That is, the mantissa power table is obtained from the mantissa X ₁ and used to specify the power value of the mantissa part of the input value X, and the mantissa of the input value X associated with the index index 1 Multiple sets of power values for parts are included. Here, the mantissa part of the input value X, represented by the formula (19) in the ^{_{(1 + X 1/2 23}} ), exponent of power is the exponent Y.

Power table storing unit 104 in decimal, Sadamari the value of the fractional X _amari, and fractional X _amari to the index, fraction containing the power of the value of the radix (base) when representing the input value X in the floating-point number Holds a power table. That is, in the power table of the decimal number, the index index2 obtained from the decimal number X _amari and used to specify the power value of the radix of the input value X, and the radix of the input value X associated with the index index2 Multiple sets with power values are included.

The power calculation unit 105 refers to the mantissa power table of the mantissa power table holding unit 103 and the mantissa power table of the decimal power table holding unit 104, and the mantissa X ₁ from the mantissa / exponent separation unit 101, The calculated value P is obtained from the integer X _int and the decimal number X _amari from the integer / decimal separator 102. The power calculation unit 105 supplies the calculated calculation value P to the integer conversion unit 106. The integer conversion unit 106 calculates and outputs the integer part of the number obtained by adding the constant α to the calculation value P from the power calculation unit 105.

In this way, the arithmetic processing unit 91 performs the exponentiation operation of the exponent Y with respect to the input value X, and an integer of the number obtained by adding a predetermined constant α to the operation value P = ^XY obtained as a result. Find the part and output it. Therefore, for example, when the input value X is (AX / 2 ^{q / 4} ) in the formula (1), the power index Y is 3/4, and the constant α is “−0.0946 + 0.5”, The arithmetic processing device 91 is a device corresponding to the quantization unit 27 of FIG. That is, in such a case, the arithmetic processing unit 91 is a quantization device that nonlinearly quantizes the input value X as an input audio signal.

  Next, with reference to the flowchart of FIG. 6, the power calculation process by the calculation processing device 91 will be described.

In step S41, the mantissa power table holding unit 103 generates a mantissa power table. That is, the mantissa power table holding unit 103 sets the mantissa power table size to 2 ^N = SIZE, and the floating point obtained by raising the mantissa part of the input value X shown in the following equation (24) to the Y power Generates a mantissa power table consisting of power values frctable [i] of type data.

Here, the table size SIZE is the number of numbers that can be represented by N-bit data, and power values frctable [i] corresponding to the number of table sizes SIZE are prepared. Further, the variable i of the exponential value frctable [i] indicates the value of the index index1 obtained from mantissa X _1, variable i = 0, · · ·, are (SIZE-1).

If the index index1 and many of the high-order bits of the value of the mantissa X _1, (1 + i / SIZE) ^Y in the formula (24), for the values of the mantissa X _1, obtained by multiplication Y mantissa part of the input value X the approximation of a value ^{_{(1 + X 1/2 23}} ) Y.

  When the mantissa power table holding unit 103 obtains each power value frctable [i] for each of the (SIZE) variable values i, the mantissa power table holding unit 103 associates the value i with the power value frctable [i]. To generate and hold a mantissa power table.

In step S42, the decimal power table holding unit 104 generates a decimal power table. That is, power table storing unit 104 in decimal, when the table size of the fractional powers table and 2 ^N = SIZE, 2 is a base of the input values shown in the following equation (25) X (calculated value P) X _amari Generates a power table of decimal numbers consisting of power values twotable [i] of floating-point data obtained by multiplication.

Here, the variable i of the power value twotable [i] indicates the value of the index index2 obtained from the decimal number X _amari , and the variable i = 0,..., (SIZE−1).

If the index index2 is a value of several high-order bits of the decimal number X _amari , 2 ^{(i / SIZE)} in equation (25 ⁾ is the power of the base value “2” of the input value X with respect to the value of the decimal number X _amari to the X _amari power The value of 2 ^ X _{amari is} an approximate value.

  When the power table holding unit 104 of decimal numbers obtains each power value twotable [i] for each of the values i of (SIZE) variables, the value i is associated with the power value twotable [i]. To generate and hold a power table of decimal numbers.

  Note that the process of generating the mantissa power table and the decimal power table may be performed once before the power calculation of the input value X. In other words, once these tables are generated, then when performing a power operation of the input value X, a mantissa power table and a decimal power table already generated and held may be used.

In step S43, the mantissa / exponent separating unit 101 obtains the mantissa X ₁ and exponent X ₂ of the supplied input values X, to supply a mantissa X ₁ in exponentiation unit 105, the index X ₂ integer / fraction separation To the unit 102.

Here, for example, when the input value X is the floating-point type data shown in FIG. 4, the lower 23 bits of the input value X data are the mantissa X ₁ data, and the input value X data the value obtained by subtracting the bias value from 8 bits portion from 30 bit to 23 bit of is the exponent X ₂ data. That is, the mantissa X ₁ and the exponent X ₂ are integer type data representing the mantissa part and the exponent part of the floating-point number.

In step S 44, the integer / decimal separator 102 obtains an integer X _int and a decimal X _amari of the product of the exponent X ₂ from the mantissa / exponent separator 101 and the supplied exponent Y, and Supply.

Specifically, the integer / decimal separator 102 obtains the product (X ₂ × Y) of the exponent X ₂ and the power exponent Y, and uses the product to obtain the integer X _int by the following equation (26).

That is, when the product (X ₂ × Y) is 0 or more, the integer part of the product is extracted to be an integer X _int, and when the product (X ₂ × Y) is less than 0, An integer part of the product is extracted, and a value obtained by further subtracting 1 from the integer part is set as an integer X _int . The integer X _int data is integer type data.

Further, the integer / decimal separator 102 uses the product (X ₂ × Y) to obtain the decimal X _amari by the following equation (27).

In the equation (27), the integer part of the value obtained by multiplying the product (X ₂ × Y) by subtracting the integer part of the product (difference) and further multiplying by 2 ²³ is defined as the decimal X _amari. . That is, the value of the fractional part of the product (X ₂ × Y) can be obtained by obtaining the difference between the product (X ₂ × Y) and the integer part of the product. Then, by multiplying the 2 ²³ to the value of the fractional part, by extracting the integer part of a value obtained as a result, the fractional part of the product (X ₂ × Y) is, the decimal point is positioned in the 23 th bit fixed Converted to decimal data.

In step S45, the power calculation unit 105, by using the mantissa X ₁ supplied from the mantissa / exponent separation unit 101, a power value ^{_{(1 + X 1/2 23}} ) Y mantissa part of the input value X for the exponent Y Ask.

That is, the power calculation unit 105 calculates the following equation (28) to obtain the value of the upper N bits from the 22nd bit of the mantissa X ₁ as the index index1, and uses the index index1 to The power value of the mantissa part of the input value X is obtained.

In Expression (28), “>>” indicates a right shift. As shown in FIG. 4, since the mantissa X ₁ is a 23-bit value, if the mantissa X ₁ (23-N) bits shifted right, it is possible to retrieve the value of the upper N bits of the mantissa X ₁ .

The exponent operation unit 105 uses the value of the upper N bits extracted from the mantissa X ₁ as the index index 1, and sets the exponent value frctable [index 1] with the index index 1 as the value of the variable i as the mantissa of the mantissa power table holding unit 103. Get from the power table. Then, the obtained exponential value frctable [index1] is, power of the value of the mantissa part of the input value _{X (1 + X 1/2} 23) are ^Y.

In step S _<b > 46, the power calculation unit 105 uses the decimal number X _amari supplied from the integer / decimal number separation unit 102 to obtain a power of 2 that is a radix of the input value X using the decimal number X _amari as a power exponent.

  That is, the power calculation unit 105 calculates the following expression (30) and expression (31) to obtain the index index2, and uses the index index2 to calculate the power of the radix of the input value X from the expression (32). Ask for.

  In Expression (30), “>>” indicates a right shift, and in Expression (31), “&” indicates a logical product operation.

That is, the power calculation unit 105, by right shifting the fraction X _amari only (23-N) bits, retrieve the values of the upper bits from the (23-N) th bit of the fraction X _amari and index2 '. Here, the fractional X _amari by calculation of equation (27), since there is a fixed-point number-point position is 23 bit, right shifting the fraction X _amari only (23-N) bits, the fractional X _amari The value of the upper bit is extracted from the (23-N) th bit of the decimal part.

The power calculation unit 105 obtains an N-bit index index2 by performing an AND operation between the index2 ′ obtained in this way and (SIZE−1), and uses the index index2 as the value of the variable i. The raised power value twotable [index2] is obtained from the power table of decimal numbers in the power table holding unit 104 of decimal numbers. Then, the acquired power value twotable [index2] is set to a power value of 2 (2 ^ (X _amari )) as a radix.

Here, by performing a logical AND operation of formula (31), when the product of formula (26) (X ₂ × Y) is negative, and one subtraction from integer product (X ₂ × Y) Is equivalent to performing the following operation. That is, the operations of the equations (31) and (26) subtract 1 from the product integer X _int when the fraction X _amari in the product (X ₂ × Y) = (X _int × X _amari ) is negative. This is equivalent to adding 1 to the product decimal X _amari .

  When such an operation is performed, the number of conditional branches required when the power value specified by the index index2 is obtained from the power table of the decimal number using the index index2 can be reduced, and the power can be raised more quickly. You will be able to get the value.

  In addition, when the exponentiation operation of 2 is performed by dividing into a power exponent fraction and an integer using a table, by adding 1 to the decimal and subtracting 1 from the integer when the power exponent is negative, A technique for reducing the number of conditional branches for table lookup is described in Japanese Patent Application Laid-Open No. 2004-172700.

As described above, the power of a value ^{_{(1 + X 1/2 23}} ) Y, power value (2 ^ (X _amari)) and is determined by the table lookup.

In step S47, the power calculation unit 105, using power of a value ^{_{(1 + X 1/2 23}} ) Y, and the power of the value _{(2 ^ (X amari))} , and integer X _int from Integer / fractional separation unit 102 To obtain the calculated value P.

  That is, the power calculation unit 105 obtains the calculated value P by calculating the following equation (33).

Here, in the formula (33), ^{_{"(1 + X 1/2 23}} ) Y " so and "2 ^ X _amari" has already been obtained, and exponent integer X _int, is the cardinality of the input value X What is necessary is just to obtain | require the value of 2 power "2 ^ _Xint ".

Therefore, the power calculation unit 105 calculates the power value “2 ^ X _int ” by calculating Expression (34).

In Expression (34), “<<” indicates a left shift. That is, the power calculating section 105, power value "2 ^ X _int" to be obtained, i.e. the calculated value P, to the floating-point format data based on the IEEE754, bias component to the integer X _int " 127 "is added and left shifted by 23 bits.

The left shift operation is performed because, as shown in FIG. 4, the exponent part of the floating-point number is the part from the 30th bit to the 23rd bit in the data. As a result, floating-point type data whose exponent is “X _int +127” is obtained. Incidentally, exponential value ^{_{(1 + X 1/2 23}} ) Y and exponential value (2 ^ X _amari) are also adapted to be a floating-point data in advance by or operation.

Further, exponentiation unit 105, ^{_{"(1 + X 1/2 23}} ) Y ", "2 ^ X _amari", and "2 ^ X _int" and by substituting the equation (33) described above, the calculated value P Get the floating-point data shown. The calculation value P obtained in this way is supplied from the power calculation unit 105 to the integer conversion unit 106.

  In step S48, the integer conversion unit 106 converts the calculation value P supplied from the power calculation unit 105 into an integer and outputs it, and the power calculation process ends.

  That is, the integer conversion unit 106 calculates the following equation (35) to obtain the integer part of the number obtained by adding the constant α to the operation value P, and the obtained value is converted into an integer operation value. Output as an output value P.

As described above, the processing unit 91 separates the input value X in mantissa X ₁ and exponent X ₂ floating-point numbers, and mantissa X _1, fractional X _amari obtained from the exponent X ₂ and exponent Y and by using the integer X _int, it calculates the power of the input value X.

In this way, by calculating the power of the input value X using the mantissa X ₁ obtained from the input value X, the decimal number X _amari and the integer X _int, it is simpler and easier for any input value X. The power can be calculated with high accuracy.

That is, by performing the power operation in this way, the power exponent is not limited to a fractional expression, and even if it is a floating-point number such as Y = 3.141592, the power can be quickly raised with simple processing. Can be performed. In addition, since the calculation using the mantissa X ₁ and the exponent X ₂ of the floating-point number is performed, complicated processing using the conventional exponent adjustment table shown in the above-described equation (12) is not necessary.

  Furthermore, using (SIZE) mantissa power tables and (SIZE) fractional power tables, that is, using only a total of (SIZE x 2) tables, the power calculation can be performed easily and quickly. It can be carried out. In particular, compared with the example of the conventional patent document 1, the number of tables can be reduced to 1 / B, and the memory capacity of the memory storing the tables can be greatly reduced.

  In the above description, an example in which the mantissa power table and the decimal power table have the same table size has been described. However, the table sizes may be different depending on required accuracy.

  Further, the format (format) of the floating point number is not limited to the single precision floating point format, and may be a double precision floating point format.

[Second Embodiment]
By the way, the present applicant sets power exponent Y = 3.141592 and uses L = 8192 data to calculate the above-described equation (17), thereby calculating the power of the arithmetic processing unit 91 based on the relative error average T. When N = 8, that is, when the table size SIZE = 256, T = 6.0 × 10 ⁻³ . Further, when N = 16, that is, when the table size SIZE = 65536, T = 3.85 × 10 ⁻⁶ .

  From this evaluation result, the arithmetic processing unit 91 requires less memory capacity to record the mantissa power table and the fractional power table, but it is necessary to increase the table size to increase the accuracy of the power operation. I understand that there is.

  Therefore, by performing interpolation processing on the values of the mantissa power table and decimal power table (power value) in the arithmetic processing device, the accuracy of the power operation can be improved without increasing the table size. To.

  Specifically, for example, as shown in FIG. 7, the arithmetic processing unit 91 calculates the upper N bits from the 22nd bit of the mantissa part from the 22nd bit to the 0th bit of the floating point number data. Used to obtain a power value. In other words, since the power value is obtained by approximation using the upper N bits, this approximation includes an error.

  Therefore, the power value is obtained from the 22nd bit using the upper N bits, and the remaining (23-N) bit, that is, the (22-N) th bit to the 0th bit is obtained. By using the interpolation process for the power value, the accuracy of the power operation is improved.

  In such a case, the arithmetic processing unit is configured as shown in FIG. In FIG. 8, parts corresponding to those in FIG. 5 are denoted by the same reference numerals, and description thereof is omitted.

  The arithmetic processing unit 131 includes a mantissa / exponent separation unit 101, an integer / decimal separation unit 102, a mantissa power table holding unit 103, a decimal power table holding unit 104, a power operation unit 105, an integer conversion unit 106, and an interpolation processing unit. 141. That is, the arithmetic processing unit 131 is further provided with an interpolation processing unit 141 in addition to the arithmetic processing unit 91.

Interpolation processing unit 141 obtains an index index1 with mantissa X ₁ from mantissa / exponent separation unit 101, a power table for the mantissa of the mantissa of the power table holding unit 103, a plurality of table values in the vicinity of the index index1 (exponentiation Value). Further, the interpolation processing unit 141 performs interpolation processing using the table values obtained from the mantissa of the power table, thereby a power of a value of the mantissa part of the input value X obtained interpolated value ₍₁ + X 1/2 ²³ ) ^Y is supplied to the power calculation unit 105 as the power value of the mantissa part of the final input value X obtained by the interpolation process.

The interpolation processing unit 141 obtains the index index2 using the decimal number X _amari from the integer / decimal separation unit 102, and uses a plurality of table values (powers) in the vicinity of the index index2 from the decimal power table of the decimal power table holding unit 104. Value). Further, the interpolation processing unit 141 performs an interpolation process using the table value acquired from the decimal power table, and obtains an interpolation value (2 ^ X _amari ) that is a power value of the radix of the input value X obtained thereby. The final power of the radix obtained by the interpolation process is supplied to the power calculation unit 105.

  Next, with reference to the flowchart of FIG. 9, the power calculation process by the calculation processing device 131 will be described.

  Note that the processing from step S71 to step S74 is the same as the processing from step S41 to step S44 in FIG.

However, the table sizes of the mantissa power table and the decimal power table are 2 ^N + 1 = SIZE + 1 when linear interpolation is performed as interpolation processing by the interpolation processing unit 141, and second-order polynomial interpolation is performed as interpolation processing. In this case, 2 ^N + 2 = SIZE + 2.

  For example, when quadratic polynomial interpolation is performed as the interpolation processing, the mantissa power table and the decimal power table shown in Expression (24) and Expression (25) are generated, and variables i = 0,..., SIZE + 1 It is said.

Further, the mantissa X ₁ obtained by the mantissa / exponent separation unit 101 is supplied to the interpolation processing unit 141. Further, the decimal number X _amari obtained by the integer / decimal separation unit 102 is supplied to the interpolation processing unit 141, and the integer X _int is supplied to the power calculation unit 105.

In step S75, the interpolation processing unit 141 performs interpolation processing using the mantissa X ₁ from mantissa / exponent separation unit 101, the interpolation value of the power value of the mantissa part of the input value _{X (1 + X 1/2} 23) ^Y is obtained and supplied to the power calculation unit 105.

That is, the interpolation processing unit 141, by calculating equation (28) described above, obtaining the upper N bits as an index index1 from 22 bits of the mantissa X _1.

In addition, the interpolation processing unit 141 calculates the following expression (36) to obtain the lower value X _h1 that is the value of the portion from the (22-N) -th bit to the 0-th bit of the mantissa X ₁ .

In Expression (36), “&” indicates a logical product operation, and is assumed to be the same in the following description. In Expression (36), by performing a logical product operation of the mantissa X ₁ and (2 ^23-N −1), a portion from the (22−N) th bit to the 0th bit of the mantissa X ₁ is extracted. . That is, (2 ^23-N −1) is a value in which only the value of the lower (23-N) bits is “1” and the value of the other bits is “0”. only the value of the lower (23-N) bits of X ₁ are extracted.

Further, the interpolation processing unit 141 obtains the table value V _{10 to the} table value V ₁₂ of the power value of the mantissa part of the input value X by Expressions (37) to (39).

That is, the interpolation processing unit 141, a power value frctable [index1] table value V ₁₀ to which the index index1 and the value of the variable i, obtained from a power table mantissa of the mantissa of the power table holding unit 103. Likewise, the interpolation processing unit 141, the index index1 + 1 and indices index1 + 2 as exponential value frctable [index1 + 1] and exponential value frctable [index1 + 2] table values V ₁₁ and table values V ₁₂ and that the value of the variable i and mantissa power table Get from.

Then, the interpolation processing unit 141 performs an interpolation process using the lower value X _h1 and the table values V _{10 to} V _12, and an interpolated value (1 + X _1/2) of the power value of the mantissa part of the input value X ²³ ) ^{Find Y.}

For example, the interpolation processing unit 141, when performing a linear interpolation as the interpolation process by calculating equation (40) obtains an interpolation value _{H = (1 + X 1/} 2 23) Y.

  Note that “a” and “xin” in Equation (40) are obtained by Equation (41) and Equation (42), respectively.

That is, when the linear interpolation is performed as the interpolation processing, as shown in FIG. 10, is regarded as a table value V ₁₀ as the origin, the gradient a of the power value is determined for index, the value of the index (index1) is in xin The power value of time is obtained as the interpolation value H. In FIG. 10, the vertical axis indicates the power value, and the horizontal axis indicates the value of the index index1.

Further, for example, the interpolation processing unit 141, when performing a second-order polynomial interpolation as the interpolation process by calculating equation (43) obtains an interpolation value _{H = (1 + X 1/} 2 23) Y.

  Note that “a”, “b”, and “xin” in the equation (43) are obtained by the equations (44) to (46), respectively.

That is, when quadratic polynomial interpolation is performed as the interpolation processing, as shown in FIG. 11, the table value V ₁₀ is regarded as the origin, and the square value of the index value xin obtained from the lower value X _h1 is multiplied. The coefficient a and the coefficient b multiplied by the value xin are obtained, and the power value when the value of the index (index1) is xin is obtained as the interpolation value H. In FIG. 11, the vertical axis indicates the power value, and the horizontal axis indicates the value of the index index1.

Incidentally, the interpolation processing unit 141, the case without interpolation, the table value V _10, the interpolation value of power values of the mantissa part of the input value _{X (1 + X 1/2} 23) to ^Y.

Returning to Fig. 9, when the final input value interpolation value as a power value of the mantissa part of the _{X (1 + X 1/2} 23) Y is required, the process proceeds from step S75 to step S76.

In step S76, the interpolation processing unit 141 performs an interpolation process using the decimal number X _amari from the integer / decimal separation unit 102 to obtain an interpolation value (2 ^ X _amari ) of the power of the radix of the input value X. , And supplied to the power calculation unit 105.

That is, the interpolation processing unit 141 calculates the above-described Expression (30) and Expression (31), and extracts the value of the upper N bits from the 22nd bit of the fixed-point decimal number X _amari as index2.

Further, the interpolation processing unit 141 calculates the following expression (47) to obtain the lower value X _h2 that is the value of the portion from the (22-N) th bit to the 0th bit of the decimal number X _amari .

In the equation (47), as in the case of the equation (36), by performing an AND operation between the decimal number X _amari and (2 ^23-N −1), the (22−N) -th bit of the decimal number X _amari is obtained. Portions up to the 0th bit are extracted.

Further, the interpolation processing unit 141 obtains the table value V _{20 to the} table value V ₂₂ of the power of the radix of the input value X by using the equations (48) to (50).

That is, the interpolation processing unit 141 sets the power value twotable [index2] of the radix of the input value X with the index index2 as the value of the variable i as the table value V ₂₀ , from the decimal power table of the decimal power table holding unit 104. get.

Likewise, the interpolation processing unit 141, as an index index2 + 1 and index index2 + 2 values and the exponential value Twotable variable i [index2 + 1] and exponential value twotable [index2 + 2] table values V ₂₁ and table values V ₂₂ and fractional power table Get from.

Then, the interpolation processing unit 141 performs an interpolation process using the lower value X _h2 and the table value V _{20 to the} table value V _22, and an interpolation value (2 ^ X _amari ) of the power value of the radix of the input value X. Ask for.

For example, when performing linear interpolation as the interpolation processing, the interpolation processing unit 141 calculates the equation (40) to (42) to obtain the interpolation value H = (2 ^ X _amari ). In this case, the lower value X _h1 , the table value V ₁₀ , and the table value V ₁₁ in the equations (40) to (42) are the lower value X _h2 , the table value V ₂₀ , and the table value V _21. (Replaced).

Further, for example, when performing quadratic polynomial interpolation as the interpolation processing, the interpolation processing unit 141 calculates the interpolation value H = (2 ^ X _amari ) by calculating Expression (43) to Expression (46). In this case, the lower value X _h1 , the table value V ₁₀ , the table value V ₁₁ , and the table value V ₁₂ in the equations (43) to (46) are the lower value X _h2 , the table value V ₂₀ , and the table value V. ₂₁ and the table value V ₂₂ .

When the interpolation processing unit 141 does not perform the interpolation processing, the table value V ₂₀ is set to the interpolation value (2 ^ X _amari ) of the power of the radix of the input value X.

In step S77, the power calculation unit 105, since the integer X _int from Integer / fractional separation unit 102, the interpolation value from the interpolation processing section _{141 (1 + X 1/2} 23) Y and the interpolation value (2 ^ X _amari) Then, the calculation value P is obtained by calculating the above-described equations (33) and (34).

  Thereafter, the process of step S78 is performed, and the exponentiation calculation process ends. However, the process of step S78 is the same as the process of step S48 of FIG.

  In this way, the arithmetic processing unit 131 performs an interpolation process using the table value acquired from the mantissa power table, obtains the power value of the mantissa part of the final input value X, and uses the decimal power table. Interpolation processing is performed using the acquired table value, and the final power value of the radix of the input value X is obtained. Then, the arithmetic processing unit 131 obtains the arithmetic value P by using the obtained power value and converts it to an integer.

  In this way, the table size of the mantissa power table and the power table of the decimal number is obtained by performing the interpolation process to obtain the power value of the mantissa part of the input value X and the power value of the radix of the input value X. The accuracy of the power operation can be improved without increasing it.

  Specifically, the present applicant sets power exponent of the arithmetic processing unit 131 based on the relative error average T obtained by calculating the above equation (17) using L = 8192 pieces of data with power index Y = 3.141592. The calculation accuracy was evaluated. When N = 8, that is, when the table size is SIZE = 256, FIG. 12 shows a combination of the case where the interpolation processing is added to the value of the mantissa power table and the value of the decimal power table, and the case where the interpolation processing is not added. The evaluation results shown in Fig. 1 were obtained.

  FIG. 12 shows the value of the relative error average T for each combination of the case where the interpolation process is added and the case where the interpolation process is not added. That is, the character “decimal: no interpolation” indicates that the value of the decimal power table is used for calculation of the operation value P without performing interpolation processing, and the characters “decimal: linear interpolation” and “decimal: secondary” are used. “Interpolation” indicates that linear interpolation and quadratic polynomial interpolation are performed on the values of the power table of the decimal and used for calculation of the calculation value P.

  Similarly, the character “mantissa: no interpolation” indicates that the value of the mantissa power table is used for calculation of the operation value P without performing interpolation processing, and the characters “mantissa: linear interpolation” and “mantissa: 2” are used. “Next interpolation” indicates that the value of the mantissa power table is subjected to linear interpolation and quadratic polynomial interpolation and used to calculate the operation value P.

In FIG. 12, it can be seen that the power calculation accuracy is improved by performing an interpolation process on at least one of the value of the mantissa power table or the value of the decimal power table. For example, the secondary when subjected to linear interpolation T = 5.31 × 10 ^-6, and the both values and the value of the fraction of power table of the mantissa of the power table for both values of and fractional power table of the mantissa of the power table When polynomial interpolation is performed, T = 3.93 × 10 ⁻⁸ .

  In this way, the relative error average value when second-order polynomial interpolation is performed on both table values is the value obtained when N = 16, that is, when the table size SIZE = 65536, in the conventional quantization apparatus 51. The accuracy is equal to or better than the calculation accuracy of the integer part using a table.

  Further, when N = 1,..., 8, that is, when the table size is SIZE = 2,..., 256, interpolation is performed for both the mantissa power table value and the decimal power table value. The result shown in FIG. 13 was obtained as the relative error average T when the processing was not performed, when the linear interpolation was performed, and when the second-order polynomial interpolation was performed.

  In the figure, the “table size” column indicates the number (number) of table sizes SIZE, and each of the characters “no interpolation”, “linear interpolation”, and “secondary interpolation” is a mantissa. The figure shows the case where the interpolation table is not subjected to the power table value and the value of the decimal power table, when the linear interpolation is performed, and when the second-order polynomial interpolation is performed.

  In FIG. 13, when the table size is “16” and linear interpolation is performed, and when the table size is “4” and quadratic polynomial interpolation is performed, the table size of “no interpolation” is “256”. It can be seen that an accuracy equivalent to the accuracy is realized.

That is, when the table size is “256” and the interpolation process is not performed, the relative error average T = 6.00 × 10 ⁻³ . When linear interpolation is performed with a table size of “16”, the relative error average T = 1.37 × 10 ⁻³ , and when linear interpolation is performed with the table size of “4”, the relative error average T = 2.52. × 10 ^-3 . As described above, the arithmetic processing unit 131 can perform a power calculation with higher accuracy with a smaller table size (number of tables) by performing the interpolation process.

In the above description, the example in which the mantissa power table and the decimal power table have the same table size has been described. However, the table sizes may be different depending on the accuracy required for the power operation. . When the table size is changed, the bit position at the time of the interpolation process performed by the interpolation processing unit 141, that is, the size of the lower value X _h1 or the lower value X _h2 is also changed according to the size.

  In addition, it has been explained that interpolation processing is performed on both the mantissa power table value and the decimal power table value, but depending on the amount of interpolation processing and the required calculation accuracy, either value is set. Interpolation processing may be performed, or different interpolation processing may be performed. Further, the interpolation processing is not limited to linear interpolation or quadratic polynomial interpolation, but may be performed by higher-order polynomial interpolation or spline interpolation.

[Third Embodiment]
By the way, in the above, when calculating the arithmetic value P obtained by the exponentiation calculation into an integer, it explained that the integer was performed after adding the constant α to the arithmetic value P. For example, as shown in the equation (1), in many standards such as quantization of audio signals, the value of the power exponent Y is often determined, so the constant α is added to the calculated value P. Instead of adding α ^{1 / Y} to the input value X in advance, the integer part of the calculated value can be obtained by a simple calculation.

That is, assuming that the input value so far is X ′ (the input value X described above), the value obtained by adding α ^{1 / Y} to X ′ is a new input value X = X ′ + α ^{1 / Y and} a power operation is performed. Used for. For example, in the case of quantization of the audio signal shown in Expression (1), the input value is X = X ′ + α ^4/3 .

  Thus, when the value of the constant α to the 1 / Yth power is added to the variable X ′ to obtain the input value X, the arithmetic processing unit is configured as shown in FIG. In FIG. 14, portions corresponding to those in FIG. 5 are denoted by the same reference numerals, and description thereof is omitted as appropriate.

  The arithmetic processing unit 171 includes a mantissa / exponent separation unit 101, an integer / decimal separation unit 102, a mantissa power table holding unit 181, a decimal power table holding unit 182, and a power integer conversion unit 183.

In this arithmetic processing unit 171, the input value X = X ′ + α ^{1 / Y} is supplied to the mantissa / exponent separator 101, and the exponent ^Y is supplied to the integer / decimal separator 102. That is, the arithmetic processing unit 171 adds the constant α ^{1 / Y} to the variable X ′ to obtain the input value X, and supplies the input value X to the mantissa / exponent separation unit 101.

The mantissa power table holding unit 181 holds a mantissa power table including the power value of the mantissa part of the input value X determined by the value of the mantissa X ₁ . In the mantissa power table, the power value of the mantissa part of the input value X is a fixed-point number whose decimal point position is the 23rd bit.

Power table storing unit 182 in decimal, Sadamari the value of the fractional X _amari, fractional power of containing the power of the value of the radix (bottom) of the input value X (calculated value (P + alpha)) to fractional X _amari to the index Holding a table.

  Note that the power of the radix of the input value X in the decimal power table is a fixed-point number whose decimal point position is the 23rd bit.

The power integer conversion unit 183 refers to the mantissa power table of the mantissa power table holding unit 181 and the mantissa power table of the decimal power table holding unit 182, and the mantissa X ₁ from the mantissa / exponent separation unit 101 The integer part of the calculated value (P + α) is obtained from the integer X _int and the decimal number X _amari from the integer / decimal separator 102 and output. Here, the calculated value (P + α) is a value constant alpha is added to the calculated value P = X ^'Y.

  Next, with reference to the flowchart of FIG. 15, the power calculation process by the calculation processing device 171 will be described.

In step S111, the mantissa power table holding unit 181 generates a mantissa power table. That is, power table storing unit 181 of the mantissa, if the table size of the mantissa of the power table and 2 ^N = SIZE, shown in the following equation (51), the input value power values obtained mantissa portion of the X and multiply Y Generate a power table of mantissa consisting of frctable [i].

Here, the table size SIZE is the number of numbers that can be represented by N-bit data, and power values frctable [i] corresponding to the number of table sizes SIZE are prepared. Further, the variable i of the exponential value frctable [i] indicates the value of the index index1 obtained from mantissa X _1, variable i = 0, · · ·, are (SIZE-1).

For example, if the index index1 and many of the high-order bits of the value of the mantissa X _1, (1 + i / SIZE) ^Y in the formula (51), for the values of the mantissa X _1, the mantissa part of the input value X to multiply Y the values obtained ^{_{(1 + X 1/2 23}} ) the approximation of ^Y. Furthermore, (calculation of int (A)) Formula (51), approximation (1 + i / SIZE) ^Y 2 ²³ is integer is multiplied, the approximate value is a fixed point of. That is, the power value frctable [i] is a fixed-point number whose decimal point position is the 23rd bit.

  When the mantissa power table holding unit 181 determines each power value frctable [i] for each of the (SIZE) variable values i, the mantissa power table holding unit 181 associates the value i with the power value frctable [i]. To generate and hold a mantissa power table.

In step S112, the decimal power table holding unit 182 generates a decimal power table. In other words, the decimal power table holding unit 182 is obtained by raising the base 2 of the input value X represented by the following equation (52) to the X _amari power, where the table size of the decimal power table is 2 ^N = SIZE. Generate a power table of decimal numbers consisting of power values twotable [i].

Here, the variable i of the power value twotable [i] indicates the value of the index index2 obtained from the decimal number X _amari , and the variable i = 0,..., (SIZE−1).

Assuming that the index index2 is a value of several high-order bits of the decimal number X _amari , 2 ^{(i / SIZE)} in the equation (52) is the X _amari power of the base “2” of the input value X with respect to the value of the decimal number X _amari. The value of 2 ^ X _{amari is} an approximate value. Furthermore, in Formula (52), is 2 ²³ is multiplied integer approximation value 2 ^{(i / SIZE),} the approximate value is a fixed point of. That is, the power value twotable [i] is a fixed-point number whose decimal point position is the 23rd bit.

  When the power table holding unit 182 of decimal numbers finds each power value twotable [i] for each value i of (SIZE) variables, the value i and the power value twotable [i] are associated with each other. To generate and hold a power table of decimal numbers.

  Note that the process of generating the mantissa power table and the decimal power table may be performed once before the power calculation of the input value X. In other words, once these tables are generated, then when performing a power operation of the input value X, a mantissa power table and a decimal power table already generated and held may be used.

When the mantissa power table and the decimal power table are generated in this manner, the processes of step S113 and step S114 are performed thereafter. These processes are the same as the processes of step S43 and step S44 of FIG. Since it is the same, the description is abbreviate | omitted. The mantissa X ₁ of the input value X = X ′ + α ^{1 / Y obtained by} the mantissa / exponent separation unit 101 is supplied to the power integer conversion unit 183, and the exponent X of the input value X = X ′ + α ^{1 / Y} ₂ is supplied to the integer / decimal separator 102.

Further, the integer X _int and the decimal number X _amari of the product of the exponent X ₂ and the power exponent Y, which are obtained by the integer / decimal separator 102 calculating the formulas (26) and (27), are a power integer transform. To the unit 183.

In step S115, power integer transform unit 183, using a mantissa X ₁ supplied from the mantissa / exponent separation unit 101, should a power of a value of the mantissa part of the input value X for the index _{Y (1 + X 1/2} 23) Y Ask for.

Specifically, the power integer conversion unit 183 calculates the index index1 by calculating Expression (28), and calculates the power value of the mantissa part of the input value X from Expression (29) using the index index1. . That is, the power integer conversion unit 183 obtains the power value frctable [index1] with the index index1 as the value of the variable i from the mantissa power table of the mantissa power table holding unit 181. Then, the obtained exponential value frctable [index1] is, power of the value of the mantissa part of the input value _{X (1 + X 1/2} 23) are ^Y.

In step S116, the power integer conversion unit 183 uses the decimal number X _amari supplied from the integer / decimal number separation unit 102 to obtain the power of 2, which is the base of the input value X, with the decimal number X _amari as a power exponent.

Specifically, the power integer conversion unit 183 calculates an index index2 by calculating the following expressions (30) and (31), and uses the index index2 to calculate the radix of the input value X from the expression (32). Find the power value of. That is, the power integer conversion unit 183 acquires the power value twotable [index2] with the index index2 as the value of the variable i from the power table of the decimal number in the power table holding unit 182 of the decimal number. Then, the acquired power value twotable [index2] is set to a power value of 2 (2 ^ (X _amari )) as a radix.

In step S117, the power integer transform unit 183, a power value ^{_{(1 + X 1/2 23}} ) Y, and the power of the value _{(2 ^ (X amari))} , and integer X _int from Integer / fractional separation unit 102 Using this, the integer part of the calculated value (P + α) is obtained, and the obtained value is output as an output value which is an integerized calculated value (P + α).

  That is, the power integer conversion unit 183 obtains the integer part of the calculated value (P + α) by calculating the following equation (53).

Here, in the formula (53), “>>” indicates a right shift. Power integer transform unit 183, when the integer X _int is greater than or equal to 0, ^{_{"(1 + X 1/2 23}} ) Y × 2 ^ X amari " a (46-X _int) by shifted right bit calculated value (P + alpha ) (Int) (P + α) of the integer part of. Further, when the integer X _int is less than 0, the power integer conversion unit 183 sets the value “0” as the value (int) (P + α) of the integer part of the operation value (P + α).

Note that the right shift of (46−X _int ) bits is performed when the integer X _int is 0 or more for the following reason. That is, power value obtained by the table lookup ^{_{(1 + X 1/2 23}} ) Y, and exponential value 2 ^ X _amari, because the decimal point is at the position of 23 th bit, the decimal point of the product of the values of their exponential value The position is the 46th bit.

The arithmetic value (P + alpha), to represent (in the usual decimal) without using radix, exponential value ^{_{(1 + X 1/2 23}} ) Y and decimal point of the product of the value of the exponential value 2 ^ X _amari The position may be moved to the lower bit side by an integer X _int (left shift operation).

Therefore, when the integer X _int is greater than zero, the exponential value ^{_{(1 + X 1/2 23}} ) Y, if only the right shift (46-X _int) bit value of the product of the exponential value 2 ^ X _amari, operation The value of the integer part of the value (P + α) is obtained. When the integer X _int is negative (less than 0), the calculated value (P + α) is less than 1, and therefore the integer part of the calculated value (P + α) is set to 0.

  When the integer part of the operation value (P + α) is obtained in this way, the power integer conversion unit 183 outputs the integer part of the operation value (P + α), that is, the operation value (P + α) converted to an integer, so that the power operation The process ends.

As described above, the processing unit 171, a value that the constant alpha ^{1 / Y} is added to the value X 'as a new input value X, the product of power values obtained by using the table, the integer X The integer part of the calculated value (P + α) is obtained from _int using shift calculation.

Thus, the value of the integer part of the calculation value (P + α) can be obtained more easily and quickly. That is, it is not necessary to obtain the arithmetic value P once and then further obtain the integer part of the arithmetic value (P + α). With reference to the mantissa power table and the decimal power table, the mantissa X ₁ , the decimal number X _amari, and From the integer X _int , the integer part of the calculated value (P + α) can be obtained directly by shift calculation. Therefore, a processing block corresponding to the integer conversion unit 106 in FIG. 5 is not required, and the arithmetic processing device 171 can be downsized.

  In the above description, the example in which the mantissa power table and the decimal power table have the same table size has been described. However, the table sizes may be different depending on the accuracy required for the power operation. .

[Fourth Embodiment]
Incidentally, in the example described in the above, the mantissa part of the input value _{X (1 + X 1/2} 23) _{is, 1.0 ≦ (1 + X 1} /2 23) is <2.0, the fractional X _amari is a 0.0 ≦ X _amari <1.0 Yes, the power index Y was a constant.

  Therefore, in order to obtain the integer part of the operation value P (or operation value (P + α)) from the input value X, the power operation is directly performed by the power operation device without using the mantissa power table or the decimal power table. However, the amount of processing does not increase that much. That is, the power arithmetic device can be expected to be downsized. Therefore, an integer part of the operation value (P + α) may be obtained from the input value X using a power operation device that performs an operation on a floating point number.

  In such a case, the arithmetic processing unit is configured as shown in FIG. 16, for example. In FIG. 16, portions corresponding to those in FIG. 5 are denoted with the same reference numerals, and description thereof will be omitted as appropriate.

The arithmetic processing unit 211 includes a mantissa / exponent separator 101, an integer / decimal separator 102, and a power integer converter 221. Further, in the arithmetic processing unit 211, the input value X = X ′ + α ^{1 / Y} is supplied to the mantissa / exponent separator 101, and the exponent ^Y is supplied to the integer / decimal separator 102 and the power integer converter 221. The input value X is the same as that in the third embodiment described above, and the input value X = X ′ + α ^{1 / Y.}

Power integer transform unit 221 performs, for example, calculation of the floating point number is composed of such exponentiation device, mantissa X ₁ from mantissa / exponent separation unit 101, integer X _int and decimal integer / fraction separating unit 102 X _amari, and using the supplied exponent Y, determine the integer portion of the calculated value (P + α), and outputs.

  Next, with reference to the flowchart of FIG. 17, power calculation processing by the calculation processing device 211 will be described.

In addition, since the process of step S141 and step S142 is the same as the process of step S43 and step S44 of FIG. 6, the description is abbreviate | omitted. Note that the mantissa X ₁ of the input value X obtained by the mantissa / exponent separator 101 is supplied to the power integer converter 221, and the exponent X ₂ is supplied to the integer / decimal separator 102.

Further, the integer X _int and the decimal number X _amari of the product of the exponent X ₂ and the power exponent Y, which are obtained by the integer / decimal separator 102 calculating the formulas (26) and (27), are a power integer transform. To the unit 221.

In step S 143, the power integer conversion unit 221 uses the exponent Y supplied and the mantissa X ₁ supplied from the mantissa / exponent separation unit 101 to perform a power operation unit built in the power integer conversion unit 221. Accordingly, should a power of a value of the mantissa part of the input value X for the index _{Y (1 + X 1/2} 23) determining the ^Y.

In step S144, power integer transform unit 221 uses the fractional X _amari supplied from the integer / fraction separating unit 102, the exponentiation device built into power integer transform unit 221, and the exponent a fraction X _amari The power of 2 that is the radix of the input value X is obtained. As a result, a power value of 2 (2 ^ (X _amari )) is obtained.

In step S145, power integer transform unit 221, a power value obtained ^{_{(1 + X 1/2 23}} ) Y, and a power value _{(2 ^ (X amari))} , and an integer X _int from Integer / fractional separation unit 102 Is used to find the integer part of the calculated value (P + α) from the above equation (53). The power integer conversion unit 221 then outputs the integer part of the calculated value (P + α) as an output value, and the power calculation process ends.

  In this way, the arithmetic processing unit 211 uses the power arithmetic unit to perform direct power arithmetic and obtains an integer part of the arithmetic value (P + α) from the input value X. In this way, the arithmetic processing unit 211 can be reduced in size by performing the power operation with a small amount of processing by the power arithmetic unit.

[Fifth Embodiment]
By the way, in the arithmetic processing unit 171 of the third embodiment described above, the interpolation processing of the values of the mantissa power table and the power table of the decimal number is not performed, so that the power calculation accuracy, that is, the calculation of the integer part of the operation value is performed. In order to improve accuracy, it is necessary to increase the size of these tables.

  Specifically, L pieces of data consisting of an integer part R of the operation value (P + α) calculated by the arithmetic processing unit 171 and an integer part Q of the operation value (P + α) obtained by calculation using a mathematical library are stored. It is assumed that the following equation (54) is calculated using the set, the absolute error average U is obtained, and the calculation accuracy of the integer part R is evaluated.

In equation (54), R _i represents the i-th sample of L integer parts (samples) of the integer part R calculated by the arithmetic processing unit 171, and Q _i is a mathematical library obtained by, and an integer part corresponding to R _i.

For example, the index Y = 3.141592 should, were evaluated in the calculation accuracy of the integral part R as L = 8192, when N in the table size 2 ^N is eight, that is, when the SIZE = 256, absolute error Mean U = It was 2.09 × 10 ¹ and so high accuracy could not be obtained. Further, when ^N in the table size 2 ^N is 16, that is, when SIZE = 65536, the absolute error average U = 1.15 × 10 ⁻² is obtained, and higher accuracy is obtained than in the case of N = 8.

  As can be seen from the evaluation result based on the absolute error average U, the arithmetic processing unit 171 needs to increase the size of the mantissa power table and the decimal power table in order to improve the arithmetic accuracy of the integer part. There is.

Therefore, by making the input value X = X ′ + α ^{1 / Y} and interpolating the values of the mantissa power table and the decimal power table, the arithmetic value can be converted into an integer and the integer can be converted into an integer. Improve the calculation accuracy.

  In such a case, the arithmetic processing unit is configured as shown in FIG. 18, for example. In FIG. 18, the same reference numerals are given to the portions corresponding to those in FIG. 5 or FIG. 8, and description thereof will be omitted as appropriate.

  The arithmetic processing unit 251 includes a mantissa / exponent separation unit 101, an integer / decimal separation unit 102, an interpolation processing unit 141, a mantissa power table holding unit 261, a decimal power table holding unit 262, and a power integer conversion unit 263. The

The mantissa power table holding unit 261 holds a mantissa power table including a table value that is a power value of the mantissa part of the input value X, which is determined by the value of the mantissa X ₁ . The table value in the mantissa power table is a fixed-point number whose decimal point position is the 23rd bit.

The decimal power table holding unit 262 holds a power table of decimal numbers including a table value that is a power value of the base (base) of the input value X, which is determined by the value of the decimal number X _amari , with the decimal number X _amari being a power index. is doing. The table value in the power table of decimal numbers is a fixed-point number with the decimal point position at the 23rd bit.

Further, the power value (table value) of the mantissa power table holding unit 261 and the power value (table value) of the decimal power table holding unit 262 are supplied to the interpolation processing unit 141. Further, in the interpolation processing unit 141, an interpolation value (1 + X) that is a power value of the mantissa part of the input value X is obtained by interpolation processing using the table values from the mantissa power table holding unit 261 and the decimal power table holding unit 262. _1/2 ^{23) Y,} and input value a power of the value is interpolated values radix X (2 ^ X _amari) is obtained. These interpolation values are supplied from the interpolation processing unit 141 to the power integer conversion unit 263.

The power integer conversion unit 263 uses the interpolation value from the interpolation processing unit 141 and the integer X _int from the integer / decimal number separation unit 102 to obtain and output the integer part of the calculated value (P + α).

  Next, with reference to the flowchart of FIG. 19, the power calculation process by the calculation processing device 251 will be described.

In step S171, the mantissa power table holding unit 261 generates a mantissa power table. For example, when quadratic polynomial interpolation is performed as an interpolation process by the interpolation processing unit 141, the mantissa power table holding unit 261 sets the table size of the mantissa power table to 2 ^N + 2 = SIZE + 2. Then, the mantissa power table holding unit 261 generates a mantissa power table composed of table values frctable [i] represented by the following equation (55).

Here, the variable i of the table values frctable [i] indicates the value of the index index1 obtained from mantissa X _1, variable i = 0, · · ·, are (SIZE + 1).

For example, if the index index1 and many of the high-order bits of the value of the mantissa X _1, (1 + i / SIZE) ^Y in the formula (55), for the values of the mantissa X _1, the mantissa part of the input value X to multiply Y the values obtained ^{_{(1 + X 1/2 23}} ) the approximation of ^Y. Furthermore, in Formula (55), is 2 ²³ is multiplied integer an approximation ^{(1 + i / SIZE) Y} , the approximate value is a fixed point of. That is, the table value frctable [i] is a fixed-point number whose decimal point position is the 23rd bit.

  When the mantissa power table holding unit 261 obtains each of the table values frctable [i] for each of the values i of (SIZE + 2) variables, the value i is associated with the table value frctable [i]. To generate and hold a mantissa power table.

As the interpolation process, when linear interpolation is performed by the interpolation processing unit 141, the table size of the power table of the mantissa is 2 ^N + 1 = SIZE + 1, and the mantissa composed of the table value frctable [i] in Expression (55) A power-of-power table is generated.

In step S172, the decimal power table holding unit 262 generates a power table of decimal numbers. For example, when the interpolation processing unit 141 performs quadratic polynomial interpolation as the interpolation processing, the decimal power table holding unit 262 sets the table size of the decimal power table to 2 ^N + 2 = SIZE + 2. Then, the decimal power table holding unit 262 generates a decimal power table composed of table values twotable [i] represented by the following equation (56).

Here, the variable i of the table value twotable [i] indicates the value of the index index2 obtained from the decimal number X _amari , and the variable i = 0,..., (SIZE + 1).

If the index index2 is a value of several high-order bits of the decimal number X _amari , 2 ^{(i / SIZE)} in the equation (56) is the X _amari power of the base “2” of the input value X with respect to the value of the decimal number X _amari. The value of 2 ^ X _{amari is} an approximate value. Furthermore, in Formula (56), is 2 ²³ is multiplied integer approximation value 2 ^{(i / SIZE),} the approximate value is a fixed point of. That is, the table value twotable [i] is a fixed-point number whose decimal point position is the 23rd bit.

  When the power table holding unit 262 of decimal numbers obtains each of the table values twotable [i] for each of the values i of (SIZE + 2) variables, the values i and the table values twotable [i] are associated with each other. Generate and maintain a fractional power table.

As the interpolation processing, when linear interpolation is performed by the interpolation processing unit 141, the table size of the power table of the decimal number is 2 ^N + 1 = SIZE + 1, and the decimal number composed of the table value twotable [i] in Expression (56) A power-of-power table is generated.

  Further, the process of generating the mantissa power table and the decimal power table may be performed once before the power calculation of the input value X. In other words, once these tables are generated, then when performing a power operation of the input value X, a mantissa power table and a decimal power table already generated and held may be used.

When the mantissa power table and the decimal power table are generated in this manner, the processes of step S173 and step S174 are performed thereafter. These processes are the same as the processes of step S43 and step S44 of FIG. Since it is the same, the description is abbreviate | omitted. The mantissa X ₁ of the input value X obtained by the mantissa / exponent separator 101 is supplied to the interpolation processor 141, and the exponent X ₂ is supplied to the integer / decimal separator 102.

Further, the integer X _int and the decimal number X _amari of the product of the exponent X ₂ and the power exponent Y, which are obtained by the integer / decimal separator 102 calculating the formulas (26) and (27), are a power integer transform. Is supplied to the unit 263 and the interpolation processing unit 141.

In step S175, the interpolation processing unit 141 performs interpolation processing using the mantissa X ₁ from mantissa / exponent separation unit 101, the interpolation value of the power value of the mantissa part of the input value _{X (1 + X 1/2} 23) ^Y is obtained and supplied to the power integer conversion unit 263.

That is, the interpolation processing unit 141, by calculating equation (28) described above, obtaining the upper N bits as an index index1 from 22 bits of the mantissa X _1.

Further, the interpolation processing unit 141, by calculating equation (36) described above, obtaining the lower value X _h1 is the value of the part of the mantissa X ₁ from (22-N) th bit to 0-th bit.

Further, the interpolation processing unit 141 obtains the table value V _{10 to the} table value V ₁₂ of the power value of the mantissa part of the input value X by Expressions (37) to (39).

That is, the interpolation processing unit 141, as a table value frctable [index1] table value V ₁₀ to which the index index1 and the value of the variable i, obtained from a power table mantissa of the mantissa of the power table holding unit 261. Likewise, the interpolation processing unit 141, the index index1 + 1 and the index index1 + 2 to the value of the variable i and table value frctable [index1 + 1] and table values frctable [index1 + 2] table values V ₁₁ and the table value V ₁₂ of the mantissa of a power table Get from.

Then, the interpolation processing unit 141 performs an interpolation process using the lower value X _h1 and the table values V _{10 to} V _12, and an interpolated value (1 + X _1/2) of the power value of the mantissa part of the input value X ²³ ) ^{Find Y.}

For example, the interpolation processing unit 141, when performing a linear interpolation as the interpolation process by calculating equation (40) through (42), determine the interpolation value _{H = (1 + X 1/} 2 23) Y. Further, for example, the interpolation processing unit 141, when performing a second-order polynomial interpolation as the interpolation process by calculating equation (43) through (46), the interpolation value _{H = (1 + X 1/} 2 23) Y Ask.

Incidentally, the interpolation processing unit 141, the case without interpolation, the table value V _10, the interpolation value of power values of the mantissa part of the input value _{X (1 + X 1/2} 23) to ^Y.

When power of the interpolation value of the value ^{_{(1 + X 1/2 23}} ) Y mantissa part of the input value X is determined, the process proceeds from step S175 to step S176.

In step S176, the interpolation processing unit 141 performs an interpolation process using the decimal number X _amari from the integer / decimal number separation unit 102 to obtain an interpolation value (2 ^ X _amari ) of the power of the radix of the input value X. , And supplied to the power integer conversion unit 263.

That is, the interpolation processing unit 141 calculates the above-described Expression (30) and Expression (31), and extracts the value of the upper N bits from the 22nd bit of the fixed-point decimal number X _amari as index2. In addition, the interpolation processing unit 141 calculates a lower value X _h2 that is the value of the portion from the (22-N) -th bit to the 0-th bit of the decimal number X _amari by calculating Expression (47).

Further, the interpolation processing unit 141, by the equation (48) through (50), obtains the table values V ₂₀ to the table value V ₂₂ of the power values of input base value X.

That is, the interpolation processing unit 141, a power value input base value X where the index index2 the value of the variable i, that is the table value twotable [index2] as a table value V _20, fractional fractional power table holding unit 262 Get from the power table.

Likewise, the interpolation processing unit 141, as an index index2 + 1 and index index2 + 2 values and the table value Twotable of the variable i [index2 + 1] and table values twotable [index2 + 2] table values V ₂₁ and table values V ₂₂ and fractional power table Get from.

Then, the interpolation processing unit 141 performs an interpolation process using the lower value X _h2 and the table value V _{20 to the} table value V _22, and an interpolation value (2 ^ X _amari ) of the power value of the radix of the input value X. Ask for.

For example, when performing linear interpolation as the interpolation processing, the interpolation processing unit 141 calculates the equation (40) to (42) to obtain the interpolation value H = (2 ^ X _amari ). In this case, the lower value X _h1 , the table value V ₁₀ , and the table value V ₁₁ in the equations (40) to (42) are the lower value X _h2 , the table value V ₂₀ , and the table value V _21. .

Further, for example, when performing quadratic polynomial interpolation as the interpolation processing, the interpolation processing unit 141 calculates the interpolation value H = (2 ^ X _amari ) by calculating Expression (43) to Expression (46). In this case, the lower value X _h1 , the table value V ₁₀ , the table value V ₁₁ , and the table value V ₁₂ in the equations (43) to (46) are the lower value X _h2 , the table value V ₂₀ , and the table value V. ₂₁ and the table value V ₂₂ .

When the interpolation processing unit 141 does not perform the interpolation processing, the table value V ₂₀ is set to the interpolation value (2 ^ X _amari ) of the power of the radix of the input value X.

In step S177, power integer transform unit 263, the interpolation value from the interpolation processing section _{141 (1 + X 1/2} 23) Y and the interpolation value (2 ^ X _amari), and an integer X _int from Integer / fractional separation unit 102 Is used to calculate equation (53), and the integer part of the calculated value (P + α) is obtained. Then, the power integer conversion unit 263 outputs the obtained integer part as an output value, and the power calculation process ends.

  As described above, the arithmetic processing unit 251 obtains an integer part of the arithmetic value (P + α) using the interpolation value obtained by performing the interpolation processing. In this way, by performing the interpolation process to obtain the interpolated value of the power of the mantissa part of the input value X and the interpolated value of the power of the radix of the input value X, the power table of the mantissa and the power table of the decimal number are obtained. It is possible to improve the accuracy of the calculation for obtaining the integer part of the calculation value (P + α) without increasing the table size.

  Specifically, the present applicant evaluated the calculation accuracy of the integer part of the arithmetic processing unit 251 based on the absolute error average U obtained by calculating the above-described equation (54). When N = 8, that is, when SIZE = 256, when interpolation processing is added to the value of the mantissa power table (table value) and the value of the decimal power table (table value), respectively, Evaluation results shown in FIG. 20 were obtained for these combinations.

  FIG. 20 shows the value of the absolute error average U for each combination of the case where the interpolation process is added and the case where the interpolation process is not added. In other words, the character “decimal: no interpolation” indicates that the value of the decimal power table is used for calculation of the integer part of the calculated value (P + α) without performing interpolation processing, and the characters “decimal: linear interpolation” and “Decimal number: quadratic interpolation” indicates that linear interpolation and quadratic polynomial interpolation are performed on the value of the power table of the decimal and used to calculate the integer part of the calculated value (P + α).

  Similarly, the character “mantissa: no interpolation” indicates that the value of the power table of the mantissa is used for calculation of the integer part of the operation value (P + α) without performing the interpolation process, and the character “mantissa: linear interpolation” is used. "Mantissa: quadratic interpolation" indicates that linear interpolation and quadratic polynomial interpolation are performed on the value of the exponent table of the mantissa and used to calculate the integer part of the calculated value (P + α).

In FIG. 20, it can be seen that the calculation accuracy of the integer portion is improved by performing interpolation processing on at least one of the value of the mantissa power table or the value of the decimal power table. For example, if linear interpolation is applied to both the value of the mantissa power table and the value of the decimal power table, U = 1.71 × 10 ⁻² , and both the value of the mantissa power table and the value of the decimal power table are quadratic. When the polynomial interpolation is performed, U = 2.44 × 10 ⁻⁴ .

  In this way, the absolute error average value when the second-order polynomial interpolation is applied to both table values is the table when N = 16, that is, when SIZE = 65536, in the conventional quantizer 51. The accuracy is equal to or better than the calculation accuracy of the integer part used.

In the above description, the example in which the mantissa power table and the decimal power table have the same table size has been described. However, the table sizes may be different depending on the accuracy required for the power operation. . When the table size is changed, the bit position at the time of the interpolation process performed by the interpolation processing unit 141, that is, the size of the lower value X _h1 or the lower value X _h2 is also changed according to the size.

  In addition, it has been explained that interpolation processing is performed on both the mantissa power table value and the decimal power table value, but depending on the amount of interpolation processing and the required calculation accuracy, either value is set. Interpolation processing may be performed, or different interpolation processing may be performed. Furthermore, the interpolation processing is not limited to linear interpolation and quadratic polynomial interpolation, and may be performed by higher-order polynomial interpolation or spline interpolation.

  Furthermore, in the above description, the case where the radix of the input value X as a floating-point number is “2” has been described, but this radix is not limited to 2 and can be any value.

  The series of processes described above can be executed by hardware or can be executed by software. When a series of processing is executed by software, a program constituting the software may execute various functions by installing a computer incorporated in dedicated hardware or various programs. For example, it is installed from a program recording medium in a general-purpose personal computer or the like.

  FIG. 21 is a block diagram illustrating a configuration example of hardware of a computer that executes the above-described series of processing by a program.

  In a computer, a CPU (Central Processing Unit) 501, a ROM (Read Only Memory) 502, and a RAM (Random Access Memory) 503 are connected to each other by a bus 504.

  An input / output interface 505 is further connected to the bus 504. The input / output interface 505 includes an input unit 506 including a keyboard, mouse, and microphone, an output unit 507 including a display and a speaker, a recording unit 508 including a hard disk and a non-volatile memory, and a communication unit 509 including a network interface. A drive 510 for driving a removable medium 511 such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory is connected.

  In the computer configured as described above, the CPU 501 loads the program recorded in the recording unit 508 to the RAM 503 via the input / output interface 505 and the bus 504 and executes the program, for example. Is performed.

  The program executed by the computer (CPU 501) is, for example, a magnetic disk (including a flexible disk), an optical disk (CD-ROM (Compact Disc-Read Only Memory), DVD (Digital Versatile Disc), etc.), a magneto-optical disk, or a semiconductor. The program is recorded on a removable medium 511 that is a package medium including a memory or the like, or provided via a wired or wireless transmission medium such as a local area network, the Internet, or digital satellite broadcasting.

  The program can be installed in the recording unit 508 via the input / output interface 505 by attaching the removable medium 511 to the drive 510. Further, the program can be received by the communication unit 509 via a wired or wireless transmission medium and installed in the recording unit 508. In addition, the program can be installed in the ROM 502 or the recording unit 508 in advance.

  The program executed by the computer may be a program that is processed in time series in the order described in this specification, or in parallel or at a necessary timing such as when a call is made. It may be a program for processing.

  The embodiment of the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the gist of the present invention.

It is a figure which shows the structure of the conventional encoding apparatus. It is a figure which shows the structure of the conventional quantization apparatus. It is a flowchart explaining the quantization process by the conventional quantization apparatus. It is a figure which shows the structure of the data of the floating point type which shows a single precision floating point number. It is a figure which shows the structural example of one Embodiment of the arithmetic processing apparatus to which this invention is applied. It is a flowchart explaining a power calculation process. It is a figure explaining the part used in order to obtain a power value in floating point type data. It is a figure which shows the other structural example of an arithmetic processing unit. It is a flowchart explaining a power calculation process. It is a figure explaining linear interpolation. It is a figure explaining a quadratic polynomial interpolation. It is a figure which shows a relative error average. It is a figure which shows a relative error average. It is a figure which shows the other structural example of an arithmetic processing unit. It is a flowchart explaining a power calculation process. It is a figure which shows the other structural example of an arithmetic processing unit. It is a flowchart explaining a power calculation process. It is a figure which shows the other structural example of an arithmetic processing unit. It is a flowchart explaining a power calculation process. It is a figure which shows an absolute value error average. It is a figure which shows the structural example of a computer.

Explanation of symbols

  91 arithmetic processing unit, 101 mantissa / exponent separation unit, 102 integer / decimal separation unit, 103 mantissa power table holding unit, 104 decimal power table holding unit, 105 power operation unit, 106 integer conversion unit, 131 arithmetic processing unit, 141 interpolation processing unit, 171 arithmetic processing unit, 181 mantissa power table holding unit, 182 decimal power table holding unit, 183 power integer conversion unit, 211 arithmetic processing unit, 221 power integer conversion unit, 251 arithmetic processing unit, 261 mantissa Power table holding unit, 262 decimal power table holding unit, 263 power integer conversion unit

Claims (11)

An arithmetic processing device that performs a power of a predetermined input value X with a constant Y as a power exponent,
In floating-point data, the mantissa X ₁ is a mantissa representing the mantissa when that expresses the input value X in the floating-point number, the exponent for exponentiation upon representing said input values X in the floating-point number A mantissa / exponent separation means for separating the input value X into an exponent X _{2 of}
An integer / decimal separating means for separating the product of the exponent X ₂ and the constant Y into an integer X _int that is an integer part of the product and a decimal X _amari that is a decimal part of the product;
First recording means for recording a power value of the mantissa of the input value X, which is determined with respect to the mantissa X _{1 and} has the constant Y as a power exponent;
Determined with respect to the fractional X _amari, a second recording unit operable to fractional X _amari to the index, record the exponential value of the bottom when the representing said input values X in the floating-point number,
The power value of the mantissa obtained from the first recording means using the mantissa X ₁ , the power value of the base obtained from the second recording means using the decimal number X _amari , and the integer X _An arithmetic processing unit comprising: a power calculating means for calculating a power of the input value X, using the constant Y as a power exponent from _int . The mantissa and X ₁ using the obtained from the first recording means, performs interpolation processing using a plurality of the power values, further comprising an interpolation means for obtaining the final the exponential value of the mantissa,
The power calculation means is a power of the input value X with the constant Y as a power exponent from the power value of the base, the integer X _int , and the power value of the mantissa obtained by the interpolation means. The arithmetic processing device according to claim 1. Interpolating using a plurality of power values obtained from the second recording means using the decimal number X _amari , and further comprising an interpolation means for obtaining the final power value of the base,
The power calculation means is a power of the input value X using the constant Y as a power exponent from the power value of the mantissa, the integer X _int , and the power value of the base obtained by the interpolation means. The arithmetic processing device according to claim 1. An arithmetic processing unit that performs a power of a predetermined input value X with a constant Y as a power exponent;
In floating-point data, the mantissa X ₁ is a mantissa representing the mantissa when that expresses the input value X in the floating-point number, the exponent for exponentiation upon representing said input values X in the floating-point number A mantissa / exponent separation means for separating the input value X into an exponent X _{2 of}
An integer / decimal separating means for separating the product of the exponent X ₂ and the constant Y into an integer X _int that is an integer part of the product and a decimal X _amari that is a decimal part of the product;
First recording means for recording a power value of the mantissa of the input value X, which is determined with respect to the mantissa X _{1 and} has the constant Y as a power exponent;
Determined with respect to the fractional X _amari, a second recording unit operable to fractional X _amari to the index, record the exponential value of the bottom when the representing said input values X in the floating-point number,
The power value of the mantissa obtained from the first recording means using the mantissa X ₁ , the power value of the base obtained from the second recording means using the decimal number X _amari , and the integer X an arithmetic processing method of an arithmetic processing device comprising: a power calculating means for calculating a power of the input value X from the _{int with the} constant Y as a power exponent,
The mantissa / exponent separation means separates the input value X into the mantissa X ₁ and the exponent X ₂ ,
The integer / decimal separating means separates the product of the exponent X ₂ and the constant Y into the integer X _int and the decimal X _amari ;
An arithmetic processing method including a step of calculating a power of the input value X, wherein the power calculation means uses the constant Y as a power exponent. In an arithmetic processing unit that performs a power of a predetermined input value X with a constant Y as a power exponent,
In floating point type data, a mantissa X ₁ which is a mantissa representing a mantissa when the input value X is represented by a floating point number, and an exponent part representing an exponent when the input value X is represented by a floating point number The input value X is separated into an index X ₂ that is
The product of the exponent X ₂ and the constant Y, separated an integer X _int is an integer part of the product, in a fraction X _amari a fractional part of the product,
The mantissa obtained using the X _1, determined with respect to the mantissa X _1, power value of the mantissa of the input value X to the constant Y the exponent was obtained using the fractional X _amari, the fractional The constant Y is defined as a power exponent from a power value that uses the decimal value X _amari at the base when the input value X is expressed as a floating-point number, and the integer X _int , which is determined with respect to X _amari . A program for executing a process including a step of calculating a power of the input value X. An arithmetic processing unit that obtains an integer of a power value of a predetermined input value X with a constant Y as a power exponent,
In floating-point data, the mantissa X ₁ is a mantissa representing the mantissa when that expresses the input value X in the floating-point number, the exponent for exponentiation upon representing said input values X in the floating-point number A mantissa / exponent separation means for separating the input value X into an exponent X _{2 of}
An integer / decimal separating means for separating the product of the exponent X ₂ and the constant Y into an integer X _int that is an integer part of the product and a decimal X _amari that is a decimal part of the product;
The input value X represented by a floating-point number, which is determined with respect to the mantissa X ₁ , is a power value of the mantissa of the input value X having the constant Y as a power exponent, and the decimal number X _amari is a power exponent. Obtained by subtracting the integer X _int from the number of bits from the least significant bit of the fixed-point data to the decimal point position, for the fixed-point data that represents the product of the power of the base An arithmetic processing unit comprising: a power integer conversion unit that performs a right shift operation by the number of bits indicating the number to be obtained to obtain the integer of the power value of the input value X. First recording means for recording the power value of the mantissa of the input value X, which is determined with respect to the mantissa X ₁ ;
Second recording means for recording the power value of the base determined for the decimal number X _amari ; and
The power integer converting means is the power value of the mantissa acquired from the first recording means using the mantissa X ₁ and the power acquired from the second recording means using the decimal number X _amari. The arithmetic processing device according to claim 6, wherein the integer of the power value of the input value X is obtained using the power value of the base. The mantissa and X ₁ using the obtained from the first recording means, performs interpolation processing using a plurality of the power values, further comprising an interpolation means for obtaining the final the exponential value of the mantissa,
The arithmetic processing apparatus according to claim 7, wherein the power integer conversion unit obtains the integer of the power value of the input value X using the power value of the mantissa obtained by the interpolation unit. Interpolating using a plurality of power values obtained from the second recording means using the decimal number X _amari , and further comprising an interpolation means for obtaining the final power value of the base,
The arithmetic processing device according to claim 7, wherein the power integer conversion unit obtains the integer of the power value of the input value X using the power value of the base obtained by the interpolation unit. An arithmetic processing unit that obtains an integer of a power value of a predetermined input value X with a constant Y as a power exponent;
In floating-point data, the mantissa X ₁ is a mantissa representing the mantissa when that expresses the input value X in the floating-point number, the exponent for exponentiation upon representing said input values X in the floating-point number A mantissa / exponent separation means for separating the input value X into an exponent X _{2 of}
An integer / decimal separating means for separating the product of the exponent X ₂ and the constant Y into an integer X _int that is an integer part of the product and a decimal X _amari that is a decimal part of the product;
The input value X represented by a floating-point number, which is determined with respect to the mantissa X ₁ , is a power value of the mantissa of the input value X having the constant Y as a power exponent, and the decimal number X _amari is a power exponent. Obtained by subtracting the integer X _int from the number of bits from the least significant bit of the fixed-point data to the decimal point position, for the fixed-point data that represents the product of the power of the base An arithmetic processing method of an arithmetic processing device, comprising: a power integer conversion unit that performs a right shift operation by the number of bits indicating the number to be obtained and obtains the integer of the power value of the input value X,
The mantissa / exponent separation means separates the input value X into the mantissa X ₁ and the exponent X ₂ ,
The integer / decimal separating means separates the product of the exponent X ₂ and the constant Y into the integer X _int and the decimal X _amari ;
An arithmetic processing method including a step in which the power integer conversion means obtains the integer of the power value of the input value X. In an arithmetic processing unit that obtains an integer of a power value of a predetermined input value X with a constant Y as a power exponent,
In floating point type data, a mantissa X ₁ which is a mantissa representing a mantissa when the input value X is represented by a floating point number, and an exponent part representing an exponent when the input value X is represented by a floating point number The input value X is separated into an index X ₂ that is
The product of the exponent X ₂ and the constant Y, separated an integer X _int is an integer part of the product, in a fraction X _amari a fractional part of the product,
The input value X represented by a floating-point number, which is determined with respect to the mantissa X ₁ , is a power value of the mantissa of the input value X having the constant Y as a power exponent, and the decimal number X _amari is a power exponent. Obtained by subtracting the integer X _int from the number of bits from the least significant bit of the fixed-point data to the decimal point position, for the fixed-point data that represents the product of the power of the base A program for executing a process including a step of calculating a right power value of the input value X by performing a right shift operation by the number of bits indicating a given number.

Images