JP2009276990A - Computing device, its calculation method, signal processing device, computing device control program, and recording medium in which program is recorded - Google Patents

Abstract

The calculation accuracy of a calculation device is improved.
In a calculation method of a logarithmic operation device that performs logarithmic operation on an input value X and outputs an output value logX, the value of an operation parameter α is set based on the input value X (S12). The input value X is converted to the calculation target value Z by the calculation conversion function Z = αX including the set value of the calculation parameter α (S13). A logarithmic operation is performed on the converted operation target value Z, and an operation result value logZ is obtained (S14). The calculation result value logZ is converted into the output value logX using the output conversion function logX = logZ−logα including the value of the output parameter logα set based on the value of the calculation parameter α (S15). The value of the calculation parameter α is set so that a part or all of the range of the calculation target value Z within which the error of the calculation result value logZ is within the allowable range falls within the value range of the calculation conversion function Z = αX. Is called.
[Selection] Figure 1

Description

  The present invention relates to an arithmetic device that performs an operation on an input value and outputs an output value, a control method therefor, a signal processing device, an arithmetic device control program, and a recording medium on which the program is recorded. Specifically, the present invention relates to an arithmetic unit that performs logarithmic calculation, such as used for calculating decibels.

  The decibel is a kind of index that represents the ratio of the amount proportional to the square of the amplitude of the wave, the ratio of the magnitude of energy transmitted to a unit time through a certain surface, and the other ratio in a logarithmic scale. The decibel value is 10 times the common logarithm of the above ratio, and the decibel unit is dB. An example of the amount proportional to the square of the amplitude of the wave is the intensity of the sound proportional to the square of the amplitude of the sound pressure. An example of the magnitude of energy transmitted per unit time through a certain surface is AC power transmitted through a conductor.

  The decibel is frequently used as an indicator of the intensity of waves such as sound waves and electromagnetic waves. This is due to the following reason. That is, according to Non-Patent Document 1, if the intensity of the stimulus is R and the magnitude of the sense of the stimulus is E, E is proportional to the logarithm of R. This is known as the Weber-Fechner law. Based on this law, a decibel that widely expresses the ratio of the signal intensity of a wave to a certain reference value on a logarithmic scale is widely used. From this, it is important that the logarithm can be calculated with high accuracy for calculating decibels in a circuit or software that handles wave signals such as sound wave signals and electromagnetic wave signals.

  According to Patent Document 1 and Non-Patent Document 2, as a method of calculating a logarithm, there is an STL (Sequential Table Look-up) method in which a function is calculated while sequentially referring to a table. FIG. 9 shows an algorithm for obtaining a logarithm logX of a real number X satisfying 1 ≦ X <2 by using the STL method (step S100 (hereinafter sometimes abbreviated as “S100”. The same applies to other steps). )). In the present application, the logarithm log is a common logarithm with a base of 10.

As shown in FIG. 9, first, variables j, S _j, and P _j are initialized as shown in the following equation (step S111).
j = 0, P ₀ = 0, S ₀ = X−1 (1).

Next, a determination condition C _{j + 1} is obtained from the variable S _j based on the following equation (S112).
C _{j + 1} = 2S _j − (1 + 2− ^j S _j ) (2).

Next, depending on whether or not the determination condition C _{j + 1} is 0 or more, a variable a _{j + 1} · A _{j + 1} is obtained based on the following equation (S113 to S115).
When C _{j + 1} ≧ 0, a _{j + 1} = 1, A _{j + 1} = 1−2 ^−j−1 ,
When C _{j + 1} <0, a _{j + 1} = 0, A _{j + 1} = 1 (3).

Next, the variable S _{j + 1} · P _{j + 1} is obtained from the variable a _{j + 1} · A _{j + 1} based on the following equation, and the variable j is changed to j + 1 (S116).
_{P j + 1 = P j -logA} j + 1, S j + 1 = 2S j A j + 1 -a j + 1 (4).

Next, the above steps S112 to S116 are repeated until j = N (S117). Then, logX from the variable _{P N} is obtained by the following equation (S118).
logX = P _N (5).

  FIG. 10 shows an example of a conventional logarithmic arithmetic device that implements the algorithm (S100) shown in FIG. The logarithmic arithmetic unit 110 performs logarithmic calculation logY on one or more input real numbers Y and outputs the result. As shown in the figure, the STL arithmetic circuit 120, the arithmetic range conversion unit 130, and the output A range conversion unit 131 is provided.

  As shown in FIG. 9, the STL calculation circuit 120 calculates a logarithm logX from a real number X satisfying 1 ≦ X <2 by using the STL method. That is, the real number X is a calculation target value that is a calculation target in the STL calculation circuit 120, and the logarithm logX is a calculation result value that is a result calculated by the STL calculation circuit 120. Details of the STL arithmetic circuit 120 will be described later.

  In the following, the range of calculation target values that can be input to the STL calculation circuit 120 is referred to as “calculation range”, and the range of calculation result values calculated by the STL calculation circuit 120 for the calculation target values in the calculation range is “ This is referred to as “calculation result range”. For example, in the case of FIG. 9, the calculation range is a real number of 1 or more and less than 2, and the calculation result range is a real number of 0 or more and less than log2.

  The arithmetic range conversion unit 130 converts the input value Y input to the logarithmic arithmetic unit 110 into a numerical value suitable for the arithmetic range in the STL arithmetic circuit 120 and sends it to the STL arithmetic circuit 120 as the arithmetic target value X. It is.

  Specifically, the calculation range conversion unit 130 uses the range of the input value Y (positive real number) as the domain and the range of the calculation target value X (real number between 1 and 2) as the range, and the input value Y Is converted in advance into a calculation target value X. Next, the calculation range conversion unit 130 sets the value of the calculation range parameter included in the calculation range conversion function based on the input value Y. Then, the calculation range conversion unit 130 calculates the calculation target value X from the input value Y by using the calculation range conversion function including the set calculation range parameter value, and calculates the calculated calculation target value X. The data is sent to the STL arithmetic circuit 120.

  The output range conversion unit 131 converts the calculation result value logX calculated by the STL calculation circuit 120 into a numerical value suitable for the output range output from the logarithmic calculation device 110, and outputs it as an output value logY.

  Specifically, the output range conversion unit 131 uses the range of the operation result value logX (a real number greater than or equal to 0 and less than log2) as the domain, the range of the output value logY (the real number) as the range, and the operation result value logX as the range. An output range conversion function for converting the output value logY is set in advance. Next, the output range conversion unit 131 sets the value of the output range parameter included in the output range conversion function based on the value of the calculation range parameter set by the calculation range conversion unit 130. Then, the output range conversion unit 131 calculates the output value logY from the operation result value logX by using the output range conversion function including the set output range parameter value, and outputs the calculated output value logY. To do.

Next, the STL arithmetic circuit 120 will be described. As illustrated in FIG. 10, the STL arithmetic circuit 120 includes a repetition processing unit 121 that repeatedly performs processing, and a counter 129 that counts the current number j of repetitions in the repetition processing unit 121. In addition, the iterative processing unit 121 performs condition determination by calculating the determination condition C _{j + 1 according} to the above equation (2) and the two registers 122 and 123 that store the values of the two variables S _j and P _j , respectively. Unit 128, LUT (Look Up Table) 124 that stores the value of log (1-2 ^−j−1 ) in advance, barrel shifter 125 that shifts the value of variable S _j of register 122, and the above equation (4) It is the structure provided with the calculating parts 126 * 127 which calculates.
US Pat. No. 3,631,230 (issued December 28, 1971) Toshiro Oga, "Multimedia System Engineering", Corona Inc., 2004 Naoki Takagi, “VLSI Algorithm for Arithmetic Operations”, Corona Inc., 2005

FIG. 11 is a graph showing the relationship between a real number X satisfying 1 ≦ X <2 and log ₁₀ X numerically calculated using the STL method shown in FIG. (A) ~ (f) of FIG. 11 are graphs in the case where the calculated _{log 10} X repetition number N as 5-10. In the graph of the figure, the horizontal axis is a real number X, and the vertical axis is log ₁₀ X. Also, the thick line is the above-mentioned numerical calculation. For comparison, log ₁₀ X calculated by floating-point processing is shown as a thin line as an expected value.

  Referring to FIG. 11, it can be understood that increasing the number of repetitions N reduces errors (shifts of thick lines with respect to thin lines) and improves accuracy. However, it can be understood that there is a large error in the region near X = 1.3 and the region where 1.7 ≦ X <2, and that the error is not improved much by increasing the number of repetitions N.

  In the case of FIG. 11, the maximum value of the error is around 0.1. In general, the power decibel is obtained by multiplying the logarithmic value by 10, while the voltage decibel is obtained by multiplying the logarithmic value by 20 because the power is proportional to the square of the voltage. Accordingly, when the error of the logarithmic value obtained by the STL method is 0.1, an error of 1 to 2 dB occurs in the decibel.

  The present invention has been made in view of the above problems, and an object of the present invention is to provide an arithmetic device with improved arithmetic accuracy.

  An arithmetic device according to the present invention is an arithmetic device that performs an operation on an input value that is input and outputs an output value. In order to solve the above problem, the value of a parameter for calculation is calculated based on the input value. An arithmetic conversion function including a calculation setting means to be set and a calculation parameter value set by the calculation setting means for converting the input value to a calculation target value that is a target value of the calculation A conversion unit, a calculation unit that performs the calculation on the calculation target value converted by the calculation conversion unit and obtains a calculation result value that is a result of the calculation, and is set based on the value of the calculation parameter. An output conversion function including an output parameter value, and an output conversion means for converting the calculation result value obtained by the calculation means into the output value. The error is Depending on the value, the setting means for calculation is such that a part or all of the range of the calculation target value within which the error of the calculation result value falls within an allowable range falls within the range of the conversion function for calculation. Further, the value of the calculation parameter is set.

  An arithmetic method for an arithmetic device according to the present invention is an arithmetic method for an arithmetic device that performs an operation on an input value that is input and outputs an output value. A calculation setting step in which the calculation device sets the calculation parameter value, and a calculation conversion function including the calculation parameter value set in the calculation setting step. An arithmetic conversion step in which the arithmetic device converts the input value into an arithmetic target value, and the arithmetic device performs the arithmetic operation on the arithmetic target value converted in the arithmetic conversion step, so that the arithmetic operation is performed. And an output conversion function including an output parameter value set based on the value of the operation parameter, and an operation result acquired in the operation step. An output conversion step in which the arithmetic device converts a value into the output value. In the calculation step, an error in the calculation result value depends on the calculation target value, and the calculation setting step Then, the value of the calculation parameter is set so that a part or all of the range of the calculation target value within which the error of the calculation result value falls within an allowable range falls within the range of the calculation conversion function. It is characterized by that.

  According to the above configuration and method, first, the value of the operation parameter of the operation conversion function is set based on the input value input to the operation device. At this time, the value of the calculation parameter is set so that a part or all of the range of the calculation target value within which the error of the calculation result value is within the allowable range falls within the range of the calculation conversion function.

  Next, the input value is converted into a calculation target value by a calculation conversion function including the value of the calculation parameter. At this time, the converted calculation target value is included in the range of the calculation target value such that the error of the calculation result value is within the allowable range.

  Next, a calculation is performed on the converted calculation target value, and a calculation result value is acquired. At this time, the obtained calculation result value has an error within an allowable range, so that the calculation accuracy can be improved. The calculation result value is converted into an output value by an output conversion function including the value of the output parameter set based on the calculation parameter, and is output from the calculation device.

  Therefore, an output value with improved calculation accuracy can be output by the calculation device and the calculation method according to the present invention. In addition, although the allowable range of the error of the calculation result value is, for example, about 5% of the expected value, it depends on the calculation accuracy required for the calculation device.

  The arithmetic device according to the present invention further includes a storage unit that stores correspondence information in which the range of the input value is associated with the value of the arithmetic parameter, and the arithmetic setting unit includes the input value. It is preferable that the value of the calculation parameter corresponding to the range to be searched is set by searching from the correspondence information in the storage unit. In this case, the value of the calculation parameter such that a part or all of the range of the calculation target value within which the error of the calculation result value falls within an allowable range falls within the range of the calculation conversion function is input. Can be easily obtained from the value.

  An example of the calculation performed by the calculation means is calculation based on the STL method. This calculation based on the STL method can be applied to the calculation of functions such as exponential functions, logarithmic functions, trigonometric functions, quotients, and square roots.

  By the way, in the calculation based on the STL method, for example, as shown in FIGS. 9 and 10, table reference, shift calculation, calculation condition determination, and calculation based on the determined calculation condition are repeatedly performed. For this reason, as the number of repetitions increases, the calculation time becomes longer.

  Therefore, in the arithmetic device according to the present invention, the arithmetic means has a configuration in which a plurality of arithmetic units are connected in series, and each of the arithmetic units stores a first register and a value of a second variable, respectively. And a second register, a condition determination unit that determines a calculation condition, a shifter that shifts the value of the first variable in the first register based on the calculation condition determined by the condition determination unit, and a first register in the first register Based on the value of one variable, the value of the first variable shifted by the shifter, and the calculation condition determined by the condition determination unit, a first calculation unit that performs a first calculation, and a second register in the second register A second calculation unit that performs a second calculation based on the value of the two variables and the calculation condition determined by the condition determination unit, wherein the first calculation unit and the second calculation unit are the first calculation and the second calculation unit, respectively. Of the second operation The result value is sent to the first register and the second register in the arithmetic unit at the next stage, and with respect to the arithmetic unit at the first stage, the value of the first variable is a value based on the arithmetic target value, and the second variable Is a value based on the calculation target value or an initial value, and the result of the second calculation performed by the second calculation unit with respect to the final calculation unit may be the calculation result value.

  In this case, a shifter that performs shift, a condition determination unit that determines a calculation condition, and a plurality of calculation units including first and second calculation units that perform calculation based on the determined calculation condition are connected in series. The number of repetitions can be reduced, and an increase in calculation time can be suppressed.

  In addition, if it is a signal processing device that processes at least one of a sound wave and an electromagnetic wave signal, and is a signal processing device that uses the arithmetic device having the above-described configuration to calculate the intensity of the signal, the same effect as described above The effect of can be produced.

  Moreover, each means of the said arithmetic unit can be performed on a computer by a calculation program. Furthermore, the arithmetic program can be executed on an arbitrary computer by storing the arithmetic program in a computer-readable recording medium.

  As described above, the arithmetic device according to the present invention is such that the value of the arithmetic parameter of the arithmetic conversion function is within an allowable range based on the input value input to the arithmetic device. Since part or all of the range of the calculation target value is set to be within the range of the calculation conversion function, the input value is converted into the calculation target value by the calculation conversion function including the value of the calculation parameter. Then, the calculation is performed on the converted calculation target value, and the obtained calculation result value has an error within an allowable range, so that the calculation accuracy can be improved.

  An embodiment of the present invention will be described with reference to FIGS. FIG. 2 shows an outline of the logarithmic arithmetic apparatus of this embodiment. The logarithmic arithmetic device (arithmetic device) 1 of the present embodiment is suitable for an arithmetic device that calculates the intensity of the signal in a signal processing device that processes a sound wave and / or electromagnetic wave signal.

  The logarithmic arithmetic unit 1 shown in FIG. 2 is more accurate than the conventional logarithmic arithmetic unit 110 shown in FIG. 10 between the arithmetic range converter 130 and the STL arithmetic circuit (arithmetic unit) 120. Is different from the point that the calculation result range conversion unit 11 is provided between the output range conversion unit 131 and the STL calculation circuit 120, and the other configurations are the same. In addition, the same code | symbol is attached | subjected to the structure which has the function similar to the structure demonstrated by the said background art, and the description is abbreviate | omitted.

  The high-precision calculation range conversion unit 10 converts the calculation range numerical value X from the calculation range conversion unit 130 into a numerical value suitable for the high-precision calculation range. Here, the high-precision calculation range refers to a part or all of the range of the calculation target value in which the error of the calculation result value in the STL calculation circuit 120 is within the allowable range.

  For example, when the calculation of the STL calculation circuit 120 is as shown in the graph of FIG. 11F, the high-precision calculation range is 1 ≦ Z <1.71 excluding 1.71 or more, or 1 ≦ Z <1.25 and 1.35 ≦ Z <1.71 excluding the vicinity of 1.3. Whether or not the calculation target value Z = 1.3 should be excluded depends on whether or not the error of the calculation result value is within the allowable range. Note that the allowable range of the error depends on the calculation accuracy required for the logarithmic calculation device 1.

  The high-precision calculation range conversion unit 10 sends the converted numerical value Z in the high-precision calculation range to the STL calculation circuit 120 as a calculation target value. As a result, the calculation result value logZ calculated by the STL calculation circuit 120 has an error within an allowable range. That is, the calculation in the STL calculation circuit 120 is a highly accurate calculation.

  The calculation result range conversion unit 11 converts the calculation result value logZ calculated by the STL calculation circuit 120 into a numerical value logX suitable for the calculation result range described above. The calculation result range conversion unit 11 sends the converted numerical value logX to the output range conversion unit 131.

  Next, details of the high-accuracy calculation range conversion unit 10, the calculation result range conversion unit 11, the calculation range conversion unit 130, and the output range conversion unit 131 will be described with reference to FIGS. First, details of the calculation range conversion unit 130 and the output range conversion unit 131 will be described.

  As described above, the arithmetic range conversion unit 130 converts the input value Y, which is an arbitrary positive real number, into the numerical value X, which is a real number that satisfies 1 ≦ X <2. The output range conversion unit 131 converts a numerical value logX that is a logarithm of the numerical value X into an output value logY that is a logarithm of the input value Y.

By the way, an arbitrary positive real number Y can be expressed by a real number X (where 1 ≦ X <2), an integer k (where 0 ≦ k ≦ 3), and an integer l satisfying the following equation.
Y = X × 2 ^k × 10 ^l (6).

This is due to the following reason. That is, since the real number X satisfies 1 ≦ X <2, X × 2 ^k is 1 ≦ X × 2 ^k <2 when k = 0, and 2 ≦ X × 2 ^k <4 when k = 1. When k = 2, 4 ≦ X × 2 ^k <8, and when k = 3, 8 ≦ X × 2 ^k <16. Therefore, when 0 ≦ k ≦ 3 (k is an integer) and 1 ≦ X <2 (X is a real number), X × 2 ^k is 1 ≦ X × 2 ^k <16, and any real number greater than or equal to 1 and less than 10 Can be expressed. Further, by changing the digit by 10 ^l (l is an integer), X × 2 ^k × 10 ^l can express any positive real number Y.

Further, taking the logarithm of the above equation (6), the following equation is obtained.
logY = logX + k * log2 + l * log10≈logX + 0.301k + 1 (7).
Therefore, if the logarithm log X of any real number X satisfying 1 ≦ X <2 can be calculated, the logarithm log Y of any positive real number Y is also calculated by using the calculated log logX, the integer k, and the integer l. It can be calculated.

  As described above, in the present embodiment, the calculation range conversion unit 130 first sets the equation (6) as the above-described calculation range conversion function, and uses the parameters k and l included in the equation (6) as the calculation range parameters. It is preset as (calculation parameter). Next, the calculation range conversion unit 130 sets the values of the calculation range parameters k and l based on the input value Y and the above equation (6). Then, the calculation range conversion unit 130 calculates the calculation range numerical value X from the input value Y based on the set values of the calculation range parameters k and l and the above equation (6), and calculates the calculation range The numerical value X is sent to the high-accuracy calculation range conversion unit 10.

  On the other hand, in the output range conversion unit 131, the above equation (7) is preset as an output range conversion function. Then, the output range conversion unit 131 obtains the output value logY from the calculation result range numerical value logX based on the values of the calculation range parameters k and l set by the calculation range conversion unit 130 and the above equation (7). The calculated output value logY is output.

  FIG. 3 shows a schematic configuration of the calculation range conversion unit 130, the output range conversion unit 131, the high-precision calculation range conversion unit 10, and the calculation result range conversion unit 11. As shown in the figure, the calculation range conversion unit 130 includes an input value acquisition unit 132, a calculation range setting unit (calculation setting means) 133, a calculation range correspondence table (corresponding information) 134, and a calculation range calculation unit ( (Conversion means for calculation) 135 is provided.

  The input value acquisition unit 132 acquires the input value Y input to the logarithmic arithmetic unit 1. The input value acquisition unit 132 sends the acquired input value Y to the calculation range setting unit 133 and the calculation range calculation unit 135.

The calculation range correspondence table 134 includes a correspondence relationship between the input value Y and the calculation range parameters k and l in a table format. The calculation range correspondence table 134 is set in advance based on the equation (6). FIG. 4 shows an example of the calculation range correspondence table 134. The range of the input value Y and the calculation range parameter l are associated with (a) in the figure, and the range of the calculated value Y / 10 ^l and the calculation range parameter k are shown in (b) of the figure. Are associated.

  The calculation range setting unit 133 refers to the calculation range correspondence table 134 and sets the values of the calculation range parameters k and l corresponding to the input value Y from the input value acquisition unit 132. The calculation range setting unit 133 sends the set values of the calculation range parameters k and l to the calculation range calculation unit 135 and the output range conversion unit 131.

Specifically, the calculation range setting unit 133 acquires the value of the calculation range parameter l corresponding to the input value Y with reference to a table as shown in FIG. Next, the operation range for setting section 133 calculates the Y / 10 ^l, indicating the value of the operation range for the parameter k corresponding to a calculation result calculated value Y / 10 ^l, for example in (b) of FIG. 4 Get by referring to a table like this.

  The calculation range calculation unit 135 substitutes the input value Y from the input value acquisition unit 132 and the values of the calculation range parameters k and l from the calculation range setting unit 133 into the above equation (6) for calculation. By doing so, the numerical value X for the calculation range is calculated. The calculation range calculation unit 135 sends the calculated calculation range value X to the high-precision calculation range conversion unit 10.

  On the other hand, as shown in FIG. 3, the output range conversion unit 131 includes a calculation result range acquisition unit 136 and an output value calculation unit (output conversion means) 137.

  The calculation result range acquisition unit 136 acquires the calculation result range numerical value logX from the calculation result range conversion unit 11. The calculation result range acquisition unit 136 sends the acquired calculation result range numerical value logX to the output value calculation unit 137.

  The output value calculation unit 137 calculates the calculation result range numerical value logX from the calculation result range acquisition unit 136 and the values of the calculation range parameters k and l from the calculation range conversion unit 130 in the above equation (7). By substituting and calculating, the output value logY is calculated. The output value calculation unit 137 outputs the calculated output value logY from the logarithmic operation device 1.

  Next, details of the high-accuracy calculation range conversion unit 10 and the calculation result range conversion unit 11 added in the present embodiment will be described. As described above, the high-accuracy calculation range conversion unit 10 converts the calculation range numerical value X from the calculation range conversion unit 130 into a numerical value suitable for the high-precision calculation range. The calculation result range conversion unit 11 converts the calculation result value logZ calculated by the STL calculation circuit 120 into a numerical value logX suitable for the calculation result range.

  The processing content of the high-precision calculation range conversion unit 10 converting the calculation range numerical value X into the high-precision calculation range numerical value Z is determined as follows. That is, first, the calculation range is divided into the high-precision calculation range and the other low-precision calculation ranges. The high-precision calculation range and the low-precision calculation range may each be divided into a plurality of small ranges.

Next, the conversion function for the high-precision calculation range that converts the numerical value of the low-precision calculation range into the numerical value of the high-precision calculation range and converts the numerical value of the high-precision calculation range into the numerical value of the high-precision calculation range. Determine the parameters for the high-precision calculation range. As an example of the conversion function for the high-precision calculation range, the following expression can be given.
Z = αX (8).

  Therefore, in the present embodiment, the high-accuracy calculation range conversion unit 10 first sets the equation (8) as the high-precision calculation range conversion function, and sets the parameter α included in the equation (8) as the high-precision calculation range. Are preset as operation parameters (calculation parameters). Next, the high-precision calculation range conversion unit 10 sets the value of the high-precision calculation range parameter α based on the calculation range numerical value X and the above equation (8). Then, the high-accuracy calculation range conversion unit 10 calculates the high-precision calculation range value Z from the calculation range value X based on the set value of the high-precision calculation range parameter α and the above equation (8). The calculated numerical value Z for the high precision calculation range is sent to the STL calculation circuit 120 as the calculation target value.

Moreover, when the logarithm of the above equation (8) is taken, the following equation is obtained.
logZ = logα + logX (9).
Therefore, the calculation result range conversion unit 11 first prepares an LUT in which values that can be taken by the high-precision calculation range parameter α and the logarithmic log α value of the value are associated in advance. Next, the calculation result range conversion unit 11 reads the logarithm log α value corresponding to the value of the high accuracy calculation range parameter α set by the high accuracy calculation range conversion unit 10 from the LUT. Then, the calculation result range conversion unit 11 calculates the calculation result range numerical value logX from the calculation result value logZ from the STL calculation circuit 120 based on the read logarithm log α value and the above equation (9). The calculated operation result range numerical value logX is sent to the output range conversion unit 131.

  Next, the configuration of the high-accuracy calculation range conversion unit 10 and the calculation result range conversion unit 11 will be described. As shown in FIG. 3, the high-accuracy calculation range conversion unit 10 includes a calculation range acquisition unit 12, a high-precision calculation range setting unit (setting unit) 13, and a high-precision calculation range correspondence table (corresponding information). 14 and a high-precision calculation range calculation unit (calculation conversion means) 15.

  The calculation range acquisition unit 12 acquires the calculation range numerical value X from the calculation range conversion unit 130. The calculation range acquisition unit 12 sends the acquired calculation range numerical value X to the high accuracy calculation range setting unit 13 and the high accuracy calculation range calculation unit 15.

  The high-precision calculation range correspondence table 14 includes a correspondence relationship between the calculation range numerical value X and the high-precision calculation range parameter α in a table format. The high-precision calculation range correspondence table 14 is set in advance based on the above equation (8).

  FIG. 5 shows an example of the high-accuracy calculation range correspondence table 14. (A) of the figure shows an example in which 1 ≦ X <1.71 is set as the high-precision calculation range and 1.71 ≦ X <2 is set as the low-precision calculation range. In the illustrated example, when the calculation range numerical value X is included in the low-precision calculation range (1.71 ≦ X <2), the high-precision calculation range numerical value Z = αX is the high-precision calculation range (1 ≦ X <1. 71), α = 0.85 is set.

  On the other hand, when the calculation range numerical value X is included in the high-precision calculation range, α = 1 is set. This is also considered to be the high-precision arithmetic range numerical value Z as it is without converting the arithmetic range numerical value X.

  5B, 1 ≦ X <1.1 and 1.35 ≦ X <1.71 are the first and second high-precision calculation ranges, respectively, and 1.1 ≦ X <1. 35 and 1.71 ≦ X <2 are shown as the first and second low-precision calculation ranges, respectively. In the illustrated example, when the calculation range numerical value X is included in the first low-precision calculation range (1.1 ≦ X <1.35), the high-precision calculation range value Z = αX is the second high-precision calculation. Α = 1.25 is set so as to be included in the range (1.35 ≦ X <1.71). Further, when the calculation range numerical value X is included in the second low-precision calculation range (1.71 ≦ X <2), the high-precision calculation range numerical value Z = αX is the second high-precision calculation range (1.35). Α = 0.85 is set so as to be included in ≦ X <1.71).

  On the other hand, when the calculation range numerical value X is included in the first and second high-precision calculation ranges (1.1 ≦ X <1.35 and 1.71 ≦ X <2), α = 1 is set. . This is also considered to be the high-precision arithmetic range numerical value Z as it is without converting the arithmetic range numerical value X.

  The high-precision calculation range setting unit 13 refers to the high-precision calculation range correspondence table 14 and sets the value of the high-precision calculation range parameter α corresponding to the calculation range value X from the calculation range acquisition unit 12. To do. The high-precision calculation range setting unit 13 sends the set value of the set high-precision calculation range parameter α to the high-precision calculation range calculation unit 15 and the calculation result range conversion unit 11.

  The high-precision calculation range calculation unit 15 calculates the calculation range numerical value X from the calculation range acquisition unit 12 and the value of the high-precision calculation range parameter α from the high-precision calculation range setting unit 13 from the above formula ( The numerical value Z for high-precision calculation range is calculated by substituting into 8) and calculating. The high-precision calculation range calculation unit 15 sends the calculated high-precision calculation range numerical value Z to the STL calculation circuit 120.

  On the other hand, the calculation result range conversion unit 11 includes a high-precision calculation result range acquisition unit 16, a calculation result range LUT 17, and a calculation result range calculation unit (output conversion means) 18, as shown in FIG. It is a configuration.

  The high-precision calculation result range acquisition unit 16 acquires a high-precision calculation result range numerical value logZ as a calculation result value calculated by the STL calculation circuit 120. The high-precision calculation result range acquisition unit 16 sends the acquired high-precision calculation result range numerical value logZ to the calculation result range calculation unit 18.

  The calculation result range LUT 17 stores possible values of the high-precision calculation range parameter α set by the high-precision calculation range conversion unit 10 and the logarithm log α of the value in association with each other. When the calculation result range LUT 17 acquires the value of the high-precision calculation range parameter α from the high-precision calculation range conversion unit 10, it sends the corresponding logarithm log α value to the calculation result range calculation unit 18.

  Note that the value of the high-accuracy calculation range parameter α is two in the example of FIG. 5A and three in the example of FIG. 5B. Therefore, since the calculation result range LUT 17 only needs to store several sets of associated values, it does not significantly affect the increase in processing and the circuit scale. Further, when the value of the parameter α for the high accuracy calculation range is 1, the logarithm log α is 0. Therefore, the calculation result range LUT 17 does not store the case of α = 1, and the calculation result is obtained when the value of the high-precision calculation range parameter α received from the high-precision calculation range conversion unit 10 is not stored. You may make it send 0 to the calculation part 18 for ranges. In this case, the number of values stored in the calculation result range LUT 17 can be further reduced.

  The calculation result range calculation unit 18 substitutes the high-precision calculation result range numerical value logZ from the high-precision calculation result range acquisition unit 16 and the numerical value log α from the calculation result range LUT 17 into the equation (9). To calculate the calculation result range numerical value logX. The calculation result range calculation unit 18 sends the calculated calculation result range numerical value logX to the output range conversion unit 131.

  Next, processing operations in the logarithmic arithmetic apparatus 1 having the above-described configuration will be described with reference to FIG. FIG. 1 shows a processing flow of the high-accuracy calculation range conversion unit 10, the STL calculation circuit 120, and the calculation result range conversion unit 11 in the logarithmic calculation apparatus 1.

  As shown in FIG. 1, the high-accuracy calculation range conversion unit 10 first calculates a calculation range numerical value X (1 ≦ X <2) obtained by converting the input value Y, which is a positive real number, by the calculation range conversion unit 130. The calculation range acquisition unit 12 acquires (S11). Next, the high-accuracy calculation range setting unit 13 corresponds to the value of the high-accuracy calculation range parameter α corresponding to the range including the calculation range numerical value X acquired by the calculation range acquisition unit 12. It is read from the table 14 and set (S12). Next, using the value of the high-precision calculation range parameter α set by the high-precision calculation range setting unit 13, the high-precision calculation range calculation unit 15 calculates Z = αX, thereby obtaining the calculation range. The numerical value Z for high accuracy calculation range is calculated from the numerical value X for calculation range acquired by the unit 12 (S13).

  Next, the STL calculation circuit 120 performs logarithmic calculation based on the STL method for the high-precision calculation range numerical value Z calculated by the high-precision calculation range conversion unit 10 to obtain a high-precision calculation result range that is a calculation result value. A numerical value logZ is obtained (S14). Next, the calculation result range conversion unit 11 uses the logarithm logα of the high-precision calculation range parameter α set by the high-precision calculation range conversion unit 10 to calculate logX = logZ−logα, thereby obtaining the STL. The calculation result range numerical value logX is calculated from the high-precision calculation result range numerical value logZ obtained by the calculation of the calculation circuit 120 (S15). Then, the output range conversion unit 131 converts the calculated calculation result range numerical value logX into the output range numerical value logY, and outputs it as an output value. Thereafter, the processing operation is terminated.

6 and 7 are graphs showing the relationship between a real number X satisfying 1 ≦ X <2 and a calculation result range numerical value logX calculated by the logarithmic arithmetic unit 1 of the present embodiment using the real number X as a calculation range numerical value. It is. Both FIGS. 6 and 7 (a) ~ (f) are graphs in a case of calculating the _{log 10} X repetition number N as 5-10. In the graph of the figure, the horizontal axis is a real number X, and the vertical axis is log ₁₀ X. Also, the thick line is the above-mentioned numerical calculation. For comparison, the expected value is indicated by a thin line.

  Furthermore, FIG. 6 is a graph in the case where the high-precision calculation range correspondence table 14 in the high-precision calculation range conversion unit 10 is the table shown in FIG. On the other hand, FIG. 7 is a graph in the case where the high precision calculation range correspondence table 14 is the table shown in FIG.

  Comparing the graph of FIG. 6 with the graph of FIG. 11, the logarithmic operation device 1 of the present embodiment significantly improves the error of logX at 1.7 ≦ X <2 compared to the conventional logarithmic operation device 110. Can understand. Specifically, in the graph of FIG. 11, the error when X is in the vicinity of 2 is about 0.06, which is the maximum. On the other hand, in the graph of FIG. 6, the error when X is in the vicinity of 2 is approximately zero. Since the expected value when X is close to 2 is about 0.3, the error of logX is improved by about 20% (= (0.06-0) ÷ 0.3) at the maximum.

  Furthermore, when the graph of FIG. 7 is compared with the graph of FIG. 6, the table shown in FIG. 5B is used more effectively when the table shown in FIG. It can be understood that the error of logX near X = 1.3 is improved.

  In the present embodiment, the calculation range conversion unit 130 and the high-precision calculation range conversion unit 10 are configured separately, but may be integrated into one configuration. In this case, the calculation range acquisition unit 12 of the high-precision calculation range conversion unit 10 can be omitted. In the present embodiment, the output range conversion unit 131 and the calculation result range conversion unit 11 have different configurations, but may be integrated into one configuration. In this case, the calculation result range acquisition unit 136 of the output range conversion unit 131 can be omitted.

  In the present embodiment, the STL arithmetic circuit 120 is configured to perform repetitive arithmetic with one arithmetic unit (repetitive processing unit 121) as in the prior art, but a plurality of arithmetic units are connected in series. In addition, a configuration in which serial calculation is performed can also be adopted.

FIG. 8 shows a schematic configuration of an STL arithmetic circuit (arithmetic means) 20 in which N arithmetic units 21 are connected in series. As shown in the figure, the STL arithmetic circuit 20 includes N arithmetic units 21 connected in series, one LUT 124 for storing the value of log (1-2− ^j−1 ) in advance, and the value of the variable _PN . And a single register 123d for storing.

Each arithmetic unit 21 is different from the iterative processing unit 121 shown in FIG. 2 and the like in that the LUT 124 that stores the value of log (1-2− ^j−1 ) in advance is omitted, and the other configurations are the same. It is. In the STL arithmetic circuit 20, instead of providing the LUT 124 in each arithmetic unit 21, one LUT 124 common to the N arithmetic units 21 is provided.

  In FIG. 8, the first stage (j = 0) arithmetic unit 21a, the second stage (j = 1) arithmetic unit 21b, and the final stage (j = N−1) arithmetic unit 21c are shown. In the following, a member number is assigned to the first stage configuration, b is added to the member number in the second stage configuration, and c is added to the member number in the last stage configuration.

As shown in FIG. 8, in the arithmetic unit 21 at each stage, the arithmetic unit (first arithmetic unit) 126 that performs the operation of S _{j + 1} based on the above equation (4), the value of the arithmetic result is calculated. The unit 21 sends the value to the register (first register) 122 that stores the value of S _{j + 1} . Similarly, a calculation unit (second calculation unit) 127 that performs the calculation of P _{j + 1} based on the above formula (4) stores the value of the calculation result and the value of P _{j + 1} in the calculation unit 21 in the next stage ( (Second register) 123.

In the first stage of the operation unit 21a, a value based on the calculation target value Z in the register 122a for storing the value of S ₀ is stored. Also, the register 123a for storing the values of _{P 0} the initial value (0) is stored. Note that the first-stage condition determination unit 128a has the determination condition C ₁ = −1 and does not depend on the value of the register 122a.

In the final-stage arithmetic unit 21c, the arithmetic unit 127c that calculates _PN based on the above equation (4) sends the value of the arithmetic result to a new register 123d that stores the value of _PN . The value of _PN stored in the register 123d is an operation result value logZ obtained by logarithmically calculating the operation target value Z. Note that the final-stage computing unit 126c that performs the computation of _SN omits sending the value of the computation result. For this reason, the final stage calculation unit 126c and the final stage barrel shifter (shifter) 125c may be omitted.

  In the STL arithmetic circuit 20 shown in FIG. 8, the counter 129 is omitted compared to the STL arithmetic circuit 120 shown in FIG. 2 and the like, but (N−1) arithmetic units 21 and one register 123d are added. As a result, the circuit scale increases. On the other hand, when sequentially calculating a plurality of calculation target values, each calculation unit 21 can immediately perform a calculation for the next calculation target value when the calculation for a certain calculation target value is completed. Compared with the STL operation circuit 120, the operation can be performed quickly.

  For example, assuming that the change of the input signal Y is the frequency f [Hz], the operation clock of the STL arithmetic circuit 120 with N repetitions is required to be N × f [Hz] or more, but the operation of the STL arithmetic circuit 20 The clock may remain at f [Hz]. Note that which of the STL arithmetic circuits 20 and 120 is adopted is determined from the viewpoints of processing speed and power consumption in the technology and library when implemented in the LSI of the logarithmic arithmetic unit 1.

  When the logarithmic arithmetic unit 1 of this embodiment is mounted on an LSI, it is particularly effective for a communication baseband LSI such as an LSI that handles sound, a baseband processing LSI for mobile phones that handles electromagnetic waves, a baseband LSI for broadcast reception, and the like. It is. In these LSIs, the decibels of the intensity of sound and electromagnetic waves are calculated, and further control is performed based on the calculation results. Therefore, by applying the present invention, accurate decibels can be calculated and the above decibel amount is further increased. It is possible to accurately perform control based on this.

  The present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims. That is, embodiments obtained by combining technical means appropriately modified within the scope of the claims are also included in the technical scope of the present invention.

  For example, in the high-precision calculation range correspondence table 14, the calculation range is divided into two in FIG. 5A and four in FIG. 5B, and the value of α is set for each. However, if an arbitrary value in the low-precision calculation range can be converted into a high-precision calculation range value by Z = αX, the calculation range can be divided by an arbitrary number of divisions.

In the present application, the logarithm log is described as a common logarithm having a base of 10, but the present invention can also be applied to arithmetic operations of logarithms having an arbitrary base such as a natural logarithm. In this case, the logarithm log _u (1-2 ^-j-1 ) value based on the desired base u may be stored in the LUT 124.

In the present application, the variable A _{j + 1} is set to A _{j + 1} = 1−2− ^j−1 or A _{j + 1} = 1 as shown in the above equation (3), but is composed of addition and subtraction of powers of 1 and 2. It can be changed to any expression. Other examples of variables A _{j + 1} include A _{j + 1} = 1 + 2 ^−j−1 or A _{j + 1} = 1, A _{j + 1} = 1−2 ^−j or A _{j + 1} = 1, A _{j + 1} = 1 + 2 ^−j or A _{j + 1} = 1, etc. Is mentioned.

  In the present application, the present invention is applied to the calculation based on the STL method of the logarithmic function. However, any function that can be calculated based on the STL method can be set as the calculation target of the present invention. For example, according to Patent Document 1, the STL method can be applied to exponential functions, quotients, and square root operations. As for trigonometric functions, calculation based on the CORDIC (Coordinate Rotation Digital Computer) method is generally used (see Non-Patent Document 2). However, since it is an exponential function when considered in the complex domain, calculation based on the STL method is also possible. is there.

  Therefore, the present invention can also be applied to operations based on the STL method for elementary functions such as exponential functions, trigonometric functions, quotients, square roots, and the like that satisfy the additive theorem. Note that the high-precision calculation range conversion function may be changed according to the function to be applied. For example, when applied to the calculation of an exponential function, it is preferable that Z = X + α be a conversion function for a high-precision calculation range.

  Finally, each block of the logarithmic arithmetic unit 1 may be configured by hardware logic, or may be realized by software using a CPU as follows.

  That is, the logarithmic arithmetic unit 1 includes a CPU (central processing unit) that executes instructions of a control program that realizes each function, a ROM (read only memory) that stores the program, and a RAM (random access memory) that expands the program. And a storage device (recording medium) such as a memory for storing the program and various data. An object of the present invention is a recording medium on which a program code (execution format program, intermediate code program, source program) of a control program of the logarithmic arithmetic unit 1 which is software for realizing the functions described above is recorded so as to be readable by a computer. This can also be achieved by supplying the logarithmic arithmetic unit 1 and reading and executing the program code recorded on the recording medium by the computer (or CPU or MPU).

  Examples of the recording medium include a tape system such as a magnetic tape and a cassette tape, a magnetic disk such as a floppy (registered trademark) disk / hard disk, and an optical disk such as a CD-ROM / MO / MD / DVD / CD-R. Card system such as IC card, IC card (including memory card) / optical card, or semiconductor memory system such as mask ROM / EPROM / EEPROM / flash ROM.

  The logarithmic arithmetic unit 1 may be configured to be connectable to a communication network, and the program code may be supplied via the communication network. The communication network is not particularly limited. For example, the Internet, intranet, extranet, LAN, ISDN, VAN, CATV communication network, virtual private network, telephone line network, mobile communication network, satellite communication. A net or the like is available. Also, the transmission medium constituting the communication network is not particularly limited. For example, even in the case of wired such as IEEE 1394, USB, power line carrier, cable TV line, telephone line, ADSL line, etc., infrared rays such as IrDA and remote control, Bluetooth ( (Registered trademark), 802.11 wireless, HDR, mobile phone network, satellite line, terrestrial digital network, and the like can also be used. The present invention can also be realized in the form of a computer data signal embedded in a carrier wave in which the program code is embodied by electronic transmission.

  As described above, the present invention converts a value within the range of the calculation target value such that the accuracy of the calculation result value is low into a value within the range of the calculation target value such that the accuracy of the calculation result value is high. As a result, the calculation accuracy is improved, so that the present invention can be applied to any calculation device having a large error in a specific part of the calculation result value.

It is a flowchart which shows the flow of the process in the logarithmic arithmetic unit which is one Embodiment of this invention. It is a block diagram which shows schematic structure of the said logarithmic arithmetic unit. It is a block diagram which shows schematic structure of the conversion part for calculation ranges, the conversion part for output ranges, the conversion part for high precision calculation ranges, and the conversion part for calculation result ranges in the said logarithmic calculating device. It is a figure which shows an example of the correspondence table for calculation ranges in the said conversion part for calculation ranges in a table format. It is a figure which shows an example of the high precision calculation range corresponding | compatible table in the said high precision calculation range conversion part, and another example by a table format. It is a graph which shows an example of the relationship between the calculation target value by the calculation of the said logarithmic calculating device, and a calculation result value. It is a graph which shows the other example of the relationship between the calculation object value by the calculation of the said logarithmic calculating device, and a calculation result value. It is a block diagram which shows the modification of the STL arithmetic circuit in the said logarithmic arithmetic unit. It is a flowchart which shows the flow of the process of the logarithm calculation based on STL method. It is a block diagram which shows schematic structure of the conventional logarithmic arithmetic unit. It is a graph which shows an example of the relationship between the calculation object value by the calculation of the said conventional logarithmic calculating apparatus, and a calculation result value.

Explanation of symbols

1 Logarithmic arithmetic unit (arithmetic unit)
10 High-precision calculation range conversion unit 11 Calculation result range conversion unit 12 Calculation range acquisition unit 13 High-precision calculation range setting unit (setting unit for calculation)
14 Correspondence table for high-precision calculation range (correspondence information)
15 Calculation unit for high-precision calculation range (conversion means for calculation)
16 High-precision calculation result range acquisition unit 18 Calculation result range calculation unit (output conversion means)
20 STL arithmetic circuit (arithmetic means)
21 arithmetic unit 21a first arithmetic unit 21c final arithmetic unit 120 STL arithmetic circuit (arithmetic means)
121 Repeat processing unit 122/123 register (first / second register)
124 LUT
125 barrel shifter (shifter)
126 · 127 arithmetic unit (first and second arithmetic units)
128 Condition Determination Unit 129 Counter 130 Calculation Range Conversion Unit 131 Output Range Conversion Unit 132 Input Value Acquisition Unit 133 Calculation Range Setting Unit (Calculation Setting Unit)
134 Calculation range correspondence table (correspondence information)
135 Calculation Range Calculation Unit (Calculation Conversion Unit)
136 Calculation Result Range Acquisition Unit 137 Output Value Calculation Unit (Output Conversion Unit)
α: Parameter for high-precision calculation range (parameter for calculation)
k · l: Parameter for calculation range (parameter for calculation)

Claims (8)

An arithmetic device that performs an operation on an input value and outputs an output value,
Calculation setting means for setting the value of the calculation parameter based on the input value;
An arithmetic conversion function including an arithmetic parameter value set by the arithmetic setting means, and an arithmetic conversion means for converting the input value into an arithmetic target value that is a target value of the arithmetic;
A calculation unit that performs the calculation on the calculation target value converted by the calculation conversion unit and acquires a calculation result value that is a result of the calculation;
An output conversion function including an output parameter value set based on the value of the operation parameter, and an output conversion means for converting the operation result value obtained by the operation means into the output value. ,
The calculation means has an error in the calculation result value depending on the calculation target value,
The calculation setting means sets the calculation parameter so that a part or all of the range of the calculation target value within which the error of the calculation result value falls within an allowable range falls within a value range of the conversion function for calculation. An arithmetic device characterized by setting a value. A storage unit for storing correspondence information in which the range of the input value and the value of the calculation parameter are associated with each other;
The calculation setting means searches for and sets the value of the calculation parameter corresponding to the range in which the input value is included from the correspondence information in the storage unit. Arithmetic unit.   The computing device according to claim 1, wherein the computing means performs computation based on an STL method. The calculation means has a configuration in which a plurality of calculation units are connected in series,
Each of the arithmetic units is
A first register and a second register for storing values of the first variable and the second variable, respectively;
A condition determination unit for determining calculation conditions;
A shifter for shifting the value of the first variable in the first register based on the calculation condition determined by the condition determination unit;
A first calculation unit that performs a first calculation based on the value of the first variable in the first register, the value of the first variable shifted by the shifter, and the calculation condition determined by the condition determination unit;
A second calculation unit that performs a second calculation based on the value of the second variable in the second register and the calculation condition determined by the condition determination unit;
The first calculation unit and the second calculation unit respectively send the values of the results of the first calculation and the second calculation to the first register and the second register in the next stage calculation unit,
Regarding the first stage arithmetic unit, the value of the first variable is a value based on the calculation target value, and the value of the second variable is a value based on the calculation target value or an initial value,
The computing device according to claim 3, wherein the result of the second computation performed by the second computing unit with respect to the final stage computation unit is the computation result value. A signal processing device for processing at least one of a sound wave and an electromagnetic wave,
A signal processing apparatus using the arithmetic unit according to any one of claims 1 to 4 to calculate the intensity of the signal.   An arithmetic program for operating the arithmetic device according to any one of claims 1 to 4, wherein the arithmetic program causes a computer to function as each of the above means.   A computer-readable recording medium on which the arithmetic program according to claim 6 is recorded. An arithmetic method of an arithmetic device that performs an operation on an input value and outputs an output value,
A calculation setting step in which the calculation device sets the value of the calculation parameter based on the input value;
A calculation conversion step in which the calculation device converts the input value into a calculation target value, which is a calculation target value, in a calculation conversion function including the value of the calculation parameter set in the calculation setting step. When,
A calculation step in which the calculation device performs the calculation on the calculation target value converted in the calculation conversion step to obtain a calculation result value as a result of the calculation;
An output conversion function that includes an output parameter value that is set based on the value of the calculation parameter, and in which the calculation device converts the calculation result value acquired in the calculation step into the output value. Steps, and
In the calculation step, an error of the calculation result value depends on the calculation target value,
In the calculation setting step, the calculation parameter is set such that a part or all of the range of the calculation target value within which an error of the calculation result value is within an allowable range falls within a range of the calculation conversion function. An arithmetic method for an arithmetic device, wherein a value is set.

Images