JP5939073B2 - Analysis support method, analysis support program, and analysis support apparatus - Google Patents

Description

  The present invention relates to an analysis support method, an analysis support program, and an analysis support apparatus.

  Conventionally, leakage current increases with the high integration of semiconductor integrated circuits. For example, the leakage current increases the power consumption and heat generation of the semiconductor integrated circuit, and degrades the circuit performance.

  Therefore, countermeasures are taken by accurately estimating the leakage current during circuit design. Due to the miniaturization of the process, the variation due to the process is increasing with respect to the circuit leakage current. As a method for estimating the circuit leakage current more accurately in consideration of variations, for example, statistical leakage current analysis can be cited. The statistical leakage current analysis is a method of calculating a distribution of variation in leakage current of the entire circuit, for example, as a total sum of variations in leakage current of each element in the analysis target circuit. As a technique for statistically estimating the leakage current, for example, a Monte Carlo method is known in which a definite leakage current analysis of millions of elements is repeated tens of thousands of times (for example, see Patent Document 1 below).

  Moreover, the importance sampling method is known as an example of the method in the Monte Carlo method (for example, refer to the following Patent Document 2 or Non-Patent Document 1).

  In order to estimate the delay amount of the path in the semiconductor integrated circuit, the Monte Carlo method is used (for example, refer to Patent Document 3 below). Further, a technique is known in which probability analysis is performed by a probability analysis process when parameters used in the design of a semiconductor integrated circuit are modeled (see, for example, Patent Document 4 below).

JP2011-237889A JP 2010-160787 A JP 2009-129150 A Special table 2008-523516

Paul Glasserman, two others, “Efficient Monte Carlo methods for value-at-risk”, [online], Mastering Risk: Vol2, Final Times-Plenty Hall, 2001, May 10, 2012 URL: http: // www2. gsb. columnia. edu / factory / plasserman / Other / masteringrisk. pdf>

  However, in the method of statistically estimating the leakage current by the above-described Monte Carlo method, it is difficult to accurately estimate the leakage current if the number of random numbers generated is small. On the other hand, if the number of occurrences of random numbers for determining whether the estimated amount of leak current is accurate, the amount of calculation increases.

  In one aspect, an object of the present invention is to provide an analysis support method, an analysis support program, and an analysis support apparatus that can determine the certainty of an estimated leakage current amount with a small amount of calculation.

  According to one aspect of the present invention, a constant value related to a leakage current unique to an element in a circuit to be analyzed, and a first weight for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution A coefficient value and a second weighting factor value for a second random variable representing a variation in leakage current common to the element group in the analysis target circuit are obtained for each element in the analysis target circuit, and generated. A first candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability An expression representing an average value of a normal distribution having a leak current amount obtained, a product of the first weighting coefficient and the first random variable, and the constant as a parameter, the second random variable and the second weight Product with coefficient Is obtained from the storage device when the variation function of the leakage current amount of the circuit to be analyzed, which is a parameter for each element, is expanded from the storage device, and the obtained value of the constant and the first The value of the term is calculated by giving the value of the weighting factor and the value of the second weighting factor, the standard deviation is smaller than the standard normal distribution, and the value of the second random variable in the variation function is A normal distribution for determining a value, wherein the characteristic value of the normal distribution that is the average of the distribution of the leakage current amount obtained by the variation function is the acquired first leakage current amount, and the obtained value of the term Calculated based on the first leakage current amount, obtaining the variation function from the storage device, and calculating the constant, the first weighting factor, and the second weighting factor in the obtained variation function. Of the obtained constant And the value of the first weighting factor and the value of the second weighting factor, and the second probability that is generated a predetermined number of times by the calculated feature quantity in the second random variable in the variation function By giving a variable value, the second leakage current amount for the predetermined number of times is calculated, and based on the magnitude relationship between the first leakage current amount and the calculated second leakage current amount for the predetermined number of times, An analysis support method and an analysis support for calculating an index indicating a ratio of the second leak current amount larger than the first leak current amount among the second leak current amount for the predetermined number of times and outputting the index indicating the ratio A program and an analysis support device are proposed.

  According to one embodiment of the present invention, the certainty of the estimated leakage current amount can be determined with a small amount of calculation.

FIG. 1 is an explanatory diagram showing an operation example by the analysis support apparatus according to the present invention. FIG. 2 is a block diagram illustrating a hardware configuration example of the analysis support apparatus. FIG. 3 is an explanatory diagram illustrating an example of the analysis target circuit. FIG. 4 is an explanatory diagram of an example of the contents stored in the data table. FIG. 5 is a block diagram illustrating a functional configuration of the analysis support apparatus. FIG. 6 is an explanatory diagram showing the cumulative distribution of the standard normal distribution. FIG. 7 is an explanatory diagram illustrating an approximation example when the calculated probability is greater than a predetermined range. FIG. 8 is an explanatory diagram showing an approximation example when the calculated probability is smaller than the predetermined range. FIG. 9 is a flowchart (part 1) illustrating an example of an analysis support processing procedure by the analysis support apparatus. FIG. 10 is a flowchart (part 2) illustrating an example of the analysis support processing procedure by the analysis support apparatus. FIG. 11 is a flowchart showing a detailed description of the calculation process of the probability y by ISMC shown in FIGS. 9 and 10.

  Exemplary embodiments of an analysis support method, an analysis support program, and an analysis support apparatus according to the present invention will be described below in detail with reference to the accompanying drawings.

  FIG. 1 is an explanatory diagram showing an operation example by the analysis support apparatus according to the present invention. Here, the leak current is a current that flows out at a place that should not flow in the electronic circuit. The analysis support apparatus 100 obtains a first leakage current amount with a cumulative occurrence probability equal to or less than a predetermined probability by simple leakage current analysis, and is calculated by a distribution of random variables that obtains a value close to the first leakage current amount. A probability that the calculation of the second leakage current amount is larger than the first leakage current amount is calculated. Thereby, the certainty of the calculated first current amount can be determined with a small amount of calculation.

Although the calculation method of the first leakage current amount is not particularly limited, an example will be described later.
As shown in the distribution d2, the first leakage current amount includes the range of the leakage current amount of the analysis target circuit in which the cumulative occurrence probability is equal to or less than the predetermined probability, and the leakage current amount of the analysis target circuit in which the generation probability is greater than the predetermined probability. , And boundary value candidates. An example of the analysis target circuit will be described later with reference to FIG.

  In the conventional leakage current analysis, the leakage current amount of the analysis target circuit is the sum of the leakage current amounts of the respective elements in the analysis target circuit. The amount of leakage current of each element includes the value of a constant a regarding the leakage current unique to the element included in the analysis target circuit, the value of the first weighting factor b for the first random variable α, and the value of the second random variable β. And the value of the second weighting factor c. The first random variable α represents a variation in leak current inherent to the element according to a standard normal distribution. The second random variable β represents a variation in leak current common to the element groups in the analysis target circuit. As shown in the distribution d0, the standard normal distribution has an average of “0” and a standard deviation of “1”. The variation function L0 for calculating the leakage current amount of the analysis target circuit is the sum of the leakage current amounts of the respective elements. Details of the variation function L0 will be described later.

  In the present embodiment, the second leakage current amount of the analysis target circuit is calculated by the variation function L1 obtained by approximating the variation function L0 represented by the sum of the leakage current amounts of the elements. The variation function L1 is a product of the first weighting factor b and the first random variable and an expression representing an average value of a normal distribution with the constant a as a parameter, and the product of the second random variable and the second weighting factor c. Are parameters for each element. Details of obtaining the fluctuation function L1 from the fluctuation function L0 will be described later.

  The analysis support apparatus 100 gives the value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c to the variation function L1, and generates a random number for the second random number β a predetermined number of times. To calculate the second leakage current amount. The value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c are stored in advance in a storage device accessible by the analysis support apparatus 100. The analysis support apparatus 100 calculates an index indicating the ratio of the second leakage current amount larger than the first leakage current amount among the predetermined number of second leakage current amounts.

  Since the standard normal distribution is wide, if the second random variable β is generated according to the standard normal distribution, the random number must be generated about tens of thousands of times. Therefore, in the present embodiment, the analysis support apparatus 100 generates a random number of the second random variable β by the importance sampling Monte Carlo method. The analysis support apparatus 100 gives the value of the constant a, the first weighting coefficient b, the second weighting coefficient c to the variation function L1, and the amount of leak current obtained when the second random variable β is generated randomly is the first. A value close to one leakage current amount is generated.

  Therefore, the analysis support apparatus 100 is a normal distribution that has a smaller distribution width than the standard normal distribution and determines the value of the second random variable β in the variation function L1, and is a distribution of the amount of leakage current obtained by the variation function. A feature value of a normal distribution in which the average of the first leakage current amount is calculated is calculated. The characteristic amount of the normal distribution is, for example, an average m (θ) and a standard deviation σ (θ) as shown in the distribution d1. Details of the average m (θ) and the standard deviation σ (θ) will be described later. As shown in the distribution d1, the random variable of the normal distribution is ξ. Since the distribution width of the normal distribution is smaller than that of the standard normal distribution, the number of random numbers generated can be reduced.

  The analysis support apparatus 100 calculates the second leakage current amount for the predetermined number of times by giving the second random variable β in the variation function L1 the value generated a predetermined number of times based on the feature value of the normal distribution. Then, the analysis support apparatus 100 calculates an index representing a ratio of the second leakage current amount that is larger than the first leakage current amount among the predetermined number of second leakage current amounts. For example, if the predetermined number of times is 100 and the amount of leak current greater than the first leak current amount is one out of 100 second leak current amounts, the index indicating the ratio is “0.01”. The probability may be a ratio or a ratio such as “99: 1”, and is not particularly limited. The analysis support apparatus 100 outputs an index representing the ratio. The output format may be stored in a storage device accessible by the analysis support apparatus 100, or may be displayed on a display accessible by the analysis support apparatus 100.

  For example, the analysis support apparatus 100 may calculate the probability y that the second leakage current amount based on the index indicating the ratio is larger than the first leakage current amount. A detailed calculation formula of the probability y will be described later. If the total value of the predetermined probability and the probability y that the second leakage current amount is larger than the first leakage current amount is close to “1”, the first leakage current amount is likely to be accurate. For example, when the predetermined probability is 0.990 and the probability y that the second leakage current amount is larger than the first leakage current amount is 0.01, the total value of the predetermined probability and the probability y is 1.0. For this reason, the first leakage current amount includes a range of the leakage current amount of the analysis target circuit in which the cumulative occurrence probability is equal to or less than the predetermined probability, and a range of the leakage current amount of the analysis target circuit in which the generation probability is greater than the predetermined probability. There is a high possibility that it is a boundary value.

  The user may determine how close the total value is to “1” and whether or not the first leakage current amount is likely to be accurate. The analysis support apparatus 100 may provide a range including an error and determine whether or not the total value is included in the range. For example, when the predetermined probability is 0.990, the range is set as “0.01 ± error”.

  In the present embodiment, an example is shown in which the probability y that the second leakage current amount based on the index indicating the ratio is greater than the first leakage current amount is calculated. However, the second leakage current amount based on the index indicating the ratio is A probability smaller than the first leakage current amount may be calculated. In this case, if the difference value between the predetermined probability and the probability that the second leakage current amount is smaller than the first leakage current amount is close to “0”, there is a high possibility that the first leakage current amount is accurate.

  According to the analysis support apparatus 100, the certainty of the leakage current amount can be determined with a small amount of calculation.

(Hardware configuration example of the analysis support apparatus 100)
FIG. 2 is a block diagram illustrating a hardware configuration example of the analysis support apparatus. In FIG. 2, the analysis support apparatus 100 includes a CPU (Central Processing Unit) 201, a ROM (Read-Only Memory) 202, a RAM (Random Access Memory) 203, a magnetic disk drive 204, and a magnetic disk 205. Have. The analysis support apparatus 100 includes an optical disc drive 206, an optical disc 207, a display 208, an interface (I / F) 209, a keyboard 210, and a mouse 211. Each unit is connected by a bus 200.

  Here, the CPU 201 governs overall control of the analysis support apparatus 100. The ROM 202 stores a program such as a boot program. The RAM 203 is used as a work area for the CPU 201. The magnetic disk drive 204 controls reading / writing of data with respect to the magnetic disk 205 according to the control of the CPU 201. The magnetic disk 205 stores data written under the control of the magnetic disk drive 204.

  The optical disk drive 206 controls reading / writing of data with respect to the optical disk 207 according to the control of the CPU 201. The optical disk 207 stores data written under the control of the optical disk drive 206, or causes the computer to read data stored on the optical disk 207. In FIG. 2, ROM 202, RAM 203, magnetic disk 205, and optical disk 207 are described as storage devices. However, the present invention is not limited to this. For example, an SSD (Solid State Drive) using a flash memory is used. You may have.

  The display 208 displays data such as a document, an image, and function information as well as a cursor, an icon, or a tool box. As the display 208, for example, a CRT, a TFT liquid crystal display, a plasma display, or the like can be adopted.

  The I / F 209 is connected to a network NET such as a LAN (Local Area Network), a WAN (Wide Area Network), and the Internet through a communication line, and is connected to other devices via the network NET. The I / F 209 manages an internal interface with the network NET, and controls input / output of data from an external device. For example, a modem or a LAN adapter may be employed as the I / F 209.

  The keyboard 210 has keys for inputting characters, numbers, various instructions, and the like, and inputs data. Moreover, a touch panel type input pad or a numeric keypad may be used. The mouse 211 performs cursor movement, range selection, window movement, size change, and the like. A trackball or a joystick may be used as long as they have the same function as a pointing device. In FIG. 2, the keyboard 210 and the mouse 211 are cited as input means, and the display 208 is cited as output means. However, the present invention is not limited to this. For example, the display 208 may be a touch panel display as input means and output means.

(Analysis target circuit)
FIG. 3 is an explanatory diagram illustrating an example of the analysis target circuit. The analysis target circuit 300 is a semiconductor integrated circuit that is an analysis target of leakage current at the time of circuit design. The analysis target circuit 300 includes cells C1 to Cn (n ≧ 1). The cell is information indicating elements such as an AND gate, a NAND gate, an OR gate, a buffer, INV (inverter), and FF included in the analysis target circuit 300. A part of the analysis target circuit 300 is extracted and displayed. Here, for the sake of explanation, it is assumed that the analysis target circuit 300 includes cells C1 to Cn.

(Data table storage contents)
FIG. 4 is an explanatory diagram of an example of the contents stored in the data table. In FIG. 4, the data table 400 has fields of cell ID, constant a, first weighting factor b, and second weighting factor c. By setting information in each field, variation data (401-1 to 401-1) for each of the cells C1 to Cn is stored as a record. The data table 400 is realized by a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207 shown in FIG.

  The cell ID is an identifier of the cell Ci included in the target circuit (i = 1, 2,..., N). The constant a, the first weighting factor b, and the second weighting factor c are stored for each cell Ci. Here, a method for specifying the value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c will be described. The creator of the data table 400 simulates the amount of leakage current using a SPICE simulator using conditions such as a specific voltage and a specific temperature for each cell type. Then, the creator specifies the value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c so as to follow the following formula (1) from the leak current amount calculated by the simulation. Alternatively, the creator may specify the constant a, the first weighting factor b, and the second weighting factor c from the actually measured value of the leakage current by using a TEG (Test Element Group) for each element.

(Functional configuration example of the analysis support apparatus 100)
FIG. 5 is a block diagram illustrating a functional configuration of the analysis support apparatus. The analysis support apparatus 100 includes a constant coefficient acquisition unit 501, a variation function acquisition unit 502, a simple leak current amount calculation unit 503, a first leak current amount acquisition unit 504, and a term acquisition unit 505. . The analysis support apparatus 100 includes a term value calculation unit 506, a normal distribution calculation unit 507, a fluctuation function acquisition unit 508, a second leakage current amount calculation unit 509, and a probability calculation unit 510. The analysis support apparatus 100 includes a comparison unit 511, a third leakage current amount acquisition unit 512, a fourth leakage current amount calculation unit 513, and an output unit 514.

  Specifically, the processing from the constant coefficient acquisition unit 501 to the output unit 514 is coded in an analysis program stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207 shown in FIG. . Then, the CPU 201 reads the analysis program from the storage device and executes the processing coded in the analysis program, whereby the processing from the constant coefficient acquisition unit 501 to the output unit 514 is realized. The CPU 201 may read the analysis program from the network NET via the I / F 209.

  Here, the fluctuation functions L0 and L1 for calculating the leakage current amount of the analysis target circuit 300 will be described. The variation function IC for calculating the leakage current amount of each cell in the analysis target circuit 300 is expressed as a function of a random variable based on the gate length, gate width, etc. of the transistor in the cell as in the following formula (1). The

  IC = exp (a + b · α + c · β) (1)

  As described above, α is a first random variable that represents a variation in leak current inherent to a cell according to a standard normal distribution with an average of “0” and a standard deviation of “1”. As described above, β is a second random variable representing a variation in leak current common to the element groups in the analysis target circuit 300 in accordance with a standard normal distribution with an average “0” and a standard deviation “1”. As described above, “a” is a constant “a” related to the leak current inherent to the cell. As described above, b is the first weighting factor b for the first random variable α. As described above, c is the second weighting factor c for the second random variable β.

  The value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c are stored in the data table 400 as described above.

  The variation function L0 for calculating the leakage current amount of the entire analysis target circuit 300 is the sum of variations in leakage currents of the cells C1 to Cn as shown in the following equation (2).

L0 = IC1 + IC2 + ... + ICn
= Exp (a1 + b1 · α1 + c1 · β) + exp (a2 + b2 · α2 + c2 · β) +... + Exp (an + bn · αn + cn · β) (2)

  In the case of the variation function L0, random numbers must be generated tens of thousands of times using Monte Carlo or the like for each of the first random variable α and the second random variable β. An actual semiconductor integrated circuit has millions of elements. Even if the first random variable α is different for each cell, there is a high possibility that the variation is offset by the millions of elements. That is, even if the variation of some elements is remarkable, if there are millions of elements, the variation of each element is canceled out and approaches the average (the law of large numbers).

  Here, the product of the first random variable α and the first weighting factor b in the above formula (2) and the function of the probability distribution indicated by the constant a substitute for the average value of the probability distribution.

  The relationship between the variation function L0 and the variation function L1 shown in the above equation (3) is the variation function L0≈the variation function L1. As a result, the leakage current amount of the entire analysis target circuit 300 is calculated without generating random values for the value of the first random variable α by Monte Carlo simulation. Therefore, it is possible to reduce the amount of calculation required for estimating the leakage current of the entire analysis target circuit 300. The variation function L1 is stored in the storage device in advance. The variation function L1 may be created by the user, or may be converted from the variation function L0 to the variation function L1 by the analysis support apparatus 100.

  Here, the average value of the lognormal distribution represented by the function I represented by the constant a and the multiplication result of the first random variable α and the first weighting coefficient b will be described. A function I represented by the constant a and the multiplication result of the first random variable α and the first weighting coefficient b is the following equation (4).

  I = exp (a + b · α) (4)

  Since the first random variable α follows a standard normal distribution, the probability density function p (x) of the first random variable α is expressed by the following equation (5).

  Therefore, the average value of the lognormal distribution represented by the function I is the following formula (6).

  Since the variation function L1 is the sum of a plurality of exponential functions, n exponential functions are calculated when the leakage current amount is calculated once. Furthermore, since the second random variable β is generated with random numbers tens of thousands of times, the amount of leakage current is calculated tens of thousands of times. Therefore, in the present embodiment, a single exponential function that can obtain a leakage current amount approximated to a leakage current amount at a predetermined probability from a normal distribution obtained by approximating the normal distribution of the leakage current amount of the analysis target circuit 300. Provide the represented variation function L2. As a result, the number of times the exponential function is calculated can be reduced, and an approximate amount of leakage current can be obtained without generating the value of the second random variable β as a random number.

  The variation function L2 is a function that varies with the second random variable β expressed by one exponential function by approximating the variation function L1 that is the sum of a plurality of exponential functions. The approximation method may be Wilkinson approximation or an empirical rule.

The average A is an expression that can calculate the value of the average A of the normal distribution represented by the variation function L2. B ² is an expression that can calculate the value of B ² that is the square of the standard deviation B of the normal distribution represented by the variation function L2. The statistical information of the normal distribution is the average A value and the standard deviation B value. Here, although also shown in the drawings, the fluctuation function L2, the average A, and B ² are shown in the following formulas (7) to (9), respectively. Expressions (7) to (9) are stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207.

Here, the derivation of the respective values of the averages A and B ² from the fluctuation function L1 and the fluctuation function L2 will be described. For example, when there is no variation (typ value), β = 0, and when the variation function L1 matches the variation function L2, the following equation (10) is obtained. When the following formula (10) is solved for the average A, the above formula (8) is obtained.

When the average value of the normal distribution represented by the variation function L1 matches the average value of the normal distribution represented by the variation function L2, the following equation (11) is obtained. When the following equation (11) is solved for B ² , the above equation (9) is obtained.

  The constant coefficient acquisition unit 501 acquires the value of the constant a, the value of the first weighting coefficient b, and the value of the second weighting coefficient c for each element in the analysis target circuit 300 from the storage device. As described above, the value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c for each element are stored in the data table 400.

Variation function acquiring unit 502, a variation function L2 stored in the storage device acquires the average A, and B ^2, the. Simple leakage current calculator 503, the average A, and B ^2, the respectively, giving the values of the constants a, the value of the first weighting factor b, the value of the second weighting factor c, and Thus, the average A value and the B ² value are calculated. Simple leakage current calculator 503, the variation function L2, by giving the value of the average A, the value of B ^2, the value of the second random variable when the probability of accumulation of the standard normal distribution has a predetermined probability Then, the leakage current amount at a predetermined probability in the cumulative probability distribution obtained by integrating the approximated normal distribution is calculated.

  The leakage current amount calculated by the simple leakage current amount calculation unit 503 includes the range of the leakage current amount of the analysis target circuit 300 in which the occurrence probability is equal to or less than the predetermined probability, and the analysis target circuit 300 in which the occurrence probability is greater than the predetermined probability. It becomes a candidate for a boundary value between the range of the leakage current amount.

  FIG. 6 is an explanatory diagram showing the cumulative distribution of the standard normal distribution. Here, the second random variable when each of the first predetermined probability p1, the second predetermined probability p2 smaller than the first predetermined probability p1, and the third predetermined probability p3 larger than the first predetermined probability p1 is obtained. The value of β is shown. The values of the first predetermined probability p1, the second predetermined probability p2, and the third predetermined probability p3 are specified by the user and the designer of the analysis support apparatus 100, respectively.

  For example, when the first predetermined probability p1 is 0.990, the value of the second random variable when the accumulation of the standard normal distribution becomes the first predetermined probability p1 is 2.33. When the second predetermined probability p2 is 0.930, the value of the second random variable when the accumulation of the standard normal distribution becomes the first predetermined probability p1 is 1.5. When the third predetermined probability p3 is 0.999, the value of the second random variable when the accumulation of the standard normal distribution becomes the first predetermined probability p1 is 3.99.

  Here, the leakage current amount obtained by giving the value of the second random variable when the cumulative occurrence probability becomes the predetermined probability to the variation function L2 is referred to as a leakage current amount corresponding to the predetermined probability. The simple leakage current amount calculation unit 503 calculates a leakage current amount corresponding to each of the first predetermined probability p1, the second predetermined probability p2, and the third predetermined probability p3. The calculation result is stored in the storage device.

  The first leakage current amount acquisition unit 504 acquires a first leakage current amount. As described with reference to FIG. 1, the first leakage current amount is the range of the leakage current amount of the analysis target circuit 300 in which the occurrence probability is equal to or less than the first predetermined probability p1, and the analysis target in which the occurrence probability is greater than the first predetermined probability p1. This is a candidate for the first boundary value of the range of the leakage current amount of the circuit 300. Specifically, the first leakage current amount acquisition unit 504 acquires the first leakage current amount from the storage device when the calculation result obtained by the simple leakage current amount calculation unit 503 is stored in the storage device. Also good. Alternatively, the first leakage current amount acquisition unit 504 may acquire the first leakage current amount input by the user using the input unit. For example, a keyboard 210 is an example of the input means.

  Next, in the present embodiment, the analysis support apparatus 100 reduces the number of iterations required for calculating the leakage current amount by the importance sampling method. That is, the analysis support apparatus 100 generates a random number of the value of the second random variable in the variation function L1 by a normal distribution obtained from the variation function L1 with a leakage current amount close to the first leakage current amount. Thereby, the certainty of the first leak current amount calculated simply can be determined with a small calculation amount.

  The term acquisition unit 505 acquires a term when the variation function L1 of the leakage current amount of the analysis target circuit 300 is Taylor-expanded from the storage device. Here, the third order differential coefficient is assumed to be small, and the second order differential coefficient is also covered. The result of Taylor expansion of the variation function L1 is shown in the following formula (12). It is assumed that the zero-order term d, the first-order term e, and the second-order term o shown in the following formulas (13) to (15) are stored in the storage device.

  The term value calculation unit 506 calculates the value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c for the zeroth-order term d, the first-order term e, and the second-order term o. , The value of the zeroth-order term d, the value of the first-order term e, and the value of the second-order term o are calculated.

  The normal distribution calculation unit 507 is a normal distribution that has a standard deviation smaller than that of the standard normal distribution and determines the value of the second random variable β in the variation function L1, and is a distribution of the leakage current amount obtained by the variation function L1. A feature amount of a normal distribution whose average is the first leakage current amount is calculated. Specifically, the normal distribution calculation unit 507 performs normalization based on the value of the zeroth-order term d, the value of the first-order term e, the value of the second-order term o, and the first leakage current amount. The distribution feature amount is calculated. As described above, the feature amounts are the standard deviation σ (θ) and the average m (θ), which will be described later with Expression (21) and Expression (22).

Here, the importance sampling Monte Carlo method will be briefly described. For example, when k is a random variable and p is a distribution density function of k, the average E _p [f] is expressed by the following equation (16). βj is an independent random number by p.

  According to Chebyshev's inequality, the following equations (17) and (18) are expressed.

ε is an arbitrary positive number. The smaller the Var _p [f], the smaller the sample number (N) of the Monte Carlo method. In the importance Monte Carlo method, the distribution density function is changed from p to q as shown in the following equations (19) and (20). In particular, it is changed to q where the dispersion shown in the equation (20) becomes small.

p is a function that follows a standard normal distribution. P shown in Expression (20) is different from p shown in Expression (5) described above. “Probability that L1 (k)> first leakage current amount” is Prob {L1> x}. “F (k) = Prob {L1> x}”. q is a standard deviation σ (θ) and is a function according to a normal distribution having an average m (θ). σ (θ) ² and average m (θ) are shown in the following equations (21) and (22), respectively.

σ (θ) ² = 1 / (1-2 · θ · o) (21)
m (θ) = θ · e · σ (θ) ² (22)

  Expressions (21) and (22) are stored in a storage device such as the RAM 203, the ROM 202, the magnetic disk 205, and the optical disk 207. p (k) / q (k) can be expressed as in the following formula (23).

  p (k) / q (k) = Exp {θ · Q (k) + φ (θ)) (23)

  Q (k) is the result of quadratic approximation by Taylor expansion of the variation function L1. φ (θ) is expressed by the following equation (24), and the second moment is expressed by the following equation (25).

φ (θ) = d · θ + (1/2) · {(θ ² · e ² ) / (1-2 · θ · o)}-log (1-2 · θ · o) (24)

If (−θ _x + φ (θ)) is minimized, the second moment is minimized. Therefore, when φ ′ (θ _x ) = x, the second moment is minimized, and the variance (= Var _q [fp / q]) is minimized.

  Prob {L1> x} is shown in the following formula (26). Here, x in Prob {L1> x} is the first leakage current amount. The approximate expression of Prob {L1> x} is shown in the following expression (27), expression (28), and expression (29).

  As described above, since Q (k) is a result of second order approximation of L1 by Taylor expansion, Q (k) is expressed by the following equation (30).

Q (k) = d + e · k + o · k ² (30)

  f (k) is 1 (L1> x). Here, 1 () is, for example, a function that returns 1 if () is true, and returns 0 if () is false. ξ is a random variable that follows a normal distribution with a standard deviation of σ (θ) and an average of m (θ). θ is calculated by the following equation (31) to equation (34).

u · θ ² + v · θ + w = 0 (31)
u = d · o ² · (x−d) + e ² · o (32)
v = 4 · o · (xd) −e ² + 2 · o ² (33)
w = x−d−o (34)

  X in the equations (32) to (34) is the first leakage current amount. Here, the expressions (29) and (31) to (34) are stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207.

For example, the normal distribution calculation unit 507 calculates the feature amount of the normal distribution. The normal distribution calculation unit 507 calculates the value of u, the value of v, and the value of w by giving the value of each term calculated by the term value calculation unit 506 to the equations (32) to (34). The normal distribution calculation unit 507 calculates the value of θ by giving the value of u, the value of v, and the value of w to Equation (31). The normal distribution calculation unit 507 calculates the value of σ (θ) ² by giving the value of θ and the value of o to Equation (21). The normal distribution calculation unit 507 can calculate the value of σ (θ) by calculating the positive square root of the value of σ (θ) ² . The normal distribution calculation unit 507 calculates the value of m (θ) by giving the value of e, the value of θ, and the value of σ (θ) ^{2 to} Equation (22). Each calculation result by the normal distribution calculation unit 507 is stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, for example.

  The variation function acquisition unit 508 acquires the variation function L1 from the storage device. The second leak current amount calculation unit 509 uses the constant value a, the first weighting factor b, and the second weighting factor c in the variation function L1 as the acquired constant a value, the first weighting factor b value, and the first weighting factor b. The value of the weighting factor c of 2 is given. The second leakage current amount calculation unit 509 gives the second probability variable β in the variation function L1 by giving the value of the second probability variable ξ generated a predetermined number of times based on the calculated feature amount, so that the second number of times corresponding to the second number of times. Calculate the amount of leakage current. The calculation result is stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, for example. The predetermined number (M) is stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207. The predetermined number of times may be determined by the designer of the analysis support apparatus 100 or may be determined by the user. For example, when designing the analysis support apparatus 100, the designer calculates the second leakage current amount based on the number of times of a plurality of patterns, calculates the probability described for the plurality of patterns, and sets the number of times that the probability converges. The number of times may be determined. The predetermined number M when the random number is generated by the normal distribution of the present embodiment is about 1/50 of the predetermined number N when the random number is generated by the standard normal distribution.

  Based on the magnitude relationship between the first leak current amount and the second leak current amount for a predetermined number of times, the probability calculation unit 510 calculates a second leak larger than the first leak current amount among the second leak current amount for the predetermined number of times. An index indicating the ratio of the current amount is calculated. The index representing the ratio may be a probability or a ratio. The output unit 514 outputs an index representing the ratio. As an output format, for example, the data may be stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, or may be displayed on the display 208.

  The comparison unit 511 may derive an index representing the certainty that the first leakage current amount is the first boundary value based on the index representing the ratio. Specifically, for example, the comparison unit 511 may compare the index indicating the ratio with a predetermined value determined by the first predetermined probability p1, and output the comparison result.

  In addition, the probability calculation unit 510 may calculate a probability that the second leakage current amount based on the ratio index is larger than the first leakage current amount. Specifically, the probability calculation unit 510 calculates the probability based on the above equation (29). The output unit 514 outputs a probability that the two leak current amount is larger than the first leak current amount. As an output format, for example, the data may be stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, or may be displayed on the display 208.

  The comparison unit 511 may calculate the total value of the probability calculated by the probability calculation unit 510 and the first predetermined probability p1, and determine whether the total value is a predetermined value. For example, the predetermined value is “1”. Since a calculation error may occur, it may be determined whether or not the total value is a value close to “1”. For example, the comparison unit 511 may determine whether or not the total value is included in “1 ± error”. The error is set by the user.

  Alternatively, the comparison unit 511 may compare the calculated probability with a range defined by the first predetermined probability p1 (hereinafter referred to as “predetermined range”). The predetermined range is, for example, “1-first predetermined probability p1 ± error”. The predetermined range is stored in advance in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207. The output unit 514 outputs the comparison result. For example, the output unit 514 may store the comparison result in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, or may display the comparison result on the display 208.

  When the calculated probability is included in the predetermined range, the output unit 514 may output the first leakage current amount as the first boundary value, or the first leakage current amount may be the first boundary value. May output a high value. As an output format, for example, the data may be stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, or may be displayed on the display 208.

  The third leakage current amount acquisition unit 512 acquires the third leakage current amount when the total value of the calculated probability and the predetermined probability is larger than the predetermined value. The case where the total value of the calculated probability and the predetermined probability is larger than the predetermined value is a case where the calculated probability is larger than the predetermined range. Here, the third leak current amount includes the leak current amount range of the analysis target circuit 300 in which the occurrence probability is equal to or less than the second predetermined probability p2, and the leak of the analysis target circuit 300 in which the occurrence probability is greater than the second predetermined probability p2. This is a second boundary value candidate for the current amount range. As described above, it is assumed that the third leakage current amount corresponding to the second predetermined probability p2 is stored in the storage device in advance.

  The fourth leakage current amount calculation unit 513 calculates the first leakage current amount based on the ratio between the calculated probability and the value based on the second predetermined probability p2 and the ratio between the first leakage current amount and the third leakage current amount. A fourth leakage current amount that is a candidate for the boundary value is calculated. The value based on the second predetermined probability p2 is, for example, “1−second predetermined probability p2”. Specifically, the fourth leakage current amount calculation unit 513 calculates the fourth leakage current amount by calculating the following equation (35).

x2 = first leakage current amount y2 = calculated probability y1 = | 1-second predetermined probability p2 |
x1 = leakage current amount corresponding to the second predetermined probability p2 y3 = | 1-first predetermined probability p1 |
x = x1 + (y3-y1). (x2-x1) / (y2-y1) (35)

  FIG. 7 is an explanatory diagram illustrating an approximation example when the calculated probability is greater than a predetermined range. When the calculated probability is larger than the predetermined range, the first boundary value is smaller than the first leakage current amount. Therefore, the fourth leakage current amount calculation unit 513 includes the calculated probability, the second predetermined probability p2 smaller than the first predetermined probability p1, the first leakage current amount, and the first leakage current amount, 2 A linear approximation is performed based on the third leakage current amount corresponding to the predetermined probability p2. As a result, as indicated by the graph d4, a leakage current amount that is a new candidate for the first boundary value is calculated.

  The output unit 514 outputs the calculated fourth leakage current amount as a candidate for the first boundary value. As an output format, for example, the data may be stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, or may be displayed on the display 208.

  Thereby, according to the analysis support apparatus 100, it is possible to provide a leakage current amount that is highly likely to be more accurate than a leakage current amount that is simply calculated.

  The normal distribution calculation unit 507 has a standard deviation smaller than that of the standard normal distribution and is a second normal distribution that determines the value of the second random variable β in the variation function L1, and the amount of leakage current obtained by the variation function L1. A second feature amount of the second normal distribution is calculated in which the average of the distribution is the fourth leakage current amount. Specifically, the normal distribution calculation unit 507 calculates the standard deviation σ (θ of the second normal distribution based on the expressions (31) to (34) described above and the expressions (21) and (22) described above. ) And average m (θ). Here, the normal distribution calculation unit 507 is given the fourth leakage current amount as x included in the above-described equations (32) to (34).

  The second leakage current amount calculation unit 509 includes a constant value, a first weighting factor, and a second weighting factor in the variation function L1, a constant value, a first weighting factor value, and a second weighting factor value. ,give. The second leak current amount calculation unit 509 gives the second leak variable for the predetermined number of times by giving the value of the second random variable generated the predetermined number of times by the second feature amount to the second random variable β in the variation function L1. Calculate the amount of current.

  Based on the magnitude relationship between the fourth leakage current amount and the fifth leakage current amount for a predetermined number of times, the probability calculation unit 510 generates a fifth larger than the fourth leakage current amount among the fifth leakage current amount for the predetermined number of times. A second index indicating the ratio of the leakage current amount is calculated. The output unit 514 outputs a second index indicating the ratio.

  Further, the probability calculation unit 510 may calculate a probability that the fifth leakage current amount based on the second index indicating the ratio is larger than the fourth leakage current amount. Similar to the case where the second leakage current amount is larger than the first leakage current amount, the comparison unit 511 adds the probability that the fifth leakage current amount is larger than the fourth leakage current amount and the first predetermined probability p1. It may be determined whether or not the value is a predetermined value. Alternatively, the comparison unit 511 may determine whether or not the probability that the fifth leakage current amount is larger than the fourth leakage current amount is within a predetermined range.

  Until the total value of the probability calculated by the probability calculation unit 510 and the first predetermined probability p1 reaches a predetermined value, or the probability falls within a predetermined range, the analysis support apparatus 100 performs the fourth distribution from the normal distribution calculation unit 507 to the fourth. The processing of the leakage current amount calculation unit 513 may be repeated. Then, the leakage current amount calculated by the fourth leakage current amount calculation unit 513 when the total value becomes a predetermined value or the probability falls within a predetermined range may be output as the first boundary value.

  Accordingly, it is possible to provide a leakage current amount that is highly likely to be a boundary value when the cumulative occurrence probability is the first predetermined probability p1. Furthermore, it is possible to reduce the amount of calculation for calculating the leakage current amount.

  The third leakage current amount acquisition unit 512 acquires the third leakage current amount when the total value of the calculated probability and the predetermined probability is smaller than the predetermined value. The case where the total value of the calculated probability and the predetermined probability is smaller than the predetermined value is a case where the calculated probability is smaller than the predetermined range. Here, the third leakage current amount is the range of the leakage current amount of the circuit to be analyzed 300 in which the occurrence probability is equal to or less than the third predetermined probability p3 greater than the first predetermined probability p1, and the occurrence probability is greater than the third predetermined probability p3. This is a candidate for the third boundary value of the range of the leakage current amount of the circuit 300 to be analyzed. As described above, it is assumed that the third leakage current amount corresponding to the third predetermined probability p3 is stored in the storage device in advance.

  The fourth leakage current amount calculation unit 513 calculates the first leakage current amount based on the ratio between the calculated probability and the value based on the third predetermined probability p3, and the ratio between the first leakage current amount and the third leakage current amount. A fourth leakage current amount that is a candidate for the boundary value is calculated. The value based on the third predetermined probability p3 is, for example, “1−third predetermined probability p3”. Specifically, the fourth leakage current amount calculation unit 513 calculates the fourth leakage current amount by calculating the following equation (36).

x1 = first leakage current amount y1 = calculated probability y2 = third predetermined probability p3
x2 = leakage current amount corresponding to the third predetermined probability p3 y3 = | 1-first predetermined probability p1 |
x = x1 + (0.01-y1). (x2-x1) / (y2-y1) (36)

  FIG. 8 is an explanatory diagram showing an approximation example when the calculated probability is smaller than the predetermined range. In the above equation (36), as shown in FIG. 8, linear approximation is performed based on the amount of leakage current and the probability that have been found. When the calculated probability is smaller than the predetermined range, the first boundary value is larger than the first leakage current amount. Therefore, the fourth leakage current amount calculation unit 513 has a calculated probability, a third predetermined probability p3 greater than the first predetermined probability p1, a first leakage current amount, and a first leakage current amount greater than the first leakage probability amount. 3 A linear approximation is performed by the third leakage current amount corresponding to the predetermined probability p3. As a result, as shown in the graph d5, a leakage current amount that is a new candidate for the first boundary value is calculated.

  The output unit 514 outputs the calculated fourth leakage current amount as a candidate for the first boundary value. As an output format, for example, the data may be stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207, or may be displayed on the display 208.

  Thereby, according to the analysis support apparatus 100, it is possible to provide a leakage current amount that is highly likely to be more accurate than a leakage current amount that is simply calculated.

  The normal distribution calculation unit 507 has a standard deviation smaller than that of the standard normal distribution and is a second normal distribution that determines the value of the second random variable β in the variation function L1, and the amount of leakage current obtained by the variation function L1. A second feature amount of the second normal distribution is calculated in which the average of the distribution is the fourth leakage current amount. Specifically, the normal distribution calculation unit 507 calculates the standard deviation σ (θ of the second normal distribution based on the expressions (31) to (34) described above and the expressions (21) and (22) described above. ) And average m (θ). Here, the normal distribution calculation unit 507 is given the fourth leakage current amount as x included in the above-described equations (32) to (34).

  The second leakage current amount calculation unit 509 includes a constant value, a first weighting factor, and a second weighting factor in the variation function L1, a constant value, a first weighting factor value, and a second weighting factor value. ,give. The second leak current amount calculation unit 509 gives the second leak variable for the predetermined number of times by giving the value of the second random variable generated the predetermined number of times by the second feature amount to the second random variable β in the variation function L1. Calculate the amount of current.

  Based on the magnitude relationship between the fourth leakage current amount and the fifth leakage current amount for a predetermined number of times, the probability calculation unit 510 generates a fifth larger than the fourth leakage current amount among the fifth leakage current amount for the predetermined number of times. A second index indicating the ratio of the leakage current amount is calculated. The output unit 514 outputs a second index indicating the ratio.

  Further, the probability calculation unit 510 may calculate a probability that the fifth leakage current amount based on the second index indicating the ratio is larger than the fourth leakage current amount. Similarly to the above-described probability that the second leakage current amount is larger than the first leakage current amount, the comparison unit 511 determines that the total value of the probability that the fifth leakage current amount is larger than the fourth leakage current amount and the first predetermined probability p1 is predetermined. It may be determined whether or not it is a value. Alternatively, the comparison unit 511 may determine whether the probability is within a predetermined range.

  Until the total value of the probability calculated by the probability calculation unit 510 and the first predetermined probability p1 reaches a predetermined value, or until the calculated probability falls within a predetermined range, the analysis support apparatus 100 performs the normal distribution calculation unit 507. To the fourth leakage current amount calculation unit 513 may be repeated. Then, the leakage current amount calculated by the fourth leakage current amount calculation unit 513 when the total value becomes a predetermined value or the probability falls within a predetermined range may be output as the first boundary value.

  Accordingly, it is possible to provide a leakage current amount that is highly likely to be a boundary value when the cumulative occurrence probability is a predetermined probability. Furthermore, it is possible to reduce the amount of calculation for calculating the leakage current amount.

  In addition, the probability calculation unit 510 may calculate a probability that the second leakage current amount is smaller than the first leakage current amount based on the index indicating the ratio. In this case, “1 (L1 (ξ)> x)” in the above equation (29) becomes “1 (L1 (ξ) <x)”. The comparison unit 511 may calculate a difference value between the probability that the second leakage current amount is smaller than the first leakage current amount and the first predetermined probability p1, and determine whether the difference value is a predetermined value. Here, the predetermined value is “0”. Alternatively, the comparison unit 511 may determine whether or not the probability that the second leakage current amount is smaller than the first leakage current amount is the first predetermined probability p1. Alternatively, the comparison unit 511 may determine whether or not the difference value is within a predetermined range. Here, the predetermined range is, for example, “first predetermined probability p1 ± error”.

  When the probability that the second leakage current amount is smaller than the first leakage current amount is larger than the first predetermined probability p1, the third leakage current amount acquisition unit 512 acquires the third leakage current amount corresponding to the second predetermined probability p2. . The fourth leakage current amount calculation unit 513 performs linear approximation based on the ratio between the calculated probability and the second predetermined probability p2 and the ratio between the first leakage current amount and the third leakage current amount. A fourth leakage current amount that is a candidate for the first boundary value is calculated.

  When the probability that the second leakage current amount is smaller than the first leakage current amount is smaller than the first predetermined probability p1, the third leakage current amount acquisition unit 512 acquires the third leakage current amount corresponding to the third predetermined probability p3. . The fourth leakage current amount calculation unit 513 performs linear approximation based on the ratio between the calculated probability and the third predetermined probability p3 and the ratio between the first leakage current amount and the third leakage current amount. A fourth leakage current amount that is a candidate for the first boundary value is calculated.

(Analysis support processing procedure)
9 and 10 are flowcharts illustrating an example of an analysis support processing procedure by the analysis support apparatus. The analysis support apparatus 100 acquires the value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c (step S901). The analysis support apparatus 100 has leakage current amounts (xini, x1, x2) corresponding to the cumulative probabilities of the first predetermined probability p1 to the third predetermined probability p3 (for example, 0.990, 0.930, 0.999, respectively). ) Is acquired (step S902).

  The analysis support apparatus 100 sets x = xini (step S903), and performs the calculation process of the probability y by ISMC (step S904). The analysis support apparatus 100 determines whether or not the probability y is within a predetermined range (step S905). When the probability y is within the predetermined range (step S905: Yes), the process proceeds to step S1009. When the probability y is not within the predetermined range (step S905: No), the analysis support apparatus 100 determines whether the probability y is larger than the predetermined range (step S906).

  When the probability y is larger than the predetermined range (step S906: Yes), the analysis support apparatus 100 sets x2 = xini (step S907) and y2 = y (step S908). The analysis support apparatus 100 sets “y1 = | 1−second predetermined probability p2 |” (step S909), and proceeds to step S1001. For example, y1 = 0.067.

  When the probability y is smaller than the predetermined range (step S906: No), the analysis support apparatus 100 sets x1 = xini (step S910) and y1 = y (step S911). The analysis support apparatus 100 sets “y2 = | 1−third predetermined probability p3 |” (step S912), and proceeds to step S1001. For example, y2 = 0.001.

  The analysis support apparatus 100 calculates “x = x1 + (0.01−y1) · (x2−x1) / (y2−y1)” (step S1001), and ISMC (Importance Sampling Monte Carlo, Importance Sampling Monte Carlo method). The probability y is calculated according to (Step S1002). Here, since the first predetermined probability p1 is 0.990, “0.01 = 1−first predetermined probability p1” is set in step S1001. The analysis support apparatus 100 determines whether the probability y is within a predetermined range (step S1003). If the probability y is within the predetermined range (step S1003: Yes), the analysis support apparatus 100 proceeds to step S1009. When the probability y is not within the predetermined range (step S1003: No), the analysis support apparatus 100 determines whether the probability y is larger than the predetermined range (step S1004).

  When the probability y is larger than the predetermined range (step S1004: Yes), the analysis support apparatus 100 sets x2 = x (step S1005), sets y2 = y (step S1006), and returns to step S1001. When the probability y is smaller than the predetermined range (step S1004: No), the analysis support apparatus 100 sets x1 = x (step S1007), sets y1 = y (step S1008), and returns to step S1001.

  In the case of No in step S905 or in the case of Yes in step S1003, the analysis support apparatus 100 outputs x as the leakage current amount at the first predetermined probability p1 (step S1009), and ends the series of processes.

  FIG. 11 is a flowchart showing a detailed description of the calculation process of the probability y by ISMC shown in FIGS. 9 and 10. The analysis support apparatus 100 acquires a term (zero-order term d, first-order term e, second-order term o) in which the variation function L1 is Taylor-expanded (step S1101). The analysis support apparatus 100 gives the value of the constant a, the value of the first weighting factor b, and the value of the second weighting factor c to each of the terms, and calculates the value of each term (step S1102).

  The analysis support apparatus 100 calculates the feature amount of the normal distribution d1 (step S1103), and acquires the variation function L1 (step S1104). As described above, the feature amounts are the average m (θ) and the standard deviation σ (θ). The analysis support apparatus 100 sets j = 0 (step S1105), and determines whether j <the predetermined number of times M (step S1106). If j <predetermined number M (step S1106: Yes), the analysis support apparatus 100 generates a random number based on the normal distribution d1 (step S1107). The analysis support apparatus 100 calculates the second leakage current amount by giving the value of the constant a, the value of the first weighting factor b, the value of the second weighting factor c, and the generated random number to the variation function L1 ( Step S1108). The analysis support apparatus 100 stores the calculation result (step S1109).

  The analysis support apparatus 100 sets “j = j + 1” (step S1110) and returns to step S1106. If j <the predetermined number of times M is not satisfied (step S1106: No), the analysis support apparatus 100 calculates Prob {L1> x} (y) (step S1111), outputs the probability y (step S1112), and a series of processes Exit.

  As described above, the analysis support apparatus calculates a normal distribution of random variables that can calculate a value close to a candidate first leakage current amount with a cumulative probability of occurrence being a predetermined probability, and the second leakage current is calculated based on the normal distribution. Calculate the amount. The analysis support apparatus calculates an index of a ratio that is larger than the first leakage current amount in the second leakage current amount. Thereby, the user can determine whether or not the first leakage current amount is accurate based on the calculated index, and can determine whether or not to estimate the first leakage current amount again. Therefore, the analysis support apparatus can determine the certainty of the first leakage current amount with a small amount of calculation.

  In addition, the analysis support apparatus derives an index representing the certainty that the first leakage current amount is a boundary value based on the index indicating the ratio. Thus, the user can determine whether or not the first leakage current amount is accurate only by referring to an index representing the certainty. Therefore, the analysis support apparatus can determine the certainty of the first leakage current amount with a small amount of calculation.

  In addition, the analysis support apparatus has a first occurrence probability that the cumulative occurrence probability is smaller than the first predetermined probability when the total value of the probability that the second leakage current amount is larger than the first leakage current amount and the first predetermined probability is larger than the predetermined value. (2) Linear approximation is performed using the third leakage current amount and the first leakage current amount, which have a predetermined probability. Thereby, the analysis support apparatus newly calculates a candidate fourth leakage current amount whose cumulative occurrence probability is the first predetermined probability. As a result, the analysis support apparatus can newly provide a leak current amount candidate to the user.

  In addition, the analysis support apparatus determines that the cumulative occurrence probability is larger than the first predetermined probability when the total value of the probability that the second leakage current amount is larger than the first leakage current amount and the first predetermined probability is smaller than the predetermined value. 3 Linear approximation is performed by the third leakage current amount and the first leakage current amount having a predetermined probability. Thus, the analysis support apparatus newly calculates a candidate fourth leakage current amount whose cumulative probability is the first predetermined probability.

  In addition, the analysis support apparatus calculates a normal distribution in which a value close to the calculated fourth leakage current amount is obtained by a variation function related to the calculation of the leakage current amount. The analysis support apparatus newly calculates the second leakage current amount based on the normal distribution. The analysis support apparatus calculates a probability that the second leakage current amount is larger than the fourth leakage current amount. As a result, the analysis support apparatus can determine the certainty of the leak current amount as a new candidate with a small amount of calculation. Furthermore, by repeating the calculation of the leakage current amount of the new candidate by linear approximation and the determination of the certainty of the leakage current amount of the new candidate, the leakage current amount at which the cumulative occurrence probability becomes the first predetermined probability is obtained. Can be provided.

  The analysis support method described in this embodiment can be realized by executing a program prepared in advance on a computer such as a personal computer or a workstation. The analysis support program is recorded on a computer-readable recording medium such as a hard disk, a flexible disk, a CD-ROM, an MO, and a DVD, and is executed by being read from the recording medium by the computer. The analysis support program may be distributed through a network such as the Internet.

  The following additional notes are disclosed with respect to the embodiment described above.

(Supplementary note 1)
A constant value relating to a leakage current unique to the element in the analysis target circuit, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, and the analysis target circuit A value of a second weighting factor for a second random variable representing a variation in a common leak current among the element groups in each element in the analysis target circuit,
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. Get one leak current amount,
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, Obtain a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from the storage device,
The value of the term is calculated by giving the acquired value of the constant, the value of the first weighting factor, and the value of the second weighting factor to the acquired term.
A standard distribution having a standard deviation smaller than the standard normal distribution and determining the value of the second random variable in the variation function, wherein the average of the distribution of the leakage current amount obtained by the variation function is obtained. A feature amount of a normal distribution that becomes one leakage current amount is calculated based on the calculated value of the term and the acquired first leakage current amount,
Obtaining the variation function from the storage device;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated a predetermined number of times by the calculated feature quantity to the second random variable in the variation function, the second leak current amount for the predetermined number of times is obtained. Calculate
Based on the magnitude relationship between the first leakage current amount and the calculated second leakage current amount for the predetermined number of times, the second leakage current amount for the predetermined number of times is greater than the first leakage current amount. Calculate an index indicating the ratio of the second leakage current amount,
Outputting an index indicating the ratio,
An analysis support method characterized by executing processing.

(Appendix 2) The computer
Deriving an index representing the certainty that the first leakage current amount is the boundary value based on the calculated index indicating the ratio;
Outputting an index representing the derived certainty,
The analysis support method according to appendix 1, wherein the process is executed.

(Supplementary note 3)
When the total value of the probability that the second leakage current amount based on the calculated index indicating the ratio is greater than the first leakage current amount and the predetermined probability is greater than a predetermined value, the occurrence probability is the predetermined probability (hereinafter, The range of the leakage current amount of the circuit to be analyzed that is less than or equal to a second predetermined probability that is smaller than the “first predetermined probability”) and the leakage current of the circuit to be analyzed in which the occurrence probability is greater than the second predetermined probability The third leak current amount that is a candidate of the boundary value between the range of the amount,
Based on the ratio between the large probability and the value based on the second predetermined probability, and the ratio between the acquired first leakage current amount and the acquired third leakage current amount, the occurrence probability is the first. A fourth candidate for a boundary value between a range of the leakage current amount of the analysis target circuit that is not more than a predetermined probability and a range of the leakage current amount of the analysis target circuit that has the occurrence probability larger than the first predetermined probability. Calculate the amount of leakage current,
Outputting the calculated fourth leakage current amount;
The analysis support method according to Supplementary Note 1 or 2, wherein the process is executed.

(Appendix 4) The computer
The standard deviation is smaller than the standard normal distribution and is a second normal distribution for determining the value of the second random variable in the variation function, and the average of the distribution of the leakage current amount obtained by the variation function is calculated. Calculating the second characteristic amount of the second normal distribution that becomes the fourth leakage current amount based on the calculated value of the term and the calculated fourth leakage current amount;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated the predetermined number of times by the calculated second feature amount to the second random variable in the variation function, the fifth leak corresponding to the predetermined number of times Calculate the amount of current,
Based on the magnitude relationship between the calculated fourth leakage current amount and the calculated fifth leakage current amount for the predetermined number of times, the fourth leakage current amount among the fifth leakage current amount for the predetermined number of times. Calculating a second index indicating a ratio of the large fifth leakage current amount;
Outputting a second index indicating the ratio,
4. The analysis support method according to appendix 3, wherein the process is executed.

(Appendix 5) The computer
When the total value of the probability that the second leakage current amount based on the calculated index indicating the ratio is larger than the first leakage current amount and the predetermined probability is smaller than a predetermined value, the occurrence probability is the predetermined probability (hereinafter, The range of the leakage current amount of the circuit to be analyzed that is equal to or less than a second predetermined probability that is greater than the “first predetermined probability”) and the leakage current of the circuit to be analyzed in which the occurrence probability is greater than the second predetermined probability The third leak current amount that is a candidate of the boundary value between the range of the amount,
Based on the ratio between the large probability and the value based on the second predetermined probability, and the ratio between the acquired first leakage current amount and the acquired third leakage current amount, the occurrence probability is the first. A fourth candidate for a boundary value between a range of the leakage current amount of the analysis target circuit that is not more than a predetermined probability and a range of the leakage current amount of the analysis target circuit that has the occurrence probability larger than the first predetermined probability. Calculate the amount of leakage current,
Outputting the calculated fourth leakage current amount;
The analysis support method according to Supplementary Note 1 or 2, wherein the process is executed.

(Supplementary Note 6) A second normal distribution having a standard deviation smaller than that of the standard normal distribution and determining the value of the second random variable in the variation function, wherein the leakage current amount distribution obtained by the variation function is Calculating a second feature amount of the second normal distribution that becomes the fourth leakage current amount calculated as an average based on the calculated value of the term and the calculated fourth leakage current amount;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated the predetermined number of times by the calculated second feature amount to the second random variable in the variation function, the fifth leak corresponding to the predetermined number of times Calculate the amount of current,
Based on the magnitude relationship between the fourth leakage current amount and the calculated fifth leakage current amount for the predetermined number of times, the fifth leakage current amount for the predetermined number of times is greater than the fourth leakage current amount. Calculate a second index indicating the ratio of the fifth leakage current amount,
Outputting a second index indicating the ratio,
The analysis support method according to appendix 5, wherein the process is executed.

(Appendix 7)
A constant value relating to a leakage current unique to the element in the analysis target circuit, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, and the analysis target circuit A value of a second weighting factor for a second random variable representing a variation in a common leak current among the element groups in each element in the analysis target circuit,
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. Get one leak current amount,
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, Obtain a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from the storage device,
The value of the term is calculated by giving the acquired value of the constant, the value of the first weighting factor, and the value of the second weighting factor to the acquired term.
A standard distribution having a standard deviation smaller than the standard normal distribution and determining the value of the second random variable in the variation function, wherein the average of the distribution of the leakage current amount obtained by the variation function is obtained. A feature amount of a normal distribution that becomes one leakage current amount is calculated based on the calculated value of the term and the acquired first leakage current amount,
Obtaining the variation function from the storage device;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated a predetermined number of times by the calculated feature quantity to the second random variable in the variation function, the second leak current amount for the predetermined number of times is obtained. Calculate
Based on the magnitude relationship between the first leakage current amount and the calculated second leakage current amount for the predetermined number of times, the second leakage current amount for the predetermined number of times is greater than the first leakage current amount. Calculate an index indicating the ratio of the second leakage current amount,
Outputting an index indicating the ratio,
An analysis support program characterized by causing processing to be executed.

(Supplementary note 8) A constant value related to a leakage current unique to the element in the analysis target circuit, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, A constant coefficient acquisition unit that acquires, for each element in the analysis target circuit, a value of a second weighting factor for a second random variable that represents a variation in leakage current common to the element group in the analysis target circuit;
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. A first leakage current amount acquisition unit for acquiring one leakage current amount;
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, A term acquisition unit that acquires a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from a storage device;
By giving the term obtained by the term obtaining unit, the value of the constant obtained by the constant coefficient obtaining unit, the value of the first weighting factor, and the value of the second weighting factor, A term value calculation unit for calculating the value of the term;
A normal distribution having a standard deviation smaller than that of the standard normal distribution and determining a value of the second random variable in the variation function, wherein an average of a distribution of leakage current amounts obtained by the variation function is the first leakage A normal distribution calculation unit that calculates the characteristic amount of the normal distribution that becomes the first leakage current amount acquired by the current amount acquisition unit based on the calculated value of the term and the acquired first leakage current amount When,
A variation function obtaining unit for obtaining the variation function from the storage device;
The constant value, the first weighting factor, and the second weighting factor in the variation function acquired by the variation function acquisition unit include the acquired constant value, the first weighting factor value, and the first weighting factor. And a value of the second random variable generated a predetermined number of times by the feature amount calculated by the normal distribution calculating unit is given to the second random variable in the variation function. A second leakage current amount calculation unit for calculating a second leakage current amount for the predetermined number of times,
Based on the magnitude relationship between the first leakage current amount and the second leakage current amount for the predetermined number of times calculated by the second leakage current amount calculation unit, the second leakage current amount for the predetermined number of times is calculated. A probability calculating unit for calculating an index indicating a ratio of the second leakage current amount larger than the first leakage current amount;
An output unit that outputs an index indicating the ratio calculated by the probability calculation unit;
An analysis support apparatus characterized by comprising:

(Supplementary note 9) A value of a constant related to a leakage current unique to the element in the circuit to be analyzed, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, A constant coefficient acquisition unit that acquires, for each element in the analysis target circuit, a value of a second weighting factor for a second random variable that represents a variation in leakage current common to the element group in the analysis target circuit;
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. A first leakage current amount acquisition unit for acquiring one leakage current amount;
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, A term acquisition unit that acquires a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from a storage device;
By giving the term obtained by the term obtaining unit, the value of the constant obtained by the constant coefficient obtaining unit, the value of the first weighting factor, and the value of the second weighting factor, A term value calculation unit for calculating the value of the term;
A normal distribution having a standard deviation smaller than that of the standard normal distribution and determining a value of the second random variable in the variation function, wherein an average of a distribution of leakage current amounts obtained by the variation function is the first leakage A normal distribution calculation unit that calculates the characteristic amount of the normal distribution that becomes the first leakage current amount acquired by the current amount acquisition unit based on the calculated value of the term and the acquired first leakage current amount When,
A variation function obtaining unit for obtaining the variation function from the storage device;
The constant value, the first weighting factor, and the second weighting factor in the variation function acquired by the variation function acquisition unit include the acquired constant value, the first weighting factor value, and the first weighting factor. And a value of the second random variable generated a predetermined number of times by the feature amount calculated by the normal distribution calculating unit is given to the second random variable in the variation function. A second leakage current amount calculation unit for calculating a second leakage current amount for the predetermined number of times,
Based on the magnitude relationship between the first leakage current amount and the second leakage current amount for the predetermined number of times calculated by the second leakage current amount calculation unit, the second leakage current amount for the predetermined number of times is calculated. A probability calculating unit for calculating an index indicating a ratio of the second leakage current amount larger than the first leakage current amount;
An output unit that outputs an index indicating the ratio calculated by the probability calculation unit;
An analysis support apparatus comprising: a computer having:

(Supplementary Note 10) A value of a constant related to a leakage current unique to the element in the circuit to be analyzed, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, Obtaining a value of a second weighting factor for a second random variable representing a variation in leak current common to the element group in the analysis target circuit for each element in the analysis target circuit;
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. Get one leak current amount,
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, Obtain a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from the storage device,
The value of the term is calculated by giving the acquired value of the constant, the value of the first weighting factor, and the value of the second weighting factor to the acquired term.
A standard distribution having a standard deviation smaller than the standard normal distribution and determining the value of the second random variable in the variation function, wherein the average of the distribution of the leakage current amount obtained by the variation function is obtained. A feature amount of a normal distribution that becomes one leakage current amount is calculated based on the calculated value of the term and the acquired first leakage current amount,
Obtaining the variation function from the storage device;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated a predetermined number of times by the calculated feature quantity to the second random variable in the variation function, the second leak current amount for the predetermined number of times is obtained. Calculate
Based on the magnitude relationship between the first leakage current amount and the calculated second leakage current amount for the predetermined number of times, the second leakage current amount for the predetermined number of times is greater than the first leakage current amount. Calculate an index indicating the ratio of the second leakage current amount,
Outputting an index indicating the ratio,
A recording medium on which an analysis support program for causing a computer to execute processing is recorded.

DESCRIPTION OF SYMBOLS 100 Analysis support apparatus 300 Analysis object circuit 501 Constant coefficient acquisition part 504 1st leak current amount acquisition part 505 Term acquisition part 506 Term value calculation part 507 Normal distribution calculation part 508 Fluctuation function acquisition part a constant b 1st weight coefficient c Second weighting factor α First random variable β, ξ Second random variable xini First leakage current amount L1 Fluctuation function d 0th-order term e First-order term o Second-order term y Probability

Claims (8)

Computer
A constant value relating to a leakage current unique to the element in the analysis target circuit, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, and the analysis target circuit A value of a second weighting factor for a second random variable representing a variation in a common leak current among the element groups in each element in the analysis target circuit,
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. Get one leak current amount,
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, Obtain a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from the storage device,
The value of the term is calculated by giving the acquired value of the constant, the value of the first weighting factor, and the value of the second weighting factor to the acquired term.
A standard distribution having a standard deviation smaller than the standard normal distribution and determining the value of the second random variable in the variation function, wherein the average of the distribution of the leakage current amount obtained by the variation function is obtained. A feature amount of a normal distribution that becomes one leakage current amount is calculated based on the calculated value of the term and the acquired first leakage current amount,
Obtaining the variation function from the storage device;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated a predetermined number of times by the calculated feature quantity to the second random variable in the variation function, the second leak current amount for the predetermined number of times is obtained. Calculate
Based on the magnitude relationship between the first leakage current amount and the calculated second leakage current amount for the predetermined number of times, the second leakage current amount for the predetermined number of times is greater than the first leakage current amount. Calculate an index indicating the ratio of the second leakage current amount,
Outputting an index indicating the ratio,
An analysis support method characterized by executing processing. The computer is
Deriving an index representing the certainty that the first leakage current amount is the boundary value based on the calculated index indicating the ratio;
Outputting an index representing the derived certainty,
The analysis support method according to claim 1, wherein processing is executed. The computer is
When the total value of the probability that the second leakage current amount based on the calculated index indicating the ratio is greater than the first leakage current amount and the predetermined probability is greater than a predetermined value, the occurrence probability is the predetermined probability (hereinafter, The range of the leakage current amount of the circuit to be analyzed that is less than or equal to a second predetermined probability that is smaller than the “first predetermined probability”) and the leakage current of the circuit to be analyzed in which the occurrence probability is greater than the second predetermined probability The third leak current amount that is a candidate of the boundary value between the range of the amount,
Based on the ratio between the large probability and the value based on the second predetermined probability, and the ratio between the acquired first leakage current amount and the acquired third leakage current amount, the occurrence probability is the first. A fourth candidate for a boundary value between a range of the leakage current amount of the analysis target circuit that is not more than a predetermined probability and a range of the leakage current amount of the analysis target circuit that has the occurrence probability larger than the first predetermined probability. Calculate the amount of leakage current,
Outputting the calculated fourth leakage current amount;
The analysis support method according to claim 1, wherein the process is executed. The computer is
The standard deviation is smaller than the standard normal distribution and is a second normal distribution for determining the value of the second random variable in the variation function, and the average of the distribution of the leakage current amount obtained by the variation function is calculated. Calculating the second characteristic amount of the second normal distribution that becomes the fourth leakage current amount based on the calculated value of the term and the calculated fourth leakage current amount;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated the predetermined number of times by the calculated second feature amount to the second random variable in the variation function, the fifth leak corresponding to the predetermined number of times Calculate the amount of current,
Based on the magnitude relationship between the calculated fourth leakage current amount and the calculated fifth leakage current amount for the predetermined number of times, the fourth leakage current amount among the fifth leakage current amount for the predetermined number of times. Calculating a second index indicating a ratio of the large fifth leakage current amount;
Outputting a second index indicating the ratio,
The analysis support method according to claim 3, wherein the process is executed. The computer is
When the total value of the probability that the second leakage current amount based on the calculated index indicating the ratio is larger than the first leakage current amount and the predetermined probability is smaller than a predetermined value, the occurrence probability is the predetermined probability (hereinafter, The range of the leakage current amount of the circuit to be analyzed that is equal to or less than a second predetermined probability that is greater than the “first predetermined probability”) and the leakage current of the circuit to be analyzed in which the occurrence probability is greater than the second predetermined probability The third leak current amount that is a candidate of the boundary value between the range of the amount,
Based on the ratio between the large probability and the value based on the second predetermined probability, and the ratio between the acquired first leakage current amount and the acquired third leakage current amount, the occurrence probability is the first. A fourth candidate for a boundary value between a range of the leakage current amount of the analysis target circuit that is not more than a predetermined probability and a range of the leakage current amount of the analysis target circuit that has the occurrence probability larger than the first predetermined probability. Calculate the amount of leakage current,
Outputting the calculated fourth leakage current amount;
The analysis support method according to claim 1, wherein the process is executed. The standard deviation is smaller than the standard normal distribution and is a second normal distribution for determining the value of the second random variable in the variation function, and the average of the distribution of the leakage current amount obtained by the variation function is calculated. Calculating the second characteristic amount of the second normal distribution that becomes the fourth leakage current amount based on the calculated value of the term and the calculated fourth leakage current amount;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated the predetermined number of times by the calculated second feature amount to the second random variable in the variation function, the fifth leak corresponding to the predetermined number of times Calculate the amount of current,
Based on the magnitude relationship between the fourth leakage current amount and the calculated fifth leakage current amount for the predetermined number of times, the fifth leakage current amount for the predetermined number of times is greater than the fourth leakage current amount. Calculate a second index indicating the ratio of the fifth leakage current amount,
Outputting a second index indicating the ratio,
6. The analysis support method according to claim 5, wherein processing is executed. On the computer,
A constant value relating to a leakage current unique to the element in the analysis target circuit, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, and the analysis target circuit A value of a second weighting factor for a second random variable representing a variation in a common leak current among the element groups in each element in the analysis target circuit,
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. Get one leak current amount,
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, Obtain a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from the storage device,
The value of the term is calculated by giving the acquired value of the constant, the value of the first weighting factor, and the value of the second weighting factor to the acquired term.
A standard distribution having a standard deviation smaller than the standard normal distribution and determining the value of the second random variable in the variation function, wherein the average of the distribution of the leakage current amount obtained by the variation function is obtained. A feature amount of a normal distribution that becomes one leakage current amount is calculated based on the calculated value of the term and the acquired first leakage current amount,
Obtaining the variation function from the storage device;
The obtained constant value, the first weighting factor, and the second weighting factor, the obtained constant value, the first weighting factor value, and the second weighting factor value, , And giving the value of the second random variable generated a predetermined number of times by the calculated feature quantity to the second random variable in the variation function, the second leak current amount for the predetermined number of times is obtained. Calculate
Based on the magnitude relationship between the first leakage current amount and the calculated second leakage current amount for the predetermined number of times, the second leakage current amount for the predetermined number of times is greater than the first leakage current amount. Calculate an index indicating the ratio of the second leakage current amount,
Outputting an index indicating the ratio,
An analysis support program characterized by causing processing to be executed. A constant value relating to a leakage current unique to the element in the analysis target circuit, a value of a first weighting factor for a first random variable representing a variation in leakage current unique to the element according to a standard normal distribution, and the analysis target circuit A constant coefficient acquisition unit that acquires, for each element in the analysis target circuit, a value of a second weighting coefficient for a second random variable that represents a variation in leakage current common to the elements in the group;
A candidate for a boundary value between a range of the leakage current amount of the analysis target circuit in which the occurrence probability is equal to or less than a predetermined probability and a range of the leakage current amount of the analysis target circuit in which the occurrence probability is greater than the predetermined probability. A first leakage current amount acquisition unit for acquiring one leakage current amount;
A product of the first weighting factor and the first random variable and an expression representing an average value of a normal distribution with the constant as a parameter, and a product of the second random variable and the second weighting factor, A term acquisition unit that acquires a term when the variation function of the leakage current amount of the analysis target circuit as a parameter for each element is Taylor-expanded from a storage device;
By giving the term obtained by the term obtaining unit, the value of the constant obtained by the constant coefficient obtaining unit, the value of the first weighting factor, and the value of the second weighting factor, A term value calculation unit for calculating the value of the term;
A normal distribution having a standard deviation smaller than that of the standard normal distribution and determining a value of the second random variable in the variation function, wherein an average of a distribution of leakage current amounts obtained by the variation function is the first leakage A normal distribution calculation unit that calculates the characteristic amount of the normal distribution that becomes the first leakage current amount acquired by the current amount acquisition unit based on the calculated value of the term and the acquired first leakage current amount When,
A variation function obtaining unit for obtaining the variation function from the storage device;
The constant value, the first weighting factor, and the second weighting factor in the variation function acquired by the variation function acquisition unit include the acquired constant value, the first weighting factor value, and the first weighting factor. And a value of the second random variable generated a predetermined number of times by the feature amount calculated by the normal distribution calculating unit is given to the second random variable in the variation function. A second leakage current amount calculation unit for calculating a second leakage current amount for the predetermined number of times,
Based on the magnitude relationship between the first leakage current amount and the second leakage current amount for the predetermined number of times calculated by the second leakage current amount calculation unit, the second leakage current amount for the predetermined number of times is calculated. A probability calculating unit for calculating an index indicating a ratio of the second leakage current amount larger than the first leakage current amount;
An output unit that outputs an index indicating the ratio calculated by the probability calculation unit;
An analysis support apparatus characterized by comprising:

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