JP4337719B2 - COMPUTER DEVICE AND COMPUTER PROCESSING PROGRAM - Google Patents

Description

The present invention relates to a calculation apparatus and a calculation processing program for calculating a logarithmic function with high accuracy.

  In the conventional computing device, the calculation of the logarithmic function requires a very complicated process, which hinders the speeding-up. As one method for calculating this at a high speed, IEEE (US Electric Electronics) It is conceivable to reduce the complexity of the approximation used to calculate the natural logarithm while achieving numerical accuracy that matches the floating-point accuracy of the academic society (see, for example, Patent Document 1). .

  In such a logarithmic function calculation apparatus, high-speed calculation processing and high precision are required. In particular, in the calculation using the logarithmic function [log (1 + x)], the value of x is “1”. If it is less than “0” (0 <| x | <1), there is a problem that an error increases because a digit loss corresponding to the set effective number of digits occurs in the calculation of “1 + x” in parentheses.

  For example, in decimal 16-digit arithmetic, when [log (1 + x)] is obtained with x = 1.23456789E-17, the substitution formula is [log (1 + 1.23456789E-17)]. [Log (1) = 0] due to a digit loss at the calculation stage of “1 + x”. If no digit loss occurs, [log (1 + 1.23456789E-17) = 1.23456789E-17] is correct.

  In order to prevent such miscalculations, in the C language, [log1p (x) (= log (1 + x) can be calculated by giving x to the variable part of the function as it is, separately from the [log (x)] function. )] The function is defined on the program, and a calculation in which x is directly substituted by the following Taylor expansion formula is executed, so that a calculation without dropping digits can be performed even if the value of x is small.

log (1 + x) = x- (1/2) x ^ 2 + (1/3) x ^ 3- (1/4) x ^ 4 +… (| x | <1)
In the description of the calculation formula in this specification, the numerical value immediately after the symbol [^] indicates an exponent of power, for example, [x ^ 2] means the square of x.

  On the other hand, in the calculation process of the exponential function that is the inverse function of the logarithmic function, particularly in the calculation using the exponential function [exp (x) -1], the value of x is less than “1” (0 <| When x | <1) is small, the calculation result first becomes a value near 1 in the calculation of “exp (x)”, and the value corresponding to the set effective digit number in the calculation of “exp (x) −1” thereafter. There is a problem that errors are increased because of the loss of digits.

  For example, in decimal 16-digit arithmetic, when [exp (x) -1] is obtained with x = 1.23456789E-17, the substitution expression is [exp (1.23456789E-17) -1]. [Exp (1.23456789E-17) = 1] due to a digit loss at the calculation stage of “1.23456789E-17)”. Then, [exp (1.23456789E-17) -1 = 0] is obtained, and the calculation result becomes 0 due to a digit loss. If no digit loss occurs, the correct value is [exp (1.23456789E-17) -1 = 1.23456789E-17].

  For this reason, for this exponential function, separately from the [exp (x)] function, the [exp (x) -1] function is defined on the C language program, and the calculation is performed using the following Taylor expansion formula. Calculations without dropping digits are made possible.

exp (x) -1 = (1/1!) x + (1/2!) x ^ 2 + (1/3!) x ^ 3 + (1/4!) x ^ 4 +…
JP 2001-306301 A

  In this way, with the logarithmic function, the [log1p (x)] function can be used to perform highly accurate logarithmic calculations. However, for each numerical calculation, the programmer can use the [log1p (x)] and [log (x)] functions There is a problem that it is very difficult to use properly when [log (a + x)] changes, for example, a = 3 or a = 1. .

  As for exponential functions, the [exp (x) -1] function can be used to perform exponential calculations with high accuracy, but the programmer can use [exp (x) -1] and [exp (x)] functions for each numerical calculation. It is necessary to be aware of the function and use it properly, especially when [exp (x) -a] changes, for example, a = 3 or a = 1. There is.

  In addition, even when [10 ^ x] or [x ^ y] is included in the calculation formula, these formulas are converted into the exponential function and the logarithmic function for calculation processing. .

  And such calculations using [log (1 + x)] [exp (x) -1] [10 ^ x] [x ^ y] frequently occur in various fields such as compound interest calculation and accumulation calculation It is a big problem to do.

The present invention has been made in view of such problems, and it is possible to appropriately perform logarithmic function calculation processing according to the state of the input calculation formula, and to obtain a high-precision calculation result without digit loss. An object of the present invention is to provide a calculation device and a calculation processing program.

The calculation apparatus according to the present invention includes a calculation formula storage means for storing an input calculation formula, and whether the calculation formula stored by the calculation formula storage means includes a calculation formula portion of addition and subtraction of 1 and a numerical value. This is detected when it is detected by the calculation formula part detection means for detecting whether or not the calculation formula part of the addition / subtraction of 1 and a numerical value is included in the calculation formula by the calculation formula part detection means. The numerical value of the calculation formula part is stored as an exponent part and a mantissa part, and the detection numerical value storage means for storing an identification flag indicating the detection of the calculation formula part, and the detection numerical value stored in the calculation formula stored by the calculation formula storage means A logarithmic function detecting means for detecting whether or not a logarithmic function having the calculation formula portion indicated by the identification flag stored by the storage means as an argument is included; and the logarithmic function detecting means adds the calculating formula to the calculating formula. portion When it is detected that a logarithmic function as an argument is included, the detection numerical value storage means detects whether the absolute value of the numerical value stored as the exponent part and the mantissa part is less than 1 or less When the absolute value of the numerical value is detected to be less than 1 by the means and the less than 1 detection means, the logarithmic function is calculated with high accuracy by directly using the numerical value stored in the detected numerical value storage means. When the absolute value of the numerical value is detected to be less than 1 by the accuracy logarithm calculation means and the less than 1 detection means, the logarithmic function is calculated using the calculation result of the calculation formula part detected by the calculation formula part detection means. And normal logarithm calculation means for performing calculation .

  According to this, it is appropriately determined whether or not the “numerical value” in the calculation formula part of addition and subtraction of 1 and a numerical value argument of the logarithmic function included in the calculation formula is less than 1, and [log (1+ x)] function can be accurately switched between the calculation of the high-precision logarithmic function and the normal logarithmic function using the [log (x)] function.

According to the computing device of claim 1 (claim 4) of the present invention (calculation processing program), "Numerical" in formulas portion addition and subtraction of 1 and the value, the argument of the logarithmic function included in the formula Of the logarithm function using the [log (1 + x)] function and the normal logarithmic function using the [log (x)] function It is possible to perform a calculation process in which the calculation is accurately switched.

Therefore, according to the present invention, a calculation apparatus and a calculation processing program capable of appropriately performing a logarithmic function calculation process according to the state of the input calculation formula and obtaining a high-precision calculation result without any digit loss Can provide.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 is a block diagram showing a configuration of an electronic circuit of an electronic computing device 10 according to an embodiment of the present invention.

  The electronic computing device 10 includes a control unit (CPU) 11 composed of a computer or the like.

  The control unit (CPU) 11 stores in the ROM 12A in the memory 12 in response to a calculation request signal from a PC (personal computer) terminal 20A directly connected or a PC terminal 20B connected via a communication network N such as the Internet. A calculation processing program 12a1 stored in advance, a calculation processing program read from the external recording medium 13 via the recording medium reading unit 14, or a Web server on the communication network (Internet) N (in this case, a program server (not shown) The calculation processing program downloaded via the transmission control unit 15 is started, and the RAM 12B in the memory 12 is used as a work (working) memory to control the operation of each part of the circuit and perform calculation processing.

  The control unit (CPU) 11 is connected to the memory 12, the recording medium reading unit 14, and the power transmission control unit 15, and the PC terminal 20 </ b> A via an external device connection unit 17 such as a shared memory 16 and a USB terminal. Are connected directly.

  In this electronic computing device 10, a calculation process corresponding to a calculation request input with a desired calculation formula is executed by a communication process from the directly connected PC terminal 20A, and the calculation result is sent to the PC terminal 20A of the calculation request source. A calculation process corresponding to a calculation request input with a desired calculation formula using the calculation processing server 21 is executed by a response transmission or a communication process from the network connection PC terminal 20B, and the calculation result is sent to the calculation request source. Response transmission to the PC terminal 20B.

  The ROM 12A in the memory 12 is provided with an official memory 12a2 in addition to the calculation processing program 12a1 for managing various calculation processes in the electronic calculation apparatus 10.

  The formula memory 12a2 stores in advance a large number of formulas used in various fields of calculation processing such as compound interest calculation formulas, accumulation calculation formulas, and [log (x )] Function calculation routines and [log1p (x) (= log (1 + x)] function calculation routines for performing high-precision logarithmic function calculation processing by directly giving x to the variable part of the function In this high-precision logarithmic function calculation routine, a calculation in which x is directly substituted by the following Taylor expansion formula is executed, so that even if the value of x is small, a calculation without dropping digits can be performed.

log (1 + x) = x- (1/2) x ^ 2 + (1/3) x ^ 3- (1/4) x ^ 4 +… (| x | <1)
Furthermore, in the official memory 12a2, there are [exp (x)] function calculation routines for performing normal exponential function calculation processing and [exp (x) -1] for high-precision exponential function calculation processing. The function calculation routine is stored. This high-precision exponential function calculation routine can perform calculations without dropping digits by executing the following Taylor expansion formula.

exp (x) -1 = (1/1!) x + (1/2!) x ^ 2 + (1/3!) x ^ 3 + (1/4!) x ^ 4 +…
The RAM 12B in the memory 12 includes a calculation formula memory 12b1, a calculation accuracy memory 12b2, a variable memory 12b3, a calculation formula status detection register 12b4, and a calculation result numerical value memory 12b5.

  The calculation formula memory 12b1 stores and stores a calculation formula input in response to a calculation request from the direct connection PC terminal 20A or the network connection PC terminal 20B.

  The calculation accuracy memory 12b2 stores and stores the specified calculation accuracy (the number of significant digits) together with a calculation formula associated with a calculation request from the direct connection PC terminal 20A or the network connection PC terminal 20B.

  The variable memory 12b3 stores and stores symbols indicating variables included in the calculation formula stored in the calculation formula memory 12b1.

  The calculation condition detection register 12b4 has a plurality of registers R1, R2, R3, and R4. From the calculation expression stored in the calculation expression memory 12b1, the “1 ± numerical value” portion or “exp (numerical value) −1” ”Is detected, each time the detection is made, the mantissa part, exponent part, and sign of the“ number ”are stored in each register Rn, and the“ 1 ± number ”part is detected. In this case, the flag “1” is set.

  The calculation result numerical value memory 12b5 stores the numerical value of the final calculation result calculated according to the calculation request.

  That is, in the electronic computing device 10, in the course of calculation processing according to a calculation request accompanied by a desired calculation formula, the logarithmic function [log1p (x)] function or the exponential function [exp (x) -1] function is used. The “1 ± numerical value” portion and the “exp (numerical value) −1” portion, which are assumed to require high-precision calculation processing using Taylor expansion, are detected and held in the status detection register 12b4. The register 12b4 When it is determined that the numerical value held in 1 is less than 1, the [log1p (x)] function (high-precision logarithmic function calculation routine) or the [exp (x) -1] function (high-precision exponential function calculation routine) ), And if it is determined that the number is 1 or more, the [log (x)] function (normal logarithmic function calculation routine) or the [exp (x)] function (normal exponential function calculation routine) By performing the usual logarithmic function calculation processing and normal exponential function calculation processing by So that computation of the logarithmic function and exponential function is properly performed in the calculation that.

  Next, the calculation function by the electronic calculation apparatus 10 having the above configuration will be described.

  FIG. 2 is a flowchart showing the overall processing of the calculation function by the electronic calculation apparatus 10.

  FIG. 3 is a flowchart showing the calculation processing of the calculation formula accompanying the overall processing of the calculation function in the electronic calculation apparatus 10.

  FIG. 4 is a diagram showing a numerical processing state on the RAM 12B accompanying the calculation process when a calculation request of a calculation formula [loge (1 + 1.23456789E-17)] including a logarithmic function is input in the electronic calculation apparatus 10. It is.

  FIG. 5 shows a calculation process when a calculation request of a calculation formula [loge (A): A = 1 + 1.23456789E-17)] including a logarithmic function and a variable value is input in the electronic calculation apparatus 10. It is a figure which shows the numerical processing state on RAM12B.

  The electronic computer 10 first determines whether the type of calculation request is “official calculation processing” or “calculation processing of the received calculation formula” (step S1). In the case of the direct connection PC terminal 20A, the user-specified official calculation formula is read from the official memory defined by the communication calculation program, or the network connection PC terminal 20B accesses the calculation processing server 21. An arbitrary formula is input by acquiring the formula specified by the user, and the number of digits of desired calculation accuracy is input along with this (step S2).

  On the other hand, in the case of “calculation processing of received calculation formula”, an arbitrary calculation formula is input and the number of digits of calculation accuracy is input in the directly connected PC terminal 20A or the network connection PC terminal 20B (step S3).

  When a calculation request is received from the directly connected PC terminal 20A, the calculation formula and calculation accuracy data written in the shared memory 16 are read out, and the calculation from the network PC terminal 20B is read. In the case of a request, the calculation formula and calculation accuracy data are received via the transmission control unit 15 (step S4).

  Then, for example, as shown in FIG. 4 (A) or FIG. 5 (A), a calculation formula [loge (1 + 1.23456789E-17)] received from the PC terminal 20A (20B) or a calculation in which a variable value is set. Each data of the formula [loge (A): A = 1 + 1.23456789E-17)] and the calculation accuracy [16 digits] is calculated by the calculation formula in the RAM 12B as shown in FIG. 4 (B) or FIG. 5 (B). They are stored in the memory 12b1 and the calculation accuracy memory 12b2, respectively (step S5).

  Here, it is determined whether or not the formula stored in the calculation formula memory 12b1 in the RAM 12B includes the left side portion of any formula stored in advance in the formula memory 12 in the ROM 12A ( Step S6).

  For example, if it is determined that the left side part of the formula [10 ^ x] or [x ^ y] is included in the formula received by the calculation request, the left side part of the formula in the formula [10 ^ x ] And [x ^ y] are converted into [exp (x * loge (10))] and [exp (y * loge (x))] respectively on the right side thereof and rewritten in the calculation formula memory 12b1 (step S6). → S7).

  Then, the calculation process shown in FIG. 3 is executed for the calculation formula stored in the calculation formula memory 12b1 (step SA).

  On the other hand, as shown in FIG. 4B or FIG. 5B, the calculation formula received and stored by the calculation request is [loge (1 + 1.23456789E-17)] or [loge (A): A = 1 + 1.23456789E-17)], it is determined that the left side of the formula is not included, and the calculation process shown in FIG. 3 is executed for the calculation formula (step SA).

  When the calculation processing of the calculation formula in FIG. 3 is started, for example, as shown in FIG. 4B or FIG. 5B, the calculation formula [loge (1 ++) stored in the calculation formula memory 12b1 in the RAM 12B. 1.23456789E-17)] or [loge (A): A = 1 + 1.23456789E-17)] is read out. At this time, as shown in FIG. 5B, when there is a numerical substitution setting [A = 1 + 1.23456789E-17] for the variable [A] in the read calculation formula, As shown in (C), the calculation formula [loge (1 + 1.23456789E-17)] substituted with the set numerical value is rewritten (step A1).

  Then, regarding the read calculation formula [loge (1 + 1.23456789E-17)], the presence of the calculation formula portion in the “1 + numerical value” format or the “1−numerical value” format is detected in order from the top. In this case, the “numerical value” refers to various numerical values such as integers and decimal numbers (step A2).

  When the calculated formula part [1 + 1.23456789E-17] in the “1 + numerical value” format is detected for the read formula [loge (1 + 1.23456789E-17)], FIG. C) or as shown in FIG. 5D, the calculation formula part [1 + 1.23456789E-17] in the “1 + numerical value” format in the calculation formula [loge (1 + 1.23456789E-17)] is the status detection register. It is rewritten to the specification of the leading free register R1 of 12b4 to be [loge (R1)], and the sign [+] and exponent part [-17] of the numerical part [+ 1.23456789E-17] with respect to this register R1 The mantissa part [1.23456789] is saved, and the flag “1” indicating “1 + numerical value” is set (step A3 → A4).

  Thereafter, if there is a continuation calculation formula for the calculation formula read out from the calculation formula memory 12b1, the calculation formula portion in the “1 + numerical value” format or the “1-numerical value” format is further added from the subsequent calculation formula. Is detected, and the register processing similar to the above is repeated (steps A5 → A6 → A3 → A4).

  Then, when the calculation expression read out from the calculation expression memory 12b1 is repeated until the end of the calculation expression portion in the same “1 ± numerical value” format and the register processing are repeated, for example, FIG. Alternatively, as shown in FIG. 5D, for the calculation formula [loge (R1)] rewritten and stored in the calculation formula memory 12b1, the first “1 ± number” when the flag “1” is set. ”Format detection part (in this case, (R1) part), it is detected whether it is an argument of the logarithmic function (step A5 → A7).

  Here, if it is detected that the detection part [(R1)] in the “1 ± numerical value” format in the calculation formula [loge (R1)] is an argument of the logarithmic function [loge], It is determined whether or not the absolute value of the numerical value rewritten and stored in the designated register R1 with the sign [+], the exponent part [-17], and the mantissa part [1.23456789] is less than 1 (step A8 → A9). ).

  Then, the absolute value [1.23456789E-17] of the detected part [(R1)] in the “1 ± numerical value” format detected as being an argument of the logarithmic function [loge] is determined to be less than 1. When the logarithmic function is calculated, the number of significant digits stored in the calculation accuracy memory 12b2 by the Taylor expansion formula using the [log1p (x)] function based on the high-precision logarithmic function calculation routine stored in the ROM 12A. The calculation is executed with high accuracy according to (step A9 → A10).

  On the other hand, when it is determined that the absolute value of the numerical value of the detected portion in the “1 ± numerical value” format detected as an argument of the logarithmic function [loge] is not less than 1, but 1 or more, The logarithmic function is calculated based on the number of significant digits stored in the calculation accuracy memory 12b2 using the normal [log (x)] function based on the normal logarithmic function calculation routine stored in the ROM 12A (step A9 → A11). .

  Thereafter, when there is a continuation calculation formula rewritten in the calculation formula memory 12b1, there is “1 ± numerical value” stored in the register Rn from the subsequent calculation formula. If it is detected whether the detection part of the format is an argument of the logarithmic function, and if it is detected that it is an argument of the logarithmic function, the calculation of the logarithmic function according to the determination of the absolute value of less than 1/1 or more is the same Execution is repeated (steps A12 → A13 → A8 to A11).

  For the calculation formula rewritten and stored in the calculation formula memory 12b1, logarithmic function argument detection processing for the detection portion in the same “1 ± numerical value” format and determination of the absolute value of the numerical value are performed until the end. When the logarithmic function calculation process is repeated, the presence of a calculation formula portion in the form of “exp (numerical value) −1” or “exp (numerical value) +1” is detected in order from the top of the calculation formula (step A12). → A14).

  FIG. 6 shows a calculation process when a calculation request of a calculation formula [exp (A) -1: A = 1.23456789E-17)] including an exponential function and a variable value is input in the electronic calculation apparatus 10. It is a figure which shows the numerical processing state on RAM12B.

  For example, as shown in FIG. 6A, the calculation formula [exp (A) -1: A = 1.23456789E-17)] and the calculation accuracy [16 digits] received with the calculation request are shown in FIG. As shown in FIG. 6, after being stored in the calculation formula memory 12b1 and calculation accuracy memory 12b2 in the RAM 12B (steps S1 to S5), as shown in FIG. With the calculation formula [exp (1.23456789E-17) -1] being rewritten (step A1), the calculation formula [exp (1.23456789E-17) -1] is passed through the steps A2 to A12. , When a calculation formula portion in the form of “exp (numerical value) -1” is detected (steps A14 and A15), the numerical value portion [1.23456789E-17] is detected as shown in FIG. 6D. When saved as a sign [+], an exponent part [-17], and a mantissa part [1.23456789] with respect to the first free register R1 of the register 12b4 The absolute value of the number is determined whether or not less than 1 (step A16).

  When it is determined that the absolute value [1.23456789E-17] of the numerical value detected to be the exponential function [exp (numerical value) -1] is less than 1, the calculation of the exponential function is performed in the ROM 12A. Is calculated with high precision according to the number of significant digits stored in the calculation precision memory 12b2 by the Taylor expansion formula using the [exp (x) -1] function based on the high precision exponential function calculation routine stored in (Step A16). → A17).

  On the other hand, when it is determined that the absolute value of the numerical value detected to be an exponential function [exp (numerical value) -1] is not less than 1, but 1 or more, the calculation of the exponential function is stored in the ROM 12A. Based on the normal exponential function calculation routine, the normal [exp (x)] function is used to execute according to the number of significant digits stored in the calculation accuracy memory 12b2 (step A16 → A18).

  Thereafter, when there is a continuation calculation formula rewritten and stored in the calculation formula memory 12b1, a calculation formula in the form of “exp (numerical value) −1” is further calculated from the subsequent calculation formula. The portion is detected, and the calculation of the exponential function is repeated according to the determination of the absolute value of the numerical value less than 1/1 or more (steps A19 → A20 → A15 to A18).

  Then, with respect to the calculation formula rewritten and stored in the calculation formula memory 12b1, the exponential function calculation according to the detection processing in the same “exp (numerical value) −1” format and the determination of the absolute value of the numerical value is performed until the end. When the process is repeated, the calculation process of the remaining uncalculated portion is executed, and as shown in FIG. 4D, FIG. 5E, or FIG. [1.23456789E-17] is stored in the calculation result numerical value memory 12b5 in the RAM 12B (step A19 → A21).

  Thus, when the calculation processing of the series of calculation formulas in FIG. 3 is executed (steps SA (A1 to A21)), the numerical data of the calculation result stored in the calculation result numerical memory 12b5 in the RAM 12B is calculated this time. The PC terminal that is the request source is notified as follows (step S8).

  That is, when the calculation request source is the directly connected PC terminal 20A, the numerical data of the calculation result read from the calculation result numerical memory 12b5 is written in the shared memory 16 and thus directly connected via the connection unit 17. Completion of calculation processing is notified to the connected PC terminal 20A.

  When the calculation request source is the network connection PC terminal 20B, the numerical data of the calculation result read from the calculation result numerical memory 12b5 is transmitted to the network connection PC terminal 20B via the transmission control unit 15. The completion of the calculation process is notified.

  FIG. 7 shows a calculation formula [FV = PMT * ((1 + r) ^ n-1) /r:PMT=100,000,000:r=0.012345678901] in which the calculation formula is set and the variable value is set in the electronic calculation apparatus 10. : n = 10)] is a diagram showing a numerical processing state (No. 1) on the RAM 12B accompanying the calculation process when the calculation request is input.

  FIG. 8 shows a calculation formula [FV = PMT * ((1 + r) ^ n-1) /r:PMT=100,000,000:r=0.012345678901] in which the calculation formula is set and the variable value is set in the electronic calculator 10. : n = 10)] is a diagram showing a numerical processing state (No. 2) on the RAM 12B accompanying the calculation process when the calculation request is input.

  For example, as shown in FIG. 8A, the calculation formula [FV = PMT * ((1 + r) ^ n-1) /r:PMT=100,000,000:r=0.012345678901:n=10 )] And the calculation accuracy [11 digits] are stored in the calculation formula memory 12b1 and the calculation accuracy memory 12b2 in the RAM 12B as shown in FIG. 8B (steps S1 to S5), FIG. ), The corresponding formula [x ^ y = exp (y * loge (x))] in which the formula corresponding part [(1 + r) ^ n] in the formula is stored in the formula memory 12a2 in advance. Is converted to [FV = PMT * (exp (n * loge (1 + r))-1) / r] and rewritten in the calculation formula memory 12b1 (steps S6 → S7).

Then, the calculation formula [FV = PMT * (exp (n * loge (1 + r))-1) / r] read from the calculation formula memory 12b1
[PMT] [r] [n] is substituted with [PMT = 100,000,000: r = 0.012345678901: n = 10], respectively, and as shown in FIG.
[FV = 100,000,000 * (exp (10 * loge (1 + 0.012345678901))-1) /0.012345678901]
(Step A1).

For the calculation formula [FV = 100,000,000 * (exp (10 * loge (1 + 0.012345678901))-1) /0.012345678901], the calculation formula portion [1 + 0.012345678901] in the “1 + number” format is used. ] Is detected, the calculation formula portion [1 + 0.012345678901] in the “1 + numerical value” format in the calculation formula is designated as the first free register R1 of the status detection register 12b4 as shown in FIG. To [FV = 100,000,000 * (exp (10 * loge (R1))-1) /0.012345678901] and the sign [+] · exponent of the numerical part [+0.012345678901] for this register R1 The part [-2] and the mantissa part [1.2345678901] are stored, and a flag “1” indicating “1 + numerical value” is set (steps A2 to A4).

  Here, the detection part [(R1)] indicated by the flag “1” in the form of “1 + numerical value” in the formula [FV = 100,000,000 * (exp (10 * loge (R1))-1) /0.012345678901] Is detected as an argument of the logarithmic function [loge], and is then rewritten and stored in the designated register R1 as a sign [+], an exponent part [-2], and a mantissa part [1.2345678901]. Since it is determined that the absolute value of the numerical value is less than 1, the calculation accuracy of the logarithmic function is calculated by the Taylor expansion formula using the [log1p (x)] function based on the high-precision logarithmic function calculation routine stored in the ROM 12A. Calculation is executed with high accuracy according to the number of significant digits stored in the memory 12b2 (steps A7 to A10).

Specifically, it is calculated as [loge (1 + 0.012345678901) = 1.2270092482E-02]. As shown in FIG. 8F, the calculation formula in the calculation formula memory 12b1 is
[FV = 100,000,000 * (exp (10 * (1.2270092482E-02) -1) /0.012345678901].

  Then, a calculation formula portion [exp (10 * (1.2270092482E-02) -1] in the form of “exp (numerical value) −1” is detected for the calculation formula, and as shown in FIG. The part [10 * (1.2270092482E-02) = 1.2270092482E-01] is stored as the sign [+], the exponent part [-1], and the mantissa part [1.2270092482] with respect to the first free register R2 of the status detection register 12b4. (Steps A14 and A15).

  Then, since the absolute value [1.2270092482E-01] of the numerical value detected to be the exponential function [exp (numerical value) -1] is determined to be less than 1, the calculation of the exponential function is stored in the ROM 12A. Based on the stored high-precision exponential function calculation routine, high-precision calculation is executed according to the number of significant digits stored in the calculation accuracy memory 12b2 by the Taylor expansion formula using the [exp (x) -1] function (step A16 → A17).

Specifically, it is calculated as [exp (1.2270092482E-01) = 0.13054625206]. As shown in FIG. 8G, the calculation formula in the calculation formula memory 12b1 is
[FV = 100,000,000 * (0.13054625206) /0.012345678901].

  Then, the calculation processing of the remaining uncalculated portion is executed, and as shown in FIG. 8H, the final calculation result numerical data [1,057,424,651.2] is stored in the calculation result numerical memory 12b5 in the RAM 12B (step A21). ).

  Then, the numerical data [1,057,424,651.2] of the calculation result stored in the calculation result numerical memory 12b5 in the RAM 12B is notified to the PC terminal 20A (20B) which is the current calculation request source (step S8).

  Therefore, according to the calculation function of the electronic calculation apparatus 10 having the above-described configuration, the logarithmic function [log1p (x)] function or the exponential function [exp ( x) -1] The “1 ± numerical value” portion and the “exp (numerical value) −1” portion, which are assumed to require high-precision calculation processing using Taylor expansion by the function, are detected and the contents are detected by the status detection register 12b4. And the [log1p (x)] function (high-precision logarithmic function calculation routine) or [exp (x) -1] function is determined when it is determined that the numerical value held in the register 12b4 is less than 1. (High-precision exponential function calculation routine) Performs high-precision calculation processing, and if it is determined that the number is 1 or more, [log (x)] function (normal logarithmic function calculation routine) or [exp (x)] function Normal logarithmic function calculation processing and normal exponential function by (normal exponential function calculation routine) By performing arithmetic processing, logarithmic functions and exponential functions are appropriately processed in all calculations, so the programmer is aware of each numerical calculation in advance and uses the [log1p (x)] function and [log (x )] Function or the [exp (x) -1] function and the [exp (x)] function are not required to be used separately, and a high-precision calculation result without any digit loss can be easily obtained.

In the above-described embodiment, the calculation of the logarithmic function has been described in the case of the natural logarithm [loge (x)] over the whole, but even in the case of the common logarithm [log ₁₀ (x)], What is the calculated value of the natural logarithm [loge (x)] and the calculated value of the common logarithm [log ₁₀ (x)]?
log ₁₀ (x) = (loge (x)) / 2.30258509
Therefore, by simply adding the difference of the constant rate to the logarithmic function calculation result, the logarithmic function of any base can easily obtain a high-precision calculation result with no precision loss by the same calculation process. Obtainable.

  Note that the methods described in the embodiment, that is, the calculation function overall processing shown in the flowchart of FIG. 2 and the calculation formula calculation processing accompanying the overall processing of the calculation function shown in the flowchart of FIG. As a program that can be executed, external recording such as a memory card (ROM card, RAM card, etc.), magnetic disk (floppy (registered trademark) disk, hard disk, etc.), optical disk (CD-ROM, DVD, etc.), semiconductor memory, etc. It can be stored in the medium 13 and distributed. Then, the computer reads the program recorded in the external recording medium 13 by the recording medium reading unit 14, and the operation is controlled by the read program, thereby calculating the logarithmic function and exponential function described in the above embodiment. The calculation function of the calculation formula involving the above can be realized, and the same processing by the method described above can be executed.

  Further, program data for realizing each of the above methods can be transmitted on a communication network (Internet) N as a program code form, and a computer terminal (program server) connected to the communication network (Internet) N ) From the program data, and the calculation function of the calculation formula involving the logarithmic function and the exponential function can be realized.

  Note that the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the invention in the implementation stage. Further, the embodiments include inventions at various stages, and various inventions can be extracted by appropriately combining a plurality of disclosed constituent elements. For example, even if some constituent requirements are deleted from all the constituent requirements shown in the embodiment or some constituent features are combined, the problem described in the column of the problem to be solved by the invention can be solved. When the effect described in the column of effect is obtained, a configuration in which this constituent requirement is deleted or combined can be extracted as an invention.

1 is a block diagram showing a configuration of an electronic circuit of an electronic computing device 10 according to an embodiment of the present invention. 4 is a flowchart showing overall processing of calculation functions by the electronic calculation apparatus 10; 6 is a flowchart showing calculation processing of a calculation formula associated with the overall processing of the calculation function in the electronic calculation apparatus 10; The figure which shows the numerical processing state on RAM12B accompanying the calculation process at the time of the calculation request | requirement of the calculation formula [loge (1 + 1.23456789E-17)] containing a logarithmic function being input in the said electronic calculation apparatus. In the electronic computing device 10, a calculation request [loge (A): A = 1 + 1.23456789E-17)] including a logarithmic function and a variable value is input on the RAM 12B accompanying the calculation process when a calculation request is input. The figure which shows a numerical processing state. In the electronic calculation device 10, when a calculation request of a calculation formula [exp (A) -1: A = 1.23456789E-17)] including an exponential function and setting a variable value is input, the calculation process on the RAM 12B is performed. The figure which shows a numerical processing state. A calculation formula [FV = PMT * ((1 + r) ^ n-1) /r:PMT=100,000,000:r=0.012345678901:n=10] in which the calculation formula of the accumulation calculation is specified and the variable value is set in the electronic calculation apparatus 10 The figure which shows the numerical processing state (the 1) on RAM12B accompanying the calculation process at the time of the calculation request | requirement of ()] input. A calculation formula [FV = PMT * ((1 + r) ^ n-1) /r:PMT=100,000,000:r=0.012345678901:n=10] in which the calculation formula of the accumulation calculation is specified and the variable value is set in the electronic calculation apparatus 10 The figure which shows the numerical processing state (the 2) on RAM12B accompanying the calculation process at the time of the calculation request | requirement of ()] input.

Explanation of symbols

10: Electronic computing device 11: CPU (control unit)
12 ... Memory 12A ... ROM
12a1 ... calculation processing program 12a2 ... official memory 12B ... RAM
12b1 ... Calculation formula memory 12b2 ... Calculation accuracy memory 12b3 ... Variable memory 12b4 ... Calculation formula status detection register 12b5 ... Calculation result numerical memory 13 ... External recording medium 14 ... Recording medium reading unit 15 ... Transmission control unit 16 ... Shared memory 17 ... External device connection unit 20A ... Direct connection PC terminal 20B ... Net connection PC terminal 21 ... Calculation processing server N ... Communication network (Internet)

Claims (4)

A calculation device for calculating a formula including a function,
Calculation formula storage means for storing the input calculation formula;
A calculation formula part detection means for detecting whether or not the calculation formula stored in the calculation formula storage means includes a calculation formula part of addition and subtraction of 1 and a numerical value;
When this calculation formula part detection means detects that the calculation formula includes a calculation formula part of addition and subtraction of 1 and a numerical value, the numerical value of the detected calculation formula part is converted into an exponent part and a mantissa part. And a detection numerical value storage means for storing an identification flag indicating detection of the calculation formula part ,
Logarithmic function detection means for detecting whether or not the calculation formula stored by the calculation formula storage means includes a logarithmic function whose argument is the calculation formula portion indicated by the identification flag stored by the detected numerical value storage means When,
When the logarithmic function detection means detects that the calculation formula includes a logarithmic function having the calculation formula part as an argument, the absolute value of the numerical value stored as the exponent part and the mantissa part by the detected numerical value storage means Less than 1 detection means for detecting whether the value is less than 1;
High-precision logarithmic calculation for calculating a logarithmic function with high accuracy by directly using a numerical value stored in the detected numerical value storage means when the absolute value of the numerical value is detected to be less than 1 by the less than 1 detection means Means,
Ordinary logarithmic calculation for calculating a logarithmic function using the calculation result of the formula part detected by the formula part detection means when the absolute value of the numerical value is detected to be less than 1 by the less than 1 detection means Means,
A computing device comprising: Furthermore, it comprises digit number storage means for storing the number of significant digits of the input calculated numerical value,
2. The calculation apparatus according to claim 1, wherein the high-precision logarithm calculation unit and the normal logarithm calculation unit calculate a logarithmic function according to the number of significant digits stored in the digit number storage unit. The calculation formula storage means has rewrite storage means for rewriting and storing a calculation formula in which the set value is substituted for the variable when the input calculation formula includes a variable and a set value of the variable. The calculation apparatus according to claim 1 , wherein the calculation apparatus is a computer. A calculation processing program for controlling a computer of a calculation device,
The computer,
Calculation formula storage means for storing the input calculation formula,
Calculation formula part detection means for detecting whether or not the calculation formula stored in the calculation formula storage means includes a calculation formula part of addition and subtraction of 1 and a numerical value;
When this calculation formula part detection means detects that the calculation formula includes a calculation formula part of addition and subtraction of 1 and a numerical value, the numerical value of the detected calculation formula part is converted into an exponent part and a mantissa part. Detection numerical value storage means for storing an identification flag indicating detection of the calculation formula part
Logarithmic function detection means for detecting whether or not the calculation formula stored by the calculation formula storage means includes a logarithmic function whose argument is the calculation formula portion indicated by the identification flag stored by the detected numerical value storage means ,
When the logarithmic function detection means detects that the calculation formula includes a logarithmic function having the calculation formula part as an argument, the absolute value of the numerical value stored as the exponent part and the mantissa part by the detected numerical value storage means Less than 1 detection means for detecting whether the value is less than 1;
High-precision logarithmic calculation for calculating a logarithmic function with high accuracy by directly using a numerical value stored in the detected numerical value storage means when the absolute value of the numerical value is detected to be less than 1 by the less than 1 detection means means,
Ordinary logarithmic calculation for calculating a logarithmic function using the calculation result of the formula part detected by the formula part detection means when the absolute value of the numerical value is detected to be less than 1 by the less than 1 detection means means,
A computer-readable calculation processing program designed to function as a computer.

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