JPH0214728B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to an arithmetic method for x ^y and x ^1/y .

[Prior art and its problems]

Generally, small electronic calculators for calculating functions are equipped with the function of inputting a numerical value x and a numerical value y to calculate x ^y or x ^1/y . In this type of small electronic calculator, even if the above-mentioned number y is a decimal number that becomes an integer by creating its reciprocal, the calculation loop of x ^y or x ^1/y is performed using the number y as a decimal number. I used it to get the answer.

However, when the numerical value y is a decimal number, the calculation precision of the above-mentioned x ^y and x ^1/y is lower than when the numerical value y is an integer, and as mentioned above, the numerical value y is its reciprocal. If it is a decimal that becomes an integer by creating an integer, the answer of calculating x ^y or x ^1/y with the value y as a decimal, and the integer that is the reciprocal of the above value y as the value y, x ^y is x ^{1/ y} or x ^1/y to x ^y
In some cases, the answer calculated by replacing

On the other hand, the above-mentioned small electronic calculator treats the case where x is a negative number as an error because the answer may be an imaginary number.

However, even if x is a negative number in x ^y , an answer exists if y is an integer, and if y is an odd number in x ^1/y , that is, at least one real root exists in the odd root of a negative number. However, conventional small electronic calculators have the disadvantage of not being able to obtain these answers.

As a means to solve these shortcomings,
A judgment means is provided to judge whether the numerical value y is an integer or an odd number, and when the judgment means determines that the numerical value y is an integer or an odd number, even if the numerical value x is a negative number, x ^y An arithmetic method that can find the answer or the real root of x ^1/y can be considered.

However, even if the calculation method described above is implemented based on a conventional small electronic calculator, if the number y is a decimal, it will be treated as an error, and the number y will actually be Even if it is a decimal number, if its reciprocal is an integer, input the reciprocal into the number y, replace x ^y with x ^1/y , and x ^1/y with x ^y , and perform the calculation to obtain a real number. Although it is possible to obtain such an answer, it has the drawback of not being able to obtain such an answer.

[Purpose of the invention]

In view of the above circumstances, this invention provides x ^y or
When calculating x ^1/y , if the number y is a decimal and its reciprocal is an integer, the calculation is performed with high precision, and if x is a negative number, y is an integer or an odd number. The purpose of this invention is to provide an arithmetic method that can be applied even when determining whether or not the answer is a real value.

[Key points of the invention]

In order to achieve the above-mentioned object, this invention
When specifying the operation of x ^y or x ^1/y , determine whether the data y is an integer or not. If it is determined that it is not an integer, create the reciprocal of the above data y and determine whether the reciprocal is an integer. However, if the above reciprocal is an integer, the reciprocal is used as data y, and when specifying the operation of x ^y ,
The main point is that the calculation of x ^1/y is performed, and when the calculation of x ^1/y is specified, the calculation of x ^y is performed.

〔Example〕

Hereinafter, one embodiment of the present invention will be described with reference to the drawings. In Figure 1, 10 is the numeric keypad 10
In addition to function keys 102 such as 1, +, -, ×, ÷, etc., the keyboard is equipped with a key 103 for calculating x ^y , which is a type of function key, a key 104 for calculating x ^1/y , and an equal key 105. It is.
This keyboard 10 creates a key code for the operated key based on the timing signal input from the control section 11 and sends it to the control section 11 and also sends it to the RAM 13 via the input selector 12. The input selector 12 selects a signal instructed by the control unit 11 from among various input signals and outputs the signal to the RAM 13.
This is a circuit that supplies The RAM 13 also includes an X register 131 that stores data x or display data at x ^y or x _1/y , a Y register 132 that stores data y, and an auxiliary Y' register 13
3. F register 13 that stores the operation instruction code
4. C register 13 used as a counter
5. It consists of an S register 136 for storing a sign flag and an arithmetic register (not shown).
Note that x _s , y _s , and y′ _s are sign digits that store sign flags indicating positive or negative, and when they are negative numbers, the sign flag becomes “1”. The address and read/write designation of this RAM 13 are made by the control section 11, and the contents of this RAM 13 are specified by the control section 11.
The output selector 14 controlled by the output selector 14 selects which register's contents are to be output to which, and outputs them to the arithmetic circuit 15, the absolute value generation circuit 16, the reciprocal number generation circuit 17, and the judgment circuit 18. Further, the contents of the X register 131 are sent to a display section (not shown) via the output selector 14 and displayed. When the control signal a is applied from the control unit 11, the arithmetic circuit 15 calculates the data x stored in the X register 131, the data y stored in the Y register 132, the data x ^y stored in the F register 134, or Read the x ^1/y instruction code and execute x ^y or
This is a circuit that performs the calculation x ^1/y , and the calculation result is sent to the X register 1 of the RAM 13 via the input selector 12.
31. Furthermore, when an instruction code specifying another operation is input, the operation according to the instruction code is performed. The absolute value creation circuit 16 is a circuit that creates the absolute value of input data when the control signal b is applied from the control section 11. The reciprocal number creation circuit 17 is a circuit that creates a reciprocal number of input data when the control signal C is applied from the control unit 11. Further, the judgment circuit 18
Input data is determined according to the control signal supplied from the control unit 11 as an integer/decimal number, positive/negative number, odd/even number, x ^y designation or x ^1/y designation, etc. It performs various judgment processes and sends the judgment results to the control section 11. Note that this control unit 11 controls the entire system, and the keyboard 10
It judges the input key code and sends control signals to each circuit, and also performs overall timing control.

Next, the operation of this embodiment configured as described above will be explained with reference to the flowchart of FIG.

First, when calculating x ^y or x ^1/y , enter the x data using the numeric keypad 101 of the keyboard 10, then press the x ^y key 103 or x ^1/y
Operate key 104. After entering the y data using the numeric keypad 101, press the equal key 105.
operate. The data x output from the keyboard 10 is sent to the RAM 13 via the input selector 12.
Written to register 131. At this time, the control unit 1
1 to input selector 12 and keyboard 10
a control signal is provided that causes the selection of a signal from
A control signal is applied to the RAM 13 to designate the address of the X register 131 and to designate writing. Further, the data y output from the keyboard 10 is similarly written to the Y register 132, and x ^y
Alternatively, the x ^1/y instruction code is written to the F register 134. When the equal key 105 is operated, the control section 11 reads the operation signal and starts the flow shown in FIG. 2. In step _S1 , the C register 135 and S register 136 in the RAM 13 are cleared. When clearing the register in RAM13, input selector 12
It is sufficient to close all the gates of , designate a predetermined address in the RAM 13, and perform writing. Next, in step _S2 , the data y written in the Y register 132 is sent to the judgment circuit 1 via the output selector 14.
8 and determines whether it is an integer or a decimal. If the judgment result is an integer, the control unit 11
If the number is a _decimal , control is performed at step _S3 . The operations after step _S3 are to check the possibility that the data y becomes an integer by taking the reciprocal of the decimal number y. That is, in step _S3 , the F register 134
Circuit 1 determines the operation instruction code written in
8 reads and determines whether it is x ^y specification or x ^1/y specification. If the judgment result is x ^y , step S ₄
Execute x ^1/y instruction code from control unit 11 to F
Write to register 134, if x ^1/y , step
Execute S ₅ and store the x ^y instruction code in F register 134.
By writing to , the instruction code of the operation in the F register 134 is exchanged between x ^y and x ^1/y . Next, in step _S6 , the control section 11
Specify the address of the C register 135 of the RAM 13, give an increment command, and
After incrementing the contents of 5, judgment circuit 1
8 and judge its contents. If the content is "1", the process goes to step _S7 , and if it is "2", the process goes to step _S8 ; however, since the C register 135 is cleared first, the process goes to step _S7 the first time. Here, the data y in the Y register 132
After temporarily saving the data y in the Y' register 133, the data y in the Y register 132 is sent to the reciprocal number creation circuit 17 to create the reciprocal of the data y, and the obtained data 1/y is written in the Y register 132. Then, the process returns to the above-mentioned step _S2 , and it is again determined whether the contents of the Y register 132 are an integer or a decimal. In other words, if you convert the data y to the reciprocal number 1/y and replace the operation instruction codes x ^y and x ^1/y , it is equivalent to the original operation, so by converting the data y that was a decimal number to the reciprocal number Therefore, it is possible to check whether the value is an integer or not. Above steps
If it is determined that it is an integer by performing the integer/decimal judgment again in _S2 , the process proceeds to step _S9 , but if it is still a decimal, the process proceeds to step S3 and step _S3 .
Execute _S4 or _S5 to return the instruction code in the F register 134 to the original instruction code. After incrementing the contents of the C register 135 in step _S6 , the judgment circuit 18 makes a judgment, and this time, as the contents of C become "2", the process advances to step _S8 and is saved in the Y' register 133. The data y is returned to the Y register 132. and step
The calculation is performed in _S10 , and in this embodiment, if the data y in x ^y or x ^1/y is a decimal and does not become an integer even if it is reciprocated, the same calculation as in the conventional case is performed. That is, if x is a negative number, an error will occur. This step S ₁₀ calculation is executed in RAM
13 to X register 1 via output selector 14
31, the contents of the Y register 132 and the F register 134 are each supplied to the arithmetic circuit 15, and the contents of the F register 1
The operation is performed based on the instruction code in 34, and the operation result is sent to the X register 1 via the input selector 12.
31.

On the other hand, when the data y is an integer, it is determined in step _S9 whether the data x is positive or negative. That is, the judgment circuit 18
is determined by reading the contents of the X register 131, and if it is positive, no problem will occur, so the process proceeds to step _S10 and performs the conventional calculation. Further, if the data x is negative, the process advances to step _S11 , and the judgment circuit 18
determines whether the data y is an odd number or an even number. If the judgment result is an even number, step
The process advances to step _S12 , and it is further determined whether the instruction code stored in the F register 134 is x ^y or x ^1/y. If it is determined that it is x ^1/y , the process directly advances to step S10, where the instruction code stored in the F register ₁₃₄ is An operation is performed. In other words, if x is negative and y is not an odd number in x ^1/y , an error will occur. If data y is determined to be an odd number in step _S11 , "1" is written from the control unit 11 to the S register 136, and in the next step _S14 , data x is sent from the X register 131 to the absolute value generation circuit 16. An absolute value is created and written to the X register 131 again. Also, in step _S12 above, the F register 134
The above step _S14 is also executed when it is determined that the instruction code stored in is ^xy . Therefore, in the next step _S10 , an operation is performed on the absolute value |x| of the data x, and even if the data x is negative, no error will occur. In step _S15 executed after the calculation is completed, the S register 13 is
6 is written to the sign digit of the X register 131. That is, when the absolute value of the data x is taken in step _S14 , "1" is written in the S register 136 in step _S13 , so it is necessary to add a negative sign to the data x again here. Can be done. Note that in other cases, the contents of the S register 136 remain "0", so there is no problem. Thus, the calculation result written in the X register 131 is sent to a display section (not shown) via the output selector 14 and displayed.

〔effect〕

As explained in detail above, according to the present invention, when specifying the operation of x ^y or x ^1/y , if the data y is a decimal, it is determined whether the reciprocal is an integer, and the reciprocal is determined to be an integer. If , the reciprocal is data y, and when specifying the operation of x ^y , the operation of x ^1/y is
When specifying the calculation of x ^1/y , the calculation of x ^y is performed, so the calculation precision for data such as 1/0.5, which is actually an integer but is expressed as a decimal number due to a different representation format, can be improved. In addition, it has the advantage that it can be fully applied even when x is a negative number and y is determined to be an integer or an odd number to obtain a real-valued answer.

[Brief explanation of drawings]

FIG. 1 is a circuit diagram illustrating an embodiment of the present invention, and FIG. 2 is a flowchart illustrating the operation of the present invention. 10...Keyboard, 13...RAM, 15...
... Arithmetic circuit, 16 ... Absolute value creation circuit, 17 ...
Reciprocal number creation circuit, 18...judgment circuit.

Claims (1)

[Claims] 1 x y and x ^1/y for data x and data ^y
a calculation means having a calculation function, a determination means for determining whether the data y is an integer, and a reciprocal 1/y of the data y when the determination means determines that the data y is not an integer. and means for inputting data 1/y created by the reciprocal number creation means to the determination means,
If this judgment means determines that the data 1/y is an integer, replace the data 1/y with data y, perform the calculation of x ^1/y when specifying the calculation of x ^y ,
An arithmetic method characterized in that when an arithmetic operation of x ^1/y is specified, an arithmetic operation of x ^y is performed.