JPH08249161A - Cubic root arithmetic unit - Google Patents

Abstract

PURPOSE: To realize a cubic root operation only by means of adding few additional circuits to a divider by dividing the index value of a given numerical value by '3', correcting the mantissa value of the given numerical value given by the remainder, calculating a new partial remainder by the mantissa value, predicting a new partial quotient, and repeating a processing for obtaining the new partial quotient until the prescribed and effective number of digits is obtained. CONSTITUTION: This arithmetic unit is provided with a means 1 for generating the index part of a cubic root based on the remainder obtained by dividing the index value of the given numerical value by '3' and correcting the mantissa value of the given numerical value, a means 2 for obtaining the initial value of the cubic root of the numerical value given from the mantissa value, a means 3 for calculating the new partial remainder based on the highest digit of the cubic root obtained from the corrected mantissa value or the partial remainder and the initial value obtained at previous time, or the quotient of N/X<2> calculated hitherto and the newly predicted partial quotient, and a means 4 for predicting the new partial quotient. The processing for obtainng the new partial quotient is repeated until the prescribed significant digits is obtained to calculate the cubic root X of a numerical value N.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a cube root arithmetic unit, and more particularly to a cube root arithmetic unit capable of performing a cube root arithmetic operation only by adding a small amount of additional circuit to a conventional divider. It is a thing.

[0002]

2. Description of the Related Art Conventionally, a method utilizing Newton's successive approximation method has been known as a method for calculating a cube root. The above Newton's iterative method is g (x) = x ³ −a
As a solution of x = 0, the following formula is applied, and x ₁ , x ₂ , ...
The cubic root is x _m .

X _{n + 1} = x _n − [{x _n ² − (a / x _n )} / {2x _n + (a / x _n ² )}] = x _n · (x _n ³ + 2a) / ( 2x _n ³ + a)

[0004]

By the way, the above method has a problem that a large number of divisions are required and the calculation time becomes very long. The present invention has been made in order to solve the above-mentioned conventional problems, and an object of the present invention is to provide a cube root arithmetic device capable of obtaining a cube root at high speed by simply adding a small amount of additional circuits to a divider. Is to provide.

[0005]

FIG. 1 is a diagram illustrating the principle of the present invention. In the figure, 1 is a means for processing a mantissa value / exponent value of a numerical value N which is input data, 2 is a corrected mantissa value DN
Means for generating initial values INIT and 3 * (INIT) ² from the upper digit of D, 3 is the corrected mantissa value DND or the partial remainder REM obtained last time, and the highest digit of the cube root obtained from the initial value INIT or A means 4 for calculating a new partial remainder based on the quotient A of N / X ² calculated so far and the newly predicted partial quotient B, and the partial quotient B from the remainder / 3 * (INIT) ² Prediction means 5 is means for holding the mantissa result.

According to the first aspect of the present invention, the given number N is divided by the square of its cube root X to obtain the number N.
In a cube root calculator for finding the cube root of a cube root, the exponent part of the cube root is generated based on the remainder obtained by dividing the exponent value of the given numerical value by 3, and the mantissa value of the given numerical value is corrected. Means for obtaining the initial value CU of the cube root of the given numerical value from the corrected mantissa value, the corrected mantissa value or the partial remainder obtained last time, and the cube root obtained from the initial value INIT Means for calculating a new partial remainder based on the highest digit of N or the quotient of N / X ² calculated so far and the newly predicted partial quotient, and the partial remainder and the initial value INIT or so far A means for predicting a new partial quotient from the calculated N / X ² quotient is provided, and the process of obtaining a new partial quotient is repeated until a predetermined number of significant digits is obtained or the partial remainder becomes 0. , Cube of number N It is configured to calculate the root.

According to the second aspect of the present invention, the given number N is divided by the square of its cube root X to obtain the number N.
In a cube root computing device for finding a cube root of a given number, a cube root computing device for finding a cube root of a number N by dividing a given number N by the square of the cube root X, as shown in FIG. The exponent part generating means for dividing the value by 3 to obtain the exponent value corrected by the remainder and generating the exponent part of the cube root, and the remainder by the exponent value by 3 corrects the mantissa value of the given numerical value. Then, a means for generating a corrected mantissa value, and the corrected mantissa value,
Obtained from the cube root initial value INIT of the given numerical value, means for obtaining 3 * (INIT) ² from the initial value INIT, the corrected mantissa value or the previously obtained partial remainder, and the initial value INIT. Based on the highest digit of the cube root or the quotient of N / X ² calculated so far and the newly predicted partial quotient, and means for calculating a new partial remainder, and the partial remainder described above in 3 * ( INIT) ² to predict a new partial quotient, a mantissa value holding means for sequentially storing the obtained partial quotient while shifting the digit, an output of the exponent part generating means and the mantissa value holding means, A means for outputting as a cube root of the numerical value N is provided, and until a predetermined number of significant digits is obtained,
Alternatively, the process of obtaining a new partial quotient is repeated until the partial remainder becomes 0, and the cube root of the numerical value N is calculated.

According to a third aspect of the present invention, in the first or second aspect of the invention, the means for calculating the partial remainder newly estimates the quotient of N / X ² calculated so far as A. When the obtained partial quotient is B, (2A + B) B is added to A ² obtained from A above to obtain (A + B) ² , and the above (A
+ B) ^{2 is used} to obtain a partial remainder correction value and subtract the correction value from the previously obtained partial remainder while repeating the above A and B to obtain the partial remainder.

[0009]

[Function] Between the numerical value N and its cube root X, ³ √ (N)
= X [hereinafter, ³ √ cube root of N (N) and is denoted], i.e., it holds the relationship N = X ³ is, X is, X = X ³ /
It can be obtained from X ² by X = N / X ² . The present invention seeks a cube root using the above relationship,
Find the cube root as follows. (1) Exponential processing and mantissa processing When a numerical value N is given, exponential processing and mantissa processing are performed as follows.

The numerical value N is, for example, 182617206.617588625.
If it is (decimal number), its cube root is ³ √ (182617206.6
17588625) = 567.345. In order to find the cube root of the numerical value, first, the numerical value 182617206.617588625 is converted so that the exponent becomes a multiple of 3. In case of the above number,
It can be converted to 0.182617206617588625 × 10 ⁶ , the mantissa is 0.182617206617588625, and the exponent is 9.

Then, a cube root (in this case, the cube root is 0.567345) is obtained for the mantissa, and the obtained cube root is ³
By multiplying √ (10 ⁹⁾ times (10 ³ times), the solution of the above cube root
You can ask for 567.345. Generally, the number N
n.nnnnnnn × 10 ^m (n is a one-digit integer, m is an integer), the exponent m is divided by 3 and the remainder is 0, n.nnnnnnn
× 10 ^m (m is a multiple of 3), when the remainder is 2, 0.nnnnnnnn
× 10 ^{m + 1} (m + 1 is a multiple of 3), and when the remainder is 1, 0.
It may be set to 0nnnnnnnn × 10 ^{m + 2} (m + 2 is a multiple of 3).

Considering this in hexadecimal notation with a mantissa part: 1.XXXXX and an exponent part: 2 ^N , the result is as follows. In the following, MOD is the remainder of N / 3. MOD (N / 3) = 0: 1.XXXXX * 2 ^N MOD (N / 3) = 2: 0.1XXXXX * 2 ^{N + 1} MOD (N / 3) = 1: 0.01XXXXX * 2 ^{N + 2} (2) Calculation of cube root Next, regarding the mantissa part 0.182617206617588625 (decimal number) of 182617206.617588625 (decimal number), the cube root of the higher digit
Calculate ³ √ (0.182). This cube root (referred to as initial value INIT) can be generated using a decoder or the like.

Here, the value of the upper digit is the initial value of the cube root.
If it is INIT, the quotient of the next digit will be (INIT)
Since it can be predicted from ² (higher digit of divisor X ² ) and partial remainder (this is called Rem), the operation of X = N / X ² is
This can be performed by obtaining the initial value INIT, then obtaining the partial remainder, and repeating the process of predicting the partial quotient of the next digit.

Next, the divisor X in the calculation of N / X ^2
2 , prediction of dividend N (= X ³ ), partial remainder, and quotient will be described. Where cube root X is X = ABCD
(A, B, C and D are hexadecimal numbers). (i) Regarding divisor X ^{2 When the} first digit is A X ² = A ² (A is created from the above initial value) When the second digit B is X ² = (A + B) ² = A ² + 2AB + B ² = A ² + (2A + B) B At the third digit C X ² = (A + B + C) ² = (A + B) ² +2 (A + B) C + C ² = (A + B) ² + {2 (A + B) + C} C ... Same as below ... Thus, the divisor X ² is the divisor [A ² , (A + B) ² , ...] used in the previous process,
Add the newly predicted partial quotient [B, C, ...] to twice the previous cube root [2A, 2 (A + B), ...] and multiply by the newly predicted partial quotient [B, C, ...] It can be created by combining.

Since the predicted quotient is at most several bits (4 bits), no multiplier is required, and the division factor creating circuit of the divider is used. (ii) Regarding dividend and partial remainder ・ When the dividend is the first digit A X ³ = A ^{3 When the} second digit B X ³ = (A + B) ³ = A ³ + 3A ² B + 3AB ² + B ³ = A ³ + (3A ² + 3AB + B ² ) B At the third digit C X ³ = (A + B + C) ³ = (A + B) ³ +3 (A + B) ² C + 3 (A + B) C ² + C ³ = (A + B) ³ + {3 (A + B) ² +3 (A + B ) C + C ² } C ... Same as below ... The dividend X ³ is [3A ² B + 3AB ² +] to the value [A ³ , (A + B) ³ , ...] Used in the previous processing as described above.
B ³ ], [3 (A + B) ² C + 3 (A + B) C ² +
C ³ ], ... Can be obtained by adding the correction.

Here, 3A ² B + 3AB ² + B ³ = {2
A ² + (A + B) ² + AB} B, A ² is obtained as the previous divisor X ² , and (A + B) ² is obtained as a new divisor, so use this. You can Similarly, for A and B, the values used for obtaining the divisor can be used. (iii) Prediction of quotient When a numerical value N is given, as described above, the exponential processing is performed, and the initial value of the cube root (INIT described above) is obtained from the upper digit of the mantissa in the state where this processing is completed.

This is to obtain the upper bit of the divisor (X ² ) for the quotient prediction (prediction of the next partial quotient by the dividend, the partial remainder and the divisor) in the above division. Above (i
In the example of obtaining the partial quotient of the second digit shown in i), if the cube root is up to the second digit, the partial remainder of N / X ² is
The difference (A + B) ³ −A ³ when the cube root A at the first digit is obtained corresponds to the cube root value by B at the second digit.

The difference (A + B) ³ −A ³ is the above 3A.
² B + 3 AB ² + B ³ , which can be transformed as follows. ^{3A 2 B + 3AB 2 + B} 3 = {(2A + B) 2 - (A 2 + AB)} B = {(2A + B) 2 - (A 2 + B / 2) 2 + (B / 2) 2} B = [(2A + B) ² - {(1/2) · (2A 2 + B)} 2 + (B / 2) 2} B = (2A + B) 2 {1- (1/4) + B 2 / (2A + B) 2} B i.e., the [ (2A + B) ² {1- (1/4) + B
² / (2A + B) ² } B] remains as a partial remainder (hereinafter referred to as a partial remainder Y). In addition,
In the above equation, since A is the cube root of the previous process, {2 (A + B + C) + D} ² ,
It becomes {2 (A + B + C + D) + E} ² , ...

In the above partial remainder Y, (2A +
Since B) ² is much greater than the square B ² newly predicted partial quotient ^{B, B 2 / (2A +} B) can be considered as ^{2 ≒ 0, {1- (1/4} ) + B 2 / (2A + B) ² } ≒
It can be regarded as (3/4). Similarly, since 2A + B can also be regarded as 2A, the above Y can be expressed as follows. Y = (2A) ² · (3/4) · B = 3A ² B That is, the next partial quotient B can be predicted by the partial remainder Y and 3A ² . That is, the partial quotient of the next digit (corresponding to B above) can be predicted from the partial quotient of the previous digit (corresponding to A above) and the partial remainder Y. Here, since the upper digit of the divisor A ² is INIT ² , even if INIT ² is used for quotient prediction, a large error does not occur.

Therefore, for the quotient prediction of division, N /
3 (INIT) from the cube root's initial value INIT before processing X ^2.
The cube root can be obtained by calculating ² and predicting the quotient of each digit sequentially from 3 (INIT) ² and the partial remainder. FIG. 2 is a flow chart showing the above process, and the procedure for obtaining a cube root in the present invention will be described with reference to the same figure. The figure shows processing in hexadecimal. In step S1, input data is set. In step S2, the exponent and the mantissa are corrected so that the exponent becomes a multiple of 3 as described above.

Then, in step S11, a cube root index is created from the corrected index / 3. Further, in step 3, the corrected mantissa is used as the initial value (INIT).
To create 3INIT for quotient prediction in step S4.
Create and hold ² (dividend DRS: X ² ).

[0022] In step S5, take out the first valid bit (A), to create the A ^3, in step S6, obtains the remainder Rem = DND-A ^3. And step S
In 7, the significant digit is obtained or the remainder is 0
If YES, step S
12, the calculation result is created from the obtained mantissa part and exponent part, and the process ends.

If NO in step S7, the process proceeds to step S8, and the remainder (Rem1) and divisor DRS:
The next partial quotient B (4 bits) is predicted by X ² . In step S9, a new divisor (A
+ B) ² is created, and in step S10, the next remainder
Ask for Rem2. That is, the next remainder is Rem2 = DND- (A
+ B) ³ , which is, as described above, Rem1- {2
Since this corresponds to A ² + (A + B) ² + AB} B, the following remainder Rem2 is calculated from this equation. When the next remainder is obtained, the process returns to step S7 and the above process is repeated.

FIG. 3 shows the cube root X, the divisor X ² , the dividend X ³ , the remainder N−X ³ , and the partial quotient predicted value (N−X ³ ) / (3 · INIT ² ), which are obtained as described above. It is a figure which shows an example of and its expected value. The figure shows ³ √ (182617206.61758
85) = 567.345 (decimal number) is shown in hexadecimal. When the above input data is expressed in exponential notation: 1.
826172066175885E + 08, which is a hexadecimal number, X "47
It becomes AE284769E1A493 ".

When expressed in binary, it is 1.0101.
1100010 .... * 2 ²⁷ and X = ³ √ (1.0101110001
0 ....) * 2 ⁹ It should be noted that the top 2 in hexadecimal notation
The digit ([47] above) is the exponent, which is 8 bits (25
The center of the value of 6) is set as an index 0, and is represented by an offset from the index.

Also, the cube root 567.345 is expressed as a decimal point in exponential notation.
If you show up to the lower part of, it becomes 5.673449999999999E + 02.
This is a hexadecimal number, which is X "432375851EB851EB". Same figure
, The predicted value of the partial quotient (N−X³) / (3 ・ INIT²) Finger
Expected values for the first digit and partial quotient, excluding some parts, match except for the first line
You can see that Furthermore, the divisor X ²After the 3rd digit
Becomes constant at [4E9], and as described above, 3 ・ INIT²(3
X²) Shows that partial quotient prediction is possible.

FIG. 4 is a diagram showing an example of calculation for obtaining a cube root of a decimal number for easy understanding.
182617206.617588625 (decimal) cube root ³ √ (18261
7206.617588625) = 567.345 is shown, and the initial quotient INIT of the above numerical value is 56. In the figure,
First, assuming that INIT = 56 is obtained as the initial quotient INIT, and 3 (INIT) ² is obtained from the initial quotient, 3 (INIT) ² = 940
8

The quotient of the first digit is 5, and 5³Is 125
Therefore, when the partial remainder REM is calculated, as shown in the figure.
That is 57617206617588625. The predicted quotient is the calculated partial remainder
Extra REM (If you take the 3 digits from the top, it becomes 576) and 3 (INIT)
²Calculated from (= 9408), REM / 3 (INIT)²Calculate
Then, 576/9408 = 0.0612, and the next predicted quotient is the same figure.
It becomes 6 marked with #.

Next, the above-mentioned 3A ² B + 3AB ² + B ³ ,
That is, 50616 is obtained by calculating {2A ² + (A + B) ² + AB} B. This and the partial remainder 57 obtained last time
When the next partial remainder is calculated from 617206617588625, it becomes 7001206617588625 as shown in the figure. Predicting the next partial quotient from this upper 3 digits and 3 (INIT) ² = 9408 described above yields 700/9408 = 0.0744, and the next predicted quotient is
It becomes 7 with.

Next, using the obtained partial quotient 7, the above {2A
^{When 2} + (A + B) ² + AB} B is calculated, it becomes 6668263 as shown in the figure, from which the next partial remainder can be obtained. By proceeding in the same way below,
You can ask for a cube root of 567.345.

Since the present invention obtains a cube root based on the above principle, the cube root can be obtained only by adding a simple additional circuit to the divider.

[0032]

FIG. 5 is a block diagram of a cube root calculator according to an embodiment of the present invention. In the figure, 11 is a remainder detector that obtains a remainder when the exponent of input data is divided by 3, and 12 is an operator that obtains an exponent that is a multiple of 3 based on the output of the remainder detector 11. 12 outputs the corrected exponent 3n, which is held in the register 15. And
The exponent 3n of the register 15 is divided by 3 in the arithmetic circuit 21 to obtain n, which is held in the exponent result register 24 as a cube root exponent.

Reference numeral 13 is a decoder, and the decoder 13 uses the remainder of the input data and the exponent 3 as the cube root initial value INIT.
Generate As a means for generating the initial value INIT, a table in which the upper digit of the input data and the corresponding cube root are recorded can be used in addition to the decoder. Reference numeral 14 is a mantissa correction circuit. The mantissa correction circuit 14 corrects the input data by the output of the remainder detector 11 and outputs a mantissa for which a cube root is to be obtained.

Reference numeral 16 is a register, which holds the initial value INIT and also holds 3 · INIT ² obtained by the adder / subtractor 20 described later. Reference numeral 17 is the mantissa correction circuit 14
The dividend DND output by, the register holding the partial remainder,
18 is a register for holding the dividends A ² , (A + B) ² , ... And 19 is a register for holding B ² and INIT ² .

Reference numeral 20 denotes an adder / subtractor, which is used in the register 1
The dividend (partial remainder) given by 7, 18, 19
Number, B², And a partial quotient register 23, which will be described later, and a mantissa
The figure is based on B and A given from the result register 25.
The partial remainders REM1, REM2, ...
Value INIT to 3 · INIT²To generate. Generated 3 INIT
²Are held in the register 16.

Reference numeral 22 is a quotient prediction circuit, which divides the remainder obtained by the adder / subtractor 20 by 3.INIT ² held in the register 16 to obtain a partial quotient B. The obtained partial quotient B is stored in the partial quotient register 23. Retained. Reference numeral 25 is a mantissa result register. The mantissa result register 25 sequentially holds the partial quotient held in the partial quotient register 23 while shifting the digits, and generates a mantissa part FRAC (A) of a cube root.

Next, the operation of the cube root calculator of this embodiment will be described. When the input data is given, the remainder detector 11 divides the exponent part of the input data by 3 to obtain the remainder. The arithmetic circuit 12 obtains the corrected exponent 3n based on the remainder and the exponent part of the input data. That is, as described above, when the remainder is 0, the index N of the input data is set to 3n as it is, when the remainder is 1, the index N + 1 = 3n, and when the remainder is 2, N + 2 = 3n. The index 3n is held in the register 15. The arithmetic unit 21 divides the exponent 3n by 3 to obtain the cube root exponent n, and stores it in the exponent result register 24.

On the other hand, the mantissa correction circuit 14 shifts the mantissa part of the input data according to the remainder output by the remainder detector 11 to generate a corrected mantissa and supplies it to the register 17. Further, the decoder 13 generates an initial value INIT of a cube root from the upper digit of the input data, causes the register 16 to hold it, extracts the first valid bit A from the initial value INIT, and stores it in the mantissa result register 25.

The initial value INIT held in the register 16 is given to the adder / subtractor 20, the adder / subtractor 20 generates 3 · INIT ² , and the register 16 holds 3 · INIT ² . Next, A ³ is generated from the first effective bit A, and the adder / subtractor 20
, The dividend DND stored in register 17 to A
Subtract ³ to obtain the remainder REM1 and store it in the register 17.

Further, the quotient prediction circuit 22 predicts the partial quotient B from the 3INIT ² held in the register 16 and the remainder REM1 and stores it in the partial quotient register 23. Partial quotient register 2
The partial quotient B stored in 3 is sent to and held in the mantissa result register 25. The adder / subtractor circuit 20 uses the partial quotients B to B ²
And stores generated and the register 19, and A described above, obtaining the remainder REM2 from partial quotient B and B ² and remainder REM1. Quotient prediction circuit 22 obtains the prediction value of the next partial quotient from 3 · INIT ² stored in the remainder REM2 and register 16.

Thereafter, the same process is repeated to find each digit of the cube root, and each digit of the obtained mantissa is sequentially stored in the mantissa result register 25 while shifting the digit. Then, when the remainder becomes 0 or when the mantissa is obtained up to a predetermined significant digit,
The exponent stored in the exponent result register 24 and the mantissa stored in the mantissa result register 25 are output as the calculation result.

[0042]

As described above, according to the present invention, after the exponent / mantissa processing of the input data N, the initial value INIT is obtained from the higher digit of the corrected mantissa and the partial remainder of the division is calculated. While predicting the partial quotient from the initial value INIT and the partial remainder, the cube root X is obtained from X = N / X ² (N is the input data, X is its cube root), so a simple adder circuit is added to the divider. The cube root can be obtained by simply adding it.

[Brief description of drawings]

FIG. 1 is a principle diagram of the present invention.

FIG. 2 is a diagram showing a processing procedure for obtaining a cube root of the present invention.

FIG. 3 is a calculation example (hexadecimal number) of cubic root calculation according to the present invention.
FIG.

FIG. 4 is a calculation example (decimal number) of cubic root calculation according to the present invention.
FIG.

FIG. 5 is a block diagram of a cube root calculator according to an embodiment of the present invention.

[Explanation of symbols]

1 Mantissa Value / Exponent Value Processing Means 2 Means for Generating Initial Values INIT and 3 * (INIT) ² 3 Means for Calculating Partial Remainder 4 Means for Predicting Partial Quotient 5 Means for Retaining Mantissa Result 11 Residue Detector 12 Calculation Unit 13 decoder 14 mantissa correction circuit 15 register 16 register 17 register 18 register 19 register 20 adder-subtractor 21 arithmetic circuit 22 quotient prediction circuit 23 partial quotient register 24 exponent result register 25 mantissa result register

Claims (3)

[Claims] 1. A cube root arithmetic unit for obtaining a cube root of a numerical value N by dividing the given numerical value N by the square of its cube root X, based on a remainder obtained by dividing an exponent value of the given numerical value by 3. , Means for generating an exponent part of the cube root and correcting the mantissa value of the given numerical value, means for obtaining the initial value INIT of the cube root of the given numerical value from the corrected mantissa value, and the corrected The mantissa value or the partial remainder obtained last time,
Means for calculating a new partial remainder based on the most significant digit of the cube root obtained from the initial value INIT or the quotient of N / X ² calculated so far, and the newly predicted partial quotient, and the partial remainder And initial value INIT or N calculated so far
Means for predicting a new partial quotient from the quotient of / X ² and repeating the process of obtaining a new partial quotient until a predetermined number of significant digits is obtained or the partial remainder becomes 0, A cube root arithmetic circuit characterized by calculating a cube root. 2. A cube root computing device for obtaining a cube root of a numerical value N by dividing the given numerical value N by the square of its cubic root X, wherein the exponent value of the given numerical value is divided by 3 The exponent part generating means for obtaining the exponent part corrected by the remainder to generate the exponent part of the cube root, and the remainder by the exponent value of 3 are used to correct the mantissa value of the given numerical value and generate the corrected mantissa value. Means and the initial value INIT of the cube root of the given value from the corrected mantissa value, and 3 * (INIT) from the initial value INIT
² means, and the corrected mantissa value or the partial remainder obtained last time,
Means for calculating a new partial remainder based on the most significant digit of the cube root obtained from the initial value INIT or the quotient of N / X ² calculated so far, and the newly predicted partial quotient, and the partial remainder Is divided by 3 * (INIT) ² described above, a means for predicting a new partial quotient, a mantissa value holding means for sequentially storing the obtained partial quotient while shifting the digit, the exponent part generating means, and the mantissa value. Means for outputting the output of the holding means as a cube root of the numerical value N, and repeating the processing for obtaining a new partial quotient until a predetermined number of significant digits is obtained or the partial remainder becomes 0, and the numerical value N A cube root arithmetic circuit characterized by calculating a cube root of. Wherein means for calculating the partial remainder until the quotient of the calculated N / X ² to A, the newly predicted partial quotient when a B, and A ² obtained from the A ( Two
A + B) B is added to obtain (A + B) ² , the correction value of the partial remainder is obtained from the above (A + B) ² , and the correction value is subtracted from the previously obtained partial remainder.
3. The cube root arithmetic circuit according to claim 1 or 2, wherein the partial remainder is repeatedly obtained while updating.