JPS5939773B2 - Logarithmic function calculation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a calculation method for a logarithmic function in a computer, and more particularly to a method for calculating a base 10 logarithmic function kg10X for an arbitrary positive number x. A typical method for calculating log1oX is, for example, ln(1+Y)=Y-Y2/ 2+Y3/
3 +...+(-1)n-IYn/n +...
(1) However, first find the natural logarithm lnX using the approximate formula expressed as 0≦Y<1, then divide the result by 1n10=2.30258509... There is one in which the quotient is a function value of log1oX.

However, according to this method, when applying equation (1), there is a restriction that 0≦Y<1, and therefore various pre-processing is required. An object of the present invention is to provide a logarithmic function calculation method that requires less preprocessing and overall processing than conventional methods, is simpler, and therefore has faster calculation speed.

Another object of the present invention is to provide a logarithmic function calculation method that provides highly accurate calculation results.

Normally, internal data in a computer that handles scientific and technical calculations, including logarithmic functions, etc., has a structure in which normalized fixed dB5l points are displayed. Expressing this mathematically, we get
x=x×10N(2) However, ]≦1x1<10, N=integer.

(In Equation 1, x is the mantissa part and N is the exponent part. In other words, the internal data has the mantissa part x and the exponent part N independently.The present invention focuses on this data structure and inputs This method attempts to obtain a logarithmic function value by separately processing the mantissa and exponent parts of antilog data.

It is expressed as an input true value X & clock time expression.

Since the antilog number X>0 in equation (2), x>0. By taking the logarithm of both sides of equation (2), the following holds true.

N on the right side is the exponent part N of equation (2) and is an integer value.
On the other hand, the term 1Cg10X is 1≦o<10, so 1>
It can be seen that 1Cg10X≧0, that is, it is a decimal value.
That is, the exponent part N of the operand X is processed as it is to be the integer part of the operation result, and the logarithm value of the mantissa part x of the operand X is calculated and processed to be the decimal part of the operation result. By doing so, the logarithmic function value for the operand X can be easily obtained.

Moreover, since the mantissa part X is 1≦x<10, for example, Ha
If we use Stings' approximation formula (see pages 129 to 131 of "Approximate Calculation Methods for Electronic Computers" by Hastings, translated by Hitoshi Takeuchi, published by Tokyo Tosho in 1973),
1 (GlOX can be found with only a few steps.

Next, one embodiment of the present invention will be described using the drawings.

FIG. 1 shows the hardware for implementing the invention. In the figure, the part including 1a and 1b is a circular holding type Z register in which the operation result is finally stored;
2 is a circular holding type w register. The Z register is normally held through data lines C and b, but when a right shift command occurs, data paths A and b excluding the least significant digit (4 bits) 1b are opened and a one-digit right shift is performed. 3 is an antilogous number
Read-only memory (hereinafter referred to as ROM) stores instructions for separately processing the mantissa and exponent parts of a numerical value input as
4 is an address register (hereinafter referred to as AR) that sequentially specifies the address of ROM3, 5 is an instruction decoder (hereinafter referred to as 1D) that decodes the output of ROM3, and G1 to G5 are outputs Inst. Gate that opens and closes by, 6 is Z
A timing generator that generates timing to specify the digit to be processed in the register or w register; 7 is an adder circuit for adding 1 in decimal to the contents of the w register; 8
is a determination circuit that determines whether the contents of the Z register are 1t01, and if it is O, modifies AR4 with its output.

9 is one digit (4) to shift the contents of the Z register to the left.
Register 10 (bit) is a 1-digit (4-bit) register for shifting the contents of the w register to the left.When a left shift instruction occurs, register 1 or 2 is shifted to the left because one additional digit is circulated. Ru.

Reference numeral 11 denotes a logarithm calculator for calculating logarithmic values having a base of 10.

Z registers 1a, 1b. Each of the W registers 2 is composed of 8 digits (32 bits) D1 to D8 as shown in FIG. D8 is an exponent data storage section (represented by mnemonics ZE and WE, respectively).

As shown in Figure 3, the fixed point position of the data is D6.
, 0. is written to the w register. Data of 2×1012 is stored in the Z register as an initial value. From this initial state, 10g10(
2X1012). Below is step 1 in Figure 2.
The explanation will be given in order. (Step 1) An instruction ZM+WM is issued to transfer the mantissa data of the Z register to the w register.

The output of ROM3 is decoded by ID5. ID5 uses its output to cause the timing generator 6 to generate timings corresponding to D, to D6, and at the same time gates G3 and G4.
to open. Therefore, the contents of ZM are transferred to WM of w register 2 through signal line e. Figure 3 2 shows the contents of each register after the step 1 instruction is executed.
This means that 2×10 rays are stored in the register.
(Step 2) The command 10g10W+W is issued. That is, a logarithmic operation is performed using the contents of the w register 2 as input, and the result of this operation is stored in the W register again. The data flow in this step is 2→G5→
k→11→n→G4→2. Figure 3 shows the contents of each register after the step 2 instruction is executed.Since the decimal point of the data is fixed at D6, 10g102-0.30103 is stored in the W register. Become. (Step 3) In order to transfer the mantissa part of W to Z again, execute the instruction WM-+ZM.

The data flow in this step is 2→G5→j+
G1→1. FIG. 3 shows the contents of each register after the step 3 instruction is executed. (Step 4)
ZE=0? A judgment order is issued.

If the content of ZE is O, that is, there is no integer part, the operation is finished. In order to distinguish from the case where ZE is not O, the determination circuit 8 determines whether the content of ZE is O. The data flow at this time is 1→G3→d→8. If it is O, the determination circuit 8 modifies the address register 4 through h and sets the address to the calculation end routine. (
Step 5) A command ZM-+LS is issued. ZE
If the content of is not O, an integer part exists, so ZM is shifted to the left by one digit in order to link the mantissa part, that is, the decimal part data of the Z register, and the content of ZE. The data flow in this step is 1→G3→f→9→g→G1→1
It is. FIG. 3 4 shows the contents of the register before the left shift, and FIG. 3 5 shows the contents of the register after the shift. (Step 6) ZD8=0?
A judgment order is issued.

ZE. ．． Since the content of ZE is the integer part of the operation result, it is necessary to shift the content of ZE to the right together with ZM and transfer it to the mantissa part in order to normalize it. In this case, if ZE is 2 digits, 2 digits,
If it is 1 digit (ZD8=0), a 1 digit right shift is required, and in order to distinguish between them, it is determined that ZD8=O, and if it is O, the address is moved to step 9. (Steps 7 and 8)
Shift z to the right by the command Z→RS.

The data flow at this time is 1a-+G2→a→b→G
1→1a. At the same time WE+14WE. 1 is added to WE in order to store the number of shifts in WE. The data flow at this time is 2 → G5 → s7
T4G4→2, and FIG. 36 is the result. Steps 7 and 8 are not executed when ZD8=0. (
Step 9) Perform the same operation as step 7.

Figure 3.7 shows the result, and the Z register contains 1.23.
The exponent part 01 is stored in 010 and WE. (
Step 10) A command WE→ZE is issued.

The data stored in WE is transferred to ZE, and 1.
23010X1001 is stored. This state is shown in FIG. 38. As is clear from the above description, the present invention has the effect that not only the preprocessing but also the overall processing is extremely small and simple compared to the conventional method, and therefore the calculation speed is high.

[Brief explanation of drawings]

Figure 1 is a block diagram showing an example of hardware for implementing the present invention, Figure 2 is a flowchart of the calculation method of the present invention, and Figures 1 to 8 are the flowchart of Figure 2. FIG. 7 is a diagram showing the contents of the Z register and the W register at eight points in the chart. 1a and 1b... Z register where the calculation result is finally stored, 2... W register, 3...
. . . Read-only memory (ROM) that stores instructions for separately processing the mantissa and exponent parts of the numerical value input as the true number X, 4 . . . Address register (AR)
, 5... Ethics decoder (ID), 6...
Timing generator, 7...addition circuit for adding 1 to the contents of the W register, 8...judgment circuit, 9 and 10...for left shift One digit (
4-bit) register, 11... Heat calculation unit for calculating logarithmic values with base 10, G1 to G5...
····Gate.

Claims (1)

[Claims] 1 Log_1_ with arbitrary positive number X as an antilog number and base 10
In the calculation method of the logarithmic function expressed as 0X, a calculation result storage means for storing the calculation result, a calculation means for calculating the logarithmic value having a base of 10, and a mantissa of the numerical value input as the above-mentioned antilog number. an instruction storage means storing an instruction for separately processing the exponent part and the exponent part; the instruction storage means causes the arithmetic means to calculate a logarithmic value for the mantissa part according to the instruction of the instruction storage means; The decimal part of the arithmetic result is stored in the arithmetic result storage means, but the exponent part is stored in the arithmetic result storage means as an integer part of the arithmetic result without being operated by the arithmetic means. A calculation method for logarithmic functions characterized by the following.