KR102670314B1 - Device and Method for Calculating Function Approximation in Floating Point - Google Patents

Abstract

A method and apparatus for computing function approximation in floating point representation are disclosed.
According to one aspect of the present invention, in a computer implementation method for calculating a function approximation in a floating point expression, a preprocessed input is generated by replacing the exponent part of the input with a preset value, and an offset ( A first instruction execution step of generating an offset); A second instruction execution step of obtaining an approximation result of a function for the preprocessed input; and a third instruction execution step of calculating an approximation value of the function for the input by post-processing the approximation result using the offset.

Description

{Device and Method for Calculating Function Approximation in Floating Point}

Embodiments of the present invention relate to a method and device for calculating a function approximation using a floating point representation, and more specifically, to a method and device for calculating an approximation of a function using a minimum number of instructions based on a floating point format.

The content described in this section simply provides background information about the present invention and does not constitute prior art.

In the field of neural networks, various transcendental functions are used for calculations. Examples of transcendental functions include exponential functions, logarithmic functions, or square root functions. Computing devices such as PCs and cloud servers calculate the values of transcendental functions.

However, there is a problem that it takes tens to hundreds of cycles for the computing device to accurately calculate the values of transcendental functions.

To solve this problem, methods for quickly calculating the values of transcendental functions are being studied. There are two representative ways to reduce the calculation time for transcendental functions.

First, there is a way to add a dedicated computational unit designed to calculate the values of transcendental functions. For example, the first method is to calculate the value of the transcendental function using a hardware accelerator or AI (Artificial Intelligent) accelerator. The first method can reduce the time required to calculate the transcendental function by using dedicated hardware.

However, since the dedicated hardware device or dedicated hardware unit occupies a large area or volume, the first method has the disadvantage of low usability.

Second, there is an approximation method that divides the input range of the transcendental function into several sections and then outputs the approximate value of the transcendental function in each section. For example, the second method approximates the transcendental function with either a linear function or a polynomial function for each individual interval, and uses the approximated function to calculate the approximate value of the transcendental function for the input value. This is called piecewise linear approximation or piecewise polynomial approximation.

However, according to the second method, there is a problem that the approximation error of the approximate value increases in individual sections where the change in the transcendental function value is large. For example, the larger the input value of the exponential function, the larger the approximation error, and the closer the input value of the logarithmic function is to 0, the larger the approximation error.

To reduce the approximation error, the second method can apply pre-processing to the input value and post-processing to the approximate value. Here, preprocessing is mapping the input value to the domain of a function with less change than the given function. Post-processing is to convert the results calculated from the mapped domain to the original domain.

Specifically, the second method can calculate the approximate value of the transcendental function for the input value by preprocessing the input value according to the transcendental function, obtaining an approximate value of the function for the preprocessed value, and postprocessing the approximate value again. The approximation method using pre-processing and post-processing can reduce approximation errors in sections where there is a large change in the transcendental function value.

However, the conventional method of calculating transcendental function approximation requires a large number of instructions because it uses both floating point (FP) and integer (INT) expressions when performing pre-processing and post-processing. There is a downside to losing. Due to the number of instructions required for pre-processing and post-processing, it takes a lot of time to calculate the approximation of the transcendental function.

Specifically, a processor that calculates a conventional transcendental function approximation calculates a transcendental function approximation using arithmetic instructions such as four arithmetic operations. At this time, the processor supports number systems of floating point representation and integer representation. To support the two number systems, the processor uses instructions that convert numbers expressed as floating point to integers or instructions that convert numbers expressed as integers to floating point along with arithmetic instructions. In addition, when performing pre-processing and post-processing for transcendental functions, the processor uses instructions to extract the value of the exponential part from a number expressed in floating point, an instruction to change the value of the exponential part to a specific value, and a specific condition. Accordingly, a large number of instructions are used, including instructions that apply specific operations to the value extracted from the exponent part.

As such, because the processor executes many instructions and consumes a lot of time to perform pre-processing and post-processing, a problem occurs in which the number of transcendental function calculations per unit time is lowered. In particular, in neural networks that calculate numerous transcendental function values, research is needed on methods to efficiently increase the calculation processing speed of transcendental function values and the construction of efficient commands.

Embodiments of the present invention define and use instructions that can efficiently process pre-processing and post-processing for function approximation in a floating-point representation number system, thereby reducing the number of instructions and time required for function approximation. The main purpose is to provide methods and devices.

Other embodiments of the present invention map a given input to a domain with little change in the function value, obtain an approximate value of the function within the mapped domain, and convert the approximate value within the mapped domain back to the domain of the given input, The purpose is to provide a computational method and device to reduce approximation errors even in domains where there is a large change in function values.

According to one aspect of the present invention, in a computer implementation method for calculating a function approximation in a floating point expression, a preprocessed input is generated by replacing the exponent part of the input with a preset value, and an offset ( A first instruction execution step of generating an offset); A second instruction execution step of obtaining an approximation result of a function for the preprocessed input; and a third instruction execution step of calculating an approximation value of the function for the input by post-processing the approximation result using the offset.

According to another aspect of the present embodiment, a memory for storing instructions; and a processor executing the instructions, wherein the processor generates a preprocessed input by replacing the exponent part of the input with a preset value, generates an offset according to the substitution of the exponent part of the input, and performs the preprocessing. An arithmetic device is provided that calculates an approximation of the function for the input by obtaining an approximation result of the function for the input and post-processing the approximation result using the offset.

According to another aspect of this embodiment, a computer-readable recording medium recording a computer program for executing the method of any one of claims 1 to 12 is provided.

As described above, according to an embodiment of the present invention, by defining and using instructions that can efficiently process pre-processing and post-processing for function approximation in the floating point representation number system, the number of instructions required for function approximation is increased. and time required can be reduced.

According to another embodiment of the present invention, the given input is mapped to a domain with little change in the function value, an approximate value of the function is obtained within the mapped domain, and the approximate value within the mapped domain is converted back to the domain of the given input. , approximation error can be reduced even in sections where the change in function value is large.

1 is a diagram illustrating a half-precision floating point according to an embodiment of the present invention.
Figure 2 is a configuration diagram of an operation system according to an embodiment of the present invention.
Figure 3 is a flowchart for explaining a method of calculating function approximation according to an embodiment of the present invention.
Figure 4 is a diagram illustrating instructions for calculating function approximation according to an embodiment of the present invention.
5A and 5B are diagrams showing an exponential function for input and an exponential function for preprocessed input.
5C and 5D are diagrams for comparing conventional instructions for approximation of a natural exponential function and instructions according to an embodiment of the present invention.
Figures 6a and 6b are diagrams showing a logarithmic function for input and a logarithmic function for preprocessed input.
6C and 6D are diagrams for comparing conventional instructions for approximating a logarithmic function and instructions according to an embodiment of the present invention.
7A and 7B are diagrams showing the square root function for the input and the square root function for the preprocessed input.
7C and 7D are diagrams for comparing conventional instructions for approximating a square root function and instructions according to an embodiment of the present invention.
Figures 8a and 8b are diagrams showing the reciprocal square root function for the input and the reciprocal square root function for the preprocessed input.
8C and 8D are diagrams for comparing conventional instructions for approximating the reciprocal square root function with instructions according to an embodiment of the present invention.
9A and 9B are diagrams showing a reciprocal function for an input and a reciprocal function for a preprocessed input.
9C and 9D are diagrams for comparing conventional instructions for approximating a reciprocal function with instructions according to an embodiment of the present invention.

Hereinafter, some embodiments of the present invention will be described in detail through illustrative drawings. When adding reference numerals to components in each drawing, it should be noted that the same components are given the same reference numerals as much as possible even if they are shown in different drawings. Additionally, in describing the present invention, if it is determined that a detailed description of a related known configuration or function may obscure the gist of the present invention, the detailed description will be omitted.

Additionally, when describing the components of the present invention, terms such as first, second, A, B, (a), and (b) may be used. These terms are only used to distinguish the component from other components, and the nature, sequence, or order of the component is not limited by the term. Throughout the specification, when a part is said to 'include' or 'have' a certain component, this means that it does not exclude other components but may further include other components, unless specifically stated to the contrary. . Additionally, terms such as 'unit' and 'module' used in the specification refer to a unit that processes at least one function or operation, and may be implemented through hardware, software, or a combination of hardware and software.

1 is a diagram illustrating floating point numbers according to an embodiment of the present invention.

Referring to Figure 1, the configuration of a half-precision floating point is shown.

Floating Point (FP) representation refers to IEEE Standard 754 floating point representation.

The precision of floating point can be half-precision, single-precision, or double-precision. Half-precision floating point points are expressed with 16 bits, single-precision floating point points are expressed with 32 bits, and double-precision floating point points are expressed with 64 bits.

The composition of floating point includes a bit sign, exponent (E), and mantissa (M). For example, a half-precision floating point consists of a 1-bit sign bit, a 5-bit exponent part, and a 10-bit mantissa bit.

Single-precision floating point representation can be normalized number, subnormal number, zero (+/- zero), NaN (Not a Number), and infinity (+/- Infinity) depending on the values of the exponent and mantissa. ) can be indicated.

A regular value represents a common number and can be converted to decimal representation. It is expressed in the form of . E is the exponent part, and M is the mantissa part. The exponent part is assumed to contain a bias. The mantissa has a leading 1 implied. If the mantissa is a number with a leading 1, the normal value is Express it in form.

Unlike regular values, the mantissa of non-normal values does not have a leading 1. Non-normal values have decimal representation expressed in form. In half-precision floating point is defined as -14. Numbers close to 0 can be expressed through non-normal values.

Because the exponent part does not have a sign bit, a bias is used to handle negative numbers. The exponent part of a regular value can use a bias where the most significant bit is 1 bit. In half-precision floating point representation, the exponent part, which has a range of -15 to 16, can be expressed in the range of 0 to 31 through bias. For example, if the binary bit string of the exponent part is 10000, it is calculated as 16 in decimal representation, but since the bias bit string is also 10000, it actually means an exponent of 0. Therefore, in decimal representation The value of becomes 1. As another example, if the binary bit string of the exponent part is 01111, it is calculated as 15 in decimal representation, but actually means -1. The value of becomes 0.5.

Figure 2 is a configuration diagram of an operation system according to an embodiment of the present invention.

Referring to FIG. 2 , the computing system 20 includes a data memory 200, a program memory 210, and a processor 220.

The computing system 20 can extract valid information by analyzing input data in real time based on a neural network, judge the situation based on the extracted information, or control the configuration of the electronic device on which the computing system 20 is mounted. there is. The data memory 200, program memory 210, and processor 220 may be implemented with one semiconductor chip or a plurality of semiconductor chips.

Data memory 200 and program memory 210 may store programs, data, or instructions.

The data memory 200 and program memory 210 may be implemented using memory such as dynamic RAM (DRAM) or static RAM (SRAM).

The processor 220 controls the overall operation of the computing system 20.

The processor 220 may receive input data from at least one of the data memory 200 and the program memory 210 through a system bus and generate an information signal based on the input data. According to one embodiment of the present invention, the processor 220 may perform function approximation for a function using programs and data stored in the data memory 200 and the program memory 210.

The processor 220 may be a central processing unit (CPU) or a neural network processing unit (NPU).

Otherwise, the processor 220 may be a hardware accelerator for performing calculations according to neural network models. A hardware accelerator generally includes an engine that specifically performs matrix operations such as convolution operations; A processor that performs a non-linear function, such as an activation function, or a pooling function; on-chip memory; and DMA (Direct Memory Access) for external memory access.

When the processor 220 is implemented as a CPU or NPU, the processor 220 may include a control unit (not shown), a register (not shown), an operation unit (not shown), and a memory access unit (not shown). there is. The register is a place where the operation input and output of the operation unit is stored, and the memory access unit is a component that performs access to the data memory 200 and the program memory 210. The control unit controls the operation of the processor 220 (eg, power management, interrupt processing, etc.).

The computing device according to an embodiment of the present invention may be implemented on the computing system 20 or the processor 220. The computational device can also be implemented as a hardware accelerator for neural network computation.

Figure 3 is a flowchart for explaining a method of calculating function approximation according to an embodiment of the present invention.

Below, a schematic operation of the computing device according to an embodiment of the present invention will be described.

According to one embodiment of the present invention, the computing device separates only the mantissa part of the input from the floating point expression, applies sectional function approximation, and then reflects the exponent part of the input in the approximation result to calculate the final approximation value.

The process of separating the mantissa part of the input is the process of replacing the exponent part with bias or bias plus 1 (bias + 1). If the exponent of the input is replaced with the bias or bias plus 1, the preprocessed input has the range 1 to 2 or 1 to 4 in decimal representation. In general, when mapping an input from a transcendental function to a domain with a range of 1 to 4, the amount of change in the transcendental function becomes small in that range. For example, the amount of change of the exponential function in the input range of 1 to 2 is smaller than the amount of change of the exponential function in the input range of 10 to 11. In other words, the process of replacing the exponent part of the input with the bias or the bias plus 1 means the process of mapping the input from a domain with a large change in the function to a domain with a small change in the function.

Since the computing device calculates function approximation in a domain where the change amount of the function is small, the approximation error can be reduced compared to function approximation in a domain where the change amount of the function is large.

Furthermore, in performing preprocessing of the input before approximation and postprocessing of the approximation result after approximation, conventional computing devices use a large number of arithmetic operation instructions and logic operation instructions. Unlike this, the computing device according to an embodiment of the present invention uses instructions that can efficiently implement pre-processing and post-processing tasks for domain mapping when calculating transcendental functions, thereby increasing the number of instructions used in pre-processing and post-processing tasks. Minimize.

Accordingly, the computing device can reduce the approximation error and improve the computational speed by reducing the computational cycle.

Below, specific operations of the computing device according to an embodiment of the present invention will be described.

Referring to FIG. 3, the computing device generates a preprocessed input by replacing the exponent part of the input with a preset value and generates an offset according to the replacement of the exponent part of the input (S300).

According to one embodiment of the present invention, the computing device generates a preprocessed input by replacing the exponent part of the input with a bias that is a preset value. The purpose of the calculation device to replace the exponent part of the input with a bias is to reduce approximation errors.

If the exponent of the input is unbiased, the input has a wide domain. In a wide domain of unbiased input, there is a section where the amount of change in the function is large. Therefore, even if function approximation is performed on input that has not been preprocessed, a large approximation error may occur due to a section in which the change amount of the function is large.

Conversely, when the exponent part of the input is replaced with bias, the value indicated by the exponent part becomes 2 ⁰ or 1. At this time, the input value is converted to a value in the range expressed by the mantissa, so it has a narrow domain of 1 to 2. In particular, in the case of transcendental functions, the amount of change in the transcendental function is small in the range of the domain expressed by the mantissa. In other words, replacing the exponent part of the input with a bias means that the input is mapped to a domain where the change in the function is small. The calculation device can reduce approximation errors because it performs approximation in sections where the amount of change in the function is small.

Meanwhile, according to an embodiment of the present invention, the arithmetic device may generate an offset based on the difference between the exponent part of the input and a preset value. If the preset value is a bias, the arithmetic device may generate an offset based on the difference between the exponent of the input and the bias. The difference between the exponent and bias of the input refers to the actual value of the exponent in decimal representation.

The offset is used to calculate the approximation value of the function for the originally intended input from the approximation result of the function for the preprocessed input. In terms of the exponent of the input, the offset is used to adjust the exponent of the approximation result by taking into account the exponent before being replaced with a bias. From the input mapping perspective, the offset is used to transform the mapped input back to the original domain, to a domain where the change in the function is small.

According to another embodiment of the present invention, the arithmetic device generates an offset by shifting one-bit by the difference between the exponent part of the input and a preset value. If the preset value is a bias, the arithmetic device generates an offset by shifting the original bit by the difference between the exponent part of the input and the bias. For example, if the difference between the exponent of the input and the bias is 3, the arithmetic device can left-shift the original bit to generate a binary bit string of 1000 as an offset. At this time, the offset is 8 in decimal representation. The offset generated through the above operation can be used to approximate an exponential function. An example of this is depicted in Figure 5d.

According to an embodiment of the present invention, the computing device may replace the exponent part of the input with a different value depending on whether the difference between the exponent part of the input and the bias is odd or even. Furthermore, the computing device may generate different offsets depending on whether the difference between the exponent of the input and the bias is odd or even. Examples of this are depicted in Figures 7d and 8d.

If the difference between the exponent of the input and the bias is an even number, the computing device generates a preprocessed input by replacing the exponent of the input with the bias. Furthermore, the arithmetic unit generates an offset by performing a bit shift on the difference between the exponent of the input and the bias. For example, the computing device may generate an offset by right shifting the difference between the exponent of the input and the bias by 1. The offset generated through the above operation can be used for approximation of the square root function or the square root reciprocal function.

If the difference between the exponent of the input and the bias is an odd number, the computing device generates a preprocessed input by replacing the exponent of the input with the sum of the bias and the odd number. Furthermore, the computing device generates an offset by performing a bit shift on the difference between the exponent of the input and the sum. For example, the computing device generates a preprocessed input by replacing the exponent of the input with a bias plus 1 (bias + 1). Additionally, the arithmetic device subtracts the bias plus 1 (bias + 1) from the exponent part of the input, and right-shifts the subtraction result by 1 to generate an offset. Shifting the subtraction result to the right by 1 corresponds to the operation of removing the square root of the subtraction result. The offset generated through the above operation can be used for approximation of the square root function or the square root reciprocal function.

The computing device obtains the approximation result of the function for the preprocessed input (S302).

Specifically, the computing device divides the input range of the function into a plurality of sections and applies a linear approximation or polynomial approximation to the function for each section. The computing device can calculate a function approximation value for the preprocessed input through section-by-section approximation. The calculated approximate value is called the approximation result.

Meanwhile, the function approximation value for the preprocessed input can be calculated based on a look-up table. The calculation device divides the entire input value range into a plurality of detailed sections, stores in advance a lookup table with approximation coefficients set for each of the multiple input ranges corresponding to each section, and refers to the stored lookup table to obtain a function approximation value for the input value. can be calculated. Here, in the straight line approximation method, the approximation coefficients include slope and offset. In the polynomial approximation method, the approximation coefficients may include the coefficients and offsets of the polynomial function. For example, the computing device identifies the input range that includes the input, obtains the approximation coefficient set in the input range by referring to the lookup table, and calculates the approximation value of the function for the input using the approximation coefficient.

The computing device calculates the approximate value of the function for the input by post-processing the approximation result using the offset (S304). At this time, the approximation value of the function for the input is called the final approximation value.

Specifically, the computing unit adjusts the exponent part of the approximation result based on the offset. The adjusted approximation result becomes an approximation of the function for the input originally sought. From a mapping perspective, the exponent of the approximation result is adjusted according to the offset, so that the input is mapped from a domain with a large change in the function to a domain with a small change in the function.

According to one embodiment of the present invention, the arithmetic device calculates an approximate value of a function for an input based on the sum of the exponent and the offset of the approximation result. This operation can be used for approximation of exponential and square root functions.

According to one embodiment of the present invention, the arithmetic device calculates an approximation value of a function for an input based on the difference between an exponent and an offset of the approximation result. This operation can be used for the approximation of the reciprocal function and the reciprocal function of the square root.

According to one embodiment of the present invention, the computing device calculates an approximate value of a function for an input by performing a Multiply Accumulate (MAC) operation on an offset, a preset logarithmic value, and an approximation result. This operation can be used to approximate logarithmic functions. An example of this is depicted in Figure 6d.

Meanwhile, according to an embodiment of the present invention, the computing device can adjust the input by multiplying the input by a preset logarithmic value before preprocessing the input. Afterwards, the arithmetic unit performs preprocessing on the exponent part of the adjusted input and generates an offset. Furthermore, the computing device obtains an approximation result of an exponential function associated with a preset logarithmic value, rather than the target function to be approximated. That is, the computing device obtains an approximation result of an exponential function associated with a preset logarithmic value for the preprocessed input. Afterwards, the computing device can post-process the approximation result using the offset to calculate an approximation value of the target function for the input. This operation can be used for approximation of natural exponential functions. An example of this is depicted in Figure 5d.

According to one embodiment of the present invention, if the approximation value of the function for the input is outside the expression range of the floating point system, the arithmetic device sets the final approximation value to either zero or infinity. This is called clipping.

Steps S300, S302, and S304 are performed by the computing device executing one instruction for each step. That is, the computing device generates step S300 as a first instruction, generates step S302 as a second instruction, and generates step S304 as a third instruction. The computing device calculates an approximate value of the function by executing each instruction. The computing device may calculate an approximate value of a function for an input by combining the embodiment of the first instruction and the embodiment of the third instruction.

According to one embodiment of the present invention, one to two pre-processing instructions and one post-processing instruction are used for function approximation, so the computing device can calculate the function approximation with a minimum number of instructions.

Figure 4 is a diagram illustrating instructions for calculating function approximation according to an embodiment of the present invention.

Referring to Figure 4, a combination of an embodiment of a first instruction and an embodiment of a third instruction is shown. Based on each combination, the computing device can calculate the exponential function, the logarithmic function, the square root function, the reciprocal function of the square root, and the approximation of the reciprocal function.

The Extract_Exp() command is the first command that generates a preprocessed input by replacing the exponent of the input with a bias or a bias plus 1, and generates an offset according to the substitution. By the Extract_Exp() instruction, the input is mapped to the range 1 to 2 or the range 1 to 4. X' is the preprocessed input, E _st is the offset, Y is the result of approximation of the function to the preprocessed input, and Y' is the final approximation value. The symbols << and >> indicate bit shift operations.

The Apply_ExpOffset() command is a third command that calculates the approximate value of the function for the input by post-processing the approximation result using the offset. The Apply_ExpOffset() command is a command that obtains the final approximation value of a function for the input by adding or subtracting an offset to the exponent of the approximation result calculated from the preprocessed input.

According to an embodiment of the present invention, the computing device defines and uses dedicated instructions that can efficiently perform pre-processing and post-processing for transcendental function approximation in a floating-point representation number system, so that the minimum You can calculate the approximation of a function using the instructions.

5A and 5B are diagrams showing an exponential function for input and an exponential function for preprocessed input.

Referring to Figure 5A, the natural exponential function y for input x is shown.

To reduce the approximation error of the natural exponential function y for the input x, the computing device can use piecewise approximation. Specifically, the computing device divides the entire input into 8 sections and applies a linear approximation or polynomial approximation to the natural exponential function y. The computing device may calculate an approximate value of a function y for input x using function approximation within an interval corresponding to input x.

Since the amount of change in the natural exponential function y is relatively small in the section S ₀ to the section S ₄ , the approximation error between the true value and the approximated value is small even if the calculation device applies linear approximation or polynomial approximation for each section.

However, since the amount of change in the natural exponential function y is relatively large in the section S ₅ to section S ₇ , when the calculation device applies linear approximation or polynomial approximation for each section, the approximation error between the true value and the approximated value is large.

To reduce approximation error, the computing device maps the input from a domain with a large change in the function to a domain with a small change in the function.

Referring to Figure 5b, the exponential function y _t for input t is shown. Input t is the mapped input x.

The domain range of input t is narrower than the domain range of input x. The domain range of input x is 0 to 10, while the domain range of input t is 1 to 2.

Additionally, the amount of change in function y _t with respect to input t is smaller than the amount of change in function y with respect to input x.

Even if _the input When applying function approximation in the t domain, the approximation error is smaller than when applying function approximation in the x domain.

The computing device can obtain an approximation value of the function y for the input x by converting the approximation result in the t domain back to the domain of the input x.

Hereinafter, the instructions and execution order used to perform preprocessing of input, approximation of a function for the preprocessed input, and postprocessing of the approximation result will be described in comparison with a conventional computing device.

5C and 5D are diagrams for comparing conventional instructions for approximating a natural exponential function and instructions according to an embodiment of the present invention.

Conventional computing devices use Equation 1 to approximate a natural exponential function.

In Equation 1, a means the integer part, and b means the decimal part.

Referring to Equation 1, the conventional arithmetic device inputs Multiply and separate the multiplication result into an integer part and a decimal part. A conventional arithmetic device calculates a first value with 2 as the base and an integer portion as an exponent, and a second value with 2 as the base and a decimal portion as an exponent. Finally, the conventional computing device can calculate the multiplication of the first value and the second value as the value of the natural exponential function.

The result of multiplying the first value and the second value can be expressed as a floating point (FP). At this time, the exponent a of the first value is the input x and Corresponds to the integer part of the multiplication result. In other words, the integer part of the multiplication result corresponds to the exponent part of the natural exponential function. A conventional arithmetic device can generate the first value by left-shifting the original bit by the integer part.

Meanwhile, a conventional computing device applies function approximation to the second value. The second value can be modeled as an exponential function with the decimal part as input and base 2. At this time, since the decimal part has a value between 0 and 1, the second value has a value between 1 and 2. The expression range of the decimal part is narrow compared to the input x, and the amount of change in the second value is small within the expression range. Therefore, even if function approximation is applied to the second value, the approximation error is small.

Conventional computing devices calculate the final approximation of the natural exponential function for the input by multiplying the approximation of the first and second values.

Referring to FIG. 5C, instructions for a conventional computing device to perform function approximation according to Equation 1 are shown.

Conventional computing devices input Adjust the input by multiplying (S500).

At this time, the input is expressed as FP.

A conventional computing device extracts the integer part of the adjusted input (S502).

A conventional computing device can extract the integer portion of the adjusted input by executing an instruction that converts a number expressed in FP into an integer (INT) representation. The extracted integer part is expressed as INT. In this process, the fractional part of the adjusted input is ignored.

A conventional computing device converts the expression of the integer part from INT to FP (S504).

A conventional computing device converts the expression of the integer part into FP by executing an instruction that converts a number expressed in INT into an FP expression.

A conventional computing device extracts the fractional part of the adjusted input (S506).

A conventional computing device can extract the decimal part of the adjusted input by subtracting the integer part of the adjusted input from the adjusted input in the FP representation system.

A conventional computing device separates the input adjusted through the above steps into an integer part and a decimal part.

A conventional computing device calculates the approximation result for the decimal part by applying sectional approximation to an exponential function with base 2 (S508).

Specifically, a conventional computing device can take the fractional part of the adjusted input as input and apply function approximation to an exponential function with 2 as the base. Since the amount of change in the exponential function depending on the expression range of the decimal part is less than the amount of change in the natural exponential function depending on the expression range of the input, the conventional computing device can obtain an approximation result with less approximation error.

Meanwhile, a conventional arithmetic device generates an offset by left-shifting a one-bit by an integer (S510).

When one bit is left shifted in binary representation, a value with a base of 2 and an exponent of the shift amount is created. In other words, the offset is a value with 2 as the base and the integer part as the exponent. At this time, the offset is expressed as INT.

A conventional arithmetic device converts the expression of the offset from INT to FP (S512).

A conventional computing device calculates the final approximation value by multiplying the approximation result by an offset (S514). A conventional computing device can obtain an approximation value of a natural exponential function for an input as shown in Equation 1 by multiplying the approximation result for the decimal part by an offset.

As a result, the conventional computing device uses four instructions to preprocess the input and three instructions to postprocess the approximation result, excluding the instruction in step S508.

In contrast, the computing device according to an embodiment of the present invention uses Equation 2 to approximate a natural exponential function using a small number of instructions.

Referring to Equation 2, the arithmetic unit uses the natural exponential function You can multiply and express the multiplication result in the exponent and mantissa. is the exponent part of the multiplication result, is the mantissa of the multiplication result.

The arithmetic unit calculates a function approximation on the mantissa of the multiplication result. And the arithmetic unit uses 2 as the base and the third value ( ) is calculated. The third value is a value related to the offset. The arithmetic unit calculates the approximation value of the natural exponential function by adding a third value to the exponent part of the approximation result.

Referring to FIG. 5D, instructions for a computing device according to an embodiment of the present invention to perform function approximation according to Equation 2 are shown.

The computing device according to an embodiment of the present invention inputs Adjust the input by multiplying (S520).

The arithmetic unit generates a preprocessed input by replacing the exponent of the adjusted input with a bias, and generates an offset by shifting the one-bit by the difference between the exponent and the bias (S522).

In other words, the preprocessed input is a value where the exponent is the bias and the mantissa is the mantissa of the adjusted input. The preprocessed input has a value of 1 to 2 in decimal representation. When the difference between the exponent and the bias is called the shift amount, the offset is a value whose base is 2 in binary representation and the shift amount is the exponent. For example, if the difference between the exponent of the input and the bias is 2, the offset is the binary bit string 100, which in decimal representation is 4.

The computing device calculates the approximation result for the preprocessed input by applying sectional approximation to the exponential function with base 2 (S524).

Specifically, the computing device divides the base 2 exponential function into several sections and identifies the section to which the preprocessed input belongs. The computing device can directly calculate the linear approximation coefficient or polynomial approximation coefficient in the identified section, or obtain it from a previously stored lookup table. The computing device obtains an approximation result from either a linear approximation coefficient or a polynomial approximation coefficient and a preprocessed input. Since the range of the preprocessed input in decimal representation is 1 to 2, the range of the approximation result is 2 to 4. Since the range of the approximation result is 2 to 4, the exponent of the approximation result in the FP expression is the bias plus 1.

The computing device calculates the final approximation value of the natural exponential function for the input by adding an offset to the exponent part of the approximation result (S526).

Briefly explaining steps S520 to S526, the computing device separates only the mantissa part of the input from the floating point expression, applies sectional function approximation, and then reflects the exponent part of the input in the approximation result to calculate the final approximation value.

The computing device according to an embodiment of the present invention uses two instructions to preprocess the input and one instruction to postprocess the approximation result, except for the instruction in step S524. Since each instruction in step S520, step S522, and step S526 is based on the FP expression, a conversion instruction between INT and FP is not required. The computational unit minimizes preprocessing and postprocessing instructions based solely on floating point representation.

Additionally, since the computing device calculates function approximation in a domain where the change amount of the function is small, approximation errors can be reduced compared to function approximation in a domain where the change amount of the function is large.

Figures 6a and 6b are diagrams showing a logarithmic function for input and a logarithmic function for preprocessed input.

Referring to Figure 6A, the logarithmic function y for input x is shown.

Since the amount of change in the logarithmic function y is relatively small in the section S ₁ to the section S ₇ , the approximation error between the true value and the approximated value is small even if the calculation device applies linear approximation or polynomial approximation for each section.

However, since the amount of change in the logarithmic function y is relatively large in the section S ₀ , when the computing device applies linear approximation or polynomial approximation for each section, the approximation error between the true value and the approximated value is large.

To reduce approximation error, the computing device maps the input from a domain with a large change in the function to a domain with a small change in the function.

Referring to Figure 6b, the logarithmic function y _t for input t is shown.

The domain range of input t is narrower than the domain range of input x. Additionally, the amount of change in function y _t with respect to input t is smaller than the amount of change in function y with respect to input x. The amount of change in the logarithmic function in the range of input t is smaller than the amount of change in the logarithmic function in the range of input x.

Even if _the input When applying function approximation in the t domain, the approximation error is smaller than when applying function approximation in the x domain.

The computing device can obtain an approximation value of the function y for the input x by converting the approximation result in the t domain back to the domain of the input x.

Hereinafter, the instructions and execution order used to perform preprocessing of input, approximation of a function for the preprocessed input, and postprocessing of the approximation result will be described in comparison with a conventional computing device.

6C and 6D are diagrams for comparing conventional instructions for approximating a logarithmic function and instructions according to an embodiment of the present invention.

Conventional computing devices use Equation 3 to approximate a logarithmic function.

In Equation 3, k is the exponent of input x, is the mantissa of input x.

Referring to Equation 3, the conventional arithmetic device uses the exponent k, log(2), and By performing a Multiply-Accumulate (MAC) operation, the function value of the logarithmic function for input x is calculated.

At this time, the conventional computing device is A sectional approximation can be applied to . Since the mantissa of input x has a value of 1 to 2, the expression range is narrower than that of input x. Additionally, the amount of change in the logarithmic function in the range of the mantissa of input x is smaller than the amount of change in the logarithmic function in the range of input x. The approximation error for the mantissa of input x is smaller than the approximation error for input x. Therefore, the conventional computing device can reduce the approximation error through section-by-section approximation to the mantissa part of the input x.

A conventional computing device can calculate the final approximation value of a logarithmic function for input x by performing a MAC operation on the exponent k, log(2), and the approximation value.

Referring to FIG. 6C, instructions for a conventional computing device to perform function approximation according to Equation 3 are shown.

A conventional computing device extracts the exponent part of the input (S600).

A conventional computing device can extract the exponent part of an input by executing instructions related to a shift operation, a mask operation, and a subtraction operation on the input. In order for a conventional computing device to extract the exponent part of the input, three instructions are required.

A conventional computing device replaces the extracted exponent with a bias (S602).

A conventional computing device can replace the extracted exponent with a bias by executing instructions related to a bit-wise mask operation and OR operation on the exponent of the input. In order to replace the exponent extracted by a conventional computing device with a bias, two instructions are required.

Through steps S600 and S602, the conventional computing device preprocesses the input.

A conventional computing device calculates the approximation result for the preprocessed input by applying sectional approximation to the logarithmic function (S508).

A conventional computing device obtains an approximation result of a logarithmic function for a preprocessed input. Since the amount of change in the logarithmic function according to the expression range of the preprocessed input is less than the amount of change in the logarithmic function according to the expression range of the input, the conventional computing device can obtain an approximation result with a small approximation error.

The conventional computing device calculates the final approximation value of the logarithmic function for the input by performing MAC operation on the exponent part, log(2), and the approximation result (S606).

Excluding the instruction in step S604, the conventional computing device uses five instructions to preprocess the input and one instruction to postprocess the approximation result.

In contrast, the computing device according to an embodiment of the present invention calculates the approximation of the logarithmic function using Equation 3, but can obtain the approximate value of the logarithmic function with fewer instructions than a conventional computing device.

Referring to FIG. 6D, instructions for a computing device according to an embodiment of the present invention to perform function approximation according to Equation 3 are shown.

The computing device according to an embodiment of the present invention preprocesses the input by replacing the exponent part of the input with a bias, and generates the difference between the exponent part of the input and the bias as an offset (S610).

In other words, the preprocessed input is a value in which the exponent part of the input is replaced with a bias, and the offset is a value obtained by subtracting the offset from the exponent part of the input.

The computing device calculates the approximation result for the preprocessed input by applying sectional approximation to the logarithmic function (S612).

The computing device calculates the final approximation value of the logarithmic function for the input x by performing MAC operation on the offset, log(2), and the approximation result (S614). Here, log(2) may be a preset value.

The computing device according to an embodiment of the present invention uses one instruction to preprocess the input and one instruction to postprocess the approximation result, except for the instruction in step S612. Compared to conventional computing devices, the computing device can compute an approximation of a logarithmic function with a small number of instructions.

Additionally, since the computing device calculates function approximation in a domain where the change amount of the function is small, approximation errors can be reduced compared to function approximation in a domain where the change amount of the function is large.

7A and 7B are diagrams showing the square root function for input and the square root function for preprocessed input.

Referring to Figure 7A, the square root (sqrt) function y for input x is shown.

Since the amount of change in the square root function y is relatively small in the section S ₁ to the section S ₇ , the approximation error between the true value and the approximated value is small even if the calculation device applies linear approximation or polynomial approximation for each section.

However, since the amount of change in the square root function y is relatively large in the section S ₀ , when the calculation device applies linear approximation or polynomial approximation for each section, the approximation error between the true value and the approximated value is large.

To reduce approximation error, the computing device maps the input from a domain with a large change in the function to a domain with a small change in the function.

Referring to Figure 7b, the square root function y _t for input t is shown. Input t is the mapped input x.

The domain range of input t is narrower than the domain range of input x. Additionally, the amount of change in function y _t with respect to input t is smaller than the amount of change in function y with respect to input x. In other words, the amount of change in the square root function in the range of input t is less than the amount of change in the square root function in the range of input x.

Even if _the input When applying function approximation in the t domain, the approximation error is smaller than when applying function approximation in the x domain.

The computing device can obtain an approximation value of the function y for the input x by converting the approximation result in the t domain back to the domain of the input x.

Hereinafter, the instructions and execution order used to perform preprocessing of input, approximation of a function for the preprocessed input, and postprocessing of the approximation result will be described in comparison with a conventional computing device.

7C and 7D are diagrams for comparing conventional instructions for approximating a square root function and instructions according to an embodiment of the present invention.

Conventional computing devices use Equation 4 to approximate the square root function.

In Equation 4, k and n are integers greater than or equal to 0. n corresponds to the exponent part of the input.

Referring to Equation 4, the conventional arithmetic device calculates the fourth value with 2 as the base and the exponent of the input as the exponent. A conventional computing device calculates the function value of the square root function for the mantissa part of the input. A conventional computing device calculates the function value of the square root function for the input by multiplying the fourth value and the square root function value for the mantissa.

At this time, the conventional computing device is A sectional approximation can be applied to . A conventional computing device calculates the multiplication of the fourth value and the approximation result into the final approximation value of the square root function for the input x.

Meanwhile, a conventional computing device can calculate function values differently depending on whether the exponent part of the input is odd or even. When the exponent part of the input is an even number, the conventional computing device obtains an approximation result for the mantissa part of the input, and calculates the product of the fourth value and the approximation result as an approximation value of the square root function for the input x. On the other hand, when the exponent part of the input is an odd number, the conventional arithmetic device obtains an approximation result for the value of the mantissa part of the input multiplied by 2, and calculates the product of the fourth value and the approximation result as an approximation value of the square root function for the input x.

Referring to FIG. 7C, instructions for a conventional computing device to perform function approximation according to Equation 4 are shown.

A conventional computing device extracts the exponent part of the input (S700).

A conventional computing device replaces the extracted exponent with a bias (S702).

The conventional arithmetic device determines whether the exponent part of the input is odd (S704). In order for a conventional computing device to determine whether the exponent of the input is odd, two instructions are required.

If the exponent of the input is an odd number, the conventional arithmetic device decreases the exponent of the input by 1 (S706).

Additionally, the conventional arithmetic device multiplies the input whose exponent part is replaced with a bias by 2 (S708).

A conventional computing device calculates the approximation result for the preprocessed input by applying sectional approximation to the square root function (S710).

If the exponent part of the input is an even number in step S704, the conventional computing device does not perform steps S706 and S708 and immediately calculates the approximation result for the preprocessed input.

A conventional arithmetic device generates an offset by left-shifting the original bit by half of the exponent (S712).

The offset created through shifting of one bit has an INT representation.

A conventional arithmetic device converts the expression of the offset from INT to FP (S714).

A conventional computing device calculates the final approximation value of the square root function for the input by multiplying the approximation result by an offset (S716).

Excluding the instruction in step S710, a conventional computing device uses 7 to 9 instructions to preprocess the input and 4 instructions to postprocess the approximation result.

In contrast, the computing device according to an embodiment of the present invention calculates the approximation of the square root function using Equation 4, and can obtain the approximate value of the square root function with fewer instructions than a conventional computing device.

Referring to FIG. 7D, instructions for a computing device according to an embodiment of the present invention to perform function approximation according to Equation 4 are shown.

The computing device according to an embodiment of the present invention generates a preprocessed input and an offset based on whether the difference between the exponent part of the input and the bias is odd or even (S720).

If the difference between the exponent of the input and the bias is an even number, the computing device generates a preprocessed input by replacing the exponent of the input with the bias. The arithmetic unit generates an offset by right-shifting the difference between the exponent of the input and the bias by 1.

If the difference between the exponent of the input and the bias is an odd number, the computing device generates a preprocessed input by replacing the exponent of the input with the bias plus 1. The arithmetic unit subtracts the bias plus 1 (bias + 1) from the exponent part of the input, and right-shifts the subtraction result by 1 to generate an offset.

The computing device calculates the approximation result for the preprocessed input by applying sectional approximation to the square root function (S722).

The computing device calculates the final approximation value of the square root function for the input by adding an offset to the exponent of the approximation result (S724).

The computing device according to an embodiment of the present invention uses one instruction to preprocess the input and one instruction to postprocess the approximation result, except for the instruction in step S722. Compared to conventional computing devices, the computing device can calculate the approximation of the square root function with a small number of instructions.

Additionally, since the computing device calculates function approximation in a domain where the change amount of the function is small, approximation errors can be reduced compared to function approximation in a domain where the change amount of the function is large.

Figures 8a and 8b are diagrams showing the reciprocal square root function for the input and the reciprocal square root function for the preprocessed input.

Referring to FIG. 8A, the reciprocal square root (rsqrt) function y for input x is shown.

Since the amount of change in the square root reciprocal function y is relatively small in the section S ₁ to section S ₇ , the approximation error between the true value and the approximated value is small even if the calculation device applies linear approximation or polynomial approximation for each section.

However, in the interval S ₀ , the amount of change in the square root reciprocal function y is relatively large, so when the calculation device applies linear approximation or polynomial approximation for each section, the approximation error between the true value and the approximated value is large.

To reduce approximation error, the computing device maps the input from a domain with a large change in the function to a domain with a small change in the function.

Referring to Figure 8b, the square root reciprocal function y _t for the input t is shown. Input t is the mapped input x.

The amount of change in function y _t for input t is smaller than the amount of change in function y for input x. In other words, the amount of change in the reciprocal square root function in the range of input t is less than the amount of change in the reciprocal square root function in the range of input x.

Even if _the input When applying function approximation in the t domain, the approximation error is smaller than when applying function approximation in the x domain.

The computing device can obtain an approximation value of the function y for the input x by converting the approximation result in the t domain back to the domain of the input x.

Hereinafter, the instructions and execution order used to perform preprocessing of input, approximation of a function for the preprocessed input, and postprocessing of the approximation result will be described in comparison with a conventional computing device.

FIGS. 8C and 8D are diagrams for comparing conventional instructions for approximating the reciprocal square root function with instructions according to an embodiment of the present invention.

Conventional computing devices use Equation 5 to approximate the reciprocal function of the square root.

In Equation 5, k and n are integers greater than or equal to 0. n corresponds to the exponent part of the input.

Referring to Equation 5, the conventional computing device calculates the fifth value with 2 as the base and a negative number taken as the exponent of the input. A conventional arithmetic device calculates the function value of the reciprocal of the square root of the mantissa of the input. A conventional arithmetic device calculates the function value of the reciprocal square root function for the input by multiplying the fifth value and the reciprocal square root function value for the mantissa part.

At this time, the conventional computing device is A sectional approximation can be applied to . A conventional computing device calculates the multiplication of the fifth value and the approximation result into a final approximation value of the reciprocal square root function for the input x.

Meanwhile, a conventional computing device can calculate function values differently depending on whether the exponent part of the input is odd or even. When the exponent part of the input is an even number, the conventional computing device obtains an approximation result for the mantissa part of the input, and calculates the product of the fifth value and the approximation result as an approximation of the reciprocal square root function for the input x. On the other hand, when the exponent part of the input is an odd number, the conventional calculation device obtains an approximation result for the value of the mantissa part of the input multiplied by 2, and calculates the product of the fifth value and the approximation result as an approximation of the reciprocal square root function for the input x do.

Referring to FIG. 8C, instructions for a conventional computing device to perform function approximation according to Equation 5 are shown.

Since steps S800 to S808 and steps S812 to S814 correspond to steps S700 to S708 and steps S712 to S714, detailed descriptions are omitted.

In step S810, the conventional computing device calculates the approximation result for the preprocessed input by applying sectional approximation to the reciprocal square root function (S810).

The conventional computing device calculates the final approximation value of the reciprocal square root function for the input by dividing the offset by the approximation result (S816).

Excluding the instruction in step S810, a conventional computing device uses 7 to 9 instructions to preprocess the input and 4 instructions to postprocess the approximation result.

In contrast, the computing device according to an embodiment of the present invention calculates the approximation of the reciprocal square root function using Equation 5, and can obtain the approximate value of the reciprocal square root function with fewer instructions than a conventional computing device.

Referring to FIG. 8D, instructions for a computing device according to an embodiment of the present invention to perform function approximation according to Equation 5 are shown.

Since step S820 corresponds to step S720 and step S822 corresponds to step 810, detailed description is omitted.

The arithmetic unit calculates the final approximation value of the reciprocal square root function for the input by subtracting the offset from the exponent of the approximation result (S824).

The computing device according to an embodiment of the present invention uses one instruction to preprocess the input and one instruction to postprocess the approximation result, except for the instruction in step S822. Compared to conventional computing devices, the computing device can calculate the approximation of the inverse square root function with a small number of instructions.

Additionally, since the computing device calculates function approximation in a domain where the change amount of the function is small, approximation errors can be reduced compared to function approximation in a domain where the change amount of the function is large.

9A and 9B are diagrams showing a reciprocal function for an input and a reciprocal function for a preprocessed input.

Referring to Figure 9A, the reciprocal function y for input x is shown.

To reduce the approximation error of the reciprocal function y for the input x, the computing device may use piecewise approximation.

Since the amount of change in the reciprocal function y is relatively small in the section S ₁ to the section S ₇ , the approximation error between the true value and the approximated value is small even if the calculation device applies linear approximation or polynomial approximation for each section.

However, since the amount of change in the reciprocal function y is relatively large in the section S ₀ , when the computing device applies linear approximation or polynomial approximation for each section, the approximation error between the true value and the approximated value is large.

To reduce approximation error, the computing device maps the input from a domain with a large change in the function to a domain with a small change in the function.

Referring to Figure 9b, the reciprocal function y _t for input t is shown. Input t is the mapped input x.

The amount of change in function y _t for input t is smaller than the amount of change in function y for input x. In other words, the amount of change in the reciprocal function in the range of input t is less than the amount of change in the reciprocal function in the range of input x.

Even if _the input When applying function approximation in the t domain, the approximation error is smaller than when applying function approximation in the x domain.

The computing device can obtain an approximation value of the function y for the input x by converting the approximation result in the t domain back to the domain of the input x.

Hereinafter, the instructions and execution order used to perform preprocessing of input, approximation of a function for the preprocessed input, and postprocessing of the approximation result will be described in comparison with a conventional computing device.

9C and 9D are diagrams for comparing conventional instructions for approximating a reciprocal function and instructions according to an embodiment of the present invention.

Conventional computing devices use Equation 6 to approximate the reciprocal function.

Referring to Equation 6, the conventional computing device calculates the sixth value with 2 as the base and a negative number taken as the exponent of the input. A conventional arithmetic device calculates the function value of the reciprocal function for the mantissa part of the input. A conventional arithmetic device calculates the function value of the reciprocal function for the input by multiplying the sixth value and the reciprocal function value for the mantissa part.

At this time, the conventional arithmetic device can apply section-by-section approximation to the reciprocal function value of the mantissa. A conventional computing device calculates the multiplication of the sixth value and the approximation result to the final approximation value of the reciprocal function for the input x.

Referring to FIG. 8C, instructions for a conventional computing device to perform function approximation according to Equation 6 are shown.

A conventional computing device extracts the exponent part of the input (S900).

A conventional computing device replaces the extracted exponent with a bias (S902).

A conventional computing device calculates the approximation result for the preprocessed input by applying section-by-section approximation to the reciprocal function (S904).

A conventional arithmetic device generates an offset by shifting the original bit to the left by the exponent (S906).

A conventional computing device converts the expression of the offset from INT to FP (S908).

A conventional computing device calculates the final approximation value of the reciprocal function for the input by dividing the approximation result by the offset (S910).

Excluding the instruction in step S904, the conventional computing device uses five instructions to preprocess the input and three instructions to postprocess the approximation result.

In contrast, the computing device according to an embodiment of the present invention calculates the approximation of the reciprocal function using Equation 6, and can obtain the approximate value of the reciprocal function with fewer instructions than a conventional computing device.

The computing device according to an embodiment of the present invention preprocesses the input by replacing the exponent part of the input with a bias, and generates the difference between the exponent part of the input and the bias as an offset (S920).

The computing device calculates the approximation result for the preprocessed input by applying section-by-section approximation to the reciprocal function (S922).

The computing device calculates the final approximation value of the reciprocal function for the input by subtracting the offset from the exponent of the approximation result (S924).

The computing device according to an embodiment of the present invention uses one instruction to preprocess the input and one instruction to postprocess the approximation result, except for the instruction in step S922. Compared to conventional computing devices, the computing device can calculate the approximation of the reciprocal function with a small number of instructions.

Additionally, since the computing device calculates function approximation in a domain where the change amount of the function is small, approximation errors can be reduced compared to function approximation in a domain where the change amount of the function is large.

Table 1 is for comparing the number of conventional instructions and the number of instructions according to an embodiment of the present invention.

function Number of instructions according to the conventional method Number of instructions according to the present disclosure Pretreatment After treatment Sum Pretreatment After treatment Sum exponent (exp) 4 3 7(100%) 2 One 3(43%) log 5 One 6(100%) One One 2(33%) square root (sqrt) 9 4 13(100%) One One 2(15%) Reciprocal of square root (rsqrt) 9 3 12(100%) One One 2(17%) reciprocal 5 3 8(100%) One One 2(25%)

Referring to Table 1, the number of instructions used in the operation method according to an embodiment of the present invention is less than the number of instructions according to the conventional method. Accordingly, the calculation method according to an embodiment of the present invention can reduce overhead to 15 to 43% compared to the conventional method. In Figure 3, steps S300 to S304 are described as being sequentially executed. However, this is merely an exemplary description of the technical idea of an embodiment of the present invention. In other words, a person of ordinary skill in the technical field to which an embodiment of the present invention pertains can change the sequence shown in FIG. 3 and perform one of processes S300 to S304 without departing from the essential characteristics of an embodiment of the present invention. Since the above processes can be applied in various modifications and variations by executing them in parallel, FIG. 3 is not limited to a time series order.

Meanwhile, the processes shown in FIG. 3 can be implemented as computer-readable codes on a computer-readable recording medium. Computer-readable recording media include all types of recording devices that store data that can be read by a computer system. In other words, such computer-readable recording media include non-transitory media such as ROM, RAM, CD-ROM, magnetic tape, floppy disk, and optical data storage devices. Additionally, computer-readable recording media can be distributed across networked computer systems so that computer-readable code can be stored and executed in a distributed manner.

Additionally, the components of the present invention may use integrated circuit structures such as memory, processor, logic circuit, look-up table, etc. These integrated circuit structures execute each function described herein through control of one or more microprocessors or other control devices. Additionally, the components of the present invention may be specifically implemented by a program or portion of code that includes one or more executable instructions for performing specific logical functions and is executed by one or more microprocessors or other control devices. Additionally, the components of the present invention may include or be implemented by a central processing unit (CPU), a microprocessor, etc. that perform their respective functions. Additionally, the components of the present invention may store instructions executed by one or more processors in one or more memories.

The above description is merely an illustrative explanation of the technical idea of the present embodiment, and those skilled in the art will be able to make various modifications and variations without departing from the essential characteristics of the present embodiment. Accordingly, the present embodiments are not intended to limit the technical idea of the present embodiment, but rather to explain it, and the scope of the technical idea of the present embodiment is not limited by these examples. The scope of protection of this embodiment should be interpreted in accordance with the claims below, and all technical ideas within the equivalent scope should be interpreted as being included in the scope of rights of this embodiment.

20: operation system 200: data memory
210: program memory 220: processor

Claims (14)

In a computer implementation method for calculating an approximation of a function for an input expressed in floating point numbers
generating a preprocessed input by replacing the exponent part of the input with a preset value;
generating an offset according to replacement of the exponent part of the input;
calculating an approximation result of a function for the preprocessed input; and
Calculating an approximation of the function for the input by post-processing the approximation result using the offset.
Including,
A method in which the amount of change in the function at the location of the preprocessed input is less than the amount of change in the function at the location of the input. According to paragraph 1,
The step of generating the preprocessed input is,
A method comprising generating the preprocessed input by replacing exponents of the input with a bias. According to paragraph 1,
The step of generating the offset is,
A method comprising generating the offset based on a difference between an exponent of the input and the preset value. According to paragraph 1,
The step of generating the offset is,
A method comprising generating the offset by shifting an original bit by a difference between the exponent of the input and the preset value. According to paragraph 1,
The step of generating the preprocessed input is,
A method comprising replacing the exponent of the input with a different value depending on whether the difference between the exponent of the input and the bias is odd or even. According to clause 5,
The substitution step is,
If the difference value is an even number, generating the preprocessed input by replacing the exponent of the input with a bias,
The step of generating the offset is,
generating the offset by performing a bit shift on the difference between the exponent of the input and the bias. According to clause 5,
The substitution step is,
When the difference value is an odd number, generating the preprocessed input by replacing the exponent part of the input with the sum of a bias and an odd number,
The step of generating the offset is,
Generating the offset by performing a bit shift on the difference between the exponent of the input and the sum. According to paragraph 1,
calculating an approximation of the function,
Computing an approximation of the function for the input based on a sum of the offset and an exponent of the approximation result. According to paragraph 1,
The step of calculating the approximate value of the function is,
Computing an approximation of the function for the input based on a difference between the exponent of the approximation result and the offset. According to paragraph 1,
The step of calculating the approximate value of the function is,
If the approximation of the function for the input is outside the representation range of the floating point system, setting the approximation to either zero or infinity. According to paragraph 1,
Further comprising adjusting the input by multiplying the input by a preset logarithmic value before preprocessing the input,
The step of calculating the approximation result of the function is,
A method comprising calculating an approximation result of an exponential function associated with the preset logarithmic value for the preprocessed input. According to paragraph 1,
The step of calculating the approximate value of the function is,
A method comprising calculating an approximation value of the function for the input by performing a Multiply Accumulate (MAC) operation on the offset, a preset logarithmic value, and the approximation result. Memory for storing instructions; and
It includes a processor that executes the instructions,
The processor,
Generate a preprocessed input by replacing the exponent part of the input with a preset value, and generate an offset according to the substitution of the exponent part of the input,
Calculate the approximation result of the function for the preprocessed input,
By post-processing the approximation result using the offset, an approximation value of the function for the input is calculated,
A computing device, wherein the amount of change in the function at the location of the preprocessed input is less than the amount of change in the function at the location of the input. A computer-readable recording medium recording a computer program for executing the method of any one of claims 1 to 12.

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