WO2021056507A1

WO2021056507A1 - Method for processing floating point number, device, and mobile platform

Info

Publication number: WO2021056507A1
Application number: PCT/CN2019/108872
Authority: WO
Inventors: 徐功林; 刘子男; 韩彬
Original assignee: 深圳市大疆创新科技有限公司
Priority date: 2019-09-29
Filing date: 2019-09-29
Publication date: 2021-04-01
Also published as: CN112189184A

Abstract

A method for processing a floating point number, a device, and a mobile platform. The method comprises: acquiring a processing instruction of a floating point number (S201); at a storage address of a mantissa data segment, reading a high-bit sub-data segment and a low-bit sub-data segment of the mantissa data segment, respectively (S202); according to the numerical value of the high-bit sub-data segment, searching in a preset numerical value table of a corresponding calculation mode for and obtaining a first value (S203); inputting the numerical value of the high-bit sub-data segment and the numerical value of the low-bit sub-data segment into an addition operation unit such that the addition operation unit executes an operation according to an addition operation formula of the corresponding calculation mode so as to obtain a second value (S204); inputting the first value and the second value into a first multiplier to obtain a first product result (S205); and according to the first product result, acquiring the numerical value of a mantissa data segment of an operation result of a floating point number in a calculation mode, and storing same at a mantissa data segment address of the operation result of the corresponding floating point number in the calculation mode (S206). Thus, operation efficiency is improved.

Description

Floating point number processing method, equipment and movable platform

Technical field

The embodiments of the present application relate to the field of data processing technology, and in particular, to a floating-point number processing method, device, and movable platform.

Background technique

In computer systems, the industry has proposed a variety of expressions for real numbers, which are more fixed-point numbers than typical ones. In fixed-point number expressions, the decimal point is fixedly located in the middle of all the real numbers. However, in the fixed-point number expression method, the fixed decimal point position determines the integer part and the decimal part of the fixed number of digits, which is not conducive to expressing very large numbers or very small numbers at the same time. Therefore, the floating-point number expression method was also proposed. Among them, floating-point number is a digital representation of a certain subset of rational numbers, which is used to approximate any real number in a computer. Floating-point calculations refer to operations involving floating-point numbers, which are usually accompanied by approximation or rounding. Generally, simpler operations such as addition, subtraction, multiplication, and comparison can be performed on floating-point numbers. In some application scenarios, floating-point numbers are also required to perform some non-linear operations, such as calculating the reciprocal, calculating the square root, and calculating the reciprocal square root. . However, because the nonlinear calculation process is more complicated, it takes up more processing resources, which reduces the processing efficiency.

Summary of the invention

The embodiments of the present application provide a floating-point number processing method, device, and a movable platform, which improve the operating efficiency of floating-point numbers and reduce hardware costs.

In the first aspect, an embodiment of the present application provides a floating-point number processing method, including:

Acquiring a processing instruction of a floating-point number, the processing instruction is used to indicate a calculation mode of the floating-point number, and the floating-point number includes a mantissa data segment;

At the storage address of the mantissa data section, respectively read the high-order sub-data section and the low-order sub-data section of the mantissa data section;

According to the value of the high-order sub-data segment, the first value is found in a preset value table corresponding to the calculation mode, and the preset value table includes the value of the high-order sub-data segment and calculated by a first calculation formula Correspondence of the results obtained;

Input the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment into an addition unit, so that the addition unit performs an operation according to an addition formula corresponding to the calculation mode to obtain a second value;

Input the first value and the second value to a first multiplier to obtain a first product result;

According to the first product result, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the address of the mantissa data segment corresponding to the operation result of the floating-point number in the calculation mode ；

Wherein, the product of the first operation formula and the addition operation formula constitutes the polynomial part of the Taylor expansion of the function expression corresponding to the calculation mode.

In a second aspect, an embodiment of the present application provides a floating-point number processing device, including: a processor, an addition unit, a first multiplier, a first storage device, and a second storage device;

The first storage device is used to store floating-point numbers and calculation results of floating-point numbers in calculation mode;

The second storage device is used to store preset value tables corresponding to different calculation modes respectively;

The processor is used to:

At the storage address of the mantissa data segment, respectively reading the high-order sub-data segment and the low-order sub-data segment of the mantissa data segment from the first storage device;

According to the value of the high-order sub-data segment, the first value is obtained by looking up the preset value table corresponding to the calculation mode stored in the second storage device, and the preset value table includes the value of the high-order sub-data segment. Correspondence between the value and the result calculated by the first calculation formula;

Input the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment into the addition unit, so that the addition unit performs an operation according to the addition formula corresponding to the calculation mode to obtain a second value;

Input the first value and the second value calculated by the addition unit into a first multiplier to obtain a first product result;

According to the first product result obtained by the first multiplier, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the second storage device corresponding to the float The address of the mantissa data segment of the operation result of the point in the calculation mode;

In a third aspect, an embodiment of the present application provides a movable platform, including: a movable platform body and the floating-point number processing device according to the embodiment of the present application in the first aspect, wherein the floating-point number processing device is installed in the On the movable platform body.

In a fourth aspect, an embodiment of the present application provides a readable storage medium with a computer program stored on the readable storage medium; when the computer program is executed, it implements the float described in the embodiment of the present application in the first aspect. Point processing method.

In a fifth aspect, an embodiment of the present application provides a program product, the program product includes a computer program, the computer program is stored in a readable storage medium, and at least one processor of a removable platform can download from the readable storage medium The computer program is read, and the at least one processor executes the computer program to enable the mobile platform to implement the floating-point number processing method described in the embodiment of the present application in the first aspect.

According to the floating-point number processing method, device and movable platform provided by the embodiments of the present application, the first value is obtained by looking up the value of the upper sub-data segment in the mantissa data segment of the floating-point number in the preset value table corresponding to the calculation mode The preset value table includes the corresponding relationship between the value of the high-order sub-data segment and the result calculated by the first calculation formula; and the value of the high-order sub-data segment and the value of the low-order sub-data segment in the mantissa data segment The numerical value is input to the addition unit, so that the addition unit performs an operation according to the addition formula corresponding to the calculation mode to obtain a second value; then the first value and the second value are input to the first multiplier, Obtain the first product result; and then, according to the first product result, obtain the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode; wherein the product of the first operation formula and the addition operation formula , Constitute the polynomial part of the Taylor expansion of the function expression corresponding to the calculation mode. In this embodiment, the preset value table of the higher sub-data segment in the mantissa data segment corresponding to different types of calculation modes is pre-stored, instead of the preset value table corresponding to the entire mantissa data segment, which reduces the storage capacity of the preset value table. Improved the speed of checking the preset value table. In addition, different types of calculation modes reuse addition units and multipliers, and perform simple linear operations to obtain the results of various types of nonlinear complex operations, reduce hardware costs, and improve computing efficiency.

Description of the drawings

In order to more clearly describe the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description These are some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative work.

Fig. 1 is a schematic architecture diagram of an unmanned aerial system according to an embodiment of the present application;

2 is a flowchart of a floating-point number processing method provided by an embodiment of the application;

FIG. 3 is a schematic diagram of a format of a floating point number provided by an embodiment of the application;

4 is a schematic diagram of the high-order sub-data segment and the low-order sub-data segment in the mantissa data segment of a floating-point number provided by an embodiment of the application;

FIG. 5 is a schematic diagram of the hardware architecture provided by an embodiment of the application;

6 is a schematic structural diagram of a floating-point number processing device provided by an embodiment of the application;

FIG. 7 is a schematic structural diagram of a movable platform provided by an embodiment of this application;

FIG. 8 is a schematic structural diagram of a movable platform provided by another embodiment of the application.

detailed description

In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments It is a part of the embodiments of the present application, but not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by a person of ordinary skill in the art without creative work shall fall within the protection scope of this application.

The embodiments of the present application provide floating-point number processing methods, equipment, and mobile platforms, where the mobile platforms can be handheld phones, handheld PTZ, unmanned aerial vehicles, unmanned vehicles, unmanned ships, robots, or self-driving cars, etc. . The following description of the mobile platform of this application uses drones as an example. It will be obvious to those skilled in the art that other types of drones can be used without restriction, and the embodiments of the present application can be applied to various types of drones. For example, the drone can be a small or large drone. In some embodiments, the drone may be a rotorcraft, for example, a multi-rotor drone that is propelled by multiple propulsion devices through the air. The embodiments of the present application are not limited to this, and the drone It can also be other types of drones.

Fig. 1 is a schematic architecture diagram of an unmanned aerial system according to an embodiment of the present application. In this embodiment, a rotary wing drone is taken as an example for description.

The unmanned aerial system 100 may include a drone 110, a display device 130, and a remote control device 140. Among them, the UAV 110 may include a power system 150, a flight control system 160, a frame, and a pan/tilt 120 carried on the frame. The drone 110 can wirelessly communicate with the remote control device 140 and the display device 130.

The frame may include a fuselage and a tripod (also called a landing gear). The fuselage may include a center frame and one or more arms connected to the center frame, and the one or more arms extend radially from the center frame. The tripod is connected with the fuselage, and is used for supporting the UAV 110 when it is landed.

The power system 150 may include one or more electronic governors (referred to as ESCs) 151, one or more propellers 153, and one or more motors 152 corresponding to the one or more propellers 153, wherein the motors 152 are connected to Between the electronic governor 151 and the propeller 153, the motor 152 and the propeller 153 are arranged on the arm of the UAV 110; the electronic governor 151 is used to receive the driving signal generated by the flight control system 160 and provide driving according to the driving signal Current is supplied to the motor 152 to control the speed of the motor 152. The motor 152 is used to drive the propeller to rotate, thereby providing power for the flight of the drone 110, and the power enables the drone 110 to achieve one or more degrees of freedom of movement. In some embodiments, the drone 110 may rotate about one or more rotation axes. For example, the aforementioned rotation axis may include a roll axis (Roll), a yaw axis (Yaw), and a pitch axis (pitch). It should be understood that the motor 152 may be a DC motor or an AC motor. In addition, the motor 152 may be a brushless motor or a brushed motor.

The flight control system 160 may include a flight controller 161 and a sensing system 162. The sensing system 162 is used to measure the attitude information of the drone, that is, the position information and state information of the drone 110 in space, such as three-dimensional position, three-dimensional angle, three-dimensional velocity, three-dimensional acceleration, and three-dimensional angular velocity. The sensing system 162 may include, for example, at least one of sensors such as a gyroscope, an ultrasonic sensor, an electronic compass, an inertial measurement unit (IMU), a vision sensor, a global navigation satellite system, and a barometer. For example, the global navigation satellite system may be the Global Positioning System (GPS). The flight controller 161 is used to control the flight of the drone 110, for example, it can control the flight of the drone 110 according to the attitude information measured by the sensor system 162. It should be understood that the flight controller 161 can control the drone 110 according to pre-programmed program instructions, and can also control the drone 110 by responding to one or more remote control signals from the remote control device 140.

The pan/tilt head 120 may include a motor 122. The pan/tilt is used to carry the camera 123. The flight controller 161 can control the movement of the pan/tilt 120 through the motor 122. Optionally, as another embodiment, the pan/tilt head 120 may further include a controller for controlling the movement of the pan/tilt head 120 by controlling the motor 122. It should be understood that the pan-tilt 120 may be independent of the drone 110 or a part of the drone 110. It should be understood that the motor 122 may be a DC motor or an AC motor. In addition, the motor 122 may be a brushless motor or a brushed motor. It should also be understood that the pan-tilt can be located on the top of the drone, or on the bottom of the drone.

The photographing device 123 may be, for example, a device for capturing images, such as a camera or a video camera, and the photographing device 123 may communicate with the flight controller and take pictures under the control of the flight controller. The imaging device 123 of this embodiment at least includes a photosensitive element, and the photosensitive element is, for example, a Complementary Metal Oxide Semiconductor (CMOS) sensor or a Charge-coupled Device (CCD) sensor. It can be understood that the camera 123 can also be directly fixed to the drone 110, so the pan/tilt 120 can be omitted.

The display device 130 is located on the ground end of the unmanned aerial system 100, can communicate with the drone 110 in a wireless manner, and can be used to display the attitude information of the drone 110. In addition, the image photographed by the photographing device 123 may also be displayed on the display device 130. It should be understood that the display device 130 may be an independent device or integrated in the remote control device 140.

The remote control device 140 is located on the ground end of the unmanned aerial system 100, and can communicate with the drone 110 in a wireless manner for remote control of the drone 110.

It should be understood that the aforementioned naming of the components of the unmanned aerial system is only for identification purposes, and should not be understood as a limitation to the embodiments of the present application.

Wherein, when processing the image taken by the above-mentioned photographing device 123, the processing of floating-point numbers is involved, and the processing of floating-point numbers can refer to the relevant descriptions in the following embodiments. It should be noted that the processing of floating-point numbers is not limited to the above-mentioned application scenarios, and can also be applied to related fields such as sensors, image transmission, and intelligent driving. The processing of floating-point numbers can all adopt the solutions of the embodiments of the present application.

Fig. 2 is a flowchart of a floating-point number processing method provided by an embodiment of the application. As shown in Fig. 2, the method of this embodiment may include:

S201. Obtain a processing instruction of a floating-point number.

In this embodiment, the floating-point number includes a mantissa data segment, and the floating-point number can also include a sign data segment and an exponent data segment, as shown in FIG. 3, where the sign data segment (s) is a 1-bit (sign) bit. ), the exponent data segment (Exponent) is an 8-bit exponent bit (e), and the mantissa data segment (Mantissa) is a 23-bit decimal place (m). It should be noted that the mantissa data segment omits the implicit bit 1, namely Mantissa The actual representation is 1.m. Therefore, the value represented by the normalized floating point number is:

Val＝(-1) ^sign *2 ^e-bias *(1.m)

And the value of bias is 127.

In this embodiment, a processing instruction for a floating-point number is acquired. The processing instruction is used to indicate a calculation mode of the floating-point number.

), or, calculate the square root (e.g. calculate

), or to calculate the reciprocal of the root (for example, to calculate

), this embodiment is not limited to this.

Among them, the floating-point number processing instruction can be an instruction determined in the process of processing the data. If the floating-point number needs to be reciprocated, it is determined that the obtained calculation mode for indicating the floating-point number is the processing instruction for calculating the reciprocal. ; If it is necessary to perform square root operation on a floating-point number, it is determined that the processing instruction used to indicate that the calculation mode of the floating-point number is the calculation square root is obtained; if it is necessary to perform the reciprocal square root operation on the floating-point number, it is determined to obtain The calculation mode used to indicate the floating-point number is a processing instruction for calculating the reciprocal of the root.

S202: At the storage address of the mantissa data section, read the high-order sub-data section and the low-order sub-data section of the mantissa data section respectively.

In this embodiment, after the processing instruction of the floating-point number is obtained, the storage address of the mantissa data segment of the floating-point number is determined, and then the mantissa data segment is read at the storage address of the mantissa data segment, where the reading of this embodiment The method is to read the high-order sub-data segment and the low-order sub-data segment of the mantissa data segment respectively.

S203: According to the value of the high-order sub-data segment, the first value is obtained by searching in the preset value table of the corresponding calculation mode.

In this embodiment, preset value tables corresponding to different calculation modes are pre-stored, that is, the preset value tables corresponding to different calculation modes may be different. Taking each calculation mode including: calculating the reciprocal, calculating the square root, and calculating the reciprocal square root as an example, this embodiment has three preset value tables pre-stored, namely: the preset value table corresponding to the reciprocal calculation, and the one corresponding to the calculation root. Preset value table, corresponding to the preset value table for calculating the reciprocal root.

In addition, the preset value table includes the corresponding relationship between the value of the upper sub-data segment of each floating-point number and the result calculated by the first calculation formula. Among them, for different calculation modes, the first calculation formula may be different. In this embodiment, after the high-order sub-data segment is read, the first value is obtained from the preset value table corresponding to the calculation mode according to the value of the high-order sub-data segment. The value of the data segment is calculated by the first calculation formula.

S204. Input the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment into the addition unit, so that the addition unit performs the operation according to the addition operation formula corresponding to the calculated mode to obtain the second value.

In this embodiment, after reading the value of the high-order sub-data segment and the value of the low-order sub-data segment, the value of the high-order sub-data segment and the data of the low-order sub-data segment are input to the addition unit, and then the addition unit calculates according to the corresponding The addition formula of the pattern is to perform operations on the value of the upper sub-data segment and the data of the lower sub-data segment to obtain the second value. Among them, for different calculation modes, the corresponding addition operation formula may be different.

It should be noted that the execution order of S203 and S204 is in no particular order.

S205. Input the first value and the second value to the first multiplier to obtain a first product result.

In this embodiment, after the first value and the second value are calculated, the first value and the second value are input to the multiplier. The multiplier is called the first multiplier. The first multiplier combines the first value with the second value. Multiply to obtain a product result, which is called the first product result.

S206: Obtain the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode according to the first product result, and store the mantissa data segment address of the operation result of the corresponding floating-point number in the calculation mode.

In this embodiment, according to the first product result, the value of the mantissa data section of the operation result of the floating-point number in the calculation mode is obtained, and the value of the mantissa data section of the operation result of the floating-point number in the calculation mode is stored. Enter the address of the mantissa data segment corresponding to the operation result of the floating-point number in this calculation mode.

In this embodiment, the first value is found in the preset value table corresponding to the calculation mode according to the value of the upper sub-data segment in the mantissa data segment of the floating-point number, and the preset value table includes the upper sub-data. The corresponding relationship between the value of the segment and the result calculated by the first operation formula; and input the value of the high-order sub-data segment and the value of the low-order sub-data segment in the mantissa data segment into the addition unit, so that the addition unit Perform operations according to the addition formula corresponding to the calculation mode to obtain the second value; then input the first value and the second value into the first multiplier to obtain the first product result; and then according to the first product As a result, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained; wherein, the product of the first operation formula and the addition operation formula constitutes Taylor of the function expression corresponding to the calculation mode The polynomial part of the expansion. In this embodiment, the preset value table of the higher sub-data segment in the mantissa data segment corresponding to different types of calculation modes is pre-stored, instead of the preset value table corresponding to the entire mantissa data segment, which reduces the storage capacity of the preset value table. Improved the speed of checking the preset value table. In addition, different types of calculation modes reuse addition units and multipliers, and perform simple linear operations to obtain the results of various types of nonlinear complex operations, reduce hardware costs, and improve computing efficiency.

In some embodiments, the sum of the number of bits in the high-order sub-data segment and the number of low-order sub-data bits of the mantissa data segment is equal to the number of bits in the mantissa data segment. Take 23 bits in the mantissa data segment as an example (as shown in Figure 4), such as m0-m22, if the number of bits in the upper sub-data segment is 9, that is, m0-m8, correspondingly, the lower sub-data segment The number of digits is 14, which is m9-m22.

Optionally, the number of bits in the upper sub-data segment and the number of bits in the mantissa data segment are determined according to the accuracy of the remainder part corresponding to the Taylor expansion. For example: if the precision of the remainder part is less than or equal to 2-18, the number of bits in the upper sub-data segment is 9. Because in the calculation of the calculation result in the calculation mode, the remainder part corresponding to the Taylor expansion is omitted, so the accuracy of the remainder part is actually related to the accuracy of the calculation result. Therefore, in this embodiment, the accuracy of the calculation result can be adjusted according to actual needs.

In some embodiments, the above-mentioned addition operation unit includes a selector and an adder. Accordingly, a possible implementation of the above-mentioned S204 may include S2041 and S2042:

S2041. Input the numerical value of the low-order sub-data segment to the selector, so that the selector assigns the numerical value of the low-order sub-data segment to the calculation coefficient corresponding to the calculation mode to obtain a third value.

S2042. Input the numerical value of the high-order sub-data segment and the third value to the adder to obtain the second value.

In this embodiment, the numerical value of the low-order sub-data segment is input into the selector, and the selector assigns the numerical value of the low-order sub-data segment to the calculation coefficient corresponding to the calculation mode to obtain the third value, wherein, for different types of calculation modes , The calculation coefficients assigned to the lower sub-data bits may be different. For example: the third value is multiplied by the value of the lower sub-data segment as the third value.

After the third value is obtained, the numerical value of the high-order sub-data segment and the third value are input to the adder, and the adder adds the numerical value of the high-order sub-data segment to the third value, and the value obtained by the addition is used as the second value.

Therefore, this embodiment multiplexes selectors, adders, and multipliers, and performs simple addition and multiplication operations to obtain results of various types of nonlinear complex operations, reduces hardware costs, and improves operation efficiency.

In some embodiments, if the calculation mode includes calculating the reciprocal, the first calculation formula is

The addition operation formula is a+(-1)t. If the calculation mode includes a square root, the first calculation formula is

The addition operation formula is

If the calculation mode includes calculating the reciprocal root, the first calculation formula is

The addition operation formula is

Wherein, a is the value of the upper sub-data segment, and t is the value of the lower sub-data segment.

Among them, the selector may include calculating the reciprocal according to the calculation mode, the calculation coefficient assigned to t is -1, and the third value is (-1)t; the selector may include calculating the square root according to the calculation mode, and the selection is assigned _{to t n} The calculation coefficient is

Get the third value

The selector can include calculating the reciprocal root of the square according to the calculation mode, and select the calculation coefficient given to t as

Get the third value

In some embodiments, a possible implementation manner of obtaining the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode according to the first product result in the foregoing S205 may include S2051-S2052:

S2051. Obtain the value of the preset number of digits after the first preset value in the first product result.

S2052, according to the value of the preset number of digits, obtain the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.

In this embodiment, the preset number of bits is the number of bits in the mantissa data segment, and the number of bits in the mantissa data segment is, for example, 23 bits.

Determine the number of digits of the first preset value in the order from high to low in the first product result. This digit is called the Kth digit, for example, and obtain the Kth in the order from high to low in the first product result. +1 to K+23 digits, and then according to the K+1 digits to K+23 digits, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained. The above-mentioned first preset value is, for example, 1.

In some embodiments, a possible implementation manner of the foregoing S2052 may be:

If the above calculation mode includes the reciprocal calculation, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating point number in the calculation mode. That is, the value of the K+1 to K+23 in the order from high to low in the first product result is determined as the value of the mantissa data segment of the operation result of the floating-point number under the reciprocal calculation .

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the floating-point number is obtained in the calculation mode according to the parity of the value of the exponent data segment of the floating-point number and the value of the preset number of bits. The value of the mantissa data field of the operation result below.

For example: the calculation mode is calculation root, if the value of the exponent data segment of the floating-point number is an odd number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode , That is, the value of the K+1 to K+23 in the order from high to low in the first product result is determined as the operation of the floating-point number under the square root of the calculation or the reciprocal root of the calculation The value of the mantissa data segment of the result.

If the value of the exponent data segment of the floating-point number is an even number, the value of the preset number of digits and the second preset value are input to the second multiplier to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after the first preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode. Optionally, the second preset value is, for example,

After obtaining the second product result, determine the number of digits of the first first preset value (for example, 1) in the order from high to low in the second product result. This digit is called, for example, the Pth digit, and the second product is obtained The value from the P+1 digit to the P+23 digit in the order from high to low in the result, and the value from the P+1 digit to the P+23 digit is determined as the floating point number in the calculation. Or calculate the value of the mantissa data segment of the operation result under the reciprocal root of the square.

For example: the calculation mode is to calculate the reciprocal root. If the value of the exponent data segment of the floating-point number is an even number, the value of the preset digits is used as the mantissa data segment of the operation result of the floating-point number in the calculation mode Numerical value. If the value of the exponent data segment is an odd number, the value of the preset number of digits and the second preset value are input to the second multiplier to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after a preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.

For the symbol data segment of the floating-point number, in some embodiments, after the processing instruction of the floating-point number is acquired, the value of the symbol data segment of the floating-point number is acquired at the storage address of the symbol data segment, and the value of the symbol data segment is obtained according to the symbol data segment. Numerical value, the value of the symbol data segment of the operation result of the floating-point number in the calculation mode is obtained and the address of the symbol data segment corresponding to the operation result of the floating-point number in the calculation mode is stored.

If the calculation mode includes the reciprocal calculation, the value of the symbol data segment is used as the value of the symbol data segment of the operation result of the floating-point number in the calculation mode.

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the third preset value (for example, 0) is used as the value of the symbol data segment of the calculation result of the floating-point number in the calculation mode.

For the exponent data segment in the floating-point number, in some embodiments, after obtaining the processing instruction of the floating-point number, read the value of the exponent data segment at the storage address of the exponent data segment; according to the exponent data The value of the segment, the value of the exponent data segment of the operation result of the floating-point number in the calculation mode is obtained and the address of the exponent data segment corresponding to the operation result of the floating-point number in the calculation mode is stored.

If the calculation mode includes the reciprocal calculation, the value of the exponent data segment of the operation result of the floating-point number in the calculation mode is obtained according to the value of the mantissa data segment and the value of the exponent data segment. Optionally, if the value of the mantissa data segment is the third preset value, the value of 254-E _i is used as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode; If the value of the mantissa data segment is not the third preset value, the value of 253-E _i is used as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode.

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the calculation result of the floating-point number in the calculation mode is obtained according to the parity of the value of the exponent data segment and the value of the exponent data segment The value of the index data segment.

Optionally, the calculation mode includes calculating a square root, and if the value of the exponent data segment is an odd number, then

Determined as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode; if the value of the exponent data segment is an even number, then

The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode.

Optionally, the calculation mode includes calculating the reciprocal root, and if the value of the exponent data segment is an odd number and the value of the mantissa data segment is not equal to a third preset value, then

Determine the value of the exponent data segment as the result of the calculation of the floating-point number in the calculation mode; if the value of the exponent data segment is an odd number and the value of the mantissa data segment is equal to the third preset value, then

Wherein, the aforementioned E _i is the value of the exponent data segment before the calculation.

The following describes the calculation of the reciprocal of floating-point numbers, the calculation of the square root, and the calculation of the reciprocal root of a floating-point number with the hardware architecture shown in Figure 5. Among them, the calculation of the reciprocal, the calculation of the square root, and the calculation of the sign data of the floating-point number before the reciprocal root segment S _i, the index data segment E _i, mantissa data segment M _i. Or the reciprocal of the square root calculation, or the reciprocal square root is calculated for each symbol data segment S _i, the index data segment E _i, the mantissa data segment is calculated as M _i, symbol data segment obtained after calculation is S _0, The exponent data segment is E ₀ , and the mantissa data segment is M ₀ .

Calculate the reciprocal of a floating point number:

_{Therefore, S 0} =S _i can be obtained from the above formula,

Wherein, when M _i = 0, then _{E 0 = 2 * 127-E} i = 254-E i, when M _i ≠ 0, then _{E 0 = 2 * 127-E} i -1 = 253-E i.

S ₀ and E _{0 are} easy to calculate. Therefore, the key to calculating the reciprocal of a floating-point number is to calculate

The numerical value. The following mainly explains _{how to calculate M 0} , among which, the Taylor formula is used to

Expand for calculation.

Let x=a _n +t _n =1.M _i , and the calculation mode is the reciprocal calculation, then set function one:

It can be seen that f(x)∈(0.5,1]

Perform a first-order expansion on this function one:

And the first-order Taylor error term is expressed as:

If the calculated result is accurate to the 18th digit of the mantissa, that is

Thus, t _n ≤ 2 ^-9 .

Among them, a _n includes a total of 9 bits in the mantissa data segment of the floating-point number and m0-m8, and t _n is a total of 14 bits in the mantissa data segment of the floating-point number.

And the above function one can be simplified to

Therefore, when calculating the reciprocal, the first arithmetic formula above is

The above-mentioned addition operation formula is a _n +(-1)t _n .

Meanwhile, a _n may be expressed as:

And k is an integer. According to the different values of k, calculate

Thereby, a preset value table corresponding to the calculated reciprocal is obtained in advance and stored, where k is determined by m0 to m8.

Based on Figure 5, when the reciprocal of a floating-point number needs to be calculated, in the first stage, the selector 1 calculates the reciprocal according to the selected calculation mode, selects E _i to assign the coefficient -1, and outputs -E _{i to the adder 1} . The selector 2 calculates the reciprocal according to the selected calculation mode, and determines the selector 3 corresponding to the calculated reciprocal from the selector 3, the selector 4, and the selector 5. _{If the value of M 0} of the floating-point number is 0, select 254 in selector 3 and output to adder 1, and adder 1 outputs E′ _i =254-E _i to selector 6, if the value of M ₀ of floating-point number If the value is not 0, 253 in selector 4 is selected and output to adder 1, and adder 1 outputs E′ _i =253-E _i to selector 6. The selector 7 calculates the reciprocal according to the selected calculation mode, selects -t _n _{, assigns a coefficient of -1 to the lower sub-data segment (t n} ) of the mantissa data segment in the floating-point number, and outputs it to the adder 2, and the floating-point number The high-order sub-data segment (a _n ) of the mantissa data segment is input to the adder 2, and the adder 2 outputs (a _n -t _n ) to the multiplier 1.

In addition, obtain the preset value table corresponding to the calculated reciprocal from the stored preset value table, and obtain from the preset value table according to the a _{n in the floating point number}

And output to the multiplier 1.

In the second stage, the selector 6 calculates the reciprocal according to the selected calculation mode, and chooses to assign the coefficient 1 _{to E′ i} _{to obtain E 0} =E′ _i and output it to the register 1. Multiplier 1 will (a _n -t _n ) and

Multiply to get

The product of the value of and the value of (a _n -t _n ). The product is 48 bits, for example. Determine the position of the first 1 in the product of 48 bits. This bit is the hidden bit of _{M 0.} The bit starts from the high bit to the low bit and takes 23 bits in order, that is, 24 bits are obtained, and the 24 bits are stored in register 2.

In the third stage, the selector 8 calculates the reciprocal according to the selected calculation mode, obtains the 24-bit value from the register 2 and outputs it to obtain M ₀ . _{In addition, the E 0} stored in the register 1 is obtained and output. At the same time, the selector 9 calculates the reciprocal according to the selected calculation mode, and selects the output S ₀ =S _i . _{Calculating S 0} in the third stage and _{temporarily storing E 0} in the register can ensure that the timing _{of S 0} , E ₀ , and M _{0 in the operation result is synchronized.}

Therefore, this embodiment stores

The reciprocal of the floating-point number is obtained by looking up the table and simple addition and multiplication operations in the preset data table of the operation result. Since this embodiment only stores the operation result of the upper sub-data section in the mantissa data section, the pre-set data table is reduced The storage capacity reduces the hardware cost and also improves the computing efficiency.

Calculate the square root of floating-point numbers:

Therefore, from the above formula, we can get:

Since the square root of a negative number is an invalid operation, S ₀ =0.

If E _i is odd, then

If E _i is even, then

If E _i is odd, then

If E _i is even, then

here

It can be represented by 24'hB504F3.

Expand for calculation.

Let x=a _n +t _n =1.M _i , and the calculation mode is the reciprocal calculation, then set the function two:

It can be seen that

Perform a first-order expansion on this function two:

And the first-order Taylor error term is expressed as:

If the calculated result is accurate to the 18th digit of the mantissa, that is

Thus, t _n ≤ 2 ^-9 .

And the above function two can be simplified to

Therefore, when calculating the square root, the first arithmetic formula above is

The above addition formula is

Meanwhile, a _n may be expressed as:

And k is an integer. According to the different values of k, calculate

Thereby, a preset numerical table corresponding to the square root of the calculation is obtained in advance and stored, where k is determined by m0 to m8.

Based on Figure 5, when the square root of a floating-point number needs to be calculated, in the first stage, the selector 1 calculates the square root according to the selected calculation mode, selects E _i to assign a coefficient of 1, and outputs E _{i to the adder 1} . The selector 2 is the calculation root based on the selected calculation mode, and the selector 4 corresponding to the calculation root is determined from the selector 3, the selector 4, and the selector 5. _{If E i} of the floating-point number is odd, select 127 in selector 4 and output to adder 1, and adder 1 outputs E′ _i =E _i +127 to selector 6, if E _i of the floating-point number is even, Then 126 in the selector 4 is selected and output to the adder 1, and the adder 1 outputs E′ _i =E _i +126 to the selector 6.

The selector 7 calculates the square root according to the selected calculation mode, selects t _n <<1, and assigns _{the low-order sub-data segment (t n} ) of the mantissa data segment in the floating-point number

And output to adder 2. At the same time, the high-order sub-data segment (a _n ) of the mantissa data segment in the floating-point number is input to adder 2, and adder 2 outputs

Give the multiplier 1. In addition, obtain the preset value table corresponding to the square root from the stored preset value table, and obtain it from the preset value table according to the a _{n in the floating point number}

And output to the multiplier 1.

In the second stage, the selector 6 calculates the square root according to the selected calculation mode, and selects E′ _i >>1 to assign coefficients _{to E′ i}

obtain

And output to register 1. Multiplier 1 will

versus

Multiply to get

And the value of

The product of the value of, the product is 48bit, for example, determine the position of the first 1 in the product of 48bit, and take 23bit from the next bit of the bit from high to low, that is, 24bit is obtained, and the 24bit Store in register 2 and output the 24 bits to multiplier 2.

In the third stage, the multiplier 2 multiplies the input 24-bit value

Output a 48-bit product, and then determine the position of the first 1 in the 48-bit product. From the next bit of the bit, take 23 bits from high to low to obtain 24 bits. If E _i is an odd number, selector 8 chooses to obtain the 24-bit value from register 2 and output it to obtain M ₀ , if E _i is an even number, selector 8 selects the 24-bit value obtained through multiplier 2 and outputs it to Obtain M ₀ . _{In addition, the E 0} stored in the register 1 is obtained and output. At the same time, the selector 9 calculates the square root according to the selected calculation mode, and selects the output S ₀ =0. _{Calculating S 0} in the third stage and _{temporarily storing E 0} in the register can ensure that the timing _{of S 0} , E ₀ , and M _{0 in the operation result is synchronized.}

Therefore, this embodiment stores

The pre-set data table of the calculation result of the calculation result is obtained by looking up the table and simple addition and multiplication operations to obtain the root of the floating-point number. Since this embodiment only stores the calculation result of the upper sub-data section in the mantissa data section, the preset data table is reduced The storage capacity reduces the hardware cost and also improves the computing efficiency.

Calculate the reciprocal root of a floating-point number:

Therefore, from the above formula, we can get:

Since the square root of a negative number is an invalid operation, S ₀ =0.

If E _i is odd and M _i =0, then

If E _i is odd and M _i ≠ 0, then

If E _i is even, then

If E _i is odd, then

If E _i is even, then

here

It can be represented by 24'hB504F3.

Expand for calculation.

Let x=a _n +t _n =1.M _i , the calculation mode is the reciprocal calculation, then set the function three:

It can be seen that

Perform a first-order expansion on this function three:

And the first-order Taylor error term is expressed as:

If the calculated result is accurate to the 18th digit of the mantissa, that is

Thus, t _n ≤ 2 ^-9 .

And the above function three can be simplified to

Meanwhile, a _n may be expressed as:

And k is an integer.

In a possible implementation, the above-mentioned first calculation formula can be set as

The above first calculation formula can be set as

The above addition formula is

According to the different values of k, calculate

Thereby, a preset numerical table corresponding to the reciprocal root of the calculation is obtained in advance and stored, where k is determined by m0 to m8.

Based on Figure 5, when it is necessary to calculate the reciprocal root of a floating-point number, in the first stage, the selector 1 calculates the reciprocal root according to the selected calculation mode, chooses to _{assign a coefficient of -1 to E i} , and sends it to the adder 1 Output -E _i . The selector 2 calculates the reciprocal root of the calculation according to the selected calculation mode, and determines the selector 5 corresponding to the reciprocal root of the calculation from the selector 3, the selector 4, and the selector 5. _{If E i} of the floating point number is odd and _{the value of M 0} is 0, then 381 in selector 5 is selected and output to adder 1, and adder 1 outputs E′ _i =381-E _i to selector 6, if floating If the E _i of the point is odd and _{the value of M 0} is not 0, select 379 in selector 5 and output it to adder 1, and adder 1 outputs E′ _i =379-E _i to selector 6, if the floating point number If E _i is an even number, select 380 in selector 5 and output to adder 1, and adder 1 outputs E′ _i =380-E _i to selector 6.

The selector 7 calculates the reciprocal square root according to the selected calculation mode, and selects -(t _n <<1) to assign _{the lower sub-data segment (t n} ) of the mantissa data segment in the floating-point number

And output to the multiplier 1.

obtain

And output to register 1. Multiplier 1 will

versus

Multiply to get

And the value of

In the third stage, the multiplier 2 multiplies the input 24-bit value

Output a 48-bit product, and then determine the position of the first 1 in the 48-bit product. From the next bit of the bit, take 23 bits from high to low to obtain 24 bits. If E _i is an even number, selector 8 chooses to obtain the 24-bit value from register 2 and output it to obtain M ₀ , if E _i is an odd number, selector 8 selects the 24-bit value obtained through multiplier 2 and outputs it, Obtain M ₀ . _{In addition, the E 0} stored in the register 1 is obtained and output. At the same time, the selector 9 calculates the reciprocal root of the calculation according to the selected calculation mode, and selects the output S ₀ =0.

_{Calculating S 0} in the third stage and _{temporarily storing E 0} in the register can ensure that the timing _{of S 0} , E ₀ , and M _{0 in the operation result is synchronized.} Moreover, the first calculation formula in this implementation is

The hardware of the third stage can be made the same as the hardware of the third stage when calculating the prescription, which saves the hardware cost.

In another possible implementation manner, the above-mentioned first calculation formula can be set as

The above addition formula is

According to the different values of k, calculate

Thereby, a preset numerical table corresponding to the reciprocal root of the calculation is obtained in advance and stored, where k is determined by m0 to m8. When need to calculate

, According to the pre-stored m0 to m8 and

The corresponding preset value table of the corresponding relationship to obtain the corresponding

The value of and is obtained by the above addition operation unit

The value of will be obtained through the first multiplier

And the value of

The product of the values, the product is 48bit.

If E _i is an odd number, take the position of the first 1 in the product obtained by the first multiplier and take 24 bits in the order of MSB from high to low, and then multiply by 2 through the second multiplier to obtain a 48-bit product. And determine the position of the first 1 in the product obtained by the second multiplier. This bit is used as _{the hidden bit of M 0} _{, and 23 bits are taken as M 0} in the order from the next bit to the low bit. If E _i is an even number, the position of the first 1 in the product obtained by the first multiplier is taken from high to low in order of 24 bits, and then through the third multiplier and

Multiply to obtain a 48-bit product, and determine the position of the first 1 in the product obtained by the third multiplier. This bit is used as _{the hidden bit of M 0} , starting from the next bit in the order from high to low Take 23bit as M ₀ .

In another possible implementation, there are two preset value tables for calculating the reciprocal root of the square, namely the first preset value table and the second preset value table, and the first preset value table corresponds to E _i as an even number. , Then the above-mentioned first calculation formula corresponding to the first preset value table can be set as

The second preset value table corresponding to E _i is odd, then the above-mentioned first calculation formula corresponding to the second preset value table can be set as

The above addition formula is

According to the different values of k, calculate

In this way, the first preset value table corresponding to the reciprocal root of the calculation is obtained in advance and stored. In addition, according to the different values of k, the calculation

Thereby, a second preset value table corresponding to the reciprocal root of the calculation is obtained in advance and stored, where k is determined by m0 to m8. When need to calculate

, If E _i is an even number, according to the pre-stored m0 to m8 and

The first preset value table of the corresponding relationship to obtain the corresponding

The value of and is obtained by the above addition operation unit

The value of will be obtained through the multiplier

And the value of

The product of the value of, the product is 48bit, and the position of the first 1 in the product of the 48bit is determined. This bit is used as _{the implicit bit of M 0} , and 23bit is taken from the next bit to the low bit in order from the next bit. As M ₀ . If E _i is an odd number, according to the pre-stored m0 to m8 and

The second preset value table of the corresponding relationship to obtain the corresponding

The value of and is obtained by the above addition operation unit

The value of will be obtained through the multiplier

And the value of

The product of the value of, the product is 48bit, and the position of the first 1 in the product of the 48bit is determined. This bit is used as _{the implicit bit of M 0} , and 23bit is taken from the next bit to the low bit in order from the next bit. As M ₀ .

Therefore, this embodiment stores and

The preset data table of the related operation result is obtained by looking up the table and simple addition and multiplication operations to obtain the reciprocal root of the floating-point number. Since this embodiment only stores the operation result of the upper sub-data segment in the mantissa data segment, the preset value is reduced. The storage capacity of the data table reduces the hardware cost and also improves the computing efficiency.

It should be noted that the accuracy of calculating floating-point numbers in each calculation mode can be determined according to the number of bits of the remainder of Taylor expansion, and the remainder can be represented _{by t n.} For example, the number of bits of the remainder, determining the number of bits of the mantissa section data obtained by dividing a _n t _n and the number of bits. The more the number of bits obtained by dividing a _n, the less the number of bits corresponding to t _n, t and thus the number of bits _n corresponding to the remainder of the fewer. Thus, a number of bits by dividing the adjusted and a _n t _n, the result may be adjusted precision floating-point arithmetic. Notably, the more bits a _n, a _n corresponding greater range of possible values (e.g., number of bits. 9 is a _n, a _n is in the range [0, 512)), then the corresponding a _n The storage capacity of the preset data table will increase, and the data quantity of the look-up table will increase. Therefore, in some embodiments, the number of bits can be appropriately adjusted with a _n t _n bits by, sacrifice some amount of computation to improve accuracy.

6 is a schematic structural diagram of a floating-point number processing device provided by an embodiment of the application. As shown in FIG. 6, the floating-point number processing device 600 of this embodiment may include: a processor 601, an addition unit 602, and a first multiplier 603 , The first storage device 604 and the second storage device 605. Optionally, the first storage device 604 and the second storage device 605 may be the same storage device or different storage devices. Optionally, the floating-point number processing device 600 may further include a second multiplier 606.

The first storage device 604 is configured to store floating-point numbers and calculation results of floating-point numbers in calculation mode;

The second storage device 605 is configured to store preset value tables corresponding to different calculation modes respectively;

The processor 601 is configured to:

At the storage address of the mantissa data segment, read the high-order sub-data segment and the low-order sub-data segment of the mantissa data segment from the first storage device 604;

According to the value of the high-order sub-data segment, the first value is obtained by looking up the preset value table corresponding to the calculation mode stored in the second storage device 605, and the preset value table includes the high-order sub-data segment The corresponding relationship between the value of and the result calculated by the first calculation formula;

Input the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment into the addition unit 602, so that the addition unit 602 performs an operation according to the addition operation formula corresponding to the calculation mode to obtain a second value;

Input the first value and the second value calculated by the addition unit 602 into the first multiplier 603 to obtain a first product result;

According to the first product result obtained by the first multiplier 603, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device 604 corresponding to the The address of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

In some embodiments, the addition unit 602 includes a selector 6021 and an adder 6022, and the processor 601 is specifically configured to:

Input the numerical value of the low-order sub-data segment to the selector, so that the selector 6021 assigns the numerical value of the low-order sub-data segment to the calculation coefficient corresponding to the calculation mode to obtain a third value;

The numerical value of the high-order sub-data segment and the third value are input to the adder 6022 to obtain the second value.

In some embodiments, the sum of the number of bits in the upper sub-data segment and the number of lower sub-data bits is equal to the number of bits in the mantissa data segment.

In some embodiments, the number of bits in the upper sub-data segment and the number of bits in the mantissa data segment are determined according to the accuracy of the remainder part corresponding to the Taylor expansion.

In some embodiments, the calculation mode includes calculating the reciprocal, calculating the square root, and calculating the reciprocal square root.

The addition operation formula is a+(-1)t;

If the calculation mode includes a square root, the first calculation formula is

The addition operation formula is

In some embodiments, the processor 601 is specifically configured to:

Acquiring the value of the preset number of digits after the first preset value in the first product result;

Obtaining the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode according to the value of the preset number of digits;

Wherein, the preset number of bits is the number of bits of the mantissa data segment.

In some embodiments, the processor 601 is specifically configured to:

If the calculation mode includes the reciprocal calculation, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.

In some embodiments, the floating point number further includes: an exponent data segment; and the processor 601 is specifically configured to:

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the calculation of the floating-point number in the calculation mode is obtained according to the parity of the value of the exponent data segment and the value of the preset number of bits The value of the mantissa data segment of the result.

In some embodiments, the calculation mode includes calculating a square root, and the processor 601 is specifically configured to:

If the value of the exponent data segment is an odd number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, the value of the preset number of digits and the second preset value are input to the second multiplier 606 to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after the first preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.

In some embodiments, the calculation mode includes calculating the reciprocal root, and the processor 601 is specifically configured to:

If the value of the exponent data segment is an even number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an odd number, the value of the preset number of bits and the second preset value are input to the second multiplier 606 to obtain a second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after the first preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.

In some embodiments, the floating-point number includes a symbol data segment; the processor 601 is further configured to:

At the storage address of the symbol data segment, read the value of the symbol data segment from the first storage device 604;

According to the value of the symbol data segment, the value of the symbol data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device 604 corresponding to the floating-point number in the calculation mode The symbol data segment address of the operation result below.

In some embodiments, the processor 601 is specifically configured to:

If the calculation mode includes a reciprocal calculation, use the value of the symbol data segment as the value of the symbol data segment of the operation result of the floating-point number in the calculation mode;

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the third preset value is used as the value of the symbol data segment of the operation result of the floating-point number in the calculation mode.

In some embodiments, the floating point number includes an exponent data segment; the processor 601 is further configured to:

At the storage address of the index data segment, read the value of the index data segment from the first storage device 604;

According to the value of the exponent data segment, the value of the exponent data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device 604 corresponding to the floating-point number in the calculation mode The address of the exponent data segment of the operation result under.

In some embodiments, the processor 601 is specifically configured to:

If the calculation mode includes the reciprocal calculation, obtain the value of the exponent data segment of the operation result of the floating-point number in the calculation mode according to the value of the mantissa data segment and the value of the exponent data segment;

In some embodiments, the calculation mode includes calculating the reciprocal, and the processor 601 is specifically configured to:

If the value of the mantissa data segment is the third preset value, use the value of 254-E _i as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode;

If the value of the mantissa data segment is not the third preset value, use the value of 253-E _i as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode;

Wherein, E _i is the value of the exponent data segment before calculation.

If the value of the exponent data segment is an odd number, then

The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, then

Wherein, E _i is the value of the exponent data segment before calculation.

If the value of the exponent data segment is odd and the value of the mantissa data segment is not equal to the third preset value, then

If the value of the exponent data segment is an odd number and the value of the mantissa data segment is equal to the third preset value, then

If the value of the exponent data segment is an even number, then

Wherein, E _i is the value of the exponent data segment before calculation.

Optionally, the floating-point number processing device 600 of this embodiment may further include: a memory (not shown in the figure) for storing program codes. The memory is used for storing program codes. When the program codes are executed, the floating-point number The processing device 600 can implement the above-mentioned technical solutions.

The floating-point number processing device of this embodiment can be used to implement the technical solutions of FIG. 2 and the corresponding method embodiment, and its implementation principles and technical effects are similar, and will not be repeated here.

FIG. 7 is a schematic structural diagram of a movable platform provided by an embodiment of the application. As shown in FIG. 7, the movable platform 700 of this embodiment may include: a processor 701, an addition unit 702, a first multiplier 703, and a first multiplier 703. A storage device 704 and a second storage device 705. Optionally, the first storage device 704 and the second storage device 705 may be the same storage device or different storage devices. Optionally, the movable platform 700 may further include a second multiplier 706.

The first storage device 704 is configured to store floating-point numbers and calculation results of floating-point numbers in calculation mode;

The second storage device 705 is configured to store preset value tables corresponding to different calculation modes, respectively;

The processor 701 is configured to:

At the storage address of the mantissa data segment, read the high-order sub-data segment and the low-order sub-data segment of the mantissa data segment from the first storage device 704, respectively;

According to the value of the high-order sub-data segment, the first value is obtained by looking up a preset value table corresponding to the calculation mode stored in the second storage device 705, and the preset value table includes the high-order sub-data segment The corresponding relationship between the value of and the result calculated by the first calculation formula;

Input the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment into the addition unit 702, so that the addition unit 702 performs an operation according to the addition operation formula corresponding to the calculation mode to obtain a second value;

Input the first value and the second value calculated by the addition unit 702 into a first multiplier 703 to obtain a first product result;

According to the first product result obtained by the first multiplier 703, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device 704. The address of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

In some embodiments, the addition unit 702 includes a selector 7021 and an adder 7022, and the processor 701 is specifically configured to:

Inputting the numerical value of the low-order sub-data segment to the selector, so that the selector 7021 assigns the numerical value of the low-order sub-data segment to the calculation coefficient corresponding to the calculation mode to obtain a third value;

The numerical value of the high-order sub-data segment and the third value are input to the adder 7022 to obtain the second value.

The addition operation formula is a+(-1)t;

The addition operation formula is

In some embodiments, the processor 701 is specifically configured to:

In some embodiments, the floating point number further includes: an exponent data segment; and the processor 701 is specifically configured to:

In some embodiments, the calculation mode includes calculating a square root, and the processor 701 is specifically configured to:

If the value of the exponent data segment is an odd number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating point number in the calculation mode;

If the value of the exponent data segment is an even number, the value of the preset number of digits and the second preset value are input to the second multiplier 706 to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after the first preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.

In some embodiments, the calculation mode includes calculating the reciprocal root, and the processor 701 is specifically configured to:

If the value of the exponent data segment is an odd number, the value of the preset number of bits and the second preset value are input to the second multiplier 706 to obtain a second multiplication result, and the second multiplication result is obtained The value of the preset number of digits after the first preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.

In some embodiments, the floating-point number includes a symbol data segment; the processor 701 is further configured to:

At the storage address of the symbol data segment, read the value of the symbol data segment from the first storage device 704;

According to the value of the symbol data segment, the value of the symbol data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device 704 corresponding to the floating-point number in the calculation mode The symbol data segment address of the operation result below.

In some embodiments, the processor 701 is specifically configured to:

In some embodiments, the floating point number includes an exponent data segment; the processor 701 is further configured to:

At the storage address of the index data segment, read the value of the index data segment from the first storage device 704;

According to the value of the exponent data segment, the value of the exponent data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device 704 corresponding to the floating-point number in the calculation mode The address of the exponent data segment of the operation result under.

In some embodiments, the processor 701 is specifically configured to:

In some embodiments, the calculation mode includes calculating the reciprocal, and the processor 701 is specifically configured to:

Wherein, E _i is the value of the exponent data segment before calculation.

If the value of the exponent data segment is an odd number, then

If the value of the exponent data segment is an even number, then

Wherein, E _i is the value of the exponent data segment before calculation.

If the value of the exponent data segment is an even number, then

Wherein, E _i is the value of the exponent data segment before calculation.

Optionally, the movable platform 700 of this embodiment may further include: a memory (not shown in the figure) for storing program codes, the memory is used for storing program codes, and when the program codes are executed, the movable platform 700 can implement the above-mentioned technical solutions.

The movable platform of this embodiment can be used to implement the technical solutions of FIG. 2 and the corresponding method embodiments, and its implementation principles and technical effects are similar, and will not be repeated here.

FIG. 8 is a schematic structural diagram of a movable platform provided by another embodiment of this application. As shown in FIG. 8, the movable platform 800 of this embodiment may include: a movable platform body 801 and a floating-point number processing device 802.

Wherein, the floating-point number processing device 802 is installed on the movable platform body 801. The floating-point number processing device 802 may be a device independent of the movable platform body 801.

Among them, the floating-point number processing device 802 can adopt the structure of the device embodiment shown in FIG. 6, and it can correspondingly execute the technical solutions of the embodiment of FIG. 2 and its corresponding method. Its implementation principles and technical effects are similar, and will not be repeated here. .

A person of ordinary skill in the art can understand that all or part of the steps in the above method embodiments can be implemented by a program instructing relevant hardware. The foregoing program can be stored in a computer readable storage medium. When the program is executed, it is executed. Including the steps of the foregoing method embodiment; and the foregoing storage medium includes: read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), magnetic disks or optical disks, etc., which can store program codes Medium.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the application, not to limit them; although the application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: It is still possible to modify the technical solutions described in the foregoing embodiments, or equivalently replace some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present application. range.

Claims

A floating-point number processing method, characterized in that it comprises:

Acquiring a processing instruction of a floating-point number, the processing instruction is used to indicate a calculation mode of the floating-point number, and the floating-point number includes a mantissa data segment;

At the storage address of the mantissa data section, respectively read the high-order sub-data section and the low-order sub-data section of the mantissa data section;

According to the value of the high-order sub-data segment, the first value is found in a preset value table corresponding to the calculation mode, and the preset value table includes the value of the high-order sub-data segment and calculated by a first calculation formula Correspondence of the results obtained;

Input the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment into an addition unit, so that the addition unit performs an operation according to an addition formula corresponding to the calculation mode to obtain a second value;

Input the first value and the second value to a first multiplier to obtain a first product result;

According to the first product result, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the address of the mantissa data segment corresponding to the operation result of the floating-point number in the calculation mode ；

Wherein, the product of the first operation formula and the addition operation formula constitutes the polynomial part of the Taylor expansion of the function expression corresponding to the calculation mode.
The method according to claim 1, wherein the addition operation unit comprises a selector and an adder, and the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment are input to the addition unit, so that The addition operation unit executes the addition operation formula corresponding to the calculation mode to obtain the second value, including:

Inputting the numerical value of the low-order sub-data segment to the selector, so that the selector assigns the numerical value of the low-order sub-data segment to the calculation coefficient corresponding to the calculation mode to obtain a third value;

The numerical value of the high-order sub-data segment and the third value are input to the adder to obtain the second value.
The method according to claim 1 or 2, wherein the sum of the number of bits in the upper sub-data segment and the number of lower sub-data bits is equal to the number of bits in the mantissa data segment.
The method according to claim 3, wherein the number of bits in the high-order sub-data segment and the number of bits in the mantissa data segment are determined according to the accuracy of the remainder part corresponding to the Taylor expansion.
The method according to any one of claims 1 to 4, wherein the calculation mode includes calculating the reciprocal, calculating the square root, and calculating the reciprocal square root.
The method of claim 5, wherein:

If the calculation mode includes calculating the reciprocal, the first calculation formula is
The addition operation formula is a+(-1)t;

If the calculation mode includes a square root, the first calculation formula is
The addition operation formula is

If the calculation mode includes calculating the reciprocal root, the first calculation formula is
The addition operation formula is

Wherein, a is the value of the upper sub-data segment, and t is the value of the lower sub-data segment.
The method according to any one of claims 1 to 6, wherein the obtaining the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode according to the first product result comprises :

Acquiring the value of the preset number of digits after the first preset value in the first product result;

Obtaining the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode according to the value of the preset number of digits;

Wherein, the preset number of bits is the number of bits of the mantissa data segment.
The method according to claim 7, wherein the obtaining the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode according to the value of the preset number of digits comprises:

If the calculation mode includes the reciprocal calculation, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.
The method according to claim 7, wherein the floating-point number further comprises: an exponent data segment; and the calculation result of the floating-point number in the calculation mode is obtained according to the value of the preset number of digits The value of the mantissa data segment, including:

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the calculation of the floating-point number in the calculation mode is obtained according to the parity of the value of the exponent data segment and the value of the preset number of bits The value of the mantissa data segment of the result.
The method according to claim 9, wherein the calculation mode includes a square root, and the floating-point number is obtained according to the parity of the exponent data segment and the value of the preset number of bits. The value of the mantissa data segment of the calculation result in the calculation mode includes:

If the value of the exponent data segment is an odd number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, the value of the preset number of digits and the second preset value are input to the second multiplier to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after a preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.
The method according to claim 9, wherein the calculation mode includes calculating the reciprocal root of the square, and the floating-point number is obtained according to the parity of the exponent data segment and the value of the preset number of bits. The value of the mantissa data segment of the operation result in the calculation mode includes:

If the value of the exponent data segment is an even number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an odd number, the value of the preset number of digits and the second preset value are input to the second multiplier to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after a preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.
The method according to any one of claims 1-11, wherein the floating-point number comprises a symbol data segment; the method further comprises:

Reading the value of the symbol data segment at the storage address of the symbol data segment;

According to the value of the symbol data segment, the value of the symbol data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the symbol data segment corresponding to the operation result of the floating-point number in the calculation mode address.
The method according to claim 12, wherein the obtaining the value of the symbol data segment of the operation result of the floating-point number in the calculation mode according to the value of the symbol data segment comprises:

If the calculation mode includes a reciprocal calculation, use the value of the symbol data segment as the value of the symbol data segment of the operation result of the floating-point number in the calculation mode;

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the third preset value is used as the value of the symbol data segment of the operation result of the floating-point number in the calculation mode.
The method according to any one of claims 1-13, wherein the floating-point number comprises an exponent data segment; the method further comprises:

Reading the value of the index data segment at the storage address of the index data segment;

According to the value of the exponent data segment, the value of the exponent data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the exponent data segment corresponding to the operation result of the floating-point number in the calculation mode address.
The method according to claim 14, wherein the obtaining the value of the exponent data segment of the operation result of the floating-point number in the calculation mode according to the value of the exponent data segment comprises:

If the calculation mode includes the reciprocal calculation, obtain the value of the exponent data segment of the operation result of the floating-point number in the calculation mode according to the value of the mantissa data segment and the value of the exponent data segment;

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the calculation result of the floating-point number in the calculation mode is obtained according to the parity of the value of the exponent data segment and the value of the exponent data segment The value of the index data segment.
The method according to claim 15, wherein the exponent data segment of the operation result of the floating-point number in the calculation mode is obtained according to the value of the mantissa data segment and the value of the exponent data segment The value of includes:

If the value of the mantissa data segment is the third preset value, use the value of 254-E i as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode;

If the value of the mantissa data segment is not the third preset value, use the value of 253-E i as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode;

Wherein, E i is the value of the exponent data segment before calculation.
The method according to claim 15, wherein the calculation mode includes a square root, and the floating-point number is obtained according to the parity of the value of the exponent data segment and the value of the exponent data segment. The numerical value of the exponent data segment of the calculation result in the calculation mode includes:

If the value of the exponent data segment is an odd number, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

Wherein, E i is the value of the exponent data segment before calculation.
The method according to claim 15, wherein the calculation mode includes calculating the reciprocal root of the square, and obtaining the floating-point number according to the parity of the value of the exponent data segment and the value of the exponent data segment The value of the exponent data segment of the calculation result in the calculation mode includes:

If the value of the exponent data segment is odd and the value of the mantissa data segment is not equal to the third preset value, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an odd number and the value of the mantissa data segment is equal to the third preset value, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

Wherein, E i is the value of the exponent data segment before calculation.
A floating-point number processing device, characterized by comprising: a processor, an addition unit, a first multiplier, a first storage device, and a second storage device;

The first storage device is used to store floating-point numbers and calculation results of floating-point numbers in calculation mode;

The second storage device is used to store preset value tables corresponding to different calculation modes respectively;

The processor is used to:

Acquiring a processing instruction of a floating-point number, the processing instruction is used to indicate a calculation mode of the floating-point number, and the floating-point number includes a mantissa data segment;

At the storage address of the mantissa data segment, respectively reading the high-order sub-data segment and the low-order sub-data segment of the mantissa data segment from the first storage device;

According to the value of the high-order sub-data segment, the first value is obtained by looking up the preset value table corresponding to the calculation mode stored in the second storage device, and the preset value table includes the value of the high-order sub-data segment. Correspondence between the value and the result calculated by the first calculation formula;

Input the numerical value of the high-order sub-data segment and the numerical value of the low-order sub-data segment into the addition unit, so that the addition unit performs an operation according to the addition formula corresponding to the calculation mode to obtain a second value;

Inputting the first value and the second value calculated by the addition unit into a first multiplier to obtain a first product result;

According to the first product result obtained by the first multiplier, the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the second storage device corresponding to the float The address of the mantissa data segment of the operation result of the point in the calculation mode;

Wherein, the product of the first operation formula and the addition operation formula constitutes the polynomial part of the Taylor expansion of the function expression corresponding to the calculation mode.
The device according to claim 19, wherein the addition operation unit comprises a selector and an adder, and the processor is specifically configured to:

Inputting the numerical value of the low-order sub-data segment to the selector, so that the selector assigns the numerical value of the low-order sub-data segment to the calculation coefficient corresponding to the calculation mode to obtain a third value;

The numerical value of the high-order sub-data segment and the third value are input to the adder to obtain the second value.
The device according to claim 19 or 20, wherein the sum of the number of bits in the upper sub-data segment and the number of lower sub-data bits is equal to the number of bits in the mantissa data segment.
The device according to claim 21, wherein the number of bits of the high-order sub-data segment and the number of bits of the mantissa data segment are determined according to the accuracy of the remainder part corresponding to the Taylor expansion.
The device according to any one of claims 19-22, wherein the calculation mode comprises calculating the reciprocal, calculating the square root, and calculating the reciprocal square root.
The device of claim 23, wherein:

If the calculation mode includes calculating the reciprocal, the first calculation formula is
The addition operation formula is a+(-1)t;

If the calculation mode includes a square root, the first calculation formula is
The addition operation formula is

If the calculation mode includes calculating the reciprocal root, the first calculation formula is
The addition operation formula is

Wherein, a is the value of the upper sub-data segment, and t is the value of the lower sub-data segment.
The device according to any one of claims 19-24, wherein the processor is specifically configured to:

Acquiring the value of the preset number of digits after the first preset value in the first product result;

Obtaining the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode according to the value of the preset number of digits;

Wherein, the preset number of bits is the number of bits of the mantissa data segment.
The device according to claim 25, wherein the processor is specifically configured to:

If the calculation mode includes the reciprocal calculation, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.
The device according to claim 25, wherein the floating point number further comprises: an exponent data segment; and the processor is specifically configured to:

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the calculation of the floating-point number in the calculation mode is obtained according to the parity of the value of the exponent data segment and the value of the preset number of bits The value of the mantissa data segment of the result.
28. The device according to claim 27, wherein the calculation mode includes calculating a square root, and the processor is specifically configured to:

If the value of the exponent data segment is an odd number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, the value of the preset number of digits and the second preset value are input to the second multiplier to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after a preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.
The device according to claim 27, wherein the calculation mode comprises calculating the reciprocal root, and the processor is specifically configured to:

If the value of the exponent data segment is an even number, the value of the preset number of digits is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an odd number, the value of the preset number of digits and the second preset value are input to the second multiplier to obtain the second multiplication result, and the second multiplication result is obtained. The value of the preset number of digits after a preset value is used as the value of the mantissa data segment of the operation result of the floating-point number in the calculation mode.
The device according to any one of claims 19-29, wherein the floating-point number comprises a symbol data segment; and the processor is further configured to:

At the storage address of the symbol data segment, read the value of the symbol data segment from the first storage device;

According to the value of the symbol data segment, the value of the symbol data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device corresponding to the floating-point number in the calculation mode The address of the symbol data segment of the result of the operation.
The device according to claim 30, wherein the processor is specifically configured to:

If the calculation mode includes a reciprocal calculation, use the value of the symbol data segment as the value of the symbol data segment of the operation result of the floating-point number in the calculation mode;

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the third preset value is used as the value of the symbol data segment of the operation result of the floating-point number in the calculation mode.
The device according to any one of claims 19-31, wherein the floating-point number comprises an exponent data segment; and the processor is further configured to:

Reading the value of the index data segment from the first storage device at the storage address of the index data segment;

According to the value of the exponent data segment, the value of the exponent data segment of the operation result of the floating-point number in the calculation mode is obtained and stored in the first storage device corresponding to the floating-point number in the calculation mode The address of the exponent data segment of the result of the operation.
The device according to claim 32, wherein the processor is specifically configured to:

If the calculation mode includes the reciprocal calculation, obtain the value of the exponent data segment of the operation result of the floating-point number in the calculation mode according to the value of the mantissa data segment and the value of the exponent data segment;

If the calculation mode includes the calculation of the square root or the calculation of the reciprocal root of the square, the calculation result of the floating-point number in the calculation mode is obtained according to the parity of the value of the exponent data segment and the value of the exponent data segment The value of the index data segment.
The device according to claim 33, wherein the calculation mode includes calculating a reciprocal, and the processor is specifically configured to:

If the value of the mantissa data segment is the third preset value, use the value of 254-E i as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode;

If the value of the mantissa data segment is not the third preset value, use the value of 253-E i as the value of the exponent data segment of the operation result of the floating-point number in the calculation mode;

Wherein, E i is the value of the exponent data segment before calculation.
The device according to claim 33, wherein the calculation mode includes calculating a square root, and the processor is specifically configured to:

If the value of the exponent data segment is an odd number, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

Wherein, E i is the value of the exponent data segment before calculation.
The device according to claim 33, wherein the calculation mode comprises calculating a reciprocal root, and the processor is specifically configured to:

If the value of the exponent data segment is odd and the value of the mantissa data segment is not equal to the third preset value, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an odd number and the value of the mantissa data segment is equal to the third preset value, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

If the value of the exponent data segment is an even number, then
The value of the exponent data segment determined as the operation result of the floating-point number in the calculation mode;

Wherein, E i is the value of the exponent data segment before calculation.
A movable platform, comprising: a movable platform body and the floating-point number processing device according to any one of claims 19-36, wherein the floating-point number processing device is installed on the movable platform body on.
The mobile platform according to claim 37, wherein the mobile platform comprises a handheld phone, a handheld pan/tilt, a drone, an unmanned vehicle, an unmanned boat, a robot, or an autonomous vehicle.
A readable storage medium, characterized in that a computer program is stored on the readable storage medium; when the computer program is executed, the floating-point number processing method according to any one of claims 1-18 is realized.