Using a Fixed Point Math Library
Contents
1. ISO IEC TR 18037 2008 Programming Languages C Extensions to support Embedded Processors Website and Support Renesas Technology Website http www renesas com Inquiries http www renesas com inquiry csc renesas com Revision Record Description Rev Date Page Summary 1 00 Sept 01 09 First edition issued REU05B0116 0100 Rev 1 00 November 2009 Page 14 of 15 l SH2 SH2A Family E EN ESAS Using a Fixed Point Library Notes regarding these materials 1 This document is provided for reference purposes only so that Renesas customers may select the appropriate Renesas products for their use Renesas neither makes warranties or representations with respect to the accuracy or completeness of the information contained in this document nor grants any license to any intellectual property rights or any other rights of Renesas or any third party with respect to the information in this document 2 Renesas shall have no liability for damages or infringement of any intellectual property or other rights arising out of the use of any information in this document including but not limited to product data diagrams charts programs algorithms and application circuit examples 3 You should not use the products or the technology described in this document for the purpose of military applications such as the development of weapons of mass destruction or for the purpose of any other military use When exporting2. safety margin This means you can add two numbers of the same resolution without worrying about overflow If you need to add more than two numbers you will have to scale if your numbers will cause an overflow Finally as a general rule we will pick the size of variable then pick the resolution we will need to fit this range into the magnitude of the number Sometimes this means we will carry extra resolution bits but this is usually not an issue since the library will multiply and normalize on its return so it costs us little REU05B0116 0100 Rev 1 00 November 2009 Page 6 of 15 l SH2 SH2A Family m EN ESAS Using a Fixed Point Library For the following example we will assume a 12 bit ADC with an input voltage range Vef range of SVDC You can adjust the equations accordingly for 3 3V operation Also Code in these examples if written for clarity Example 1 Voltage Sensor Assume you need to monitor an incoming DC bus voltage in a lighting control design To do this you use a simple voltage divider on the DC bus and apply it to the input of the ADC Since this is a line powered application you need to divide it down by about 100 1 You re resulting schematic is shown in Figure 5 with V_BUS attached to the ADC HIGH VOLTAGE R40 475K 14W 1 R42 475K 1 4W 1 D12 200mA 40V y Figure 5 Voltage Monitor You chose to do all you work with 16 Bit Fixed Point math but you want to choose a resolution t
3. R rather than izi x Re asx s ee ko R ETEC H OO FFF8018E R motor_volts_M10 D 2630 FFF80198 R motor_volts_float 2 568359 FFF80100 R current measured M10 D 2160 FFF80104 R current_measured float 2 109375 FFF80108 3 R buffer Current OK FFF8010 R 0 H 43 c FFF8010c R i H 75 u FFF8010D R 2 H 72 r FFF8010E R 3 H 72 r FFF8010F R 4 H 65 e FFF80110 R 5 H 6e n FFF80111 R 6 H 74 t FFF80112 R 7 H 20 FFF80113 R 8 H 4f O FFF80114 R 9 H 4b K FFF80115 R 10 H 2e FFF80116 R 11 H 2e FFF80117 R 12 H OO FFF80118 R 13 H OO FFF80119 R 14 H OO FFF80114A R 15 H OO FFF8011B R 16 H OO FFF8011C R 17 H OO FFF8011D R 18 H OO FFF8011E R 19 H OO FFFSO11F 4 gt A gt Watchi A watch2 A watchs A watcha Figure 1 Watch Window 3 3 Simulating Motor Voltage Generation When ad_demo 0 the demonstration generates a simulated motor voltage out of the PWM channels in complementary mode For the Motor voltage demonstration we picked a value that could easily be both simulated and verified in the demonstration For this demo it is set up to generate simulate Sine wave voltages to the Motor of 0 5V so functionality can easily be confirmed with an oscilloscope By varying the potentiometer which represents the commande
4. zixl x RRi os x B jor g x RR Sx ad dero FFFEOLGE Value 2l R motor_volts_M10 D 2630 FFF80198 R ad demo H 01 FFF8018 R motor_volts_float 2 568359 FFF80100 R antok volts M10 D 5115 FFF80198 R current measured M10 D 2160 FFF80104 a 4 99 R current_measured_float 2 109375 FFF80108 R motor_volts_float 4 995117 FFF6010 amp R buffer current OK FFFS010 R current_measured M10 D 5297 FFF80104 R 0 H 43 C FFF8010C R current_measured float 5 172852 FFF8010i R 1 H 7S u FFF8010D R buffer Over Current F R 2 H 72 r FFF8010E R 0 H 4f O FFF8010 R 3 H 72 r FFF8010F R fogs igi Gara R 4 H 65 e FFF80110 1 a b SRE l R 5 H 6e n FFF80111 R 2 H 6S e FFF80101 R 6 H 74 t FFF80112 R 3 H 72 r FFF8010 R 7 H 20 FFF80113 R 4 H 2d FFF8011 R 8 H 4f O FFF80114 R 5 H 43 C FFF8011 R 9 H 4b K FFF80115 z ne R 10 H Ze FFF80116 R 6 H 75 u PFF8011 R 11 H 2e FFF80117 R 7 H 72 xr PFF8011 R 12 H OO FFF80118 R 8 H 72 r FFF8011 R 13 H OO FFF80119 R 9 H 65 e FFF8011 R 14 H OO FFF8011A R k i iy R 15 H OO FFF8011B 20 R 16 H 00 FFF8011C R 11 H 74 t FFF8011 R 17 H OO FFF8011D R 12 H 00 FFF8011 R 18 H OO FFF8O11E R 13 H 00 FFF8011 R 19 H OO FFF8O11F R 14
5. H 00 FFF8011 R 15 H 00 FFF8011 R 16 H 00 FFF80111 s 4 a F watchs Watcha A Watch3 A Watcha 4 gt Watch Watch2 A Watch3 Watch4 Figure 4 Watch Windows showing Normal and Over Current Detection REU05B0116 0100 Rev 1 00 November 2009 Page 5 of 15 SH2 SH2A Family 4 Selecting Resolutions for Variables It is important to select the proper resolutions when using a fixed point library You can simply select a resolution and live with the resulting rounding error or you can select the maximum resolution minimize the rounding error and provide the dynamic range required by your application In addition you must be aware that large number may cause overflow errors in your calculations It is recommended that you check the ranges of the math used on your fixed point numbers including making sure some of the intermediate values do not cause overflow Picking resolutions that do not have you carrying around excess fractional bits i e bits not needed to meet the accuracy requirements of your system will reduce the chances of overflowing your results when you add or do scaled multiply operations Before we jump into the hardware examples it might be good to discuss some Fixed Point Basics starting with notation Qf This notation just designates the number of fractional bits f and not the size of the number For example Q5 only says that there are 5 fractional
6. are in 2 so 1 bit is 12800 Assume we read 3072 from the ADC now intuitively we know that this is 12 5A but let s go through the math Subtract 0 current offset 3072 2048 1024 1024 0 012207031 in 2 2 AMPS in 2 so your current is 1024 12800 2 3200 but remember this is 2 so your current is 3200 2 12 5A Code wise with the Fixed Point library this would look something like this NOTE the zero current offset is hard coded in this example Actual Zero Current Offset could be determined in software at run time Comment on Coding Style In this demo we chose to add a suffix on the variables that are in fixed point format We chose to do this so we did not have to keep referring back to the declaration to determine its resolution If we see a variable xyz M10 we know it is in resolution 10 So one example of how this helps keep things straight is in the scaled multiply If you multiply abc_M5 and def M7 and you are putting it into a variable xyz_M1 0 you know you need to scale back by 2 Some may chose to use prefix such as FIX 0_abc either way it is a good idea to do whatever necessary to keep your resolutions correct REU05B0116 0100 Rev 1 00 November 2009 Page 8 of 15 l SH2 SH2A Family E EN ESAS Using a Fixed Point Library define I ADC BIT 12800L OLZZOTOSL im 2 20 define OVER_CURRENT 5120L 20 volts in 2 8 tdefine ZERO I _ OFFSET 2048L Midpoint on 12 bit ADC EIXOS MOTOT CUrren
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10. Build Configurations iodefi Linkage Order MCRF Generate Makefile proc_macros _def h common_def h ixmath h Figure 9 Build Toolchain Menu SuperH RISC engine Standard Toolchain 2 xj Configuration C C Assembly Link Library Standard Library CPU 4 gt Debug z enu B a All Loaded Projects pree citoi S FP Demo cael flirayfies S files C source file C source file H E C C gt Assembly Assembly source file Linkage symbol file orev orev 4 4 I Use entry point mm control Jauto Options Link Library noprelink rom D R nomessage list CONFIGDIR PROJECT NAME map nooptimize start DVECTTBL DINTTBL 00 PResetPRGPintPRG 08 v xl Figure 10 Link Library Tab REU05B0116 0100 Rev 1 00 November 2009 Page 12 of 15 2E NESAS SH2 SH2A Family Using a Fixed Point Library source file C source file C C gt Assembly ea Up Down E noprelink pN nomessagi 1 fist CO1 FIGDIR SPROJECTNAME map nooptimize 2 NetcDVECTTBLDINTTBL O0 PR esi bAG PlntPRG 08 xl smmm A ers e Figure 11 Adding Library Directory 7 Glossary FPU Floating Point Unit QSG Quick Start Guide REU05B0116 0100 Rev 1 00 November 2009 Page 13 of 15 SH2 SH2A Family References Fixed Point Library Users Manual REJO5J0001 0101 Wikipedia http en wikipedia org wiki Fixed point_arithmetic
11. Hz M 5 00rms 29 Sep 03 13 30 CH1 2 00VBy al xl RR OX R ad_demo H 00 FFF8018E R motor_volts_M10 D 5120 FFF80198 R motor_volts_ float 5 FFF80100 R current_measured M10 D O FFF80104 R current_measured_float 0 FFF80108 R buffer FFF8010C Figure 3 Sine wave full voltage generated post RC filter and Associated Watch Values REU05B0116 0100 Rev 1 00 November 2009 Page 4 of 15 l SH2 SH2A Family E EN ESAS Using a Fixed Point Library 3 4 Simulating Current Readings When ad_demo 1 the demonstration uses the potentiometer to simulate the input from a current sensor Since the variables are set for auto update simply double click the ad_demo entry and change the value to 1 in the dialog box Once ad_demo equals 1 the potentiometer readings will be reflected in the current measured_M10 The potentiometer is scaled to simulate a sensor that reads from 0 to 10 amperes full scale in resolution 2 The floating point value will be displayed in current measured _float In the demonstration we set the Over current value to 5 Amperes Note that when you cross 5 Amperes the string in the buffer goes from Current OK to Over Current NOTE current measured _float is only used for readability It would not be used in normal motor control applications rather you would work with the fixed point version current_measured_M10
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14. ancel IV Relative Path J Hide Project Files y LA Figure 8 Select Fixed Point Library file NOTE Be sure to select the correct library based on device type being used SH2 or SH2A REU05B0116 0100 Rev 1 00 November 2009 Page 11 of 15 QE NESANS l SH2 SH2A Family Using a Fixed Point Library 6 2 As Library in Build Environment The SH2A Fixed Point Library is simple to add as a common library to any existing HEW project To incorporate the Library from a central library directory into an existing project navigate through the menu Build gt SuperH RISC Engine Standard Toolchain gt Link Library Tab gt Library Files gt Add See figures Figure 9 through Figure 11 This project will now always use the lib file at this directory location when a build is performed In this example Library is in a folder named UserLib For more information on Library files refer to the HEW User s Manual 3FP_Demo High performance Embedded Workshop FP_Demo c pit 2 gt File Edit View Project Build Debug Setup Tools Test Window Device Help iD ech g 8 EA SuperH RISC engine Standard Toolchain SS eel eae Lint eem 0 8 ioe E e ea eg Ctrl F7 A a Multiple El C source file Clean Current Project a2 we Av ey Clean All Projects ch ee Update All Dependencies al 2 Stop Tool Execution Ctrl Break proc_ Include Exclude Build E ype_ B E dbsct c Build Phases Z typed a El OA _dbc
15. bits and does not say number of bits Typically Signed 16 or 32 bit variables are used Qm f This form define both the magnitude m and the Fractional part f A number like Q3 28 says that you have 3 integer bits and 28 fractional bits With 1 sign bit this fits in a signed 32 bit variable fxm b Similar to Qm f it use the second bit number b to describe the number of bits this a number like fx1 6 is fixed point number with magnitude bit and 15 fractional bits s m f This describe the whole number sign s magnitude m and fractional part f So a number like 0 8 0 describe an unsigned 8 bit integer Next we will look at some of the basic rules In fixed point arithmetic we are basically doing exponential arithmetic so we have to abide the rule for exponential arithmetic Adding amp Subtracting to add or subtract fixed point numbers they must be the same resolution For example to add a Q5 and a Q7 you must convert one of them In general you would convert the lower resolution up to the higher resolution because it would simply mean shifting in 0 s on the LSB end and thus not affecting the actual answer Multiplying to multiply you simply multiply the numbers and add the Q factor to determine the resolution of the new number In general this is not a problem for two reasons a most modern MCUs have a hardware multiplier and secondly most libraries will use the correct intermediate value for 16x16 32 bit res
16. d voltage the motor voltage will go from 0 5 Volts The fixed point value in resolution 2 will be displayed in the watch window in motor_volts M10 The equivalent floating point will be displayed motor_volts_float The Motor Volts can be viewed as an output by adding a simple RC filter to the PWM output pin Select the RC time constant such that it filters the 20 kHz carrier while not filtering the fundamental 50Hz The scope shots will look as seen in Figure 2 and Figure 3 NOTE motor_volts float is only used for readability It would not be used in normal motor control applications rather you would work with the fixed point version motor_volts_ M10 REU05B0116 0100 Rev 1 00 November 2009 Page 3 of 15 rCENESAS SH2 SH2A Family Using a Fixed Point Library CURSOR Type Source CH1 Tek EE Acq Complete M Pos 2 360ms aY 256V Cursor 2 1 28 CH1 Z 2 564 lt 10Hz M 5 00ms 29 Sep 03 13 30 CH1 2 00VBy zixl RRimgx Name R ad demo H 00 FFF8018E R motor_volts_M10 D 2565 FFF80198 R motor_volts_float 2 504883 FFF80100 R current_measured M10 D O FFF80104 R current _ measured float 0 FFF80108 R buffer FFF8010C Figure 2 Sine wave half voltage generated post RC filter and Associated Watch Values CURSOR Type Source CH1 M Pos 2 360ms Tek Ja Stop aY 5 264 Cursor 1 0 004 CH1 Y 2 564 50 0461
17. e If ad_demo is set to logic 1 the potentiometer will be used to simulate the reading from a current sensor and the resulting values displayed in the watch window We provided two scenarios to give examples that the resolution and size of variables are determined by the system requirements The engineer can choose these based on the range of numbers he needs to represent as well as the dynamic range he needs for his control system to operate properly IMPORTANT NOTE The demonstration code calls the floating point library in order to display the actual values in the watch windows When using the Fixed Point library it is never required to convert the fixed point values to floating point for your calculations control loops etc There may be some reasons for converting Fixed Point to Floating Point such as displaying fixed point values in easily readable floating point form on the User Interface or sending data to another program MCU that might need Floating Point results However the fixed point versions of the variables are all you need to use in the math application itself REU05B0116 0100 Rev 1 00 November 2009 Page 2 of 15 l SH2 SH2A Family E EN ESAS Using a Fixed Point Library 3 2 Adding Correct Watch Variable The project built session is saved with the correct watch variable for the demonstration assigned In the event the session is not correct add the correct watch variables as shown in Figure 1 Be sure they are set to Auto update
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19. emo Requirements scernu aa ener ceca aa a E i E aa a iaa 2 2 Building the Code cee eee enn ne irinin tenant ee eee ENAR ANNAA AE NEERA A NAANA ANEREN AEREE AEAEE EE 2 3 Running the Demonstration Code eccccceceeeeeeeeeeeeeeeeeeeeeseeeeeeseeeeeeeseeeaeeeeeeeeaeeeseeaeeeseenaeeeseenaees 2 4 Selecting Resolutions for Variables 0 0 00 ceccceeeeeeeeeeeeee eee eeneeeee eee ee tees eeeeeeeeeeiaeeeseeneeeessneeeeeeaes 6 5 Multiple Build Configurations ssenari A ceased eden Seen eae 9 6 Appendix A Library Usage in HEW 3 ccccvssncccsssncccesspnnndevestnneces ssecces ARRAN ENAERE EKNER 10 Ue GIOSSANY ate vea eae etlcee a vie eed Aa eee a Sees 13 REU05B0116 0100 Rev 1 00 November 2009 Page 1 of 15 SH2 SH2A Family 1 Demo Requirements The following items are required in order to build and run this demonstration 1 1 Required Renesas Development Tools software The following tools and their versions are required for building the demonstration and following the tutorial Evaluation editions of these tools are all available for download from our website e High performance Embedded Workshop HEW Version 4 06 xx xx or later http www renesas com download Web Search Keyword High performance Embedded Workshop e Renesas SuperH RISC Engine Standard Toolchain Version 9 3 Release 00 or later http www renesas com download Web Search Keyword SuperH Compiler 1 2 Required Hardware for Demo The following item
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21. ics products or if you have any other inquiries Note 1 Renesas Electronics as used in this document means Renesas Electronics Corporation and also includes its majority owned subsidiaries Note 2 Renesas Electronics product s means any product developed or manufactured by or for Renesas Electronics RENESAS APPLICATION NOTE SH2 SH2A Family Using a Fixed Point Math Library Introduction The purpose of this application note is to give examples of using the Fixed Point Math library for the SH2 and SH2A families In many applications it is necessary to maintain accuracy when doing math and floating point type calculations are desirable However many smaller microcontrollers do not have an FPU available When this happens engineers typically resort to fixed point math which can help maintain the best dynamic range while using the Integer math instructions and multiplier hardware of a non FPU microcontroller unit This application note does not review Fixed Point concepts or number ranges those are left to the Fixed Point Library Users manual see references section Rather this attempts to give examples of real life uses of fixed point libraries NOTE This application note is not intended for the SH2A families with integrated FPU in the core although it may be helpful in these devices when receiving fixed point data from other Microcontrollers and or applications Target Device SH2 SH2A Contents 1 D
22. o minimize your error You must evaluate the range of the number Therefore maximum HIGH_VOLTAGE measurable is Vref R40 R42 R43 5 950K 10K 480 volts In order to fit this into a 16 bit fixed point representation and cover the range let s assume bit for sign and one bit for safety margin Therefore we will use 14 bit and a resulting resolution of Log 2 480 5 09 or resolution 5 This means to represent the maximum value of 480 volts we should use FIX5 resolution So 480 volts would result in a value of 15360 Your ADC bit weight would then be 480 4096 or 0 1171875 Using the same reasoning we should then use a resolution of Log 2 0 117875 17 084 so round down 17 so numbers read from ADC are in 2 so 1 bit is 15360 So suppose we read 2048 from the ADC intuitively we know that is 240VDC but let s go through the math 2048 0 117875 in 2 2 HIGH_VOLTAGE in 2 so your HIGH_VOLTAGE is 2048 15360 2 7680 but remember this is 2 so your voltage is 7680 2 240VDC Code wise with the Fixed Point library this would look something like this REU05B0116 0100 Rev 1 00 November 2009 Page 7 of 15 QE NESAS SH2 SH2A Family Using a Fixed Point Library define VBUS ADC BIT 15360 0 117975 im 2 17 define BUS_OVERVOLTAGE 12800L 400 volts in 2 5 TS high voltage 0 O until read by ADC void reac bws voltage void FIX17 raw_reading
23. oject To incorporate the Library locally into an existing project drag and drop the SH2A Fixed Point Library folder into the project directory where you are working Then simply navigate through the menu Project gt Add Files to Project gt Library See Figure 6 through Figure 8 This will make it local to this project For more information on Library files refer to the HEW User s Manual 3FP_Demo High performance Embedded Workshop FP_Demo c Deug Set Current Project Insert Project e ow is Dependent Projects a P Edit Project Gonfiquration Create Project Type Add Files Remove Files File Extensions Components ied Figure 6 Add File Add files to project FP_Demo 2 x Look in O FixedP_Demo e e Ee Debug Debug_SH 24_FLASH_E104 USB_SYSTE Release SimDebug_SH24 FPU_Cycle SimDebug_SH24 FPU_Func Files of type Library file LIB gt Cancel Library file LIB Library information file LBP Preprocessed C source file P Preprocessed C source file PP tratara tta t Profile file PRO Relocatable file REL KKK ES main Figure 7 Select LIB type REU05B0116 0100 Rev 1 00 November 2009 Page 10 of 15 SH2 SH2A Family ax _ Lookin o SH_FixLib Ex al sh2fix lib File name Jsh2afix lib Files of type Library file LIB 7 C
24. raw_reading get AD data V_BUS Fixed Point Multiply scaled back by 2 12 results in 2 5 value high voltage FIX mul SCALE12 raw_ reading VBUS_ADC BIT Example 2 Current Sensor Assume you need to monitor current in a motor winding in a motor control design So you chose a high side DCCT DC Current Transducer From the data sheet you see that it outputs a signal at 1 OOmV A So your full current range is 2 5 100mV A or 25A or a range of 50A NOTE Remember for these examples a reading of 2048 1 2 full scale is actually 0A since this is a bi directional current sensor i e current flows and is measured in both directions You chose to do all you work with 16 Bit Fixed Point math but you want to choose a resolution to minimize your error So you must evaluate the range of the number The DCCT determines the maximum current we can measure In order to fit this into a 16 bit fixed point representation and cover the range let s assume 1 bit for sine and one bit for safety margin Therefore we will use 14 bit and a resulting resolution of Log 2 50 8 35 so you use resolution 8 This means to represent the maximum value of 25 volts we should use FIX8 resolution So 25A would result in a value of 6400 Your ADC bit weight would then be 25 4096 12 bit ADC or 0 012207031 Using the same reasoning we should then use a resolution of Log 2 0 012207031 TBD so chose 20 so numbers read from ADC
25. rtain use conditions Further Renesas Electronics products are not subject to radiation resistance design Please be sure to implement safety measures to guard them against the possibility of physical injury and injury or damage caused by fire in the event of the failure of a Renesas Electronics product such as safety design for hardware and software including but not limited to redundancy fire control and malfunction prevention appropriate treatment for aging degradation or any other appropriate measures Because the evaluation of microcomputer software alone is very difficult please evaluate the safety of the final products or system manufactured by you Please contact a Renesas Electronics sales office for details as to environmental matters such as the environmental compatibility of each Renesas Electronics product Please use Renesas Electronics products in compliance with all applicable laws and regulations that regulate the inclusion or use of controlled substances including without limitation the EU RoHS Directive Renesas Electronics assumes no liability for damages or losses occurring as a result of your noncompliance with applicable laws and regulations This document may not be reproduced or duplicated in any form in whole or in part without prior written consent of Renesas Electronics Please contact a Renesas Electronics sales office if you have any questions regarding the information contained in this document or Renesas Electron
26. s are needed for the demo below e RSK for SH7286 includes E10A for Starter Kits http www renesas com rsk 1 3 Demonstration Software The Demonstration software is intended for use with the Renesas RSK board More detailed documentation on the RSK hardware is included with the kit or can be downloaded from the Renesas Web site 2 Building the Code The demonstration software can be built by opening the HEW Workspace FP_Demo hws and building the code using the Build All icon The resulting FP_Demo abs file in the Debug directory can then be downloaded using the E10A and HEW 3 Running the Demonstration Code The demonstration is setup to use data from the potentiometer connected to ADC Unit 0 channel 0 It is assumed the user has already setup the SH7286 RSK using the QSG and is familiar with the operation of the E10A and the SH Family tool chains The user should refer to the RSK schematic for additional detail as necessary 3 1 Overview The demonstration uses the Potentiometer on the RSK to simulate readings from current sensors and to generate commanded motor voltages in a motor control scenario Since it has only one Potentiometer it cannot run both scenarios at the same time It uses a static variable named ad_demo to select which scenario to run When ad_demo is set to logic 0 it uses the potentiometer to simulate commanded motor voltages which are then turned into PWM Sine waves of the correct voltag
27. t Op 0 until read by ADC void reac current void FIX8 re reading raw_reading get_AD data V_BUS 2 20 reading tay _weechingy lt AHINO I ORESIEIE ff Moltioly 2 20 bie weight scaled becek by 2 12 results im 2 68 velve moror CUEEeine FIX _mul_SCALE12 raw_reading ITADE BIT 5 Multiple Build Configurations The demo contains two Build setting The normal build simply called Debug will run the demo code as described above The additional session is called Debug with vectors Debug_with_vectors will include a series of test vectors to be included in the build These will run through a series of functions calls that attempt to exercise a large number of functions calls This may be beneficial to software engineers using Fixed Point for the first time to see the input numbers and the results of the fixed point function call NOTE It is impossible to test all the permutations of the input values possible so these are included as examples only Any issues with the fixed point library should be reported to Renesas Tech Support REU05B0116 0100 Rev 1 00 November 2009 Page 9 of 15 QE NESAS SH2 SH2A Family Using a Fixed Point Library 6 Appendix A Library Usage in HEW This section will show a practical example of how the Filter Library may be integrated into an overall HEW Project 6 1 Local to Project The SH2A Fixed Point Library is simple to add locally to any existing HEW pr
28. t be easily detached from your products Renesas shall have no liability for damages arising out of such detachment 12 This document may not be reproduced or duplicated in any form in whole or in part without prior written approval from Renesas 13 Please contact a Renesas sales office if you have any questions regarding the information contained in this document Renesas semiconductor products or if you have any other inquiries 2009 Renesas Technology Corp All rights reserved REU05B0116 0100 Rev 1 00 November 2009 Page 15 of 15
29. ult and then return a normalized number Dividing For most MCUs dividing is an issue since most divides are multi clock No way around it you just need to minimize the number of divides That being said if you have a constant that you need to divide by a one simple performance enhancement is to multiply by its inverse This is easy to do with fixed point arithmetic Scaled Multiplication This is a little unique This is used when multiplying numbers of two different resolutions For example if you want to multiply a number of Q5 and Q7 The resulting would be Q to the 12 and without scaled multiply the library would not know what resolution to return So for example suppose you want to multiply Voltage and Current to get power P IE but I is in Q10 and E is in Q5 perfect if you need P in Q15 probably in a 32 bit signed return value But suppose you need P as a 16 bit signed result in Q8 You would called a scaled multiply with a scaling value of 5 i e result will be Q12 you need to scale back by Q5 to get result in Q8 Overflow Overflow is something that you must contend with but it is easy to avoid Multiplying numbers of the same resolution is usually not a problem since they are normalized on return Adding is a minor issue because in most control systems you multiply and divide Overflow on One level of addition can be avoided by providing an additional bit When we are selecting resolution we will always allow 1 bit which we will call
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