Post by thread:[PICLIST] Can you crack this formula with a PIC ?

It's a formula to calculate water vapour pressure given a temperature in Deg C float calculateWaterWVP(float Temp) { float a,tempInK,c,d,e,wvp; tempInK = Temp + 273.15; a = -6096.9385 * (1/tempInK); c = -2.711193 * 0.01 * tempInK; d = 1.673952 * 0.00001 * (tempInK * tempInK); e = 2.433502 * (log(tempInK)/log(10)/0.434294509); wvp = exp(a + 21.2409642 + c + d + e); return wvp; } */ If you can do this, you get a medal ! Regards, Darren -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

On Thu, 26 Oct 2000, Darren Logan wrote: > It's a formula to calculate water vapour pressure given a temperature in Deg C > > float calculateWaterWVP(float Temp) > { > float a,tempInK,c,d,e,wvp; > > tempInK = Temp + 273.15; > a = -6096.9385 * (1/tempInK); > c = -2.711193 * 0.01 * tempInK; > d = 1.673952 * 0.00001 * (tempInK * tempInK); > e = 2.433502 * (log(tempInK)/log(10)/0.434294509); > > > wvp = exp(a + 21.2409642 + c + d + e); > return wvp; > > } */ > > If you can do this, you get a medal ! Darren, The easiest way to solve this is with a lookup table (with at least first order interpolation). However, before anyone can propose a solution you'll need to answer this question: how accurate does it have to be? How accurate is the temperature? Scott -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

Darren, I did it. #include <pic.h> #include <math.h> float calculateWaterWVP(float Temp) { float a,tempInK,c,d,e,wvp; tempInK = Temp + 273.15; a = -6096.9385 * (1/tempInK); c = -2.711193 * 0.01 * tempInK; d = 1.673952 * 0.00001 * (tempInK * tempInK); e = 2.433502 * (log(tempInK)/log(10)/0.434294509); wvp = exp(a + 21.2409642 + c + d + e); return wvp; } void main (void) { calculateWaterWVP (5); } ------------------------------------------------------- > cd . > picc -16F876 -E -G -O -Zg1 -L-N temp.c F:\>picc -16F876 -E -G -O -Zg1 -L-N temp.c HI-TECH C COMPILER (Microchip PIC) V7.86 PL3 Copyright (C) 1984-2000 HI-TECH SOFTWARE Serial no: CPIC-06468; Licensed to: Andy Kunz, Montana Design Memory Usage Map: Program ROM $0000 - $0054 $0055 ( 85) words Program ROM $0209 - $07FF $05F7 ( 1527) words $064C ( 1612) words total Program ROM Bank 0 RAM $0020 - $0058 $0039 ( 57) bytes Bank 0 RAM $0070 - $007B $000C ( 12) bytes $0045 ( 69) bytes total Bank 0 RAM F:\> -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

It's a formula to calculate water vapour pressure given a temperature in Deg C float calculateWaterWVP(float Temp) { float a,tempInK,c,d,e,wvp; tempInK = Temp + 273.15; a = -6096.9385 * (1/tempInK); c = -2.711193 * 0.01 * tempInK; d = 1.673952 * 0.00001 * (tempInK * tempInK); e = 2.433502 * (log(tempInK)/log(10)/0.434294509); wvp = exp(a + 21.2409642 + c + d + e); return wvp; } */ If you can do this, you get a medal ! (Accuracy of result = 1% or better) Regards, Darren -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

main() is pretty tiny, only a few words (< 10 I bet). Overhead would include Startup (erases all RAM to 0, only a few bytes) FP Lib (most of the code) Subroutine (a significant but much smaller chunk). Andy David VanHorn <spam_OUTdvanhornTakeThisOuTCEDAR.NET> on 10/26/2000 01:08:42 PM Please respond to pic microcontroller discussion list <.....PICLISTKILLspam@spam@MITVMA.MIT.EDU> To: PICLISTKILLspamMITVMA.MIT.EDU cc: (bcc: Andrew Kunz/TDI_NOTES) Subject: Re: Can you crack this formula with a PIC ? > >Program ROM $0000 - $0054 $0055 ( 85) words >Program ROM $0209 - $07FF $05F7 ( 1527) words > $064C ( 1612) words total Program ROM > >Bank 0 RAM $0020 - $0058 $0039 ( 57) bytes >Bank 0 RAM $0070 - $007B $000C ( 12) bytes > $0045 ( 69) bytes total Bank 0 RAM How much of that is system overhead? IOW: if void Main(void) { } -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details. -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

At 01:26 PM 10/26/00 -0400, you wrote: >main() is pretty tiny, only a few words (< 10 I bet). > >Overhead would include > >Startup (erases all RAM to 0, only a few bytes) >FP Lib (most of the code) >Subroutine (a significant but much smaller chunk). I don't use C on pics, so I don't know how much overhead to expect, but if you had a number from an empty "main" to compare to, then it would be more meaningful. Still, it looks to be a pretty expensive function, implemented that way. 1% accuracy would imply that a lookup table with 255 entries would seem to be a lot smaller, and no doubt faster. (Depends also how you define that 1% :) -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

>I don't use C on pics, so I don't know how much overhead to expect, but if >you had a number from an empty "main" to compare to, then it would be more >meaningful. Still, it looks to be a pretty expensive function, implemented >that way. < 50 bytes >1% accuracy would imply that a lookup table with 255 entries would seem to >be a lot smaller, and no doubt faster. (Depends also how you define that >1% :) A floating point (4 byte) table would require 1024 bytes, plus lookup overhead, and would be limited to 255 discrete inputs. His was for a floating-point input (4 bytes) so a PIC wouldn't have adequate table space. But it still might be adequate for a table spanning 100 degrees. Andy -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

At 02:30 PM 10/26/00 -0400, you wrote: > >I don't use C on pics, so I don't know how much overhead to expect, but if > >you had a number from an empty "main" to compare to, then it would be more > >meaningful. Still, it looks to be a pretty expensive function, implemented > >that way. > >< 50 bytes I misunderstood then, you said (I thought) that the empty main would be pretty small (I was thinking tens of bytes) and the compiled routine was something like 1600? > >1% accuracy would imply that a lookup table with 255 entries would seem to > >be a lot smaller, and no doubt faster. (Depends also how you define that > >1% :) > >A floating point (4 byte) table would require 1024 bytes, plus lookup >overhead, >and would be limited to 255 discrete inputs. Hmm.. I don't know how "granular" the temperature input can be, but over any range, a 255 entry table introduces roughly 1/2% error. (rounding) Output value would then be one of 255 different numbers, which could be some constant, plus a scaled byte from the table. Harder to say what the absolute accuracy here would be, but it seems to be on the order of 1/2% also. >His was for a floating-point input (4 bytes) so a PIC wouldn't have adequate >table space. That's computing to a much higher accuracy than he said he needed though. -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

At 01:08 PM 10/26/00 EDT, you wrote: >It's a formula to calculate water vapour pressure given a temperature in Deg C {Quote hidden}> > float calculateWaterWVP(float Temp) > { > float a,tempInK,c,d,e,wvp; > > tempInK = Temp + 273.15; > a = -6096.9385 * (1/tempInK); > c = -2.711193 * 0.01 * tempInK; > d = 1.673952 * 0.00001 * (tempInK * tempInK); > e = 2.433502 * (log(tempInK)/log(10)/0.434294509); > > > wvp = exp(a + 21.2409642 + c + d + e); > return wvp; > > } */ > >If you can do this, you get a medal ! > >(Accuracy of result = 1% or better) How nonlinear is this function OVER THE RANGE OF INTEREST? How much resolution do you need (for display, it may be unacceptable to have poor resolution, even if the accuracy is ok)? Since this is a SISO function of temperature, I'd be tempted to use either a lookup table with linear interpolation or a polynomial fit to the analytical function above. Using 16-32 bit fixed point integer math, depending. Best regards, =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Spehro Pefhany --"it's the network..." "The Journey is the reward" .....speffKILLspam.....interlog.com Info for manufacturers: http://www.trexon.com Embedded software/hardware/analog Info for designers: http://www.speff.com Contributions invited->The AVR-gcc FAQ is at: http://www.bluecollarlinux.com =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

As Scott mentioned, you need first to describe the input, the output, the precision, and the range. You could easily perform this exact calculation in a C compiler (A good one with a math library and 32 or 64 bit floating point numbers), but it would take a bit of time during operation. But let's say instead that you need it to be faster. If you define your input to be within a range, define an acceptable error, and know how good your input is, then you can take several shortcuts. If you need it to be really fast, or you have lots of code space available, use a lookup table. Assume your sensor doesn't give you any better resolution than .1 degree celsius, and you're only making these measurements between 0 and 100 degrees celsius. You would only need a 1000 entry lookup table to get your answer, if you can fit it into a byte. If you needed 16 bit output, you would use a 2000 entry table, and it would still take fewer than 20 instruction cycles to get your answer. It wouldn't surprise my too much if a 16-bit math library including LOG and EXP took that much code space anyway, so a table would be your best bet. A lot of good code revolves around developing your own scales. Many coders use 0-256 to indicate angle, rather than 0 to 359. They lose resolution that they don't need. If it gives you enough information, you can translate 0 to 100 degrees celsius to 0 to 256 Degrees Darren. Translate WVP values of 611 to 101419 to an easier to deal with 0-65536 Logans. Now re-write the equation to accept 0-256 degrees Darren and give 0-65536 Logans, make a table and off you go. Using excel, I see that a reasonable approximation of your equation on these two new scales would be y = -1E-09x^6 + 2E-06x^5 + 0.0001x^4 + 0.0189x^3 + 0.8347x^2 + 27.411x - 28.536. You can use your favorite spreadsheet to generate number for a table, or write a program to do so. -Adam Darren Logan wrote: {Quote hidden}> > It's a formula to calculate water vapour pressure given a temperature in Deg C > > float calculateWaterWVP(float Temp) > { > float a,tempInK,c,d,e,wvp; > > tempInK = Temp + 273.15; > a = -6096.9385 * (1/tempInK); > c = -2.711193 * 0.01 * tempInK; > d = 1.673952 * 0.00001 * (tempInK * tempInK); > e = 2.433502 * (log(tempInK)/log(10)/0.434294509); > > wvp = exp(a + 21.2409642 + c + d + e); > return wvp; > > } */ > > If you can do this, you get a medal ! > > Regards, > Darren > > -- > http://www.piclist.com hint: The PICList is archived three different > ways. See http://www.piclist.com/#archives for details. -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

On Thu, 26 Oct 2000, M. Adam Davis wrote: > As Scott mentioned, you need first to describe the input, the output, the > precision, and the range. You could easily perform this exact calculation in a > C compiler (A good one with a math library and 32 or 64 bit floating point > numbers), but it would take a bit of time during operation. > > But let's say instead that you need it to be faster. If you define your input > to be within a range, define an acceptable error, and know how good your input > is, then you can take several shortcuts. > > If you need it to be really fast, or you have lots of code space available, use > a lookup table. Assume your sensor doesn't give you any better resolution than > .1 degree celsius, and you're only making these measurements between 0 and 100 > degrees celsius. You would only need a 1000 entry lookup table to get your Actually, I bet you'd need far fewer than a 1000 entry table. It depends on the linearity of the function as Spehro suggests. For example, the sine wave functions on my web page use a 16 entry table and still achieve a +/- 1 count resolution (for an 8 bit result). However, the symmetry properties allow only a quarter of the sine wave to be include. So effectively, there are 64 samples. Then linear interpolation is used to get the rest of the accuracy. If the function is highly non-linear yet relatively monotonic, then a small look table is still adequate. (For example, the table entries could store the deviations from an easy-to-calculate function that closely approximates the real function). If the function is oscillatory (which I doubt it is considering how physical things generally don't have a oscillatory responses to temperature) then it would be much more difficult to use a look-up table. However it's not impossible... Scott -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

> How nonlinear is this function OVER THE RANGE OF INTEREST? Very non-linear, exponential! Try this instead This one for temps above freezing. Note temps in Cel. VaporPressure := 6.11*Power(10,(T*7.5)/(T+237.3)) this one for temps below freezing IF you want the frost point! VaporPressure := 6.11*Power(10,(T*9.5)/(T+265.5)) These are pretty good over the meteorlogical range of temps (-40 to 50 Cel.) BTW, the vapor pressure is no better than the accuracy of the temperature measurement! Jim Korman Spehro Pefhany wrote: {Quote hidden}> > At 01:08 PM 10/26/00 EDT, you wrote: > >It's a formula to calculate water vapour pressure given a temperature in > Deg C > > > > float calculateWaterWVP(float Temp) > > { > > float a,tempInK,c,d,e,wvp; > > > > tempInK = Temp + 273.15; > > a = -6096.9385 * (1/tempInK); > > c = -2.711193 * 0.01 * tempInK; > > d = 1.673952 * 0.00001 * (tempInK * tempInK); > > e = 2.433502 * (log(tempInK)/log(10)/0.434294509); > > > > > > wvp = exp(a + 21.2409642 + c + d + e); > > return wvp; > > > > } */ > > > >If you can do this, you get a medal ! > > > >(Accuracy of result = 1% or better) > > How nonlinear is this function OVER THE RANGE OF INTEREST? > > How much resolution do you need (for display, it may be unacceptable > to have poor resolution, even if the accuracy is ok)? > > Since this is a SISO function of temperature, I'd be tempted to use > either a lookup table with linear interpolation or a polynomial fit to > the analytical function above. Using 16-32 bit fixed point integer > math, depending. > > Best regards, > > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= > Spehro Pefhany --"it's the network..." "The Journey is the reward" > EraseMEspeffspam_OUTTakeThisOuTinterlog.com Info for manufacturers: http://www.trexon.com > Embedded software/hardware/analog Info for designers: http://www.speff.com > Contributions invited->The AVR-gcc FAQ is at: http://www.bluecollarlinux.com > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= > > -- > http://www.piclist.com hint: The PICList is archived three different > ways. See http://www.piclist.com/#archives for details. -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

Darren, this is not the answer you are looking for but I designed a PIC16x (40-pin chip) based weather station several years ago. I needed to do the Dew Point, Heat Index, and other equations which are incredibly complicated and subjective. Since I was already implementing a bus-based system using a 512KBye SRAM to store sensor data, I did the calculations in Excel, wrote a simple C program to download the data tables to the PIC, and used simple fixed-point math in the PIC to deal with it all. - Tom At 12:20 PM 10/26/00 EDT, Darren Logan wrote: >It's a formula to calculate water vapour pressure given a temperature in Deg C {Quote hidden}> > float calculateWaterWVP(float Temp) > { > float a,tempInK,c,d,e,wvp; > > tempInK = Temp + 273.15; > a = -6096.9385 * (1/tempInK); > c = -2.711193 * 0.01 * tempInK; > d = 1.673952 * 0.00001 * (tempInK * tempInK); > e = 2.433502 * (log(tempInK)/log(10)/0.434294509); > > > wvp = exp(a + 21.2409642 + c + d + e); > return wvp; > > } */ > >If you can do this, you get a medal ! > >Regards, >Darren ------------------------------------------------------------------------ Tom Handley New Age Communications Since '75 before "New Age" and no one around here is waiting for UFOs ;-) -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! use listservspam_OUTmitvma.mit.edu?body=SET%20PICList%20DIGEST

I suppose the output was a single tri-color LED which signified whether to wear a t-shirt, long-sleeved shirt, light jacket or coat... ;-) -Adam Tom Handley wrote: {Quote hidden}> > Darren, this is not the answer you are looking for but I designed a PIC16x > (40-pin chip) based weather station several years ago. I needed to do the > Dew Point, Heat Index, and other equations which are incredibly complicated > and subjective. Since I was already implementing a bus-based system using > a 512KBye SRAM to store sensor data, I did the calculations in Excel, wrote > a simple C program to download the data tables to the PIC, and used simple > fixed-point math in the PIC to deal with it all. > > - Tom > > At 12:20 PM 10/26/00 EDT, Darren Logan wrote: > >It's a formula to calculate water vapour pressure given a temperature in > Deg C > > > > float calculateWaterWVP(float Temp) > > { > > float a,tempInK,c,d,e,wvp; > > > > tempInK = Temp + 273.15; > > a = -6096.9385 * (1/tempInK); > > c = -2.711193 * 0.01 * tempInK; > > d = 1.673952 * 0.00001 * (tempInK * tempInK); > > e = 2.433502 * (log(tempInK)/log(10)/0.434294509); > > > > > > wvp = exp(a + 21.2409642 + c + d + e); > > return wvp; > > > > } */ > > > >If you can do this, you get a medal ! > > > >Regards, > >Darren > > ------------------------------------------------------------------------ > Tom Handley > New Age Communications > Since '75 before "New Age" and no one around here is waiting for UFOs ;-) > > -- > http://www.piclist.com#nomail Going offline? Don't AutoReply us! > use @spam@listservKILLspammitvma.mit.edu?body=SET%20PICList%20DIGEST -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! use KILLspamlistservKILLspammitvma.mit.edu?body=SET%20PICList%20DIGEST

Hi, I was impressed by HiTech C's compilation of this. But. 1% is doable with 8 bits, i.e. table output can be on 8 bits. Input accuracy does not relate to this linearly however. In particular you lose precision in the log operation. So your input precision could be 10% to obtain output 1% under certain circumstances. On the other hand, I'd run the little program: for(temp = MIN_TEMP; temp <= MAX_TEMP; temp += TEMP_STEP) printf("%-10f\t%-10f\n",i,calculateWaterWVP(temp)); to obtain a pretty table that will speak volumes about what you need to do. You can modify the program to calculate the (output) table values themselves and to obtain the required input precision for each table domain (the precision will vary because of your nonlinear dependency - esp. the log operation). The easiest way to do this is to have a variable float temp0 = MIN_TEMP-1; and for each calculated value display only if the reduced (to 1%) value is different from temp0, then set temp0 so the calculated temp. This will remove all the intermediary results from the table, giving the domain boundaries for the table. In the end you will likely end up with a table that may be largish depending on your temperature domain or use several interpolation points, as Scott has said. This being said, maybe you need to purchase HITECH C ? ;-) Peter PS: I do not work for them. PS2: Of course you run this on a PC not on a PIC. -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! use RemoveMElistservTakeThisOuTmitvma.mit.edu?body=SET%20PICList%20DIGEST

Hehehe, actually here in Oregon you just assume rain but look out the window just in case. I use an accurate commercial rain gage when all I need is to measure the depth of the puddles out back ;-) - Tom At 01:13 PM 10/27/00 -0400, Adam wrote: >I suppose the output was a single tri-color LED which signified whether to wear >a t-shirt, long-sleeved shirt, light jacket or coat... ;-) > >-Adam > >Tom Handley wrote: >> >> Darren, this is not the answer you are looking for but I designed a PIC16x >> (40-pin chip) based weather station several years ago. I needed to do the >> Dew Point, Heat Index, and other equations which are incredibly complicated >> and subjective. Since I was already implementing a bus-based system using >> a 512KBye SRAM to store sensor data, I did the calculations in Excel, wrote >> a simple C program to download the data tables to the PIC, and used simple >> fixed-point math in the PIC to deal with it all. >> >> - Tom ------------------------------------------------------------------------ Tom Handley New Age Communications Since '75 before "New Age" and no one around here is waiting for UFOs ;-) -- http://www.piclist.com hint: To leave the PICList spamBeGonepiclist-unsubscribe-requestspamBeGonemitvma.mit.edu

Could you tell us please the range of Temp ? Regards, Imre On Thu, 26 Oct 2000, Darren Logan wrote: {Quote hidden}> It's a formula to calculate water vapour pressure given a temperature in Deg C > > float calculateWaterWVP(float Temp) > { > float a,tempInK,c,d,e,wvp; > > tempInK = Temp + 273.15; > a = -6096.9385 * (1/tempInK); > c = -2.711193 * 0.01 * tempInK; > d = 1.673952 * 0.00001 * (tempInK * tempInK); > e = 2.433502 * (log(tempInK)/log(10)/0.434294509); > > > wvp = exp(a + 21.2409642 + c + d + e); > return wvp; > > } */ > > If you can do this, you get a medal ! > > Regards, > Darren > > -- > http://www.piclist.com hint: The PICList is archived three different > ways. See http://www.piclist.com/#archives for details. > > > > > > -- http://www.piclist.com hint: To leave the PICList TakeThisOuTpiclist-unsubscribe-requestEraseMEspam_OUTmitvma.mit.edu