Recently while coding sample rate convertor I had real bad experience with floating point numbers in Matlab. I guess it will be same even if we use C or any other language. Actually 2.0 was represented as 1.9999999999 so the phase selection logic advanced by one step while the previous value was picked for data computation. Anyone have similar experieces about floating point handling? Is there any good document on same? Regards Bharat
floating point design careabouts
Started by ●January 19, 2011
Reply by ●January 19, 20112011-01-19
bharat pathak <bharat@n_o_s_p_a_m.arithos.com> wrote:> Recently while coding sample rate convertor I had real bad > experience with floating point numbers in Matlab. I guess it > will be same even if we use C or any other language. Actually > 2.0 was represented as 1.9999999999 so the phase selection logic > advanced by one step while the previous value was picked for > data computation.> Anyone have similar experieces about floating point handling? > Is there any good document on same?There are many good references. Many will come up putting "floating point" into google. (Or even "flaoting point") The one called "What every computer scientist should know about floating point" is a good starting point. -- glen
Reply by ●January 19, 20112011-01-19
Reply by ●January 19, 20112011-01-19
On 01/19/2011 03:13 AM, bharat pathak wrote:> Recently while coding sample rate convertor I had real bad > experience with floating point numbers in Matlab. I guess it > will be same even if we use C or any other language. Actually > 2.0 was represented as 1.9999999999 so the phase selection logic > advanced by one step while the previous value was picked for > data computation. > > Anyone have similar experieces about floating point handling? > Is there any good document on same?There are three cardinal rules that I find helpful in using floating point. Nearly all the documents that I see relating to it are elaborations of these three -- so I'll just give you the rules, and let you extrapolate from there: Rule 1: Floating point is a resource hog. This isn't an issue if you're using a PC or other 'big iron' machine, because floating point is already built in and hogging resources even when you're not using them. But if you're designing a small system with a fixed-point processor, or a system built around an FPGA, it counts in either low speed, large silicon area, or some combination thereof. Rule 2: Floating point cannot be counted on to be exact. Never, ever put something in your code that boils down to if (this_float == that_float) Do this, and you will get lots and lots of false negatives. Most of the time that I do this, I find that I can get away with if (this_float < that_float) -- and then I need to be strict about doing just one test. The rest of the time you have to use if (fabs(this_float - that_float) < some_tolerance) -- and choosing the tolerance can be a bear. (Note that this is what you seem to have run afoul of). Rule 3: Floating point isn't as precise as you think. If you have a 32 bit floating point number, then you really only have 25 effective bits of precision in the mantissa. Nearly always you can fix this by just using double-precision (which Scilab and I think Matlab do as routine) -- but on some machines this forks you right back to Rule 1. Of course, if you're working in C or C++ you have to explicitly use 'double'. Moreover, in the embedded world I've run across at least one compiler (TI's Code Composter for the 28xx processor) that treated the 'double' keyword as 'please screw me over by using single precision here when I really need double' (they did this because of Rule 1, and their processor's 'sorta floating point' architecture that was fast with 32-bit floating point, and _not_ fast with 64-bit). -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●January 19, 20112011-01-19
On 01/19/2011 06:13 AM, bharat pathak wrote:> Recently while coding sample rate convertor I had real bad > experience with floating point numbers in Matlab. I guess it > will be same even if we use C or any other language. Actually > 2.0 was represented as 1.9999999999 so the phase selection logic > advanced by one step while the previous value was picked for > data computation. > > Anyone have similar experieces about floating point handling? > Is there any good document on same? > > Regards > BharatBharat: You must have had something else going on. Matlab uses the IEEE 754 double precision floating point format, which is able to represent the integer 2 exactly. -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Reply by ●January 19, 20112011-01-19
On 01/19/2011 10:00 AM, Randy Yates wrote:> On 01/19/2011 06:13 AM, bharat pathak wrote: >> Recently while coding sample rate convertor I had real bad >> experience with floating point numbers in Matlab. I guess it >> will be same even if we use C or any other language. Actually >> 2.0 was represented as 1.9999999999 so the phase selection logic >> advanced by one step while the previous value was picked for >> data computation. >> >> Anyone have similar experieces about floating point handling? >> Is there any good document on same? >> >> Regards >> Bharat > > Bharat: > > You must have had something else going on. Matlab uses the IEEE 754 > double precision floating point format, which is able to represent > the integer 2 exactly.two = (4.0 / 3.0) - (1.0 / 3.0). Or two = exp(log(2.0)). or two = 1 / (cos(%pi / 4)^2) etc. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●January 19, 20112011-01-19
On 01/19/2011 01:06 PM, Tim Wescott wrote:> On 01/19/2011 10:00 AM, Randy Yates wrote: >> On 01/19/2011 06:13 AM, bharat pathak wrote: >>> Recently while coding sample rate convertor I had real bad >>> experience with floating point numbers in Matlab. I guess it >>> will be same even if we use C or any other language. Actually >>> 2.0 was represented as 1.9999999999 so the phase selection logic >>> advanced by one step while the previous value was picked for >>> data computation. >>> >>> Anyone have similar experieces about floating point handling? >>> Is there any good document on same? >>> >>> Regards >>> Bharat >> >> Bharat: >> >> You must have had something else going on. Matlab uses the IEEE 754 >> double precision floating point format, which is able to represent >> the integer 2 exactly. > > two = (4.0 / 3.0) - (1.0 / 3.0). > > Or > > two = exp(log(2.0)). > > or > > two = 1 / (cos(%pi / 4)^2) > > etc. >Of course. I presumed from his text that he was utilizing a floating point variable as an integer index. Perhaps I was mistaken. -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Reply by ●January 19, 20112011-01-19
On 01/19/2011 11:03 AM, Randy Yates wrote:> On 01/19/2011 01:06 PM, Tim Wescott wrote: >> On 01/19/2011 10:00 AM, Randy Yates wrote: >>> On 01/19/2011 06:13 AM, bharat pathak wrote: >>>> Recently while coding sample rate convertor I had real bad >>>> experience with floating point numbers in Matlab. I guess it >>>> will be same even if we use C or any other language. Actually >>>> 2.0 was represented as 1.9999999999 so the phase selection logic >>>> advanced by one step while the previous value was picked for >>>> data computation. >>>> >>>> Anyone have similar experieces about floating point handling? >>>> Is there any good document on same? >>>> >>>> Regards >>>> Bharat >>> >>> Bharat: >>> >>> You must have had something else going on. Matlab uses the IEEE 754 >>> double precision floating point format, which is able to represent >>> the integer 2 exactly. >> >> two = (4.0 / 3.0) - (1.0 / 3.0). >> >> Or >> >> two = exp(log(2.0)). >> >> or >> >> two = 1 / (cos(%pi / 4)^2) >> >> etc. >> > > Of course. I presumed from his text that he was utilizing a floating > point variable as an integer index. Perhaps I was mistaken.Need to ask the OP. The correct type-safe way to do this would be to use an integer type, but that's not the safest way to do it under Scilab. And yes, Scilab is exceedingly safe with floating point if you're doing 'integer' math with it. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●January 19, 20112011-01-19
On 01/19/2011 02:08 PM, Tim Wescott wrote:> On 01/19/2011 11:03 AM, Randy Yates wrote: >> On 01/19/2011 01:06 PM, Tim Wescott wrote: >>> On 01/19/2011 10:00 AM, Randy Yates wrote: >>>> On 01/19/2011 06:13 AM, bharat pathak wrote: >>>>> Recently while coding sample rate convertor I had real bad >>>>> experience with floating point numbers in Matlab. I guess it >>>>> will be same even if we use C or any other language. Actually >>>>> 2.0 was represented as 1.9999999999 so the phase selection logic >>>>> advanced by one step while the previous value was picked for >>>>> data computation. >>>>> >>>>> Anyone have similar experieces about floating point handling? >>>>> Is there any good document on same? >>>>> >>>>> Regards >>>>> Bharat >>>> >>>> Bharat: >>>> >>>> You must have had something else going on. Matlab uses the IEEE 754 >>>> double precision floating point format, which is able to represent >>>> the integer 2 exactly. >>> >>> two = (4.0 / 3.0) - (1.0 / 3.0). >>> >>> Or >>> >>> two = exp(log(2.0)). >>> >>> or >>> >>> two = 1 / (cos(%pi / 4)^2) >>> >>> etc. >>> >> >> Of course. I presumed from his text that he was utilizing a floating >> point variable as an integer index. Perhaps I was mistaken. > > Need to ask the OP. The correct type-safe way to do this would be to use an integer type, but that's not the safest way to do it > under Scilab.It's Matlab - one reason folks use it is so they don't HAVE to worry about "type safety." And why are you talking about Scilab? -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Reply by ●January 19, 20112011-01-19
On 01/19/2011 11:18 AM, Randy Yates wrote:> On 01/19/2011 02:08 PM, Tim Wescott wrote: >> On 01/19/2011 11:03 AM, Randy Yates wrote: >>> On 01/19/2011 01:06 PM, Tim Wescott wrote: >>>> On 01/19/2011 10:00 AM, Randy Yates wrote: >>>>> On 01/19/2011 06:13 AM, bharat pathak wrote: >>>>>> Recently while coding sample rate convertor I had real bad >>>>>> experience with floating point numbers in Matlab. I guess it >>>>>> will be same even if we use C or any other language. Actually >>>>>> 2.0 was represented as 1.9999999999 so the phase selection logic >>>>>> advanced by one step while the previous value was picked for >>>>>> data computation. >>>>>> >>>>>> Anyone have similar experieces about floating point handling? >>>>>> Is there any good document on same? >>>>>> >>>>>> Regards >>>>>> Bharat >>>>> >>>>> Bharat: >>>>> >>>>> You must have had something else going on. Matlab uses the IEEE 754 >>>>> double precision floating point format, which is able to represent >>>>> the integer 2 exactly. >>>> >>>> two = (4.0 / 3.0) - (1.0 / 3.0). >>>> >>>> Or >>>> >>>> two = exp(log(2.0)). >>>> >>>> or >>>> >>>> two = 1 / (cos(%pi / 4)^2) >>>> >>>> etc. >>>> >>> >>> Of course. I presumed from his text that he was utilizing a floating >>> point variable as an integer index. Perhaps I was mistaken. >> >> Need to ask the OP. The correct type-safe way to do this would be to >> use an integer type, but that's not the safest way to do it >> under Scilab. > > It's Matlab - one reason folks use it is so they don't HAVE to worry > about "type safety." > > And why are you talking about Scilab?Because I forgot the OP was working in Matlab and not Scilab! Although both statements work the same in Scilab or Matlab. And you don't _have_ to worry about type safety in Scilab or Matlab until you trip over it while carrying a platter full of precious crystal. And yes, on my bad days I _am_ a bit of a code nazi. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
