Rounding in Floats
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Hi,
Continuing with my issues with decimals, I'm having one issue that is not clear to me why it happens. If I do: (9.1 + (-2.0)) roundTo: 0.1. "7.1000000000000005" I expect to get a single decimal Float (rounded with whatever precision, but a single decimal). Even if I do something like this: 7.1 roundTo: 0.1 It gives the wrong result. In VW and VAST it provides the right result. (9.1 + (-2.0)) roundTo: 0.1 "7.1" In Dolphin it also returns the wrong result, it seems to use the same algorithm to round it. Is this a bug? Esteban A. Maringolo |
Re: Rounding in Floats
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> On 6 Sep 2020, at 16:06, Esteban Maringolo <[hidden email]> wrote: > > Hi, > > Continuing with my issues with decimals, I'm having one issue that is > not clear to me why it happens. > > If I do: > (9.1 + (-2.0)) roundTo: 0.1. > "7.1000000000000005" > > I expect to get a single decimal Float (rounded with whatever > precision, but a single decimal). > > Even if I do something like this: > 7.1 roundTo: 0.1 > > It gives the wrong result. > > In VW and VAST it provides the right result. > (9.1 + (-2.0)) roundTo: 0.1 "7.1" > > In Dolphin it also returns the wrong result, it seems to use the same > algorithm to round it. > > Is this a bug? Maybe. But I would not approach the problem of rounding like that. You probably want to control how numbers are printed. I would keep the numbers themselves at maximum internal precision and only do something when printing them. 1 / 3 asFloat printShowingDecimalPlaces: 1. Since you like Seaside, the following is even much more powerful (has *many* options): GRNumberPrinter new precision: 1; print: 1/3 asFloat. Check it out. > > Esteban A. Maringolo > |
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Hi Sven,
On Sun, Sep 6, 2020 at 11:57 AM Sven Van Caekenberghe <[hidden email]> wrote: > > On 6 Sep 2020, at 16:06, Esteban Maringolo <[hidden email]> wrote: > > (9.1 + (-2.0)) roundTo: 0.1. > > "7.1000000000000005" > > Is this a bug? > > Maybe. > > But I would not approach the problem of rounding like that. > You probably want to control how numbers are printed. It is not for printing but for testing. I want to assert that a certain calculation gives the expected result. And then it fails because of the difference above when it is "semantically" correct. > I would keep the numbers themselves at maximum internal precision and only do something when printing them. I do. I'm implementing the full WHS specification [1], and it mentions that most calculations should preserve the maximum internal precision and even introduces some weird situation where you have an "index" that is rounded and another one that is called the same way but must not be rounded because is going to used to compute some other value. For most calculations it specifies it must round to 1 decimal or even to no decimal, based on a round up if the decimal is greater or equal than zero (e.g. 1.5 becomes 2), except for negative numbers, in which case it rounds "down" (-1.5 becomes 1). > 1 / 3 asFloat printShowingDecimalPlaces: 1. > > Since you like Seaside, the following is even much more powerful (has *many* options): > GRNumberPrinter new precision: 1; print: 1/3 asFloat. I'm already using the GRNumberPrinter and also the Date printer to print these values. Regards! [1] https://en.wikipedia.org/wiki/Handicap_(golf)#World_Handicap_System |
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Hi Esteban,
> It is not for printing but for testing. I want to assert that a > certain calculation gives the expected result. > And then it fails because of the difference above when it is > "semantically" correct. If you want reliable precision tests with IEEE floats, you should use rounding to powers of 2, not 10. Round to 1/8 or 1/16, but not to 1/10. The fundamental issue is that 1/10 does not have an exact finite representation in base 2. No matter how I/O libraries handle the conversion between base 2 (in the binary representation of IEEE floats) and base 10 (in the text representation), there will always be bad surprises because the expectations we have from working in base 10 cannot all be met with an internal representation in base 2. So if your goal is not fundamentally related to I/O, forget about I/O and design your code to work the binary level, in particular for testing. However, if your problem specification explicitly requires precision guarantees in base 10 (which seems to be your case, from a quick glance at the Wikipedia page you cite), then it's best to avoid binary floats completely. Rationals (fractions) are one option, scaled integers another one. Konrad. |
Re: Rounding in Floats
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In reply to this post by Esteban A. Maringolo
> On 6 Sep 2020, at 22:21, Esteban Maringolo <[hidden email]> wrote: > > It is not for printing but for testing. I want to assert that a > certain calculation gives the expected result. Then you should use #assert:closeTo: and friends. (9.1 + (-2.0)) closeTo: 7.1 precision: 0.00001. Floats should always be compared using an epsilon (precision) value in tests, not using equality. |
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BTW why closeTo: is initialized by default with a value of 0.0001 ?
https://github.com/pharo-project/pharo/issues/3067
Sent from my iPhone On 7 Sep 2020, at 20:10, Sven Van Caekenberghe <[hidden email]> wrote:
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In reply to this post by Sven Van Caekenberghe-2
Hi Sven,
On Mon, Sep 7, 2020 at 9:10 AM Sven Van Caekenberghe <[hidden email]> wrote: > > On 6 Sep 2020, at 22:21, Esteban Maringolo <[hidden email]> wrote: > > > > It is not for printing but for testing. I want to assert that a > > certain calculation gives the expected result. > > Then you should use #assert:closeTo: and friends. > (9.1 + (-2.0)) closeTo: 7.1 precision: 0.1. I remembered about it, and implemented my own #assertDifferential:equals: which I first did convert to ScaledDecimals and then compares with #roundedByScale. > Floats should always be compared using an epsilon (precision) value in tests, not using equality. Sure, but 7.1 roundTo: 0.1 should return 7.1. Shouldn't it? Regards! Esteban A. Maringolo |
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Esteban,
You can instead use `7.1 round: 1` to get 7.1. It's not the problem of the rounding algorithm. It's because IEEE float can't express the exact value of 0.1. --- tomo 2020年9月7日(月) 21:28 Esteban Maringolo <[hidden email]>: > > Hi Sven, > > On Mon, Sep 7, 2020 at 9:10 AM Sven Van Caekenberghe <[hidden email]> wrote: > > > > On 6 Sep 2020, at 22:21, Esteban Maringolo <[hidden email]> wrote: > > > > > > It is not for printing but for testing. I want to assert that a > > > certain calculation gives the expected result. > > > > Then you should use #assert:closeTo: and friends. > > (9.1 + (-2.0)) closeTo: 7.1 precision: 0.1. > > I remembered about it, and implemented my own > #assertDifferential:equals: which I first did convert to > ScaledDecimals and then compares with #roundedByScale. > > > Floats should always be compared using an epsilon (precision) value in tests, not using equality. > > Sure, but 7.1 roundTo: 0.1 should return 7.1. Shouldn't it? > > Regards! > > Esteban A. Maringolo > |
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Hi Tomohiro,
Thanks, that certainly is the simplest solution that does exactly what I need. Maybe roundTo: should be considered harmful when using Floats. (and it is very unlikely anybody is going to round to something other than a power of 10) Best regards! Esteban A. Maringolo On Mon, Sep 7, 2020 at 9:51 AM Tomohiro Oda <[hidden email]> wrote: > > Esteban, > > You can instead use `7.1 round: 1` to get 7.1. > It's not the problem of the rounding algorithm. > It's because IEEE float can't express the exact value of 0.1. > --- > tomo > > 2020年9月7日(月) 21:28 Esteban Maringolo <[hidden email]>: > > > > Hi Sven, > > > > On Mon, Sep 7, 2020 at 9:10 AM Sven Van Caekenberghe <[hidden email]> wrote: > > > > > > On 6 Sep 2020, at 22:21, Esteban Maringolo <[hidden email]> wrote: > > > > > > > > It is not for printing but for testing. I want to assert that a > > > > certain calculation gives the expected result. > > > > > > Then you should use #assert:closeTo: and friends. > > > (9.1 + (-2.0)) closeTo: 7.1 precision: 0.1. > > > > I remembered about it, and implemented my own > > #assertDifferential:equals: which I first did convert to > > ScaledDecimals and then compares with #roundedByScale. > > > > > Floats should always be compared using an epsilon (precision) value in tests, not using equality. > > > > Sure, but 7.1 roundTo: 0.1 should return 7.1. Shouldn't it? > > > > Regards! > > > > Esteban A. Maringolo > > > |
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In reply to this post by Esteban A. Maringolo
"7.1 roundTo: 0.1 should return 7.1" You're still not getting it. 7.1 IS NOT 71/10. 0.1 IS NOT 1/10. Binary floating point CANNOT represent either of those numbers. You seem to be assuming that Pharo is making some mistake. It isn't. All it is doing is refusing to lie to you. #include <math.h> #include <stdio.h> int main(void) { printf("%.18f\n", 7.1); printf("%.18f\n", round(7.1 / 0.1) * 0.1); return 0; } % a.out 7.099999999999999645 7.100000000000000533 Does this help? "7.1" is a bit LESS than 7.1. "7.1 roundTo: 0.1" is a bit MORE than 7.1. This is the best that the computer's hardware can do. The systems that print 7.1 are LYING to you, and Pharo is not. On Tue, 8 Sep 2020 at 00:28, Esteban Maringolo <[hidden email]> wrote: Hi Sven, |
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On Tue, Sep 8, 2020 at 12:16 AM Richard O'Keefe <[hidden email]> wrote:
> > "7.1 roundTo: 0.1 should return 7.1" > You're still not getting it. I was until Konrad explained it. > Binary floating point CANNOT represent either of those numbers. > You seem to be assuming that Pharo is making some mistake. > It isn't. All it is doing is refusing to lie to you. <snip> > The systems that print 7.1 are LYING to you, > and Pharo is not. I'm not assuming a mistake from Pharo, I had a wrong expectation what to get if I round to that precision. I don't know whether other systems lie or simply fulfill user expectations, if you send the #roundTo: to a float, I did expect to get a number with the same precision. That is my expectation as a user. As in the other thread I expected two scaled decimals that are printed equal to also be compared as equal (which they don't). Whether there is a good reason for those behaviors is beyond my current comprehension, but it certainly doesn't follow the "principle of least surprise". In any case, the method proposed by Tomohiro solved my issues. Regards, Esteban A. Maringolo |
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If you are going to use floating point numbers in any programming language, Pharo included, you need to understand something about them. Things like - the relevant precision is *fixed*; a Float in Pharo is *always* a 64-bit IEEE floating-point number, which amongst other things means (to a first approximation) 54 binary digits of precision. It doesn't make the slightest amount of difference how many decimal digits you use when writing the number, the precision is *always* 54 binary digits. So you *did* get the precision out of rounding that you put in, it's just that the precision you put in was not what you thought it was. - almost all modern architectures offer BINARY arithmetic, not decimal. (The main exceptions are IBM z/series and IBM POWER, which offer binary *and* decimal.) Rounding a number to n decimals is ALWAYS problematic using binary floats. This has little or nothing to do with Smalltalk: it's the hardware. (This is why you are advised to keep money in cents, not dollars.) - Again, this is NOT a language issue, it is a hardware issue. IF you understand how binary floating point arithmetic works, then the arithmetic you get in C or R or Smalltalk or Matlab does not surprise you at all. If you DON'T understand how binary floating point arithmetic works, the hardware will *get* you sooner or later. - ScaledDecimal in Pharo didn't have to violate the principle of least surprise, but it does, big time. - It would be really nice if Pharo offered true decimal arithmetic as an option. There may already be a package for this. On Tue, 8 Sep 2020 at 15:46, Esteban Maringolo <[hidden email]> wrote: On Tue, Sep 8, 2020 at 12:16 AM Richard O'Keefe <[hidden email]> wrote: |
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In reply to this post by Esteban A. Maringolo
I'm coming back to this because I've been bitten by these floating
points things again. If in Pharo [1] you do: a := 6.7 + (32.8 - 35) It will produce: 4.499999999999997 Which, when rounded, will produce 4. In other places [2] I do the same simple addition and subtraction it produces 4.5, that when rounded will produce 5. I know now that Pharo doesn't lie to me while other systems do, and all that Richard pointed to before. The issue here is that I'm following some calculation formula that was defined in some of the "other" systems, and so when I follow such a formula I get these edgy cases where my system produces a different output. In this case the formula is for golf handicap calculations, and it caused my system to give 4 instead of 5 to a player, resulting in giving the first place to a player other than the one deserved. It was no big deal (it's not The Masters), but these cases appear from time to time. Is there any way to "configure" the floating point calculation to behave as the "other systems"? What is the best way to anticipate these situations, am I the only one being bitten by these issues? Thanks in advance for any hints about these problems. Best regards, [1] Dolphin Smalltalk, JS, Python, Ruby, Dart produces the same output as Pharo. [2] VisualWorks, VAST, Excel, VB and all calculators I tried Esteban A. Maringolo On Tue, Sep 8, 2020 at 12:45 AM Esteban Maringolo <[hidden email]> wrote: > > On Tue, Sep 8, 2020 at 12:16 AM Richard O'Keefe <[hidden email]> wrote: > > > > "7.1 roundTo: 0.1 should return 7.1" > > You're still not getting it. > > I was until Konrad explained it. > > > Binary floating point CANNOT represent either of those numbers. > > You seem to be assuming that Pharo is making some mistake. > > It isn't. All it is doing is refusing to lie to you. > <snip> > > The systems that print 7.1 are LYING to you, > > and Pharo is not. > > I'm not assuming a mistake from Pharo, I had a wrong expectation what > to get if I round to that precision. > I don't know whether other systems lie or simply fulfill user > expectations, if you send the #roundTo: to a float, I did expect to > get a number with the same precision. > That is my expectation as a user. As in the other thread I expected > two scaled decimals that are printed equal to also be compared as > equal (which they don't). > > Whether there is a good reason for those behaviors is beyond my > current comprehension, but it certainly doesn't follow the "principle > of least surprise". > > In any case, the method proposed by Tomohiro solved my issues. > > Regards, > > Esteban A. Maringolo |
Re: Rounding in Floats
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> On 14 Jun 2021, at 22:44, Esteban Maringolo <[hidden email]> wrote: > > I'm coming back to this because I've been bitten by these floating > points things again. > > If in Pharo [1] you do: > a := 6.7 + (32.8 - 35) > > It will produce: > 4.499999999999997 > > Which, when rounded, will produce 4. But, a roundTo: 0.1 "=> 4.5" > In other places [2] I do the same simple addition and subtraction it > produces 4.5, that when rounded will produce 5. > > I know now that Pharo doesn't lie to me while other systems do, and > all that Richard pointed to before. > > The issue here is that I'm following some calculation formula that was > defined in some of the "other" systems, and so when I follow such a > formula I get these edgy cases where my system produces a different > output. > > In this case the formula is for golf handicap calculations, and it > caused my system to give 4 instead of 5 to a player, resulting in > giving the first place to a player other than the one deserved. > It was no big deal (it's not The Masters), but these cases appear from > time to time. > > Is there any way to "configure" the floating point calculation to > behave as the "other systems"? > > What is the best way to anticipate these situations, am I the only one > being bitten by these issues? > > Thanks in advance for any hints about these problems. > > > Best regards, > > [1] Dolphin Smalltalk, JS, Python, Ruby, Dart produces the same output as Pharo. > [2] VisualWorks, VAST, Excel, VB and all calculators I tried > > > > Esteban A. Maringolo > > On Tue, Sep 8, 2020 at 12:45 AM Esteban Maringolo <[hidden email]> wrote: >> >> On Tue, Sep 8, 2020 at 12:16 AM Richard O'Keefe <[hidden email]> wrote: >>> >>> "7.1 roundTo: 0.1 should return 7.1" >>> You're still not getting it. >> >> I was until Konrad explained it. >> >>> Binary floating point CANNOT represent either of those numbers. >>> You seem to be assuming that Pharo is making some mistake. >>> It isn't. All it is doing is refusing to lie to you. >> <snip> >>> The systems that print 7.1 are LYING to you, >>> and Pharo is not. >> >> I'm not assuming a mistake from Pharo, I had a wrong expectation what >> to get if I round to that precision. >> I don't know whether other systems lie or simply fulfill user >> expectations, if you send the #roundTo: to a float, I did expect to >> get a number with the same precision. >> That is my expectation as a user. As in the other thread I expected >> two scaled decimals that are printed equal to also be compared as >> equal (which they don't). >> >> Whether there is a good reason for those behaviors is beyond my >> current comprehension, but it certainly doesn't follow the "principle >> of least surprise". >> >> In any case, the method proposed by Tomohiro solved my issues. >> >> Regards, >> >> Esteban A. Maringolo |
Re: Rounding in Floats
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BTW, I recently wrote my own float printer, as an experiment.
NeoJSONFloatPrinter lowPrecision print: a. => 4.5 What I wanted was a human friendly, compact float printer, that tries to go for the shortest, simplest number. It prefers integers and goes to scientific notation when needed, while limiting the precision. Maybe it is interesting to look at the code. But I am far from an expert. > On 14 Jun 2021, at 23:23, Sven Van Caekenberghe <[hidden email]> wrote: > > > >> On 14 Jun 2021, at 22:44, Esteban Maringolo <[hidden email]> wrote: >> >> I'm coming back to this because I've been bitten by these floating >> points things again. >> >> If in Pharo [1] you do: >> a := 6.7 + (32.8 - 35) >> >> It will produce: >> 4.499999999999997 >> >> Which, when rounded, will produce 4. > > But, > > a roundTo: 0.1 "=> 4.5" > >> In other places [2] I do the same simple addition and subtraction it >> produces 4.5, that when rounded will produce 5. >> >> I know now that Pharo doesn't lie to me while other systems do, and >> all that Richard pointed to before. >> >> The issue here is that I'm following some calculation formula that was >> defined in some of the "other" systems, and so when I follow such a >> formula I get these edgy cases where my system produces a different >> output. >> >> In this case the formula is for golf handicap calculations, and it >> caused my system to give 4 instead of 5 to a player, resulting in >> giving the first place to a player other than the one deserved. >> It was no big deal (it's not The Masters), but these cases appear from >> time to time. >> >> Is there any way to "configure" the floating point calculation to >> behave as the "other systems"? >> >> What is the best way to anticipate these situations, am I the only one >> being bitten by these issues? >> >> Thanks in advance for any hints about these problems. >> >> >> Best regards, >> >> [1] Dolphin Smalltalk, JS, Python, Ruby, Dart produces the same output as Pharo. >> [2] VisualWorks, VAST, Excel, VB and all calculators I tried >> >> >> >> Esteban A. Maringolo >> >> On Tue, Sep 8, 2020 at 12:45 AM Esteban Maringolo <[hidden email]> wrote: >>> >>> On Tue, Sep 8, 2020 at 12:16 AM Richard O'Keefe <[hidden email]> wrote: >>>> >>>> "7.1 roundTo: 0.1 should return 7.1" >>>> You're still not getting it. >>> >>> I was until Konrad explained it. >>> >>>> Binary floating point CANNOT represent either of those numbers. >>>> You seem to be assuming that Pharo is making some mistake. >>>> It isn't. All it is doing is refusing to lie to you. >>> <snip> >>>> The systems that print 7.1 are LYING to you, >>>> and Pharo is not. >>> >>> I'm not assuming a mistake from Pharo, I had a wrong expectation what >>> to get if I round to that precision. >>> I don't know whether other systems lie or simply fulfill user >>> expectations, if you send the #roundTo: to a float, I did expect to >>> get a number with the same precision. >>> That is my expectation as a user. As in the other thread I expected >>> two scaled decimals that are printed equal to also be compared as >>> equal (which they don't). >>> >>> Whether there is a good reason for those behaviors is beyond my >>> current comprehension, but it certainly doesn't follow the "principle >>> of least surprise". >>> >>> In any case, the method proposed by Tomohiro solved my issues. >>> >>> Regards, >>> >>> Esteban A. Maringolo |
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In reply to this post by Sven Van Caekenberghe-2
Hi Sven,
> > If in Pharo [1] you do: > > a := 6.7 + (32.8 - 35) > > It will produce: > > 4.499999999999997 > > Which, when rounded, will produce 4. > But, > a roundTo: 0.1 "=> 4.5" Sure, but what initiated this thread was a reference to roundTo: 0.1 which produced a "wrong" output. (9.1 + (-2.0)) roundTo: 0.1 "=> 7.1000000000000005" 7.1 roundTo: 0.1 "=> 7.1000000000000005" However, at this point I know that Pharo "does the right, raw, thing" (at least compared to other mainstream languages), but it still produces a surprise effect. In particular when people go to Excel to "check that your system does the right thing", uses the same formula and it gives a different result to them. Then open a calculator (or a physical one) and it gives the same number as Excel. So an hour after the fact you're arguing about floating point implementations to non-technical people :-) Regards! Esteban A. Maringolo |
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In reply to this post by Esteban A. Maringolo
It's not quite clear what is happening in the other systems.
Here is R > 6.7 + (32.8 - 35) [1] 4.5 > round(6.7 + (32.8 - 35)) [1] 4 The result *is* 4.499999.... but is *printed* as 4.5. Here is Gambit Scheme > (+ 6.7 (- 32.8 35)) 4.499999999999997 > (round (+ 6.7 (- 32.8 35))) 4. Here is astc Smalltalk 6.7 + (32.8 - 35) printOn: Transcript Transcript tab. (6.7 + (32.8 - 35)) rounded printOn: Transcript. Transcript cr. 4.499999999999997 4 And here is Python >>> x = 6.7 + (32.8 - 35) >>> x 4.499999999999997 >>> round(x) 4 For what it's worth, I expected ScaledDecimal to act like fixed point arithmetic, and implemented it that way in my own Smalltalk library, where two ScaledDecimals *do* print the same if and only if they are numerically exactly the same. What Squeak and Pharo do is exceedingly odd: a ScaledDecimal is an exact rational number (Integer or Fraction) combined with a precision that is used for printing, not for calculation. There really isn't any principle of least surprise when it comes to floating- point arithmetic. It's full of surprises and edge cases. Excel in particular is notorious for messing up due to trying to pretend all is well. In this particular case, the exact result is 4.5 There are at least three rules for rounding such numbers: rounding out (5), rounding in (4), and rounding in [banker'salgorithm] (4 here, but 5.5 -> 6). So you are pushing up against an edge case for exact hand calculation! I think you need to re-express your entire calculation to use exact arithmetic. That or get agreement on "de minimis non curat lex". On Tue, 15 Jun 2021 at 08:45, Esteban Maringolo <[hidden email]> wrote: > > I'm coming back to this because I've been bitten by these floating > points things again. > > If in Pharo [1] you do: > a := 6.7 + (32.8 - 35) > > It will produce: > 4.499999999999997 > > Which, when rounded, will produce 4. > > In other places [2] I do the same simple addition and subtraction it > produces 4.5, that when rounded will produce 5. > > I know now that Pharo doesn't lie to me while other systems do, and > all that Richard pointed to before. > > The issue here is that I'm following some calculation formula that was > defined in some of the "other" systems, and so when I follow such a > formula I get these edgy cases where my system produces a different > output. > > In this case the formula is for golf handicap calculations, and it > caused my system to give 4 instead of 5 to a player, resulting in > giving the first place to a player other than the one deserved. > It was no big deal (it's not The Masters), but these cases appear from > time to time. > > Is there any way to "configure" the floating point calculation to > behave as the "other systems"? > > What is the best way to anticipate these situations, am I the only one > being bitten by these issues? > > Thanks in advance for any hints about these problems. > > > Best regards, > > [1] Dolphin Smalltalk, JS, Python, Ruby, Dart produces the same output as Pharo. > [2] VisualWorks, VAST, Excel, VB and all calculators I tried > > > > Esteban A. Maringolo > > On Tue, Sep 8, 2020 at 12:45 AM Esteban Maringolo <[hidden email]> wrote: > > > > On Tue, Sep 8, 2020 at 12:16 AM Richard O'Keefe <[hidden email]> wrote: > > > > > > "7.1 roundTo: 0.1 should return 7.1" > > > You're still not getting it. > > > > I was until Konrad explained it. > > > > > Binary floating point CANNOT represent either of those numbers. > > > You seem to be assuming that Pharo is making some mistake. > > > It isn't. All it is doing is refusing to lie to you. > > <snip> > > > The systems that print 7.1 are LYING to you, > > > and Pharo is not. > > > > I'm not assuming a mistake from Pharo, I had a wrong expectation what > > to get if I round to that precision. > > I don't know whether other systems lie or simply fulfill user > > expectations, if you send the #roundTo: to a float, I did expect to > > get a number with the same precision. > > That is my expectation as a user. As in the other thread I expected > > two scaled decimals that are printed equal to also be compared as > > equal (which they don't). > > > > Whether there is a good reason for those behaviors is beyond my > > current comprehension, but it certainly doesn't follow the "principle > > of least surprise". > > > > In any case, the method proposed by Tomohiro solved my issues. > > > > Regards, > > > > Esteban A. Maringolo |
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On Mon, Jun 14, 2021 at 10:37 PM Richard O'Keefe <[hidden email]> wrote:
> For what it's worth, I expected ScaledDecimal to act like fixed point > arithmetic, and implemented it that way in my own Smalltalk library, where > two ScaledDecimals *do* print the same if and only if they are numerically > exactly the same. > What Squeak and Pharo do is exceedingly odd: a ScaledDecimal > is an exact rational number (Integer or Fraction) combined with a precision that > is used for printing, not for calculation. I pointed out before the weird behavior of ScaledDecimals in Pharo, two ScaledDecimal that print the same are not equal. Giving some weird comparison issues as result. > There really isn't any principle of least surprise when it comes to floating- > point arithmetic. It's full of surprises and edge cases. Excel in particular > is notorious for messing up due to trying to pretend all is well. > In this particular case, the exact result is 4.5 Well... for the end user, it produces what they'd expect. So it might mess up, but in a spreadsheet 6.7 - 2.2 should give 4.5. > There are at least three rules for rounding such numbers: rounding out (5), > rounding in (4), and rounding in [banker'salgorithm] (4 here, but 5.5 -> 6). > So you are pushing up against an edge case for exact hand calculation! I implemented a Float>>#roundedHandicap method that does something like the banking algorithm, but rounds positive numbers towards the next integer and negative numbers towards zero. E.g. 0.49 -> 0 0.5 -> 1 -0.5 -> 0 -0.51 -> -1 Nothing uses more than one decimal, so a ScaledDecimal would work but the specification says that it should use all possible precision in intermediate calculations, so I cannot use it. > I think you need to re-express your entire calculation to use exact arithmetic. I really don't know how to do this, any pointers? Nothing is more straightforward than addition and subtraction to me, 6.7 - 2.2 is the simplest it can get. The common formula here is: h * s / 113 + (r - p), but in this particular case s was 113 so it removed the "troubling" part. > That or get agreement on "de minimis non curat lex". I had to search for that expression. Now I know, I agree. Regards, Esteban A. Maringolo > > > On Tue, 15 Jun 2021 at 08:45, Esteban Maringolo <[hidden email]> wrote: > > > > I'm coming back to this because I've been bitten by these floating > > points things again. > > > > If in Pharo [1] you do: > > a := 6.7 + (32.8 - 35) > > > > It will produce: > > 4.499999999999997 > > > > Which, when rounded, will produce 4. > > > > In other places [2] I do the same simple addition and subtraction it > > produces 4.5, that when rounded will produce 5. > > > > I know now that Pharo doesn't lie to me while other systems do, and > > all that Richard pointed to before. > > > > The issue here is that I'm following some calculation formula that was > > defined in some of the "other" systems, and so when I follow such a > > formula I get these edgy cases where my system produces a different > > output. > > > > In this case the formula is for golf handicap calculations, and it > > caused my system to give 4 instead of 5 to a player, resulting in > > giving the first place to a player other than the one deserved. > > It was no big deal (it's not The Masters), but these cases appear from > > time to time. > > > > Is there any way to "configure" the floating point calculation to > > behave as the "other systems"? > > > > What is the best way to anticipate these situations, am I the only one > > being bitten by these issues? > > > > Thanks in advance for any hints about these problems. > > > > > > Best regards, > > > > [1] Dolphin Smalltalk, JS, Python, Ruby, Dart produces the same output as Pharo. > > [2] VisualWorks, VAST, Excel, VB and all calculators I tried > > > > > > > > Esteban A. Maringolo > > > > On Tue, Sep 8, 2020 at 12:45 AM Esteban Maringolo <[hidden email]> wrote: > > > > > > On Tue, Sep 8, 2020 at 12:16 AM Richard O'Keefe <[hidden email]> wrote: > > > > > > > > "7.1 roundTo: 0.1 should return 7.1" > > > > You're still not getting it. > > > > > > I was until Konrad explained it. > > > > > > > Binary floating point CANNOT represent either of those numbers. > > > > You seem to be assuming that Pharo is making some mistake. > > > > It isn't. All it is doing is refusing to lie to you. > > > <snip> > > > > The systems that print 7.1 are LYING to you, > > > > and Pharo is not. > > > > > > I'm not assuming a mistake from Pharo, I had a wrong expectation what > > > to get if I round to that precision. > > > I don't know whether other systems lie or simply fulfill user > > > expectations, if you send the #roundTo: to a float, I did expect to > > > get a number with the same precision. > > > That is my expectation as a user. As in the other thread I expected > > > two scaled decimals that are printed equal to also be compared as > > > equal (which they don't). > > > > > > Whether there is a good reason for those behaviors is beyond my > > > current comprehension, but it certainly doesn't follow the "principle > > > of least surprise". > > > > > > In any case, the method proposed by Tomohiro solved my issues. > > > > > > Regards, > > > > > > Esteban A. Maringolo |
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In reply to this post by Esteban A. Maringolo
On 15/06/2021 01:03, Esteban Maringolo wrote:
> Sure, but what initiated this thread was a reference to roundTo: 0.1 > which produced a "wrong" output. > > (9.1 + (-2.0)) roundTo: 0.1 "=> 7.1000000000000005" > 7.1 roundTo: 0.1 "=> 7.1000000000000005" > > However, at this point I know that Pharo "does the right, raw, thing" > (at least compared to other mainstream languages), but it still > produces a surprise effect. That's the "floating point surprise" that everyone has at some point, no matter the language and runtime system. If that surprise is a problem for you, are you sure that floating-point arithmetic is what you really want? Maybe your needs are better served with integers and fractions. Konrad. |
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Have you considered using fixed-point arithmetic? For example:
7.1s2 roundTo: 0.1s2 The rule of thumb I stick to is to use FP only if I know the inaccuracies won't bite me. Funny enough, both 7.1 and 0.1 are already not accurately representable as floats. (And by coincidence, I prepared exam questions about floats for my students yesterday. ) Kind regards, Steffen Konrad Hinsen schrieb am Dienstag, 15. Juni 2021 07:02:30 (+02:00): > On 15/06/2021 01:03, Esteban Maringolo wrote: > > Sure, but what initiated this thread was a reference to roundTo: 0.1 > > which produced a "wrong" output. > > > > (9.1 + (-2.0)) roundTo: 0.1 "=> 7.1000000000000005" > > 7.1 roundTo: 0.1 "=> 7.1000000000000005" > > > > However, at this point I know that Pharo "does the right, raw, thing" > > (at least compared to other mainstream languages), but it still > > produces a surprise effect. > > That's the "floating point surprise" that everyone has at some point, no matter the language and runtime system. If that surprise is a problem for you, are you sure that floating-point arithmetic is what you really want? Maybe your needs are better served with integers and fractions. > > > Konrad. > > -- Gesendet mit Vivaldi Mail. Laden Sie Vivaldi kostenlos von vivaldi.com herunter. |
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