Re: [Mingw-users] msvcrt printf bug
Wow, you went to some pretty length defending Alexandru's (and my own)
arguments! Well done (and thx): it's exactly what I (and I'm sure
> So, to Alexandru Tei (the
> original poster) and Emanuel Falkenauer, stand your ground, you
> are right! (And don't let the personal attacks get you down.)
Indeed: I already told Alexandru to take it easy and keep the good work
he's doing, the unfortunate (and unfair) personal attacks
notwithstanding. ;-) As for me... well, I've got so many of those in
the past already that I guess I've seen it all... and I clearly
developed a serious rhino skin. :-)
The only thing I'm now puzzled about are the 80-bit FPU Intel registers:
so are they (as you seem to imply) or are they not (as KHMan asserts)
actually used these days - in, say, Xeons which I'm on? I.e. could
actually our programs run differently on, say, AMDs?
Thanks & "Happy Floating-Point Hacking" as you say,
On 03-Feb-17 04:38, K. Frank wrote:
> Hello List (and Alexandru)!
> I see that I'm coming late to the party, but I would like to chime in.
> On Sat, Jan 14, 2017 at 9:02 AM, <tei@xxxxxxxxx> wrote:
>> I encountered a loss of precision printing a float with C printf.
> There are a couple of common misconceptions running through
> this thread that I would like to correct.
> Short story: Floating-point numbers are well-defined, precise,
> accurate, exact mathematical objects. Floating-point arithmetic
> (when held to the standard of the "laws of arithmetic") in not
> always exact.
> Unfortunately, when you conflate these two issues and conclude
> that floating-point numbers are these mysterious, fuzzy, squishy
> things that can never under any circumstances be exact, you create
> the kind of floating-point FUD that runs through this thread, this
> email list, and the internet in general.
> (This kind of FUD shows up in a number of forms. You'll see,
> for example: "Never test for equality between two floating-point
> numbers." "Never test a floating-point number for equality with
> zero." "Floating-point numbers are fuzzy and inexact, so equality
> of floating-point numbers is meaningless." When you see this on
> the internet (and you will), don't believe it! Now, it's true that
> when you have two floating-point numbers that are the results
> of two independent chains of floating-point calculations it
> generally won't make sense to test for exact equality, but
> there are many cases where it does.)
> Worse yet (as is typical with FUD), when people call out this
> FUD (on the internet, not just this list), they get attacked
> with scorn and ad hominem arguments. So, to Alexandru Tei (the
> original poster) and Emanuel Falkenauer, stand your ground, you
> are right! (And don't let the personal attacks get you down.)
> Let me start with an analogy:
> Consider the number 157/50. It is a well-defined, precise, accurate,
> exact mathematical object. It's a rational number, which makes it
> also a real number (but it's not, for example, an integer). There
> is nothing fuzzy or imprecise or inaccurate about it.
> It has as its decimal representation 3.14 (and is precisely equal to
> 3.14). Now if we use it as an approximation to the real number pi,
> we find that it is an inexact value for pi -- it is only an approximation.
> But the fact that 3.14 is not exactly equal to pi doesn't make 3.14
> somehow squishy or inaccurate. 3.14 is exactly equal to 314 divided
> by 100 and is exactly equal to the average of 3.13 and 3.15. It's
> just not exactly equal to pi (among many other things).
> Now it is true that the vast majority of floating-point numbers
> running around in our computers are the results of performing
> floating-point arithmetic, and the large majority of these numbers
> are inexact approximations to the "correct" values (where by correct
> I mean the real-number results that would be obtained by performing
> real arithmetic on the floating-point operands). And anybody
> performing substantive numerical calculations on a computer needs
> to understand this, and should be tutored in it if they don't.
> (By the way, Alexandru asked nothing about floating-point calculations
> in his original post, and everything he has said in this thread indicates
> that he does understand how floating-point calculations work, so I have no
> reason to think that he needs to be tutored in the fact that floating-point
> arithmetic can be inexact.)
> Alexandru asked about printing out floating-point numbers. People
> have called this the "decimal" or "ASCII" representation of a
> floating-point numbers. I will stick to calling it the "decimal
> representation," by which I will mean a decimal fraction, of
> potentially arbitrary precision, that approximates a given
> floating-point number.
> In keeping with my point that floating-point numbers are well-defined,
> precise mathematical values, it is the case that every floating-point
> number is exactly equal to a single, specific decimal fraction.
> Alexandru complains that msvcrt doesn't use as its decimal representation
> of a floating-point number the decimal fraction that is exactly equal to it.
> This is a perfectly legitimate complaint.
> Now an implementation can use as its decimal representation of floating-point
> numbers whatever it wants -- it's a quality-of-implementation issue.
> The implementation could always print out floating-point numbers with
> two significant decimal digits. Or it could use ten significant digits,
> and add three to the last significant digit just for fun. But there is
> a preferred, canonically distinguished decimal representation for floating-point
> numbers -- use the unique decimal fraction (or ASCII string or whatever you
> want to call it) that is exactly equal to the floating-point number. "Exactly
> equal" -- what could get more canonical than that?
> In fairness, I don't consider this to be a particularly important
> quality-of-implementation issue. I do prefer that my implementations
> use the canonically distinguished decimal representation, but I don't care
> enough to have retrofitted mingw to do so (or to set the _XOPEN_SOURCE
> flag). But it isn't hard to get this right (i.e., to use the canonically
> distinguished representation), and apparently both glibc and Embarcadero/Borland
> have done so.
> I would argue that the glibc/Borland implementation is clearly better in
> this regard than that of msvcrt, and that there is no basis on which one
> could argue that the msvcrt implementation is better. (Again, in fairness,
> microsoft probably felt that is was a better use of a crack engineer's
> time to more smoothly animate a tool-tip fade-out than to implement the
> better decimal representation, and from a business perspective, they
> were probably right. But it's not that hard, so they could have done
> On Mon, Jan 16, 2017 at 3:17 PM, Keith Marshall <km@xxxxxxxxxxxxxxxxx> wrote:
>> On 16/01/17 16:51, Earnie wrote:
>> Regardless, it is a bug to emit more significant digits than the
>> underlying data format is capable of representing ... a bug by
>> which both glibc and our implementation are, sadly, afflicted;
>> that the OP attempts to attribute any significance whatsoever to
>> those superfluous digits is indicative of an all too common gap
>> in knowledge ... garbage is garbage, whatever form it may take.
> Here Keith claims that the glibc/Borland implementation is actually
> a bug. This is the kind of FUD we need to defend against.
> I create a floating-point number however I choose, perhaps by
> twiddling bits. (And perhaps not by performing a floating-point
> operation.) The number that I have created is perfectly well-defined
> and precise, and it is not a bug to be able to print out the decimal
> representation to which it is exactly equal. An implementation that
> lets me print out the exactly correct decimal representation is better
> than an implementation that does not.
> The floating-point number that I created may well have a well-defined,
> precise -- and even useful -- mathematical meaning, Keith's assertion
> that "garbage is garbage," notwithstanding.
> To reiterate this point ...
> On Wed, Jan 18, 2017 at 4:39 PM, Keith Marshall <khall@xxxxxxxxxxx> wrote:
>> On 18/01/17 10:00, tei@xxxxxxxxx wrote:
>>> Emanuel, thank you very much for stepping in. I am extremely happy
>>> that you found my code useful.
>> Great that he finds it useful; depressing that neither of you cares
>> in the slightest about accuracy; rather, you are both chasing the
>> grail of "consistent inaccuracy".
> Representing a floating-point number with the decimal fraction
> (or ASCII string or whatever you want to call it) that is exactly,
> mathematically equal to that floating-point number is, quite
> simply, accuracy, rather than inaccuracy.
> Granted, there are times when it may not be important or useful
> to do so, but there are times when it is.
>>> I will use cygwin when I need a more accurate printf.
>> Yes, I deliberately said "consistently inaccurate"; see, cygwin's
>> printf() is ABSOLUTELY NOT more accurate than MinGW's, (or even
>> Microsoft's, probably, for that matter). You keep stating these
>> (sadly all too widely accepted) myths:
> Alexandru is right here, and is stating truths. The printf() that
> emits the decimal fraction that is exactly, mathematically equal
> to the floating-point number being printed is in a very legitimate
> and substantive sense more accurate than the one that does not.
>>> Every valid floating point representation that is not NaN or inf
>>> corresponds to an exact, non recurring fraction representation in
>> In the general case, this is utter and absolute nonsense!
> On the contrary, Alexandru is completely correct here
> (Note: "utter and absolute nonsense" <-- FUD alert!)
> Alexandru's statement is sensible, relevant, and mathematically
> completely correct.
>>> There is no reason why printf shouldn't print that exact
>>> representation when needed, as the glibc printf does.
> Absolutely correct, Alexandru. If I or Alexandru or Emanuel wants
> the exact representation it's a plus that the implementation provides
> it for us.
>> Pragmatically, there is every reason. For a binary representation
>> with N binary digits of precision, the equivalent REPRESENTABLE
>> decimal precision is limited to a MAXIMUM of N * log10(2) decimal
> Again, you conflate the inaccuracy of some floating-point calculations
> with individual floating point numbers themselves. Individual
> floating-point numbers have mathematically well-defined, precise,
> accurate values (and some of us want to print those values out).
> Let me repeat this point in the context of a comment of Peter's:
> On Thu, Jan 19, 2017 at 6:19 AM, Peter Rockett <sprocket@xxxxxxxxxxxxx> wrote:
>> On 19/01/17 08:21, tei@xxxxxxxxx wrote:
>> I suspect the OP's conceptual problem lies in viewing every float in
>> splendid isolation rather than as part of a computational system.
> On the contrary, the conceptual problem underlying the FUD in this
> thread is conflation of the properties of the overall computational
> system with the individual floating-point numbers, and attributing
> to the individual floating-point numbers, which are well-defined and
> exact, the inexactness of some floating-point operations.
> Floating-point numbers make perfect sense and are perfectly well-defined
> "in splendid isolation" and to assume that all floating-point numbers of
> legitimate interest are the results of inexact floating-point computations
> is simply wrong.
>> Or another take: If you plot possible floating point representations on a
>> real number line, you will have gaps between the points. The OP is trying
>> print out numbers that fall in the gaps!
> When I read Alexandru's original post, it appears to me that he is trying
> to print out individual, specific floating-point numbers. That's his use
> case. I see nothing to suggest that he is trying to print out values in
> the gaps. (Alexandru clearly knows that floating-point numbers are discrete
> points on the real number line with gaps between them.)
> On Sun, Jan 15, 2017 at 10:08 PM, KHMan <cainherb@xxxxxxxx> wrote:
>> On 1/16/2017 8:56 AM, John Brown wrote:
>> I do not think there are canonical conversion algorithms that must
>> always be upheld, so I did not have an expectation that glibc must
>> be canonical.
> There is a canonically distinguished conversion algorithm -- it's the
> one that produces the decimal representation that is mathematically
> equal to the floating-point number. To repeat myself: Mathematical
> equality, what's more canonical than that?
> But, of course, this algorithm does not need to be upheld. I am quite
> sure that it is not required by either the c or c++ standard, and I
> am pretty sure that IEEE 754 is silent on this matter. (I also don't
> think that this issue is that important. But it is legitimate, and
> an implementation that does uphold this conversion algorithm is a
> better implementation.)
>> The glibc result is one data point, msvcrt is also one data point.
>> He claims to have his own float to string, but knowing digits of
>> precision limitations and the platform difference, why is he so
>> strident in knocking msvcrt? Curious. I won't score that, so we
>> are left with two data points running what are probably
>> non-identical algorithms.
> But it's more than just data points. We have a canonical representation.
> From this thread, we have three data points -- msvcrt, glibc, and
> Borland (plus Alexandru's roll-your-own) -- and (apparently, as I
> haven't tested them myself) glibc and Borland (and Alexandru's)
> produce the canonical representation, while msvcrt doesn't, so
> msvcrt is not canonical and is also the odd man out.
>> For that expectation we pretty much need everyone to be using the same
>> conversion algorithm.
> Yes, and we probably won't have everyone using the same conversion
> algorithm (for example, msvcrt). Well that's what standards are for,
> and some things don't get standardized. But if everyone were to use
> the same algorithm (for example, the canonical decimal representation),
> then this whole thread would be much simpler, and life would be easier
> for Emanuel.
> There are some side comments I would like to make:
> Two distinct, but related issues have been discussed. The first is
> whether printf() should print out the exact decimal representation
> of a floating-point number (Alexandru), and the second is whether
> different implementations should print out the same representation
> (Emanuel). Both are desirable goals, and if you get the first (for
> all implementations), you get the second.
> My preference, of course, would be to have all implementations print
> out the exact representation (when asked to). But you could, say,
> have printf() print out the (specific-floating-point-number-dependent)
> minimum number of digits for which you get "round-trip consistency"
> (i.e., floating-point number --> printf() --> ASCII --> scanf() -->
> back to the same floating-point number). That would be reasonable,
> and would solve Emanuel's problem. (Or you could print out the minimum
> number of "consistency" digits, and swap the last two digits just for fun.
> That would be less reasonable, but would also solve Emanuel's problem.)
> My point is that a canonically distinguished representation exists,
> so, even if you only care about the second issue, it's easier to
> get various implementations to hew to that canonical representation,
> rather than to some well-defined, but semi-arbitrary representation
> that I (or someone else) might make up.
> In retort to Keith's claim that such a standard across implementations,
> such as my "swap the last two digits" standard, would be chasing "consistent
> inaccuracy" (Of, course, the canonical representation would be "consistent
> accuracy."), Emanuel has presented a perfectly logical and valid use case
> for this. Sure, there are other ways Emanuel could achieve his goal of
> cross-checking the output of different builds, but this is a good one.
> More importantly, all of us (including Emanuel) agree that he has no
> right to expect the floating-point results of his different builds to
> be the exactly the same. (Nothing in the c or c++ standard, nor in
> IEEE 754 requires this.) However, he enjoys the happy accident that
> the floating-point results do agree, so it's unfortunate that printf()
> from mingw/msvcrt and Borland print out different values, and that he
> therefor has to go through additional work to cross-check his results.
> That he can use Emanuel's code or set the _XOPEN_SOURCE flag to
> resolve this issue is a good thing, but the fact that he has to take this
> extra step is a minor negative.
> Last, and quite tangential, Kein-Hong took a dig at Intel and the 8087:
> On Fri, Jan 20, 2017 at 7:54 PM, KHMan <herbnine@xxxxxxxx> wrote:
>> On 1/21/2017 6:18 AM, mingw@xxxxxxxxxxxxx wrote:
>> AFAIK it is only with 8087 registers -- just about the only
>> company who did this was Intel. Didn't really worked out,
> Actually, it worked out quite well for some important use cases,
> and kudos to Intel for doing this.
> Often in numerical analysis you perform linear algebra on large
> systems. Often with large systems round-off error accumulates
> excessively, and when the systems are ill-conditioned, the round-off
> error is further amplified.
> Often, as part of the linear-algebra algorithm, you compute a sum
> of products, that is, the inner product of two vectors. It turns
> out (and, if you're a numerical analyst, you can prove, given conditions
> on the linear systems involved), that you do not need to perform the
> entire calculation with higher precision to get dramatically more
> accurate results -- you can get most of the benefit just using higher
> precision to compute the inner products. The inner-product computation
> (a chain of multiply-accumulates) fits trivially in the 8087 floating-point
> registers (without register spill), and the use of the 8087's 80-bit
> extended-precision just on these inner-product computations yields
> dramatically more accurate results in many cases.
> There are various engineering considerations for not using extended-precision
> registers (some legitimate, some less so), but Intel, for whatever reason,
> decided that they wanted to do floating-point right, they hired Kahan to
> help them, and we're all the better for it.
> Look, I understand the frustration felt by many commenters here, particularly
> that expressed by Keith and Kein-Hong. Stack Overflow and forums and bulletin
> boards and chat rooms (and even classrooms, where they use things like, you
> know, "blackboards" and "chalk") are filled with naive confusion about
> floating-point arithmetic, with questions of the sort "I did x = y / z, and
> w = x * z, and x and w don't test equal. How can this be? Mercy! It must
> be a compiler bug!" And now you have to tutor another generation of novice
> programmers in how floating-point arithmetic works. It gets old.
> But it's counter-productive to tutor them with misinformation. Floating-point
> numbers are what they are and are mathematically perfectly well defined.
> Floating-point arithmetic is inexact when understood as an approximation
> to real-number arithmetic. Let's tutor the next generation in what actually
> happens: Two perfectly well-defined floating-point operands go into a
> floating-point operation, and out comes a perfectly well-defined (if you're
> using a well-defined standard such as IEEE 754) floating-point result that
> in general, is not equal to the real-number result you would have obtained
> if you had used real-number arithmetic on the floating-point operands.
> But, to repeat Emanuel's comment, "it's not as if a FPU had a Schrödinger cat
> embedded!" The floating-point operation doesn't sometimes give you one
> (inherently fuzzy) floating-point result and sometimes another (inherently
> fuzzy) result. It gives you a single, consistent, perfectly well-defined
> (if you're using a well-defined standard) result that makes perfectly good
> mathematical sense. Furthermore, it's also not as if the data bus connecting
> memory to the FPU has an embedded Schrödinger cat, and that these (squishy,
> fuzzy, inexact) floating-point numbers get fuzzed up somehow by cat hair as
> they travel around inside our computers.
> The way floating-point numbers -- and floating-point arithmetic -- really work
> is completely precise and mathematically well defined, even if it's subtle
> and complex -- and different from real-number arithmetic. And how it really
> works -- not FUD -- is what we need to help the next generation of people
> doing substantive numerical calculations learn.
> Happy Floating-Point Hacking!
> K. Frank
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