Rounding in Floats

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Rounding in Floats

Esteban A. Maringolo
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

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Re: Rounding in Floats

Sven Van Caekenberghe-2


> 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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Re: Rounding in Floats

Esteban A. Maringolo
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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Re: Rounding in Floats

khinsen
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.

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Re: Rounding in Floats

Sven Van Caekenberghe-2
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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Re: Rounding in Floats

SergeStinckwich
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:



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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Re: Rounding in Floats

Esteban A. Maringolo
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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Re: Rounding in Floats

tomo
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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Re: Rounding in Floats

Esteban A. Maringolo
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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Re: Rounding in Floats

Richard O'Keefe
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,

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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Re: Rounding in Floats

Esteban A. Maringolo
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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Re: Rounding in Floats

Richard O'Keefe
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:
>
> "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