[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

I have started a discussion at 
https://discuss.python.org/t/allow-fractions-fraction-to-return-1-6-for-0-17-0-167-0-1667-etc
 .  Your feedback there would be much appreciated.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

> I gave the code example in order to make that clear.

Yep, that didn't help: reverse engineering the intended behaviour from a 
complicated piece of code isn't easy. An up-front description of the intended 
behaviour would be better.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

Re python-ideas: there's a mailing list: 

https://mail.python.org/archives/list/python-id...@python.org/

But the https://discuss.python.org/c/ideas/ category also works for this.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

In case there are others who are unsure about "python-ideas" ... I believe the 
discussion page https://discuss.python.org/c/ideas is what was meant.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

> Please watch the tone. It is borderline abusive and dismissive.

I apologize for the adverse impact there.  I will be more careful.

> Also, my expectation for Fraction("0.0015") would be to give Fraction(3, 
> 2000), the same as would be given by Fraction(Decimal("0.0015")).

Yes, 0.0015 would be 3/2000.  However, in my example "0.0015" is the right 
endpoint of [0.0005, 0.0015), not the value "0.001" that we are seeking the 
fraction for.

> Perhaps this tracker issue should be closed and moved to python-ideas.  The 
> notions are currently too immature to warrant more core developer time.

You have more experience with this than I.  I defer to you.

> Agreed. It seems that what Lee wants is some kind of blend between the 
> simplest fraction and the closest fraction, and it's not clear exactly how 
> that blend would work.

Drat.  I gave the code example in order to make that clear.  I guess we can 
continue to discuss this at "python-ideas".  My quick web search for that turns 
up a lot of things.  If you could give me a lead -- is there a web URL for 
that, is it an e-mail list, etc.?

Thank you all for your valuable comments.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

Okay, let's close here; as Raymond says, that doesn't prevent further 
discussion on python-ideas.

> The notions are currently too immature to warrant more core developer time.

Agreed. It seems that what Lee wants is some kind of blend between the simplest 
fraction and the closest fraction, and it's not clear exactly how that blend 
would work.

--
resolution:  -> rejected
stage:  -> resolved
status: open -> closed

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Raymond Hettinger]

Raymond Hettinger  added the comment:

>  Nor will it achieve world peace.

Please watch the tone. It is borderline abusive and dismissive.

> we can invoke the attached as best_fraction(Fraction("0.001"),
> Fraction("0.0005"), Fraction("0.0015")) to get the output
> Fraction(1, 1000).

-1 I am solidly against this.  The other inputs to Fraction() are exact 
conversions.  The proposal works against a core concept behind the fraction 
module. 

Also, my expectation for Fraction("0.0015") would be to give Fraction(3, 2000), 
the same as would be given by Fraction(Decimal("0.0015")).

> But if it solves enough use cases then it is worth discussing, yes?

Perhaps this tracker issue should be closed and moved to python-ideas.  The 
notions are currently too immature to warrant more core developer time.

Also, it would be nice to have research into what other languages and libraries 
do for fractional approximations of decimal strings.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

> The 12 semitones in an octave are separated ...

Right, this functionality would not solve the semitones / cents problem.  Nor 
will it achieve world peace.  But if it solves enough use cases then it is 
worth discussing, yes?

I haven't written the string parsing, but once we know that "0.001" means to 
look in [0.0005, 0.0015) then we can invoke the attached as 
best_fraction(Fraction("0.001"), Fraction("0.0005"), Fraction("0.0015")) to get 
the output Fraction(1, 1000).

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Added file: https://bugs.python.org/file50627/best_fraction.py

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Raymond Hettinger]

Raymond Hettinger  added the comment:

Also note for the music example that the notion of "near enough" isn't 
equidistant about the "simple fraction".  The sense of nearness is logarithmic 
and is measured in "cents" which are hundredths of an equal-tempered semitone 
(i.e a one octave consists of 1200 cents).

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Raymond Hettinger]

Raymond Hettinger  added the comment:

I don't think the standard library should go down this path.  

Mark's disinclinations all make sense to me, but I'm also concerned that the 
API would be almost unusable in practical situations.  Users would tend to know 
their input fraction and that they have a desire for "simplification", but it 
would be challenging for them to come with a surrounding interval that made 
sense.  We could attempt to infer an interval from the input, but a user is 
likely to have a poorly specified idea of what they actually want.  The 
operating principle here is, "refuse the temptation to guess".

Here's a little exercise for the API.  The 12 semitones in an octave are 
separated by a frequency ratio of 2**(1/12).  For example, if A is 440 Hz, then 
A# is 440*2**(1/12) = 466.16 Hz.  Note pairs sound the most harmonious when the 
ratio of their frequencies is a "near" a small fraction.  Determine the small 
fraction for each of the twelve notes.  For example, a perfect fifth has the 
frequency ratio of 2**(7/12) -> 1.498307 — it it "perfect" because it 
"close-enough" to the small integer ratio of 3 : 2.  Notice the vague 
requirements of "near", "close-enough" and "small integer ratio".

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

> What about for an input of "0.001"? Your current specification would give 
> 1/667, but I'm betting that you'd actually prefer 1/1000.

You would win that bet.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

> I'd modify the optimization to be that we continue to seek the smallest 
> denominator, but in the case that multiple numerators would give ratios 
> within the computed interval then we choose the numerator among these that 
> gives the ratio closest to the input value.

Hmm. This is getting more DWIM-like (Do What I Mean) by the minute. :-)

What about for an input of "0.001"? Your current specification would give 
1/667, but I'm betting that you'd actually prefer 1/1000.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

>It would return 1/7 for "0.1" and 1/4 for "0.2". Is it what you expected?

I answered "yes" before, but I am now thinking "no".  In the case of "0.1", the 
smallest numerator achievable is 1, but there are multiple denominators that 
would give a value within [0.05, 0.15).  So, I'd choose the denominator that 
gives the ratio that is closet to the input value.

This is similar to the "16e2" example but with the roles of numerator and 
denominator reversed.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

The example of "16e2" would yield the interval [1550, 1650).  The smallest 
denominator possible is 1.  The smallest numerator that works with that 
denominator is 1550, but I don't like 1550/1 as the answer.

To cover these edge cases, I'd modify the optimization to be that we continue 
to seek the smallest denominator, but in the case that multiple numerators 
would give ratios within the computed interval then we choose the numerator 
among these that gives the ratio closest to the input value.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

> One more example: what interval is implied by an input string of "1600"? Is 
> it (1550, 1650)? Or (1595, 1605)? Or even (1599.5, 1600.5).

The rule would be to look at the last digit supplied and assume that the 
rounding is there.  So "1600" gives [1599.5, 1600.5) and "16e2" gives [1550, 
1650).

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

> You may be interested in the "simplefractions" module on PyPI, which solves 
> the exact task "find the simplest fraction in a given interval".

I haven't seen that code and I am interested; I will take a look.  Perhaps code 
from there can be imported / incorporated in our implementation here.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

One more example: what interval is implied by an input string of "1600"? Is it 
(1550, 1650)? Or (1595, 1605)? Or even (1599.5, 1600.5).

Sorry, I just don't see this working - there are two many arbitrary choices 
involved in guessing what interval the user intended. Much better to require 
the user to give that interval directly.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

> For another problematic example, suppose the string supplied is "0.10"

We would treat "0.1", "0.10", "0.100", etc. all differently.  In all cases we 
would assume rounding to compute the last digit.  Similarly for "3e-10", 
"3.0e-10" == "30e-11", "3.00e-11", etc.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

> depending on which rounding mode was used (round-ties-to-even, 
> round-ties-to-away), the interval may be half-open, open or closed.

I think we will get the majority of the use cases if we pick one rounding 
strategy and stick with it.  In later version we could support more if we found 
the demand: in addition to assume_rounded=True we could allow 
assume_rounded="round_towards_zero", etc.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

>It would return 1/7 for "0.1" and 1/4 for "0.2". Is it what you expected?

Yes.  Or putting it another way, if that's not the right answer then whoever 
rounded the number should have retained more digits.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

Lee Newberg  added the comment:

>This sounds interesting, but also rather similar to what the 
>`limit_denominator` method can get you. 

`Fractions("0.17").limit_denominator()` and 
`Fractions("0.17").limit_denominator(n)`
for n > 28 do not give 1/6.  So, I'd have to guess at n until I get 1/6.  
Instead, I'd like to have the digits actually presented "0.17" determine the 
interval [0.165, 0.175) which then determines the fraction.

In particular, "0.170" would give a different answer ... a fraction within 
[0.1695, 0.1705).

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

Sigh:

> the next representable value up from 0.01 is 0.011

should say:

> the next representable value up from 0.10 is 0.11

I think I'll duck out and give my brain a rest before commenting further.

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

> in which case the interval we need is [0.095, 0.15]

Whoops, sorry; brain fail. If we're rounding to two sig figs, the next 
representable value up from 0.01 is 0.011, while the next one down is 0.099, so 
the interval we'd be interested in would be [0.0995, 0.105].

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Mark Dickinson]

Mark Dickinson  added the comment:

> the constructed Fraction first computes the range of the values that the 
> input string could have been rounded from

There's too much magic and guesswork here for my liking; I don't really see 
this as feasible. Moreover, depending on which rounding mode was used 
(round-ties-to-even, round-ties-to-away), the interval may be half-open, open 
or closed.

For another problematic example, suppose the string supplied is "0.10". How are 
we to guess whether this was the result of rounding to two decimal places after 
the point (in which case the interval we need is [0.095, 0.105]), or whether 
it's the result of rounding to two significant figures (in which case the 
interval we need is [0.095, 0.15])?

> and then computes the fraction in that half-open interval with the lowest 
> numerator and denominator

This part, however, is well-defined and can be done efficiently. You may be 
interested in the "simplefractions" module on PyPI, which solves the exact task 
"find the simplest fraction in a given interval".

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Serhiy Storchaka]

Serhiy Storchaka  added the comment:

It would return 1/7 for "0.1" and 1/4 for "0.2". Is it what you expected?

--
nosy: +serhiy.storchaka

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Zachary Ware]

Zachary Ware  added the comment:

This sounds interesting, but also rather similar to what the 
`limit_denominator` method can get you.  Can you provide examples that can't be 
handled nicely by `limit_denominator` to strengthen your case?

--
nosy: +mark.dickinson, rhettinger, zach.ware
versions: +Python 3.11

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[issue46780] Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.

[Lee Newberg]

New submission from Lee Newberg :

For example, a string such as "0.167" could be rounded from anything in 
[0.1665, 0.1675).  Within that interval, the fraction with the lowest numerator 
and denominator is 1/6.

Here it is proposed that we add a new flag to the Fractions constructor, 
perhaps called `_assume_rounded`, which defaults to False and then yields no 
change from current behavior.  However, when it is True, the constructed 
Fraction first computes the range of the values that the input string could 
have been rounded from, and then computes the fraction in that half-open 
interval with the lowest numerator and denominator.  This is described at 
https://en.wikipedia.org/wiki/Continued_fraction#Best_rational_within_an_interval,
 which uses continued fractions to arrive at the answer.

For extra bells and whistles, we'd support strings like "0x0.2AAB" which is 
hexadecimal for 1/6 rounded to that many places.  In this case, we'd find 1/6 
as the fraction with lowest numerator and denominator in the interval 
[0x0.2AAA8, 0x0.2AAB8).  Likewise for binary, octal, and any other formats 
supported by Python.

--
components: Library (Lib)
messages: 413418
nosy: Leengit
priority: normal
severity: normal
status: open
title: Allow Fractions to return 1/6 for "0.17", "0.167", "0.1667", etc.
type: enhancement

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