# bug #53683: numerical output format for float values with magnitude greater than precision is wrong

 Submitter: Dan Sebald Submitted: Wed 18 Apr 2018 12:46:11 AM UTC Category: Interpreter Severity: 3 - Normal Priority: 5 - Normal Item Group: Regression Status: None Assigned to: None Originator Name: Open/Closed:  * Open Release:  * dev Operating System:  * Any
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## Discussion

Fri 20 Apr 2018 06:41:02 AM UTC, comment #9:

This is bigger than I initially thought.  At first I was thinking a one line fix for 4.4, but there is more to it.  Yes, there is one detail that just doesn't make sense with regard to common definitions.  Here is fixed point with 5 fractional digits (and is sort of what what Matlab is doing with its "4 digits after the decimal point"):

0.00333
0.03333
0.33333
3.33333
33.33333
333.33333
3333.33333
33333.33333
333333.33333
3333333.33333
33333333.33333

The following would be 5 significant digits, something similar to floating point

0.0033333
0.033333
0.33333
3.3333
33.333
333.33
3333.3
33333
333330
3333300
33333000

Then for the sake of space, at either extreme one might use engineering notation rather than such a long string of numerals.

Octave is following a floating point progression at the start, then transitions to a fixed point progression at the following point:

ans =  3333.3
ans =  33333.33333

Why should the larger number get more fractional resolution?  That's the one point I disagree with.  Just how many significant digits there are, whether it is fixed point or floating point is all a matter of choice.

I can see where this gets more complicated, if one considers groups of numbers.  For example, the following illustrates that it is the smallest number of the group that governs the overall fractional digits:

octave:7> rand(10,1) * 3e2
ans =

195.96153
32.12849
125.35201
91.77371
0.76179
128.33099
14.58701
257.34665
151.51730
209.94001

octave:8> rand(10,1) * 3e2
ans =

259.38
281.53
110.50
278.94
216.12
116.73
173.32
129.39
134.56
288.86

octave:9> rand(10,1) * 3e2
ans =

233.796
131.497
162.690
100.161
162.110
25.142
122.527
267.176
49.537
79.511

Or more precisely, governed by whatever number has the most fractional digits.  In the following there are numbers greater than that transition point mentioned above; they therefore have five digits to the right of the decimal point):

octave:40> rand(10,1) * 3e4
ans =

7900.99571
6466.43122
18928.80875
10963.55305
12949.62312
19015.19955
22253.92189
12301.65306
20224.36300
22761.48407

Dan Sebald <sebald>
Thu 19 Apr 2018 09:39:37 PM UTC, comment #8:

For 5.0, maybe we should decide what behavior we really want to have, define that precisely, then try to make it happen.

John W. Eaton <jwe>
Thu 19 Apr 2018 09:38:25 PM UTC, comment #7:

I agree that the use of the terms precision or "significant figures" is sloppy, so the documentation could use some work.

But the values shown aren't wrong, are they?  I don't think we are displaying more digits than are valid for the computed values.

John W. Eaton <jwe>
Thu 19 Apr 2018 08:13:32 PM UTC, comment #6:

Well, I'd say that current behavior is wrong, no matter the interpretation.  I'm not a real stickler for exact compatibility, but the issue here is that Matlab appears to be saying nothing about "precision" or (what Octave states in the documentation) "with 5 significant figures".  To me, "significant figures" can only be interpreted as precision, and Octave is sort of doing that in the first half of the progression below.  Anyway, Matlab just says "4 digits after the decimal point".  Perhaps once that no longer makes reasonable sense, then it switches to exponent notation.

Dan Sebald <sebald>
Thu 19 Apr 2018 07:07:08 PM UTC, comment #5:

After reverting the changeset mentioned in comment #3, the behavior is

octave:1> for i = -2:8; 10^i/3, endfor
ans =  0.0033333
ans =  0.033333
ans =  0.33333
ans =  3.3333
ans =  33.333
ans =  333.33
ans =  3333.3
ans =  33333.33333
ans =  333333.33333
ans =  3333333.33333
ans =  33333333.33333

so that's not it.

What's weird about the Matlab behavior is that it sometimes shows just a few non-zero digits, but always 4 after the decimal until it would need more than 7.  Whatever.  The "best" behavior here is pretty subjective.

John W. Eaton <jwe>
Wed 18 Apr 2018 10:24:35 AM UTC, comment #4:

fyi matlab 2017a switches to scientific notation:

>> for i = -2:8; 10^i/3, end
ans =
0.0033
ans =
0.0333
ans =
0.3333
ans =
3.3333
ans =
33.3333
ans =
333.3333
ans =
3.3333e+03
ans =
3.3333e+04
ans =
3.3333e+05
ans =
3.3333e+06
ans =
3.3333e+07

Nicholas Jankowski <nrjank>
Wed 18 Apr 2018 01:46:58 AM UTC, comment #3:

Ah, OK, thanks for the clarification.  This then probably goes back to this changeset:

Changeset:
24789 (a4d4ec566fd7) improve formatting of large values in pr-output functions …
http://hg.savannah.gnu.org/hgweb/octave/rev/a4d4ec566fd7

I'll leave this for someone else to investigate.

Dan Sebald <sebald>
Wed 18 Apr 2018 01:21:06 AM UTC, comment #2:

In previous versions of Octave:

for i = -2:8; 10^i/3, endfor
ans =  0.0033333
ans =  0.033333
ans =  0.33333
ans =  3.3333
ans =  33.333
ans =  333.33
ans =  3333.3
ans =    3.3333e+04
ans =    3.3333e+05
ans =    3.3333e+06
ans =    3.3333e+07

I believe Matlab also switches to scientific notation when the range of the value exceeds the output precision setting.

Mike Miller <mtmiller>
Wed 18 Apr 2018 01:09:27 AM UTC, comment #1:

Here's a changeset that will address this bug, but the fix may not be 100% accurate as to what the intended behavior is.  It procudes

octave:1> for i=-2:8
>   10^i / 3
> endfor
ans =  0.0033333
ans =  0.033333
ans =  0.33333
ans =  3.3333
ans =  33.333
ans =  333.33
ans =  3333.3
ans =   33333
ans =  333333
ans = 3333333
ans = 33333333

which shows how the right side digits is eventually discarded.  Note in the changeset that I actually chose the ld and rd to reflect the scientific or engineering understanding of "precision", not the computer/C interpretation.  Here's the formula change:

if (digits > 0)
{
-          ld = digits;
-          rd = (prec > digits ? prec - digits : prec);
+          ld = (prec > digits ? digits : prec);
+          rd = (prec > digits ? prec - digits : 0);
}

where my expectation was that ld limited to prec (i.e., 5) would create

ans = 33333000

rather than

ans = 33333333

as an example; but obviously it doesn't do that.  In some sense, what I intended could be a desirable behavior for those who want to present data in a paper or something and limit the precision to, say, three digits without having to do the rounding manually.  Do something manually always opens the door for mistakes so why not let the computer do the rounding?

Nonetheless, I suspect the that ld precision is interpreted in a C sense at the following point in the code:

template <typename T>
std::ostream&
operator << (std::ostream& os, const pr_formatted_float<T>& pff)
{
octave::preserve_stream_state stream_state (os);

float_format real_fmt = pff.m_ff;

if (real_fmt.fw >= 0)
os << std::setw (real_fmt.fw);

if (real_fmt.prec >= 0)
os << std::setprecision (real_fmt.prec);

os.flags (static_cast<std::ios::fmtflags>
(real_fmt.fmt | real_fmt.up | real_fmt.sp));

os << pff.m_val;

return os;
}

So, there are a few questions, the most primary being what the output should do in terms of "precision".  It might be good to create a set of tests with perhaps fifty examples of all the various formats...in string format, then just output the result to a string and compare.  If the attached change is small enough and fixes an obvious bug, then apply as it is, but in the long run this may need a more extensive review.

Dan Sebald <sebald>
Wed 18 Apr 2018 12:46:11 AM UTC, original submission:

It caught my attention that the output format is displaying too much precision for numbers that have magnitude greater than the number of digits of precision, stated imprecisely.  That is, notice the progression:

octave:1> for i=-2:8
>   10^i / 3
> endfor
ans =  0.0033333
ans =  0.033333
ans =  0.33333
ans =  3.3333
ans =  33.333
ans =  333.33
ans =  3333.3
ans =  33333.33333
ans =  333333.33333
ans =  3333333.33333
ans =  33333333.33333

that once the left digits hits 5 the right digits jumps back up to five.

Here are some related bug reports, but they aren't quite the same issue:

Dan Sebald <sebald>

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