Add a description about formatting decimal.Decimal with the e/E symbol by __format__.

[1nftf]

Test output

# Compare different precision on Decimal.
format(Decimal('0'), ".0E")      '0E+0'
format(Decimal('0'), ".1E")      '0.0E+1'
format(Decimal('0'), ".2E")      '0.00E+2'
format(Decimal('0'), ".3E")      '0.000E+3'
format(Decimal('0'), ".30E")     '0.000000000000000000000000000000E+30'
format(Decimal('-0.0'), ".0E")   '-0E-1'
format(Decimal('-0.0'), ".1E")   '-0.0E+0'
format(Decimal('-0.0'), ".2E")   '-0.00E+1'
format(Decimal('-0.0'), ".3E")   '-0.000E+2'
format(Decimal('-0.0'), ".30E")  '-0.000000000000000000000000000000E+29'

# Compare different 0 values.
format(0, ".3E")                '0.000E+00'
format(0.0, ".3E")              '0.000E+00'
format(-0.0, ".3E")             '-0.000E+00'
format(0j, ".3E")               '0.000E+00+0.000E+00j'
format(Decimal('0'), ".3E")     '0.000E+3'
format(Decimal('-0.0'), ".3E")  '-0.000E+2'

# Compare different format methods.
format(Decimal('0'), ".30E")                          '0.000000000000000000000000000000E+30'
format(1234512345123451234512345, ".30E")             '1.234512345123451205320704000000E+24'
format(Decimal('1234512345123451234512345'), ".30E")  '1.234512345123451234512345000000E+24'
"%.30E" % (Decimal('0'),)                             '0.000000000000000000000000000000E+00'  # exponent is 0, because the value is converted to float first
"%.30E" % (1234512345123451234512345,)                '1.234512345123451205320704000000E+24'
"%.30E" % (Decimal('1234512345123451234512345'),)     '1.234512345123451205320704000000E+24'

NOTE: The internal exponent of the Decimal, rather than its sign, is causing the difference.
It seams that precision will affect exponent.

• When formatting Decimal('0'), the exponent is equal to precision.
• When formatting Decimal('-0.0'), the exponent is equal to precision-1.

In addition to the above behavior, the exponent is not padded to
two digits, which also makes it inconsistent with the built-in types.

Although the results are numerically correct, and the document
(https://docs.python.org/3/library/string.html#format-specification-mini-language)
does not limit the exponent when the coefficient is 0.
However, this can be confusing for users.

Maybe the document needs to add a description.note, or change the result of Decimal type
to be consistent with built-in types.

Test script

from decimal import Decimal

templates = (
    'format({v}, ".{p}E")',
    # 'f"{{{v}:.{p}E}}"',
    # '"{{:.{p}E}}".format({v})',
    # '"%.{p}E" % ({v},)',

    # 'format({v}, ".{p}e")'
    # 'f"{{{v}:.{p}e}}"',
    # '"{{:.{p}e}}".format({v})',
    # '"%.{p}e" % ({v},)',
)

values = (
    # 0,
    # 0.0,
    # -0.0,
    # complex(0),
    Decimal('0'),
    Decimal('-0.0'),

    # 0.001,
    # Decimal('0.001'),

    # 1,
    # 1.0,
    # Decimal('1'),

    # 10,
    # 10.0,
    # Decimal('10'),

    # 100,
    # 100.0,
    # Decimal('100'),

    # 1234512345123451234512345,
    # 1234512345123451234512345.0,
    # Decimal('1234512345123451234512345'),
)

precision = (
    0,
    1,
    2,
    3,
    # 4,
    # 5,
    # 6,
    # 7,
    # 8,
    # 9,
    # 10,
    30,
    # 100,
    # 1000,
    # 10000,
)

results = [
    ((expr := t.format(v=repr(v), p=p)), eval(expr))
    for t in templates
        for v in values
            for p in precision
]

max_len_expr = max(len(expr) for expr, val in results)
for expr, val in results:
    print(f"{expr}{' ' * ((max_len_expr)-len(expr))}  {repr(val)}")

Linked PRs

• gh-142019: Add description about the exponent of result formatted with presentation type 'e'. #142084

[mdickinson]

Decimal instances differ from floats in that they have significant trailing zeros. For example, Decimal("10"), Decimal("10.0") and "Decimal("1e1") are distinct (although equal under ==) and the difference affects the output of some operations. So the base exponent of a Decimal instance is an extra piece of information beyond just the numerical value.

To the extent that it's possible, formatting tries to preserve this extra information. That's the reason for the behaviour you're seeing here.

>>> x = Decimal('0')
>>> s = format(x, '.2e')
>>> s
'0.00e+2'
>>> y = Decimal(s)
>>> x.as_tuple() == y.as_tuple()
True

Above we've reconstructed y from its formatted representation, and the reconstructed y has exactly the same internal representation as x had. If s were "0.00e+0" instead, we would have lost the exponent information.

In addition to the above behavior, the exponent is not padded to
two digits, which also makes it inconsistent with the built-in types.

This is a separate issue: I'd recommend opening a separate tracker issue if you want to pursue this. But this behaviour is mandated by the specification that the decimal module implements, so changing it would be a tough sell. From the spec (emphasis mine):

this comprises the letter ‘E’ followed immediately by the adjusted exponent converted to a character form. The latter is in base ten, using the characters 0 through 9 with no leading zeros, always prefixed by a sign character

[mdickinson]

Note that the spec itself does not prescribe how .e-style formatting should work: it describes two operations: to-scientific-string, which roughly corresponds to g-style formatting (but without precision control), and to-engineering-string, which is like e-style formatting (again with no precision control) but with the displayed exponent constrained to be a multiple of 3.

So there's some reading-between-the-lines necessary to implement full-fledged float-style formatting from Decimal.

But the spirit of preserving the exponent information is present in the to-engineering-string description. E.g., in the to-engineering-string specification:

if the number is a zero, the zero will have a decimal point and one or two trailing zeros added, if necessary, so that the original exponent of the zero would be recovered by the to-number conversion.

[serhiy-storchaka]

Decimal represents not only an approximate value, but also its precision. Decimal('0') is not the same as Decimal('0.000'). The former represents a value between Decimal('-0.5') and Decimal('0.5'), the latter -- between Decimal('-0.0005') and Decimal('0.0005'). Formatting tries to preserve this property.

>>> format(Decimal('0'), ".2E")
'0.00E+2'
>>> Decimal('0.00E+2')
Decimal('0')
>>> format(Decimal('0.000'), ".2E")
'0.00E-1'
>>> Decimal('0.00E-1')
Decimal('0.000')

So this is not a bug, but a feature.

[1nftf]

This issue is more about formatting values with the e/E symbol (with a given precision),
rather than converting the value to a scientific or engineering string.

When converting/serializing, you might want to keep as much information as possible.

When formatting, you usually intend to display them in a uniform format.

# These
format(Decimal('0.0'), ".3E")    '0.000E+2'
f"{Decimal('0.0'):.3E}"          '0.000E+2'
"{:.3E}".format(Decimal('0.0'))  '0.000E+2'
"%.3E" % (Decimal('0.0'),)       '0.000E+00'  # the Decimal is implicitly converted to a float

# Instead of these
Decimal('0.0').to_eng_string())             '0.0'
getcontext().to_eng_string(Decimal('0.0'))  '0.0'
getcontext().to_sci_string(Decimal('0.0'))  '0.0'

For users who are not familiar with the Decimal class (like me), it
might be expected that Decimal behaves similarly to float.
"0.000E+2" rather than "0.000E+00" is indeed a bit strange, and it
took me a little time to find the reason.

Documents compare

These two documents only define how to convert decimal floating-point
numbers to strings, not how to format them.

• https://speleotrove.com/decimal/daconvs.html
• https://docs.python.org/3/library/decimal.html

The formatting behavior is defined in these documents.

• https://docs.python.org/3/library/string.html#format-specification-mini-language
• https://en.cppreference.com/w/c/io/fprintf
  (I think printf behavior can be seen as the de facto standard for c style formatting.)

The cpp document requires the exponent to be 0 when the value is 0,
and requires the exponent to be padded to two digits. These is also
the behavior of python float.

However the python document omitted above requirements.
I'm not sure if this is intentionally relaxed for Decimal, or the
Decimal.__format__ implementer only followed the simplified python
document.

Proposal

My opinion is that we can add a more detailed description of the
different behavior.

But if possible, we can make Decimal's format behavior more similar to
float, and then update the documentation to describe the printf-like
behavior.

---

P.S. I never said this is a bug. The tag I gave this issue from the
beginning was #docs, not #type-bug .

[skirpichev]

I think this might be closed.

Though, maybe new issue should be opened, about minimum number of digits in the exponent for 'e'/'g' formats. I don't think that the decimal spec forbids here using the printf-style formatting also for Decimal's. The Decimal constructor also accepts padding zeros in the exponent. The only question is: does it worth a backward compatibility break?

[1nftf]

But a non-zero exponent will make the padding less useful.
And the '%' formatting will yield a different result due to implicit conversion to float.

>>> format(1 / Decimal('inf'), ".2e")
'0.00e-1000024'
>>> "%.2e" % (1 / Decimal('inf'))
'0.00e+00'

[1nftf]

If current Decimal format behavior is considered a feature and will
not change in future. A description like these can be added.

When the value is equal to zero, the exponent is always zero for float,
and internal exponent plus number of digits after decimal point for
Decimal.