Decimal: Inconsistent precision with large integers (≥29 digits) in arithmetic operations

[PeterShinners]

Bug report

Bug description:

The decimal.Decimal class is inconsistent when handling very large integers, over 29. Mathematical operations that should be equivalent (like Decimal(-v) and -Decimal(v)) produce different results, with some operations unexpectedly switching to scientific notation and losing precision.

This breaks mathematical consistency and can cause silent precision loss in applications that process large numbers, particularly financial, scientific, or cryptographic applications where precision is critical.

Steps to Reproduce:

from decimal import Decimal

# Bug occurs with integers having 29+ digits
v = 98765432109876543210987654321

# These should be equal but aren't (and does work as expected with smaller values):
result1 = Decimal(-v)  # Full precision: -98765432109876543210987654321
result2 = -Decimal(v)  # Scientific notation: -9.876543210987654321098765432E+28

assert result1 == result2  # This fails!

# abs() is also affected:
large_negative = Decimal('-98765432109876543210987654321')
assert abs(large_negative) == Decimal('98765432109876543210987654321')  # This fails too!

Expected Result: Both expressions should produce identical Decimal values with full precision preserved.

Actual Result: One method preserves full precision while the other switches to scientific notation, causing mathematically equivalent expressions to be unequal.

Additional Information:

• Affects Python 3.12.3 (and likely other versions)
• Threshold is exactly 29 digits
• Works correctly for numbers with 28 digits or fewer
• Affects abs(), negation, and potentially other arithmetic operations
• Can cause silent precision loss in calculations

CPython versions tested on:

3.12

Operating systems tested on:

Windows

[PeterShinners]

I just confirmed this behavior is the same on Python 3.14a4.

Python 3.14.0a4 (main, Feb  5 2025, 19:18:05) [MSC v.1942 64 bit (AMD64)] on win32

[zware]

Please read up on the decimal module's context. Quoting from the page:

The module design is centered around three concepts: the decimal number, the context for arithmetic, and signals.

Python 3.13.7 (main, Aug 14 2025, 00:00:00) [GCC 15.2.1 20250808 (Red Hat 15.2.1-1)] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> from decimal import Decimal, getcontext
>>> getcontext()
Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999, capitals=1, clamp=0, flags=[], traps=[InvalidOperation, DivisionByZero, Overflow])
>>> # Note the starting prec[ision]
>>> getcontext().prec = 30
>>> v = 98765432109876543210987654321
>>> result1 = Decimal(-v)
>>> result2 = -Decimal(v)
>>> assert result1 == result2
>>> result1
Decimal('-98765432109876543210987654321')
>>> result2
Decimal('-98765432109876543210987654321')

[skirpichev]

The decimal.Decimal class is inconsistent when handling very large integers, over 29.

It's not inconsistent, it's how floating-point arithmetic works (regardless on whether it's binary or decimal). Floating-point numbers have fixed precision (which is controlled by context).

I.e. precision for the default context is 28, as pointed you above. That means, your integer value is not exactly representable in this context. The Decimal constructor preserves exact value for your integer number (same it does for builtin float's), but any arithmetic operation will trigger a normalization (number will be rounded to context's precision as specified by rounding settings). Simplest way to trigger this - use just unary plus:

>>> v = 98765432109876543210987654321
>>> Decimal(v)
Decimal('98765432109876543210987654321')
>>> +Decimal(v)
Decimal('9.876543210987654321098765432E+28')
>>> Decimal(v) == +Decimal(v)
False

It's not just about the number of digits, trailing zeros might fit into context's exponent range and an integer still be exactly representable, see e.g. slightly adjusted your example:

>>> v2 = 9876543210987654321098765432 * 10**10
>>> Decimal(v2)
Decimal('98765432109876543210987654320000000000')
>>> +Decimal(v2)
Decimal('9.876543210987654321098765432E+37')
>>> Decimal(v2) == +Decimal(v2)
True