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[3.12] gh-126165: Improve docs of function math.isclose (GH-126215) #126381

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[3.12] gh-126165: Improve docs of function math.isclose (GH-126215) #126381

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18 changes: 10 additions & 8 deletions Doc/library/cmath.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -221,19 +221,21 @@ Classification functions
``False`` otherwise.

Whether or not two values are considered close is determined according to
given absolute and relative tolerances.
given absolute and relative tolerances. If no errors occur, the result will
be: ``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``.

*rel_tol* is the relative tolerance -- it is the maximum allowed difference
between *a* and *b*, relative to the larger absolute value of *a* or *b*.
For example, to set a tolerance of 5%, pass ``rel_tol=0.05``. The default
tolerance is ``1e-09``, which assures that the two values are the same
within about 9 decimal digits. *rel_tol* must be greater than zero.

*abs_tol* is the minimum absolute tolerance -- useful for comparisons near
zero. *abs_tol* must be at least zero.

If no errors occur, the result will be:
``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``.
within about 9 decimal digits. *rel_tol* must be nonnegative and less
than ``1.0``.

*abs_tol* is the absolute tolerance; it defaults to ``0.0`` and it must be
nonnegative. When comparing ``x`` to ``0.0``, ``isclose(x, 0)`` is computed
as ``abs(x) <= rel_tol * abs(x)``, which is ``False`` for any ``x`` and
rel_tol less than ``1.0``. So add an appropriate positive abs_tol argument
to the call.

The IEEE 754 special values of ``NaN``, ``inf``, and ``-inf`` will be
handled according to IEEE rules. Specifically, ``NaN`` is not considered
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18 changes: 10 additions & 8 deletions Doc/library/math.rst
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Expand Up @@ -142,19 +142,21 @@ Number-theoretic and representation functions
``False`` otherwise.

Whether or not two values are considered close is determined according to
given absolute and relative tolerances.
given absolute and relative tolerances. If no errors occur, the result will
be: ``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``.

*rel_tol* is the relative tolerance -- it is the maximum allowed difference
between *a* and *b*, relative to the larger absolute value of *a* or *b*.
For example, to set a tolerance of 5%, pass ``rel_tol=0.05``. The default
tolerance is ``1e-09``, which assures that the two values are the same
within about 9 decimal digits. *rel_tol* must be greater than zero.

*abs_tol* is the minimum absolute tolerance -- useful for comparisons near
zero. *abs_tol* must be at least zero.

If no errors occur, the result will be:
``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``.
within about 9 decimal digits. *rel_tol* must be nonnegative and less
than ``1.0``.

*abs_tol* is the absolute tolerance; it defaults to ``0.0`` and it must be
nonnegative. When comparing ``x`` to ``0.0``, ``isclose(x, 0)`` is computed
as ``abs(x) <= rel_tol * abs(x)``, which is ``False`` for any ``x`` and
rel_tol less than ``1.0``. So add an appropriate positive abs_tol argument
to the call.

The IEEE 754 special values of ``NaN``, ``inf``, and ``-inf`` will be
handled according to IEEE rules. Specifically, ``NaN`` is not considered
Expand Down
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