address review: move inline footnotes 5-7

Author: skirpichev

peps/pep-0812.rst

@@ -143,14 +143,19 @@ be implemented with this approach simply by:
 
 
 It's pioneered by the C99 standard ([3]_, [4]_).  This is also how complex
-arithmetic is implemented in the Ada language [5]_.  Some mathematical libraries
-(like the GNU GSL [6]_) or the GNU MPC [7]_) have special routines to implement
-mixed-mode arithmetic for complex numbers, i.e., when one operand either
-pure-real or pure-imaginary.  As a side effect, this also introduces some
-performance boost for operations with mixed types (e.g., multiplication of
-complex and real numbers costs only two real multiplications, not four).
-Although it's more important that in the IEC floating-point arithmetic results
-here are uniquely determined by the usual mathematical formulae.
+arithmetic is implemented in the Ada language, see the `Ada 2022 Reference
+Manual, Annex G <http://ada-auth.org/standards/22rm/RM-Final.pdf>`_.  Some
+mathematical libraries (like the GNU GSL, see the `GSL Reference Manual, §5.5
+<https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf>`_) or the GNU MPC, see
+the `MPC Reference Manual, §5.7
+<https://www.multiprecision.org/downloads/mpc-1.3.1.pdf>`_) have special
+routines to implement mixed-mode arithmetic for complex numbers, i.e., when one
+operand either pure-real or pure-imaginary.  As a side effect, this also
+introduces some performance boost for operations with mixed types (e.g.,
+multiplication of complex and real numbers costs only two real multiplications,
+not four).  Although it's more important that in the IEC floating-point
+arithmetic results here are uniquely determined by the usual mathematical
+formulae.
 
 For a first step, :cpython-pr:`124829` added in the CPython 3.14 mixed-mode
 rules for complex arithmetic, combining real and complex operands.  So, some
@@ -205,7 +210,7 @@ of the complex arithmetic.
 Upcoming C2y standard abandons the imaginary type
 -------------------------------------------------
 
-That [8]_ might be viewed as a failure of the new approach: no compiler from major
+That [5]_ might be viewed as a failure of the new approach: no compiler from major
 players had a correct implementation of the C99 Annex G.
 
 On the other hand, this might be also viewed as an indication of poor adoption of
@@ -215,7 +220,7 @@ arithmetic from the C language, and things will hardly be changed soon.
 
 It's also important to note that removal documents from the C language
 committee don't discuss mathematical arguments for the imaginary types at all
-[9]_.
+[6]_.
 
 
 Specification
@@ -316,12 +321,12 @@ result has real type.  If either operand has complex type, then the result has
 complex type.
 
 This specification does not indicate how exactly the results are to be evaluated
-[10]_ for complex multiplication (when *both* operands are complex numbers) and
+[7]_ for complex multiplication (when *both* operands are complex numbers) and
 for division when the right operand is a complex number.  Though, if
 the implementation of floating-point arithmetic supports the IEC 60559
 floating-point standard, results of all mixed-mode operations, except for
 division, are specified above unambiguously and it's also expected that
-multiplication always must be commutative [11]_, and that division compute result
+multiplication always must be commutative [8]_, and that division compute result
 without undue overflow or underflow.
 
 The ``*`` and ``/`` operators satisfy the following infinity properties for
@@ -609,23 +614,14 @@ Footnotes
    by Jim Thomas and Jerome T. Coonen, The Journal of C Language Translation,
    Volume 5, Number 3, March 1994.
 
-.. [5] `Ada 2022 Reference Manual
-   <http://ada-auth.org/standards/22rm/RM-Final.pdf>`_, Annex G.
-
-.. [6] `GNU Scientific Library, Release 2.7
-   <https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf>`_, §5.5.
-
-.. [7] `The GNU Multiple Precision Complex Library, Edition 1.3.1
-   <https://www.multiprecision.org/downloads/mpc-1.3.1.pdf>`_, §5.7.
-
-.. [8] `N3274: Remove imaginary types
+.. [5] `N3274: Remove imaginary types
    <https://www.open-std.org/jtc1/sc22/wg14/www/docs/n3274.pdf>`_.
    https://open-std.org/, WG14.  June 14, 2024.
 
-.. [9] See `N3206: The future of imaginary types
+.. [6] See `N3206: The future of imaginary types
    <https://open-std.org/JTC1/SC22/WG14/www/docs/n3206.htm>`_, WG14. 2023.
 
-.. [10] Another alternative for the multiplication of complex numbers
+.. [7] Another alternative for the multiplication of complex numbers
    (with only three multiplies), see e.g. "Handbook of Floating-Point
    Arithmetic" by Muller at al, 2010, Algorithm 4.8:
 
@@ -641,7 +637,7 @@ Footnotes
 
    Other variants include using a fused multiply-add (FMA) instruction.
 
-.. [11] Its easy to smash this property, as shows the `following algorithm
+.. [8] Its easy to smash this property, as shows the `following algorithm
    <https://www.mjr19.org.uk/IT/IEEE_complex.html>`_:
 
        .. code:: python