+ add another algorithm for multiplication

python · skirpichev · Dec 5, 2023 · Oct 29, 2025 · Oct 31, 2025 · Oct 31, 2025
commit a31d7c134de756ccbf652b0b153e1be57d8f795e
@@ -321,7 +321,7 @@ 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, and that division compute result
+multiplication always must be commutative [11]_, and that division compute result
 without undue overflow or underflow.
 
 The ``*`` and ``/`` operators satisfy the following infinity properties for
@@ -627,7 +627,7 @@ Footnotes
 .. [9] See `N3206: The future of imaginary types
    <https://open-std.org/JTC1/SC22/WG14/www/docs/n3206.htm>`_, WG14. 2023.
 
-.. [10] For example, one alternative for the multiplication of complex numbers is
+.. [10] 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:
 
@@ -643,6 +643,28 @@ Footnotes
 
    Other variants include using a fused multiply-add (FMA) instruction.
 
+.. [11] Its easy to smash this property, as shows the `following algorithm
+   <https://www.mjr19.org.uk/IT/IEEE_complex.html>`_:
+
+       .. code:: python
+
+          def mul3(z, w):
+              x, y = z.real, z.imag
+              u, v = w.real, w.imag
+              t = x*(u + v)
+              return complex(t - v*(x + y), t + u*(y - x))
+
+   Example on IEC 60559-conformant system:
+
+       .. code:: pycon
+
+          >>> z = 1e308+1.6e308j
+          >>> w = 0.1+1j
+          >>> mul3(z, w)
+          (-inf+1.1600000000000002e+308j)
+          >>> mul3(w, z)
+          (inf+infj)
+
 
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