[hackers] [libzahl] A description of the Karatsuba algorithm || Mattias Andrée

[git]

commit b9ba3cb8db7ad2541ed923f8e80956f7230b2ac8
Author:     Mattias Andrée <maand...@kth.se>
AuthorDate: Sun Mar 6 21:48:04 2016 +0100
Commit:     Mattias Andrée <maand...@kth.se>
CommitDate: Sun Mar 6 21:48:04 2016 +0100

    A description of the Karatsuba algorithm
    
    Signed-off-by: Mattias Andrée <maand...@kth.se>

diff --git a/src/zmul.c b/src/zmul.c
index 53e19f5..5b35d93 100644
--- a/src/zmul.c
+++ b/src/zmul.c
@@ -7,6 +7,12 @@ zmul(z_t a, z_t b, z_t c)
 {
        /*
         * Karatsuba algorithm
+        * 
+        * Basically, this how you were toughed to multiply large numbers
+        * by hand in school: 4010⋅3020 = (4000 + 10)(3000 + 20) =
+        = 40⋅30⋅10⁴ + (40⋅20 + 30⋅10)⋅10² + 10⋅20, but the 
middle is
+        * optimised to only one multiplication:
+        * 40⋅20 + 30⋅10 = (40 + 10)(30 + 20) − 40⋅30 − 10⋅20.
         */
 
        size_t m, m2;