From 48d52c0fccb23c213402476992c42664f07cdca1 Mon Sep 17 00:00:00 2001 From: Tim Peters Date: Wed, 14 Aug 2002 17:07:32 +0000 Subject: [PATCH] k_mul() comments: Simplified the simplified explanation of why ah*bh and al*bl "always fit": it's actually trivial given what came before. --- Objects/longobject.c | 9 +++------ 1 file changed, 3 insertions(+), 6 deletions(-) diff --git a/Objects/longobject.c b/Objects/longobject.c index 1c4a343cf7c..348dcc49dbd 100644 --- a/Objects/longobject.c +++ b/Objects/longobject.c @@ -1792,12 +1792,9 @@ Else (bsize is odd and asize < bsize) ah and al each have at most shift digits, so ah+al has at most shift digits + 1 bit, and (ah+al)*(bh+bl) has at most 2*shift+1 digits + 2 bits, and again 2*shift+2 digits is enough to hold it. -Note that the "lazy" analysis is enough to show that there's always enough -room to subtract al*bl and ah*bh. al and bl each have no more than shift -digits, so al*bl has no more than 2*shift, so there's at least one digit -to spare in the remaining allocated digits. The same is true for ah*bh when -bsize is even. When bsize is odd, ah*bh has at most 2*shift+2 digits, and -there are at least that many remaining allocated digits when bsize is odd. +Note that since there's always enough room for (ah+al)*(bh+bl), and that's +clearly >= each of ah*bh and al*bl, there's always enough room to subtract +ah*bh and al*bl too. */ /* b has at least twice the digits of a, and a is big enough that Karatsuba