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Date: Thu, 27 Jun 2013 21:58:29 -0700
From: David Schultz <das@FreeBSD.ORG>
To: Eitan Adler <lists@eitanadler.com>
Subject: Re: operation precedence bug: lib/msun/src
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On Wed, Jun 19, 2013, Eitan Adler wrote:
> Does the following look correct?
[...]
> diff --git a/lib/msun/src/s_fma.c b/lib/msun/src/s_fma.c
[...]
> -		if (bits_lost != 1 ^ (int)(hibits & 1)) {
> +		if (bits_lost != (1 ^ (int)(hibits & 1))) {

No, logical xor is intended: If we lost one bit due to
denormalization, we need to adjust if the low bit is 1, and if we
lost more than one bit, we need to adjust if the low bit is 0.

I apologize for writing 6 lines of code that would take pages to
explain. The relevant background (guard and sticky bits) is covered
in the following book chapter if you're interested:

    http://uenics.evansville.edu/~mr56/ece752/AppendixH.pdf