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Re: IEEE 754 and fused-madd (was: Re: patch: rs6000 specific)
- From: Geoff Keating <geoffk at geoffk dot org>
- To: Dale Johannesen <dalej at apple dot com>
- Cc: gcc-patches at gcc dot gnu dot org
- Date: 07 Dec 2001 14:49:55 -0800
- Subject: Re: IEEE 754 and fused-madd (was: Re: patch: rs6000 specific)
- References: <74BD58BB-EB52-11D5-8923-003065C86F94@apple.com>
- Reply-to: Geoff Keating <geoffk at redhat dot com>
Dale Johannesen <email@example.com> writes:
> All right, so I need to generate additional FMA patterns by modifying
> Our FP expert says all the required transformations are IEEE-compliant.
> Before I get too far into it, does anybody want to dispute this? Here are
> the patterns. The claim is that each of them can be transformed safely
> into the first one in its group.
Under IEEE arithmetic, A - B is equivalent to A + (-B). So those
changes are safe.
Also, ((-A) * B) is equivalent to -(A * B). The sign bits for the
result of a multiplication is the XOR of the sign bits of the inputs,
and a negation performs a logical NOT of the sign bit, so all
expressions involving MINUS and MUL can be simplified to (A * B) or
-(A * B).
In IEEE arithmetic, A + B can never generate -0; it's always +0. A
consequence of this is that -(A + B) can never generate +0. This
means that the transformation (A - B) to -(B - A) is not valid;
likewise -((-A) - B) to A+B is not valid either.
> A*C + B
> B + A*C
These are safe. Addition and multiplication are both commutative
under IEEE arithmetic.
> -(A*C - B)
> ((-A)*C) + B
This change is not safe. ((-A)*C)+B) is equivalent to (B - A*C),
but as discussed above, that's not the same as -(A*C - B).
> -((-B) + A*C)
This change is safe.
> B - A*C
This change is not safe.
> A*C -B
> -B + A*C
This is OK...
> -(B - A*C)
> -((-A)*C + B)
... these are not.
> -(A*C + B)
> ((-A)*C) -B
This is not OK.
> (-B) - A*C
Neither is this...
> -(B + A*C)
... but this is OK.
- Geoffrey Keating <firstname.lastname@example.org> <email@example.com>