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Re: [PATCH] Evaluate pow(x,n) at compile-time
- From: Roger Sayle <roger at www dot eyesopen dot com>
- To: Geoff Keating <geoffk at geoffk dot org>
- Cc: gcc-patches at gcc dot gnu dot org
- Date: Thu, 10 Apr 2003 10:11:50 -0600 (MDT)
- Subject: Re: [PATCH] Evaluate pow(x,n) at compile-time
Hi Geoff,
> I think your real_powi is not as accurate as the system pow() routine
> could be, correct? I don't think we should start folding constants to
> less-accurate values than the system routines would provide.
No. GCC's real_powi function is likely to be far more accurate than
the system pow. For example, it is calculated internally with 158+
bit accuracy, and only then rounded to the targets floating point
representation. All multiplications are monotonic, so we also never
overflow or underflow and later use/need the bits we'd have lost.
This is much like real_sqrt which is also more accurate the FPSQRT
instructions provided on some processors.
Many poor system pow() routines also use exp(n*log(x)) which has
*much* worse precision.
And if this weren't enough, we only constant fold pow(x,n) when the
user specifies "-ffast-math" or "-funsafe-math-optimizations", just
so there are no surprises with the improved accuracy.
[Don't you trust me? :>]
Roger
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