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Re: [PATCH] Some more trigonometric optimizations
- From: Brad Lucier <lucier at math dot purdue dot edu>
- To: roger at eyesopen dot com (Roger Sayle)
- Cc: gcc-patches at gcc dot gnu dot org, lucier at math dot purdue dot edu (Brad Lucier)
- Date: Mon, 9 Jun 2003 18:10:43 -0500 (EST)
- Subject: Re: [PATCH] Some more trigonometric optimizations
> -sin(x) = sin(-x)
> -tan(x) = tan(-x)
> -atan(x) = atan(-x)
I suppose moving the minus signs outside the argument make these expressions
more canonical somehow?
> sin(x)/cos(x) = tan(x)
> cos(x)/sin(x) = 1.0/tan(x)
> tan(x)*cos(x) = sin(x)
> cos(x)*tan(x) = sin(x)
> sin(x)/tan(x) = cos(x)
> tan(x)/sin(x) = 1.0/cos(x)
These all get the "wrong" answer when the numerator and denominator have
common zeros (or the multiplicand is zero and the multiplier is infinite),
but they're OK, I guess for unsafe-math-optimizations.
Brad