Re: [PATCH] Fix error in powf for x close to 1 and large y

       Dear Fabian,

that was fast! Thank you very much.

Paul

> From: Fabian Schriever <[email protected]>
> Date: Fri, 11 Dec 2020 16:57:35 +0100
> 
> This patch fixes the error found by Paul Zimmermann (see
> https://homepages.loria.fr/PZimmermann/papers/#accuracy) regarding x
> close to 1 and rather large y (specifically he found the case
> powf(0x1.ffffeep-1,-0x1.000002p+27) which returns +Inf instead of the
> correct value). We found 2 more values for x which show the same faulty
> behaviour, and all 3 are fixed with this patch. We have tested all
> combinations for x in [+1.fffdfp-1, +1.00020p+0] and y in
> [-1.000007p+27, -1.000002p+27] and [1.000002p+27,1.000007p+27].
> ---
>  newlib/libm/math/ef_pow.c | 2 +-
>  1 file changed, 1 insertion(+), 1 deletion(-)
> 
> diff --git a/newlib/libm/math/ef_pow.c b/newlib/libm/math/ef_pow.c
> index e3579f071..07b225f8c 100644
> --- a/newlib/libm/math/ef_pow.c
> +++ b/newlib/libm/math/ef_pow.c
> @@ -138,7 +138,7 @@ ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
>      /* |y| is huge */
>  	if(iy>0x4d000000) { /* if |y| > 2**27 */
>  	/* over/underflow if x is not close to one */
> -	    if(ix<0x3f7ffff8) return (hy<0)? __math_oflowf(0):__math_uflowf(0);
> +	    if(ix<0x3f7ffff4) return (hy<0)? __math_oflowf(0):__math_uflowf(0);
>  	    if(ix>0x3f800007) return (hy>0)? __math_oflowf(0):__math_uflowf(0);
>  	/* now |1-x| is tiny <= 2**-20, suffice to compute 
>  	   log(x) by x-x^2/2+x^3/3-x^4/4 */
> -- 
> 2.26.1.windows.1
>