huge powf error

huge powf error

[Paul Zimmermann]

       Hi,

while pursuing my analysis of the accuracy of mathematical libraries [1],
I noticed that Newlib 3.3.0 powf(0x1.ffffeep-1,-0x1.000002p+27) gives +Inf
instead of 0xe.a9a99p+100 which is largely inside the binary32 range. (The
same issue appears with OpenLibm 0.7.0.)

Best regards,
Paul Zimmermann

[1] https://homepages.loria.fr/PZimmermann/papers/#accuracy

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

[Fabian Schriever]

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

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

[Paul Zimmermann]

       Dear Fabian,

that was fast! Thank you very much.

Paul

> From: Fabian Schriever <fabian.schriever@gtd-gmbh.de>
> 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
> 

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

[Jeff Johnston]

Thanks Fabian.  Patch applied.  Supplied sample powf call above tested
against glibc and newlib with/without patch.

-- Jeff J.

On Fri, Dec 11, 2020 at 11:02 AM Fabian Schriever <
fabian.schriever@gtd-gmbh.de> wrote:

> 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
>
>
>