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Message-Id: <p9u0wmxr8sun.fsf@coriandre.loria.fr>
Date: Sat, 19 Aug 2023 08:10:56 +0200
From: Paul Zimmermann <Paul.Zimmermann@...ia.fr>
To: Szabolcs Nagy <nsz@...t70.net>
Cc: musl@...ts.openwall.com
Subject: Re: [PATCH 1/2] math: fix ld80 acoshl(x) for x < 0

       Dear Szabolcs,

ok for me, I now get a largest error of 2.99 ulp:

NEW acosh 0 -1 0x1.1ecdb5b8f0c5d79p+0l [3] [2.99] 2.98085 2.980840623325726

Thank you for fixing that rapidly!

Paul

> Date: Fri, 18 Aug 2023 23:16:00 +0200
> From: Szabolcs Nagy <nsz@...t70.net>
> Cc: musl@...ts.openwall.com
> 
> acosh(x) is nan for x < 1, but x < 0 cases were not handled specially
> and acoshl gave wrong result for some -0x1p32 < x < -2 values, e.g.:
> 
> acoshl(-0x1p20) returned -inf,
> acoshl(-0x1.4p20) returned -0x1.db365758403aa9acp+0L,
> 
> fixed by checking the sign bit and handling it specially.
> 
> reported by Paul Zimmermann.
> ---
>  src/math/acoshl.c | 10 +++++++---
>  1 file changed, 7 insertions(+), 3 deletions(-)
> 
> diff --git a/src/math/acoshl.c b/src/math/acoshl.c
> index 8d4b43f6..943cec17 100644
> --- a/src/math/acoshl.c
> +++ b/src/math/acoshl.c
> @@ -10,14 +10,18 @@ long double acoshl(long double x)
>  long double acoshl(long double x)
>  {
>  	union ldshape u = {x};
> -	int e = u.i.se & 0x7fff;
> +	int e = u.i.se;
>  
>  	if (e < 0x3fff + 1)
> -		/* |x| < 2, invalid if x < 1 or nan */
> +		/* 0 <= x < 2, invalid if x < 1 */
>  		return log1pl(x-1 + sqrtl((x-1)*(x-1)+2*(x-1)));
>  	if (e < 0x3fff + 32)
> -		/* |x| < 0x1p32 */
> +		/* 2 <= x < 0x1p32 */
>  		return logl(2*x - 1/(x+sqrtl(x*x-1)));
> +	if (e & 0x8000)
> +		/* x < 0 or x = -0, invalid */
> +		return (x - x) / (x - x);
> +	/* 0x1p32 <= x or nan */
>  	return logl(x) + 0.693147180559945309417232121458176568L;
>  }
>  #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
> -- 
> 2.41.0
> 
> 

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