Re: [musl] [PATCH] Properly simplified nextafter()

[Szabolcs Nagy <nsz@port70.net>]

* Stefan Kanthak <stefan.kanthak@nexgo.de> [2021-08-10 08:23:46 +0200]:
> <https://git.musl-libc.org/cgit/musl/plain/src/math/nextafter.c>
> has quite some superfluous statements:
> 
> 1. there's absolutely no need for 2 uint64_t holding |x| and |y|;
> 2. IEEE-754 specifies -0.0 == +0.0, so (x == y) is equivalent to
>    (ax == 0) && (ay == 0): the latter 2 tests can be removed;

you replaced 4 int cmps with 4 float cmps (among other things).

it's target dependent if float compares are fast or not.
(the i386 machine where i originally tested this preferred int
cmp and float cmp was very slow in the subnormal range and
iirc it also raises the non-standard input denormal exception,
which is fine i guess. of course soft float abis much prefer int
cmp so your code is likely much slower and bigger there).

but i'm not against the change, it is likely better on modern
machines. did you try to benchmark it? or check the code size?

> 3. there's absolutely no need to compare the signs of x and y
>    with the sign of the direction: its sufficient to test that
>    direction and sign of x match;
> 4. a proper compiler/optimizer should be able to reuse the results
>    of the comparision (x == y) for (x < y) or (x > y) and
>    (x == 0.0) for (x < 0.0) or (x > 0.0).
> 
>    JFTR: if ((x < 0.0) == (x < y)) is equivalent to
>          if ((x > 0.0) == (x > y))
> 
> --- -/src/math/nextafter.c
> +++ +/src/math/nextafter.c
> @@ -3,20 +3,15 @@
>  double nextafter(double x, double y)
>  {
>         union {double f; uint64_t i;} ux={x}, uy={y};
> -       uint64_t ax, ay;
>         int e;
> 
>         if (isnan(x) || isnan(y))
>                 return x + y;
> -       if (ux.i == uy.i)
> +       if (x == y)
>                 return y;
> -       ax = ux.i & -1ULL/2;
> -       ay = uy.i & -1ULL/2;
> -       if (ax == 0) {
> -               if (ay == 0)
> -                       return y;
> +       if (x == 0.0)
>                 ux.i = (uy.i & 1ULL<<63) | 1;
> -       } else if (ax > ay || ((ux.i ^ uy.i) & 1ULL<<63))
> +       else if ((x < 0.0) == (x < y))
>                 ux.i--;
>         else
>                 ux.i++;