Re: [PATCH] Optimize sin(atan(x)) and cos(atan(x)), take 3 (PR tree-optimization/86829)

[Christophe Lyon <christophe dot lyon at linaro dot org>]

On Tue, 16 Oct 2018 at 18:04, Giuliano Augusto Faulin Belinassi
<giuliano.belinassi@usp.br> wrote:
>
> Hello, Christophe
>     Could you please dump the assembly of cosatanf here?
>
>
Sure:
        .global cosatanf
        .syntax unified
        .arm
        .fpu softvfp
        .type   cosatanf, %function
cosatanf:
.LFB3:
        .loc 1 44 1 is_stmt 1
        .cfi_startproc
        @ args = 0, pretend = 0, frame = 0
        @ frame_needed = 0, uses_anonymous_args = 0
.LVL50:
        .loc 1 45 5
        .loc 1 44 1 is_stmt 0
        push    {r4, lr}
        .cfi_def_cfa_offset 8
        .cfi_offset 4, -8
        .cfi_offset 14, -4
        .loc 1 45 12
        bl      atanf
.LVL51:
        .loc 1 46 1
        pop     {r4, lr}
        .cfi_restore 14
        .cfi_restore 4
        .cfi_def_cfa_offset 0
        .loc 1 45 12
        b       cosf
.LVL52:
        .cfi_endproc
.LFE3:
        .size   cosatanf, .-cosatanf

So, upon entry we have r0=0x5f800000
atanf returns 0x3fc90fdb
and cosf returns 0xb33bbd2e


> On Tue, Oct 16, 2018 at 12:23 PM Christophe Lyon
> <christophe.lyon@linaro.org> wrote:
> >
> > On Tue, 16 Oct 2018 at 17:15, Giuliano Augusto Faulin Belinassi
> > <giuliano.belinassi@usp.br> wrote:
> > >
> > > Hello. Sorry for the late reply.
> > >
> > > > but then cosatanf is computed as (ie there's not call to cosatanf()):
> > > >        movw    r3, #48430
> > > >        movt    r3, 45883
> > > > so r3=0xb33bbd2e (-4.371139E-8) which is not zero.
> > > Does this behavior is still present if we change the line 58 to:
> > >     int __attribute__ ((optimize("O0")))
> > > in sinatan-1.c?
> >
> > No, this now generates:
> >         ldr     r0, [fp, #-32]
> >         bl      cosatanf
> > where r0=0x5f800000, and cosatanf() returns 0xb33bbd2e
> > (ie the same value as what was computed by GCC)
> >
> > > On Fri, Oct 12, 2018 at 3:24 PM Christophe Lyon
> > > <christophe.lyon@linaro.org> wrote:
> > > >
> > > > On Fri, 12 Oct 2018 at 20:01, Giuliano Augusto Faulin Belinassi
> > > > <giuliano.belinassi@usp.br> wrote:
> > > > >
> > > > > > fc is built with:
> > > > > >        mov     r0, #0
> > > > > >        movt    r0, 24448
> > > > > > so r0=0x5f800000 (1.8446744E19) which looks ok
> > > > >
> > > > > this is correct. My x86_64 yields the same value
> > > > >
> > > > > > but then cosatanf is computed as (ie there's not call to cosatanf()):
> > > > > >        movw    r3, #48430
> > > > > >        movt    r3, 45883
> > > > > > so r3=0xb33bbd2e (-4.371139E-8) which is not zero.
> > > > >
> > > > > Ugh. So GCC replaced the function call with a precomputed value? This
> > > > > does not happens in my x86_64. Maybe it is Ofast's fault?
> > > > > Also, it seems that GCC is precomputing cos(atan(x)) before the
> > > > > substitution, as the following python script yields the same result:
> > > > >
> > > >
> > > > Yes, I was surprised to see that.
> > > >
> > > > > import numpy as np
> > > > > x = np.float32 (1.8446744e19)
> > > > > print (np.cos (np.arctan (x))
> > > > >
> > > > > I would also like to add that -4.371139E-8 is very far away from
> > > > > 5.421011E-20, which is a "more" correct value for this computation. So
> > > > > returning 0 may be a better option?
> > > > > On Fri, Oct 12, 2018 at 12:57 PM Jeff Law <law@redhat.com> wrote:
> > > > > >
> > > > > > On 10/12/18 9:51 AM, Giuliano Augusto Faulin Belinassi wrote:
> > > > > > > Hello
> > > > > > >      What is the output of these functions on such arch? Since the
> > > > > > > test didn't fail for the sinatan counterpart, an possible explanation
> > > > > > > would be that the calculation of the sqrf, sqrt and sqrtl (lines
> > > > > > > 62-64) yielded a number that is far behind of what it should be.
> > > > > > > However, I am still not sure about this, so I will investigate
> > > > > > > further.
> > > > > > >      How about I  write a small program to check if the result
> > > > > > > obtained by this calculation is what it should be?
> > > > > > I suspect it's less the architecture and more the underlying library.
> > > > > > As Christophe mentioned, both issues are with newlib which is an C
> > > > > > library primarily used in the emebedded space.  I believe it's math code
> > > > > > derives from early BSD libm and likely hasn't been stressed for this
> > > > > > kind of correctness.  It's lightly maintained (primarily for cygwin).
> > > > > >
> > > > > > I'm going to run the testcases in my arm linux chroots.  That should
> > > > > > allow us to rule out codegen issues as those chroots will be using glibc
> > > > > > for their math library.
> > > > > >
> > > > > > jeff