[PATCH 4/4] math: Fix inaccurate sin/cos/tan for large arguments (BZ 34376)
Carlos O'Donell
carlos@redhat.com
Thu Jul 16 22:07:44 GMT 2026
On 7/16/26 5:21 PM, Adhemerval Zanella wrote:
> The Payne-Hanek range reducer __branred delivers the reduced argument
> as a double-double with only about 93 significant bits. For arguments
> extremely close to a multiple of pi/2 the true reduced argument can be
> as small as 2^-61, so most of those bits cancel and sin/cos/tan can be
> wrong by up to ~143000 ulp. This inaccuracy used to be handled by the
> multiple-precision slow paths, which was removed by by commit
s/by by/by/g
Detected by LLM.
> 649095838b8 ("sin/cos slow paths: remove slow paths from huge range
> reduction") and commit 476d692e8a8 ("math: Remove slow paths in tan
> [BZ #15267]").
>
> Restore the fdlibm e_rem_pio2.c (removed as unused by commit
> ca3aac57efa "Remove unused math files") and use __ieee754_rem_pio2 for
> the huge-argument reduction instead of __branred, which is removed.
>
> It also does not depend on precise IEEE double rounding, so the nofma
> and vector-width workarounds for branred.c are no longer needed.
>
> The file is restored trimmed to its huge-argument path, the callers
> reduce smaller arguments themselves and handle non-finite inputs, so
> only 1e8 < |x| < 2^1024 reaches __ieee754_rem_pio2.
>
> Checked on x86_64-linux-gnu, aarch64-linux-gnu, armv7a-linux-gnueabihf,
> and i686-linux-gnu.
LGTM.
You can keep my RB if you adjust the minor typo.
Reviewed-by: Carlos O'Donell <carlos@redhat.com>
> ---
> math/Makefile | 2 +-
> math/auto-libm-test-in | 17 ++
> math/auto-libm-test-out-cos | 252 +++++++++++++++++++++++++++
> math/auto-libm-test-out-sin | 228 ++++++++++++++++++++++++
> math/auto-libm-test-out-tan | 183 +++++++++++++++++++
> sysdeps/generic/math_private.h | 1 -
> sysdeps/ieee754/dbl-64/Makefile | 2 -
> sysdeps/ieee754/dbl-64/branred.c | 143 ---------------
> sysdeps/ieee754/dbl-64/branred.h | 79 ---------
> sysdeps/ieee754/dbl-64/e_rem_pio2.c | 76 ++++++++
> sysdeps/ieee754/dbl-64/s_sin.c | 14 +-
> sysdeps/ieee754/dbl-64/s_sincos.c | 10 +-
> sysdeps/ieee754/dbl-64/s_tan.c | 11 +-
> sysdeps/m68k/m680x0/fpu/e_rem_pio2.c | 1 +
> sysdeps/x86_64/fpu/Makefile | 12 --
> 15 files changed, 780 insertions(+), 251 deletions(-)
> delete mode 100644 sysdeps/ieee754/dbl-64/branred.c
> delete mode 100644 sysdeps/ieee754/dbl-64/branred.h
> create mode 100644 sysdeps/ieee754/dbl-64/e_rem_pio2.c
> create mode 100644 sysdeps/m68k/m680x0/fpu/e_rem_pio2.c
>
> diff --git a/math/Makefile b/math/Makefile
> index 7a9352c2cd6..5b48e533002 100644
> --- a/math/Makefile
> +++ b/math/Makefile
> @@ -358,13 +358,13 @@ type-ldouble-yes := ldouble
> # double support
> type-double-suffix :=
> type-double-routines := \
> - branred \
> e_cosh_data \
> e_coshsinh_data \
> e_exp_data \
> e_log2_data \
> e_log_data \
> e_pow_log_data \
> + e_rem_pio2 \
> e_sinh_data \
> e_tanh_data \
> k_rem_pio2 \
> diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
> index c2c57523e48..73737235de2 100644
> --- a/math/auto-libm-test-in
> +++ b/math/auto-libm-test-in
> @@ -5061,6 +5061,12 @@ cos -1.57079697
> cos 0x2.3c6ef4p-12
> # the next value generates larger error bounds on x86_64 (binary128)
> cos 0xe.6672d458b05edf50af4fab1a42p+40
> +# Large arguments close to a multiple of pi/2, stressing the range reducer
> +# (bug 34376).
> +cos 0x1.69eab0985179bp+246
> +cos 0x1.8577cec54ab8p+47
> +cos 0x1.dbd58768f97p+45
> +cos 0x1.0e826ceb0c5cp+46
OK. Nice add back more tests.
>
> cospi 0
> cospi -0
> @@ -9491,6 +9497,12 @@ sin 0x1.d12ed2p-12
> sin -0x6.e2368c006c018228p+16
> # the next value generates larger error bounds on x86_64 (binary128)
> sin 0x5.6a5005df4363833413fa44f74ae8p+64
> +# Large arguments close to a multiple of pi/2, stressing the range reducer
> +# (bug 34376).
> +sin 0x1.4c96c11134d36p+578
> +sin 0x1.69eab0985179bp+246
> +sin 0x1.2419db13f80ap+50
> +sin 0x1.0e826ceb0c5cp+47
> sin max
> sin -max
> sin min
> @@ -10007,6 +10019,11 @@ tan 0x1p-60
> tan 0x1p-100
> tan 0x1p-600
> tan 0x1p-10000
> +# Large arguments close to a multiple of pi/2, stressing the range reducer
> +# (bug 34376).
> +tan 0x1.69eab0985179bp+246
> +tan 0x1.8577cec54ab8p+47
> +tan 0x1.dbd58768f97p+45
> tan max
> tan -max
> tan min
> diff --git a/math/auto-libm-test-out-cos b/math/auto-libm-test-out-cos
> index 795a6eb447a..eee17d057c3 100644
> --- a/math/auto-libm-test-out-cos
> +++ b/math/auto-libm-test-out-cos
> @@ -3389,3 +3389,255 @@ cos 0xe.6672d458b05edf50af4fab1a42p+40
> = cos tonearest ibm128 0xe.6672d458b05edf50af4fab1a4p+40 : 0x1.ff56b710bf1d3d367f604dfafap-4 : inexact-ok
> = cos towardzero ibm128 0xe.6672d458b05edf50af4fab1a4p+40 : 0x1.ff56b710bf1d3d367f604dfafap-4 : inexact-ok
> = cos upward ibm128 0xe.6672d458b05edf50af4fab1a4p+40 : 0x1.ff56b710bf1d3d367f604dfafa8p-4 : inexact-ok
> +cos 0x1.69eab0985179bp+246
> += cos downward binary32 0xf.fffffp+124 : 0xd.a5f96p-4 : inexact-ok
> += cos tonearest binary32 0xf.fffffp+124 : 0xd.a5f96p-4 : inexact-ok
> += cos towardzero binary32 0xf.fffffp+124 : 0xd.a5f96p-4 : inexact-ok
> += cos upward binary32 0xf.fffffp+124 : 0xd.a5f97p-4 : inexact-ok
> += cos downward binary64 0xf.fffffp+124 : 0xd.a5f963cdefe68p-4 : inexact-ok
> += cos tonearest binary64 0xf.fffffp+124 : 0xd.a5f963cdefe7p-4 : inexact-ok
> += cos towardzero binary64 0xf.fffffp+124 : 0xd.a5f963cdefe68p-4 : inexact-ok
> += cos upward binary64 0xf.fffffp+124 : 0xd.a5f963cdefe7p-4 : inexact-ok
> += cos downward intel96 0xf.fffffp+124 : 0xd.a5f963cdefe6d52p-4 : inexact-ok
> += cos tonearest intel96 0xf.fffffp+124 : 0xd.a5f963cdefe6d53p-4 : inexact-ok
> += cos towardzero intel96 0xf.fffffp+124 : 0xd.a5f963cdefe6d52p-4 : inexact-ok
> += cos upward intel96 0xf.fffffp+124 : 0xd.a5f963cdefe6d53p-4 : inexact-ok
> += cos downward m68k96 0xf.fffffp+124 : 0xd.a5f963cdefe6d52p-4 : inexact-ok
> += cos tonearest m68k96 0xf.fffffp+124 : 0xd.a5f963cdefe6d53p-4 : inexact-ok
> += cos towardzero m68k96 0xf.fffffp+124 : 0xd.a5f963cdefe6d52p-4 : inexact-ok
> += cos upward m68k96 0xf.fffffp+124 : 0xd.a5f963cdefe6d53p-4 : inexact-ok
> += cos downward binary128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fb2fp-4 : inexact-ok
> += cos tonearest binary128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fb2fp-4 : inexact-ok
> += cos towardzero binary128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fb2fp-4 : inexact-ok
> += cos upward binary128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fb2f8p-4 : inexact-ok
> += cos downward ibm128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fbp-4 : inexact-ok
> += cos tonearest ibm128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fb4p-4 : inexact-ok
> += cos towardzero ibm128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fbp-4 : inexact-ok
> += cos upward ibm128 0xf.fffffp+124 : 0xd.a5f963cdefe6d529f6b6009fb4p-4 : inexact-ok
> += cos downward binary64 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff8p-60 : inexact-ok
> += cos tonearest binary64 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4p-60 : inexact-ok
> += cos towardzero binary64 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4p-60 : inexact-ok
> += cos upward binary64 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4p-60 : inexact-ok
> += cos downward intel96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa8p-60 : inexact-ok
> += cos tonearest intel96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa8p-60 : inexact-ok
> += cos towardzero intel96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fap-60 : inexact-ok
> += cos upward intel96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fap-60 : inexact-ok
> += cos downward m68k96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa8p-60 : inexact-ok
> += cos tonearest m68k96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa8p-60 : inexact-ok
> += cos towardzero m68k96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fap-60 : inexact-ok
> += cos upward m68k96 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fap-60 : inexact-ok
> += cos downward binary128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54c08p-60 : inexact-ok
> += cos tonearest binary128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54c08p-60 : inexact-ok
> += cos towardzero binary128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54c04p-60 : inexact-ok
> += cos upward binary128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54c04p-60 : inexact-ok
> += cos downward ibm128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54ep-60 : inexact-ok
> += cos tonearest ibm128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54cp-60 : inexact-ok
> += cos towardzero ibm128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54cp-60 : inexact-ok
> += cos upward ibm128 0x5.a7aac26145e6cp+244 : -0x5.87b3b2715dff4fa463303df54cp-60 : inexact-ok
> +cos 0x1.8577cec54ab8p+47
> += cos downward binary32 0xc.2bbe8p+44 : -0x6.99b478p-4 : inexact-ok
> += cos tonearest binary32 0xc.2bbe8p+44 : -0x6.99b47p-4 : inexact-ok
> += cos towardzero binary32 0xc.2bbe8p+44 : -0x6.99b47p-4 : inexact-ok
> += cos upward binary32 0xc.2bbe8p+44 : -0x6.99b47p-4 : inexact-ok
> += cos downward binary64 0xc.2bbe8p+44 : -0x6.99b47311dbff4p-4 : inexact-ok
> += cos tonearest binary64 0xc.2bbe8p+44 : -0x6.99b47311dbff4p-4 : inexact-ok
> += cos towardzero binary64 0xc.2bbe8p+44 : -0x6.99b47311dbffp-4 : inexact-ok
> += cos upward binary64 0xc.2bbe8p+44 : -0x6.99b47311dbffp-4 : inexact-ok
> += cos downward intel96 0xc.2bbe8p+44 : -0x6.99b47311dbff313p-4 : inexact-ok
> += cos tonearest intel96 0xc.2bbe8p+44 : -0x6.99b47311dbff3128p-4 : inexact-ok
> += cos towardzero intel96 0xc.2bbe8p+44 : -0x6.99b47311dbff3128p-4 : inexact-ok
> += cos upward intel96 0xc.2bbe8p+44 : -0x6.99b47311dbff3128p-4 : inexact-ok
> += cos downward m68k96 0xc.2bbe8p+44 : -0x6.99b47311dbff313p-4 : inexact-ok
> += cos tonearest m68k96 0xc.2bbe8p+44 : -0x6.99b47311dbff3128p-4 : inexact-ok
> += cos towardzero m68k96 0xc.2bbe8p+44 : -0x6.99b47311dbff3128p-4 : inexact-ok
> += cos upward m68k96 0xc.2bbe8p+44 : -0x6.99b47311dbff3128p-4 : inexact-ok
> += cos downward binary128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b70ecp-4 : inexact-ok
> += cos tonearest binary128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b70e8p-4 : inexact-ok
> += cos towardzero binary128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b70e8p-4 : inexact-ok
> += cos upward binary128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b70e8p-4 : inexact-ok
> += cos downward ibm128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b72p-4 : inexact-ok
> += cos tonearest ibm128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b7p-4 : inexact-ok
> += cos towardzero ibm128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b7p-4 : inexact-ok
> += cos upward ibm128 0xc.2bbe8p+44 : -0x6.99b47311dbff3129fdf4b31b7p-4 : inexact-ok
> += cos downward binary32 0xc.2bbe7p+44 : 0x7.3a6f2p-4 : inexact-ok
> += cos tonearest binary32 0xc.2bbe7p+44 : 0x7.3a6f2p-4 : inexact-ok
> += cos towardzero binary32 0xc.2bbe7p+44 : 0x7.3a6f2p-4 : inexact-ok
> += cos upward binary32 0xc.2bbe7p+44 : 0x7.3a6f28p-4 : inexact-ok
> += cos downward binary64 0xc.2bbe7p+44 : 0x7.3a6f2368ae644p-4 : inexact-ok
> += cos tonearest binary64 0xc.2bbe7p+44 : 0x7.3a6f2368ae644p-4 : inexact-ok
> += cos towardzero binary64 0xc.2bbe7p+44 : 0x7.3a6f2368ae644p-4 : inexact-ok
> += cos upward binary64 0xc.2bbe7p+44 : 0x7.3a6f2368ae648p-4 : inexact-ok
> += cos downward intel96 0xc.2bbe7p+44 : 0x7.3a6f2368ae644188p-4 : inexact-ok
> += cos tonearest intel96 0xc.2bbe7p+44 : 0x7.3a6f2368ae64419p-4 : inexact-ok
> += cos towardzero intel96 0xc.2bbe7p+44 : 0x7.3a6f2368ae644188p-4 : inexact-ok
> += cos upward intel96 0xc.2bbe7p+44 : 0x7.3a6f2368ae64419p-4 : inexact-ok
> += cos downward m68k96 0xc.2bbe7p+44 : 0x7.3a6f2368ae644188p-4 : inexact-ok
> += cos tonearest m68k96 0xc.2bbe7p+44 : 0x7.3a6f2368ae64419p-4 : inexact-ok
> += cos towardzero m68k96 0xc.2bbe7p+44 : 0x7.3a6f2368ae644188p-4 : inexact-ok
> += cos upward m68k96 0xc.2bbe7p+44 : 0x7.3a6f2368ae64419p-4 : inexact-ok
> += cos downward binary128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be99ccp-4 : inexact-ok
> += cos tonearest binary128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be99ccp-4 : inexact-ok
> += cos towardzero binary128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be99ccp-4 : inexact-ok
> += cos upward binary128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be99dp-4 : inexact-ok
> += cos downward ibm128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be98p-4 : inexact-ok
> += cos tonearest ibm128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be9ap-4 : inexact-ok
> += cos towardzero ibm128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be98p-4 : inexact-ok
> += cos upward ibm128 0xc.2bbe7p+44 : 0x7.3a6f2368ae64418f79c248be9ap-4 : inexact-ok
> += cos downward binary64 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c362p-52 : inexact-ok
> += cos tonearest binary64 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c362p-52 : inexact-ok
> += cos towardzero binary64 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c362p-52 : inexact-ok
> += cos upward binary64 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c363p-52 : inexact-ok
> += cos downward intel96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204cp-52 : inexact-ok
> += cos tonearest intel96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204cp-52 : inexact-ok
> += cos towardzero intel96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204cp-52 : inexact-ok
> += cos upward intel96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204ep-52 : inexact-ok
> += cos downward m68k96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204cp-52 : inexact-ok
> += cos tonearest m68k96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204cp-52 : inexact-ok
> += cos towardzero m68k96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204cp-52 : inexact-ok
> += cos upward m68k96 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204ep-52 : inexact-ok
> += cos downward binary128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322c97p-52 : inexact-ok
> += cos tonearest binary128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322c97p-52 : inexact-ok
> += cos towardzero binary128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322c97p-52 : inexact-ok
> += cos upward binary128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322c98p-52 : inexact-ok
> += cos downward ibm128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322c8p-52 : inexact-ok
> += cos tonearest ibm128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322c8p-52 : inexact-ok
> += cos towardzero ibm128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322c8p-52 : inexact-ok
> += cos upward ibm128 0xc.2bbe762a55cp+44 : 0x1.2b04a1af8c36204c7ee321322dp-52 : inexact-ok
> +cos 0x1.dbd58768f97p+45
> += cos downward binary32 0x3.b7ab1p+44 : -0xe.ba3e9p-4 : inexact-ok
> += cos tonearest binary32 0x3.b7ab1p+44 : -0xe.ba3e8p-4 : inexact-ok
> += cos towardzero binary32 0x3.b7ab1p+44 : -0xe.ba3e8p-4 : inexact-ok
> += cos upward binary32 0x3.b7ab1p+44 : -0xe.ba3e8p-4 : inexact-ok
> += cos downward binary64 0x3.b7ab1p+44 : -0xe.ba3e819411018p-4 : inexact-ok
> += cos tonearest binary64 0x3.b7ab1p+44 : -0xe.ba3e81941101p-4 : inexact-ok
> += cos towardzero binary64 0x3.b7ab1p+44 : -0xe.ba3e81941101p-4 : inexact-ok
> += cos upward binary64 0x3.b7ab1p+44 : -0xe.ba3e81941101p-4 : inexact-ok
> += cos downward intel96 0x3.b7ab1p+44 : -0xe.ba3e81941101295p-4 : inexact-ok
> += cos tonearest intel96 0x3.b7ab1p+44 : -0xe.ba3e81941101294p-4 : inexact-ok
> += cos towardzero intel96 0x3.b7ab1p+44 : -0xe.ba3e81941101294p-4 : inexact-ok
> += cos upward intel96 0x3.b7ab1p+44 : -0xe.ba3e81941101294p-4 : inexact-ok
> += cos downward m68k96 0x3.b7ab1p+44 : -0xe.ba3e81941101295p-4 : inexact-ok
> += cos tonearest m68k96 0x3.b7ab1p+44 : -0xe.ba3e81941101294p-4 : inexact-ok
> += cos towardzero m68k96 0x3.b7ab1p+44 : -0xe.ba3e81941101294p-4 : inexact-ok
> += cos upward m68k96 0x3.b7ab1p+44 : -0xe.ba3e81941101294p-4 : inexact-ok
> += cos downward binary128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef598p-4 : inexact-ok
> += cos tonearest binary128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef598p-4 : inexact-ok
> += cos towardzero binary128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef59p-4 : inexact-ok
> += cos upward binary128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef59p-4 : inexact-ok
> += cos downward ibm128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef8p-4 : inexact-ok
> += cos tonearest ibm128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef4p-4 : inexact-ok
> += cos towardzero ibm128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef4p-4 : inexact-ok
> += cos upward ibm128 0x3.b7ab1p+44 : -0xe.ba3e819411012942be66959ef4p-4 : inexact-ok
> += cos downward binary32 0x3.b7ab0cp+44 : -0x9.5c959p-4 : inexact-ok
> += cos tonearest binary32 0x3.b7ab0cp+44 : -0x9.5c959p-4 : inexact-ok
> += cos towardzero binary32 0x3.b7ab0cp+44 : -0x9.5c958p-4 : inexact-ok
> += cos upward binary32 0x3.b7ab0cp+44 : -0x9.5c958p-4 : inexact-ok
> += cos downward binary64 0x3.b7ab0cp+44 : -0x9.5c95889665228p-4 : inexact-ok
> += cos tonearest binary64 0x3.b7ab0cp+44 : -0x9.5c9588966522p-4 : inexact-ok
> += cos towardzero binary64 0x3.b7ab0cp+44 : -0x9.5c9588966522p-4 : inexact-ok
> += cos upward binary64 0x3.b7ab0cp+44 : -0x9.5c9588966522p-4 : inexact-ok
> += cos downward intel96 0x3.b7ab0cp+44 : -0x9.5c9588966522227p-4 : inexact-ok
> += cos tonearest intel96 0x3.b7ab0cp+44 : -0x9.5c9588966522226p-4 : inexact-ok
> += cos towardzero intel96 0x3.b7ab0cp+44 : -0x9.5c9588966522226p-4 : inexact-ok
> += cos upward intel96 0x3.b7ab0cp+44 : -0x9.5c9588966522226p-4 : inexact-ok
> += cos downward m68k96 0x3.b7ab0cp+44 : -0x9.5c9588966522227p-4 : inexact-ok
> += cos tonearest m68k96 0x3.b7ab0cp+44 : -0x9.5c9588966522226p-4 : inexact-ok
> += cos towardzero m68k96 0x3.b7ab0cp+44 : -0x9.5c9588966522226p-4 : inexact-ok
> += cos upward m68k96 0x3.b7ab0cp+44 : -0x9.5c9588966522226p-4 : inexact-ok
> += cos downward binary128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf758f28p-4 : inexact-ok
> += cos tonearest binary128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf758f2p-4 : inexact-ok
> += cos towardzero binary128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf758f2p-4 : inexact-ok
> += cos upward binary128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf758f2p-4 : inexact-ok
> += cos downward ibm128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf759p-4 : inexact-ok
> += cos tonearest ibm128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf759p-4 : inexact-ok
> += cos towardzero ibm128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf758cp-4 : inexact-ok
> += cos upward ibm128 0x3.b7ab0cp+44 : -0x9.5c95889665222264d4becf758cp-4 : inexact-ok
> += cos downward binary64 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cp-48 : inexact-ok
> += cos tonearest binary64 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cp-48 : inexact-ok
> += cos towardzero binary64 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cp-48 : inexact-ok
> += cos upward binary64 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e11p-48 : inexact-ok
> += cos downward intel96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8p-48 : inexact-ok
> += cos tonearest intel96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8p-48 : inexact-ok
> += cos towardzero intel96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8p-48 : inexact-ok
> += cos upward intel96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdcp-48 : inexact-ok
> += cos downward m68k96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8p-48 : inexact-ok
> += cos tonearest m68k96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8p-48 : inexact-ok
> += cos towardzero m68k96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8p-48 : inexact-ok
> += cos upward m68k96 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdcp-48 : inexact-ok
> += cos downward binary128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7dbcp-48 : inexact-ok
> += cos tonearest binary128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7dcp-48 : inexact-ok
> += cos towardzero binary128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7dbcp-48 : inexact-ok
> += cos upward binary128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7dcp-48 : inexact-ok
> += cos downward ibm128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7cp-48 : inexact-ok
> += cos tonearest ibm128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7ep-48 : inexact-ok
> += cos towardzero ibm128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7cp-48 : inexact-ok
> += cos upward ibm128 0x3.b7ab0ed1f2ep+44 : 0x4.1b9121100e10cdb8bee1e90f7ep-48 : inexact-ok
> +cos 0x1.0e826ceb0c5cp+46
> += cos downward binary32 0x4.3a09b8p+44 : -0xe.e7cd2p-4 : inexact-ok
> += cos tonearest binary32 0x4.3a09b8p+44 : -0xe.e7cd2p-4 : inexact-ok
> += cos towardzero binary32 0x4.3a09b8p+44 : -0xe.e7cd1p-4 : inexact-ok
> += cos upward binary32 0x4.3a09b8p+44 : -0xe.e7cd1p-4 : inexact-ok
> += cos downward binary64 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e8p-4 : inexact-ok
> += cos tonearest binary64 0x4.3a09b8p+44 : -0xe.e7cd1817fc8ep-4 : inexact-ok
> += cos towardzero binary64 0x4.3a09b8p+44 : -0xe.e7cd1817fc8ep-4 : inexact-ok
> += cos upward binary64 0x4.3a09b8p+44 : -0xe.e7cd1817fc8ep-4 : inexact-ok
> += cos downward intel96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21fp-4 : inexact-ok
> += cos tonearest intel96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21fp-4 : inexact-ok
> += cos towardzero intel96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21ep-4 : inexact-ok
> += cos upward intel96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21ep-4 : inexact-ok
> += cos downward m68k96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21fp-4 : inexact-ok
> += cos tonearest m68k96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21fp-4 : inexact-ok
> += cos towardzero m68k96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21ep-4 : inexact-ok
> += cos upward m68k96 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21ep-4 : inexact-ok
> += cos downward binary128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21eef8p-4 : inexact-ok
> += cos tonearest binary128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21eefp-4 : inexact-ok
> += cos towardzero binary128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21eefp-4 : inexact-ok
> += cos upward binary128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21eefp-4 : inexact-ok
> += cos downward ibm128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21fp-4 : inexact-ok
> += cos tonearest ibm128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21fp-4 : inexact-ok
> += cos towardzero ibm128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21ecp-4 : inexact-ok
> += cos upward ibm128 0x4.3a09b8p+44 : -0xe.e7cd1817fc8e21eeeeb86b21ecp-4 : inexact-ok
> += cos downward binary32 0x4.3a09bp+44 : 0xa.ed559p-4 : inexact-ok
> += cos tonearest binary32 0x4.3a09bp+44 : 0xa.ed559p-4 : inexact-ok
> += cos towardzero binary32 0x4.3a09bp+44 : 0xa.ed559p-4 : inexact-ok
> += cos upward binary32 0x4.3a09bp+44 : 0xa.ed55ap-4 : inexact-ok
> += cos downward binary64 0x4.3a09bp+44 : 0xa.ed55933cc4ab8p-4 : inexact-ok
> += cos tonearest binary64 0x4.3a09bp+44 : 0xa.ed55933cc4acp-4 : inexact-ok
> += cos towardzero binary64 0x4.3a09bp+44 : 0xa.ed55933cc4ab8p-4 : inexact-ok
> += cos upward binary64 0x4.3a09bp+44 : 0xa.ed55933cc4acp-4 : inexact-ok
> += cos downward intel96 0x4.3a09bp+44 : 0xa.ed55933cc4abe86p-4 : inexact-ok
> += cos tonearest intel96 0x4.3a09bp+44 : 0xa.ed55933cc4abe86p-4 : inexact-ok
> += cos towardzero intel96 0x4.3a09bp+44 : 0xa.ed55933cc4abe86p-4 : inexact-ok
> += cos upward intel96 0x4.3a09bp+44 : 0xa.ed55933cc4abe87p-4 : inexact-ok
> += cos downward m68k96 0x4.3a09bp+44 : 0xa.ed55933cc4abe86p-4 : inexact-ok
> += cos tonearest m68k96 0x4.3a09bp+44 : 0xa.ed55933cc4abe86p-4 : inexact-ok
> += cos towardzero m68k96 0x4.3a09bp+44 : 0xa.ed55933cc4abe86p-4 : inexact-ok
> += cos upward m68k96 0x4.3a09bp+44 : 0xa.ed55933cc4abe87p-4 : inexact-ok
> += cos downward binary128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504ecdbp-4 : inexact-ok
> += cos tonearest binary128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504ecdb8p-4 : inexact-ok
> += cos towardzero binary128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504ecdbp-4 : inexact-ok
> += cos upward binary128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504ecdb8p-4 : inexact-ok
> += cos downward ibm128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504eccp-4 : inexact-ok
> += cos tonearest ibm128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504eccp-4 : inexact-ok
> += cos towardzero ibm128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504eccp-4 : inexact-ok
> += cos upward ibm128 0x4.3a09bp+44 : 0xa.ed55933cc4abe860b7fe504edp-4 : inexact-ok
> += cos downward binary64 0x4.3a09b3ac317p+44 : -0x2.1720b595836a2p-48 : inexact-ok
> += cos tonearest binary64 0x4.3a09b3ac317p+44 : -0x2.1720b595836a2p-48 : inexact-ok
> += cos towardzero binary64 0x4.3a09b3ac317p+44 : -0x2.1720b595836ap-48 : inexact-ok
> += cos upward binary64 0x4.3a09b3ac317p+44 : -0x2.1720b595836ap-48 : inexact-ok
> += cos downward intel96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17ep-48 : inexact-ok
> += cos tonearest intel96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17ep-48 : inexact-ok
> += cos towardzero intel96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dcp-48 : inexact-ok
> += cos upward intel96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dcp-48 : inexact-ok
> += cos downward m68k96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17ep-48 : inexact-ok
> += cos tonearest m68k96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17ep-48 : inexact-ok
> += cos towardzero m68k96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dcp-48 : inexact-ok
> += cos upward m68k96 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dcp-48 : inexact-ok
> += cos downward binary128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d95912ap-48 : inexact-ok
> += cos tonearest binary128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d959128p-48 : inexact-ok
> += cos towardzero binary128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d959128p-48 : inexact-ok
> += cos upward binary128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d959128p-48 : inexact-ok
> += cos downward ibm128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d9592p-48 : inexact-ok
> += cos tonearest ibm128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d9591p-48 : inexact-ok
> += cos towardzero ibm128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d9591p-48 : inexact-ok
> += cos upward ibm128 0x4.3a09b3ac317p+44 : -0x2.1720b595836a17dec3680d9591p-48 : inexact-ok
> diff --git a/math/auto-libm-test-out-sin b/math/auto-libm-test-out-sin
> index f1d21b179c9..1181f057ce8 100644
> --- a/math/auto-libm-test-out-sin
> +++ b/math/auto-libm-test-out-sin
> @@ -3389,6 +3389,234 @@ sin 0x5.6a5005df4363833413fa44f74ae8p+64
> = sin tonearest ibm128 0x5.6a5005df4363833413fa44f74ap+64 : -0xf.fdc305247e694b390edb67a7fcp-8 : inexact-ok
> = sin towardzero ibm128 0x5.6a5005df4363833413fa44f74ap+64 : -0xf.fdc305247e694b390edb67a7f8p-8 : inexact-ok
> = sin upward ibm128 0x5.6a5005df4363833413fa44f74ap+64 : -0xf.fdc305247e694b390edb67a7f8p-8 : inexact-ok
> +sin 0x1.4c96c11134d36p+578
> += sin downward binary32 0xf.fffffp+124 : -0x8.599b4p-4 : inexact-ok
> += sin tonearest binary32 0xf.fffffp+124 : -0x8.599b3p-4 : inexact-ok
> += sin towardzero binary32 0xf.fffffp+124 : -0x8.599b3p-4 : inexact-ok
> += sin upward binary32 0xf.fffffp+124 : -0x8.599b3p-4 : inexact-ok
> += sin downward binary64 0xf.fffffp+124 : -0x8.599b32844abbp-4 : inexact-ok
> += sin tonearest binary64 0xf.fffffp+124 : -0x8.599b32844aba8p-4 : inexact-ok
> += sin towardzero binary64 0xf.fffffp+124 : -0x8.599b32844aba8p-4 : inexact-ok
> += sin upward binary64 0xf.fffffp+124 : -0x8.599b32844aba8p-4 : inexact-ok
> += sin downward intel96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin tonearest intel96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin towardzero intel96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin upward intel96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin downward m68k96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin tonearest m68k96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin towardzero m68k96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin upward m68k96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin downward binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be049ap-4 : inexact-ok
> += sin tonearest binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04998p-4 : inexact-ok
> += sin towardzero binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04998p-4 : inexact-ok
> += sin upward binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04998p-4 : inexact-ok
> += sin downward ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04cp-4 : inexact-ok
> += sin tonearest ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be048p-4 : inexact-ok
> += sin towardzero ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be048p-4 : inexact-ok
> += sin upward ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be048p-4 : inexact-ok
> += sin downward binary64 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd48cp-60 : inexact-ok
> += sin tonearest binary64 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd488p-60 : inexact-ok
> += sin towardzero binary64 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd488p-60 : inexact-ok
> += sin upward binary64 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd488p-60 : inexact-ok
> += sin downward intel96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f8p-60 : inexact-ok
> += sin tonearest intel96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892fp-60 : inexact-ok
> += sin towardzero intel96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892fp-60 : inexact-ok
> += sin upward intel96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892fp-60 : inexact-ok
> += sin downward m68k96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f8p-60 : inexact-ok
> += sin tonearest m68k96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892fp-60 : inexact-ok
> += sin towardzero m68k96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892fp-60 : inexact-ok
> += sin upward m68k96 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892fp-60 : inexact-ok
> += sin downward binary128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000a84p-60 : inexact-ok
> += sin tonearest binary128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000a84p-60 : inexact-ok
> += sin towardzero binary128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000a8p-60 : inexact-ok
> += sin upward binary128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000a8p-60 : inexact-ok
> += sin downward ibm128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000cp-60 : inexact-ok
> += sin tonearest ibm128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000ap-60 : inexact-ok
> += sin towardzero ibm128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000ap-60 : inexact-ok
> += sin upward ibm128 0x5.325b0444d34d8p+576 : -0x5.bb19ef3ddd4892f2b3c334000ap-60 : inexact-ok
> +sin 0x1.69eab0985179bp+246
> += sin downward binary32 0xf.fffffp+124 : -0x8.599b4p-4 : inexact-ok
> += sin tonearest binary32 0xf.fffffp+124 : -0x8.599b3p-4 : inexact-ok
> += sin towardzero binary32 0xf.fffffp+124 : -0x8.599b3p-4 : inexact-ok
> += sin upward binary32 0xf.fffffp+124 : -0x8.599b3p-4 : inexact-ok
> += sin downward binary64 0xf.fffffp+124 : -0x8.599b32844abbp-4 : inexact-ok
> += sin tonearest binary64 0xf.fffffp+124 : -0x8.599b32844aba8p-4 : inexact-ok
> += sin towardzero binary64 0xf.fffffp+124 : -0x8.599b32844aba8p-4 : inexact-ok
> += sin upward binary64 0xf.fffffp+124 : -0x8.599b32844aba8p-4 : inexact-ok
> += sin downward intel96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin tonearest intel96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin towardzero intel96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin upward intel96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin downward m68k96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin tonearest m68k96 0xf.fffffp+124 : -0x8.599b32844aba907p-4 : inexact-ok
> += sin towardzero m68k96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin upward m68k96 0xf.fffffp+124 : -0x8.599b32844aba906p-4 : inexact-ok
> += sin downward binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be049ap-4 : inexact-ok
> += sin tonearest binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04998p-4 : inexact-ok
> += sin towardzero binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04998p-4 : inexact-ok
> += sin upward binary128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04998p-4 : inexact-ok
> += sin downward ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be04cp-4 : inexact-ok
> += sin tonearest ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be048p-4 : inexact-ok
> += sin towardzero ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be048p-4 : inexact-ok
> += sin upward ibm128 0xf.fffffp+124 : -0x8.599b32844aba906cee446be048p-4 : inexact-ok
> += sin downward binary64 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin tonearest binary64 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin towardzero binary64 0x5.a7aac26145e6cp+244 : -0xf.ffffffffffff8p-4 : inexact-ok
> += sin upward binary64 0x5.a7aac26145e6cp+244 : -0xf.ffffffffffff8p-4 : inexact-ok
> += sin downward intel96 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin tonearest intel96 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin towardzero intel96 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffp-4 : inexact-ok
> += sin upward intel96 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffp-4 : inexact-ok
> += sin downward m68k96 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin tonearest m68k96 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin towardzero m68k96 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffp-4 : inexact-ok
> += sin upward m68k96 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffp-4 : inexact-ok
> += sin downward binary128 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin tonearest binary128 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin towardzero binary128 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffffffffffffff8p-4 : inexact-ok
> += sin upward binary128 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffffffffffffff8p-4 : inexact-ok
> += sin downward ibm128 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin tonearest ibm128 0x5.a7aac26145e6cp+244 : -0x1p+0 : inexact-ok
> += sin towardzero ibm128 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffffffffffffcp-4 : inexact-ok
> += sin upward ibm128 0x5.a7aac26145e6cp+244 : -0xf.fffffffffffffffffffffffffcp-4 : inexact-ok
> +sin 0x1.2419db13f80ap+50
> += sin downward binary32 0x4.90677p+48 : 0x8.e7af1p-4 : inexact-ok
> += sin tonearest binary32 0x4.90677p+48 : 0x8.e7af1p-4 : inexact-ok
> += sin towardzero binary32 0x4.90677p+48 : 0x8.e7af1p-4 : inexact-ok
> += sin upward binary32 0x4.90677p+48 : 0x8.e7af2p-4 : inexact-ok
> += sin downward binary64 0x4.90677p+48 : 0x8.e7af14b5e0968p-4 : inexact-ok
> += sin tonearest binary64 0x4.90677p+48 : 0x8.e7af14b5e0968p-4 : inexact-ok
> += sin towardzero binary64 0x4.90677p+48 : 0x8.e7af14b5e0968p-4 : inexact-ok
> += sin upward binary64 0x4.90677p+48 : 0x8.e7af14b5e097p-4 : inexact-ok
> += sin downward intel96 0x4.90677p+48 : 0x8.e7af14b5e096b1dp-4 : inexact-ok
> += sin tonearest intel96 0x4.90677p+48 : 0x8.e7af14b5e096b1ep-4 : inexact-ok
> += sin towardzero intel96 0x4.90677p+48 : 0x8.e7af14b5e096b1dp-4 : inexact-ok
> += sin upward intel96 0x4.90677p+48 : 0x8.e7af14b5e096b1ep-4 : inexact-ok
> += sin downward m68k96 0x4.90677p+48 : 0x8.e7af14b5e096b1dp-4 : inexact-ok
> += sin tonearest m68k96 0x4.90677p+48 : 0x8.e7af14b5e096b1ep-4 : inexact-ok
> += sin towardzero m68k96 0x4.90677p+48 : 0x8.e7af14b5e096b1dp-4 : inexact-ok
> += sin upward m68k96 0x4.90677p+48 : 0x8.e7af14b5e096b1ep-4 : inexact-ok
> += sin downward binary128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006ca18p-4 : inexact-ok
> += sin tonearest binary128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006ca2p-4 : inexact-ok
> += sin towardzero binary128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006ca18p-4 : inexact-ok
> += sin upward binary128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006ca2p-4 : inexact-ok
> += sin downward ibm128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006c8p-4 : inexact-ok
> += sin tonearest ibm128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006ccp-4 : inexact-ok
> += sin towardzero ibm128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006c8p-4 : inexact-ok
> += sin upward ibm128 0x4.90677p+48 : 0x8.e7af14b5e096b1de0542a006ccp-4 : inexact-ok
> += sin downward binary32 0x4.906768p+48 : 0xf.e657bp-4 : inexact-ok
> += sin tonearest binary32 0x4.906768p+48 : 0xf.e657cp-4 : inexact-ok
> += sin towardzero binary32 0x4.906768p+48 : 0xf.e657bp-4 : inexact-ok
> += sin upward binary32 0x4.906768p+48 : 0xf.e657cp-4 : inexact-ok
> += sin downward binary64 0x4.906768p+48 : 0xf.e657b8243a248p-4 : inexact-ok
> += sin tonearest binary64 0x4.906768p+48 : 0xf.e657b8243a25p-4 : inexact-ok
> += sin towardzero binary64 0x4.906768p+48 : 0xf.e657b8243a248p-4 : inexact-ok
> += sin upward binary64 0x4.906768p+48 : 0xf.e657b8243a25p-4 : inexact-ok
> += sin downward intel96 0x4.906768p+48 : 0xf.e657b8243a24e71p-4 : inexact-ok
> += sin tonearest intel96 0x4.906768p+48 : 0xf.e657b8243a24e72p-4 : inexact-ok
> += sin towardzero intel96 0x4.906768p+48 : 0xf.e657b8243a24e71p-4 : inexact-ok
> += sin upward intel96 0x4.906768p+48 : 0xf.e657b8243a24e72p-4 : inexact-ok
> += sin downward m68k96 0x4.906768p+48 : 0xf.e657b8243a24e71p-4 : inexact-ok
> += sin tonearest m68k96 0x4.906768p+48 : 0xf.e657b8243a24e72p-4 : inexact-ok
> += sin towardzero m68k96 0x4.906768p+48 : 0xf.e657b8243a24e71p-4 : inexact-ok
> += sin upward m68k96 0x4.906768p+48 : 0xf.e657b8243a24e72p-4 : inexact-ok
> += sin downward binary128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec127p-4 : inexact-ok
> += sin tonearest binary128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec127p-4 : inexact-ok
> += sin towardzero binary128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec127p-4 : inexact-ok
> += sin upward binary128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec1278p-4 : inexact-ok
> += sin downward ibm128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec1p-4 : inexact-ok
> += sin tonearest ibm128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec14p-4 : inexact-ok
> += sin towardzero ibm128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec1p-4 : inexact-ok
> += sin upward ibm128 0x4.906768p+48 : 0xf.e657b8243a24e71ea65806ec14p-4 : inexact-ok
> += sin downward binary64 0x4.90676c4fe028p+48 : 0x7.021bca1d4944cp-52 : inexact-ok
> += sin tonearest binary64 0x4.90676c4fe028p+48 : 0x7.021bca1d4944cp-52 : inexact-ok
> += sin towardzero binary64 0x4.90676c4fe028p+48 : 0x7.021bca1d4944cp-52 : inexact-ok
> += sin upward binary64 0x4.90676c4fe028p+48 : 0x7.021bca1d4945p-52 : inexact-ok
> += sin downward intel96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1c8p-52 : inexact-ok
> += sin tonearest intel96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1c8p-52 : inexact-ok
> += sin towardzero intel96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1c8p-52 : inexact-ok
> += sin upward intel96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1dp-52 : inexact-ok
> += sin downward m68k96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1c8p-52 : inexact-ok
> += sin tonearest m68k96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1c8p-52 : inexact-ok
> += sin towardzero m68k96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1c8p-52 : inexact-ok
> += sin upward m68k96 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1dp-52 : inexact-ok
> += sin downward binary128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd3c4p-52 : inexact-ok
> += sin tonearest binary128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd3c4p-52 : inexact-ok
> += sin towardzero binary128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd3c4p-52 : inexact-ok
> += sin upward binary128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd3c8p-52 : inexact-ok
> += sin downward ibm128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd2p-52 : inexact-ok
> += sin tonearest ibm128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd4p-52 : inexact-ok
> += sin towardzero ibm128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd2p-52 : inexact-ok
> += sin upward ibm128 0x4.90676c4fe028p+48 : 0x7.021bca1d4944c1caf952c72cd4p-52 : inexact-ok
> +sin 0x1.0e826ceb0c5cp+47
> += sin downward binary32 0x8.74137p+44 : 0xa.d621p-4 : inexact-ok
> += sin tonearest binary32 0x8.74137p+44 : 0xa.d621p-4 : inexact-ok
> += sin towardzero binary32 0x8.74137p+44 : 0xa.d621p-4 : inexact-ok
> += sin upward binary32 0x8.74137p+44 : 0xa.d6211p-4 : inexact-ok
> += sin downward binary64 0x8.74137p+44 : 0xa.d6210085759ep-4 : inexact-ok
> += sin tonearest binary64 0x8.74137p+44 : 0xa.d6210085759ep-4 : inexact-ok
> += sin towardzero binary64 0x8.74137p+44 : 0xa.d6210085759ep-4 : inexact-ok
> += sin upward binary64 0x8.74137p+44 : 0xa.d6210085759e8p-4 : inexact-ok
> += sin downward intel96 0x8.74137p+44 : 0xa.d6210085759e2cbp-4 : inexact-ok
> += sin tonearest intel96 0x8.74137p+44 : 0xa.d6210085759e2cbp-4 : inexact-ok
> += sin towardzero intel96 0x8.74137p+44 : 0xa.d6210085759e2cbp-4 : inexact-ok
> += sin upward intel96 0x8.74137p+44 : 0xa.d6210085759e2ccp-4 : inexact-ok
> += sin downward m68k96 0x8.74137p+44 : 0xa.d6210085759e2cbp-4 : inexact-ok
> += sin tonearest m68k96 0x8.74137p+44 : 0xa.d6210085759e2cbp-4 : inexact-ok
> += sin towardzero m68k96 0x8.74137p+44 : 0xa.d6210085759e2cbp-4 : inexact-ok
> += sin upward m68k96 0x8.74137p+44 : 0xa.d6210085759e2ccp-4 : inexact-ok
> += sin downward binary128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240e138p-4 : inexact-ok
> += sin tonearest binary128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240e14p-4 : inexact-ok
> += sin towardzero binary128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240e138p-4 : inexact-ok
> += sin upward binary128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240e14p-4 : inexact-ok
> += sin downward ibm128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240ep-4 : inexact-ok
> += sin tonearest ibm128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240ep-4 : inexact-ok
> += sin towardzero ibm128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240ep-4 : inexact-ok
> += sin upward ibm128 0x8.74137p+44 : 0xa.d6210085759e2cb2d319f240e4p-4 : inexact-ok
> += sin downward binary32 0x8.74136p+44 : 0xf.f6bf4p-4 : inexact-ok
> += sin tonearest binary32 0x8.74136p+44 : 0xf.f6bf5p-4 : inexact-ok
> += sin towardzero binary32 0x8.74136p+44 : 0xf.f6bf4p-4 : inexact-ok
> += sin upward binary32 0x8.74136p+44 : 0xf.f6bf5p-4 : inexact-ok
> += sin downward binary64 0x8.74136p+44 : 0xf.f6bf482d31f1p-4 : inexact-ok
> += sin tonearest binary64 0x8.74136p+44 : 0xf.f6bf482d31f18p-4 : inexact-ok
> += sin towardzero binary64 0x8.74136p+44 : 0xf.f6bf482d31f1p-4 : inexact-ok
> += sin upward binary64 0x8.74136p+44 : 0xf.f6bf482d31f18p-4 : inexact-ok
> += sin downward intel96 0x8.74136p+44 : 0xf.f6bf482d31f1417p-4 : inexact-ok
> += sin tonearest intel96 0x8.74136p+44 : 0xf.f6bf482d31f1418p-4 : inexact-ok
> += sin towardzero intel96 0x8.74136p+44 : 0xf.f6bf482d31f1417p-4 : inexact-ok
> += sin upward intel96 0x8.74136p+44 : 0xf.f6bf482d31f1418p-4 : inexact-ok
> += sin downward m68k96 0x8.74136p+44 : 0xf.f6bf482d31f1417p-4 : inexact-ok
> += sin tonearest m68k96 0x8.74136p+44 : 0xf.f6bf482d31f1418p-4 : inexact-ok
> += sin towardzero m68k96 0x8.74136p+44 : 0xf.f6bf482d31f1417p-4 : inexact-ok
> += sin upward m68k96 0x8.74136p+44 : 0xf.f6bf482d31f1418p-4 : inexact-ok
> += sin downward binary128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b74918p-4 : inexact-ok
> += sin tonearest binary128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b74918p-4 : inexact-ok
> += sin towardzero binary128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b74918p-4 : inexact-ok
> += sin upward binary128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b7492p-4 : inexact-ok
> += sin downward ibm128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b748p-4 : inexact-ok
> += sin tonearest ibm128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b748p-4 : inexact-ok
> += sin towardzero ibm128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b748p-4 : inexact-ok
> += sin upward ibm128 0x8.74136p+44 : 0xf.f6bf482d31f1417ad55755b74cp-4 : inexact-ok
> += sin downward binary64 0x8.7413675862ep+44 : 0x4.2e416b2b06d4p-48 : inexact-ok
> += sin tonearest binary64 0x8.7413675862ep+44 : 0x4.2e416b2b06d44p-48 : inexact-ok
> += sin towardzero binary64 0x8.7413675862ep+44 : 0x4.2e416b2b06d4p-48 : inexact-ok
> += sin upward binary64 0x8.7413675862ep+44 : 0x4.2e416b2b06d44p-48 : inexact-ok
> += sin downward intel96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fb8p-48 : inexact-ok
> += sin tonearest intel96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fcp-48 : inexact-ok
> += sin towardzero intel96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fb8p-48 : inexact-ok
> += sin upward intel96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fcp-48 : inexact-ok
> += sin downward m68k96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fb8p-48 : inexact-ok
> += sin tonearest m68k96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fcp-48 : inexact-ok
> += sin towardzero m68k96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fb8p-48 : inexact-ok
> += sin upward m68k96 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fcp-48 : inexact-ok
> += sin downward binary128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b22000cp-48 : inexact-ok
> += sin tonearest binary128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b22001p-48 : inexact-ok
> += sin towardzero binary128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b22000cp-48 : inexact-ok
> += sin upward binary128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b22001p-48 : inexact-ok
> += sin downward ibm128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b22p-48 : inexact-ok
> += sin tonearest ibm128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b22p-48 : inexact-ok
> += sin towardzero ibm128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b22p-48 : inexact-ok
> += sin upward ibm128 0x8.7413675862ep+44 : 0x4.2e416b2b06d42fbd86d01b2202p-48 : inexact-ok
> sin max
> = sin downward binary32 0xf.fffffp+124 : -0x8.599b4p-4 : inexact-ok
> = sin tonearest binary32 0xf.fffffp+124 : -0x8.599b3p-4 : inexact-ok
> diff --git a/math/auto-libm-test-out-tan b/math/auto-libm-test-out-tan
> index 1d5999ab90d..7da92d58e23 100644
> --- a/math/auto-libm-test-out-tan
> +++ b/math/auto-libm-test-out-tan
> @@ -3032,6 +3032,189 @@ tan 0x1p-10000
> = tan tonearest binary128 0x1p-10000 : 0x1p-10000 : inexact-ok
> = tan towardzero binary128 0x1p-10000 : 0x1p-10000 : inexact-ok
> = tan upward binary128 0x1p-10000 : 0x1.0000000000000000000000000001p-10000 : inexact-ok
> +tan 0x1.69eab0985179bp+246
> += tan downward binary32 0xf.fffffp+124 : -0x9.c9ecbp-4 : inexact-ok
> += tan tonearest binary32 0xf.fffffp+124 : -0x9.c9ecap-4 : inexact-ok
> += tan towardzero binary32 0xf.fffffp+124 : -0x9.c9ecap-4 : inexact-ok
> += tan upward binary32 0xf.fffffp+124 : -0x9.c9ecap-4 : inexact-ok
> += tan downward binary64 0xf.fffffp+124 : -0x9.c9eca5a4c461p-4 : inexact-ok
> += tan tonearest binary64 0xf.fffffp+124 : -0x9.c9eca5a4c461p-4 : inexact-ok
> += tan towardzero binary64 0xf.fffffp+124 : -0x9.c9eca5a4c4608p-4 : inexact-ok
> += tan upward binary64 0xf.fffffp+124 : -0x9.c9eca5a4c4608p-4 : inexact-ok
> += tan downward intel96 0xf.fffffp+124 : -0x9.c9eca5a4c460f93p-4 : inexact-ok
> += tan tonearest intel96 0xf.fffffp+124 : -0x9.c9eca5a4c460f93p-4 : inexact-ok
> += tan towardzero intel96 0xf.fffffp+124 : -0x9.c9eca5a4c460f92p-4 : inexact-ok
> += tan upward intel96 0xf.fffffp+124 : -0x9.c9eca5a4c460f92p-4 : inexact-ok
> += tan downward m68k96 0xf.fffffp+124 : -0x9.c9eca5a4c460f93p-4 : inexact-ok
> += tan tonearest m68k96 0xf.fffffp+124 : -0x9.c9eca5a4c460f93p-4 : inexact-ok
> += tan towardzero m68k96 0xf.fffffp+124 : -0x9.c9eca5a4c460f92p-4 : inexact-ok
> += tan upward m68k96 0xf.fffffp+124 : -0x9.c9eca5a4c460f92p-4 : inexact-ok
> += tan downward binary128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbecf58p-4 : inexact-ok
> += tan tonearest binary128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbecf5p-4 : inexact-ok
> += tan towardzero binary128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbecf5p-4 : inexact-ok
> += tan upward binary128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbecf5p-4 : inexact-ok
> += tan downward ibm128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbedp-4 : inexact-ok
> += tan tonearest ibm128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbedp-4 : inexact-ok
> += tan towardzero ibm128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbeccp-4 : inexact-ok
> += tan upward ibm128 0xf.fffffp+124 : -0x9.c9eca5a4c460f92a1a2e4fbeccp-4 : inexact-ok
> += tan downward binary64 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f5p+56 : inexact-ok
> += tan tonearest binary64 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f52p+56 : inexact-ok
> += tan towardzero binary64 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f5p+56 : inexact-ok
> += tan upward binary64 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f52p+56 : inexact-ok
> += tan downward intel96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb4p+56 : inexact-ok
> += tan tonearest intel96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb8p+56 : inexact-ok
> += tan towardzero intel96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb4p+56 : inexact-ok
> += tan upward intel96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb8p+56 : inexact-ok
> += tan downward m68k96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb4p+56 : inexact-ok
> += tan tonearest m68k96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb8p+56 : inexact-ok
> += tan towardzero m68k96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb4p+56 : inexact-ok
> += tan upward m68k96 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb8p+56 : inexact-ok
> += tan downward binary128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee72382p+56 : inexact-ok
> += tan tonearest binary128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee72382p+56 : inexact-ok
> += tan towardzero binary128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee72382p+56 : inexact-ok
> += tan upward binary128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee72384p+56 : inexact-ok
> += tan downward ibm128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee723p+56 : inexact-ok
> += tan tonearest ibm128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee724p+56 : inexact-ok
> += tan towardzero ibm128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee723p+56 : inexact-ok
> += tan upward ibm128 0x5.a7aac26145e6cp+244 : 0x2.e4acf97208f51cb67baeaee724p+56 : inexact-ok
> +tan 0x1.8577cec54ab8p+47
> += tan downward binary32 0xc.2bbe8p+44 : 0x2.354dbp+0 : inexact-ok
> += tan tonearest binary32 0xc.2bbe8p+44 : 0x2.354db4p+0 : inexact-ok
> += tan towardzero binary32 0xc.2bbe8p+44 : 0x2.354dbp+0 : inexact-ok
> += tan upward binary32 0xc.2bbe8p+44 : 0x2.354db4p+0 : inexact-ok
> += tan downward binary64 0xc.2bbe8p+44 : 0x2.354db38ca5852p+0 : inexact-ok
> += tan tonearest binary64 0xc.2bbe8p+44 : 0x2.354db38ca5852p+0 : inexact-ok
> += tan towardzero binary64 0xc.2bbe8p+44 : 0x2.354db38ca5852p+0 : inexact-ok
> += tan upward binary64 0xc.2bbe8p+44 : 0x2.354db38ca5854p+0 : inexact-ok
> += tan downward intel96 0xc.2bbe8p+44 : 0x2.354db38ca5852fcp+0 : inexact-ok
> += tan tonearest intel96 0xc.2bbe8p+44 : 0x2.354db38ca5852fc4p+0 : inexact-ok
> += tan towardzero intel96 0xc.2bbe8p+44 : 0x2.354db38ca5852fcp+0 : inexact-ok
> += tan upward intel96 0xc.2bbe8p+44 : 0x2.354db38ca5852fc4p+0 : inexact-ok
> += tan downward m68k96 0xc.2bbe8p+44 : 0x2.354db38ca5852fcp+0 : inexact-ok
> += tan tonearest m68k96 0xc.2bbe8p+44 : 0x2.354db38ca5852fc4p+0 : inexact-ok
> += tan towardzero m68k96 0xc.2bbe8p+44 : 0x2.354db38ca5852fcp+0 : inexact-ok
> += tan upward m68k96 0xc.2bbe8p+44 : 0x2.354db38ca5852fc4p+0 : inexact-ok
> += tan downward binary128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dab2p+0 : inexact-ok
> += tan tonearest binary128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dab4p+0 : inexact-ok
> += tan towardzero binary128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dab2p+0 : inexact-ok
> += tan upward binary128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dab4p+0 : inexact-ok
> += tan downward ibm128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dap+0 : inexact-ok
> += tan tonearest ibm128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dbp+0 : inexact-ok
> += tan towardzero ibm128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dap+0 : inexact-ok
> += tan upward ibm128 0xc.2bbe8p+44 : 0x2.354db38ca5852fc324d592f2dbp+0 : inexact-ok
> += tan downward binary32 0xc.2bbe7p+44 : -0x1.f98ad8p+0 : inexact-ok
> += tan tonearest binary32 0xc.2bbe7p+44 : -0x1.f98ad8p+0 : inexact-ok
> += tan towardzero binary32 0xc.2bbe7p+44 : -0x1.f98ad6p+0 : inexact-ok
> += tan upward binary32 0xc.2bbe7p+44 : -0x1.f98ad6p+0 : inexact-ok
> += tan downward binary64 0xc.2bbe7p+44 : -0x1.f98ad7344f059p+0 : inexact-ok
> += tan tonearest binary64 0xc.2bbe7p+44 : -0x1.f98ad7344f059p+0 : inexact-ok
> += tan towardzero binary64 0xc.2bbe7p+44 : -0x1.f98ad7344f058p+0 : inexact-ok
> += tan upward binary64 0xc.2bbe7p+44 : -0x1.f98ad7344f058p+0 : inexact-ok
> += tan downward intel96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2cp+0 : inexact-ok
> += tan tonearest intel96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2ap+0 : inexact-ok
> += tan towardzero intel96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2ap+0 : inexact-ok
> += tan upward intel96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2ap+0 : inexact-ok
> += tan downward m68k96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2cp+0 : inexact-ok
> += tan tonearest m68k96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2ap+0 : inexact-ok
> += tan towardzero m68k96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2ap+0 : inexact-ok
> += tan upward m68k96 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2ap+0 : inexact-ok
> += tan downward binary128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038e02p+0 : inexact-ok
> += tan tonearest binary128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038e02p+0 : inexact-ok
> += tan towardzero binary128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038e01p+0 : inexact-ok
> += tan upward binary128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038e01p+0 : inexact-ok
> += tan downward ibm128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038e8p+0 : inexact-ok
> += tan tonearest ibm128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038ep+0 : inexact-ok
> += tan towardzero ibm128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038ep+0 : inexact-ok
> += tan upward ibm128 0xc.2bbe7p+44 : -0x1.f98ad7344f058d2a9d3cb9038ep+0 : inexact-ok
> += tan downward binary64 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61dp+48 : inexact-ok
> += tan tonearest binary64 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61dp+48 : inexact-ok
> += tan towardzero binary64 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61dp+48 : inexact-ok
> += tan upward binary64 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d8p+48 : inexact-ok
> += tan downward intel96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13dp+48 : inexact-ok
> += tan tonearest intel96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13ep+48 : inexact-ok
> += tan towardzero intel96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13dp+48 : inexact-ok
> += tan upward intel96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13ep+48 : inexact-ok
> += tan downward m68k96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13dp+48 : inexact-ok
> += tan tonearest m68k96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13ep+48 : inexact-ok
> += tan towardzero m68k96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13dp+48 : inexact-ok
> += tan upward m68k96 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13ep+48 : inexact-ok
> += tan downward binary128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287e07p+48 : inexact-ok
> += tan tonearest binary128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287e07p+48 : inexact-ok
> += tan towardzero binary128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287e07p+48 : inexact-ok
> += tan upward binary128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287e078p+48 : inexact-ok
> += tan downward ibm128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287ep+48 : inexact-ok
> += tan tonearest ibm128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287ep+48 : inexact-ok
> += tan towardzero ibm128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287ep+48 : inexact-ok
> += tan upward ibm128 0xc.2bbe762a55cp+44 : 0xd.b2bb1feab61d13de3fb08287e4p+48 : inexact-ok
> +tan 0x1.dbd58768f97p+45
> += tan downward binary32 0x3.b7ab1p+44 : 0x6.cb1538p-4 : inexact-ok
> += tan tonearest binary32 0x3.b7ab1p+44 : 0x6.cb1538p-4 : inexact-ok
> += tan towardzero binary32 0x3.b7ab1p+44 : 0x6.cb1538p-4 : inexact-ok
> += tan upward binary32 0x3.b7ab1p+44 : 0x6.cb154p-4 : inexact-ok
> += tan downward binary64 0x3.b7ab1p+44 : 0x6.cb1538f077ba4p-4 : inexact-ok
> += tan tonearest binary64 0x3.b7ab1p+44 : 0x6.cb1538f077ba8p-4 : inexact-ok
> += tan towardzero binary64 0x3.b7ab1p+44 : 0x6.cb1538f077ba4p-4 : inexact-ok
> += tan upward binary64 0x3.b7ab1p+44 : 0x6.cb1538f077ba8p-4 : inexact-ok
> += tan downward intel96 0x3.b7ab1p+44 : 0x6.cb1538f077ba7498p-4 : inexact-ok
> += tan tonearest intel96 0x3.b7ab1p+44 : 0x6.cb1538f077ba7498p-4 : inexact-ok
> += tan towardzero intel96 0x3.b7ab1p+44 : 0x6.cb1538f077ba7498p-4 : inexact-ok
> += tan upward intel96 0x3.b7ab1p+44 : 0x6.cb1538f077ba74ap-4 : inexact-ok
> += tan downward m68k96 0x3.b7ab1p+44 : 0x6.cb1538f077ba7498p-4 : inexact-ok
> += tan tonearest m68k96 0x3.b7ab1p+44 : 0x6.cb1538f077ba7498p-4 : inexact-ok
> += tan towardzero m68k96 0x3.b7ab1p+44 : 0x6.cb1538f077ba7498p-4 : inexact-ok
> += tan upward m68k96 0x3.b7ab1p+44 : 0x6.cb1538f077ba74ap-4 : inexact-ok
> += tan downward binary128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf017191561d4p-4 : inexact-ok
> += tan tonearest binary128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf017191561d4p-4 : inexact-ok
> += tan towardzero binary128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf017191561d4p-4 : inexact-ok
> += tan upward binary128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf017191561d8p-4 : inexact-ok
> += tan downward ibm128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf01719156p-4 : inexact-ok
> += tan tonearest ibm128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf017191562p-4 : inexact-ok
> += tan towardzero ibm128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf01719156p-4 : inexact-ok
> += tan upward ibm128 0x3.b7ab1p+44 : 0x6.cb1538f077ba749bf017191562p-4 : inexact-ok
> += tan downward binary32 0x3.b7ab0cp+44 : -0x1.62d178p+0 : inexact-ok
> += tan tonearest binary32 0x3.b7ab0cp+44 : -0x1.62d178p+0 : inexact-ok
> += tan towardzero binary32 0x3.b7ab0cp+44 : -0x1.62d176p+0 : inexact-ok
> += tan upward binary32 0x3.b7ab0cp+44 : -0x1.62d176p+0 : inexact-ok
> += tan downward binary64 0x3.b7ab0cp+44 : -0x1.62d177235023fp+0 : inexact-ok
> += tan tonearest binary64 0x3.b7ab0cp+44 : -0x1.62d177235023fp+0 : inexact-ok
> += tan towardzero binary64 0x3.b7ab0cp+44 : -0x1.62d177235023ep+0 : inexact-ok
> += tan upward binary64 0x3.b7ab0cp+44 : -0x1.62d177235023ep+0 : inexact-ok
> += tan downward intel96 0x3.b7ab0cp+44 : -0x1.62d177235023ec84p+0 : inexact-ok
> += tan tonearest intel96 0x3.b7ab0cp+44 : -0x1.62d177235023ec82p+0 : inexact-ok
> += tan towardzero intel96 0x3.b7ab0cp+44 : -0x1.62d177235023ec82p+0 : inexact-ok
> += tan upward intel96 0x3.b7ab0cp+44 : -0x1.62d177235023ec82p+0 : inexact-ok
> += tan downward m68k96 0x3.b7ab0cp+44 : -0x1.62d177235023ec84p+0 : inexact-ok
> += tan tonearest m68k96 0x3.b7ab0cp+44 : -0x1.62d177235023ec82p+0 : inexact-ok
> += tan towardzero m68k96 0x3.b7ab0cp+44 : -0x1.62d177235023ec82p+0 : inexact-ok
> += tan upward m68k96 0x3.b7ab0cp+44 : -0x1.62d177235023ec82p+0 : inexact-ok
> += tan downward binary128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254005bp+0 : inexact-ok
> += tan tonearest binary128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254005bp+0 : inexact-ok
> += tan towardzero binary128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254005ap+0 : inexact-ok
> += tan upward binary128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254005ap+0 : inexact-ok
> += tan downward ibm128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254008p+0 : inexact-ok
> += tan tonearest ibm128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254008p+0 : inexact-ok
> += tan towardzero ibm128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254p+0 : inexact-ok
> += tan upward ibm128 0x3.b7ab0cp+44 : -0x1.62d177235023ec820b6bd254p+0 : inexact-ok
> += tan downward binary64 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207cap+44 : inexact-ok
> += tan tonearest binary64 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ep+44 : inexact-ok
> += tan towardzero binary64 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ep+44 : inexact-ok
> += tan upward binary64 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ep+44 : inexact-ok
> += tan downward intel96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea7p+44 : inexact-ok
> += tan tonearest intel96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea7p+44 : inexact-ok
> += tan towardzero intel96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6cp+44 : inexact-ok
> += tan upward intel96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6cp+44 : inexact-ok
> += tan downward m68k96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea7p+44 : inexact-ok
> += tan tonearest m68k96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea7p+44 : inexact-ok
> += tan towardzero m68k96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6cp+44 : inexact-ok
> += tan upward m68k96 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6cp+44 : inexact-ok
> += tan downward binary128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064ae78p+44 : inexact-ok
> += tan tonearest binary128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064ae76p+44 : inexact-ok
> += tan towardzero binary128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064ae76p+44 : inexact-ok
> += tan upward binary128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064ae76p+44 : inexact-ok
> += tan downward ibm128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064afp+44 : inexact-ok
> += tan tonearest ibm128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064aep+44 : inexact-ok
> += tan towardzero ibm128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064aep+44 : inexact-ok
> += tan upward ibm128 0x3.b7ab0ed1f2ep+44 : -0x3.e527dfc207c9ea6ef715e064aep+44 : inexact-ok
> tan max
> = tan downward binary32 0xf.fffffp+124 : -0x9.c9ecbp-4 : inexact-ok
> = tan tonearest binary32 0xf.fffffp+124 : -0x9.c9ecap-4 : inexact-ok
> diff --git a/sysdeps/generic/math_private.h b/sysdeps/generic/math_private.h
> index 3865dcf905c..34161cc2f66 100644
> --- a/sysdeps/generic/math_private.h
> +++ b/sysdeps/generic/math_private.h
> @@ -198,6 +198,5 @@ do { \
> /* Prototypes for functions of the IBM Accurate Mathematical Library. */
> extern double __sin (double __x);
> extern double __cos (double __x);
> -extern int __branred (double __x, double *__a, double *__aa);
>
> #endif /* _MATH_PRIVATE_H_ */
> diff --git a/sysdeps/ieee754/dbl-64/Makefile b/sysdeps/ieee754/dbl-64/Makefile
> index ac2e2ecc5ea..f9f71b7b6f1 100644
> --- a/sysdeps/ieee754/dbl-64/Makefile
> +++ b/sysdeps/ieee754/dbl-64/Makefile
> @@ -1,6 +1,4 @@
> ifeq ($(subdir),math)
> -# branred depends on precise IEEE double rounding
> -CFLAGS-branred.c += $(config-cflags-nofma)
> CFLAGS-e_sqrt.c += $(config-cflags-nofma)
>
> # The symbols alias to lround
> diff --git a/sysdeps/ieee754/dbl-64/branred.c b/sysdeps/ieee754/dbl-64/branred.c
> deleted file mode 100644
> index d78c013d5a8..00000000000
> --- a/sysdeps/ieee754/dbl-64/branred.c
> +++ /dev/null
> @@ -1,143 +0,0 @@
> -/*
> - * IBM Accurate Mathematical Library
> - * Copyright (C) 2001-2026 Free Software Foundation, Inc.
> - *
> - * This program is free software; you can redistribute it and/or modify
> - * it under the terms of the GNU Lesser General Public License as published by
> - * the Free Software Foundation; either version 2.1 of the License, or
> - * (at your option) any later version.
> - *
> - * This program is distributed in the hope that it will be useful,
> - * but WITHOUT ANY WARRANTY; without even the implied warranty of
> - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
> - * GNU Lesser General Public License for more details.
> - *
> - * You should have received a copy of the GNU Lesser General Public License
> - * along with this program; if not, see <https://www.gnu.org/licenses/>.
> - */
> -/*******************************************************************/
> -/* */
> -/* MODULE_NAME: branred.c */
> -/* */
> -/* FUNCTIONS: branred */
> -/* */
> -/* FILES NEEDED: branred.h mydefs.h endian.h mpa.h */
> -/* mha.c */
> -/* */
> -/* Routine branred() performs range reduction of a double number */
> -/* x into Double length number a+aa,such that */
> -/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */
> -/* Routine returns the integer (n mod 4) of the above description */
> -/* of x. */
> -/*******************************************************************/
> -
> -#include "endian.h"
> -#include "mydefs.h"
> -#include "branred.h"
> -#include <math.h>
> -#include <math_private.h>
> -
> -#ifndef SECTION
> -# define SECTION
> -#endif
> -
> -
> -/*******************************************************************/
> -/* Routine branred() performs range reduction of a double number */
> -/* x into Double length number a+aa,such that */
> -/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */
> -/* Routine return integer (n mod 4) */
> -/*******************************************************************/
> -int
> -SECTION
> -__branred(double x, double *a, double *aa)
> -{
> - int i,k;
> - mynumber u,gor;
> - double r[6],s,t,sum,b,bb,sum1,sum2,b1,bb1,b2,bb2,x1,x2,t1,t2;
> -
> - x*=tm600.x;
> - t=x*split; /* split x to two numbers */
> - x1=t-(t-x);
> - x2=x-x1;
> - sum=0;
> - u.x = x1;
> - k = (u.i[HIGH_HALF]>>20)&2047;
> - k = (k-450)/24;
> - if (k<0)
> - k=0;
> - gor.x = t576.x;
> - gor.i[HIGH_HALF] -= ((k*24)<<20);
> - for (i=0;i<6;i++)
> - { r[i] = x1*toverp[k+i]*gor.x; gor.x *= tm24.x; }
> - for (i=0;i<3;i++) {
> - s=(r[i]+big.x)-big.x;
> - sum+=s;
> - r[i]-=s;
> - }
> - t=0;
> - for (i=0;i<6;i++)
> - t+=r[5-i];
> - bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5];
> - s=(t+big.x)-big.x;
> - sum+=s;
> - t-=s;
> - b=t+bb;
> - bb=(t-b)+bb;
> - s=(sum+big1.x)-big1.x;
> - sum-=s;
> - b1=b;
> - bb1=bb;
> - sum1=sum;
> - sum=0;
> -
> - u.x = x2;
> - k = (u.i[HIGH_HALF]>>20)&2047;
> - k = (k-450)/24;
> - if (k<0)
> - k=0;
> - gor.x = t576.x;
> - gor.i[HIGH_HALF] -= ((k*24)<<20);
> - for (i=0;i<6;i++)
> - { r[i] = x2*toverp[k+i]*gor.x; gor.x *= tm24.x; }
> - for (i=0;i<3;i++) {
> - s=(r[i]+big.x)-big.x;
> - sum+=s;
> - r[i]-=s;
> - }
> - t=0;
> - for (i=0;i<6;i++)
> - t+=r[5-i];
> - bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5];
> - s=(t+big.x)-big.x;
> - sum+=s;
> - t-=s;
> - b=t+bb;
> - bb=(t-b)+bb;
> - s=(sum+big1.x)-big1.x;
> - sum-=s;
> -
> - b2=b;
> - bb2=bb;
> - sum2=sum;
> -
> - sum=sum1+sum2;
> - b=b1+b2;
> - bb = (fabs(b1)>fabs(b2))? (b1-b)+b2 : (b2-b)+b1;
> - if (b > 0.5)
> - {b-=1.0; sum+=1.0;}
> - else if (b < -0.5)
> - {b+=1.0; sum-=1.0;}
> - s=b+(bb+bb1+bb2);
> - t=((b-s)+bb)+(bb1+bb2);
> - b=s*split;
> - t1=b-(b-s);
> - t2=s-t1;
> - b=s*hp0.x;
> - bb=(((t1*mp1.x-b)+t1*mp2.x)+t2*mp1.x)+(t2*mp2.x+s*hp1.x+t*hp0.x);
> - s=b+bb;
> - t=(b-s)+bb;
> - *a=s;
> - *aa=t;
> - return ((int) sum)&3; /* return quarter of unit circle */
> -}
> diff --git a/sysdeps/ieee754/dbl-64/branred.h b/sysdeps/ieee754/dbl-64/branred.h
> deleted file mode 100644
> index d34914d9c39..00000000000
> --- a/sysdeps/ieee754/dbl-64/branred.h
> +++ /dev/null
> @@ -1,79 +0,0 @@
> -/*
> - * IBM Accurate Mathematical Library
> - * Copyright (C) 2001-2026 Free Software Foundation, Inc.
> - *
> - * This program is free software; you can redistribute it and/or modify
> - * it under the terms of the GNU Lesser General Public License as published by
> - * the Free Software Foundation; either version 2.1 of the License, or
> - * (at your option) any later version.
> - *
> - * This program is distributed in the hope that it will be useful,
> - * but WITHOUT ANY WARRANTY; without even the implied warranty of
> - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
> - * GNU Lesser General Public License for more details.
> - *
> - * You should have received a copy of the GNU Lesser General Public License
> - * along with this program; if not, see <https://www.gnu.org/licenses/>.
> - */
> -/************************************************************************/
> -/* MODULE_NAME: branred.h */
> -/* */
> -/* */
> -/* common data and variables definition for BIG or LITTLE ENDIAN */
> -/************************************************************************/
> -
> -#ifndef BRANRED_H
> -#define BRANRED_H
> -
> -#include <dla.h>
> -
> -#ifdef BIG_ENDI
> -static const mynumber
> -
> -/**/ t576 = {{0x63f00000, 0x00000000}}, /* 2 ^ 576 */
> -/**/ tm600 = {{0x1a700000, 0x00000000}}, /* 2 ^- 600 */
> -/**/ tm24 = {{0x3e700000, 0x00000000}}, /* 2 ^- 24 */
> -/**/ big = {{0x43380000, 0x00000000}}, /* 6755399441055744 */
> -/**/ big1 = {{0x43580000, 0x00000000}}, /* 27021597764222976 */
> -/**/ hp0 = {{0x3FF921FB, 0x54442D18}} ,/* 1.5707963267948966 */
> -/**/ hp1 = {{0x3C91A626, 0x33145C07}} ,/* 6.123233995736766e-17 */
> -/**/ mp1 = {{0x3FF921FB, 0x58000000}}, /* 1.5707963407039642 */
> -/**/ mp2 = {{0xBE4DDE97, 0x40000000}}; /*-1.3909067675399456e-08 */
> -
> -#else
> -#ifdef LITTLE_ENDI
> -static const mynumber
> -
> -/**/ t576 = {{0x00000000, 0x63f00000}}, /* 2 ^ 576 */
> -/**/ tm600 = {{0x00000000, 0x1a700000}}, /* 2 ^- 600 */
> -/**/ tm24 = {{0x00000000, 0x3e700000}}, /* 2 ^- 24 */
> -/**/ big = {{0x00000000, 0x43380000}}, /* 6755399441055744 */
> -/**/ big1 = {{0x00000000, 0x43580000}}, /* 27021597764222976 */
> -/**/ hp0 = {{0x54442D18, 0x3FF921FB}}, /* 1.5707963267948966 */
> -/**/ hp1 = {{0x33145C07, 0x3C91A626}}, /* 6.123233995736766e-17 */
> -/**/ mp1 = {{0x58000000, 0x3FF921FB}}, /* 1.5707963407039642 */
> -/**/ mp2 = {{0x40000000, 0xBE4DDE97}}; /*-1.3909067675399456e-08 */
> -
> -#endif
> -#endif
> -
> -static const double toverp[75] = { /* 2/ PI base 24*/
> - 10680707.0, 7228996.0, 1387004.0, 2578385.0, 16069853.0,
> - 12639074.0, 9804092.0, 4427841.0, 16666979.0, 11263675.0,
> - 12935607.0, 2387514.0, 4345298.0, 14681673.0, 3074569.0,
> - 13734428.0, 16653803.0, 1880361.0, 10960616.0, 8533493.0,
> - 3062596.0, 8710556.0, 7349940.0, 6258241.0, 3772886.0,
> - 3769171.0, 3798172.0, 8675211.0, 12450088.0, 3874808.0,
> - 9961438.0, 366607.0, 15675153.0, 9132554.0, 7151469.0,
> - 3571407.0, 2607881.0, 12013382.0, 4155038.0, 6285869.0,
> - 7677882.0, 13102053.0, 15825725.0, 473591.0, 9065106.0,
> - 15363067.0, 6271263.0, 9264392.0, 5636912.0, 4652155.0,
> - 7056368.0, 13614112.0, 10155062.0, 1944035.0, 9527646.0,
> - 15080200.0, 6658437.0, 6231200.0, 6832269.0, 16767104.0,
> - 5075751.0, 3212806.0, 1398474.0, 7579849.0, 6349435.0,
> - 12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0,
> - 12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 };
> -
> -static const double split = CN; /* 2^27 + 1 */
> -
> -#endif
> diff --git a/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/sysdeps/ieee754/dbl-64/e_rem_pio2.c
> new file mode 100644
> index 00000000000..9e910e69995
> --- /dev/null
> +++ b/sysdeps/ieee754/dbl-64/e_rem_pio2.c
> @@ -0,0 +1,76 @@
> +/*
> + * ====================================================
> + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
> + *
> + * Developed at SunPro, a Sun Microsystems, Inc. business.
> + * Permission to use, copy, modify, and distribute this
> + * software is freely granted, provided that this notice
> + * is preserved.
> + * ====================================================
> + */
> +
> +/* __ieee754_rem_pio2(x,y)
> + *
> + * return the remainder of x rem pi/2 in y[0]+y[1]
> + * use __kernel_rem_pio2()
> + *
> + * The callers (sin, cos, sincos, and tan) reduce smaller arguments
> + * themselves and handle non-finite inputs, so only the huge-argument
> + * path of the original fdlibm routine is kept: the caller guarantees
> + * 1e8 < |x| < 2^1024.
> + */
> +
> +#include <math.h>
> +#include <math_private.h>
> +
> +/*
> + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
> + */
> +static const int32_t two_over_pi[] = {
> +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
> +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
> +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
> +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
> +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
> +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
> +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
> +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
> +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
> +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
> +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
> +};
> +
> +static const double
> + zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
> + two24 = 1.67772160000000000000e+07; /* 0x41700000, 0x00000000 */
> +
> +int32_t
> +__ieee754_rem_pio2 (double x, double *y)
> +{
> + double z;
> + double tx[3];
> + int32_t e0, i, nx, n, ix, hx;
> + uint32_t low;
> +
> + GET_HIGH_WORD (hx, x); /* high word of x */
> + ix = hx & 0x7fffffff;
> + /* set z = scalbn(|x|,ilogb(x)-23) */
> + GET_LOW_WORD (low, x);
> + e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */
> + INSERT_WORDS (z, ix - ((int32_t) (e0 << 20)), low);
> + for (i = 0; i < 2; i++)
> + {
> + tx[i] = (double) ((int32_t) (z));
> + z = (z - tx[i]) * two24;
> + }
> + tx[2] = z;
> + nx = 3;
> + while (tx[nx - 1] == zero)
> + nx--; /* skip zero term */
> + n = __kernel_rem_pio2 (tx, y, e0, nx, 2, two_over_pi);
> + if (hx < 0)
> + {
> + y[0] = -y[0]; y[1] = -y[1]; return -n;
> + }
> + return n;
> +}
> diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
> index 272d560c3e6..4fe289bdd23 100644
> --- a/sysdeps/ieee754/dbl-64/s_sin.c
> +++ b/sysdeps/ieee754/dbl-64/s_sin.c
> @@ -23,7 +23,7 @@
> /* FUNCTIONS: usin */
> /* ucos */
> /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
> -/* branred.c sincos.tbl */
> +/* e_rem_pio2.c sincos.tbl */
> /* */
> /* An ultimate sin and cos routine. Given an IEEE double machine number x */
> /* it computes sin(x) or cos(x) with ~0.55 ULP. */
> @@ -90,8 +90,6 @@ static const double
> cs4 = -4.16666666666664434524222570944589E-02,
> cs6 = 1.38888874007937613028114285595617E-03;
>
> -int __branred (double x, double *a, double *aa);
> -
> /* Given a number partitioned into X and DX, this function computes the cosine
> of the number by combining the sin and cos of X (as computed by a variation
> of the Taylor series) with the values looked up from the sin/cos table to
> @@ -239,8 +237,9 @@ __sin (double x)
> /* --------------------105414350 <|x| <2^1024------------------------------*/
> else if (k < 0x7ff00000)
> {
> - n = __branred (x, &a, &da);
> - retval = do_sincos (a, da, n);
> + double y[2];
> + n = __ieee754_rem_pio2 (x, y);
> + retval = do_sincos (y[0], y[1], n);
> }
> /*--------------------- |x| > 2^1024 ----------------------------------*/
> else
> @@ -304,8 +303,9 @@ __cos (double x)
> /* 105414350 <|x| <2^1024 */
> else if (k < 0x7ff00000)
> {
> - n = __branred (x, &a, &da);
> - retval = do_sincos (a, da, n + 1);
> + double y[2];
> + n = __ieee754_rem_pio2 (x, y);
> + retval = do_sincos (y[0], y[1], n + 1);
> }
>
> else
> diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c
> index 17f795fc14e..501031dc378 100644
> --- a/sysdeps/ieee754/dbl-64/s_sincos.c
> +++ b/sysdeps/ieee754/dbl-64/s_sincos.c
> @@ -78,7 +78,15 @@ __sincos (double x, double *sinx, double *cosx)
> unsigned int n;
>
> /* If |x| < 105414350 use simple range reduction. */
> - n = k < 0x419921FB ? reduce_sincos (x, &a, &da) : __branred (x, &a, &da);
> + if (k < 0x419921FB)
> + n = reduce_sincos (x, &a, &da);
> + else
> + {
> + double y[2];
OK. Threshold for x is x < 1.05e8 (within 1e8).
> + n = __ieee754_rem_pio2 (x, y);
> + a = y[0];
> + da = y[1];
> + }
> n = n & 3;
>
> if (n == 1 || n == 2)
> diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c
> index 6568b1cd3c5..bb949110ad0 100644
> --- a/sysdeps/ieee754/dbl-64/s_tan.c
> +++ b/sysdeps/ieee754/dbl-64/s_tan.c
> @@ -22,7 +22,7 @@
> /* FUNCTIONS: utan */
> /* */
> /* FILES NEEDED:dla.h endian.h mydefs.h utan.h */
> -/* branred.c */
> +/* e_rem_pio2.c */
> /* utan.tbl */
> /* */
> /*********************************************************************/
> @@ -59,8 +59,6 @@ __tan (double x)
>
> double retval;
>
> - int __branred (double, double *, double *);
> -
> SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
>
> /* x=+-INF, x=NaN */
> @@ -293,8 +291,11 @@ __tan (double x)
>
> /* (---) The case 1e8 < abs(x) < 2**1024 */
> /* Range reduction by algorithm iii */
> - n = (__branred (x, &a, &da)) & 0x00000001;
> - EADD (a, da, t1, t2);
> + {
> + double y[2];
> + n = __ieee754_rem_pio2 (x, y) & 0x00000001;
> + EADD (y[0], y[1], t1, t2);
> + }
> a = t1;
> da = t2;
> if (a < 0.0)
> diff --git a/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c b/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c
> new file mode 100644
> index 00000000000..6e25b021ab5
> --- /dev/null
> +++ b/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c
> @@ -0,0 +1 @@
> +/* Empty. */
> diff --git a/sysdeps/x86_64/fpu/Makefile b/sysdeps/x86_64/fpu/Makefile
> index 8af53b30758..5ad28fc5fc1 100644
> --- a/sysdeps/x86_64/fpu/Makefile
> +++ b/sysdeps/x86_64/fpu/Makefile
> @@ -67,18 +67,6 @@ CFLAGS-test-double-vlen4-avx2-wrappers.c = $(double-vlen4-arch-ext2-cflags)
> CFLAGS-test-float-vlen8-avx2-wrappers.c = $(float-vlen8-arch-ext2-cflags)
> endif
>
> -ifeq ($(subdir)$(config-cflags-mprefer-vector-width),mathyes)
> -# When compiled with -O3 -march=skylake, GCC 8 and 9 optimize some loops
> -# in branred.c with 256-bit vector instructions, which leads to store
> -# forward stall:
> -#
> -# https://gcc.gnu.org/bugzilla/show_bug.cgi?id=90579
> -#
> -# Limit vector width to 128 bits to work around this issue. It improves
> -# performance of sin and cos by more than 40% on Skylake.
> -CFLAGS-branred.c = -mprefer-vector-width=128
> -endif
> -
OK. Not required.
> ifeq ($(subdir)$(build-mathvec),benchtestsyes)
> double-vlen4-arch-ext-cflags = -mavx
> double-vlen4-arch-ext2-cflags = -mavx2
--
Cheers,
Carlos.
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