[3/6] aarch64: Add vector implementations of atan routines
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Commit Message
---
Thanks,
Joe
sysdeps/aarch64/fpu/Makefile | 1 +
sysdeps/aarch64/fpu/Versions | 4 +
sysdeps/aarch64/fpu/atan_advsimd.c | 104 +++++++++++++++++
sysdeps/aarch64/fpu/atan_sve.c | 90 +++++++++++++++
sysdeps/aarch64/fpu/atanf_advsimd.c | 109 ++++++++++++++++++
sysdeps/aarch64/fpu/atanf_sve.c | 79 +++++++++++++
sysdeps/aarch64/fpu/bits/math-vector.h | 4 +
.../fpu/test-double-advsimd-wrappers.c | 1 +
.../aarch64/fpu/test-double-sve-wrappers.c | 1 +
.../aarch64/fpu/test-float-advsimd-wrappers.c | 1 +
sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 +
sysdeps/aarch64/libm-test-ulps | 8 ++
.../unix/sysv/linux/aarch64/libmvec.abilist | 4 +
13 files changed, 407 insertions(+)
create mode 100644 sysdeps/aarch64/fpu/atan_advsimd.c
create mode 100644 sysdeps/aarch64/fpu/atan_sve.c
create mode 100644 sysdeps/aarch64/fpu/atanf_advsimd.c
create mode 100644 sysdeps/aarch64/fpu/atanf_sve.c
Comments
The 11/03/2023 12:12, Joe Ramsay wrote:
> ---
this is OK to commit.
Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>
> Thanks,
> Joe
> sysdeps/aarch64/fpu/Makefile | 1 +
> sysdeps/aarch64/fpu/Versions | 4 +
> sysdeps/aarch64/fpu/atan_advsimd.c | 104 +++++++++++++++++
> sysdeps/aarch64/fpu/atan_sve.c | 90 +++++++++++++++
> sysdeps/aarch64/fpu/atanf_advsimd.c | 109 ++++++++++++++++++
> sysdeps/aarch64/fpu/atanf_sve.c | 79 +++++++++++++
> sysdeps/aarch64/fpu/bits/math-vector.h | 4 +
> .../fpu/test-double-advsimd-wrappers.c | 1 +
> .../aarch64/fpu/test-double-sve-wrappers.c | 1 +
> .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 +
> sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 +
> sysdeps/aarch64/libm-test-ulps | 8 ++
> .../unix/sysv/linux/aarch64/libmvec.abilist | 4 +
> 13 files changed, 407 insertions(+)
> create mode 100644 sysdeps/aarch64/fpu/atan_advsimd.c
> create mode 100644 sysdeps/aarch64/fpu/atan_sve.c
> create mode 100644 sysdeps/aarch64/fpu/atanf_advsimd.c
> create mode 100644 sysdeps/aarch64/fpu/atanf_sve.c
>
> diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile
> index 606fdd804f..5bd77a749d 100644
> --- a/sysdeps/aarch64/fpu/Makefile
> +++ b/sysdeps/aarch64/fpu/Makefile
> @@ -1,5 +1,6 @@
> libmvec-supported-funcs = acos \
> asin \
> + atan \
> cos \
> exp \
> exp10 \
> diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions
> index 1037cd92bd..dfc3d2dad3 100644
> --- a/sysdeps/aarch64/fpu/Versions
> +++ b/sysdeps/aarch64/fpu/Versions
> @@ -26,6 +26,10 @@ libmvec {
> _ZGVnN2v_asin;
> _ZGVsMxv_asinf;
> _ZGVsMxv_asin;
> + _ZGVnN4v_atanf;
> + _ZGVnN2v_atan;
> + _ZGVsMxv_atanf;
> + _ZGVsMxv_atan;
> _ZGVnN4v_exp10f;
> _ZGVnN2v_exp10;
> _ZGVsMxv_exp10f;
> diff --git a/sysdeps/aarch64/fpu/atan_advsimd.c b/sysdeps/aarch64/fpu/atan_advsimd.c
> new file mode 100644
> index 0000000000..d52c07d8a0
> --- /dev/null
> +++ b/sysdeps/aarch64/fpu/atan_advsimd.c
> @@ -0,0 +1,104 @@
> +/* Double-precision AdvSIMD inverse tan
> +
> + Copyright (C) 2023 Free Software Foundation, Inc.
> + This file is part of the GNU C Library.
> +
> + The GNU C Library 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.
> +
> + The GNU C Library 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 the GNU C Library; if not, see
> + <https://www.gnu.org/licenses/>. */
> +
> +#include "v_math.h"
> +#include "poly_advsimd_f64.h"
> +
> +static const struct data
> +{
> + float64x2_t pi_over_2;
> + float64x2_t poly[20];
> +} data = {
> + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
> + [2**-1022, 1.0]. */
> + .poly = { V2 (-0x1.5555555555555p-2), V2 (0x1.99999999996c1p-3),
> + V2 (-0x1.2492492478f88p-3), V2 (0x1.c71c71bc3951cp-4),
> + V2 (-0x1.745d160a7e368p-4), V2 (0x1.3b139b6a88ba1p-4),
> + V2 (-0x1.11100ee084227p-4), V2 (0x1.e1d0f9696f63bp-5),
> + V2 (-0x1.aebfe7b418581p-5), V2 (0x1.842dbe9b0d916p-5),
> + V2 (-0x1.5d30140ae5e99p-5), V2 (0x1.338e31eb2fbbcp-5),
> + V2 (-0x1.00e6eece7de8p-5), V2 (0x1.860897b29e5efp-6),
> + V2 (-0x1.0051381722a59p-6), V2 (0x1.14e9dc19a4a4ep-7),
> + V2 (-0x1.d0062b42fe3bfp-9), V2 (0x1.17739e210171ap-10),
> + V2 (-0x1.ab24da7be7402p-13), V2 (0x1.358851160a528p-16), },
> + .pi_over_2 = V2 (0x1.921fb54442d18p+0),
> +};
> +
> +#define SignMask v_u64 (0x8000000000000000)
> +#define TinyBound 0x3e10000000000000 /* asuint64(0x1p-30). */
> +#define BigBound 0x4340000000000000 /* asuint64(0x1p53). */
> +
> +/* Fast implementation of vector atan.
> + Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
> + z=1/x and shift = pi/2. Maximum observed error is 2.27 ulps:
> + _ZGVnN2v_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
> + want 0x1.9225645bdd7c3p-1. */
> +float64x2_t VPCS_ATTR V_NAME_D1 (atan) (float64x2_t x)
> +{
> + const struct data *d = ptr_barrier (&data);
> +
> + /* Small cases, infs and nans are supported by our approximation technique,
> + but do not set fenv flags correctly. Only trigger special case if we need
> + fenv. */
> + uint64x2_t ix = vreinterpretq_u64_f64 (x);
> + uint64x2_t sign = vandq_u64 (ix, SignMask);
> +
> +#if WANT_SIMD_EXCEPT
> + uint64x2_t ia12 = vandq_u64 (ix, v_u64 (0x7ff0000000000000));
> + uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia12, v_u64 (TinyBound)),
> + v_u64 (BigBound - TinyBound));
> + /* If any lane is special, fall back to the scalar routine for all lanes. */
> + if (__glibc_unlikely (v_any_u64 (special)))
> + return v_call_f64 (atan, x, v_f64 (0), v_u64 (-1));
> +#endif
> +
> + /* Argument reduction:
> + y := arctan(x) for x < 1
> + y := pi/2 + arctan(-1/x) for x > 1
> + Hence, use z=-1/a if x>=1, otherwise z=a. */
> + uint64x2_t red = vcagtq_f64 (x, v_f64 (1.0));
> + /* Avoid dependency in abs(x) in division (and comparison). */
> + float64x2_t z = vbslq_f64 (red, vdivq_f64 (v_f64 (1.0), x), x);
> + float64x2_t shift = vreinterpretq_f64_u64 (
> + vandq_u64 (red, vreinterpretq_u64_f64 (d->pi_over_2)));
> + /* Use absolute value only when needed (odd powers of z). */
> + float64x2_t az = vbslq_f64 (
> + SignMask, vreinterpretq_f64_u64 (vandq_u64 (SignMask, red)), z);
> +
> + /* Calculate the polynomial approximation.
> + Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of
> + full scheme to avoid underflow in x^16.
> + The order 19 polynomial P approximates
> + (atan(sqrt(x))-sqrt(x))/x^(3/2). */
> + float64x2_t z2 = vmulq_f64 (z, z);
> + float64x2_t x2 = vmulq_f64 (z2, z2);
> + float64x2_t x4 = vmulq_f64 (x2, x2);
> + float64x2_t x8 = vmulq_f64 (x4, x4);
> + float64x2_t y
> + = vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, d->poly),
> + v_estrin_11_f64 (z2, x2, x4, x8, d->poly + 8), x8);
> +
> + /* Finalize. y = shift + z + z^3 * P(z^2). */
> + y = vfmaq_f64 (az, y, vmulq_f64 (z2, az));
> + y = vaddq_f64 (y, shift);
> +
> + /* y = atan(x) if x>0, -atan(-x) otherwise. */
> + y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), sign));
> + return y;
> +}
> diff --git a/sysdeps/aarch64/fpu/atan_sve.c b/sysdeps/aarch64/fpu/atan_sve.c
> new file mode 100644
> index 0000000000..35587ef212
> --- /dev/null
> +++ b/sysdeps/aarch64/fpu/atan_sve.c
> @@ -0,0 +1,90 @@
> +/* Double-precision SVE inverse tan
> +
> + Copyright (C) 2023 Free Software Foundation, Inc.
> + This file is part of the GNU C Library.
> +
> + The GNU C Library 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.
> +
> + The GNU C Library 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 the GNU C Library; if not, see
> + <https://www.gnu.org/licenses/>. */
> +
> +#include "sv_math.h"
> +#include "poly_sve_f64.h"
> +
> +static const struct data
> +{
> + float64_t poly[20];
> + float64_t pi_over_2;
> +} data = {
> + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
> + [2**-1022, 1.0]. */
> + .poly = { -0x1.5555555555555p-2, 0x1.99999999996c1p-3, -0x1.2492492478f88p-3,
> + 0x1.c71c71bc3951cp-4, -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4,
> + -0x1.11100ee084227p-4, 0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5,
> + 0x1.842dbe9b0d916p-5, -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5,
> + -0x1.00e6eece7de8p-5, 0x1.860897b29e5efp-6, -0x1.0051381722a59p-6,
> + 0x1.14e9dc19a4a4ep-7, -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10,
> + -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, },
> + .pi_over_2 = 0x1.921fb54442d18p+0,
> +};
> +
> +/* Useful constants. */
> +#define SignMask (0x8000000000000000)
> +
> +/* Fast implementation of SVE atan.
> + Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
> + z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
> + error is 2.27 ulps:
> + _ZGVsMxv_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
> + want 0x1.9225645bdd7c3p-1. */
> +svfloat64_t SV_NAME_D1 (atan) (svfloat64_t x, const svbool_t pg)
> +{
> + const struct data *d = ptr_barrier (&data);
> +
> + /* No need to trigger special case. Small cases, infs and nans
> + are supported by our approximation technique. */
> + svuint64_t ix = svreinterpret_u64 (x);
> + svuint64_t sign = svand_x (pg, ix, SignMask);
> +
> + /* Argument reduction:
> + y := arctan(x) for x < 1
> + y := pi/2 + arctan(-1/x) for x > 1
> + Hence, use z=-1/a if x>=1, otherwise z=a. */
> + svbool_t red = svacgt (pg, x, 1.0);
> + /* Avoid dependency in abs(x) in division (and comparison). */
> + svfloat64_t z = svsel (red, svdivr_x (pg, x, 1.0), x);
> + /* Use absolute value only when needed (odd powers of z). */
> + svfloat64_t az = svabs_x (pg, z);
> + az = svneg_m (az, red, az);
> +
> + /* Use split Estrin scheme for P(z^2) with deg(P)=19. */
> + svfloat64_t z2 = svmul_x (pg, z, z);
> + svfloat64_t x2 = svmul_x (pg, z2, z2);
> + svfloat64_t x4 = svmul_x (pg, x2, x2);
> + svfloat64_t x8 = svmul_x (pg, x4, x4);
> +
> + svfloat64_t y
> + = svmla_x (pg, sv_estrin_7_f64_x (pg, z2, x2, x4, d->poly),
> + sv_estrin_11_f64_x (pg, z2, x2, x4, x8, d->poly + 8), x8);
> +
> + /* y = shift + z + z^3 * P(z^2). */
> + svfloat64_t z3 = svmul_x (pg, z2, az);
> + y = svmla_x (pg, az, z3, y);
> +
> + /* Apply shift as indicated by `red` predicate. */
> + y = svadd_m (red, y, d->pi_over_2);
> +
> + /* y = atan(x) if x>0, -atan(-x) otherwise. */
> + y = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
> +
> + return y;
> +}
> diff --git a/sysdeps/aarch64/fpu/atanf_advsimd.c b/sysdeps/aarch64/fpu/atanf_advsimd.c
> new file mode 100644
> index 0000000000..589b0e8c96
> --- /dev/null
> +++ b/sysdeps/aarch64/fpu/atanf_advsimd.c
> @@ -0,0 +1,109 @@
> +/* Single-precision AdvSIMD inverse tan
> +
> + Copyright (C) 2023 Free Software Foundation, Inc.
> + This file is part of the GNU C Library.
> +
> + The GNU C Library 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.
> +
> + The GNU C Library 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 the GNU C Library; if not, see
> + <https://www.gnu.org/licenses/>. */
> +
> +#include "v_math.h"
> +#include "poly_advsimd_f32.h"
> +
> +static const struct data
> +{
> + float32x4_t poly[8];
> + float32x4_t pi_over_2;
> +} data = {
> + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
> + [2**-128, 1.0].
> + Generated using fpminimax between FLT_MIN and 1. */
> + .poly = { V4 (-0x1.55555p-2f), V4 (0x1.99935ep-3f), V4 (-0x1.24051ep-3f),
> + V4 (0x1.bd7368p-4f), V4 (-0x1.491f0ep-4f), V4 (0x1.93a2c0p-5f),
> + V4 (-0x1.4c3c60p-6f), V4 (0x1.01fd88p-8f) },
> + .pi_over_2 = V4 (0x1.921fb6p+0f),
> +};
> +
> +#define SignMask v_u32 (0x80000000)
> +
> +#define P(i) d->poly[i]
> +
> +#define TinyBound 0x30800000 /* asuint(0x1p-30). */
> +#define BigBound 0x4e800000 /* asuint(0x1p30). */
> +
> +#if WANT_SIMD_EXCEPT
> +static float32x4_t VPCS_ATTR NOINLINE
> +special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
> +{
> + return v_call_f32 (atanf, x, y, special);
> +}
> +#endif
> +
> +/* Fast implementation of vector atanf based on
> + atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1]
> + using z=-1/x and shift = pi/2. Maximum observed error is 2.9ulps:
> + _ZGVnN4v_atanf (0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1. */
> +float32x4_t VPCS_ATTR V_NAME_F1 (atan) (float32x4_t x)
> +{
> + const struct data *d = ptr_barrier (&data);
> +
> + /* Small cases, infs and nans are supported by our approximation technique,
> + but do not set fenv flags correctly. Only trigger special case if we need
> + fenv. */
> + uint32x4_t ix = vreinterpretq_u32_f32 (x);
> + uint32x4_t sign = vandq_u32 (ix, SignMask);
> +
> +#if WANT_SIMD_EXCEPT
> + uint32x4_t ia = vandq_u32 (ix, v_u32 (0x7ff00000));
> + uint32x4_t special = vcgtq_u32 (vsubq_u32 (ia, v_u32 (TinyBound)),
> + v_u32 (BigBound - TinyBound));
> + /* If any lane is special, fall back to the scalar routine for all lanes. */
> + if (__glibc_unlikely (v_any_u32 (special)))
> + return special_case (x, x, v_u32 (-1));
> +#endif
> +
> + /* Argument reduction:
> + y := arctan(x) for x < 1
> + y := pi/2 + arctan(-1/x) for x > 1
> + Hence, use z=-1/a if x>=1, otherwise z=a. */
> + uint32x4_t red = vcagtq_f32 (x, v_f32 (1.0));
> + /* Avoid dependency in abs(x) in division (and comparison). */
> + float32x4_t z = vbslq_f32 (red, vdivq_f32 (v_f32 (1.0f), x), x);
> + float32x4_t shift = vreinterpretq_f32_u32 (
> + vandq_u32 (red, vreinterpretq_u32_f32 (d->pi_over_2)));
> + /* Use absolute value only when needed (odd powers of z). */
> + float32x4_t az = vbslq_f32 (
> + SignMask, vreinterpretq_f32_u32 (vandq_u32 (SignMask, red)), z);
> +
> + /* Calculate the polynomial approximation.
> + Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
> + a standard implementation using z8 creates spurious underflow
> + in the very last fma (when z^8 is small enough).
> + Therefore, we split the last fma into a mul and an fma.
> + Horner and single-level Estrin have higher errors that exceed
> + threshold. */
> + float32x4_t z2 = vmulq_f32 (z, z);
> + float32x4_t z4 = vmulq_f32 (z2, z2);
> +
> + float32x4_t y = vfmaq_f32 (
> + v_pairwise_poly_3_f32 (z2, z4, d->poly), z4,
> + vmulq_f32 (z4, v_pairwise_poly_3_f32 (z2, z4, d->poly + 4)));
> +
> + /* y = shift + z * P(z^2). */
> + y = vaddq_f32 (vfmaq_f32 (az, y, vmulq_f32 (z2, az)), shift);
> +
> + /* y = atan(x) if x>0, -atan(-x) otherwise. */
> + y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), sign));
> +
> + return y;
> +}
> diff --git a/sysdeps/aarch64/fpu/atanf_sve.c b/sysdeps/aarch64/fpu/atanf_sve.c
> new file mode 100644
> index 0000000000..9453e7aa29
> --- /dev/null
> +++ b/sysdeps/aarch64/fpu/atanf_sve.c
> @@ -0,0 +1,79 @@
> +/* Single-precision SVE inverse tan
> +
> + Copyright (C) 2023 Free Software Foundation, Inc.
> + This file is part of the GNU C Library.
> +
> + The GNU C Library 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.
> +
> + The GNU C Library 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 the GNU C Library; if not, see
> + <https://www.gnu.org/licenses/>. */
> +
> +#include "sv_math.h"
> +#include "poly_sve_f32.h"
> +
> +static const struct data
> +{
> + float32_t poly[8];
> + float32_t pi_over_2;
> +} data = {
> + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
> + [2**-128, 1.0]. */
> + .poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f,
> + -0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f },
> + .pi_over_2 = 0x1.921fb6p+0f,
> +};
> +
> +#define SignMask (0x80000000)
> +
> +/* Fast implementation of SVE atanf based on
> + atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
> + z=-1/x and shift = pi/2.
> + Largest observed error is 2.9 ULP, close to +/-1.0:
> + _ZGVsMxv_atanf (0x1.0468f6p+0) got -0x1.967f06p-1
> + want -0x1.967fp-1. */
> +svfloat32_t SV_NAME_F1 (atan) (svfloat32_t x, const svbool_t pg)
> +{
> + const struct data *d = ptr_barrier (&data);
> +
> + /* No need to trigger special case. Small cases, infs and nans
> + are supported by our approximation technique. */
> + svuint32_t ix = svreinterpret_u32 (x);
> + svuint32_t sign = svand_x (pg, ix, SignMask);
> +
> + /* Argument reduction:
> + y := arctan(x) for x < 1
> + y := pi/2 + arctan(-1/x) for x > 1
> + Hence, use z=-1/a if x>=1, otherwise z=a. */
> + svbool_t red = svacgt (pg, x, 1.0f);
> + /* Avoid dependency in abs(x) in division (and comparison). */
> + svfloat32_t z = svsel (red, svdiv_x (pg, sv_f32 (1.0f), x), x);
> + /* Use absolute value only when needed (odd powers of z). */
> + svfloat32_t az = svabs_x (pg, z);
> + az = svneg_m (az, red, az);
> +
> + /* Use split Estrin scheme for P(z^2) with deg(P)=7. */
> + svfloat32_t z2 = svmul_x (pg, z, z);
> + svfloat32_t z4 = svmul_x (pg, z2, z2);
> + svfloat32_t z8 = svmul_x (pg, z4, z4);
> +
> + svfloat32_t y = sv_estrin_7_f32_x (pg, z2, z4, z8, d->poly);
> +
> + /* y = shift + z + z^3 * P(z^2). */
> + svfloat32_t z3 = svmul_x (pg, z2, az);
> + y = svmla_x (pg, az, z3, y);
> +
> + /* Apply shift as indicated by 'red' predicate. */
> + y = svadd_m (red, y, sv_f32 (d->pi_over_2));
> +
> + /* y = atan(x) if x>0, -atan(-x) otherwise. */
> + return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
> +}
> diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h
> index f313993d70..37aa74fe50 100644
> --- a/sysdeps/aarch64/fpu/bits/math-vector.h
> +++ b/sysdeps/aarch64/fpu/bits/math-vector.h
> @@ -51,6 +51,7 @@ typedef __SVBool_t __sv_bool_t;
>
> __vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t);
> __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t);
> +__vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t);
> __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
> __vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t);
> __vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t);
> @@ -63,6 +64,7 @@ __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t);
>
> __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t);
> __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t);
> +__vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t);
> __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
> __vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t);
> __vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t);
> @@ -80,6 +82,7 @@ __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t);
>
> __sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t);
> __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t);
> +__sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t);
> __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t);
> __sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t);
> __sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t);
> @@ -92,6 +95,7 @@ __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t);
>
> __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t);
> __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t);
> +__sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t);
> __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t);
> __sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t);
> __sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t);
> diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c
> index 5a0cbf743b..6954fe7435 100644
> --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c
> +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c
> @@ -25,6 +25,7 @@
>
> VPCS_VECTOR_WRAPPER (acos_advsimd, _ZGVnN2v_acos)
> VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin)
> +VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan)
> VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos)
> VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp)
> VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10)
> diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c
> index bd89ff6133..1173d8f9ae 100644
> --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c
> +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c
> @@ -34,6 +34,7 @@
>
> SVE_VECTOR_WRAPPER (acos_sve, _ZGVsMxv_acos)
> SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin)
> +SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan)
> SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos)
> SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp)
> SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10)
> diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c
> index 3fafca7557..387efc30f8 100644
> --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c
> +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c
> @@ -25,6 +25,7 @@
>
> VPCS_VECTOR_WRAPPER (acosf_advsimd, _ZGVnN4v_acosf)
> VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf)
> +VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf)
> VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf)
> VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf)
> VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f)
> diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c
> index b4ec9f777b..dddd4cb213 100644
> --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c
> +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c
> @@ -34,6 +34,7 @@
>
> SVE_VECTOR_WRAPPER (acosf_sve, _ZGVsMxv_acosf)
> SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf)
> +SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf)
> SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf)
> SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf)
> SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f)
> diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
> index c2b6f21b9d..24a99e10da 100644
> --- a/sysdeps/aarch64/libm-test-ulps
> +++ b/sysdeps/aarch64/libm-test-ulps
> @@ -121,11 +121,19 @@ double: 1
> float: 1
> ldouble: 2
>
> +Function: "atan_advsimd":
> +double: 1
> +float: 1
> +
> Function: "atan_downward":
> double: 1
> float: 2
> ldouble: 2
>
> +Function: "atan_sve":
> +double: 1
> +float: 1
> +
> Function: "atan_towardzero":
> double: 1
> float: 1
> diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist
> index f79eaaf241..a2d1b8fb6d 100644
> --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist
> +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist
> @@ -16,6 +16,7 @@ GLIBC_2.38 _ZGVsMxv_sin F
> GLIBC_2.38 _ZGVsMxv_sinf F
> GLIBC_2.39 _ZGVnN2v_acos F
> GLIBC_2.39 _ZGVnN2v_asin F
> +GLIBC_2.39 _ZGVnN2v_atan F
> GLIBC_2.39 _ZGVnN2v_exp10 F
> GLIBC_2.39 _ZGVnN2v_exp2 F
> GLIBC_2.39 _ZGVnN2v_log10 F
> @@ -23,6 +24,7 @@ GLIBC_2.39 _ZGVnN2v_log2 F
> GLIBC_2.39 _ZGVnN2v_tan F
> GLIBC_2.39 _ZGVnN4v_acosf F
> GLIBC_2.39 _ZGVnN4v_asinf F
> +GLIBC_2.39 _ZGVnN4v_atanf F
> GLIBC_2.39 _ZGVnN4v_exp10f F
> GLIBC_2.39 _ZGVnN4v_exp2f F
> GLIBC_2.39 _ZGVnN4v_log10f F
> @@ -32,6 +34,8 @@ GLIBC_2.39 _ZGVsMxv_acos F
> GLIBC_2.39 _ZGVsMxv_acosf F
> GLIBC_2.39 _ZGVsMxv_asin F
> GLIBC_2.39 _ZGVsMxv_asinf F
> +GLIBC_2.39 _ZGVsMxv_atan F
> +GLIBC_2.39 _ZGVsMxv_atanf F
> GLIBC_2.39 _ZGVsMxv_exp10 F
> GLIBC_2.39 _ZGVsMxv_exp10f F
> GLIBC_2.39 _ZGVsMxv_exp2 F
> --
> 2.27.0
>
@@ -1,5 +1,6 @@
libmvec-supported-funcs = acos \
asin \
+ atan \
cos \
exp \
exp10 \
@@ -26,6 +26,10 @@ libmvec {
_ZGVnN2v_asin;
_ZGVsMxv_asinf;
_ZGVsMxv_asin;
+ _ZGVnN4v_atanf;
+ _ZGVnN2v_atan;
+ _ZGVsMxv_atanf;
+ _ZGVsMxv_atan;
_ZGVnN4v_exp10f;
_ZGVnN2v_exp10;
_ZGVsMxv_exp10f;
new file mode 100644
@@ -0,0 +1,104 @@
+/* Double-precision AdvSIMD inverse tan
+
+ Copyright (C) 2023 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library 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.
+
+ The GNU C Library 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 the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
+
+#include "v_math.h"
+#include "poly_advsimd_f64.h"
+
+static const struct data
+{
+ float64x2_t pi_over_2;
+ float64x2_t poly[20];
+} data = {
+ /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+ [2**-1022, 1.0]. */
+ .poly = { V2 (-0x1.5555555555555p-2), V2 (0x1.99999999996c1p-3),
+ V2 (-0x1.2492492478f88p-3), V2 (0x1.c71c71bc3951cp-4),
+ V2 (-0x1.745d160a7e368p-4), V2 (0x1.3b139b6a88ba1p-4),
+ V2 (-0x1.11100ee084227p-4), V2 (0x1.e1d0f9696f63bp-5),
+ V2 (-0x1.aebfe7b418581p-5), V2 (0x1.842dbe9b0d916p-5),
+ V2 (-0x1.5d30140ae5e99p-5), V2 (0x1.338e31eb2fbbcp-5),
+ V2 (-0x1.00e6eece7de8p-5), V2 (0x1.860897b29e5efp-6),
+ V2 (-0x1.0051381722a59p-6), V2 (0x1.14e9dc19a4a4ep-7),
+ V2 (-0x1.d0062b42fe3bfp-9), V2 (0x1.17739e210171ap-10),
+ V2 (-0x1.ab24da7be7402p-13), V2 (0x1.358851160a528p-16), },
+ .pi_over_2 = V2 (0x1.921fb54442d18p+0),
+};
+
+#define SignMask v_u64 (0x8000000000000000)
+#define TinyBound 0x3e10000000000000 /* asuint64(0x1p-30). */
+#define BigBound 0x4340000000000000 /* asuint64(0x1p53). */
+
+/* Fast implementation of vector atan.
+ Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
+ z=1/x and shift = pi/2. Maximum observed error is 2.27 ulps:
+ _ZGVnN2v_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
+ want 0x1.9225645bdd7c3p-1. */
+float64x2_t VPCS_ATTR V_NAME_D1 (atan) (float64x2_t x)
+{
+ const struct data *d = ptr_barrier (&data);
+
+ /* Small cases, infs and nans are supported by our approximation technique,
+ but do not set fenv flags correctly. Only trigger special case if we need
+ fenv. */
+ uint64x2_t ix = vreinterpretq_u64_f64 (x);
+ uint64x2_t sign = vandq_u64 (ix, SignMask);
+
+#if WANT_SIMD_EXCEPT
+ uint64x2_t ia12 = vandq_u64 (ix, v_u64 (0x7ff0000000000000));
+ uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia12, v_u64 (TinyBound)),
+ v_u64 (BigBound - TinyBound));
+ /* If any lane is special, fall back to the scalar routine for all lanes. */
+ if (__glibc_unlikely (v_any_u64 (special)))
+ return v_call_f64 (atan, x, v_f64 (0), v_u64 (-1));
+#endif
+
+ /* Argument reduction:
+ y := arctan(x) for x < 1
+ y := pi/2 + arctan(-1/x) for x > 1
+ Hence, use z=-1/a if x>=1, otherwise z=a. */
+ uint64x2_t red = vcagtq_f64 (x, v_f64 (1.0));
+ /* Avoid dependency in abs(x) in division (and comparison). */
+ float64x2_t z = vbslq_f64 (red, vdivq_f64 (v_f64 (1.0), x), x);
+ float64x2_t shift = vreinterpretq_f64_u64 (
+ vandq_u64 (red, vreinterpretq_u64_f64 (d->pi_over_2)));
+ /* Use absolute value only when needed (odd powers of z). */
+ float64x2_t az = vbslq_f64 (
+ SignMask, vreinterpretq_f64_u64 (vandq_u64 (SignMask, red)), z);
+
+ /* Calculate the polynomial approximation.
+ Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of
+ full scheme to avoid underflow in x^16.
+ The order 19 polynomial P approximates
+ (atan(sqrt(x))-sqrt(x))/x^(3/2). */
+ float64x2_t z2 = vmulq_f64 (z, z);
+ float64x2_t x2 = vmulq_f64 (z2, z2);
+ float64x2_t x4 = vmulq_f64 (x2, x2);
+ float64x2_t x8 = vmulq_f64 (x4, x4);
+ float64x2_t y
+ = vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, d->poly),
+ v_estrin_11_f64 (z2, x2, x4, x8, d->poly + 8), x8);
+
+ /* Finalize. y = shift + z + z^3 * P(z^2). */
+ y = vfmaq_f64 (az, y, vmulq_f64 (z2, az));
+ y = vaddq_f64 (y, shift);
+
+ /* y = atan(x) if x>0, -atan(-x) otherwise. */
+ y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), sign));
+ return y;
+}
new file mode 100644
@@ -0,0 +1,90 @@
+/* Double-precision SVE inverse tan
+
+ Copyright (C) 2023 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library 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.
+
+ The GNU C Library 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 the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
+
+#include "sv_math.h"
+#include "poly_sve_f64.h"
+
+static const struct data
+{
+ float64_t poly[20];
+ float64_t pi_over_2;
+} data = {
+ /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+ [2**-1022, 1.0]. */
+ .poly = { -0x1.5555555555555p-2, 0x1.99999999996c1p-3, -0x1.2492492478f88p-3,
+ 0x1.c71c71bc3951cp-4, -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4,
+ -0x1.11100ee084227p-4, 0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5,
+ 0x1.842dbe9b0d916p-5, -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5,
+ -0x1.00e6eece7de8p-5, 0x1.860897b29e5efp-6, -0x1.0051381722a59p-6,
+ 0x1.14e9dc19a4a4ep-7, -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10,
+ -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, },
+ .pi_over_2 = 0x1.921fb54442d18p+0,
+};
+
+/* Useful constants. */
+#define SignMask (0x8000000000000000)
+
+/* Fast implementation of SVE atan.
+ Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
+ z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
+ error is 2.27 ulps:
+ _ZGVsMxv_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
+ want 0x1.9225645bdd7c3p-1. */
+svfloat64_t SV_NAME_D1 (atan) (svfloat64_t x, const svbool_t pg)
+{
+ const struct data *d = ptr_barrier (&data);
+
+ /* No need to trigger special case. Small cases, infs and nans
+ are supported by our approximation technique. */
+ svuint64_t ix = svreinterpret_u64 (x);
+ svuint64_t sign = svand_x (pg, ix, SignMask);
+
+ /* Argument reduction:
+ y := arctan(x) for x < 1
+ y := pi/2 + arctan(-1/x) for x > 1
+ Hence, use z=-1/a if x>=1, otherwise z=a. */
+ svbool_t red = svacgt (pg, x, 1.0);
+ /* Avoid dependency in abs(x) in division (and comparison). */
+ svfloat64_t z = svsel (red, svdivr_x (pg, x, 1.0), x);
+ /* Use absolute value only when needed (odd powers of z). */
+ svfloat64_t az = svabs_x (pg, z);
+ az = svneg_m (az, red, az);
+
+ /* Use split Estrin scheme for P(z^2) with deg(P)=19. */
+ svfloat64_t z2 = svmul_x (pg, z, z);
+ svfloat64_t x2 = svmul_x (pg, z2, z2);
+ svfloat64_t x4 = svmul_x (pg, x2, x2);
+ svfloat64_t x8 = svmul_x (pg, x4, x4);
+
+ svfloat64_t y
+ = svmla_x (pg, sv_estrin_7_f64_x (pg, z2, x2, x4, d->poly),
+ sv_estrin_11_f64_x (pg, z2, x2, x4, x8, d->poly + 8), x8);
+
+ /* y = shift + z + z^3 * P(z^2). */
+ svfloat64_t z3 = svmul_x (pg, z2, az);
+ y = svmla_x (pg, az, z3, y);
+
+ /* Apply shift as indicated by `red` predicate. */
+ y = svadd_m (red, y, d->pi_over_2);
+
+ /* y = atan(x) if x>0, -atan(-x) otherwise. */
+ y = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
+
+ return y;
+}
new file mode 100644
@@ -0,0 +1,109 @@
+/* Single-precision AdvSIMD inverse tan
+
+ Copyright (C) 2023 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library 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.
+
+ The GNU C Library 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 the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
+
+#include "v_math.h"
+#include "poly_advsimd_f32.h"
+
+static const struct data
+{
+ float32x4_t poly[8];
+ float32x4_t pi_over_2;
+} data = {
+ /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+ [2**-128, 1.0].
+ Generated using fpminimax between FLT_MIN and 1. */
+ .poly = { V4 (-0x1.55555p-2f), V4 (0x1.99935ep-3f), V4 (-0x1.24051ep-3f),
+ V4 (0x1.bd7368p-4f), V4 (-0x1.491f0ep-4f), V4 (0x1.93a2c0p-5f),
+ V4 (-0x1.4c3c60p-6f), V4 (0x1.01fd88p-8f) },
+ .pi_over_2 = V4 (0x1.921fb6p+0f),
+};
+
+#define SignMask v_u32 (0x80000000)
+
+#define P(i) d->poly[i]
+
+#define TinyBound 0x30800000 /* asuint(0x1p-30). */
+#define BigBound 0x4e800000 /* asuint(0x1p30). */
+
+#if WANT_SIMD_EXCEPT
+static float32x4_t VPCS_ATTR NOINLINE
+special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
+{
+ return v_call_f32 (atanf, x, y, special);
+}
+#endif
+
+/* Fast implementation of vector atanf based on
+ atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1]
+ using z=-1/x and shift = pi/2. Maximum observed error is 2.9ulps:
+ _ZGVnN4v_atanf (0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1. */
+float32x4_t VPCS_ATTR V_NAME_F1 (atan) (float32x4_t x)
+{
+ const struct data *d = ptr_barrier (&data);
+
+ /* Small cases, infs and nans are supported by our approximation technique,
+ but do not set fenv flags correctly. Only trigger special case if we need
+ fenv. */
+ uint32x4_t ix = vreinterpretq_u32_f32 (x);
+ uint32x4_t sign = vandq_u32 (ix, SignMask);
+
+#if WANT_SIMD_EXCEPT
+ uint32x4_t ia = vandq_u32 (ix, v_u32 (0x7ff00000));
+ uint32x4_t special = vcgtq_u32 (vsubq_u32 (ia, v_u32 (TinyBound)),
+ v_u32 (BigBound - TinyBound));
+ /* If any lane is special, fall back to the scalar routine for all lanes. */
+ if (__glibc_unlikely (v_any_u32 (special)))
+ return special_case (x, x, v_u32 (-1));
+#endif
+
+ /* Argument reduction:
+ y := arctan(x) for x < 1
+ y := pi/2 + arctan(-1/x) for x > 1
+ Hence, use z=-1/a if x>=1, otherwise z=a. */
+ uint32x4_t red = vcagtq_f32 (x, v_f32 (1.0));
+ /* Avoid dependency in abs(x) in division (and comparison). */
+ float32x4_t z = vbslq_f32 (red, vdivq_f32 (v_f32 (1.0f), x), x);
+ float32x4_t shift = vreinterpretq_f32_u32 (
+ vandq_u32 (red, vreinterpretq_u32_f32 (d->pi_over_2)));
+ /* Use absolute value only when needed (odd powers of z). */
+ float32x4_t az = vbslq_f32 (
+ SignMask, vreinterpretq_f32_u32 (vandq_u32 (SignMask, red)), z);
+
+ /* Calculate the polynomial approximation.
+ Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
+ a standard implementation using z8 creates spurious underflow
+ in the very last fma (when z^8 is small enough).
+ Therefore, we split the last fma into a mul and an fma.
+ Horner and single-level Estrin have higher errors that exceed
+ threshold. */
+ float32x4_t z2 = vmulq_f32 (z, z);
+ float32x4_t z4 = vmulq_f32 (z2, z2);
+
+ float32x4_t y = vfmaq_f32 (
+ v_pairwise_poly_3_f32 (z2, z4, d->poly), z4,
+ vmulq_f32 (z4, v_pairwise_poly_3_f32 (z2, z4, d->poly + 4)));
+
+ /* y = shift + z * P(z^2). */
+ y = vaddq_f32 (vfmaq_f32 (az, y, vmulq_f32 (z2, az)), shift);
+
+ /* y = atan(x) if x>0, -atan(-x) otherwise. */
+ y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), sign));
+
+ return y;
+}
new file mode 100644
@@ -0,0 +1,79 @@
+/* Single-precision SVE inverse tan
+
+ Copyright (C) 2023 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library 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.
+
+ The GNU C Library 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 the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
+
+#include "sv_math.h"
+#include "poly_sve_f32.h"
+
+static const struct data
+{
+ float32_t poly[8];
+ float32_t pi_over_2;
+} data = {
+ /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
+ [2**-128, 1.0]. */
+ .poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f,
+ -0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f },
+ .pi_over_2 = 0x1.921fb6p+0f,
+};
+
+#define SignMask (0x80000000)
+
+/* Fast implementation of SVE atanf based on
+ atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
+ z=-1/x and shift = pi/2.
+ Largest observed error is 2.9 ULP, close to +/-1.0:
+ _ZGVsMxv_atanf (0x1.0468f6p+0) got -0x1.967f06p-1
+ want -0x1.967fp-1. */
+svfloat32_t SV_NAME_F1 (atan) (svfloat32_t x, const svbool_t pg)
+{
+ const struct data *d = ptr_barrier (&data);
+
+ /* No need to trigger special case. Small cases, infs and nans
+ are supported by our approximation technique. */
+ svuint32_t ix = svreinterpret_u32 (x);
+ svuint32_t sign = svand_x (pg, ix, SignMask);
+
+ /* Argument reduction:
+ y := arctan(x) for x < 1
+ y := pi/2 + arctan(-1/x) for x > 1
+ Hence, use z=-1/a if x>=1, otherwise z=a. */
+ svbool_t red = svacgt (pg, x, 1.0f);
+ /* Avoid dependency in abs(x) in division (and comparison). */
+ svfloat32_t z = svsel (red, svdiv_x (pg, sv_f32 (1.0f), x), x);
+ /* Use absolute value only when needed (odd powers of z). */
+ svfloat32_t az = svabs_x (pg, z);
+ az = svneg_m (az, red, az);
+
+ /* Use split Estrin scheme for P(z^2) with deg(P)=7. */
+ svfloat32_t z2 = svmul_x (pg, z, z);
+ svfloat32_t z4 = svmul_x (pg, z2, z2);
+ svfloat32_t z8 = svmul_x (pg, z4, z4);
+
+ svfloat32_t y = sv_estrin_7_f32_x (pg, z2, z4, z8, d->poly);
+
+ /* y = shift + z + z^3 * P(z^2). */
+ svfloat32_t z3 = svmul_x (pg, z2, az);
+ y = svmla_x (pg, az, z3, y);
+
+ /* Apply shift as indicated by 'red' predicate. */
+ y = svadd_m (red, y, sv_f32 (d->pi_over_2));
+
+ /* y = atan(x) if x>0, -atan(-x) otherwise. */
+ return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
+}
@@ -51,6 +51,7 @@ typedef __SVBool_t __sv_bool_t;
__vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t);
@@ -63,6 +64,7 @@ __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t);
__vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t);
@@ -80,6 +82,7 @@ __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t);
__sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t);
@@ -92,6 +95,7 @@ __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t);
@@ -25,6 +25,7 @@
VPCS_VECTOR_WRAPPER (acos_advsimd, _ZGVnN2v_acos)
VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin)
+VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan)
VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos)
VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp)
VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10)
@@ -34,6 +34,7 @@
SVE_VECTOR_WRAPPER (acos_sve, _ZGVsMxv_acos)
SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin)
+SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan)
SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos)
SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp)
SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10)
@@ -25,6 +25,7 @@
VPCS_VECTOR_WRAPPER (acosf_advsimd, _ZGVnN4v_acosf)
VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf)
+VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf)
VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf)
VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf)
VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f)
@@ -34,6 +34,7 @@
SVE_VECTOR_WRAPPER (acosf_sve, _ZGVsMxv_acosf)
SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf)
+SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf)
SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf)
SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf)
SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f)
@@ -121,11 +121,19 @@ double: 1
float: 1
ldouble: 2
+Function: "atan_advsimd":
+double: 1
+float: 1
+
Function: "atan_downward":
double: 1
float: 2
ldouble: 2
+Function: "atan_sve":
+double: 1
+float: 1
+
Function: "atan_towardzero":
double: 1
float: 1
@@ -16,6 +16,7 @@ GLIBC_2.38 _ZGVsMxv_sin F
GLIBC_2.38 _ZGVsMxv_sinf F
GLIBC_2.39 _ZGVnN2v_acos F
GLIBC_2.39 _ZGVnN2v_asin F
+GLIBC_2.39 _ZGVnN2v_atan F
GLIBC_2.39 _ZGVnN2v_exp10 F
GLIBC_2.39 _ZGVnN2v_exp2 F
GLIBC_2.39 _ZGVnN2v_log10 F
@@ -23,6 +24,7 @@ GLIBC_2.39 _ZGVnN2v_log2 F
GLIBC_2.39 _ZGVnN2v_tan F
GLIBC_2.39 _ZGVnN4v_acosf F
GLIBC_2.39 _ZGVnN4v_asinf F
+GLIBC_2.39 _ZGVnN4v_atanf F
GLIBC_2.39 _ZGVnN4v_exp10f F
GLIBC_2.39 _ZGVnN4v_exp2f F
GLIBC_2.39 _ZGVnN4v_log10f F
@@ -32,6 +34,8 @@ GLIBC_2.39 _ZGVsMxv_acos F
GLIBC_2.39 _ZGVsMxv_acosf F
GLIBC_2.39 _ZGVsMxv_asin F
GLIBC_2.39 _ZGVsMxv_asinf F
+GLIBC_2.39 _ZGVsMxv_atan F
+GLIBC_2.39 _ZGVsMxv_atanf F
GLIBC_2.39 _ZGVsMxv_exp10 F
GLIBC_2.39 _ZGVsMxv_exp10f F
GLIBC_2.39 _ZGVsMxv_exp2 F