AArch64: Add vector tanpi routines

Vector variant of the new C23 tanpi. New tests pass on AArch64.
This commit is contained in:
Joe Ramsay 2025-01-03 20:13:51 +00:00 committed by Wilco Dijkstra
parent 40c3a06293
commit 080998f6e7
16 changed files with 361 additions and 2 deletions

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@ -362,4 +362,15 @@
#define __DECL_SIMD_cospif32x
#define __DECL_SIMD_cospif64x
#define __DECL_SIMD_cospif128x
#define __DECL_SIMD_tanpi
#define __DECL_SIMD_tanpif
#define __DECL_SIMD_tanpil
#define __DECL_SIMD_tanpif16
#define __DECL_SIMD_tanpif32
#define __DECL_SIMD_tanpif64
#define __DECL_SIMD_tanpif128
#define __DECL_SIMD_tanpif32x
#define __DECL_SIMD_tanpif64x
#define __DECL_SIMD_tanpif128x
#endif

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@ -80,7 +80,7 @@ __MATHCALL_VEC (cospi,, (_Mdouble_ __x));
/* Sine of pi * X. */
__MATHCALL_VEC (sinpi,, (_Mdouble_ __x));
/* Tangent of pi * X. */
__MATHCALL (tanpi,, (_Mdouble_ __x));
__MATHCALL_VEC (tanpi,, (_Mdouble_ __x));
#endif
/* Hyperbolic functions. */

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@ -25,7 +25,8 @@ libmvec-supported-funcs = acos \
sinh \
sinpi \
tan \
tanh
tanh \
tanpi
float-advsimd-funcs = $(libmvec-supported-funcs)
double-advsimd-funcs = $(libmvec-supported-funcs)

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@ -151,5 +151,10 @@ libmvec {
_ZGVnN4v_sinpif;
_ZGVsMxv_sinpi;
_ZGVsMxv_sinpif;
_ZGVnN2v_tanpi;
_ZGVnN2v_tanpif;
_ZGVnN4v_tanpif;
_ZGVsMxv_tanpi;
_ZGVsMxv_tanpif;
}
}

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@ -45,4 +45,5 @@ libmvec_hidden_proto (V_NAME_F1(sinh));
libmvec_hidden_proto (V_NAME_F1(sinpi));
libmvec_hidden_proto (V_NAME_F1(tan));
libmvec_hidden_proto (V_NAME_F1(tanh));
libmvec_hidden_proto (V_NAME_F1(tanpi));
libmvec_hidden_proto (V_NAME_F2(atan2));

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@ -145,6 +145,10 @@
# define __DECL_SIMD_tanh __DECL_SIMD_aarch64
# undef __DECL_SIMD_tanhf
# define __DECL_SIMD_tanhf __DECL_SIMD_aarch64
# undef __DECL_SIMD_tanpi
# define __DECL_SIMD_tanpi __DECL_SIMD_aarch64
# undef __DECL_SIMD_tanpif
# define __DECL_SIMD_tanpif __DECL_SIMD_aarch64
#endif
#if __GNUC_PREREQ(9, 0)
@ -200,6 +204,7 @@ __vpcs __f32x4_t _ZGVnN4v_sinhf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_sinpif (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_tanhf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_tanpif (__f32x4_t);
__vpcs __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t);
@ -230,6 +235,7 @@ __vpcs __f64x2_t _ZGVnN2v_sinh (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_sinpi (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_tanh (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_tanpi (__f64x2_t);
# undef __ADVSIMD_VEC_MATH_SUPPORTED
#endif /* __ADVSIMD_VEC_MATH_SUPPORTED */
@ -265,6 +271,7 @@ __sv_f32_t _ZGVsMxv_sinhf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_sinpif (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_tanhf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_tanpif (__sv_f32_t, __sv_bool_t);
__sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t);
@ -295,6 +302,7 @@ __sv_f64_t _ZGVsMxv_sinh (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_sinpi (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_tan (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_tanh (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_tanpi (__sv_f64_t, __sv_bool_t);
# undef __SVE_VEC_MATH_SUPPORTED
#endif /* __SVE_VEC_MATH_SUPPORTED */

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@ -0,0 +1,88 @@
/* Double-precision (Advanced SIMD) tanpi function
Copyright (C) 2024 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"
const static struct v_tanpi_data
{
float64x2_t c0, c2, c4, c6, c8, c10, c12;
double c1, c3, c5, c7, c9, c11, c13, c14;
} tanpi_data = {
/* Coefficents for tan(pi * x) computed with fpminimax
on [ 0x1p-1022 0x1p-2 ]
approx rel error: 0x1.7eap-55
approx abs error: 0x1.7eap-55. */
.c0 = V2 (0x1.921fb54442d18p1), /* pi. */
.c1 = 0x1.4abbce625be52p3, .c2 = V2 (0x1.466bc6775b0f9p5),
.c3 = 0x1.45fff9b426f5ep7, .c4 = V2 (0x1.45f4730dbca5cp9),
.c5 = 0x1.45f3265994f85p11, .c6 = V2 (0x1.45f4234b330cap13),
.c7 = 0x1.45dca11be79ebp15, .c8 = V2 (0x1.47283fc5eea69p17),
.c9 = 0x1.3a6d958cdefaep19, .c10 = V2 (0x1.927896baee627p21),
.c11 = -0x1.89333f6acd922p19, .c12 = V2 (0x1.5d4e912bb8456p27),
.c13 = -0x1.a854d53ab6874p29, .c14 = 0x1.1b76de7681424p32,
};
/* Approximation for double-precision vector tanpi(x)
The maximum error is 3.06 ULP:
_ZGVnN2v_tanpi(0x1.0a4a07dfcca3ep-1) got -0x1.fa30112702c98p+3
want -0x1.fa30112702c95p+3. */
float64x2_t VPCS_ATTR V_NAME_D1 (tanpi) (float64x2_t x)
{
const struct v_tanpi_data *d = ptr_barrier (&tanpi_data);
float64x2_t n = vrndnq_f64 (x);
/* inf produces nan that propagates. */
float64x2_t xr = vsubq_f64 (x, n);
float64x2_t ar = vabdq_f64 (x, n);
uint64x2_t flip = vcgtq_f64 (ar, v_f64 (0.25));
float64x2_t r = vbslq_f64 (flip, vsubq_f64 (v_f64 (0.5), ar), ar);
/* Order-14 pairwise Horner. */
float64x2_t r2 = vmulq_f64 (r, r);
float64x2_t r4 = vmulq_f64 (r2, r2);
float64x2_t c_1_3 = vld1q_f64 (&d->c1);
float64x2_t c_5_7 = vld1q_f64 (&d->c5);
float64x2_t c_9_11 = vld1q_f64 (&d->c9);
float64x2_t c_13_14 = vld1q_f64 (&d->c13);
float64x2_t p01 = vfmaq_laneq_f64 (d->c0, r2, c_1_3, 0);
float64x2_t p23 = vfmaq_laneq_f64 (d->c2, r2, c_1_3, 1);
float64x2_t p45 = vfmaq_laneq_f64 (d->c4, r2, c_5_7, 0);
float64x2_t p67 = vfmaq_laneq_f64 (d->c6, r2, c_5_7, 1);
float64x2_t p89 = vfmaq_laneq_f64 (d->c8, r2, c_9_11, 0);
float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, r2, c_9_11, 1);
float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, r2, c_13_14, 0);
float64x2_t p = vfmaq_laneq_f64 (p1213, r4, c_13_14, 1);
p = vfmaq_f64 (p1011, r4, p);
p = vfmaq_f64 (p89, r4, p);
p = vfmaq_f64 (p67, r4, p);
p = vfmaq_f64 (p45, r4, p);
p = vfmaq_f64 (p23, r4, p);
p = vfmaq_f64 (p01, r4, p);
p = vmulq_f64 (r, p);
float64x2_t p_recip = vdivq_f64 (v_f64 (1.0), p);
float64x2_t y = vbslq_f64 (flip, p_recip, p);
uint64x2_t sign
= veorq_u64 (vreinterpretq_u64_f64 (xr), vreinterpretq_u64_f64 (ar));
return vreinterpretq_f64_u64 (vorrq_u64 (vreinterpretq_u64_f64 (y), sign));
}

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@ -0,0 +1,88 @@
/* Double-precision (SVE) tanpi function
Copyright (C) 2024 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"
const static struct v_tanpi_data
{
double c0, c2, c4, c6, c8, c10, c12;
double c1, c3, c5, c7, c9, c11, c13, c14;
} tanpi_data = {
/* Coefficents for tan(pi * x) computed with fpminimax
on [ 0x1p-1022 0x1p-2 ]
approx rel error: 0x1.7eap-55
approx abs error: 0x1.7eap-55. */
.c0 = 0x1.921fb54442d18p1, /* pi. */
.c1 = 0x1.4abbce625be52p3, .c2 = 0x1.466bc6775b0f9p5,
.c3 = 0x1.45fff9b426f5ep7, .c4 = 0x1.45f4730dbca5cp9,
.c5 = 0x1.45f3265994f85p11, .c6 = 0x1.45f4234b330cap13,
.c7 = 0x1.45dca11be79ebp15, .c8 = 0x1.47283fc5eea69p17,
.c9 = 0x1.3a6d958cdefaep19, .c10 = 0x1.927896baee627p21,
.c11 = -0x1.89333f6acd922p19, .c12 = 0x1.5d4e912bb8456p27,
.c13 = -0x1.a854d53ab6874p29, .c14 = 0x1.1b76de7681424p32,
};
/* Approximation for double-precision vector tanpi(x)
The maximum error is 3.06 ULP:
_ZGVsMxv_tanpi(0x1.0a4a07dfcca3ep-1) got -0x1.fa30112702c98p+3
want -0x1.fa30112702c95p+3. */
svfloat64_t SV_NAME_D1 (tanpi) (svfloat64_t x, const svbool_t pg)
{
const struct v_tanpi_data *d = ptr_barrier (&tanpi_data);
svfloat64_t n = svrintn_x (pg, x);
/* inf produces nan that propagates. */
svfloat64_t xr = svsub_x (pg, x, n);
svfloat64_t ar = svabd_x (pg, x, n);
svbool_t flip = svcmpgt (pg, ar, 0.25);
svfloat64_t r = svsel (flip, svsubr_x (pg, ar, 0.5), ar);
/* Order-14 pairwise Horner. */
svfloat64_t r2 = svmul_x (pg, r, r);
svfloat64_t r4 = svmul_x (pg, r2, r2);
svfloat64_t c_1_3 = svld1rq (pg, &d->c1);
svfloat64_t c_5_7 = svld1rq (pg, &d->c5);
svfloat64_t c_9_11 = svld1rq (pg, &d->c9);
svfloat64_t c_13_14 = svld1rq (pg, &d->c13);
svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r2, c_1_3, 0);
svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r2, c_1_3, 1);
svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), r2, c_5_7, 0);
svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), r2, c_5_7, 1);
svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), r2, c_9_11, 0);
svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), r2, c_9_11, 1);
svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), r2, c_13_14, 0);
svfloat64_t p = svmla_lane (p1213, r4, c_13_14, 1);
p = svmad_x (pg, p, r4, p1011);
p = svmad_x (pg, p, r4, p89);
p = svmad_x (pg, p, r4, p67);
p = svmad_x (pg, p, r4, p45);
p = svmad_x (pg, p, r4, p23);
p = svmad_x (pg, p, r4, p01);
p = svmul_x (pg, r, p);
svfloat64_t p_recip = svdivr_x (pg, p, 1.0);
svfloat64_t y = svsel (flip, p_recip, p);
svuint64_t sign
= sveor_x (pg, svreinterpret_u64 (xr), svreinterpret_u64 (ar));
return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign));
}

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@ -0,0 +1,72 @@
/* Single-precision (Advanced SIMD) tanpi function
Copyright (C) 2024 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"
const static struct v_tanpif_data
{
float32x4_t c0, c2, c4, c6;
float c1, c3, c5, c7;
} tanpif_data = {
/* Coefficents for tan(pi * x). */
.c0 = V4 (0x1.921fb4p1f), .c1 = 0x1.4abbcep3f, .c2 = V4 (0x1.466b8p5f),
.c3 = 0x1.461c72p7f, .c4 = V4 (0x1.42e9d4p9f), .c5 = 0x1.69e2c4p11f,
.c6 = V4 (0x1.e85558p11f), .c7 = 0x1.a52e08p16f,
};
/* Approximation for single-precision vector tanpi(x)
The maximum error is 3.34 ULP:
_ZGVnN4v_tanpif(0x1.d6c09ap-2) got 0x1.f70aacp+2
want 0x1.f70aa6p+2. */
float32x4_t VPCS_ATTR V_NAME_F1 (tanpi) (float32x4_t x)
{
const struct v_tanpif_data *d = ptr_barrier (&tanpif_data);
float32x4_t n = vrndnq_f32 (x);
/* inf produces nan that propagates. */
float32x4_t xr = vsubq_f32 (x, n);
float32x4_t ar = vabdq_f32 (x, n);
uint32x4_t flip = vcgtq_f32 (ar, v_f32 (0.25f));
float32x4_t r = vbslq_f32 (flip, vsubq_f32 (v_f32 (0.5f), ar), ar);
/* Order-7 pairwise Horner polynomial evaluation scheme. */
float32x4_t r2 = vmulq_f32 (r, r);
float32x4_t r4 = vmulq_f32 (r2, r2);
float32x4_t odd_coeffs = vld1q_f32 (&d->c1);
float32x4_t p01 = vfmaq_laneq_f32 (d->c0, r2, odd_coeffs, 0);
float32x4_t p23 = vfmaq_laneq_f32 (d->c2, r2, odd_coeffs, 1);
float32x4_t p45 = vfmaq_laneq_f32 (d->c4, r2, odd_coeffs, 2);
float32x4_t p67 = vfmaq_laneq_f32 (d->c6, r2, odd_coeffs, 3);
float32x4_t p = vfmaq_f32 (p45, r4, p67);
p = vfmaq_f32 (p23, r4, p);
p = vfmaq_f32 (p01, r4, p);
p = vmulq_f32 (r, p);
float32x4_t p_recip = vdivq_f32 (v_f32 (1.0f), p);
float32x4_t y = vbslq_f32 (flip, p_recip, p);
uint32x4_t sign
= veorq_u32 (vreinterpretq_u32_f32 (xr), vreinterpretq_u32_f32 (ar));
return vreinterpretq_f32_u32 (vorrq_u32 (vreinterpretq_u32_f32 (y), sign));
}
libmvec_hidden_def (V_NAME_F1 (tanpi))
HALF_WIDTH_ALIAS_F1 (tanpi)

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@ -0,0 +1,68 @@
/* Single-precision (SVE) tanpi function
Copyright (C) 2024 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"
const static struct v_tanpif_data
{
float c0, c2, c4, c6;
float c1, c3, c5, c7;
} tanpif_data = {
/* Coefficients for tan(pi * x). */
.c0 = 0x1.921fb4p1f, .c1 = 0x1.4abbcep3f, .c2 = 0x1.466b8p5f,
.c3 = 0x1.461c72p7f, .c4 = 0x1.42e9d4p9f, .c5 = 0x1.69e2c4p11f,
.c6 = 0x1.e85558p11f, .c7 = 0x1.a52e08p16f,
};
/* Approximation for single-precision vector tanpif(x)
The maximum error is 3.34 ULP:
_ZGVsMxv_tanpif(0x1.d6c09ap-2) got 0x1.f70aacp+2
want 0x1.f70aa6p+2. */
svfloat32_t SV_NAME_F1 (tanpi) (svfloat32_t x, const svbool_t pg)
{
const struct v_tanpif_data *d = ptr_barrier (&tanpif_data);
svfloat32_t odd_coeffs = svld1rq (pg, &d->c1);
svfloat32_t n = svrintn_x (pg, x);
/* inf produces nan that propagates. */
svfloat32_t xr = svsub_x (pg, x, n);
svfloat32_t ar = svabd_x (pg, x, n);
svbool_t flip = svcmpgt (pg, ar, 0.25f);
svfloat32_t r = svsel (flip, svsub_x (pg, sv_f32 (0.5f), ar), ar);
svfloat32_t r2 = svmul_x (pg, r, r);
svfloat32_t r4 = svmul_x (pg, r2, r2);
/* Order-7 Pairwise Horner. */
svfloat32_t p01 = svmla_lane (sv_f32 (d->c0), r2, odd_coeffs, 0);
svfloat32_t p23 = svmla_lane (sv_f32 (d->c2), r2, odd_coeffs, 1);
svfloat32_t p45 = svmla_lane (sv_f32 (d->c4), r2, odd_coeffs, 2);
svfloat32_t p67 = svmla_lane (sv_f32 (d->c6), r2, odd_coeffs, 3);
svfloat32_t p = svmad_x (pg, p67, r4, p45);
p = svmad_x (pg, p, r4, p23);
p = svmad_x (pg, p, r4, p01);
svfloat32_t poly = svmul_x (pg, r, p);
svfloat32_t poly_recip = svdiv_x (pg, sv_f32 (1.0), poly);
svfloat32_t y = svsel (flip, poly_recip, poly);
svuint32_t sign
= sveor_x (pg, svreinterpret_u32 (xr), svreinterpret_u32 (ar));
return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign));
}

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@ -51,3 +51,4 @@ VPCS_VECTOR_WRAPPER (sinh_advsimd, _ZGVnN2v_sinh)
VPCS_VECTOR_WRAPPER (sinpi_advsimd, _ZGVnN2v_sinpi)
VPCS_VECTOR_WRAPPER (tan_advsimd, _ZGVnN2v_tan)
VPCS_VECTOR_WRAPPER (tanh_advsimd, _ZGVnN2v_tanh)
VPCS_VECTOR_WRAPPER (tanpi_advsimd, _ZGVnN2v_tanpi)

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@ -70,3 +70,4 @@ SVE_VECTOR_WRAPPER (sinh_sve, _ZGVsMxv_sinh)
SVE_VECTOR_WRAPPER (sinpi_sve, _ZGVsMxv_sinpi)
SVE_VECTOR_WRAPPER (tan_sve, _ZGVsMxv_tan)
SVE_VECTOR_WRAPPER (tanh_sve, _ZGVsMxv_tanh)
SVE_VECTOR_WRAPPER (tanpi_sve, _ZGVsMxv_tanpi)

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@ -51,3 +51,4 @@ VPCS_VECTOR_WRAPPER (sinhf_advsimd, _ZGVnN4v_sinhf)
VPCS_VECTOR_WRAPPER (sinpif_advsimd, _ZGVnN4v_sinpif)
VPCS_VECTOR_WRAPPER (tanf_advsimd, _ZGVnN4v_tanf)
VPCS_VECTOR_WRAPPER (tanhf_advsimd, _ZGVnN4v_tanhf)
VPCS_VECTOR_WRAPPER (tanpif_advsimd, _ZGVnN4v_tanpif)

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@ -70,3 +70,4 @@ SVE_VECTOR_WRAPPER (sinhf_sve, _ZGVsMxv_sinhf)
SVE_VECTOR_WRAPPER (sinpif_sve, _ZGVsMxv_sinpif)
SVE_VECTOR_WRAPPER (tanf_sve, _ZGVsMxv_tanf)
SVE_VECTOR_WRAPPER (tanhf_sve, _ZGVsMxv_tanhf)
SVE_VECTOR_WRAPPER (tanpif_sve, _ZGVsMxv_tanpif)

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@ -1710,11 +1710,19 @@ double: 3
float: 3
ldouble: 3
Function: "tanpi_advsimd":
double: 2
float: 2
Function: "tanpi_downward":
double: 2
float: 3
ldouble: 4
Function: "tanpi_sve":
double: 2
float: 2
Function: "tanpi_towardzero":
double: 2
float: 3

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@ -134,12 +134,17 @@ GLIBC_2.41 _ZGVnN2v_logp1 F
GLIBC_2.41 _ZGVnN2v_logp1f F
GLIBC_2.41 _ZGVnN2v_sinpi F
GLIBC_2.41 _ZGVnN2v_sinpif F
GLIBC_2.41 _ZGVnN2v_tanpi F
GLIBC_2.41 _ZGVnN2v_tanpif F
GLIBC_2.41 _ZGVnN4v_cospif F
GLIBC_2.41 _ZGVnN4v_logp1f F
GLIBC_2.41 _ZGVnN4v_sinpif F
GLIBC_2.41 _ZGVnN4v_tanpif F
GLIBC_2.41 _ZGVsMxv_cospi F
GLIBC_2.41 _ZGVsMxv_cospif F
GLIBC_2.41 _ZGVsMxv_logp1 F
GLIBC_2.41 _ZGVsMxv_logp1f F
GLIBC_2.41 _ZGVsMxv_sinpi F
GLIBC_2.41 _ZGVsMxv_sinpif F
GLIBC_2.41 _ZGVsMxv_tanpi F
GLIBC_2.41 _ZGVsMxv_tanpif F