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AArch64: Add vector cospi routines 

Vector variant of the new C23 cospi. New tests pass on AArch64.
This commit is contained in:
Joe Ramsay 2025-01-03 20:12:10 +00:00 committed by Wilco Dijkstra
parent 6050b45716
commit 40c3a06293
16 changed files with 344 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

11
bits/libm-simd-decl-stubs.h
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@ -351,4 +351,15 @@
#define __DECL_SIMD_sinpif32x
#define __DECL_SIMD_sinpif64x
#define __DECL_SIMD_sinpif128x
#define __DECL_SIMD_cospi
#define __DECL_SIMD_cospif
#define __DECL_SIMD_cospil
#define __DECL_SIMD_cospif16
#define __DECL_SIMD_cospif32
#define __DECL_SIMD_cospif64
#define __DECL_SIMD_cospif128
#define __DECL_SIMD_cospif32x
#define __DECL_SIMD_cospif64x
#define __DECL_SIMD_cospif128x
#endif

2
math/bits/mathcalls.h
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@ -76,7 +76,7 @@ __MATHCALL (atanpi,, (_Mdouble_ __x));
__MATHCALL (atan2pi,, (_Mdouble_ __y, _Mdouble_ __x));
/* Cosine of pi * X. */
__MATHCALL (cospi,, (_Mdouble_ __x));
__MATHCALL_VEC (cospi,, (_Mdouble_ __x));
/* Sine of pi * X. */
__MATHCALL_VEC (sinpi,, (_Mdouble_ __x));
/* Tangent of pi * X. */

1
sysdeps/aarch64/fpu/Makefile
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@ -8,6 +8,7 @@ libmvec-supported-funcs = acos \
cbrt \
cos \
cosh \
cospi \
erf \
erfc \
exp \

5
sysdeps/aarch64/fpu/Versions
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@ -136,6 +136,11 @@ libmvec {
_ZGVsMxv_tanhf;
}
GLIBC_2.41 {
_ZGVnN2v_cospi;
_ZGVnN2v_cospif;
_ZGVnN4v_cospif;
_ZGVsMxv_cospi;
_ZGVsMxv_cospif;
_ZGVnN2v_logp1;
_ZGVnN2v_logp1f;
_ZGVnN4v_logp1f;

1
sysdeps/aarch64/fpu/advsimd_f32_protos.h
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@ -26,6 +26,7 @@ libmvec_hidden_proto (V_NAME_F1(atanh));
libmvec_hidden_proto (V_NAME_F1(cbrt));
libmvec_hidden_proto (V_NAME_F1(cos));
libmvec_hidden_proto (V_NAME_F1(cosh));
libmvec_hidden_proto (V_NAME_F1(cospi));
libmvec_hidden_proto (V_NAME_F1(erf));
libmvec_hidden_proto (V_NAME_F1(erfc));
libmvec_hidden_proto (V_NAME_F1(exp10));

8
sysdeps/aarch64/fpu/bits/math-vector.h
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@ -69,6 +69,10 @@
# define __DECL_SIMD_cosh __DECL_SIMD_aarch64
# undef __DECL_SIMD_coshf
# define __DECL_SIMD_coshf __DECL_SIMD_aarch64
# undef __DECL_SIMD_cospi
# define __DECL_SIMD_cospi __DECL_SIMD_aarch64
# undef __DECL_SIMD_cospif
# define __DECL_SIMD_cospif __DECL_SIMD_aarch64
# undef __DECL_SIMD_erf
# define __DECL_SIMD_erf __DECL_SIMD_aarch64
# undef __DECL_SIMD_erff
@ -177,6 +181,7 @@ __vpcs __f32x4_t _ZGVnN4v_atanhf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_cbrtf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_coshf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_cospif (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_erff (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_erfcf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t);
@ -206,6 +211,7 @@ __vpcs __f64x2_t _ZGVnN2v_atanh (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_cbrt (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_cosh (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_cospi (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_erf (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_erfc (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t);
@ -240,6 +246,7 @@ __sv_f32_t _ZGVsMxv_atanhf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_cbrtf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_coshf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_cospif (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_erff (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_erfcf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t);
@ -269,6 +276,7 @@ __sv_f64_t _ZGVsMxv_atanh (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_cbrt (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_cosh (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_cospi (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_erf (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_erfc (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t);

87
sysdeps/aarch64/fpu/cospi_advsimd.c Normal file
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@ -0,0 +1,87 @@
/* Double-precision (Advanced SIMD) cospi 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"
#include "poly_advsimd_f64.h"
static const struct data
{
float64x2_t poly[10];
float64x2_t range_val;
} data = {
/* Polynomial coefficients generated using Remez algorithm,
see sinpi.sollya for details. */
.poly = { V2 (0x1.921fb54442d184p1), V2 (-0x1.4abbce625be53p2),
V2 (0x1.466bc6775ab16p1), V2 (-0x1.32d2cce62dc33p-1),
V2 (0x1.507834891188ep-4), V2 (-0x1.e30750a28c88ep-8),
V2 (0x1.e8f48308acda4p-12), V2 (-0x1.6fc0032b3c29fp-16),
V2 (0x1.af86ae521260bp-21), V2 (-0x1.012a9870eeb7dp-25) },
.range_val = V2 (0x1p63),
};
static float64x2_t VPCS_ATTR NOINLINE
special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
{
/* Fall back to scalar code. */
y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
return v_call_f64 (cospi, x, y, cmp);
}
/* Approximation for vector double-precision cospi(x).
Maximum Error 3.06 ULP:
_ZGVnN2v_cospi(0x1.7dd4c0b03cc66p-5) got 0x1.fa854babfb6bep-1
want 0x1.fa854babfb6c1p-1. */
float64x2_t VPCS_ATTR V_NAME_D1 (cospi) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
#if WANT_SIMD_EXCEPT
float64x2_t r = vabsq_f64 (x);
uint64x2_t cmp = vcaleq_f64 (v_f64 (0x1p64), x);
/* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd
to avoid them overflowing and throwing exceptions. */
r = v_zerofy_f64 (r, cmp);
uint64x2_t odd = vshlq_n_u64 (vcvtnq_u64_f64 (r), 63);
#else
float64x2_t r = x;
uint64x2_t cmp = vcageq_f64 (r, d->range_val);
uint64x2_t odd
= vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtaq_s64_f64 (r)), 63);
#endif
r = vsubq_f64 (r, vrndaq_f64 (r));
/* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */
r = vsubq_f64 (v_f64 (0.5), vabsq_f64 (r));
/* y = sin(r). */
float64x2_t r2 = vmulq_f64 (r, r);
float64x2_t r4 = vmulq_f64 (r2, r2);
float64x2_t y = vmulq_f64 (v_pw_horner_9_f64 (r2, r4, d->poly), r);
/* Fallback to scalar. */
if (__glibc_unlikely (v_any_u64 (cmp)))
return special_case (x, y, odd, cmp);
/* Reintroduce the sign bit for inputs which round to odd. */
return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
}

65
sysdeps/aarch64/fpu/cospi_sve.c Normal file
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@ -0,0 +1,65 @@
/* Double-precision (SVE) cospi 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"
#include "poly_sve_f64.h"
static const struct data
{
double poly[10];
double range_val;
} data = {
/* Polynomial coefficients generated using Remez algorithm,
see sinpi.sollya for details. */
.poly = { 0x1.921fb54442d184p1, -0x1.4abbce625be53p2, 0x1.466bc6775ab16p1,
-0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8,
0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16,
0x1.af86ae521260bp-21, -0x1.012a9870eeb7dp-25 },
.range_val = 0x1p53,
};
/* A fast SVE implementation of cospi.
Maximum error 3.20 ULP:
_ZGVsMxv_cospi(0x1.f18ba32c63159p-6) got 0x1.fdabf595f9763p-1
want 0x1.fdabf595f9766p-1. */
svfloat64_t SV_NAME_D1 (cospi) (svfloat64_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
/* Using cospi(x) = sinpi(0.5 - x)
range reduction and offset into sinpi range -1/2 .. 1/2
r = 0.5 - |x - rint(x)|. */
svfloat64_t n = svrinta_x (pg, x);
svfloat64_t r = svsub_x (pg, x, n);
r = svsub_x (pg, sv_f64 (0.5), svabs_x (pg, r));
/* Result should be negated based on if n is odd or not.
If ax >= 2^53, the result will always be positive. */
svbool_t cmp = svaclt (pg, x, d->range_val);
svuint64_t intn = svreinterpret_u64 (svcvt_s64_z (pg, n));
svuint64_t sign = svlsl_z (cmp, intn, 63);
/* y = sin(r). */
svfloat64_t r2 = svmul_x (pg, r, r);
svfloat64_t r4 = svmul_x (pg, r2, r2);
svfloat64_t y = sv_pw_horner_9_f64_x (pg, r2, r4, d->poly);
y = svmul_x (pg, y, r);
return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
}

87
sysdeps/aarch64/fpu/cospif_advsimd.c Normal file
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@ -0,0 +1,87 @@
/* Single-precision (Advanced SIMD) cospi 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"
#include "poly_advsimd_f32.h"
static const struct data
{
float32x4_t poly[6];
float32x4_t range_val;
} data = {
/* Taylor series coefficents for sin(pi * x). */
.poly = { V4 (0x1.921fb6p1f), V4 (-0x1.4abbcep2f), V4 (0x1.466bc6p1f),
V4 (-0x1.32d2ccp-1f), V4 (0x1.50783p-4f), V4 (-0x1.e30750p-8f) },
.range_val = V4 (0x1p31f),
};
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp)
{
y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
return v_call_f32 (cospif, x, y, cmp);
}
/* Approximation for vector single-precision cospi(x)
Maximum Error: 3.17 ULP:
_ZGVnN4v_cospif(0x1.d341a8p-5) got 0x1.f7cd56p-1
want 0x1.f7cd5p-1. */
float32x4_t VPCS_ATTR V_NAME_F1 (cospi) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
#if WANT_SIMD_EXCEPT
float32x4_t r = vabsq_f32 (x);
uint32x4_t cmp = vcaleq_f32 (v_f32 (0x1p32f), x);
/* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd
to avoid them overflowing and throwing exceptions. */
r = v_zerofy_f32 (r, cmp);
uint32x4_t odd = vshlq_n_u32 (vcvtnq_u32_f32 (r), 31);
#else
float32x4_t r = x;
uint32x4_t cmp = vcageq_f32 (r, d->range_val);
uint32x4_t odd
= vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (r)), 31);
#endif
/* r = x - rint(x). */
r = vsubq_f32 (r, vrndaq_f32 (r));
/* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */
r = vsubq_f32 (v_f32 (0.5f), vabsq_f32 (r));
/* Pairwise Horner approximation for y = sin(r * pi). */
float32x4_t r2 = vmulq_f32 (r, r);
float32x4_t r4 = vmulq_f32 (r2, r2);
float32x4_t y = vmulq_f32 (v_pw_horner_5_f32 (r2, r4, d->poly), r);
/* Fallback to scalar. */
if (__glibc_unlikely (v_any_u32 (cmp)))
return special_case (x, y, odd, cmp);
/* Reintroduce the sign bit for inputs which round to odd. */
return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
}
libmvec_hidden_def (V_NAME_F1 (cospi))
HALF_WIDTH_ALIAS_F1 (cospi)

61
sysdeps/aarch64/fpu/cospif_sve.c Normal file
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@ -0,0 +1,61 @@
/* Single-precision (SVE) cospi 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"
#include "poly_sve_f32.h"
static const struct data
{
float poly[6];
float range_val;
} data = {
/* Taylor series coefficents for sin(pi * x). */
.poly = { 0x1.921fb6p1f, -0x1.4abbcep2f, 0x1.466bc6p1f, -0x1.32d2ccp-1f,
0x1.50783p-4f, -0x1.e30750p-8f },
.range_val = 0x1p31f,
};
/* A fast SVE implementation of cospif.
Maximum error: 2.60 ULP:
_ZGVsMxv_cospif(+/-0x1.cae664p-4) got 0x1.e09c9ep-1
want 0x1.e09c98p-1. */
svfloat32_t SV_NAME_F1 (cospi) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
/* Using cospi(x) = sinpi(0.5 - x)
range reduction and offset into sinpi range -1/2 .. 1/2
r = 0.5 - |x - rint(x)|. */
svfloat32_t n = svrinta_x (pg, x);
svfloat32_t r = svsub_x (pg, x, n);
r = svsub_x (pg, sv_f32 (0.5f), svabs_x (pg, r));
/* Result should be negated based on if n is odd or not.
If ax >= 2^31, the result will always be positive. */
svbool_t cmp = svaclt (pg, x, d->range_val);
svuint32_t intn = svreinterpret_u32 (svcvt_s32_x (pg, n));
svuint32_t sign = svlsl_z (cmp, intn, 31);
/* y = sin(r). */
svfloat32_t r2 = svmul_x (pg, r, r);
svfloat32_t y = sv_horner_5_f32_x (pg, r2, d->poly);
y = svmul_x (pg, y, r);
return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
}

1
sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c
View File

@ -33,6 +33,7 @@ VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2)
VPCS_VECTOR_WRAPPER (cbrt_advsimd, _ZGVnN2v_cbrt)
VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos)
VPCS_VECTOR_WRAPPER (cosh_advsimd, _ZGVnN2v_cosh)
VPCS_VECTOR_WRAPPER (cospi_advsimd, _ZGVnN2v_cospi)
VPCS_VECTOR_WRAPPER (erf_advsimd, _ZGVnN2v_erf)
VPCS_VECTOR_WRAPPER (erfc_advsimd, _ZGVnN2v_erfc)
VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp)

1
sysdeps/aarch64/fpu/test-double-sve-wrappers.c
View File

@ -52,6 +52,7 @@ SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2)
SVE_VECTOR_WRAPPER (cbrt_sve, _ZGVsMxv_cbrt)
SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos)
SVE_VECTOR_WRAPPER (cosh_sve, _ZGVsMxv_cosh)
SVE_VECTOR_WRAPPER (cospi_sve, _ZGVsMxv_cospi)
SVE_VECTOR_WRAPPER (erf_sve, _ZGVsMxv_erf)
SVE_VECTOR_WRAPPER (erfc_sve, _ZGVsMxv_erfc)
SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp)

1
sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c
View File

@ -33,6 +33,7 @@ VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f)
VPCS_VECTOR_WRAPPER (cbrtf_advsimd, _ZGVnN4v_cbrtf)
VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf)
VPCS_VECTOR_WRAPPER (coshf_advsimd, _ZGVnN4v_coshf)
VPCS_VECTOR_WRAPPER (cospif_advsimd, _ZGVnN4v_cospif)
VPCS_VECTOR_WRAPPER (erff_advsimd, _ZGVnN4v_erff)
VPCS_VECTOR_WRAPPER (erfcf_advsimd, _ZGVnN4v_erfcf)
VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf)

1
sysdeps/aarch64/fpu/test-float-sve-wrappers.c
View File

@ -52,6 +52,7 @@ SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f)
SVE_VECTOR_WRAPPER (cbrtf_sve, _ZGVsMxv_cbrtf)
SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf)
SVE_VECTOR_WRAPPER (coshf_sve, _ZGVsMxv_coshf)
SVE_VECTOR_WRAPPER (cospif_sve, _ZGVsMxv_cospif)
SVE_VECTOR_WRAPPER (erff_sve, _ZGVsMxv_erff)
SVE_VECTOR_WRAPPER (erfcf_sve, _ZGVsMxv_erfcf)
SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf)

8
sysdeps/aarch64/libm-test-ulps
View File

@ -803,11 +803,19 @@ double: 2
float: 2
ldouble: 2
Function: "cospi_advsimd":
double: 2
float: 1
Function: "cospi_downward":
double: 1
float: 2
ldouble: 2
Function: "cospi_sve":
double: 2
float: 1
Function: "cospi_towardzero":
double: 1
float: 1

5
sysdeps/unix/sysv/linux/aarch64/libmvec.abilist
View File

@ -128,12 +128,17 @@ GLIBC_2.40 _ZGVsMxvv_hypot F
GLIBC_2.40 _ZGVsMxvv_hypotf F
GLIBC_2.40 _ZGVsMxvv_pow F
GLIBC_2.40 _ZGVsMxvv_powf F
GLIBC_2.41 _ZGVnN2v_cospi F
GLIBC_2.41 _ZGVnN2v_cospif F
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 _ZGVnN4v_cospif F
GLIBC_2.41 _ZGVnN4v_logp1f F
GLIBC_2.41 _ZGVnN4v_sinpif 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