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aarch64/fpu: Add vector variants of cbrt

Browse Source 
Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>
This commit is contained in:
Joe Ramsay 2024-04-30 13:49:59 +01:00 committed by Szabolcs Nagy
parent 157f89fa3d
commit 75207bde68
14 changed files with 526 additions and 0 deletions
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1
sysdeps/aarch64/fpu/Makefile
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@ -5,6 +5,7 @@ libmvec-supported-funcs = acos \
atan \
atanh \
atan2 \
cbrt \
cos \
cosh \
erf \

5
sysdeps/aarch64/fpu/Versions
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@ -94,6 +94,11 @@ libmvec {
_ZGVnN4v_atanhf;
_ZGVsMxv_atanh;
_ZGVsMxv_atanhf;
_ZGVnN2v_cbrt;
_ZGVnN2v_cbrtf;
_ZGVnN4v_cbrtf;
_ZGVsMxv_cbrt;
_ZGVsMxv_cbrtf;
_ZGVnN2v_cosh;
_ZGVnN2v_coshf;
_ZGVnN4v_coshf;

1
sysdeps/aarch64/fpu/advsimd_f32_protos.h
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@ -23,6 +23,7 @@ libmvec_hidden_proto (V_NAME_F1(asin));
libmvec_hidden_proto (V_NAME_F1(asinh));
libmvec_hidden_proto (V_NAME_F1(atan));
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(erf));

8
sysdeps/aarch64/fpu/bits/math-vector.h
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@ -57,6 +57,10 @@
# define __DECL_SIMD_atan2 __DECL_SIMD_aarch64
# undef __DECL_SIMD_atan2f
# define __DECL_SIMD_atan2f __DECL_SIMD_aarch64
# undef __DECL_SIMD_cbrt
# define __DECL_SIMD_cbrt __DECL_SIMD_aarch64
# undef __DECL_SIMD_cbrtf
# define __DECL_SIMD_cbrtf __DECL_SIMD_aarch64
# undef __DECL_SIMD_cos
# define __DECL_SIMD_cos __DECL_SIMD_aarch64
# undef __DECL_SIMD_cosf
@ -158,6 +162,7 @@ __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t);
__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_erff (__f32x4_t);
@ -183,6 +188,7 @@ __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t);
__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_erf (__f64x2_t);
@ -213,6 +219,7 @@ __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_asinhf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t);
__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_erff (__sv_f32_t, __sv_bool_t);
@ -238,6 +245,7 @@ __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_asinh (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t);
__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_erf (__sv_f64_t, __sv_bool_t);

121
sysdeps/aarch64/fpu/cbrt_advsimd.c Normal file
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@ -0,0 +1,121 @@
/* Double-precision vector (AdvSIMD) cbrt 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"
const static struct data
{
float64x2_t poly[4], one_third, shift;
int64x2_t exp_bias;
uint64x2_t abs_mask, tiny_bound;
uint32x4_t thresh;
double table[5];
} data = {
.shift = V2 (0x1.8p52),
.poly = { /* Generated with fpminimax in [0.5, 1]. */
V2 (0x1.c14e8ee44767p-2), V2 (0x1.dd2d3f99e4c0ep-1),
V2 (-0x1.08e83026b7e74p-1), V2 (0x1.2c74eaa3ba428p-3) },
.exp_bias = V2 (1022),
.abs_mask = V2(0x7fffffffffffffff),
.tiny_bound = V2(0x0010000000000000), /* Smallest normal. */
.thresh = V4(0x7fe00000), /* asuint64 (infinity) - tiny_bound. */
.one_third = V2(0x1.5555555555555p-2),
.table = { /* table[i] = 2^((i - 2) / 3). */
0x1.428a2f98d728bp-1, 0x1.965fea53d6e3dp-1, 0x1p0,
0x1.428a2f98d728bp0, 0x1.965fea53d6e3dp0 }
};
#define MantissaMask v_u64 (0x000fffffffffffff)
static float64x2_t NOINLINE VPCS_ATTR
special_case (float64x2_t x, float64x2_t y, uint32x2_t special)
{
return v_call_f64 (cbrt, x, y, vmovl_u32 (special));
}
/* Approximation for double-precision vector cbrt(x), using low-order polynomial
and two Newton iterations. Greatest observed error is 1.79 ULP. Errors repeat
according to the exponent, for instance an error observed for double value
m * 2^e will be observed for any input m * 2^(e + 3*i), where i is an
integer.
__v_cbrt(0x1.fffff403f0bc6p+1) got 0x1.965fe72821e9bp+0
want 0x1.965fe72821e99p+0. */
VPCS_ATTR float64x2_t V_NAME_D1 (cbrt) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
uint64x2_t iax = vreinterpretq_u64_f64 (vabsq_f64 (x));
/* Subnormal, +/-0 and special values. */
uint32x2_t special
= vcge_u32 (vsubhn_u64 (iax, d->tiny_bound), vget_low_u32 (d->thresh));
/* Decompose |x| into m * 2^e, where m is in [0.5, 1.0]. This is a vector
version of frexp, which gets subnormal values wrong - these have to be
special-cased as a result. */
float64x2_t m = vbslq_f64 (MantissaMask, x, v_f64 (0.5));
int64x2_t exp_bias = d->exp_bias;
uint64x2_t ia12 = vshrq_n_u64 (iax, 52);
int64x2_t e = vsubq_s64 (vreinterpretq_s64_u64 (ia12), exp_bias);
/* Calculate rough approximation for cbrt(m) in [0.5, 1.0], starting point for
Newton iterations. */
float64x2_t p = v_pairwise_poly_3_f64 (m, vmulq_f64 (m, m), d->poly);
float64x2_t one_third = d->one_third;
/* Two iterations of Newton's method for iteratively approximating cbrt. */
float64x2_t m_by_3 = vmulq_f64 (m, one_third);
float64x2_t two_thirds = vaddq_f64 (one_third, one_third);
float64x2_t a
= vfmaq_f64 (vdivq_f64 (m_by_3, vmulq_f64 (p, p)), two_thirds, p);
a = vfmaq_f64 (vdivq_f64 (m_by_3, vmulq_f64 (a, a)), two_thirds, a);
/* Assemble the result by the following:
cbrt(x) = cbrt(m) * 2 ^ (e / 3).
We can get 2 ^ round(e / 3) using ldexp and integer divide, but since e is
not necessarily a multiple of 3 we lose some information.
Let q = 2 ^ round(e / 3), then t = 2 ^ (e / 3) / q.
Then we know t = 2 ^ (i / 3), where i is the remainder from e / 3, which is
an integer in [-2, 2], and can be looked up in the table T. Hence the
result is assembled as:
cbrt(x) = cbrt(m) * t * 2 ^ round(e / 3) * sign. */
float64x2_t ef = vcvtq_f64_s64 (e);
float64x2_t eb3f = vrndnq_f64 (vmulq_f64 (ef, one_third));
int64x2_t em3 = vcvtq_s64_f64 (vfmsq_f64 (ef, eb3f, v_f64 (3)));
int64x2_t ey = vcvtq_s64_f64 (eb3f);
float64x2_t my = (float64x2_t){ d->table[em3[0] + 2], d->table[em3[1] + 2] };
my = vmulq_f64 (my, a);
/* Vector version of ldexp. */
float64x2_t y = vreinterpretq_f64_s64 (
vshlq_n_s64 (vaddq_s64 (ey, vaddq_s64 (exp_bias, v_s64 (1))), 52));
y = vmulq_f64 (y, my);
if (__glibc_unlikely (v_any_u32h (special)))
return special_case (x, vbslq_f64 (d->abs_mask, y, x), special);
/* Copy sign. */
return vbslq_f64 (d->abs_mask, y, x);
}

128
sysdeps/aarch64/fpu/cbrt_sve.c Normal file
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@ -0,0 +1,128 @@
/* Double-precision vector (SVE) cbrt 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"
const static struct data
{
float64_t poly[4];
float64_t table[5];
float64_t one_third, two_thirds, shift;
int64_t exp_bias;
uint64_t tiny_bound, thresh;
} data = {
/* Generated with FPMinimax in [0.5, 1]. */
.poly = { 0x1.c14e8ee44767p-2, 0x1.dd2d3f99e4c0ep-1, -0x1.08e83026b7e74p-1,
0x1.2c74eaa3ba428p-3, },
/* table[i] = 2^((i - 2) / 3). */
.table = { 0x1.428a2f98d728bp-1, 0x1.965fea53d6e3dp-1, 0x1p0,
0x1.428a2f98d728bp0, 0x1.965fea53d6e3dp0, },
.one_third = 0x1.5555555555555p-2,
.two_thirds = 0x1.5555555555555p-1,
.shift = 0x1.8p52,
.exp_bias = 1022,
.tiny_bound = 0x0010000000000000, /* Smallest normal. */
.thresh = 0x7fe0000000000000, /* asuint64 (infinity) - tiny_bound. */
};
#define MantissaMask 0x000fffffffffffff
#define HalfExp 0x3fe0000000000000
static svfloat64_t NOINLINE
special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
{
return sv_call_f64 (cbrt, x, y, special);
}
static inline svfloat64_t
shifted_lookup (const svbool_t pg, const float64_t *table, svint64_t i)
{
return svld1_gather_index (pg, table, svadd_x (pg, i, 2));
}
/* Approximation for double-precision vector cbrt(x), using low-order
polynomial and two Newton iterations. Greatest observed error is 1.79 ULP.
Errors repeat according to the exponent, for instance an error observed for
double value m * 2^e will be observed for any input m * 2^(e + 3*i), where i
is an integer.
_ZGVsMxv_cbrt (0x0.3fffb8d4413f3p-1022) got 0x1.965f53b0e5d97p-342
want 0x1.965f53b0e5d95p-342. */
svfloat64_t SV_NAME_D1 (cbrt) (svfloat64_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svfloat64_t ax = svabs_x (pg, x);
svuint64_t iax = svreinterpret_u64 (ax);
svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax);
/* Subnormal, +/-0 and special values. */
svbool_t special = svcmpge (pg, svsub_x (pg, iax, d->tiny_bound), d->thresh);
/* Decompose |x| into m * 2^e, where m is in [0.5, 1.0]. This is a vector
version of frexp, which gets subnormal values wrong - these have to be
special-cased as a result. */
svfloat64_t m = svreinterpret_f64 (svorr_x (
pg, svand_x (pg, svreinterpret_u64 (x), MantissaMask), HalfExp));
svint64_t e
= svsub_x (pg, svreinterpret_s64 (svlsr_x (pg, iax, 52)), d->exp_bias);
/* Calculate rough approximation for cbrt(m) in [0.5, 1.0], starting point
for Newton iterations. */
svfloat64_t p
= sv_pairwise_poly_3_f64_x (pg, m, svmul_x (pg, m, m), d->poly);
/* Two iterations of Newton's method for iteratively approximating cbrt. */
svfloat64_t m_by_3 = svmul_x (pg, m, d->one_third);
svfloat64_t a = svmla_x (pg, svdiv_x (pg, m_by_3, svmul_x (pg, p, p)), p,
d->two_thirds);
a = svmla_x (pg, svdiv_x (pg, m_by_3, svmul_x (pg, a, a)), a, d->two_thirds);
/* Assemble the result by the following:
cbrt(x) = cbrt(m) * 2 ^ (e / 3).
We can get 2 ^ round(e / 3) using ldexp and integer divide, but since e is
not necessarily a multiple of 3 we lose some information.
Let q = 2 ^ round(e / 3), then t = 2 ^ (e / 3) / q.
Then we know t = 2 ^ (i / 3), where i is the remainder from e / 3, which
is an integer in [-2, 2], and can be looked up in the table T. Hence the
result is assembled as:
cbrt(x) = cbrt(m) * t * 2 ^ round(e / 3) * sign. */
svfloat64_t eb3f = svmul_x (pg, svcvt_f64_x (pg, e), d->one_third);
svint64_t ey = svcvt_s64_x (pg, eb3f);
svint64_t em3 = svmls_x (pg, e, ey, 3);
svfloat64_t my = shifted_lookup (pg, d->table, em3);
my = svmul_x (pg, my, a);
/* Vector version of ldexp. */
svfloat64_t y = svscale_x (pg, my, ey);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (
x, svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign)),
special);
/* Copy sign. */
return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign));
}

123
sysdeps/aarch64/fpu/cbrtf_advsimd.c Normal file
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@ -0,0 +1,123 @@
/* Single-precision vector (AdvSIMD) cbrt 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"
const static struct data
{
float32x4_t poly[4], one_third;
float table[5];
} data = {
.poly = { /* Very rough approximation of cbrt(x) in [0.5, 1], generated with
FPMinimax. */
V4 (0x1.c14e96p-2), V4 (0x1.dd2d3p-1), V4 (-0x1.08e81ap-1),
V4 (0x1.2c74c2p-3) },
.table = { /* table[i] = 2^((i - 2) / 3). */
0x1.428a3p-1, 0x1.965feap-1, 0x1p0, 0x1.428a3p0, 0x1.965feap0 },
.one_third = V4 (0x1.555556p-2f),
};
#define SignMask v_u32 (0x80000000)
#define SmallestNormal v_u32 (0x00800000)
#define Thresh vdup_n_u16 (0x7f00) /* asuint(INFINITY) - SmallestNormal. */
#define MantissaMask v_u32 (0x007fffff)
#define HalfExp v_u32 (0x3f000000)
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint16x4_t special)
{
return v_call_f32 (cbrtf, x, y, vmovl_u16 (special));
}
static inline float32x4_t
shifted_lookup (const float *table, int32x4_t i)
{
return (float32x4_t){ table[i[0] + 2], table[i[1] + 2], table[i[2] + 2],
table[i[3] + 2] };
}
/* Approximation for vector single-precision cbrt(x) using Newton iteration
with initial guess obtained by a low-order polynomial. Greatest error
is 1.64 ULP. This is observed for every value where the mantissa is
0x1.85a2aa and the exponent is a multiple of 3, for example:
_ZGVnN4v_cbrtf(0x1.85a2aap+3) got 0x1.267936p+1
want 0x1.267932p+1. */
VPCS_ATTR float32x4_t V_NAME_F1 (cbrt) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
/* Subnormal, +/-0 and special values. */
uint16x4_t special = vcge_u16 (vsubhn_u32 (iax, SmallestNormal), Thresh);
/* Decompose |x| into m * 2^e, where m is in [0.5, 1.0]. This is a vector
version of frexpf, which gets subnormal values wrong - these have to be
special-cased as a result. */
float32x4_t m = vbslq_f32 (MantissaMask, x, v_f32 (0.5));
int32x4_t e
= vsubq_s32 (vreinterpretq_s32_u32 (vshrq_n_u32 (iax, 23)), v_s32 (126));
/* p is a rough approximation for cbrt(m) in [0.5, 1.0]. The better this is,
the less accurate the next stage of the algorithm needs to be. An order-4
polynomial is enough for one Newton iteration. */
float32x4_t p = v_pairwise_poly_3_f32 (m, vmulq_f32 (m, m), d->poly);
float32x4_t one_third = d->one_third;
float32x4_t two_thirds = vaddq_f32 (one_third, one_third);
/* One iteration of Newton's method for iteratively approximating cbrt. */
float32x4_t m_by_3 = vmulq_f32 (m, one_third);
float32x4_t a
= vfmaq_f32 (vdivq_f32 (m_by_3, vmulq_f32 (p, p)), two_thirds, p);
/* Assemble the result by the following:
cbrt(x) = cbrt(m) * 2 ^ (e / 3).
We can get 2 ^ round(e / 3) using ldexp and integer divide, but since e is
not necessarily a multiple of 3 we lose some information.
Let q = 2 ^ round(e / 3), then t = 2 ^ (e / 3) / q.
Then we know t = 2 ^ (i / 3), where i is the remainder from e / 3, which
is an integer in [-2, 2], and can be looked up in the table T. Hence the
result is assembled as:
cbrt(x) = cbrt(m) * t * 2 ^ round(e / 3) * sign. */
float32x4_t ef = vmulq_f32 (vcvtq_f32_s32 (e), one_third);
int32x4_t ey = vcvtq_s32_f32 (ef);
int32x4_t em3 = vsubq_s32 (e, vmulq_s32 (ey, v_s32 (3)));
float32x4_t my = shifted_lookup (d->table, em3);
my = vmulq_f32 (my, a);
/* Vector version of ldexpf. */
float32x4_t y
= vreinterpretq_f32_s32 (vshlq_n_s32 (vaddq_s32 (ey, v_s32 (127)), 23));
y = vmulq_f32 (y, my);
if (__glibc_unlikely (v_any_u16h (special)))
return special_case (x, vbslq_f32 (SignMask, x, y), special);
/* Copy sign. */
return vbslq_f32 (SignMask, x, y);
}
libmvec_hidden_def (V_NAME_F1 (cbrt))
HALF_WIDTH_ALIAS_F1 (cbrt)

122
sysdeps/aarch64/fpu/cbrtf_sve.c Normal file
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@ -0,0 +1,122 @@
/* Single-precision vector (SVE) cbrt 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"
const static struct data
{
float32_t poly[4];
float32_t table[5];
float32_t one_third, two_thirds;
} data = {
/* Very rough approximation of cbrt(x) in [0.5, 1], generated with FPMinimax.
*/
.poly = { 0x1.c14e96p-2, 0x1.dd2d3p-1, -0x1.08e81ap-1,
0x1.2c74c2p-3, },
/* table[i] = 2^((i - 2) / 3). */
.table = { 0x1.428a3p-1, 0x1.965feap-1, 0x1p0, 0x1.428a3p0, 0x1.965feap0 },
.one_third = 0x1.555556p-2f,
.two_thirds = 0x1.555556p-1f,
};
#define SmallestNormal 0x00800000
#define Thresh 0x7f000000 /* asuint(INFINITY) - SmallestNormal. */
#define MantissaMask 0x007fffff
#define HalfExp 0x3f000000
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
{
return sv_call_f32 (cbrtf, x, y, special);
}
static inline svfloat32_t
shifted_lookup (const svbool_t pg, const float32_t *table, svint32_t i)
{
return svld1_gather_index (pg, table, svadd_x (pg, i, 2));
}
/* Approximation for vector single-precision cbrt(x) using Newton iteration
with initial guess obtained by a low-order polynomial. Greatest error
is 1.64 ULP. This is observed for every value where the mantissa is
0x1.85a2aa and the exponent is a multiple of 3, for example:
_ZGVsMxv_cbrtf (0x1.85a2aap+3) got 0x1.267936p+1
want 0x1.267932p+1. */
svfloat32_t SV_NAME_F1 (cbrt) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svfloat32_t ax = svabs_x (pg, x);
svuint32_t iax = svreinterpret_u32 (ax);
svuint32_t sign = sveor_x (pg, svreinterpret_u32 (x), iax);
/* Subnormal, +/-0 and special values. */
svbool_t special = svcmpge (pg, svsub_x (pg, iax, SmallestNormal), Thresh);
/* Decompose |x| into m * 2^e, where m is in [0.5, 1.0]. This is a vector
version of frexpf, which gets subnormal values wrong - these have to be
special-cased as a result. */
svfloat32_t m = svreinterpret_f32 (svorr_x (
pg, svand_x (pg, svreinterpret_u32 (x), MantissaMask), HalfExp));
svint32_t e = svsub_x (pg, svreinterpret_s32 (svlsr_x (pg, iax, 23)), 126);
/* p is a rough approximation for cbrt(m) in [0.5, 1.0]. The better this is,
the less accurate the next stage of the algorithm needs to be. An order-4
polynomial is enough for one Newton iteration. */
svfloat32_t p
= sv_pairwise_poly_3_f32_x (pg, m, svmul_x (pg, m, m), d->poly);
/* One iteration of Newton's method for iteratively approximating cbrt. */
svfloat32_t m_by_3 = svmul_x (pg, m, d->one_third);
svfloat32_t a = svmla_x (pg, svdiv_x (pg, m_by_3, svmul_x (pg, p, p)), p,
d->two_thirds);
/* Assemble the result by the following:
cbrt(x) = cbrt(m) * 2 ^ (e / 3).
We can get 2 ^ round(e / 3) using ldexp and integer divide, but since e is
not necessarily a multiple of 3 we lose some information.
Let q = 2 ^ round(e / 3), then t = 2 ^ (e / 3) / q.
Then we know t = 2 ^ (i / 3), where i is the remainder from e / 3, which
is an integer in [-2, 2], and can be looked up in the table T. Hence the
result is assembled as:
cbrt(x) = cbrt(m) * t * 2 ^ round(e / 3) * sign. */
svfloat32_t ef = svmul_x (pg, svcvt_f32_x (pg, e), d->one_third);
svint32_t ey = svcvt_s32_x (pg, ef);
svint32_t em3 = svmls_x (pg, e, ey, 3);
svfloat32_t my = shifted_lookup (pg, d->table, em3);
my = svmul_x (pg, my, a);
/* Vector version of ldexpf. */
svfloat32_t y = svscale_x (pg, my, ey);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (
x, svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign)),
special);
/* Copy sign. */
return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign));
}

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

@ -30,6 +30,7 @@ VPCS_VECTOR_WRAPPER (asinh_advsimd, _ZGVnN2v_asinh)
VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan)
VPCS_VECTOR_WRAPPER (atanh_advsimd, _ZGVnN2v_atanh)
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 (erf_advsimd, _ZGVnN2v_erf)

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

@ -49,6 +49,7 @@ SVE_VECTOR_WRAPPER (asinh_sve, _ZGVsMxv_asinh)
SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan)
SVE_VECTOR_WRAPPER (atanh_sve, _ZGVsMxv_atanh)
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 (erf_sve, _ZGVsMxv_erf)

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

@ -30,6 +30,7 @@ VPCS_VECTOR_WRAPPER (asinhf_advsimd, _ZGVnN4v_asinhf)
VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf)
VPCS_VECTOR_WRAPPER (atanhf_advsimd, _ZGVnN4v_atanhf)
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 (erff_advsimd, _ZGVnN4v_erff)

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

@ -49,6 +49,7 @@ SVE_VECTOR_WRAPPER (asinhf_sve, _ZGVsMxv_asinhf)
SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf)
SVE_VECTOR_WRAPPER (atanhf_sve, _ZGVsMxv_atanhf)
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 (erff_sve, _ZGVsMxv_erff)

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

@ -477,11 +477,19 @@ double: 4
float: 1
ldouble: 1
Function: "cbrt_advsimd":
double: 1
float: 1
Function: "cbrt_downward":
double: 4
float: 1
ldouble: 1
Function: "cbrt_sve":
double: 1
float: 1
Function: "cbrt_towardzero":
double: 3
float: 1

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

@ -79,6 +79,8 @@ GLIBC_2.40 _ZGVnN2v_asinh F
GLIBC_2.40 _ZGVnN2v_asinhf F
GLIBC_2.40 _ZGVnN2v_atanh F
GLIBC_2.40 _ZGVnN2v_atanhf F
GLIBC_2.40 _ZGVnN2v_cbrt F
GLIBC_2.40 _ZGVnN2v_cbrtf F
GLIBC_2.40 _ZGVnN2v_cosh F
GLIBC_2.40 _ZGVnN2v_coshf F
GLIBC_2.40 _ZGVnN2v_erf F
@ -94,6 +96,7 @@ GLIBC_2.40 _ZGVnN2vv_hypotf F
GLIBC_2.40 _ZGVnN4v_acoshf F
GLIBC_2.40 _ZGVnN4v_asinhf F
GLIBC_2.40 _ZGVnN4v_atanhf F
GLIBC_2.40 _ZGVnN4v_cbrtf F
GLIBC_2.40 _ZGVnN4v_coshf F
GLIBC_2.40 _ZGVnN4v_erfcf F
GLIBC_2.40 _ZGVnN4v_erff F
@ -106,6 +109,8 @@ GLIBC_2.40 _ZGVsMxv_asinh F
GLIBC_2.40 _ZGVsMxv_asinhf F
GLIBC_2.40 _ZGVsMxv_atanh F
GLIBC_2.40 _ZGVsMxv_atanhf F
GLIBC_2.40 _ZGVsMxv_cbrt F
GLIBC_2.40 _ZGVsMxv_cbrtf F
GLIBC_2.40 _ZGVsMxv_cosh F
GLIBC_2.40 _ZGVsMxv_coshf F
GLIBC_2.40 _ZGVsMxv_erf F