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aarch64: Add vector implementations of log1p routines
May discard sign of zero.
This commit is contained in:
Joe Ramsay
Szabolcs Nagy
parent
b07038c5d3
commit
3548a4f087
@ -6577,7 +6577,7 @@ log10 0xf.bf1b2p-4
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log10 0x1.6b5f7ap+96
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log1p 0
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log1p -0
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log1p -0 no-mathvec
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log1p e-1
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log1p -0.25
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log1p -0.875
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@ -23,31 +23,31 @@ log1p 0
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= log1p tonearest ibm128 0x0p+0 : 0x0p+0 : inexact-ok
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= log1p towardzero ibm128 0x0p+0 : 0x0p+0 : inexact-ok
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= log1p upward ibm128 0x0p+0 : 0x0p+0 : inexact-ok
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log1p -0
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= log1p downward binary32 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p tonearest binary32 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p towardzero binary32 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p upward binary32 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p downward binary64 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p tonearest binary64 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p towardzero binary64 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p upward binary64 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p downward intel96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p tonearest intel96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p towardzero intel96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p upward intel96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p downward m68k96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p tonearest m68k96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p towardzero m68k96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p upward m68k96 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p downward binary128 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p tonearest binary128 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p towardzero binary128 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p upward binary128 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p downward ibm128 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p tonearest ibm128 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p towardzero ibm128 -0x0p+0 : -0x0p+0 : inexact-ok
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= log1p upward ibm128 -0x0p+0 : -0x0p+0 : inexact-ok
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log1p -0 no-mathvec
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= log1p downward binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p tonearest binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p towardzero binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p upward binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p downward binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p tonearest binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p towardzero binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p upward binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p downward intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p tonearest intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p towardzero intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p upward intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p downward m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p tonearest m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p towardzero m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p upward m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p downward binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p tonearest binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p towardzero binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p upward binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p downward ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p tonearest ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p towardzero ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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= log1p upward ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok
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log1p e-1
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= log1p downward binary32 0x1.b7e152p+0 : 0x1p+0 : inexact-ok
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= log1p tonearest binary32 0x1.b7e152p+0 : 0x1p+0 : inexact-ok
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@ -8,6 +8,7 @@ libmvec-supported-funcs = acos \
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exp2 \
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log \
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log10 \
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log1p \
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log2 \
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sin \
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tan
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@ -46,6 +46,10 @@ libmvec {
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_ZGVnN2v_log10;
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_ZGVsMxv_log10f;
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_ZGVsMxv_log10;
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_ZGVnN4v_log1pf;
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_ZGVnN2v_log1p;
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_ZGVsMxv_log1pf;
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_ZGVsMxv_log1p;
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_ZGVnN4v_log2f;
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_ZGVnN2v_log2;
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_ZGVsMxv_log2f;
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@ -59,6 +59,7 @@ __vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_exp2f (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_logf (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_log10f (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_log1pf (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_log2f (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t);
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@ -73,6 +74,7 @@ __vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_exp2 (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_log (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_log10 (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_log1p (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_log2 (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_sin (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t);
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@ -92,6 +94,7 @@ __sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_exp2f (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_logf (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_log10f (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_log1pf (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_log2f (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_sinf (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t);
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@ -106,6 +109,7 @@ __sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_exp2 (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_log (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_log10 (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_log1p (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_log2 (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_sin (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_tan (__sv_f64_t, __sv_bool_t);
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129
sysdeps/aarch64/fpu/log1p_advsimd.c
Normal file
129
sysdeps/aarch64/fpu/log1p_advsimd.c
Normal file
@ -0,0 +1,129 @@
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/* Double-precision AdvSIMD log1p
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Copyright (C) 2023 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "v_math.h"
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#include "poly_advsimd_f64.h"
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const static struct data
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{
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float64x2_t poly[19], ln2[2];
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uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask, inf, minus_one;
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int64x2_t one_top;
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} data = {
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/* Generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */
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.poly = { V2 (-0x1.ffffffffffffbp-2), V2 (0x1.55555555551a9p-2),
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V2 (-0x1.00000000008e3p-2), V2 (0x1.9999999a32797p-3),
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V2 (-0x1.555555552fecfp-3), V2 (0x1.249248e071e5ap-3),
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V2 (-0x1.ffffff8bf8482p-4), V2 (0x1.c71c8f07da57ap-4),
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V2 (-0x1.9999ca4ccb617p-4), V2 (0x1.7459ad2e1dfa3p-4),
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V2 (-0x1.554d2680a3ff2p-4), V2 (0x1.3b4c54d487455p-4),
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V2 (-0x1.2548a9ffe80e6p-4), V2 (0x1.0f389a24b2e07p-4),
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V2 (-0x1.eee4db15db335p-5), V2 (0x1.e95b494d4a5ddp-5),
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V2 (-0x1.15fdf07cb7c73p-4), V2 (0x1.0310b70800fcfp-4),
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V2 (-0x1.cfa7385bdb37ep-6) },
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.ln2 = { V2 (0x1.62e42fefa3800p-1), V2 (0x1.ef35793c76730p-45) },
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/* top32(asuint64(sqrt(2)/2)) << 32. */
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.hf_rt2_top = V2 (0x3fe6a09e00000000),
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/* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */
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.one_m_hf_rt2_top = V2 (0x00095f6200000000),
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.umask = V2 (0x000fffff00000000),
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.one_top = V2 (0x3ff),
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.inf = V2 (0x7ff0000000000000),
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.minus_one = V2 (0xbff0000000000000)
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};
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#define BottomMask v_u64 (0xffffffff)
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
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{
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return v_call_f64 (log1p, x, y, special);
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}
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/* Vector log1p approximation using polynomial on reduced interval. Routine is
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a modification of the algorithm used in scalar log1p, with no shortcut for
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k=0 and no narrowing for f and k. Maximum observed error is 2.45 ULP:
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_ZGVnN2v_log1p(0x1.658f7035c4014p+11) got 0x1.fd61d0727429dp+2
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want 0x1.fd61d0727429fp+2 . */
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VPCS_ATTR float64x2_t V_NAME_D1 (log1p) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint64x2_t ix = vreinterpretq_u64_f64 (x);
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uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x));
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uint64x2_t special = vcgeq_u64 (ia, d->inf);
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#if WANT_SIMD_EXCEPT
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special = vorrq_u64 (special,
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vcgeq_u64 (ix, vreinterpretq_u64_f64 (v_f64 (-1))));
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if (__glibc_unlikely (v_any_u64 (special)))
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x = v_zerofy_f64 (x, special);
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#else
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special = vorrq_u64 (special, vcleq_f64 (x, v_f64 (-1)));
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#endif
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/* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f
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is in [sqrt(2)/2, sqrt(2)]):
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log1p(x) = k*log(2) + log1p(f).
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f may not be representable exactly, so we need a correction term:
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let m = round(1 + x), c = (1 + x) - m.
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c << m: at very small x, log1p(x) ~ x, hence:
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log(1+x) - log(m) ~ c/m.
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We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */
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/* Obtain correctly scaled k by manipulation in the exponent.
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The scalar algorithm casts down to 32-bit at this point to calculate k and
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u_red. We stay in double-width to obtain f and k, using the same constants
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as the scalar algorithm but shifted left by 32. */
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float64x2_t m = vaddq_f64 (x, v_f64 (1));
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uint64x2_t mi = vreinterpretq_u64_f64 (m);
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uint64x2_t u = vaddq_u64 (mi, d->one_m_hf_rt2_top);
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int64x2_t ki
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= vsubq_s64 (vreinterpretq_s64_u64 (vshrq_n_u64 (u, 52)), d->one_top);
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float64x2_t k = vcvtq_f64_s64 (ki);
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/* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */
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uint64x2_t utop = vaddq_u64 (vandq_u64 (u, d->umask), d->hf_rt2_top);
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uint64x2_t u_red = vorrq_u64 (utop, vandq_u64 (mi, BottomMask));
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float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1));
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/* Correction term c/m. */
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float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1))), m);
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/* Approximate log1p(x) on the reduced input using a polynomial. Because
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log1p(0)=0 we choose an approximation of the form:
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x + C0*x^2 + C1*x^3 + C2x^4 + ...
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Hence approximation has the form f + f^2 * P(f)
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where P(x) = C0 + C1*x + C2x^2 + ...
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Assembling this all correctly is dealt with at the final step. */
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float64x2_t f2 = vmulq_f64 (f, f);
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float64x2_t p = v_pw_horner_18_f64 (f, f2, d->poly);
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float64x2_t ylo = vfmaq_f64 (cm, k, d->ln2[1]);
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float64x2_t yhi = vfmaq_f64 (f, k, d->ln2[0]);
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float64x2_t y = vaddq_f64 (ylo, yhi);
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if (__glibc_unlikely (v_any_u64 (special)))
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return special_case (vreinterpretq_f64_u64 (ix), vfmaq_f64 (y, f2, p),
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special);
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return vfmaq_f64 (y, f2, p);
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}
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118
sysdeps/aarch64/fpu/log1p_sve.c
Normal file
118
sysdeps/aarch64/fpu/log1p_sve.c
Normal file
@ -0,0 +1,118 @@
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/* Double-precision SVE log1p
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Copyright (C) 2023 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
|
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
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Lesser General Public License for more details.
|
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|
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "sv_math.h"
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#include "poly_sve_f64.h"
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static const struct data
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{
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double poly[19];
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double ln2_hi, ln2_lo;
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uint64_t hfrt2_top, onemhfrt2_top, inf, mone;
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} data = {
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/* Generated using Remez in [ sqrt(2)/2 - 1, sqrt(2) - 1]. Order 20
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polynomial, however first 2 coefficients are 0 and 1 so are not stored. */
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.poly = { -0x1.ffffffffffffbp-2, 0x1.55555555551a9p-2, -0x1.00000000008e3p-2,
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0x1.9999999a32797p-3, -0x1.555555552fecfp-3, 0x1.249248e071e5ap-3,
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-0x1.ffffff8bf8482p-4, 0x1.c71c8f07da57ap-4, -0x1.9999ca4ccb617p-4,
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0x1.7459ad2e1dfa3p-4, -0x1.554d2680a3ff2p-4, 0x1.3b4c54d487455p-4,
|
||||
-0x1.2548a9ffe80e6p-4, 0x1.0f389a24b2e07p-4, -0x1.eee4db15db335p-5,
|
||||
0x1.e95b494d4a5ddp-5, -0x1.15fdf07cb7c73p-4, 0x1.0310b70800fcfp-4,
|
||||
-0x1.cfa7385bdb37ep-6, },
|
||||
.ln2_hi = 0x1.62e42fefa3800p-1,
|
||||
.ln2_lo = 0x1.ef35793c76730p-45,
|
||||
/* top32(asuint64(sqrt(2)/2)) << 32. */
|
||||
.hfrt2_top = 0x3fe6a09e00000000,
|
||||
/* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */
|
||||
.onemhfrt2_top = 0x00095f6200000000,
|
||||
.inf = 0x7ff0000000000000,
|
||||
.mone = 0xbff0000000000000,
|
||||
};
|
||||
|
||||
#define AbsMask 0x7fffffffffffffff
|
||||
#define BottomMask 0xffffffff
|
||||
|
||||
static svfloat64_t NOINLINE
|
||||
special_case (svbool_t special, svfloat64_t x, svfloat64_t y)
|
||||
{
|
||||
return sv_call_f64 (log1p, x, y, special);
|
||||
}
|
||||
|
||||
/* Vector approximation for log1p using polynomial on reduced interval. Maximum
|
||||
observed error is 2.46 ULP:
|
||||
_ZGVsMxv_log1p(0x1.654a1307242a4p+11) got 0x1.fd5565fb590f4p+2
|
||||
want 0x1.fd5565fb590f6p+2. */
|
||||
svfloat64_t SV_NAME_D1 (log1p) (svfloat64_t x, svbool_t pg)
|
||||
{
|
||||
const struct data *d = ptr_barrier (&data);
|
||||
svuint64_t ix = svreinterpret_u64 (x);
|
||||
svuint64_t ax = svand_x (pg, ix, AbsMask);
|
||||
svbool_t special
|
||||
= svorr_z (pg, svcmpge (pg, ax, d->inf), svcmpge (pg, ix, d->mone));
|
||||
|
||||
/* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f
|
||||
is in [sqrt(2)/2, sqrt(2)]):
|
||||
log1p(x) = k*log(2) + log1p(f).
|
||||
|
||||
f may not be representable exactly, so we need a correction term:
|
||||
let m = round(1 + x), c = (1 + x) - m.
|
||||
c << m: at very small x, log1p(x) ~ x, hence:
|
||||
log(1+x) - log(m) ~ c/m.
|
||||
|
||||
We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */
|
||||
|
||||
/* Obtain correctly scaled k by manipulation in the exponent.
|
||||
The scalar algorithm casts down to 32-bit at this point to calculate k and
|
||||
u_red. We stay in double-width to obtain f and k, using the same constants
|
||||
as the scalar algorithm but shifted left by 32. */
|
||||
svfloat64_t m = svadd_x (pg, x, 1);
|
||||
svuint64_t mi = svreinterpret_u64 (m);
|
||||
svuint64_t u = svadd_x (pg, mi, d->onemhfrt2_top);
|
||||
|
||||
svint64_t ki = svsub_x (pg, svreinterpret_s64 (svlsr_x (pg, u, 52)), 0x3ff);
|
||||
svfloat64_t k = svcvt_f64_x (pg, ki);
|
||||
|
||||
/* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */
|
||||
svuint64_t utop
|
||||
= svadd_x (pg, svand_x (pg, u, 0x000fffff00000000), d->hfrt2_top);
|
||||
svuint64_t u_red = svorr_x (pg, utop, svand_x (pg, mi, BottomMask));
|
||||
svfloat64_t f = svsub_x (pg, svreinterpret_f64 (u_red), 1);
|
||||
|
||||
/* Correction term c/m. */
|
||||
svfloat64_t cm = svdiv_x (pg, svsub_x (pg, x, svsub_x (pg, m, 1)), m);
|
||||
|
||||
/* Approximate log1p(x) on the reduced input using a polynomial. Because
|
||||
log1p(0)=0 we choose an approximation of the form:
|
||||
x + C0*x^2 + C1*x^3 + C2x^4 + ...
|
||||
Hence approximation has the form f + f^2 * P(f)
|
||||
where P(x) = C0 + C1*x + C2x^2 + ...
|
||||
Assembling this all correctly is dealt with at the final step. */
|
||||
svfloat64_t f2 = svmul_x (pg, f, f), f4 = svmul_x (pg, f2, f2),
|
||||
f8 = svmul_x (pg, f4, f4), f16 = svmul_x (pg, f8, f8);
|
||||
svfloat64_t p = sv_estrin_18_f64_x (pg, f, f2, f4, f8, f16, d->poly);
|
||||
|
||||
svfloat64_t ylo = svmla_x (pg, cm, k, d->ln2_lo);
|
||||
svfloat64_t yhi = svmla_x (pg, f, k, d->ln2_hi);
|
||||
svfloat64_t y = svmla_x (pg, svadd_x (pg, ylo, yhi), f2, p);
|
||||
|
||||
if (__glibc_unlikely (svptest_any (pg, special)))
|
||||
return special_case (special, x, y);
|
||||
|
||||
return y;
|
||||
}
|
||||
128
sysdeps/aarch64/fpu/log1pf_advsimd.c
Normal file
128
sysdeps/aarch64/fpu/log1pf_advsimd.c
Normal file
@ -0,0 +1,128 @@
|
||||
/* Single-precision AdvSIMD log1p
|
||||
|
||||
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"
|
||||
|
||||
const static struct data
|
||||
{
|
||||
float32x4_t poly[8], ln2;
|
||||
uint32x4_t tiny_bound, minus_one, four, thresh;
|
||||
int32x4_t three_quarters;
|
||||
} data = {
|
||||
.poly = { /* Generated using FPMinimax in [-0.25, 0.5]. First two coefficients
|
||||
(1, -0.5) are not stored as they can be generated more
|
||||
efficiently. */
|
||||
V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f),
|
||||
V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f),
|
||||
V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) },
|
||||
.ln2 = V4 (0x1.62e43p-1f),
|
||||
.tiny_bound = V4 (0x34000000), /* asuint32(0x1p-23). ulp=0.5 at 0x1p-23. */
|
||||
.thresh = V4 (0x4b800000), /* asuint32(INFINITY) - tiny_bound. */
|
||||
.minus_one = V4 (0xbf800000),
|
||||
.four = V4 (0x40800000),
|
||||
.three_quarters = V4 (0x3f400000)
|
||||
};
|
||||
|
||||
static inline float32x4_t
|
||||
eval_poly (float32x4_t m, const float32x4_t *p)
|
||||
{
|
||||
/* Approximate log(1+m) on [-0.25, 0.5] using split Estrin scheme. */
|
||||
float32x4_t p_12 = vfmaq_f32 (v_f32 (-0.5), m, p[0]);
|
||||
float32x4_t p_34 = vfmaq_f32 (p[1], m, p[2]);
|
||||
float32x4_t p_56 = vfmaq_f32 (p[3], m, p[4]);
|
||||
float32x4_t p_78 = vfmaq_f32 (p[5], m, p[6]);
|
||||
|
||||
float32x4_t m2 = vmulq_f32 (m, m);
|
||||
float32x4_t p_02 = vfmaq_f32 (m, m2, p_12);
|
||||
float32x4_t p_36 = vfmaq_f32 (p_34, m2, p_56);
|
||||
float32x4_t p_79 = vfmaq_f32 (p_78, m2, p[7]);
|
||||
|
||||
float32x4_t m4 = vmulq_f32 (m2, m2);
|
||||
float32x4_t p_06 = vfmaq_f32 (p_02, m4, p_36);
|
||||
return vfmaq_f32 (p_06, m4, vmulq_f32 (m4, p_79));
|
||||
}
|
||||
|
||||
static float32x4_t NOINLINE VPCS_ATTR
|
||||
special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
|
||||
{
|
||||
return v_call_f32 (log1pf, x, y, special);
|
||||
}
|
||||
|
||||
/* Vector log1pf approximation using polynomial on reduced interval. Accuracy
|
||||
is roughly 2.02 ULP:
|
||||
log1pf(0x1.21e13ap-2) got 0x1.fe8028p-3 want 0x1.fe802cp-3. */
|
||||
VPCS_ATTR float32x4_t V_NAME_F1 (log1p) (float32x4_t x)
|
||||
{
|
||||
const struct data *d = ptr_barrier (&data);
|
||||
|
||||
uint32x4_t ix = vreinterpretq_u32_f32 (x);
|
||||
uint32x4_t ia = vreinterpretq_u32_f32 (vabsq_f32 (x));
|
||||
uint32x4_t special_cases
|
||||
= vorrq_u32 (vcgeq_u32 (vsubq_u32 (ia, d->tiny_bound), d->thresh),
|
||||
vcgeq_u32 (ix, d->minus_one));
|
||||
float32x4_t special_arg = x;
|
||||
|
||||
#if WANT_SIMD_EXCEPT
|
||||
if (__glibc_unlikely (v_any_u32 (special_cases)))
|
||||
/* Side-step special lanes so fenv exceptions are not triggered
|
||||
inadvertently. */
|
||||
x = v_zerofy_f32 (x, special_cases);
|
||||
#endif
|
||||
|
||||
/* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
|
||||
is in [-0.25, 0.5]):
|
||||
log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
|
||||
|
||||
We approximate log1p(m) with a polynomial, then scale by
|
||||
k*log(2). Instead of doing this directly, we use an intermediate
|
||||
scale factor s = 4*k*log(2) to ensure the scale is representable
|
||||
as a normalised fp32 number. */
|
||||
|
||||
float32x4_t m = vaddq_f32 (x, v_f32 (1.0f));
|
||||
|
||||
/* Choose k to scale x to the range [-1/4, 1/2]. */
|
||||
int32x4_t k
|
||||
= vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters),
|
||||
v_s32 (0xff800000));
|
||||
uint32x4_t ku = vreinterpretq_u32_s32 (k);
|
||||
|
||||
/* Scale x by exponent manipulation. */
|
||||
float32x4_t m_scale
|
||||
= vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku));
|
||||
|
||||
/* Scale up to ensure that the scale factor is representable as normalised
|
||||
fp32 number, and scale m down accordingly. */
|
||||
float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku));
|
||||
m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s));
|
||||
|
||||
/* Evaluate polynomial on the reduced interval. */
|
||||
float32x4_t p = eval_poly (m_scale, d->poly);
|
||||
|
||||
/* The scale factor to be applied back at the end - by multiplying float(k)
|
||||
by 2^-23 we get the unbiased exponent of k. */
|
||||
float32x4_t scale_back = vcvtq_f32_s32 (vshrq_n_s32 (k, 23));
|
||||
|
||||
/* Apply the scaling back. */
|
||||
float32x4_t y = vfmaq_f32 (p, scale_back, d->ln2);
|
||||
|
||||
if (__glibc_unlikely (v_any_u32 (special_cases)))
|
||||
return special_case (special_arg, y, special_cases);
|
||||
return y;
|
||||
}
|
||||
100
sysdeps/aarch64/fpu/log1pf_sve.c
Normal file
100
sysdeps/aarch64/fpu/log1pf_sve.c
Normal file
@ -0,0 +1,100 @@
|
||||
/* Single-precision SVE log1p
|
||||
|
||||
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
|
||||
{
|
||||
float poly[8];
|
||||
float ln2, exp_bias;
|
||||
uint32_t four, three_quarters;
|
||||
} data = {.poly = {/* Do not store first term of polynomial, which is -0.5, as
|
||||
this can be fmov-ed directly instead of including it in
|
||||
the main load-and-mla polynomial schedule. */
|
||||
0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f,
|
||||
-0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f,
|
||||
0x1.abcb6p-4f, -0x1.6f0d5ep-5f},
|
||||
.ln2 = 0x1.62e43p-1f,
|
||||
.exp_bias = 0x1p-23f,
|
||||
.four = 0x40800000,
|
||||
.three_quarters = 0x3f400000};
|
||||
|
||||
#define SignExponentMask 0xff800000
|
||||
|
||||
static svfloat32_t NOINLINE
|
||||
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
|
||||
{
|
||||
return sv_call_f32 (log1pf, x, y, special);
|
||||
}
|
||||
|
||||
/* Vector log1pf approximation using polynomial on reduced interval. Worst-case
|
||||
error is 1.27 ULP very close to 0.5.
|
||||
_ZGVsMxv_log1pf(0x1.fffffep-2) got 0x1.9f324p-2
|
||||
want 0x1.9f323ep-2. */
|
||||
svfloat32_t SV_NAME_F1 (log1p) (svfloat32_t x, svbool_t pg)
|
||||
{
|
||||
const struct data *d = ptr_barrier (&data);
|
||||
/* x < -1, Inf/Nan. */
|
||||
svbool_t special = svcmpeq (pg, svreinterpret_u32 (x), 0x7f800000);
|
||||
special = svorn_z (pg, special, svcmpge (pg, x, -1));
|
||||
|
||||
/* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
|
||||
is in [-0.25, 0.5]):
|
||||
log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
|
||||
|
||||
We approximate log1p(m) with a polynomial, then scale by
|
||||
k*log(2). Instead of doing this directly, we use an intermediate
|
||||
scale factor s = 4*k*log(2) to ensure the scale is representable
|
||||
as a normalised fp32 number. */
|
||||
svfloat32_t m = svadd_x (pg, x, 1);
|
||||
|
||||
/* Choose k to scale x to the range [-1/4, 1/2]. */
|
||||
svint32_t k
|
||||
= svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters),
|
||||
sv_s32 (SignExponentMask));
|
||||
|
||||
/* Scale x by exponent manipulation. */
|
||||
svfloat32_t m_scale = svreinterpret_f32 (
|
||||
svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k)));
|
||||
|
||||
/* Scale up to ensure that the scale factor is representable as normalised
|
||||
fp32 number, and scale m down accordingly. */
|
||||
svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four));
|
||||
m_scale = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1), s, 0.25));
|
||||
|
||||
/* Evaluate polynomial on reduced interval. */
|
||||
svfloat32_t ms2 = svmul_x (pg, m_scale, m_scale),
|
||||
ms4 = svmul_x (pg, ms2, ms2);
|
||||
svfloat32_t p = sv_estrin_7_f32_x (pg, m_scale, ms2, ms4, d->poly);
|
||||
p = svmad_x (pg, m_scale, p, -0.5);
|
||||
p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p));
|
||||
|
||||
/* The scale factor to be applied back at the end - by multiplying float(k)
|
||||
by 2^-23 we get the unbiased exponent of k. */
|
||||
svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->exp_bias);
|
||||
|
||||
/* Apply the scaling back. */
|
||||
svfloat32_t y = svmla_x (pg, p, scale_back, d->ln2);
|
||||
|
||||
if (__glibc_unlikely (svptest_any (pg, special)))
|
||||
return special_case (x, y, special);
|
||||
|
||||
return y;
|
||||
}
|
||||
@ -33,6 +33,7 @@ VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10)
|
||||
VPCS_VECTOR_WRAPPER (exp2_advsimd, _ZGVnN2v_exp2)
|
||||
VPCS_VECTOR_WRAPPER (log_advsimd, _ZGVnN2v_log)
|
||||
VPCS_VECTOR_WRAPPER (log10_advsimd, _ZGVnN2v_log10)
|
||||
VPCS_VECTOR_WRAPPER (log1p_advsimd, _ZGVnN2v_log1p)
|
||||
VPCS_VECTOR_WRAPPER (log2_advsimd, _ZGVnN2v_log2)
|
||||
VPCS_VECTOR_WRAPPER (sin_advsimd, _ZGVnN2v_sin)
|
||||
VPCS_VECTOR_WRAPPER (tan_advsimd, _ZGVnN2v_tan)
|
||||
|
||||
@ -52,6 +52,7 @@ SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10)
|
||||
SVE_VECTOR_WRAPPER (exp2_sve, _ZGVsMxv_exp2)
|
||||
SVE_VECTOR_WRAPPER (log_sve, _ZGVsMxv_log)
|
||||
SVE_VECTOR_WRAPPER (log10_sve, _ZGVsMxv_log10)
|
||||
SVE_VECTOR_WRAPPER (log1p_sve, _ZGVsMxv_log1p)
|
||||
SVE_VECTOR_WRAPPER (log2_sve, _ZGVsMxv_log2)
|
||||
SVE_VECTOR_WRAPPER (sin_sve, _ZGVsMxv_sin)
|
||||
SVE_VECTOR_WRAPPER (tan_sve, _ZGVsMxv_tan)
|
||||
|
||||
@ -33,6 +33,7 @@ VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f)
|
||||
VPCS_VECTOR_WRAPPER (exp2f_advsimd, _ZGVnN4v_exp2f)
|
||||
VPCS_VECTOR_WRAPPER (logf_advsimd, _ZGVnN4v_logf)
|
||||
VPCS_VECTOR_WRAPPER (log10f_advsimd, _ZGVnN4v_log10f)
|
||||
VPCS_VECTOR_WRAPPER (log1pf_advsimd, _ZGVnN4v_log1pf)
|
||||
VPCS_VECTOR_WRAPPER (log2f_advsimd, _ZGVnN4v_log2f)
|
||||
VPCS_VECTOR_WRAPPER (sinf_advsimd, _ZGVnN4v_sinf)
|
||||
VPCS_VECTOR_WRAPPER (tanf_advsimd, _ZGVnN4v_tanf)
|
||||
|
||||
@ -52,6 +52,7 @@ SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f)
|
||||
SVE_VECTOR_WRAPPER (exp2f_sve, _ZGVsMxv_exp2f)
|
||||
SVE_VECTOR_WRAPPER (logf_sve, _ZGVsMxv_logf)
|
||||
SVE_VECTOR_WRAPPER (log10f_sve, _ZGVsMxv_log10f)
|
||||
SVE_VECTOR_WRAPPER (log1pf_sve, _ZGVsMxv_log1pf)
|
||||
SVE_VECTOR_WRAPPER (log2f_sve, _ZGVsMxv_log2f)
|
||||
SVE_VECTOR_WRAPPER (sinf_sve, _ZGVsMxv_sinf)
|
||||
SVE_VECTOR_WRAPPER (tanf_sve, _ZGVsMxv_tanf)
|
||||
|
||||
@ -1248,11 +1248,19 @@ double: 1
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "log1p_advsimd":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "log1p_downward":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "log1p_sve":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "log1p_towardzero":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
@ -20,6 +20,7 @@ GLIBC_2.39 _ZGVnN2v_atan F
|
||||
GLIBC_2.39 _ZGVnN2v_exp10 F
|
||||
GLIBC_2.39 _ZGVnN2v_exp2 F
|
||||
GLIBC_2.39 _ZGVnN2v_log10 F
|
||||
GLIBC_2.39 _ZGVnN2v_log1p F
|
||||
GLIBC_2.39 _ZGVnN2v_log2 F
|
||||
GLIBC_2.39 _ZGVnN2v_tan F
|
||||
GLIBC_2.39 _ZGVnN2vv_atan2 F
|
||||
@ -29,6 +30,7 @@ GLIBC_2.39 _ZGVnN4v_atanf F
|
||||
GLIBC_2.39 _ZGVnN4v_exp10f F
|
||||
GLIBC_2.39 _ZGVnN4v_exp2f F
|
||||
GLIBC_2.39 _ZGVnN4v_log10f F
|
||||
GLIBC_2.39 _ZGVnN4v_log1pf F
|
||||
GLIBC_2.39 _ZGVnN4v_log2f F
|
||||
GLIBC_2.39 _ZGVnN4v_tanf F
|
||||
GLIBC_2.39 _ZGVnN4vv_atan2f F
|
||||
@ -44,6 +46,8 @@ GLIBC_2.39 _ZGVsMxv_exp2 F
|
||||
GLIBC_2.39 _ZGVsMxv_exp2f F
|
||||
GLIBC_2.39 _ZGVsMxv_log10 F
|
||||
GLIBC_2.39 _ZGVsMxv_log10f F
|
||||
GLIBC_2.39 _ZGVsMxv_log1p F
|
||||
GLIBC_2.39 _ZGVsMxv_log1pf F
|
||||
GLIBC_2.39 _ZGVsMxv_log2 F
|
||||
GLIBC_2.39 _ZGVsMxv_log2f F
|
||||
GLIBC_2.39 _ZGVsMxv_tan F
|
||||
|
||||
Loading…
Reference in New Issue
Block a user