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git://sourceware.org/git/glibc.git
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aarch64: Add vector implementations of exp10 routines
Double-precision routines either reuse the exp table (AdvSIMD) or use SVE FEXPA intruction.
This commit is contained in:
Joe Ramsay
Szabolcs Nagy
parent
067a34156c
commit
31aaf6fed9
@ -1,5 +1,6 @@
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libmvec-supported-funcs = cos \
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exp \
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exp10 \
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exp2 \
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log \
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log10 \
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@ -18,6 +18,10 @@ libmvec {
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_ZGVsMxv_sinf;
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}
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GLIBC_2.39 {
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_ZGVnN4v_exp10f;
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_ZGVnN2v_exp10;
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_ZGVsMxv_exp10f;
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_ZGVsMxv_exp10;
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_ZGVnN4v_exp2f;
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_ZGVnN2v_exp2;
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_ZGVsMxv_exp2f;
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@ -51,6 +51,7 @@ typedef __SVBool_t __sv_bool_t;
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__vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
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__vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t);
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__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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@ -60,6 +61,7 @@ __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t);
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__vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
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__vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t);
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__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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@ -74,6 +76,7 @@ __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t);
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__sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t);
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__sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t);
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__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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@ -83,6 +86,7 @@ __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t);
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__sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t);
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__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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145
sysdeps/aarch64/fpu/exp10_advsimd.c
Normal file
145
sysdeps/aarch64/fpu/exp10_advsimd.c
Normal file
@ -0,0 +1,145 @@
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/* Double-precision vector (AdvSIMD) exp10 function.
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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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/* Value of |x| above which scale overflows without special treatment. */
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#define SpecialBound 306.0 /* floor (log10 (2^1023)) - 1. */
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/* Value of n above which scale overflows even with special treatment. */
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#define ScaleBound 163840.0 /* 1280.0 * N. */
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const static struct data
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{
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float64x2_t poly[4];
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float64x2_t log10_2, log2_10_hi, log2_10_lo, shift;
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#if !WANT_SIMD_EXCEPT
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float64x2_t special_bound, scale_thresh;
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#endif
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} data = {
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/* Coefficients generated using Remez algorithm.
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rel error: 0x1.5ddf8f28p-54
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abs error: 0x1.5ed266c8p-54 in [ -log10(2)/256, log10(2)/256 ]
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maxerr: 1.14432 +0.5 ulp. */
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.poly = { V2 (0x1.26bb1bbb5524p1), V2 (0x1.53524c73cecdap1),
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V2 (0x1.047060efb781cp1), V2 (0x1.2bd76040f0d16p0) },
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.log10_2 = V2 (0x1.a934f0979a371p8), /* N/log2(10). */
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.log2_10_hi = V2 (0x1.34413509f79ffp-9), /* log2(10)/N. */
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.log2_10_lo = V2 (-0x1.9dc1da994fd21p-66),
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.shift = V2 (0x1.8p+52),
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#if !WANT_SIMD_EXCEPT
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.scale_thresh = V2 (ScaleBound),
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.special_bound = V2 (SpecialBound),
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#endif
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};
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#define N (1 << V_EXP_TABLE_BITS)
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#define IndexMask v_u64 (N - 1)
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#if WANT_SIMD_EXCEPT
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# define TinyBound v_u64 (0x2000000000000000) /* asuint64 (0x1p-511). */
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# define BigBound v_u64 (0x4070000000000000) /* asuint64 (0x1p8). */
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# define Thres v_u64 (0x2070000000000000) /* BigBound - TinyBound. */
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static inline float64x2_t VPCS_ATTR
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special_case (float64x2_t x, float64x2_t y, uint64x2_t cmp)
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{
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/* If fenv exceptions are to be triggered correctly, fall back to the scalar
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routine for special lanes. */
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return v_call_f64 (exp10, x, y, cmp);
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}
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#else
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# define SpecialOffset v_u64 (0x6000000000000000) /* 0x1p513. */
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/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
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# define SpecialBias1 v_u64 (0x7000000000000000) /* 0x1p769. */
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# define SpecialBias2 v_u64 (0x3010000000000000) /* 0x1p-254. */
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t s, float64x2_t y, float64x2_t n,
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const struct data *d)
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{
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/* 2^(n/N) may overflow, break it up into s1*s2. */
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uint64x2_t b = vandq_u64 (vcltzq_f64 (n), SpecialOffset);
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float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (SpecialBias1, b));
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float64x2_t s2 = vreinterpretq_f64_u64 (
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vaddq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (s), SpecialBias2), b));
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uint64x2_t cmp = vcagtq_f64 (n, d->scale_thresh);
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float64x2_t r1 = vmulq_f64 (s1, s1);
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float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, y, s2), s1);
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return vbslq_f64 (cmp, r1, r0);
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}
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#endif
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/* Fast vector implementation of exp10.
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Maximum measured error is 1.64 ulp.
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_ZGVnN2v_exp10(0x1.ccd1c9d82cc8cp+0) got 0x1.f8dab6d7fed0cp+5
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want 0x1.f8dab6d7fed0ap+5. */
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float64x2_t VPCS_ATTR V_NAME_D1 (exp10) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint64x2_t cmp;
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#if WANT_SIMD_EXCEPT
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/* If any lanes are special, mask them with 1 and retain a copy of x to allow
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special_case to fix special lanes later. This is only necessary if fenv
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exceptions are to be triggered correctly. */
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float64x2_t xm = x;
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uint64x2_t iax = vreinterpretq_u64_f64 (vabsq_f64 (x));
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cmp = vcgeq_u64 (vsubq_u64 (iax, TinyBound), Thres);
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if (__glibc_unlikely (v_any_u64 (cmp)))
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x = vbslq_f64 (cmp, v_f64 (1), x);
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#else
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cmp = vcageq_f64 (x, d->special_bound);
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#endif
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/* n = round(x/(log10(2)/N)). */
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float64x2_t z = vfmaq_f64 (d->shift, x, d->log10_2);
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uint64x2_t u = vreinterpretq_u64_f64 (z);
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float64x2_t n = vsubq_f64 (z, d->shift);
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/* r = x - n*log10(2)/N. */
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float64x2_t r = x;
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r = vfmsq_f64 (r, d->log2_10_hi, n);
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r = vfmsq_f64 (r, d->log2_10_lo, n);
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uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
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uint64x2_t i = vandq_u64 (u, IndexMask);
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/* y = exp10(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4. */
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float64x2_t r2 = vmulq_f64 (r, r);
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float64x2_t p = vfmaq_f64 (d->poly[0], r, d->poly[1]);
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float64x2_t y = vfmaq_f64 (d->poly[2], r, d->poly[3]);
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p = vfmaq_f64 (p, y, r2);
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y = vmulq_f64 (r, p);
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/* s = 2^(n/N). */
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u = v_lookup_u64 (__v_exp_data, i);
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float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
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if (__glibc_unlikely (v_any_u64 (cmp)))
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#if WANT_SIMD_EXCEPT
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return special_case (xm, vfmaq_f64 (s, y, s), cmp);
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#else
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return special_case (s, y, n, d);
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#endif
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return vfmaq_f64 (s, y, s);
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}
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127
sysdeps/aarch64/fpu/exp10_sve.c
Normal file
127
sysdeps/aarch64/fpu/exp10_sve.c
Normal file
@ -0,0 +1,127 @@
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/* Double-precision vector (SVE) exp10 function.
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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 "sv_math.h"
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#include "poly_sve_f64.h"
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#define SpecialBound 307.0 /* floor (log10 (2^1023)). */
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static const struct data
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{
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double poly[5];
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double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound;
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} data = {
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/* Coefficients generated using Remez algorithm.
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rel error: 0x1.9fcb9b3p-60
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abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
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max ulp err 0.52 +0.5. */
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.poly = { 0x1.26bb1bbb55516p1, 0x1.53524c73cd32ap1, 0x1.0470591daeafbp1,
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0x1.2bd77b1361ef6p0, 0x1.142b5d54e9621p-1 },
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/* 1.5*2^46+1023. This value is further explained below. */
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.shift = 0x1.800000000ffc0p+46,
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.log10_2 = 0x1.a934f0979a371p1, /* 1/log2(10). */
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.log2_10_hi = 0x1.34413509f79ffp-2, /* log2(10). */
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.log2_10_lo = -0x1.9dc1da994fd21p-59,
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.scale_thres = 1280.0,
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.special_bound = SpecialBound,
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};
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#define SpecialOffset 0x6000000000000000 /* 0x1p513. */
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/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
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#define SpecialBias1 0x7000000000000000 /* 0x1p769. */
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#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
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/* Update of both special and non-special cases, if any special case is
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detected. */
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static inline svfloat64_t
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special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
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const struct data *d)
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{
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/* s=2^n may overflow, break it up into s=s1*s2,
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such that exp = s + s*y can be computed as s1*(s2+s2*y)
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and s1*s1 overflows only if n>0. */
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/* If n<=0 then set b to 0x6, 0 otherwise. */
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svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */
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svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
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/* Set s1 to generate overflow depending on sign of exponent n. */
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svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
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/* Offset s to avoid overflow in final result if n is below threshold. */
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svfloat64_t s2 = svreinterpret_f64 (
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svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
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/* |n| > 1280 => 2^(n) overflows. */
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svbool_t p_cmp = svacgt (pg, n, d->scale_thres);
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svfloat64_t r1 = svmul_x (pg, s1, s1);
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svfloat64_t r2 = svmla_x (pg, s2, s2, y);
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svfloat64_t r0 = svmul_x (pg, r2, s1);
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return svsel (p_cmp, r1, r0);
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}
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/* Fast vector implementation of exp10 using FEXPA instruction.
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Maximum measured error is 1.02 ulp.
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SV_NAME_D1 (exp10)(-0x1.2862fec805e58p+2) got 0x1.885a89551d782p-16
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want 0x1.885a89551d781p-16. */
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svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svbool_t no_big_scale = svacle (pg, x, d->special_bound);
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svbool_t special = svnot_z (pg, no_big_scale);
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/* n = round(x/(log10(2)/N)). */
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svfloat64_t shift = sv_f64 (d->shift);
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svfloat64_t z = svmla_x (pg, shift, x, d->log10_2);
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svfloat64_t n = svsub_x (pg, z, shift);
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/* r = x - n*log10(2)/N. */
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svfloat64_t log2_10 = svld1rq (svptrue_b64 (), &d->log2_10_hi);
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svfloat64_t r = x;
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r = svmls_lane (r, n, log2_10, 0);
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r = svmls_lane (r, n, log2_10, 1);
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/* scale = 2^(n/N), computed using FEXPA. FEXPA does not propagate NaNs, so
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for consistent NaN handling we have to manually propagate them. This
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comes at significant performance cost. */
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svuint64_t u = svreinterpret_u64 (z);
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svfloat64_t scale = svexpa (u);
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/* Approximate exp10(r) using polynomial. */
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svfloat64_t r2 = svmul_x (pg, r, r);
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svfloat64_t y = svmla_x (pg, svmul_x (pg, r, d->poly[0]), r2,
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sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly + 1));
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/* Assemble result as exp10(x) = 2^n * exp10(r). If |x| > SpecialBound
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multiplication may overflow, so use special case routine. */
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if (__glibc_unlikely (svptest_any (pg, special)))
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{
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/* FEXPA zeroes the sign bit, however the sign is meaningful to the
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special case function so needs to be copied.
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e = sign bit of u << 46. */
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svuint64_t e = svand_x (pg, svlsl_x (pg, u, 46), 0x8000000000000000);
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/* Copy sign to scale. */
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scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale)));
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return special_case (pg, scale, y, n, d);
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}
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/* No special case. */
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return svmla_x (pg, scale, scale, y);
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}
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140
sysdeps/aarch64/fpu/exp10f_advsimd.c
Normal file
140
sysdeps/aarch64/fpu/exp10f_advsimd.c
Normal file
@ -0,0 +1,140 @@
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/* Single-precision vector (AdvSIMD) exp10 function.
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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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|
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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.
|
||||
|
||||
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"
|
||||
|
||||
#define ScaleBound 192.0f
|
||||
|
||||
static const struct data
|
||||
{
|
||||
float32x4_t poly[5];
|
||||
float32x4_t shift, log10_2, log2_10_hi, log2_10_lo;
|
||||
#if !WANT_SIMD_EXCEPT
|
||||
float32x4_t scale_thresh;
|
||||
#endif
|
||||
} data = {
|
||||
/* Coefficients generated using Remez algorithm with minimisation of relative
|
||||
error.
|
||||
rel error: 0x1.89dafa3p-24
|
||||
abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
|
||||
maxerr: 1.85943 +0.5 ulp. */
|
||||
.poly = { V4 (0x1.26bb16p+1f), V4 (0x1.5350d2p+1f), V4 (0x1.04744ap+1f),
|
||||
V4 (0x1.2d8176p+0f), V4 (0x1.12b41ap-1f) },
|
||||
.shift = V4 (0x1.8p23f),
|
||||
.log10_2 = V4 (0x1.a934fp+1),
|
||||
.log2_10_hi = V4 (0x1.344136p-2),
|
||||
.log2_10_lo = V4 (-0x1.ec10cp-27),
|
||||
#if !WANT_SIMD_EXCEPT
|
||||
.scale_thresh = V4 (ScaleBound)
|
||||
#endif
|
||||
};
|
||||
|
||||
#define ExponentBias v_u32 (0x3f800000)
|
||||
|
||||
#if WANT_SIMD_EXCEPT
|
||||
|
||||
# define SpecialBound 38.0f /* rint(log10(2^127)). */
|
||||
# define TinyBound v_u32 (0x20000000) /* asuint (0x1p-63). */
|
||||
# define BigBound v_u32 (0x42180000) /* asuint (SpecialBound). */
|
||||
# define Thres v_u32 (0x22180000) /* BigBound - TinyBound. */
|
||||
|
||||
static float32x4_t VPCS_ATTR NOINLINE
|
||||
special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
|
||||
{
|
||||
/* If fenv exceptions are to be triggered correctly, fall back to the scalar
|
||||
routine to special lanes. */
|
||||
return v_call_f32 (exp10f, x, y, cmp);
|
||||
}
|
||||
|
||||
#else
|
||||
|
||||
# define SpecialBound 126.0f /* rint (log2 (2^127 / (1 + sqrt (2)))). */
|
||||
# define SpecialOffset v_u32 (0x82000000)
|
||||
# define SpecialBias v_u32 (0x7f000000)
|
||||
|
||||
static float32x4_t VPCS_ATTR NOINLINE
|
||||
special_case (float32x4_t poly, float32x4_t n, uint32x4_t e, uint32x4_t cmp1,
|
||||
float32x4_t scale, const struct data *d)
|
||||
{
|
||||
/* 2^n may overflow, break it up into s1*s2. */
|
||||
uint32x4_t b = vandq_u32 (vclezq_f32 (n), SpecialOffset);
|
||||
float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, SpecialBias));
|
||||
float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b));
|
||||
uint32x4_t cmp2 = vcagtq_f32 (n, d->scale_thresh);
|
||||
float32x4_t r2 = vmulq_f32 (s1, s1);
|
||||
float32x4_t r1 = vmulq_f32 (vfmaq_f32 (s2, poly, s2), s1);
|
||||
/* Similar to r1 but avoids double rounding in the subnormal range. */
|
||||
float32x4_t r0 = vfmaq_f32 (scale, poly, scale);
|
||||
float32x4_t r = vbslq_f32 (cmp1, r1, r0);
|
||||
return vbslq_f32 (cmp2, r2, r);
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
/* Fast vector implementation of single-precision exp10.
|
||||
Algorithm is accurate to 2.36 ULP.
|
||||
_ZGVnN4v_exp10f(0x1.be2b36p+1) got 0x1.7e79c4p+11
|
||||
want 0x1.7e79cp+11. */
|
||||
float32x4_t VPCS_ATTR V_NAME_F1 (exp10) (float32x4_t x)
|
||||
{
|
||||
const struct data *d = ptr_barrier (&data);
|
||||
#if WANT_SIMD_EXCEPT
|
||||
/* asuint(x) - TinyBound >= BigBound - TinyBound. */
|
||||
uint32x4_t cmp = vcgeq_u32 (
|
||||
vsubq_u32 (vandq_u32 (vreinterpretq_u32_f32 (x), v_u32 (0x7fffffff)),
|
||||
TinyBound),
|
||||
Thres);
|
||||
float32x4_t xm = x;
|
||||
/* If any lanes are special, mask them with 1 and retain a copy of x to allow
|
||||
special case handler to fix special lanes later. This is only necessary if
|
||||
fenv exceptions are to be triggered correctly. */
|
||||
if (__glibc_unlikely (v_any_u32 (cmp)))
|
||||
x = vbslq_f32 (cmp, v_f32 (1), x);
|
||||
#endif
|
||||
|
||||
/* exp10(x) = 2^n * 10^r = 2^n * (1 + poly (r)),
|
||||
with poly(r) in [1/sqrt(2), sqrt(2)] and
|
||||
x = r + n * log10 (2), with r in [-log10(2)/2, log10(2)/2]. */
|
||||
float32x4_t z = vfmaq_f32 (d->shift, x, d->log10_2);
|
||||
float32x4_t n = vsubq_f32 (z, d->shift);
|
||||
float32x4_t r = vfmsq_f32 (x, n, d->log2_10_hi);
|
||||
r = vfmsq_f32 (r, n, d->log2_10_lo);
|
||||
uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_f32 (z), 23);
|
||||
|
||||
float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, ExponentBias));
|
||||
|
||||
#if !WANT_SIMD_EXCEPT
|
||||
uint32x4_t cmp = vcagtq_f32 (n, v_f32 (SpecialBound));
|
||||
#endif
|
||||
|
||||
float32x4_t r2 = vmulq_f32 (r, r);
|
||||
float32x4_t poly
|
||||
= vfmaq_f32 (vmulq_f32 (r, d->poly[0]),
|
||||
v_pairwise_poly_3_f32 (r, r2, d->poly + 1), r2);
|
||||
|
||||
if (__glibc_unlikely (v_any_u32 (cmp)))
|
||||
#if WANT_SIMD_EXCEPT
|
||||
return special_case (xm, vfmaq_f32 (scale, poly, scale), cmp);
|
||||
#else
|
||||
return special_case (poly, n, e, cmp, scale, d);
|
||||
#endif
|
||||
|
||||
return vfmaq_f32 (scale, poly, scale);
|
||||
}
|
||||
91
sysdeps/aarch64/fpu/exp10f_sve.c
Normal file
91
sysdeps/aarch64/fpu/exp10f_sve.c
Normal file
@ -0,0 +1,91 @@
|
||||
/* Single-precision vector (SVE) exp10 function.
|
||||
|
||||
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"
|
||||
|
||||
/* For x < -SpecialBound, the result is subnormal and not handled correctly by
|
||||
FEXPA. */
|
||||
#define SpecialBound 37.9
|
||||
|
||||
static const struct data
|
||||
{
|
||||
float poly[5];
|
||||
float shift, log10_2, log2_10_hi, log2_10_lo, special_bound;
|
||||
} data = {
|
||||
/* Coefficients generated using Remez algorithm with minimisation of relative
|
||||
error.
|
||||
rel error: 0x1.89dafa3p-24
|
||||
abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
|
||||
maxerr: 0.52 +0.5 ulp. */
|
||||
.poly = { 0x1.26bb16p+1f, 0x1.5350d2p+1f, 0x1.04744ap+1f, 0x1.2d8176p+0f,
|
||||
0x1.12b41ap-1f },
|
||||
/* 1.5*2^17 + 127, a shift value suitable for FEXPA. */
|
||||
.shift = 0x1.903f8p17f,
|
||||
.log10_2 = 0x1.a934fp+1,
|
||||
.log2_10_hi = 0x1.344136p-2,
|
||||
.log2_10_lo = -0x1.ec10cp-27,
|
||||
.special_bound = SpecialBound,
|
||||
};
|
||||
|
||||
static svfloat32_t NOINLINE
|
||||
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
|
||||
{
|
||||
return sv_call_f32 (exp10f, x, y, special);
|
||||
}
|
||||
|
||||
/* Single-precision SVE exp10f routine. Implements the same algorithm
|
||||
as AdvSIMD exp10f.
|
||||
Worst case error is 1.02 ULPs.
|
||||
_ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1
|
||||
want 0x1.ba5f9cp-1. */
|
||||
svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg)
|
||||
{
|
||||
const struct data *d = ptr_barrier (&data);
|
||||
/* exp10(x) = 2^(n/N) * 10^r = 2^n * (1 + poly (r)),
|
||||
with poly(r) in [1/sqrt(2), sqrt(2)] and
|
||||
x = r + n * log10(2) / N, with r in [-log10(2)/2N, log10(2)/2N]. */
|
||||
|
||||
/* Load some constants in quad-word chunks to minimise memory access (last
|
||||
lane is wasted). */
|
||||
svfloat32_t log10_2_and_inv = svld1rq (svptrue_b32 (), &d->log10_2);
|
||||
|
||||
/* n = round(x/(log10(2)/N)). */
|
||||
svfloat32_t shift = sv_f32 (d->shift);
|
||||
svfloat32_t z = svmla_lane (shift, x, log10_2_and_inv, 0);
|
||||
svfloat32_t n = svsub_x (pg, z, shift);
|
||||
|
||||
/* r = x - n*log10(2)/N. */
|
||||
svfloat32_t r = svmls_lane (x, n, log10_2_and_inv, 1);
|
||||
r = svmls_lane (r, n, log10_2_and_inv, 2);
|
||||
|
||||
svbool_t special = svacgt (pg, x, d->special_bound);
|
||||
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
|
||||
|
||||
/* Polynomial evaluation: poly(r) ~ exp10(r)-1. */
|
||||
svfloat32_t r2 = svmul_x (pg, r, r);
|
||||
svfloat32_t poly
|
||||
= svmla_x (pg, svmul_x (pg, r, d->poly[0]),
|
||||
sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1), r2);
|
||||
|
||||
if (__glibc_unlikely (svptest_any (pg, special)))
|
||||
return special_case (x, svmla_x (pg, scale, scale, poly), special);
|
||||
|
||||
return svmla_x (pg, scale, scale, poly);
|
||||
}
|
||||
@ -25,6 +25,7 @@
|
||||
|
||||
VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos)
|
||||
VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp)
|
||||
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)
|
||||
|
||||
@ -34,6 +34,7 @@
|
||||
|
||||
SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos)
|
||||
SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp)
|
||||
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)
|
||||
|
||||
@ -25,6 +25,7 @@
|
||||
|
||||
VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf)
|
||||
VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf)
|
||||
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)
|
||||
|
||||
@ -34,6 +34,7 @@
|
||||
|
||||
SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf)
|
||||
SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf)
|
||||
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)
|
||||
|
||||
@ -970,11 +970,19 @@ double: 2
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "exp10_advsimd":
|
||||
double: 1
|
||||
float: 2
|
||||
|
||||
Function: "exp10_downward":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "exp10_sve":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: "exp10_towardzero":
|
||||
double: 2
|
||||
float: 1
|
||||
|
||||
@ -14,14 +14,18 @@ GLIBC_2.38 _ZGVsMxv_log F
|
||||
GLIBC_2.38 _ZGVsMxv_logf F
|
||||
GLIBC_2.38 _ZGVsMxv_sin F
|
||||
GLIBC_2.38 _ZGVsMxv_sinf F
|
||||
GLIBC_2.39 _ZGVnN2v_exp10 F
|
||||
GLIBC_2.39 _ZGVnN2v_exp2 F
|
||||
GLIBC_2.39 _ZGVnN2v_log10 F
|
||||
GLIBC_2.39 _ZGVnN2v_log2 F
|
||||
GLIBC_2.39 _ZGVnN2v_tan F
|
||||
GLIBC_2.39 _ZGVnN4v_exp10f F
|
||||
GLIBC_2.39 _ZGVnN4v_exp2f F
|
||||
GLIBC_2.39 _ZGVnN4v_log10f F
|
||||
GLIBC_2.39 _ZGVnN4v_log2f F
|
||||
GLIBC_2.39 _ZGVnN4v_tanf F
|
||||
GLIBC_2.39 _ZGVsMxv_exp10 F
|
||||
GLIBC_2.39 _ZGVsMxv_exp10f F
|
||||
GLIBC_2.39 _ZGVsMxv_exp2 F
|
||||
GLIBC_2.39 _ZGVsMxv_exp2f F
|
||||
GLIBC_2.39 _ZGVsMxv_log10 F
|
||||
|
||||
Loading…
Reference in New Issue
Block a user