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92 lines
3.2 KiB
C
92 lines
3.2 KiB
C
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/* Single-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_f32.h"
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/* For x < -SpecialBound, the result is subnormal and not handled correctly by
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FEXPA. */
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#define SpecialBound 37.9
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static const struct data
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{
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float poly[5];
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float shift, log10_2, log2_10_hi, log2_10_lo, special_bound;
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} data = {
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/* Coefficients generated using Remez algorithm with minimisation of relative
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error.
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rel error: 0x1.89dafa3p-24
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abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
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maxerr: 0.52 +0.5 ulp. */
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.poly = { 0x1.26bb16p+1f, 0x1.5350d2p+1f, 0x1.04744ap+1f, 0x1.2d8176p+0f,
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0x1.12b41ap-1f },
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/* 1.5*2^17 + 127, a shift value suitable for FEXPA. */
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.shift = 0x1.903f8p17f,
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.log10_2 = 0x1.a934fp+1,
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.log2_10_hi = 0x1.344136p-2,
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.log2_10_lo = -0x1.ec10cp-27,
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.special_bound = SpecialBound,
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};
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static svfloat32_t NOINLINE
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special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
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{
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return sv_call_f32 (exp10f, x, y, special);
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}
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/* Single-precision SVE exp10f routine. Implements the same algorithm
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as AdvSIMD exp10f.
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Worst case error is 1.02 ULPs.
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_ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1
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want 0x1.ba5f9cp-1. */
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svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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/* exp10(x) = 2^(n/N) * 10^r = 2^n * (1 + poly (r)),
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with poly(r) in [1/sqrt(2), sqrt(2)] and
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x = r + n * log10(2) / N, with r in [-log10(2)/2N, log10(2)/2N]. */
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/* Load some constants in quad-word chunks to minimise memory access (last
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lane is wasted). */
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svfloat32_t log10_2_and_inv = svld1rq (svptrue_b32 (), &d->log10_2);
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/* n = round(x/(log10(2)/N)). */
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svfloat32_t shift = sv_f32 (d->shift);
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svfloat32_t z = svmla_lane (shift, x, log10_2_and_inv, 0);
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svfloat32_t n = svsub_x (pg, z, shift);
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/* r = x - n*log10(2)/N. */
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svfloat32_t r = svmls_lane (x, n, log10_2_and_inv, 1);
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r = svmls_lane (r, n, log10_2_and_inv, 2);
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svbool_t special = svacgt (pg, x, d->special_bound);
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svfloat32_t scale = svexpa (svreinterpret_u32 (z));
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/* Polynomial evaluation: poly(r) ~ exp10(r)-1. */
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svfloat32_t r2 = svmul_x (pg, r, r);
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svfloat32_t poly
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= svmla_x (pg, svmul_x (pg, r, d->poly[0]),
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sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1), r2);
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if (__glibc_unlikely (svptest_any (pg, special)))
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return special_case (x, svmla_x (pg, scale, scale, poly), special);
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return svmla_x (pg, scale, scale, poly);
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}
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