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4a9392ffc2
Optimised implementations for single and double precision, Advanced SIMD and SVE, copied from Arm Optimized Routines. As previously, data tables are used via a barrier to prevent overly aggressive constant inlining. Special-case handlers are marked NOINLINE to avoid incurring the penalty of switching call standards unnecessarily. Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>
91 lines
3.2 KiB
C
91 lines
3.2 KiB
C
/* Single-precision vector (SVE) exp 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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static const struct data
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{
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float poly[5];
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float inv_ln2, ln2_hi, ln2_lo, shift, thres;
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} data = {
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/* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
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compatibility with polynomial helpers. */
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.poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
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0x1.0e4020p-7f },
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.inv_ln2 = 0x1.715476p+0f,
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.ln2_hi = 0x1.62e4p-1f,
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.ln2_lo = 0x1.7f7d1cp-20f,
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/* 1.5*2^17 + 127. */
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.shift = 0x1.903f8p17f,
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/* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
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correctly by FEXPA. */
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.thres = 0x1.5d5e2ap+6f,
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};
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#define C(i) sv_f32 (d->poly[i])
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#define ExponentBias 0x3f800000
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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 (expf, x, y, special);
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}
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/* Optimised single-precision SVE exp function.
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Worst-case error is 1.04 ulp:
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SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
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want 0x1.ba74bap+4. */
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svfloat32_t SV_NAME_F1 (exp) (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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/* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
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x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
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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 invln2_and_ln2 = svld1rq_f32 (svptrue_b32 (), &d->inv_ln2);
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/* n = round(x/(ln2/N)). */
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svfloat32_t z = svmla_lane_f32 (sv_f32 (d->shift), x, invln2_and_ln2, 0);
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svfloat32_t n = svsub_n_f32_x (pg, z, d->shift);
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/* r = x - n*ln2/N. */
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svfloat32_t r = svmls_lane_f32 (x, n, invln2_and_ln2, 1);
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r = svmls_lane_f32 (r, n, invln2_and_ln2, 2);
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/* scale = 2^(n/N). */
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svbool_t is_special_case = svacgt_n_f32 (pg, x, d->thres);
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svfloat32_t scale = svexpa_f32 (svreinterpret_u32_f32 (z));
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/* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */
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svfloat32_t p12 = svmla_f32_x (pg, C (1), C (2), r);
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svfloat32_t p34 = svmla_f32_x (pg, C (3), C (4), r);
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svfloat32_t r2 = svmul_f32_x (pg, r, r);
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svfloat32_t p14 = svmla_f32_x (pg, p12, p34, r2);
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svfloat32_t p0 = svmul_f32_x (pg, r, C (0));
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svfloat32_t poly = svmla_f32_x (pg, p0, r2, p14);
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if (__glibc_unlikely (svptest_any (pg, is_special_case)))
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return special_case (x, svmla_f32_x (pg, scale, scale, poly),
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is_special_case);
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return svmla_f32_x (pg, scale, scale, poly);
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}
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