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7b8c134b54
Reduce MOV and MOVPRFX by improving special-case handling. Use inline helper to duplicate the entire computation between the special- and non-special case branches, removing the contention for z0 between x and the return value. Also rearrange some MLAs and MLSs - by making the multiplicand the destination we can avoid a MOVPRFX in several cases. Also change which constants go in the vector used for lanewise ops - the last lane is no longer wasted. Spotted that shift was incorrect in exp2f and exp10f, w.r.t. to the comment that explains it. Fixed - worst-case ULP for exp2f moves around but it doesn't change significantly for either routine. Worst-case error for coshf increases due to passing x to exp rather than abs(x) - updated the comment, but does not require regen-ulps. Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
88 lines
3.1 KiB
C
88 lines
3.1 KiB
C
/* Single-precision vector (SVE) exp2 function
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Copyright (C) 2023-2024 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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#define Thres 0x1.5d5e2ap+6f
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static const struct data
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{
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float c0, c2, c4, c1, c3;
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float shift, thres;
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} data = {
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/* Coefficients copied from the polynomial in AdvSIMD variant. */
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.c0 = 0x1.62e422p-1f,
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.c1 = 0x1.ebf9bcp-3f,
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.c2 = 0x1.c6bd32p-5f,
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.c3 = 0x1.3ce9e4p-7f,
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.c4 = 0x1.59977ap-10f,
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/* 1.5*2^17 + 127. */
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.shift = 0x1.803f8p17f,
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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 = Thres,
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};
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static inline svfloat32_t
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sv_exp2f_inline (svfloat32_t x, const svbool_t pg, const struct data *d)
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{
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/* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
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x = n + r, with r in [-1/2, 1/2]. */
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svfloat32_t z = svadd_x (svptrue_b32 (), x, d->shift);
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svfloat32_t n = svsub_x (svptrue_b32 (), z, d->shift);
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svfloat32_t r = svsub_x (svptrue_b32 (), x, n);
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svfloat32_t scale = svexpa (svreinterpret_u32 (z));
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/* Polynomial evaluation: poly(r) ~ exp2(r)-1.
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Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
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coefficients 1 to 4, and apply most significant coefficient directly. */
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svfloat32_t even_coeffs = svld1rq (svptrue_b32 (), &d->c0);
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svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
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svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, even_coeffs, 1);
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svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, even_coeffs, 2);
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svfloat32_t p14 = svmla_x (pg, p12, r2, p34);
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svfloat32_t p0 = svmul_lane (r, even_coeffs, 0);
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svfloat32_t poly = svmla_x (pg, p0, r2, p14);
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return svmla_x (pg, scale, scale, poly);
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}
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static svfloat32_t NOINLINE
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special_case (svfloat32_t x, svbool_t special, const struct data *d)
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{
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return sv_call_f32 (exp2f, x, sv_exp2f_inline (x, svptrue_b32 (), d),
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special);
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}
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/* Single-precision SVE exp2f routine. Implements the same algorithm
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as AdvSIMD exp2f.
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Worst case error is 1.04 ULPs.
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_ZGVsMxv_exp2f(-0x1.af994ap-3) got 0x1.ba6a66p-1
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want 0x1.ba6a64p-1. */
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svfloat32_t SV_NAME_F1 (exp2) (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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svbool_t special = svacgt (pg, x, d->thres);
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if (__glibc_unlikely (svptest_any (special, special)))
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return special_case (x, special, d);
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return sv_exp2f_inline (x, pg, d);
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}
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