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129 lines
4.1 KiB
C
129 lines
4.1 KiB
C
/* Double-precision vector (AdvSIMD) exp2 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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#include "poly_advsimd_f64.h"
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#define N (1 << V_EXP_TABLE_BITS)
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#define IndexMask (N - 1)
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#define BigBound 1022.0
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#define UOFlowBound 1280.0
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static const struct data
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{
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float64x2_t poly[4];
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float64x2_t shift, scale_big_bound, scale_uoflow_bound;
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} data = {
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/* Coefficients are computed using Remez algorithm with
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minimisation of the absolute error. */
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.poly = { V2 (0x1.62e42fefa3686p-1), V2 (0x1.ebfbdff82c241p-3),
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V2 (0x1.c6b09b16de99ap-5), V2 (0x1.3b2abf5571ad8p-7) },
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.shift = V2 (0x1.8p52 / N),
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.scale_big_bound = V2 (BigBound),
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.scale_uoflow_bound = V2 (UOFlowBound),
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};
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static inline uint64x2_t
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lookup_sbits (uint64x2_t i)
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{
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return (uint64x2_t){ __v_exp_data[i[0] & IndexMask],
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__v_exp_data[i[1] & IndexMask] };
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}
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#if WANT_SIMD_EXCEPT
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# define TinyBound 0x2000000000000000 /* asuint64(0x1p-511). */
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# define Thres 0x2080000000000000 /* asuint64(512.0) - TinyBound. */
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/* Call scalar exp2 as a fallback. */
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t x)
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{
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return v_call_f64 (exp2, x, x, v_u64 (0xffffffffffffffff));
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}
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#else
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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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static float64x2_t VPCS_ATTR
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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 (vclezq_f64 (n), v_u64 (SpecialOffset));
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float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (v_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), v_u64 (SpecialBias2)), b));
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uint64x2_t cmp = vcagtq_f64 (n, d->scale_uoflow_bound);
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float64x2_t r1 = vmulq_f64 (s1, s1);
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float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, s2, y), 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 exp2.
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Maximum measured error is 1.65 ulp.
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_ZGVnN2v_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
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want 0x1.f8db0d4df721dp-1. */
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VPCS_ATTR
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float64x2_t V_NAME_D1 (exp2) (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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uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x));
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cmp = vcgeq_u64 (vsubq_u64 (ia, v_u64 (TinyBound)), v_u64 (Thres));
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/* If any special case (inf, nan, small and large x) is detected,
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fall back to scalar for all lanes. */
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if (__glibc_unlikely (v_any_u64 (cmp)))
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return special_case (x);
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#else
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cmp = vcagtq_f64 (x, d->scale_big_bound);
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#endif
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/* n = round(x/N). */
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float64x2_t z = vaddq_f64 (d->shift, x);
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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/N. */
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float64x2_t r = vsubq_f64 (x, n);
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/* s = 2^(n/N). */
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uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
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u = lookup_sbits (u);
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float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
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/* y ~ exp2(r) - 1. */
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float64x2_t r2 = vmulq_f64 (r, r);
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float64x2_t y = v_pairwise_poly_3_f64 (r, r2, d->poly);
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y = vmulq_f64 (r, y);
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#if !WANT_SIMD_EXCEPT
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if (__glibc_unlikely (v_any_u64 (cmp)))
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return special_case (s, y, n, d);
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#endif
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return vfmaq_f64 (s, s, y);
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}
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