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e302e10213
This includes a fix for big-endian in AdvSIMD log, some cosmetic changes, and numerous small optimisations mainly around inlining and using indexed variants of MLA intrinsics. Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
137 lines
4.4 KiB
C
137 lines
4.4 KiB
C
/* Double-precision vector (Advanced SIMD) exp 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 "v_math.h"
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#define N (1 << V_EXP_TABLE_BITS)
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#define IndexMask (N - 1)
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const static volatile struct
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{
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float64x2_t poly[3];
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float64x2_t inv_ln2, ln2_hi, ln2_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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/* maxerr: 1.88 +0.5 ulp
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rel error: 1.4337*2^-53
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abs error: 1.4299*2^-53 in [ -ln2/256, ln2/256 ]. */
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.poly = { V2 (0x1.ffffffffffd43p-2), V2 (0x1.55555c75adbb2p-3),
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V2 (0x1.55555da646206p-5) },
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#if !WANT_SIMD_EXCEPT
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.scale_thresh = V2 (163840.0), /* 1280.0 * N. */
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.special_bound = V2 (704.0),
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#endif
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.inv_ln2 = V2 (0x1.71547652b82fep7), /* N/ln2. */
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.ln2_hi = V2 (0x1.62e42fefa39efp-8), /* ln2/N. */
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.ln2_lo = V2 (0x1.abc9e3b39803f3p-63),
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.shift = V2 (0x1.8p+52)
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};
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#define C(i) data.poly[i]
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#define Tab __v_exp_data
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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 (0x4080000000000000) /* asuint64 (0x1p9). */
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# define SpecialBound v_u64 (0x2080000000000000) /* BigBound - TinyBound. */
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static float64x2_t VPCS_ATTR NOINLINE
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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 to special lanes. */
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return v_call_f64 (exp, 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 inline float64x2_t VPCS_ATTR
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special_case (float64x2_t s, float64x2_t y, float64x2_t n)
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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, data.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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float64x2_t VPCS_ATTR V_NAME_D1 (exp) (float64x2_t x)
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{
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float64x2_t n, r, r2, s, y, z;
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uint64x2_t cmp, u, e;
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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), SpecialBound);
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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 = vcagtq_f64 (x, data.special_bound);
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#endif
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/* n = round(x/(ln2/N)). */
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z = vfmaq_f64 (data.shift, x, data.inv_ln2);
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u = vreinterpretq_u64_f64 (z);
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n = vsubq_f64 (z, data.shift);
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/* r = x - n*ln2/N. */
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r = x;
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r = vfmsq_f64 (r, data.ln2_hi, n);
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r = vfmsq_f64 (r, data.ln2_lo, n);
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e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
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/* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4. */
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r2 = vmulq_f64 (r, r);
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y = vfmaq_f64 (C (0), C (1), r);
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y = vfmaq_f64 (y, C (2), r2);
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y = vfmaq_f64 (r, y, r2);
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/* s = 2^(n/N). */
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u = (uint64x2_t){ Tab[u[0] & IndexMask], Tab[u[1] & IndexMask] };
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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);
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#endif
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return vfmaq_f64 (s, y, s);
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}
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