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90a6ca8b28
Previously many routines used * to load from vector types stored
in the data table. This is emitted as ldr, which byte-swaps the
entire vector register, and causes bugs for big-endian when not
all lanes contain the same value. When a vector is to be used
this way, it has been replaced with an array and the load with an
explicit ld1 intrinsic, which byte-swaps only within lanes.
As well, many routines previously used non-standard GCC syntax
for vector operations such as indexing into vectors types with []
and assembling vectors using {}. This syntax should not be mixed
with ACLE, as the former does not respect endianness whereas the
latter does. Such examples have been replaced with, for instance,
vcombine_* and vgetq_lane* intrinsics. Helpers which only use the
GCC syntax, such as the v_call helpers, do not need changing as
they do not use intrinsics.
Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>
125 lines
4.5 KiB
C
125 lines
4.5 KiB
C
/* Double-precision AdvSIMD expm1
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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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#include "poly_advsimd_f64.h"
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static const struct data
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{
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float64x2_t poly[11];
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float64x2_t invln2;
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double ln2[2];
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float64x2_t shift;
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int64x2_t exponent_bias;
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#if WANT_SIMD_EXCEPT
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uint64x2_t thresh, tiny_bound;
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#else
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float64x2_t oflow_bound;
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#endif
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} data = {
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/* Generated using fpminimax, with degree=12 in [log(2)/2, log(2)/2]. */
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.poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5),
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V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10),
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V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16),
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V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22),
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V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29) },
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.invln2 = V2 (0x1.71547652b82fep0),
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.ln2 = { 0x1.62e42fefa39efp-1, 0x1.abc9e3b39803fp-56 },
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.shift = V2 (0x1.8p52),
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.exponent_bias = V2 (0x3ff0000000000000),
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#if WANT_SIMD_EXCEPT
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/* asuint64(oflow_bound) - asuint64(0x1p-51), shifted left by 1 for abs
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compare. */
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.thresh = V2 (0x78c56fa6d34b552),
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/* asuint64(0x1p-51) << 1. */
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.tiny_bound = V2 (0x3cc0000000000000 << 1),
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#else
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/* Value above which expm1(x) should overflow. Absolute value of the
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underflow bound is greater than this, so it catches both cases - there is
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a small window where fallbacks are triggered unnecessarily. */
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.oflow_bound = V2 (0x1.62b7d369a5aa9p+9),
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#endif
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};
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static float64x2_t VPCS_ATTR NOINLINE
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special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
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{
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return v_call_f64 (expm1, x, y, special);
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}
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/* Double-precision vector exp(x) - 1 function.
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The maximum error observed error is 2.18 ULP:
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_ZGVnN2v_expm1 (0x1.634ba0c237d7bp-2) got 0x1.a8b9ea8d66e22p-2
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want 0x1.a8b9ea8d66e2p-2. */
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float64x2_t VPCS_ATTR V_NAME_D1 (expm1) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint64x2_t ix = vreinterpretq_u64_f64 (x);
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#if WANT_SIMD_EXCEPT
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/* If fp exceptions are to be triggered correctly, fall back to scalar for
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|x| < 2^-51, |x| > oflow_bound, Inf & NaN. Add ix to itself for
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shift-left by 1, and compare with thresh which was left-shifted offline -
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this is effectively an absolute compare. */
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uint64x2_t special
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= vcgeq_u64 (vsubq_u64 (vaddq_u64 (ix, ix), d->tiny_bound), d->thresh);
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if (__glibc_unlikely (v_any_u64 (special)))
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x = v_zerofy_f64 (x, special);
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#else
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/* Large input, NaNs and Infs. */
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uint64x2_t special = vcageq_f64 (x, d->oflow_bound);
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#endif
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/* Reduce argument to smaller range:
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Let i = round(x / ln2)
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and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
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exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
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where 2^i is exact because i is an integer. */
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float64x2_t n = vsubq_f64 (vfmaq_f64 (d->shift, d->invln2, x), d->shift);
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int64x2_t i = vcvtq_s64_f64 (n);
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float64x2_t ln2 = vld1q_f64 (&d->ln2[0]);
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float64x2_t f = vfmsq_laneq_f64 (x, n, ln2, 0);
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f = vfmsq_laneq_f64 (f, n, ln2, 1);
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/* Approximate expm1(f) using polynomial.
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Taylor expansion for expm1(x) has the form:
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x + ax^2 + bx^3 + cx^4 ....
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So we calculate the polynomial P(f) = a + bf + cf^2 + ...
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and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
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float64x2_t f2 = vmulq_f64 (f, f);
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float64x2_t f4 = vmulq_f64 (f2, f2);
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float64x2_t f8 = vmulq_f64 (f4, f4);
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float64x2_t p = vfmaq_f64 (f, f2, v_estrin_10_f64 (f, f2, f4, f8, d->poly));
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/* Assemble the result.
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expm1(x) ~= 2^i * (p + 1) - 1
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Let t = 2^i. */
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int64x2_t u = vaddq_s64 (vshlq_n_s64 (i, 52), d->exponent_bias);
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float64x2_t t = vreinterpretq_f64_s64 (u);
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if (__glibc_unlikely (v_any_u64 (special)))
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return special_case (vreinterpretq_f64_u64 (ix),
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vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t),
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special);
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/* expm1(x) ~= p * t + (t - 1). */
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return vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t);
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}
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