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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>
112 lines
3.7 KiB
C
112 lines
3.7 KiB
C
/* Double-precision vector (AdvSIMD) cosh function
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Copyright (C) 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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static const struct data
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{
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float64x2_t poly[3];
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float64x2_t inv_ln2;
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double ln2[2];
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float64x2_t shift, thres;
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uint64x2_t index_mask, special_bound;
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} data = {
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.poly = { V2 (0x1.fffffffffffd4p-2), V2 (0x1.5555571d6b68cp-3),
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V2 (0x1.5555576a59599p-5), },
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.inv_ln2 = V2 (0x1.71547652b82fep8), /* N/ln2. */
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/* -ln2/N. */
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.ln2 = {-0x1.62e42fefa39efp-9, -0x1.abc9e3b39803f3p-64},
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.shift = V2 (0x1.8p+52),
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.thres = V2 (704.0),
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.index_mask = V2 (0xff),
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/* 0x1.6p9, above which exp overflows. */
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.special_bound = V2 (0x4086000000000000),
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};
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static float64x2_t NOINLINE VPCS_ATTR
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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 (cosh, x, y, special);
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}
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/* Helper for approximating exp(x). Copied from v_exp_tail, with no
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special-case handling or tail. */
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static inline float64x2_t
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exp_inline (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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/* n = round(x/(ln2/N)). */
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float64x2_t z = vfmaq_f64 (d->shift, x, d->inv_ln2);
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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*ln2/N. */
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float64x2_t ln2 = vld1q_f64 (d->ln2);
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float64x2_t r = vfmaq_laneq_f64 (x, n, ln2, 0);
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r = vfmaq_laneq_f64 (r, n, ln2, 1);
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uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TAIL_TABLE_BITS);
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uint64x2_t i = vandq_u64 (u, d->index_mask);
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/* y = tail + exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */
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float64x2_t y = vfmaq_f64 (d->poly[1], d->poly[2], r);
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y = vfmaq_f64 (d->poly[0], y, r);
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y = vmulq_f64 (vfmaq_f64 (v_f64 (1), y, r), r);
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/* s = 2^(n/N). */
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u = v_lookup_u64 (__v_exp_tail_data, i);
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float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
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return vfmaq_f64 (s, y, s);
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}
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/* Approximation for vector double-precision cosh(x) using exp_inline.
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cosh(x) = (exp(x) + exp(-x)) / 2.
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The greatest observed error is in the scalar fall-back region, so is the
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same as the scalar routine, 1.93 ULP:
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_ZGVnN2v_cosh (0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021
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want 0x1.fdf28623ef923p+1021.
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The greatest observed error in the non-special region is 1.54 ULP:
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_ZGVnN2v_cosh (0x1.8e205b6ecacf7p+2) got 0x1.f711dcb0c77afp+7
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want 0x1.f711dcb0c77b1p+7. */
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float64x2_t VPCS_ATTR V_NAME_D1 (cosh) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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float64x2_t ax = vabsq_f64 (x);
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uint64x2_t special
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= vcgtq_u64 (vreinterpretq_u64_f64 (ax), d->special_bound);
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/* Up to the point that exp overflows, we can use it to calculate cosh by
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exp(|x|) / 2 + 1 / (2 * exp(|x|)). */
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float64x2_t t = exp_inline (ax);
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float64x2_t half_t = vmulq_n_f64 (t, 0.5);
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float64x2_t half_over_t = vdivq_f64 (v_f64 (0.5), t);
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/* Fall back to scalar for any special cases. */
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if (__glibc_unlikely (v_any_u64 (special)))
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return special_case (x, vaddq_f64 (half_t, half_over_t), special);
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return vaddq_f64 (half_t, half_over_t);
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}
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