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106 lines
3.6 KiB
C
106 lines
3.6 KiB
C
/* Double-precision vector (SVE) 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 "sv_math.h"
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static const struct data
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{
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float64_t poly[3];
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float64_t inv_ln2, ln2_hi, ln2_lo, shift, thres;
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uint64_t index_mask, special_bound;
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} data = {
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.poly = { 0x1.fffffffffffd4p-2, 0x1.5555571d6b68cp-3,
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0x1.5555576a59599p-5, },
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.inv_ln2 = 0x1.71547652b82fep8, /* N/ln2. */
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/* -ln2/N. */
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.ln2_hi = -0x1.62e42fefa39efp-9,
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.ln2_lo = -0x1.abc9e3b39803f3p-64,
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.shift = 0x1.8p+52,
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.thres = 704.0,
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.index_mask = 0xff,
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/* 0x1.6p9, above which exp overflows. */
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.special_bound = 0x4086000000000000,
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};
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static svfloat64_t NOINLINE
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special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
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{
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return sv_call_f64 (cosh, x, y, special);
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}
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/* Helper for approximating exp(x). Copied from sv_exp_tail, with no
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special-case handling or tail. */
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static inline svfloat64_t
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exp_inline (svfloat64_t x, const svbool_t pg, const struct data *d)
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{
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/* Calculate exp(x). */
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svfloat64_t z = svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2);
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svfloat64_t n = svsub_x (pg, z, d->shift);
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svfloat64_t r = svmla_x (pg, x, n, d->ln2_hi);
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r = svmla_x (pg, r, n, d->ln2_lo);
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svuint64_t u = svreinterpret_u64 (z);
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svuint64_t e = svlsl_x (pg, u, 52 - V_EXP_TAIL_TABLE_BITS);
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svuint64_t i = svand_x (pg, u, d->index_mask);
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svfloat64_t y = svmla_x (pg, sv_f64 (d->poly[1]), r, d->poly[2]);
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y = svmla_x (pg, sv_f64 (d->poly[0]), r, y);
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y = svmla_x (pg, sv_f64 (1.0), r, y);
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y = svmul_x (pg, r, y);
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/* s = 2^(n/N). */
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u = svld1_gather_index (pg, __v_exp_tail_data, i);
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svfloat64_t s = svreinterpret_f64 (svadd_x (pg, u, e));
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return svmla_x (pg, s, s, y);
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}
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/* Approximation for SVE 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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_ZGVsMxv_cosh (0x1.628ad45039d2fp+9) got 0x1.fd774e958236dp+1021
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want 0x1.fd774e958236fp+1021.
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The greatest observed error in the non-special region is 1.54 ULP:
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_ZGVsMxv_cosh (0x1.ba5651dd4486bp+2) got 0x1.f5e2bb8d5c98fp+8
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want 0x1.f5e2bb8d5c991p+8. */
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svfloat64_t SV_NAME_D1 (cosh) (svfloat64_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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svfloat64_t ax = svabs_x (pg, x);
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svbool_t special = svcmpgt (pg, svreinterpret_u64 (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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svfloat64_t t = exp_inline (ax, pg, d);
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svfloat64_t half_t = svmul_x (pg, t, 0.5);
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svfloat64_t half_over_t = svdivr_x (pg, t, 0.5);
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/* Fall back to scalar for any special cases. */
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if (__glibc_unlikely (svptest_any (pg, special)))
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return special_case (x, svadd_x (pg, half_t, half_over_t), special);
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return svadd_x (pg, half_t, half_over_t);
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}
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