aarch64/fpu: Add vector variants of cosh

Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com>

1 files changed, 105 insertions, 0 deletions

diff --git a/sysdeps/aarch64/fpu/cosh_sve.c b/sysdeps/aarch64/fpu/cosh_sve.c
new file mode 100644
index 0000000000..919f34604a
--- /dev/null
+++ b/sysdeps/aarch64/fpu/cosh_sve.c
@@ -0,0 +1,105 @@
+/* Double-precision vector (SVE) cosh function
+
+   Copyright (C) 2024 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "sv_math.h"
+
+static const struct data
+{
+  float64_t poly[3];
+  float64_t inv_ln2, ln2_hi, ln2_lo, shift, thres;
+  uint64_t index_mask, special_bound;
+} data = {
+  .poly = { 0x1.fffffffffffd4p-2, 0x1.5555571d6b68cp-3,
+	    0x1.5555576a59599p-5, },
+
+  .inv_ln2 = 0x1.71547652b82fep8, /* N/ln2.  */
+  /* -ln2/N.  */
+  .ln2_hi = -0x1.62e42fefa39efp-9,
+  .ln2_lo = -0x1.abc9e3b39803f3p-64,
+  .shift = 0x1.8p+52,
+  .thres = 704.0,
+
+  .index_mask = 0xff,
+  /* 0x1.6p9, above which exp overflows.  */
+  .special_bound = 0x4086000000000000,
+};
+
+static svfloat64_t NOINLINE
+special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
+{
+  return sv_call_f64 (cosh, x, y, special);
+}
+
+/* Helper for approximating exp(x). Copied from sv_exp_tail, with no
+   special-case handling or tail.  */
+static inline svfloat64_t
+exp_inline (svfloat64_t x, const svbool_t pg, const struct data *d)
+{
+  /* Calculate exp(x).  */
+  svfloat64_t z = svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2);
+  svfloat64_t n = svsub_x (pg, z, d->shift);
+
+  svfloat64_t r = svmla_x (pg, x, n, d->ln2_hi);
+  r = svmla_x (pg, r, n, d->ln2_lo);
+
+  svuint64_t u = svreinterpret_u64 (z);
+  svuint64_t e = svlsl_x (pg, u, 52 - V_EXP_TAIL_TABLE_BITS);
+  svuint64_t i = svand_x (pg, u, d->index_mask);
+
+  svfloat64_t y = svmla_x (pg, sv_f64 (d->poly[1]), r, d->poly[2]);
+  y = svmla_x (pg, sv_f64 (d->poly[0]), r, y);
+  y = svmla_x (pg, sv_f64 (1.0), r, y);
+  y = svmul_x (pg, r, y);
+
+  /* s = 2^(n/N).  */
+  u = svld1_gather_index (pg, __v_exp_tail_data, i);
+  svfloat64_t s = svreinterpret_f64 (svadd_x (pg, u, e));
+
+  return svmla_x (pg, s, s, y);
+}
+
+/* Approximation for SVE double-precision cosh(x) using exp_inline.
+   cosh(x) = (exp(x) + exp(-x)) / 2.
+   The greatest observed error is in the scalar fall-back region, so is the
+   same as the scalar routine, 1.93 ULP:
+   _ZGVsMxv_cosh (0x1.628ad45039d2fp+9) got 0x1.fd774e958236dp+1021
+				       want 0x1.fd774e958236fp+1021.
+
+   The greatest observed error in the non-special region is 1.54 ULP:
+   _ZGVsMxv_cosh (0x1.ba5651dd4486bp+2) got 0x1.f5e2bb8d5c98fp+8
+				       want 0x1.f5e2bb8d5c991p+8.  */
+svfloat64_t SV_NAME_D1 (cosh) (svfloat64_t x, const svbool_t pg)
+{
+  const struct data *d = ptr_barrier (&data);
+
+  svfloat64_t ax = svabs_x (pg, x);
+  svbool_t special = svcmpgt (pg, svreinterpret_u64 (ax), d->special_bound);
+
+  /* Up to the point that exp overflows, we can use it to calculate cosh by
+     exp(|x|) / 2 + 1 / (2 * exp(|x|)).  */
+  svfloat64_t t = exp_inline (ax, pg, d);
+  svfloat64_t half_t = svmul_x (pg, t, 0.5);
+  svfloat64_t half_over_t = svdivr_x (pg, t, 0.5);
+
+  /* Fall back to scalar for any special cases.  */
+  if (__glibc_unlikely (svptest_any (pg, special)))
+    return special_case (x, svadd_x (pg, half_t, half_over_t), special);
+
+  return svadd_x (pg, half_t, half_over_t);
+}