/*
* Double-precision SVE cosh(x) function.
*
* Copyright (c) 2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "pl_sig.h"
#include "pl_test.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 (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);
}
PL_SIG (SV, D, 1, cosh, -10.0, 10.0)
PL_TEST_ULP (SV_NAME_D1 (cosh), 1.43)
PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cosh), 0, 0x1.6p9, 100000)
PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cosh), 0x1.6p9, inf, 1000)
