diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/cosh_advsimd.c')
-rw-r--r-- | sysdeps/aarch64/fpu/cosh_advsimd.c | 108 |
1 files changed, 108 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/cosh_advsimd.c b/sysdeps/aarch64/fpu/cosh_advsimd.c new file mode 100644 index 0000000000..ec7b59637e --- /dev/null +++ b/sysdeps/aarch64/fpu/cosh_advsimd.c @@ -0,0 +1,108 @@ +/* Double-precision vector (AdvSIMD) 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 "v_math.h" + +static const struct data +{ + float64x2_t poly[3]; + float64x2_t inv_ln2, ln2, shift, thres; + uint64x2_t index_mask, special_bound; +} data = { + .poly = { V2 (0x1.fffffffffffd4p-2), V2 (0x1.5555571d6b68cp-3), + V2 (0x1.5555576a59599p-5), }, + + .inv_ln2 = V2 (0x1.71547652b82fep8), /* N/ln2. */ + /* -ln2/N. */ + .ln2 = {-0x1.62e42fefa39efp-9, -0x1.abc9e3b39803f3p-64}, + .shift = V2 (0x1.8p+52), + .thres = V2 (704.0), + + .index_mask = V2 (0xff), + /* 0x1.6p9, above which exp overflows. */ + .special_bound = V2 (0x4086000000000000), +}; + +static float64x2_t NOINLINE VPCS_ATTR +special_case (float64x2_t x, float64x2_t y, uint64x2_t special) +{ + return v_call_f64 (cosh, x, y, special); +} + +/* Helper for approximating exp(x). Copied from v_exp_tail, with no + special-case handling or tail. */ +static inline float64x2_t +exp_inline (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + /* n = round(x/(ln2/N)). */ + float64x2_t z = vfmaq_f64 (d->shift, x, d->inv_ln2); + uint64x2_t u = vreinterpretq_u64_f64 (z); + float64x2_t n = vsubq_f64 (z, d->shift); + + /* r = x - n*ln2/N. */ + float64x2_t r = vfmaq_laneq_f64 (x, n, d->ln2, 0); + r = vfmaq_laneq_f64 (r, n, d->ln2, 1); + + uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TAIL_TABLE_BITS); + uint64x2_t i = vandq_u64 (u, d->index_mask); + + /* y = tail + exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */ + float64x2_t y = vfmaq_f64 (d->poly[1], d->poly[2], r); + y = vfmaq_f64 (d->poly[0], y, r); + y = vmulq_f64 (vfmaq_f64 (v_f64 (1), y, r), r); + + /* s = 2^(n/N). */ + u = v_lookup_u64 (__v_exp_tail_data, i); + float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e)); + + return vfmaq_f64 (s, y, s); +} + +/* Approximation for vector 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: + _ZGVnN2v_cosh (0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021 + want 0x1.fdf28623ef923p+1021. + + The greatest observed error in the non-special region is 1.54 ULP: + _ZGVnN2v_cosh (0x1.8e205b6ecacf7p+2) got 0x1.f711dcb0c77afp+7 + want 0x1.f711dcb0c77b1p+7. */ +float64x2_t VPCS_ATTR V_NAME_D1 (cosh) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + float64x2_t ax = vabsq_f64 (x); + uint64x2_t special + = vcgtq_u64 (vreinterpretq_u64_f64 (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|)). */ + float64x2_t t = exp_inline (ax); + float64x2_t half_t = vmulq_n_f64 (t, 0.5); + float64x2_t half_over_t = vdivq_f64 (v_f64 (0.5), t); + + /* Fall back to scalar for any special cases. */ + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (x, vaddq_f64 (half_t, half_over_t), special); + + return vaddq_f64 (half_t, half_over_t); +} |