diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atan2f_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atan2f_advsimd.c | 116 |
1 files changed, 116 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/atan2f_advsimd.c b/sysdeps/aarch64/fpu/atan2f_advsimd.c new file mode 100644 index 0000000000..5a5a6202d1 --- /dev/null +++ b/sysdeps/aarch64/fpu/atan2f_advsimd.c @@ -0,0 +1,116 @@ +/* Single-precision AdvSIMD atan2 + + Copyright (C) 2023 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" +#include "poly_advsimd_f32.h" + +static const struct data +{ + float32x4_t poly[8]; + float32x4_t pi_over_2; +} data = { + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on + [2**-128, 1.0]. + Generated using fpminimax between FLT_MIN and 1. */ + .poly = { V4 (-0x1.55555p-2f), V4 (0x1.99935ep-3f), V4 (-0x1.24051ep-3f), + V4 (0x1.bd7368p-4f), V4 (-0x1.491f0ep-4f), V4 (0x1.93a2c0p-5f), + V4 (-0x1.4c3c60p-6f), V4 (0x1.01fd88p-8f) }, + .pi_over_2 = V4 (0x1.921fb6p+0f), +}; + +#define SignMask v_u32 (0x80000000) + +/* Special cases i.e. 0, infinity and nan (fall back to scalar calls). */ +static float32x4_t VPCS_ATTR NOINLINE +special_case (float32x4_t y, float32x4_t x, float32x4_t ret, uint32x4_t cmp) +{ + return v_call2_f32 (atan2f, y, x, ret, cmp); +} + +/* Returns 1 if input is the bit representation of 0, infinity or nan. */ +static inline uint32x4_t +zeroinfnan (uint32x4_t i) +{ + /* 2 * i - 1 >= 2 * 0x7f800000lu - 1. */ + return vcgeq_u32 (vsubq_u32 (vmulq_n_u32 (i, 2), v_u32 (1)), + v_u32 (2 * 0x7f800000lu - 1)); +} + +/* Fast implementation of vector atan2f. Maximum observed error is + 2.95 ULP in [0x1.9300d6p+6 0x1.93c0c6p+6] x [0x1.8c2dbp+6 0x1.8cea6p+6]: + _ZGVnN4vv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1 + want 0x1.967f00p-1. */ +float32x4_t VPCS_ATTR V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x) +{ + const struct data *data_ptr = ptr_barrier (&data); + + uint32x4_t ix = vreinterpretq_u32_f32 (x); + uint32x4_t iy = vreinterpretq_u32_f32 (y); + + uint32x4_t special_cases = vorrq_u32 (zeroinfnan (ix), zeroinfnan (iy)); + + uint32x4_t sign_x = vandq_u32 (ix, SignMask); + uint32x4_t sign_y = vandq_u32 (iy, SignMask); + uint32x4_t sign_xy = veorq_u32 (sign_x, sign_y); + + float32x4_t ax = vabsq_f32 (x); + float32x4_t ay = vabsq_f32 (y); + + uint32x4_t pred_xlt0 = vcltzq_f32 (x); + uint32x4_t pred_aygtax = vcgtq_f32 (ay, ax); + + /* Set up z for call to atanf. */ + float32x4_t n = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay); + float32x4_t d = vbslq_f32 (pred_aygtax, ay, ax); + float32x4_t z = vdivq_f32 (n, d); + + /* Work out the correct shift. */ + float32x4_t shift = vreinterpretq_f32_u32 ( + vandq_u32 (pred_xlt0, vreinterpretq_u32_f32 (v_f32 (-2.0f)))); + shift = vbslq_f32 (pred_aygtax, vaddq_f32 (shift, v_f32 (1.0f)), shift); + shift = vmulq_f32 (shift, data_ptr->pi_over_2); + + /* Calculate the polynomial approximation. + Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However, + a standard implementation using z8 creates spurious underflow + in the very last fma (when z^8 is small enough). + Therefore, we split the last fma into a mul and an fma. + Horner and single-level Estrin have higher errors that exceed + threshold. */ + float32x4_t z2 = vmulq_f32 (z, z); + float32x4_t z4 = vmulq_f32 (z2, z2); + + float32x4_t ret = vfmaq_f32 ( + v_pairwise_poly_3_f32 (z2, z4, data_ptr->poly), z4, + vmulq_f32 (z4, v_pairwise_poly_3_f32 (z2, z4, data_ptr->poly + 4))); + + /* y = shift + z * P(z^2). */ + ret = vaddq_f32 (vfmaq_f32 (z, ret, vmulq_f32 (z2, z)), shift); + + /* Account for the sign of y. */ + ret = vreinterpretq_f32_u32 ( + veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy)); + + if (__glibc_unlikely (v_any_u32 (special_cases))) + { + return special_case (y, x, ret, special_cases); + } + + return ret; +} |