diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atanf_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atanf_advsimd.c | 109 |
1 files changed, 109 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/atanf_advsimd.c b/sysdeps/aarch64/fpu/atanf_advsimd.c new file mode 100644 index 0000000000..589b0e8c96 --- /dev/null +++ b/sysdeps/aarch64/fpu/atanf_advsimd.c @@ -0,0 +1,109 @@ +/* Single-precision AdvSIMD inverse tan + + 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) + +#define P(i) d->poly[i] + +#define TinyBound 0x30800000 /* asuint(0x1p-30). */ +#define BigBound 0x4e800000 /* asuint(0x1p30). */ + +#if WANT_SIMD_EXCEPT +static float32x4_t VPCS_ATTR NOINLINE +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +{ + return v_call_f32 (atanf, x, y, special); +} +#endif + +/* Fast implementation of vector atanf based on + atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] + using z=-1/x and shift = pi/2. Maximum observed error is 2.9ulps: + _ZGVnN4v_atanf (0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1. */ +float32x4_t VPCS_ATTR V_NAME_F1 (atan) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + + /* Small cases, infs and nans are supported by our approximation technique, + but do not set fenv flags correctly. Only trigger special case if we need + fenv. */ + uint32x4_t ix = vreinterpretq_u32_f32 (x); + uint32x4_t sign = vandq_u32 (ix, SignMask); + +#if WANT_SIMD_EXCEPT + uint32x4_t ia = vandq_u32 (ix, v_u32 (0x7ff00000)); + uint32x4_t special = vcgtq_u32 (vsubq_u32 (ia, v_u32 (TinyBound)), + v_u32 (BigBound - TinyBound)); + /* If any lane is special, fall back to the scalar routine for all lanes. */ + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (x, x, v_u32 (-1)); +#endif + + /* Argument reduction: + y := arctan(x) for x < 1 + y := pi/2 + arctan(-1/x) for x > 1 + Hence, use z=-1/a if x>=1, otherwise z=a. */ + uint32x4_t red = vcagtq_f32 (x, v_f32 (1.0)); + /* Avoid dependency in abs(x) in division (and comparison). */ + float32x4_t z = vbslq_f32 (red, vdivq_f32 (v_f32 (1.0f), x), x); + float32x4_t shift = vreinterpretq_f32_u32 ( + vandq_u32 (red, vreinterpretq_u32_f32 (d->pi_over_2))); + /* Use absolute value only when needed (odd powers of z). */ + float32x4_t az = vbslq_f32 ( + SignMask, vreinterpretq_f32_u32 (vandq_u32 (SignMask, red)), z); + + /* 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 y = vfmaq_f32 ( + v_pairwise_poly_3_f32 (z2, z4, d->poly), z4, + vmulq_f32 (z4, v_pairwise_poly_3_f32 (z2, z4, d->poly + 4))); + + /* y = shift + z * P(z^2). */ + y = vaddq_f32 (vfmaq_f32 (az, y, vmulq_f32 (z2, az)), shift); + + /* y = atan(x) if x>0, -atan(-x) otherwise. */ + y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), sign)); + + return y; +} |