diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/acospif_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/acospif_advsimd.c | 106 |
1 files changed, 106 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/acospif_advsimd.c b/sysdeps/aarch64/fpu/acospif_advsimd.c new file mode 100644 index 0000000..8486b62 --- /dev/null +++ b/sysdeps/aarch64/fpu/acospif_advsimd.c @@ -0,0 +1,106 @@ +/* Single-Precision vector (Advanced SIMD) inverse cospi function + + Copyright (C) 2025 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 +{ + float32x4_t c0, c2, c4, inv_pi; + float c1, c3, c5, null; +} data = { + /* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2) + on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using + iterative approach for minimisation of relative error in asinpif Sollya + file. */ + .c0 = V4 (0x1.b2995ep-5f), .c1 = 0x1.8724ep-6f, + .c2 = V4 (0x1.d1301ep-7f), .c3 = 0x1.446d3cp-7f, + .c4 = V4 (0x1.654848p-8f), .c5 = 0x1.5fdaa8p-7f, + .inv_pi = V4 (0x1.45f306p-2f), +}; + +#define AbsMask 0x7fffffff + +/* Single-precision implementation of vector acospi(x). + + For |x| in [0, 0.5], use order 5 polynomial P to approximate asinpi + such that the final approximation of acospi is an odd polynomial: + + acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)). + + The largest observed error in this region is 1.23 ulps, + _ZGVnN4v_acospif (0x1.fee13ep-2) got 0x1.55beb4p-2 want 0x1.55beb2p-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.53 ulps, + _ZGVnN4v_acospif (0x1.6ad644p-1) got 0x1.fe8f96p-3 + want 0x1.fe8f9cp-3. */ +float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (acospi) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + + uint32x4_t ix = vreinterpretq_u32_f32 (x); + uint32x4_t ia = vandq_u32 (ix, v_u32 (AbsMask)); + + float32x4_t ax = vreinterpretq_f32_u32 (ia); + uint32x4_t a_le_half = vcaltq_f32 (x, v_f32 (0.5f)); + + /* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with + z2 = x ^ 2 and z = |x| , if |x| < 0.5 + z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */ + + float32x4_t z2 = vbslq_f32 (a_le_half, vmulq_f32 (x, x), + vfmsq_n_f32 (v_f32 (0.5f), ax, 0.5f)); + float32x4_t z = vbslq_f32 (a_le_half, ax, vsqrtq_f32 (z2)); + + /* Use a single polynomial approximation P for both intervals. */ + + /* Order-5 Estrin evaluation scheme. */ + float32x4_t z4 = vmulq_f32 (z2, z2); + float32x4_t z8 = vmulq_f32 (z4, z4); + float32x4_t c135 = vld1q_f32 (&d->c1); + float32x4_t p01 = vfmaq_laneq_f32 (d->c0, z2, c135, 0); + float32x4_t p23 = vfmaq_laneq_f32 (d->c2, z2, c135, 1); + float32x4_t p03 = vfmaq_f32 (p01, z4, p23); + float32x4_t p45 = vfmaq_laneq_f32 (d->c4, z2, c135, 2); + float32x4_t p = vfmaq_f32 (p03, z8, p45); + /* Add 1/pi as final coeff. */ + p = vfmaq_f32 (d->inv_pi, z2, p); + + /* Finalize polynomial: z * P(z^2). */ + p = vmulq_f32 (z, p); + + /* acospi(|x|) + = 1/2 - sign(x) * Q(|x|), for |x| < 0.5 + = 2 Q(|x|) , for 0.5 < x < 1.0 + = 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */ + + float32x4_t y = vbslq_f32 (v_u32 (AbsMask), p, x); + uint32x4_t is_neg = vcltzq_f32 (x); + float32x4_t off = vreinterpretq_f32_u32 ( + vandq_u32 (vreinterpretq_u32_f32 (v_f32 (1.0f)), is_neg)); + float32x4_t mul = vbslq_f32 (a_le_half, v_f32 (1.0f), v_f32 (-2.0f)); + float32x4_t add = vbslq_f32 (a_le_half, v_f32 (0.5f), off); + + return vfmsq_f32 (add, mul, y); +} +libmvec_hidden_def (V_NAME_F1 (acospi)) +HALF_WIDTH_ALIAS_F1 (acospi) |