diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atan2_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atan2_advsimd.c | 121 |
1 files changed, 121 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/atan2_advsimd.c b/sysdeps/aarch64/fpu/atan2_advsimd.c new file mode 100644 index 0000000..fcc6be0 --- /dev/null +++ b/sysdeps/aarch64/fpu/atan2_advsimd.c @@ -0,0 +1,121 @@ +/* Double-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_f64.h" + +static const struct data +{ + float64x2_t pi_over_2; + float64x2_t poly[20]; +} data = { + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on + the interval [2**-1022, 1.0]. */ + .poly = { V2 (-0x1.5555555555555p-2), V2 (0x1.99999999996c1p-3), + V2 (-0x1.2492492478f88p-3), V2 (0x1.c71c71bc3951cp-4), + V2 (-0x1.745d160a7e368p-4), V2 (0x1.3b139b6a88ba1p-4), + V2 (-0x1.11100ee084227p-4), V2 (0x1.e1d0f9696f63bp-5), + V2 (-0x1.aebfe7b418581p-5), V2 (0x1.842dbe9b0d916p-5), + V2 (-0x1.5d30140ae5e99p-5), V2 (0x1.338e31eb2fbbcp-5), + V2 (-0x1.00e6eece7de8p-5), V2 (0x1.860897b29e5efp-6), + V2 (-0x1.0051381722a59p-6), V2 (0x1.14e9dc19a4a4ep-7), + V2 (-0x1.d0062b42fe3bfp-9), V2 (0x1.17739e210171ap-10), + V2 (-0x1.ab24da7be7402p-13), V2 (0x1.358851160a528p-16), }, + .pi_over_2 = V2 (0x1.921fb54442d18p+0), +}; + +#define SignMask v_u64 (0x8000000000000000) + +/* Special cases i.e. 0, infinity, NaN (fall back to scalar calls). */ +static float64x2_t VPCS_ATTR NOINLINE +special_case (float64x2_t y, float64x2_t x, float64x2_t ret, uint64x2_t cmp) +{ + return v_call2_f64 (atan2, y, x, ret, cmp); +} + +/* Returns 1 if input is the bit representation of 0, infinity or nan. */ +static inline uint64x2_t +zeroinfnan (uint64x2_t i) +{ + /* (2 * i - 1) >= (2 * asuint64 (INFINITY) - 1). */ + return vcgeq_u64 (vsubq_u64 (vaddq_u64 (i, i), v_u64 (1)), + v_u64 (2 * asuint64 (INFINITY) - 1)); +} + +/* Fast implementation of vector atan2. + Maximum observed error is 2.8 ulps: + _ZGVnN2vv_atan2 (0x1.9651a429a859ap+5, 0x1.953075f4ee26p+5) + got 0x1.92d628ab678ccp-1 + want 0x1.92d628ab678cfp-1. */ +float64x2_t VPCS_ATTR V_NAME_D2 (atan2) (float64x2_t y, float64x2_t x) +{ + const struct data *data_ptr = ptr_barrier (&data); + + uint64x2_t ix = vreinterpretq_u64_f64 (x); + uint64x2_t iy = vreinterpretq_u64_f64 (y); + + uint64x2_t special_cases = vorrq_u64 (zeroinfnan (ix), zeroinfnan (iy)); + + uint64x2_t sign_x = vandq_u64 (ix, SignMask); + uint64x2_t sign_y = vandq_u64 (iy, SignMask); + uint64x2_t sign_xy = veorq_u64 (sign_x, sign_y); + + float64x2_t ax = vabsq_f64 (x); + float64x2_t ay = vabsq_f64 (y); + + uint64x2_t pred_xlt0 = vcltzq_f64 (x); + uint64x2_t pred_aygtax = vcgtq_f64 (ay, ax); + + /* Set up z for call to atan. */ + float64x2_t n = vbslq_f64 (pred_aygtax, vnegq_f64 (ax), ay); + float64x2_t d = vbslq_f64 (pred_aygtax, ay, ax); + float64x2_t z = vdivq_f64 (n, d); + + /* Work out the correct shift. */ + float64x2_t shift = vreinterpretq_f64_u64 ( + vandq_u64 (pred_xlt0, vreinterpretq_u64_f64 (v_f64 (-2.0)))); + shift = vbslq_f64 (pred_aygtax, vaddq_f64 (shift, v_f64 (1.0)), shift); + shift = vmulq_f64 (shift, data_ptr->pi_over_2); + + /* Calculate the polynomial approximation. + Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of + full scheme to avoid underflow in x^16. + The order 19 polynomial P approximates + (atan(sqrt(x))-sqrt(x))/x^(3/2). */ + float64x2_t z2 = vmulq_f64 (z, z); + float64x2_t x2 = vmulq_f64 (z2, z2); + float64x2_t x4 = vmulq_f64 (x2, x2); + float64x2_t x8 = vmulq_f64 (x4, x4); + float64x2_t ret + = vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, data_ptr->poly), + v_estrin_11_f64 (z2, x2, x4, x8, data_ptr->poly + 8), x8); + + /* Finalize. y = shift + z + z^3 * P(z^2). */ + ret = vfmaq_f64 (z, ret, vmulq_f64 (z2, z)); + ret = vaddq_f64 (ret, shift); + + /* Account for the sign of x and y. */ + ret = vreinterpretq_f64_u64 ( + veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy)); + + if (__glibc_unlikely (v_any_u64 (special_cases))) + return special_case (y, x, ret, special_cases); + + return ret; +} |