diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atan2pif_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atan2pif_advsimd.c | 138 |
1 files changed, 138 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/atan2pif_advsimd.c b/sysdeps/aarch64/fpu/atan2pif_advsimd.c new file mode 100644 index 0000000..f1f542b --- /dev/null +++ b/sysdeps/aarch64/fpu/atan2pif_advsimd.c @@ -0,0 +1,138 @@ +/* Single-Precision vector (Advanced SIMD) inverse tan2pi 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 c1, c3, c5, c7; + float c2, c4, c6, c8; + float32x4_t c0; + uint32x4_t comp_const; +} 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. */ + .c0 = V4 (0x1.45f306p-2), .c1 = V4 (-0x1.b2975ep-4), + .c2 = 0x1.0490e4p-4, .c3 = V4 (-0x1.70c272p-5), + .c4 = 0x1.0eef52p-5, .c5 = V4 (-0x1.6abbbap-6), + .c6 = 0x1.78157p-7, .c7 = V4 (-0x1.f0b406p-9), + .c8 = 0x1.2ae7fep-11, .comp_const = V4 (2 * 0x7f800000lu - 1), +}; + +#define SignMask v_u32 (0x80000000) +#define OneOverPi v_f32 (0x1.45f307p-2) + +/* 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 sign_xy, uint32x4_t cmp) +{ + /* Account for the sign of y. */ + ret = vreinterpretq_f32_u32 ( + veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy)); + + /* Since we have no scalar fallback for atan2pif, + we can instead make a call to atan2f and divide by pi. */ + ret = v_call2_f32 (atan2f, y, x, ret, cmp); + + /* Only divide the special cases by pi, and leave the rest unchanged. */ + return vbslq_f32 (cmp, vmulq_f32 (ret, OneOverPi), ret); +} + +/* Returns 1 if input is the bit representation of 0, infinity or nan. */ +static inline uint32x4_t +zeroinfnan (uint32x4_t i, const struct data *d) +{ + /* 2 * i - 1 >= 2 * 0x7f800000lu - 1. */ + return vcgeq_u32 (vsubq_u32 (vshlq_n_u32 (i, 1), v_u32 (1)), d->comp_const); +} + +/* Fast implementation of vector atan2f. Maximum observed error is 2.89 ULP: + _ZGVnN4vv_atan2pif (0x1.bd397p+54, 0x1.e79a4ap+54) got 0x1.e2678ep-3 + want 0x1.e26794p-3. */ +float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2pi) (float32x4_t y, + float32x4_t x) +{ + const struct data *d = 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, d), zeroinfnan (iy, d)); + + 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 evaluation of atanpif. */ + float32x4_t num = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay); + float32x4_t den = vbslq_f32 (pred_aygtax, ay, ax); + float32x4_t z = vdivq_f32 (num, den); + + /* Work out the correct shift for atan2pi: + -1.0 when x < 0 and ax < ay + -0.5 when x < 0 and ax > ay + 0 when x >= 0 and ax < ay + 0.5 when x >= 0 and ax > ay. */ + float32x4_t shift = vreinterpretq_f32_u32 ( + vandq_u32 (pred_xlt0, vreinterpretq_u32_f32 (v_f32 (-1.0f)))); + float32x4_t shift2 = vreinterpretq_f32_u32 ( + vandq_u32 (pred_aygtax, vreinterpretq_u32_f32 (v_f32 (0.5f)))); + shift = vaddq_f32 (shift, shift2); + + /* Calculate the polynomial approximation. */ + float32x4_t z2 = vmulq_f32 (z, z); + float32x4_t z3 = vmulq_f32 (z2, z); + float32x4_t z4 = vmulq_f32 (z2, z2); + float32x4_t z8 = vmulq_f32 (z4, z4); + + float32x4_t c2468 = vld1q_f32 (&d->c2); + + float32x4_t p12 = vfmaq_laneq_f32 (d->c1, z2, c2468, 0); + float32x4_t p34 = vfmaq_laneq_f32 (d->c3, z2, c2468, 1); + float32x4_t p56 = vfmaq_laneq_f32 (d->c5, z2, c2468, 2); + float32x4_t p78 = vfmaq_laneq_f32 (d->c7, z2, c2468, 3); + float32x4_t p14 = vfmaq_f32 (p12, z4, p34); + float32x4_t p58 = vfmaq_f32 (p56, z4, p78); + + float32x4_t poly = vfmaq_f32 (p14, z8, p58); + + /* y = shift + z * P(z^2). */ + float32x4_t ret = vfmaq_f32 (shift, z, d->c0); + ret = vfmaq_f32 (ret, z3, poly); + + if (__glibc_unlikely (v_any_u32 (special_cases))) + { + return special_case (y, x, ret, sign_xy, special_cases); + } + + /* Account for the sign of y. */ + return vreinterpretq_f32_u32 ( + veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy)); +} +libmvec_hidden_def (V_NAME_F2 (atan2pi)) +HALF_WIDTH_ALIAS_F2 (atan2pi) |