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Diffstat (limited to 'math/aarch64/advsimd/atan2f.c')
| -rw-r--r-- | math/aarch64/advsimd/atan2f.c | 127 |
1 files changed, 127 insertions, 0 deletions
diff --git a/math/aarch64/advsimd/atan2f.c b/math/aarch64/advsimd/atan2f.c new file mode 100644 index 000000000000..632014249ab0 --- /dev/null +++ b/math/aarch64/advsimd/atan2f.c @@ -0,0 +1,127 @@ +/* + * Single-precision vector atan2(x) function. + * + * Copyright (c) 2021-2024, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "v_math.h" +#include "test_sig.h" +#include "test_defs.h" + +static const struct data +{ + float32x4_t c0, pi_over_2, c4, c6, c2; + float c1, c3, c5, c7; + 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 (-0x1.55555p-2f), .c1 = 0x1.99935ep-3f, + .c2 = V4 (-0x1.24051ep-3f), .c3 = 0x1.bd7368p-4f, + .c4 = V4 (-0x1.491f0ep-4f), .c5 = 0x1.93a2c0p-5f, + .c6 = V4 (-0x1.4c3c60p-6f), .c7 = 0x1.01fd88p-8f, + .pi_over_2 = V4 (0x1.921fb6p+0f), .comp_const = V4 (2 * 0x7f800000lu - 1), +}; + +#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 sign_xy, uint32x4_t cmp) +{ + /* Account for the sign of y. */ + ret = vreinterpretq_f32_u32 ( + veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy)); + 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, const struct data *d) +{ + /* 2 * i - 1 >= 2 * 0x7f800000lu - 1. */ + return vcgeq_u32 (vsubq_u32 (vmulq_n_u32 (i, 2), v_u32 (1)), d->comp_const); +} + +/* 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 NOINLINE V_NAME_F2 (atan2) (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 call to atanf. */ + float32x4_t n = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay); + float32x4_t q = vbslq_f32 (pred_aygtax, ay, ax); + float32x4_t z = vdivq_f32 (n, q); + + /* 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, d->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 c1357 = vld1q_f32 (&d->c1); + float32x4_t p01 = vfmaq_laneq_f32 (d->c0, z2, c1357, 0); + float32x4_t p23 = vfmaq_laneq_f32 (d->c2, z2, c1357, 1); + float32x4_t p45 = vfmaq_laneq_f32 (d->c4, z2, c1357, 2); + float32x4_t p67 = vfmaq_laneq_f32 (d->c6, z2, c1357, 3); + float32x4_t p03 = vfmaq_f32 (p01, z4, p23); + float32x4_t p47 = vfmaq_f32 (p45, z4, p67); + + float32x4_t ret = vfmaq_f32 (p03, z4, vmulq_f32 (z4, p47)); + + /* y = shift + z * P(z^2). */ + ret = vaddq_f32 (vfmaq_f32 (z, ret, vmulq_f32 (z2, z)), shift); + + if (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)); +} + +HALF_WIDTH_ALIAS_F2 (atan2) + +/* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ +TEST_SIG (V, F, 2, atan2) +TEST_DISABLE_FENV (V_NAME_F2 (atan2)) +TEST_ULP (V_NAME_F2 (atan2), 2.46) +TEST_INTERVAL (V_NAME_F2 (atan2), -10.0, 10.0, 50000) +TEST_INTERVAL (V_NAME_F2 (atan2), -1.0, 1.0, 40000) +TEST_INTERVAL (V_NAME_F2 (atan2), 0.0, 1.0, 40000) +TEST_INTERVAL (V_NAME_F2 (atan2), 1.0, 100.0, 40000) +TEST_INTERVAL (V_NAME_F2 (atan2), 1e6, 1e32, 40000) |