| /* |
| * Double-precision vector atan2(x) function. |
| * |
| * Copyright (c) 2021-2023, Arm Limited. |
| * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception |
| */ |
| |
| #include "v_math.h" |
| #include "pl_sig.h" |
| #include "pl_test.h" |
| |
| #if V_SUPPORTED |
| |
| #include "atan_common.h" |
| |
| #define PiOver2 v_f64 (0x1.921fb54442d18p+0) |
| #define SignMask v_u64 (0x8000000000000000) |
| |
| /* Special cases i.e. 0, infinity, NaN (fall back to scalar calls). */ |
| VPCS_ATTR |
| NOINLINE static v_f64_t |
| specialcase (v_f64_t y, v_f64_t x, v_f64_t ret, v_u64_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 v_u64_t |
| zeroinfnan (v_u64_t i) |
| { |
| return v_cond_u64 (2 * i - 1 >= v_u64 (2 * asuint64 (INFINITY) - 1)); |
| } |
| |
| /* Fast implementation of vector atan2. |
| Maximum observed error is 2.8 ulps: |
| v_atan2(0x1.9651a429a859ap+5, 0x1.953075f4ee26p+5) |
| got 0x1.92d628ab678ccp-1 |
| want 0x1.92d628ab678cfp-1. */ |
| VPCS_ATTR |
| v_f64_t V_NAME (atan2) (v_f64_t y, v_f64_t x) |
| { |
| v_u64_t ix = v_as_u64_f64 (x); |
| v_u64_t iy = v_as_u64_f64 (y); |
| |
| v_u64_t special_cases = zeroinfnan (ix) | zeroinfnan (iy); |
| |
| v_u64_t sign_x = ix & SignMask; |
| v_u64_t sign_y = iy & SignMask; |
| v_u64_t sign_xy = sign_x ^ sign_y; |
| |
| v_f64_t ax = v_abs_f64 (x); |
| v_f64_t ay = v_abs_f64 (y); |
| |
| v_u64_t pred_xlt0 = x < 0.0; |
| v_u64_t pred_aygtax = ay > ax; |
| |
| /* Set up z for call to atan. */ |
| v_f64_t n = v_sel_f64 (pred_aygtax, -ax, ay); |
| v_f64_t d = v_sel_f64 (pred_aygtax, ay, ax); |
| v_f64_t z = v_div_f64 (n, d); |
| |
| /* Work out the correct shift. */ |
| v_f64_t shift = v_sel_f64 (pred_xlt0, v_f64 (-2.0), v_f64 (0.0)); |
| shift = v_sel_f64 (pred_aygtax, shift + 1.0, shift); |
| shift *= PiOver2; |
| |
| v_f64_t ret = eval_poly (z, z, shift); |
| |
| /* Account for the sign of x and y. */ |
| ret = v_as_f64_u64 (v_as_u64_f64 (ret) ^ sign_xy); |
| |
| if (unlikely (v_any_u64 (special_cases))) |
| { |
| return specialcase (y, x, ret, special_cases); |
| } |
| |
| return ret; |
| } |
| VPCS_ALIAS |
| |
| /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ |
| PL_SIG (V, D, 2, atan2) |
| // TODO tighten this once __v_atan2 is fixed |
| PL_TEST_ULP (V_NAME (atan2), 2.9) |
| PL_TEST_INTERVAL (V_NAME (atan2), -10.0, 10.0, 50000) |
| PL_TEST_INTERVAL (V_NAME (atan2), -1.0, 1.0, 40000) |
| PL_TEST_INTERVAL (V_NAME (atan2), 0.0, 1.0, 40000) |
| PL_TEST_INTERVAL (V_NAME (atan2), 1.0, 100.0, 40000) |
| PL_TEST_INTERVAL (V_NAME (atan2), 1e6, 1e32, 40000) |
| #endif |