1 /* 2 * Double-precision vector atan2(x) function. 3 * 4 * Copyright (c) 2021-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 #if V_SUPPORTED 13 14 #include "atan_common.h" 15 16 #define PiOver2 v_f64 (0x1.921fb54442d18p+0) 17 #define SignMask v_u64 (0x8000000000000000) 18 19 /* Special cases i.e. 0, infinity, NaN (fall back to scalar calls). */ 20 VPCS_ATTR 21 NOINLINE static v_f64_t 22 specialcase (v_f64_t y, v_f64_t x, v_f64_t ret, v_u64_t cmp) 23 { 24 return v_call2_f64 (atan2, y, x, ret, cmp); 25 } 26 27 /* Returns 1 if input is the bit representation of 0, infinity or nan. */ 28 static inline v_u64_t 29 zeroinfnan (v_u64_t i) 30 { 31 return v_cond_u64 (2 * i - 1 >= v_u64 (2 * asuint64 (INFINITY) - 1)); 32 } 33 34 /* Fast implementation of vector atan2. 35 Maximum observed error is 2.8 ulps: 36 v_atan2(0x1.9651a429a859ap+5, 0x1.953075f4ee26p+5) 37 got 0x1.92d628ab678ccp-1 38 want 0x1.92d628ab678cfp-1. */ 39 VPCS_ATTR 40 v_f64_t V_NAME (atan2) (v_f64_t y, v_f64_t x) 41 { 42 v_u64_t ix = v_as_u64_f64 (x); 43 v_u64_t iy = v_as_u64_f64 (y); 44 45 v_u64_t special_cases = zeroinfnan (ix) | zeroinfnan (iy); 46 47 v_u64_t sign_x = ix & SignMask; 48 v_u64_t sign_y = iy & SignMask; 49 v_u64_t sign_xy = sign_x ^ sign_y; 50 51 v_f64_t ax = v_abs_f64 (x); 52 v_f64_t ay = v_abs_f64 (y); 53 54 v_u64_t pred_xlt0 = x < 0.0; 55 v_u64_t pred_aygtax = ay > ax; 56 57 /* Set up z for call to atan. */ 58 v_f64_t n = v_sel_f64 (pred_aygtax, -ax, ay); 59 v_f64_t d = v_sel_f64 (pred_aygtax, ay, ax); 60 v_f64_t z = v_div_f64 (n, d); 61 62 /* Work out the correct shift. */ 63 v_f64_t shift = v_sel_f64 (pred_xlt0, v_f64 (-2.0), v_f64 (0.0)); 64 shift = v_sel_f64 (pred_aygtax, shift + 1.0, shift); 65 shift *= PiOver2; 66 67 v_f64_t ret = eval_poly (z, z, shift); 68 69 /* Account for the sign of x and y. */ 70 ret = v_as_f64_u64 (v_as_u64_f64 (ret) ^ sign_xy); 71 72 if (unlikely (v_any_u64 (special_cases))) 73 { 74 return specialcase (y, x, ret, special_cases); 75 } 76 77 return ret; 78 } 79 VPCS_ALIAS 80 81 /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ 82 PL_SIG (V, D, 2, atan2) 83 // TODO tighten this once __v_atan2 is fixed 84 PL_TEST_ULP (V_NAME (atan2), 2.9) 85 PL_TEST_INTERVAL (V_NAME (atan2), -10.0, 10.0, 50000) 86 PL_TEST_INTERVAL (V_NAME (atan2), -1.0, 1.0, 40000) 87 PL_TEST_INTERVAL (V_NAME (atan2), 0.0, 1.0, 40000) 88 PL_TEST_INTERVAL (V_NAME (atan2), 1.0, 100.0, 40000) 89 PL_TEST_INTERVAL (V_NAME (atan2), 1e6, 1e32, 40000) 90 #endif 91