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 "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 #if SV_SUPPORTED 13 14 #include "sv_atan_common.h" 15 16 /* Useful constants. */ 17 #define PiOver2 sv_f64 (0x1.921fb54442d18p+0) 18 #define SignMask sv_u64 (0x8000000000000000) 19 20 /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */ 21 __attribute__ ((noinline)) static sv_f64_t 22 specialcase (sv_f64_t y, sv_f64_t x, sv_f64_t ret, const svbool_t cmp) 23 { 24 return sv_call2_f64 (atan2, y, x, ret, cmp); 25 } 26 27 /* Returns a predicate indicating true if the input is the bit representation of 28 0, infinity or nan. */ 29 static inline svbool_t 30 zeroinfnan (sv_u64_t i, const svbool_t pg) 31 { 32 return svcmpge_u64 (pg, svsub_n_u64_x (pg, svlsl_n_u64_x (pg, i, 1), 1), 33 sv_u64 (2 * asuint64 (INFINITY) - 1)); 34 } 35 36 /* Fast implementation of SVE atan2. Errors are greatest when y and 37 x are reasonably close together. The greatest observed error is 2.28 ULP: 38 sv_atan2(-0x1.5915b1498e82fp+732, 0x1.54d11ef838826p+732) 39 got -0x1.954f42f1fa841p-1 want -0x1.954f42f1fa843p-1. */ 40 sv_f64_t 41 __sv_atan2_x (sv_f64_t y, sv_f64_t x, const svbool_t pg) 42 { 43 sv_u64_t ix = sv_as_u64_f64 (x); 44 sv_u64_t iy = sv_as_u64_f64 (y); 45 46 svbool_t cmp_x = zeroinfnan (ix, pg); 47 svbool_t cmp_y = zeroinfnan (iy, pg); 48 svbool_t cmp_xy = svorr_b_z (pg, cmp_x, cmp_y); 49 50 sv_u64_t sign_x = svand_u64_x (pg, ix, SignMask); 51 sv_u64_t sign_y = svand_u64_x (pg, iy, SignMask); 52 sv_u64_t sign_xy = sveor_u64_x (pg, sign_x, sign_y); 53 54 sv_f64_t ax = svabs_f64_x (pg, x); 55 sv_f64_t ay = svabs_f64_x (pg, y); 56 57 svbool_t pred_xlt0 = svcmplt_f64 (pg, x, sv_f64 (0.0)); 58 svbool_t pred_aygtax = svcmpgt_f64 (pg, ay, ax); 59 60 /* Set up z for call to atan. */ 61 sv_f64_t n = svsel_f64 (pred_aygtax, svneg_f64_x (pg, ax), ay); 62 sv_f64_t d = svsel_f64 (pred_aygtax, ay, ax); 63 sv_f64_t z = svdiv_f64_x (pg, n, d); 64 65 /* Work out the correct shift. */ 66 sv_f64_t shift = svsel_f64 (pred_xlt0, sv_f64 (-2.0), sv_f64 (0.0)); 67 shift = svsel_f64 (pred_aygtax, svadd_n_f64_x (pg, shift, 1.0), shift); 68 shift = svmul_f64_x (pg, shift, PiOver2); 69 70 sv_f64_t ret = __sv_atan_common (pg, pg, z, z, shift); 71 72 /* Account for the sign of x and y. */ 73 ret = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (ret), sign_xy)); 74 75 if (unlikely (svptest_any (pg, cmp_xy))) 76 { 77 return specialcase (y, x, ret, cmp_xy); 78 } 79 80 return ret; 81 } 82 83 PL_ALIAS (__sv_atan2_x, _ZGVsMxvv_atan2) 84 85 /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ 86 PL_SIG (SV, D, 2, atan2) 87 PL_TEST_ULP (__sv_atan2, 1.78) 88 PL_TEST_INTERVAL (__sv_atan2, -10.0, 10.0, 50000) 89 PL_TEST_INTERVAL (__sv_atan2, -1.0, 1.0, 40000) 90 PL_TEST_INTERVAL (__sv_atan2, 0.0, 1.0, 40000) 91 PL_TEST_INTERVAL (__sv_atan2, 1.0, 100.0, 40000) 92 PL_TEST_INTERVAL (__sv_atan2, 1e6, 1e32, 40000) 93 #endif 94