1 /* 2 * Double-precision vector atan(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 AbsMask (0x7fffffffffffffff) 19 20 /* Fast implementation of SVE atan. 21 Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using 22 z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed 23 error is 2.27 ulps: 24 __sv_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1 25 want 0x1.9225645bdd7c3p-1. */ 26 sv_f64_t 27 __sv_atan_x (sv_f64_t x, const svbool_t pg) 28 { 29 /* No need to trigger special case. Small cases, infs and nans 30 are supported by our approximation technique. */ 31 sv_u64_t ix = sv_as_u64_f64 (x); 32 sv_u64_t sign = svand_n_u64_x (pg, ix, ~AbsMask); 33 34 /* Argument reduction: 35 y := arctan(x) for x < 1 36 y := pi/2 + arctan(-1/x) for x > 1 37 Hence, use z=-1/a if x>=1, otherwise z=a. */ 38 svbool_t red = svacgt_n_f64 (pg, x, 1.0); 39 /* Avoid dependency in abs(x) in division (and comparison). */ 40 sv_f64_t z = svsel_f64 (red, svdiv_f64_x (pg, sv_f64 (-1.0), x), x); 41 /* Use absolute value only when needed (odd powers of z). */ 42 sv_f64_t az = svabs_f64_x (pg, z); 43 az = svneg_f64_m (az, red, az); 44 45 sv_f64_t y = __sv_atan_common (pg, red, z, az, PiOver2); 46 47 /* y = atan(x) if x>0, -atan(-x) otherwise. */ 48 y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign)); 49 50 return y; 51 } 52 53 PL_ALIAS (__sv_atan_x, _ZGVsMxv_atan) 54 55 PL_SIG (SV, D, 1, atan, -3.1, 3.1) 56 PL_TEST_ULP (__sv_atan, 1.78) 57 PL_TEST_INTERVAL (__sv_atan, -10.0, 10.0, 50000) 58 PL_TEST_INTERVAL (__sv_atan, -1.0, 1.0, 40000) 59 PL_TEST_INTERVAL (__sv_atan, 0.0, 1.0, 40000) 60 PL_TEST_INTERVAL (__sv_atan, 1.0, 100.0, 40000) 61 PL_TEST_INTERVAL (__sv_atan, 1e6, 1e32, 40000) 62 #endif 63