1 /* 2 * Single-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_atanf_common.h" 15 16 #define PiOver2 sv_f32 (0x1.921fb6p+0f) 17 #define AbsMask (0x7fffffff) 18 19 /* Fast implementation of SVE atanf based on 20 atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using 21 z=-1/x and shift = pi/2. 22 Largest observed error is 2.9 ULP, close to +/-1.0: 23 __sv_atanf(0x1.0468f6p+0) got -0x1.967f06p-1 24 want -0x1.967fp-1. */ 25 sv_f32_t 26 __sv_atanf_x (sv_f32_t x, const svbool_t pg) 27 { 28 /* No need to trigger special case. Small cases, infs and nans 29 are supported by our approximation technique. */ 30 sv_u32_t ix = sv_as_u32_f32 (x); 31 sv_u32_t sign = svand_n_u32_x (pg, ix, ~AbsMask); 32 33 /* Argument reduction: 34 y := arctan(x) for x < 1 35 y := pi/2 + arctan(-1/x) for x > 1 36 Hence, use z=-1/a if x>=1, otherwise z=a. */ 37 svbool_t red = svacgt_n_f32 (pg, x, 1.0f); 38 /* Avoid dependency in abs(x) in division (and comparison). */ 39 sv_f32_t z = svsel_f32 (red, svdiv_f32_x (pg, sv_f32 (-1.0f), x), x); 40 /* Use absolute value only when needed (odd powers of z). */ 41 sv_f32_t az = svabs_f32_x (pg, z); 42 az = svneg_f32_m (az, red, az); 43 44 sv_f32_t y = __sv_atanf_common (pg, red, z, az, PiOver2); 45 46 /* y = atan(x) if x>0, -atan(-x) otherwise. */ 47 return sv_as_f32_u32 (sveor_u32_x (pg, sv_as_u32_f32 (y), sign)); 48 } 49 50 PL_ALIAS (__sv_atanf_x, _ZGVsMxv_atanf) 51 52 PL_SIG (SV, F, 1, atan, -3.1, 3.1) 53 PL_TEST_ULP (__sv_atanf, 2.9) 54 PL_TEST_INTERVAL (__sv_atanf, -10.0, 10.0, 50000) 55 PL_TEST_INTERVAL (__sv_atanf, -1.0, 1.0, 40000) 56 PL_TEST_INTERVAL (__sv_atanf, 0.0, 1.0, 40000) 57 PL_TEST_INTERVAL (__sv_atanf, 1.0, 100.0, 40000) 58 PL_TEST_INTERVAL (__sv_atanf, 1e6, 1e32, 40000) 59 #endif 60