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 "v_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 #if V_SUPPORTED 13 14 #include "atanf_common.h" 15 16 #define PiOver2 v_f32 (0x1.921fb6p+0f) 17 #define AbsMask v_u32 (0x7fffffff) 18 #define TinyBound 0x308 /* top12(asuint(0x1p-30)). */ 19 #define BigBound 0x4e8 /* top12(asuint(0x1p30)). */ 20 21 #if WANT_SIMD_EXCEPT 22 static NOINLINE v_f32_t 23 specialcase (v_f32_t x, v_f32_t y, v_u32_t special) 24 { 25 return v_call_f32 (atanf, x, y, special); 26 } 27 #endif 28 29 /* Fast implementation of vector atanf based on 30 atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] 31 using z=-1/x and shift = pi/2. Maximum observed error is 2.9ulps: 32 v_atanf(0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1. */ 33 VPCS_ATTR 34 v_f32_t V_NAME (atanf) (v_f32_t x) 35 { 36 /* Small cases, infs and nans are supported by our approximation technique, 37 but do not set fenv flags correctly. Only trigger special case if we need 38 fenv. */ 39 v_u32_t ix = v_as_u32_f32 (x); 40 v_u32_t sign = ix & ~AbsMask; 41 42 #if WANT_SIMD_EXCEPT 43 v_u32_t ia12 = (ix >> 20) & 0x7ff; 44 v_u32_t special = v_cond_u32 (ia12 - TinyBound > BigBound - TinyBound); 45 /* If any lane is special, fall back to the scalar routine for all lanes. */ 46 if (unlikely (v_any_u32 (special))) 47 return specialcase (x, x, v_u32 (-1)); 48 #endif 49 50 /* Argument reduction: 51 y := arctan(x) for x < 1 52 y := pi/2 + arctan(-1/x) for x > 1 53 Hence, use z=-1/a if x>=1, otherwise z=a. */ 54 v_u32_t red = v_cagt_f32 (x, v_f32 (1.0)); 55 /* Avoid dependency in abs(x) in division (and comparison). */ 56 v_f32_t z = v_sel_f32 (red, v_div_f32 (v_f32 (-1.0f), x), x); 57 v_f32_t shift = v_sel_f32 (red, PiOver2, v_f32 (0.0f)); 58 /* Use absolute value only when needed (odd powers of z). */ 59 v_f32_t az = v_abs_f32 (z); 60 az = v_sel_f32 (red, -az, az); 61 62 /* Calculate the polynomial approximation. */ 63 v_f32_t y = eval_poly (z, az, shift); 64 65 /* y = atan(x) if x>0, -atan(-x) otherwise. */ 66 y = v_as_f32_u32 (v_as_u32_f32 (y) ^ sign); 67 68 return y; 69 } 70 VPCS_ALIAS 71 72 PL_SIG (V, F, 1, atan, -10.0, 10.0) 73 PL_TEST_ULP (V_NAME (atanf), 2.5) 74 PL_TEST_EXPECT_FENV (V_NAME (atanf), WANT_SIMD_EXCEPT) 75 PL_TEST_INTERVAL (V_NAME (atanf), 0, 0x1p-30, 5000) 76 PL_TEST_INTERVAL (V_NAME (atanf), -0, -0x1p-30, 5000) 77 PL_TEST_INTERVAL (V_NAME (atanf), 0x1p-30, 1, 40000) 78 PL_TEST_INTERVAL (V_NAME (atanf), -0x1p-30, -1, 40000) 79 PL_TEST_INTERVAL (V_NAME (atanf), 1, 0x1p30, 40000) 80 PL_TEST_INTERVAL (V_NAME (atanf), -1, -0x1p30, 40000) 81 PL_TEST_INTERVAL (V_NAME (atanf), 0x1p30, inf, 1000) 82 PL_TEST_INTERVAL (V_NAME (atanf), -0x1p30, -inf, 1000) 83 #endif 84