| /* |
| * Single-precision vector atan(x) function. |
| * |
| * Copyright (c) 2021-2022, Arm Limited. |
| * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception |
| */ |
| |
| #include "v_math.h" |
| #if V_SUPPORTED |
| |
| #include "atanf_common.h" |
| |
| #define PiOver2 v_f32 (0x1.921fb6p+0f) |
| #define AbsMask v_u32 (0x7fffffff) |
| |
| /* Fast implementation of vector atanf based on |
| atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] |
| using z=-1/x and shift = pi/2. Maximum observed error is 2.9ulps: |
| v_atanf(0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1. */ |
| VPCS_ATTR |
| v_f32_t V_NAME (atanf) (v_f32_t x) |
| { |
| /* No need to trigger special case. Small cases, infs and nans |
| are supported by our approximation technique. */ |
| v_u32_t ix = v_as_u32_f32 (x); |
| v_u32_t sign = ix & ~AbsMask; |
| |
| /* Argument reduction: |
| y := arctan(x) for x < 1 |
| y := pi/2 + arctan(-1/x) for x > 1 |
| Hence, use z=-1/a if x>=1, otherwise z=a. */ |
| v_u32_t red = v_cagt_f32 (x, v_f32 (1.0)); |
| /* Avoid dependency in abs(x) in division (and comparison). */ |
| v_f32_t z = v_sel_f32 (red, v_div_f32 (v_f32 (-1.0f), x), x); |
| v_f32_t shift = v_sel_f32 (red, PiOver2, v_f32 (0.0f)); |
| /* Use absolute value only when needed (odd powers of z). */ |
| v_f32_t az = v_abs_f32 (z); |
| az = v_sel_f32 (red, -az, az); |
| |
| /* Calculate the polynomial approximation. */ |
| v_f32_t y = eval_poly (z, az, shift); |
| |
| /* y = atan(x) if x>0, -atan(-x) otherwise. */ |
| y = v_as_f32_u32 (v_as_u32_f32 (y) ^ sign); |
| |
| return y; |
| } |
| VPCS_ALIAS |
| #endif |