diff options
Diffstat (limited to 'pl/math/v_atan_2u5.c')
-rw-r--r-- | pl/math/v_atan_2u5.c | 74 |
1 files changed, 74 insertions, 0 deletions
diff --git a/pl/math/v_atan_2u5.c b/pl/math/v_atan_2u5.c new file mode 100644 index 0000000..0f3c2cc --- /dev/null +++ b/pl/math/v_atan_2u5.c @@ -0,0 +1,74 @@ +/* + * Double-precision vector atan(x) function. + * + * Copyright (c) 2021-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "v_math.h" +#include "pl_sig.h" +#include "pl_test.h" + +#if V_SUPPORTED + +#include "atan_common.h" + +#define PiOver2 v_f64 (0x1.921fb54442d18p+0) +#define AbsMask v_u64 (0x7fffffffffffffff) +#define TinyBound 0x3e1 /* top12(asuint64(0x1p-30)). */ +#define BigBound 0x434 /* top12(asuint64(0x1p53)). */ + +/* Fast implementation of vector atan. + 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 2.27 ulps: + __v_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1 + want 0x1.9225645bdd7c3p-1. */ +VPCS_ATTR +v_f64_t V_NAME (atan) (v_f64_t x) +{ + /* Small cases, infs and nans are supported by our approximation technique, + but do not set fenv flags correctly. Only trigger special case if we need + fenv. */ + v_u64_t ix = v_as_u64_f64 (x); + v_u64_t sign = ix & ~AbsMask; + +#if WANT_SIMD_EXCEPT + v_u64_t ia12 = (ix >> 52) & 0x7ff; + v_u64_t special = v_cond_u64 (ia12 - TinyBound > BigBound - TinyBound); + /* If any lane is special, fall back to the scalar routine for all lanes. */ + if (unlikely (v_any_u64 (special))) + return v_call_f64 (atan, x, v_f64 (0), v_u64 (-1)); +#endif + + /* 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_u64_t red = v_cagt_f64 (x, v_f64 (1.0)); + /* Avoid dependency in abs(x) in division (and comparison). */ + v_f64_t z = v_sel_f64 (red, v_div_f64 (v_f64 (-1.0), x), x); + v_f64_t shift = v_sel_f64 (red, PiOver2, v_f64 (0.0)); + /* Use absolute value only when needed (odd powers of z). */ + v_f64_t az = v_abs_f64 (z); + az = v_sel_f64 (red, -az, az); + + /* Calculate the polynomial approximation. */ + v_f64_t y = eval_poly (z, az, shift); + + /* y = atan(x) if x>0, -atan(-x) otherwise. */ + y = v_as_f64_u64 (v_as_u64_f64 (y) ^ sign); + return y; +} +VPCS_ALIAS + +PL_SIG (V, D, 1, atan, -10.0, 10.0) +PL_TEST_ULP (V_NAME (atan), 1.78) +PL_TEST_EXPECT_FENV (V_NAME (atan), WANT_SIMD_EXCEPT) +PL_TEST_INTERVAL (V_NAME (atan), 0, 0x1p-30, 10000) +PL_TEST_INTERVAL (V_NAME (atan), -0, -0x1p-30, 1000) +PL_TEST_INTERVAL (V_NAME (atan), 0x1p-30, 0x1p53, 900000) +PL_TEST_INTERVAL (V_NAME (atan), -0x1p-30, -0x1p53, 90000) +PL_TEST_INTERVAL (V_NAME (atan), 0x1p53, inf, 10000) +PL_TEST_INTERVAL (V_NAME (atan), -0x1p53, -inf, 1000) + +#endif |