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Diffstat (limited to 'pl/math/sv_atan_2u5.c')
-rw-r--r-- | pl/math/sv_atan_2u5.c | 62 |
1 files changed, 62 insertions, 0 deletions
diff --git a/pl/math/sv_atan_2u5.c b/pl/math/sv_atan_2u5.c new file mode 100644 index 0000000..02ac331 --- /dev/null +++ b/pl/math/sv_atan_2u5.c @@ -0,0 +1,62 @@ +/* + * Double-precision vector atan(x) function. + * + * Copyright (c) 2021-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "pl_sig.h" +#include "pl_test.h" + +#if SV_SUPPORTED + +#include "sv_atan_common.h" + +/* Useful constants. */ +#define PiOver2 sv_f64 (0x1.921fb54442d18p+0) +#define AbsMask (0x7fffffffffffffff) + +/* Fast implementation of SVE 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. Largest errors are close to 1. The maximum observed + error is 2.27 ulps: + __sv_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1 + want 0x1.9225645bdd7c3p-1. */ +sv_f64_t +__sv_atan_x (sv_f64_t x, const svbool_t pg) +{ + /* No need to trigger special case. Small cases, infs and nans + are supported by our approximation technique. */ + sv_u64_t ix = sv_as_u64_f64 (x); + sv_u64_t sign = svand_n_u64_x (pg, 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. */ + svbool_t red = svacgt_n_f64 (pg, x, 1.0); + /* Avoid dependency in abs(x) in division (and comparison). */ + sv_f64_t z = svsel_f64 (red, svdiv_f64_x (pg, sv_f64 (-1.0), x), x); + /* Use absolute value only when needed (odd powers of z). */ + sv_f64_t az = svabs_f64_x (pg, z); + az = svneg_f64_m (az, red, az); + + sv_f64_t y = __sv_atan_common (pg, red, z, az, PiOver2); + + /* y = atan(x) if x>0, -atan(-x) otherwise. */ + y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign)); + + return y; +} + +PL_ALIAS (__sv_atan_x, _ZGVsMxv_atan) + +PL_SIG (SV, D, 1, atan, -3.1, 3.1) +PL_TEST_ULP (__sv_atan, 1.78) +PL_TEST_INTERVAL (__sv_atan, -10.0, 10.0, 50000) +PL_TEST_INTERVAL (__sv_atan, -1.0, 1.0, 40000) +PL_TEST_INTERVAL (__sv_atan, 0.0, 1.0, 40000) +PL_TEST_INTERVAL (__sv_atan, 1.0, 100.0, 40000) +PL_TEST_INTERVAL (__sv_atan, 1e6, 1e32, 40000) +#endif |