75 lines
2.5 KiB
C
75 lines
2.5 KiB
C
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/*
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* Double-precision vector atan(x) function.
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*
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* Copyright (c) 2021-2023, Arm Limited.
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* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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*/
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#include "v_math.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#if V_SUPPORTED
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#include "atan_common.h"
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#define PiOver2 v_f64 (0x1.921fb54442d18p+0)
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#define AbsMask v_u64 (0x7fffffffffffffff)
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#define TinyBound 0x3e1 /* top12(asuint64(0x1p-30)). */
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#define BigBound 0x434 /* top12(asuint64(0x1p53)). */
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/* Fast implementation of vector atan.
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Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
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z=1/x and shift = pi/2. Maximum observed error is 2.27 ulps:
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__v_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
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want 0x1.9225645bdd7c3p-1. */
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VPCS_ATTR
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v_f64_t V_NAME (atan) (v_f64_t x)
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{
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/* Small cases, infs and nans are supported by our approximation technique,
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but do not set fenv flags correctly. Only trigger special case if we need
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fenv. */
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v_u64_t ix = v_as_u64_f64 (x);
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v_u64_t sign = ix & ~AbsMask;
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#if WANT_SIMD_EXCEPT
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v_u64_t ia12 = (ix >> 52) & 0x7ff;
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v_u64_t special = v_cond_u64 (ia12 - TinyBound > BigBound - TinyBound);
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/* If any lane is special, fall back to the scalar routine for all lanes. */
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if (unlikely (v_any_u64 (special)))
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return v_call_f64 (atan, x, v_f64 (0), v_u64 (-1));
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#endif
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/* Argument reduction:
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y := arctan(x) for x < 1
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y := pi/2 + arctan(-1/x) for x > 1
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Hence, use z=-1/a if x>=1, otherwise z=a. */
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v_u64_t red = v_cagt_f64 (x, v_f64 (1.0));
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/* Avoid dependency in abs(x) in division (and comparison). */
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v_f64_t z = v_sel_f64 (red, v_div_f64 (v_f64 (-1.0), x), x);
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v_f64_t shift = v_sel_f64 (red, PiOver2, v_f64 (0.0));
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/* Use absolute value only when needed (odd powers of z). */
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v_f64_t az = v_abs_f64 (z);
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az = v_sel_f64 (red, -az, az);
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/* Calculate the polynomial approximation. */
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v_f64_t y = eval_poly (z, az, shift);
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/* y = atan(x) if x>0, -atan(-x) otherwise. */
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y = v_as_f64_u64 (v_as_u64_f64 (y) ^ sign);
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return y;
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}
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VPCS_ALIAS
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PL_SIG (V, D, 1, atan, -10.0, 10.0)
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PL_TEST_ULP (V_NAME (atan), 1.78)
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PL_TEST_EXPECT_FENV (V_NAME (atan), WANT_SIMD_EXCEPT)
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PL_TEST_INTERVAL (V_NAME (atan), 0, 0x1p-30, 10000)
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PL_TEST_INTERVAL (V_NAME (atan), -0, -0x1p-30, 1000)
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PL_TEST_INTERVAL (V_NAME (atan), 0x1p-30, 0x1p53, 900000)
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PL_TEST_INTERVAL (V_NAME (atan), -0x1p-30, -0x1p53, 90000)
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PL_TEST_INTERVAL (V_NAME (atan), 0x1p53, inf, 10000)
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PL_TEST_INTERVAL (V_NAME (atan), -0x1p53, -inf, 1000)
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#endif
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