1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
|
/*
* Single-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 "atanf_common.h"
#define PiOver2 v_f32 (0x1.921fb6p+0f)
#define AbsMask v_u32 (0x7fffffff)
#define TinyBound 0x308 /* top12(asuint(0x1p-30)). */
#define BigBound 0x4e8 /* top12(asuint(0x1p30)). */
#if WANT_SIMD_EXCEPT
static NOINLINE v_f32_t
specialcase (v_f32_t x, v_f32_t y, v_u32_t special)
{
return v_call_f32 (atanf, x, y, special);
}
#endif
/* 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)
{
/* 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_u32_t ix = v_as_u32_f32 (x);
v_u32_t sign = ix & ~AbsMask;
#if WANT_SIMD_EXCEPT
v_u32_t ia12 = (ix >> 20) & 0x7ff;
v_u32_t special = v_cond_u32 (ia12 - TinyBound > BigBound - TinyBound);
/* If any lane is special, fall back to the scalar routine for all lanes. */
if (unlikely (v_any_u32 (special)))
return specialcase (x, x, v_u32 (-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_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
PL_SIG (V, F, 1, atan, -10.0, 10.0)
PL_TEST_ULP (V_NAME (atanf), 2.5)
PL_TEST_EXPECT_FENV (V_NAME (atanf), WANT_SIMD_EXCEPT)
PL_TEST_INTERVAL (V_NAME (atanf), 0, 0x1p-30, 5000)
PL_TEST_INTERVAL (V_NAME (atanf), -0, -0x1p-30, 5000)
PL_TEST_INTERVAL (V_NAME (atanf), 0x1p-30, 1, 40000)
PL_TEST_INTERVAL (V_NAME (atanf), -0x1p-30, -1, 40000)
PL_TEST_INTERVAL (V_NAME (atanf), 1, 0x1p30, 40000)
PL_TEST_INTERVAL (V_NAME (atanf), -1, -0x1p30, 40000)
PL_TEST_INTERVAL (V_NAME (atanf), 0x1p30, inf, 1000)
PL_TEST_INTERVAL (V_NAME (atanf), -0x1p30, -inf, 1000)
#endif
|
