1 /*
2 * Single-precision atan(x) function.
3 *
4 * Copyright (c) 2022-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "atanf_common.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #define PiOver2 0x1.921fb6p+0f
13 #define AbsMask 0x7fffffff
14 #define TinyBound 0x30800000 /* asuint(0x1p-30). */
15 #define BigBound 0x4e800000 /* asuint(0x1p30). */
16 #define One 0x3f800000
17
18 /* Approximation of single-precision atan(x) based on
19 atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1]
20 using z=-1/x and shift = pi/2.
21 Maximum error is 2.88 ulps:
22 atanf(0x1.0565ccp+0) got 0x1.97771p-1
23 want 0x1.97770ap-1. */
24 float
atanf(float x)25 atanf (float x)
26 {
27 uint32_t ix = asuint (x);
28 uint32_t sign = ix & ~AbsMask;
29 uint32_t ia = ix & AbsMask;
30
31 if (unlikely (ia < TinyBound))
32 /* Avoid underflow by returning x. */
33 return x;
34
35 if (unlikely (ia > BigBound))
36 {
37 if (ia > 0x7f800000)
38 /* Propagate NaN. */
39 return __math_invalidf (x);
40 /* atan(x) rounds to PiOver2 for large x. */
41 return asfloat (asuint (PiOver2) ^ sign);
42 }
43
44 float z, az, shift;
45 if (ia > One)
46 {
47 /* For x > 1, use atan(x) = pi / 2 + atan(-1 / x). */
48 z = -1.0f / x;
49 shift = PiOver2;
50 /* Use absolute value only when needed (odd powers of z). */
51 az = -fabsf (z);
52 }
53 else
54 {
55 /* For x < 1, approximate atan(x) directly. */
56 z = x;
57 az = asfloat (ia);
58 shift = 0;
59 }
60
61 /* Calculate polynomial, shift + z + z^3 * P(z^2). */
62 float y = eval_poly (z, az, shift);
63 /* Copy sign. */
64 return asfloat (asuint (y) ^ sign);
65 }
66
67 PL_SIG (S, F, 1, atan, -10.0, 10.0)
68 PL_TEST_ULP (atanf, 2.38)
69 PL_TEST_SYM_INTERVAL (atanf, 0, 0x1p-30, 5000)
70 PL_TEST_SYM_INTERVAL (atanf, 0x1p-30, 1, 40000)
71 PL_TEST_SYM_INTERVAL (atanf, 1, 0x1p30, 40000)
72 PL_TEST_SYM_INTERVAL (atanf, 0x1p30, inf, 1000)
73