1 /*
2 * Single-precision asinh(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 "poly_scalar_f32.h"
9 #include "math_config.h"
10 #include "pl_sig.h"
11 #include "pl_test.h"
12
13 #define AbsMask (0x7fffffff)
14 #define SqrtFltMax (0x1.749e96p+10f)
15 #define Ln2 (0x1.62e4p-1f)
16 #define One (0x3f8)
17 #define ExpM12 (0x398)
18
19 float
20 optr_aor_log_f32 (float);
21
22 /* asinhf approximation using a variety of approaches on different intervals:
23
24 |x| < 2^-12: Return x. Function is exactly rounded in this region.
25
26 |x| < 1.0: Use custom order-8 polynomial. The largest observed
27 error in this region is 1.3ulps:
28 asinhf(0x1.f0f74cp-1) got 0x1.b88de4p-1 want 0x1.b88de2p-1.
29
30 |x| <= SqrtFltMax: Calculate the result directly using the
31 definition of asinh(x) = ln(x + sqrt(x*x + 1)). The largest
32 observed error in this region is 1.99ulps.
33 asinhf(0x1.00e358p+0) got 0x1.c4849ep-1 want 0x1.c484a2p-1.
34
35 |x| > SqrtFltMax: We cannot square x without overflow at a low
36 cost. At very large x, asinh(x) ~= ln(2x). At huge x we cannot
37 even double x without overflow, so calculate this as ln(x) +
38 ln(2). This largest observed error in this region is 3.39ulps.
39 asinhf(0x1.749e9ep+10) got 0x1.fffff8p+2 want 0x1.fffffep+2. */
40 float
asinhf(float x)41 asinhf (float x)
42 {
43 uint32_t ix = asuint (x);
44 uint32_t ia = ix & AbsMask;
45 uint32_t ia12 = ia >> 20;
46 float ax = asfloat (ia);
47 uint32_t sign = ix & ~AbsMask;
48
49 if (unlikely (ia12 < ExpM12 || ia == 0x7f800000))
50 return x;
51
52 if (unlikely (ia12 >= 0x7f8))
53 return __math_invalidf (x);
54
55 if (ia12 < One)
56 {
57 float x2 = ax * ax;
58 float p = estrin_7_f32 (ax, x2, x2 * x2, __asinhf_data.coeffs);
59 float y = fmaf (x2, p, ax);
60 return asfloat (asuint (y) | sign);
61 }
62
63 if (unlikely (ax > SqrtFltMax))
64 {
65 return asfloat (asuint (optr_aor_log_f32 (ax) + Ln2) | sign);
66 }
67
68 return asfloat (asuint (optr_aor_log_f32 (ax + sqrtf (ax * ax + 1))) | sign);
69 }
70
71 PL_SIG (S, F, 1, asinh, -10.0, 10.0)
72 PL_TEST_ULP (asinhf, 2.9)
73 PL_TEST_INTERVAL (asinhf, 0, 0x1p-12, 5000)
74 PL_TEST_INTERVAL (asinhf, 0x1p-12, 1.0, 50000)
75 PL_TEST_INTERVAL (asinhf, 1.0, 0x1p11, 50000)
76 PL_TEST_INTERVAL (asinhf, 0x1p11, 0x1p127, 20000)
77