1 /*
2 * Single-precision acosh(x) function.
3 *
4 * Copyright (c) 2022-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "math_config.h"
9 #include "test_sig.h"
10 #include "test_defs.h"
11
12 #define Ln2 (0x1.62e4p-1f)
13 #define MinusZero 0x80000000
14 #define SquareLim 0x5f800000 /* asuint(0x1p64). */
15 #define Two 0x40000000
16
17 /* acoshf approximation using a variety of approaches on different intervals:
18
19 x >= 2^64: We cannot square x without overflow. For huge x, sqrt(x*x - 1) is
20 close enough to x that we can calculate the result by ln(2x) == ln(x) +
21 ln(2). The greatest error in the region is 0.94 ULP:
22 acoshf(0x1.15f706p+92) got 0x1.022e14p+6 want 0x1.022e16p+6.
23
24 x > 2: Calculate the result directly using definition of asinh(x) = ln(x +
25 sqrt(x*x - 1)). Greatest error in this region is 1.30 ULP:
26 acoshf(0x1.249d8p+1) got 0x1.77e1aep+0 want 0x1.77e1bp+0.
27
28 0 <= x <= 2: Calculate the result using log1p. For x < 1, acosh(x) is
29 undefined. For 1 <= x <= 2, the greatest error is 2.78 ULP:
30 acoshf(0x1.07887p+0) got 0x1.ef9e9cp-3 want 0x1.ef9ea2p-3. */
31 float
acoshf(float x)32 acoshf (float x)
33 {
34 uint32_t ix = asuint (x);
35
36 if (unlikely (ix >= MinusZero))
37 return __math_invalidf (x);
38
39 if (unlikely (ix >= SquareLim))
40 return logf (x) + Ln2;
41
42 if (ix > Two)
43 return logf (x + sqrtf (x * x - 1));
44
45 float xm1 = x - 1;
46 return log1pf (xm1 + sqrtf (2 * xm1 + xm1 * xm1));
47 }
48
49 TEST_SIG (S, F, 1, acosh, 1.0, 10.0)
50 TEST_ULP (acoshf, 2.30)
51 TEST_INTERVAL (acoshf, 0, 1, 100)
52 TEST_INTERVAL (acoshf, 1, 2, 10000)
53 TEST_INTERVAL (acoshf, 2, 0x1p64, 100000)
54 TEST_INTERVAL (acoshf, 0x1p64, inf, 100000)
55 TEST_INTERVAL (acoshf, -0, -inf, 10000)
56