1 /*
2 * Double-precision cosh(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 #include "exp_inline.h"
12
13 #define AbsMask 0x7fffffffffffffff
14 #define SpecialBound \
15 0x40861da04cbafe44 /* 0x1.61da04cbafe44p+9, above which exp overflows. */
16
17 static double
specialcase(double x,uint64_t iax)18 specialcase (double x, uint64_t iax)
19 {
20 if (iax == 0x7ff0000000000000)
21 return INFINITY;
22 if (iax > 0x7ff0000000000000)
23 return __math_invalid (x);
24 /* exp overflows above SpecialBound. At this magnitude cosh(x) is dominated
25 by exp(x), so we can approximate cosh(x) by (exp(|x|/2)) ^ 2 / 2. */
26 double t = exp_inline (asdouble (iax) / 2, 0);
27 return (0.5 * t) * t;
28 }
29
30 /* Approximation for double-precision cosh(x).
31 cosh(x) = (exp(x) + exp(-x)) / 2.
32 The greatest observed error is in the special region, 1.93 ULP:
33 cosh(0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021
34 want 0x1.fdf28623ef923p+1021.
35
36 The greatest observed error in the non-special region is 1.03 ULP:
37 cosh(0x1.502cd8e56ab3bp+0) got 0x1.fe54962842d0ep+0
38 want 0x1.fe54962842d0fp+0. */
39 double
cosh(double x)40 cosh (double x)
41 {
42 uint64_t ix = asuint64 (x);
43 uint64_t iax = ix & AbsMask;
44
45 /* exp overflows a little bit before cosh, so use special-case handler for
46 the gap, as well as special values. */
47 if (unlikely (iax >= SpecialBound))
48 return specialcase (x, iax);
49
50 double ax = asdouble (iax);
51 /* Use double-precision exp helper to calculate exp(x), then:
52 cosh(x) = exp(|x|) / 2 + 1 / (exp(|x| * 2). */
53 double t = exp_inline (ax, 0);
54 return 0.5 * t + 0.5 / t;
55 }
56
57 TEST_SIG (S, D, 1, cosh, -10.0, 10.0)
58 TEST_ULP (cosh, 1.43)
59 TEST_SYM_INTERVAL (cosh, 0, 0x1.61da04cbafe44p+9, 100000)
60 TEST_SYM_INTERVAL (cosh, 0x1.61da04cbafe44p+9, 0x1p10, 1000)
61 TEST_SYM_INTERVAL (cosh, 0x1p10, inf, 100)
62