1 /*
2 * Double-precision cosh(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 "math_config.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #define AbsMask 0x7fffffffffffffff
13 #define SpecialBound \
14 0x40861da04cbafe44 /* 0x1.61da04cbafe44p+9, above which exp overflows. */
15
16 double
17 __exp_dd (double, double);
18
19 static double
specialcase(double x,uint64_t iax)20 specialcase (double x, uint64_t iax)
21 {
22 if (iax == 0x7ff0000000000000)
23 return INFINITY;
24 if (iax > 0x7ff0000000000000)
25 return __math_invalid (x);
26 /* exp overflows above SpecialBound. At this magnitude cosh(x) is dominated by
27 exp(x), so we can approximate cosh(x) by (exp(|x|/2)) ^ 2 / 2. */
28 double t = __exp_dd (asdouble (iax) / 2, 0);
29 return (0.5 * t) * t;
30 }
31
32 /* Approximation for double-precision cosh(x).
33 cosh(x) = (exp(x) + exp(-x)) / 2.
34 The greatest observed error is in the special region, 1.93 ULP:
35 cosh(0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021
36 want 0x1.fdf28623ef923p+1021.
37
38 The greatest observed error in the non-special region is 1.03 ULP:
39 cosh(0x1.502cd8e56ab3bp+0) got 0x1.fe54962842d0ep+0
40 want 0x1.fe54962842d0fp+0. */
41 double
cosh(double x)42 cosh (double x)
43 {
44 uint64_t ix = asuint64 (x);
45 uint64_t iax = ix & AbsMask;
46
47 /* exp overflows a little bit before cosh, so use special-case handler for the
48 gap, as well as special values. */
49 if (unlikely (iax >= SpecialBound))
50 return specialcase (x, iax);
51
52 double ax = asdouble (iax);
53 /* Use double-precision exp helper to calculate exp(x), then:
54 cosh(x) = exp(|x|) / 2 + 1 / (exp(|x| * 2). */
55 double t = __exp_dd (ax, 0);
56 return 0.5 * t + 0.5 / t;
57 }
58
59 PL_SIG (S, D, 1, cosh, -10.0, 10.0)
60 PL_TEST_ULP (cosh, 1.43)
61 PL_TEST_SYM_INTERVAL (cosh, 0, 0x1.61da04cbafe44p+9, 100000)
62 PL_TEST_SYM_INTERVAL (cosh, 0x1.61da04cbafe44p+9, 0x1p10, 1000)
63 PL_TEST_SYM_INTERVAL (cosh, 0x1p10, inf, 100)
64