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
16double
17__exp_dd (double, double);
18
19static double
20specialcase (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.  */
41double
42cosh (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
59PL_SIG (S, D, 1, cosh, -10.0, 10.0)
60PL_TEST_ULP (cosh, 1.43)
61PL_TEST_SYM_INTERVAL (cosh, 0, 0x1.61da04cbafe44p+9, 100000)
62PL_TEST_SYM_INTERVAL (cosh, 0x1.61da04cbafe44p+9, 0x1p10, 1000)
63PL_TEST_SYM_INTERVAL (cosh, 0x1p10, inf, 100)
64