1/*
2 * Double-precision tanh(x) function.
3 *
4 * Copyright (c) 2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7#include "math_config.h"
8#include "poly_scalar_f64.h"
9#include "pl_sig.h"
10#include "pl_test.h"
11
12#define AbsMask 0x7fffffffffffffff
13#define InvLn2 0x1.71547652b82fep0
14#define Ln2hi 0x1.62e42fefa39efp-1
15#define Ln2lo 0x1.abc9e3b39803fp-56
16#define Shift 0x1.8p52
17
18#define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4).  */
19#define TinyBound 0x3e40000000000000   /* asuint64 (0x1p-27).  */
20#define One 0x3ff0000000000000
21
22static inline double
23expm1_inline (double x)
24{
25  /* Helper routine for calculating exp(x) - 1. Copied from expm1_2u5.c, with
26     several simplifications:
27     - No special-case handling for tiny or special values.
28     - Simpler combination of p and t in final stage of the algorithm.
29     - Use shift-and-add instead of ldexp to calculate t.  */
30
31  /* Reduce argument: f in [-ln2/2, ln2/2], i is exact.  */
32  double j = fma (InvLn2, x, Shift) - Shift;
33  int64_t i = j;
34  double f = fma (j, -Ln2hi, x);
35  f = fma (j, -Ln2lo, f);
36
37  /* Approximate expm1(f) using polynomial.  */
38  double f2 = f * f;
39  double f4 = f2 * f2;
40  double p = fma (f2, estrin_10_f64 (f, f2, f4, f4 * f4, __expm1_poly), f);
41
42  /* t = 2 ^ i.  */
43  double t = asdouble ((uint64_t) (i + 1023) << 52);
44  /* expm1(x) = p * t + (t - 1).  */
45  return fma (p, t, t - 1);
46}
47
48/* Approximation for double-precision tanh(x), using a simplified version of
49   expm1. The greatest observed error is 2.77 ULP:
50   tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3
51			      want -0x1.bd6a21a163624p-3.  */
52double
53tanh (double x)
54{
55  uint64_t ix = asuint64 (x);
56  uint64_t ia = ix & AbsMask;
57  uint64_t sign = ix & ~AbsMask;
58
59  if (unlikely (ia > BoringBound))
60    {
61      if (ia > 0x7ff0000000000000)
62	return __math_invalid (x);
63      return asdouble (One | sign);
64    }
65
66  if (unlikely (ia < TinyBound))
67    return x;
68
69  /* tanh(x) = (e^2x - 1) / (e^2x + 1).  */
70  double q = expm1_inline (2 * x);
71  return q / (q + 2);
72}
73
74PL_SIG (S, D, 1, tanh, -10.0, 10.0)
75PL_TEST_ULP (tanh, 2.27)
76PL_TEST_SYM_INTERVAL (tanh, 0, TinyBound, 1000)
77PL_TEST_SYM_INTERVAL (tanh, TinyBound, BoringBound, 100000)
78PL_TEST_SYM_INTERVAL (tanh, BoringBound, inf, 1000)
79