1//===-- Half-precision 2^x function ---------------------------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8
9#include "src/math/exp2f16.h"
10#include "expxf16.h"
11#include "hdr/errno_macros.h"
12#include "hdr/fenv_macros.h"
13#include "src/__support/FPUtil/FEnvImpl.h"
14#include "src/__support/FPUtil/FPBits.h"
15#include "src/__support/FPUtil/cast.h"
16#include "src/__support/FPUtil/except_value_utils.h"
17#include "src/__support/FPUtil/rounding_mode.h"
18#include "src/__support/common.h"
19#include "src/__support/macros/config.h"
20#include "src/__support/macros/optimization.h"
21
22namespace LIBC_NAMESPACE_DECL {
23
24#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
25static constexpr fputil::ExceptValues<float16, 3> EXP2F16_EXCEPTS = {{
26 // (input, RZ output, RU offset, RD offset, RN offset)
27 // x = 0x1.714p-11, exp2f16(x) = 0x1p+0 (RZ)
28 {0x11c5U, 0x3c00U, 1U, 0U, 1U},
29 // x = -0x1.558p-4, exp2f16(x) = 0x1.e34p-1 (RZ)
30 {0xad56U, 0x3b8dU, 1U, 0U, 0U},
31 // x = -0x1.d5cp-4, exp2f16(x) = 0x1.d8cp-1 (RZ)
32 {0xaf57U, 0x3b63U, 1U, 0U, 0U},
33}};
34#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
35
36LLVM_LIBC_FUNCTION(float16, exp2f16, (float16 x)) {
37 using FPBits = fputil::FPBits<float16>;
38 FPBits x_bits(x);
39
40 uint16_t x_u = x_bits.uintval();
41 uint16_t x_abs = x_u & 0x7fffU;
42
43 // When |x| >= 16, or x is NaN.
44 if (LIBC_UNLIKELY(x_abs >= 0x4c00U)) {
45 // exp2(NaN) = NaN
46 if (x_bits.is_nan()) {
47 if (x_bits.is_signaling_nan()) {
48 fputil::raise_except_if_required(FE_INVALID);
49 return FPBits::quiet_nan().get_val();
50 }
51
52 return x;
53 }
54
55 // When x >= 16.
56 if (x_bits.is_pos()) {
57 // exp2(+inf) = +inf
58 if (x_bits.is_inf())
59 return FPBits::inf().get_val();
60
61 switch (fputil::quick_get_round()) {
62 case FE_TONEAREST:
63 case FE_UPWARD:
64 fputil::set_errno_if_required(ERANGE);
65 fputil::raise_except_if_required(FE_OVERFLOW);
66 return FPBits::inf().get_val();
67 default:
68 return FPBits::max_normal().get_val();
69 }
70 }
71
72 // When x <= -25.
73 if (x_u >= 0xce40U) {
74 // exp2(-inf) = +0
75 if (x_bits.is_inf())
76 return FPBits::zero().get_val();
77
78 fputil::set_errno_if_required(ERANGE);
79 fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
80
81 if (fputil::fenv_is_round_up())
82 return FPBits::min_subnormal().get_val();
83 return FPBits::zero().get_val();
84 }
85 }
86
87#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
88 if (auto r = EXP2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
89 return r.value();
90#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
91
92 // exp2(x) = exp2(hi + mid) * exp2(lo)
93 auto [exp2_hi_mid, exp2_lo] = exp2_range_reduction(x);
94 return fputil::cast<float16>(exp2_hi_mid * exp2_lo);
95}
96
97} // namespace LIBC_NAMESPACE_DECL
98

source code of libc/src/math/generic/exp2f16.cpp