1 //===-- Implementation header for expf16 ------------------------*- C++ -*-===//
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 #ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H
10 #define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H
11
12 #include "include/llvm-libc-macros/float16-macros.h"
13
14 #ifdef LIBC_TYPES_HAS_FLOAT16
15
16 #include "hdr/errno_macros.h"
17 #include "hdr/fenv_macros.h"
18 #include "src/__support/FPUtil/FEnvImpl.h"
19 #include "src/__support/FPUtil/FPBits.h"
20 #include "src/__support/FPUtil/PolyEval.h"
21 #include "src/__support/FPUtil/cast.h"
22 #include "src/__support/FPUtil/except_value_utils.h"
23 #include "src/__support/FPUtil/rounding_mode.h"
24 #include "src/__support/common.h"
25 #include "src/__support/macros/config.h"
26 #include "src/__support/macros/optimization.h"
27
28 #include "expf16_utils.h"
29
30 namespace LIBC_NAMESPACE_DECL {
31
32 namespace math {
33
expf16(float16 x)34 static constexpr float16 expf16(float16 x) {
35 #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
36 constexpr fputil::ExceptValues<float16, 2> EXPF16_EXCEPTS_LO = {{
37 // (input, RZ output, RU offset, RD offset, RN offset)
38 // x = 0x1.de4p-8, expf16(x) = 0x1.01cp+0 (RZ)
39 {0x1f79U, 0x3c07U, 1U, 0U, 0U},
40 // x = 0x1.73cp-6, expf16(x) = 0x1.05cp+0 (RZ)
41 {0x25cfU, 0x3c17U, 1U, 0U, 0U},
42 }};
43
44 constexpr fputil::ExceptValues<float16, 3> EXPF16_EXCEPTS_HI = {{
45 // (input, RZ output, RU offset, RD offset, RN offset)
46 // x = 0x1.c34p+0, expf16(x) = 0x1.74cp+2 (RZ)
47 {0x3f0dU, 0x45d3U, 1U, 0U, 1U},
48 // x = -0x1.488p-5, expf16(x) = 0x1.ebcp-1 (RZ)
49 {0xa922U, 0x3bafU, 1U, 0U, 0U},
50 // x = -0x1.55p-5, expf16(x) = 0x1.ebp-1 (RZ)
51 {0xa954U, 0x3bacU, 1U, 0U, 0U},
52 }};
53 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
54
55 using FPBits = fputil::FPBits<float16>;
56 FPBits x_bits(x);
57
58 uint16_t x_u = x_bits.uintval();
59 uint16_t x_abs = x_u & 0x7fffU;
60
61 // When 0 < |x| <= 2^(-5), or |x| >= 12, or x is NaN.
62 if (LIBC_UNLIKELY(x_abs <= 0x2800U || x_abs >= 0x4a00U)) {
63 // exp(NaN) = NaN
64 if (x_bits.is_nan()) {
65 if (x_bits.is_signaling_nan()) {
66 fputil::raise_except_if_required(FE_INVALID);
67 return FPBits::quiet_nan().get_val();
68 }
69
70 return x;
71 }
72
73 // When x >= 12.
74 if (x_bits.is_pos() && x_abs >= 0x4a00U) {
75 // exp(+inf) = +inf
76 if (x_bits.is_inf())
77 return FPBits::inf().get_val();
78
79 switch (fputil::quick_get_round()) {
80 case FE_TONEAREST:
81 case FE_UPWARD:
82 fputil::set_errno_if_required(ERANGE);
83 fputil::raise_except_if_required(FE_OVERFLOW);
84 return FPBits::inf().get_val();
85 default:
86 return FPBits::max_normal().get_val();
87 }
88 }
89
90 // When x <= -18.
91 if (x_u >= 0xcc80U) {
92 // exp(-inf) = +0
93 if (x_bits.is_inf())
94 return FPBits::zero().get_val();
95
96 fputil::set_errno_if_required(ERANGE);
97 fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
98
99 switch (fputil::quick_get_round()) {
100 case FE_UPWARD:
101 return FPBits::min_subnormal().get_val();
102 default:
103 return FPBits::zero().get_val();
104 }
105 }
106
107 // When 0 < |x| <= 2^(-5).
108 if (x_abs <= 0x2800U && !x_bits.is_zero()) {
109 #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
110 if (auto r = EXPF16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
111 return r.value();
112 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
113
114 float xf = x;
115 // Degree-3 minimax polynomial generated by Sollya with the following
116 // commands:
117 // > display = hexadecimal;
118 // > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
119 // > 1 + x * P;
120 return fputil::cast<float16>(
121 fputil::polyeval(xf, 0x1p+0f, 0x1p+0f, 0x1.0004p-1f, 0x1.555778p-3f));
122 }
123 }
124
125 #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
126 if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
127 return r.value();
128 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
129
130 // exp(x) = exp(hi + mid) * exp(lo)
131 auto [exp_hi_mid, exp_lo] = exp_range_reduction(x);
132 return fputil::cast<float16>(exp_hi_mid * exp_lo);
133 }
134
135 } // namespace math
136
137 } // namespace LIBC_NAMESPACE_DECL
138
139 #endif // LIBC_TYPES_HAS_FLOAT16
140
141 #endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H
142