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

source code of libc/src/math/generic/expf16.cpp