1//===-- Half-precision 2^x - 1 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/exp2m1f16.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/multiply_add.h"
19#include "src/__support/FPUtil/rounding_mode.h"
20#include "src/__support/common.h"
21#include "src/__support/macros/config.h"
22#include "src/__support/macros/optimization.h"
23#include "src/__support/macros/properties/cpu_features.h"
24
25namespace LIBC_NAMESPACE_DECL {
26
27#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
28static constexpr fputil::ExceptValues<float16, 6> EXP2M1F16_EXCEPTS_LO = {{
29 // (input, RZ output, RU offset, RD offset, RN offset)
30 // x = 0x1.cf4p-13, exp2m1f16(x) = 0x1.41p-13 (RZ)
31 {0x0b3dU, 0x0904U, 1U, 0U, 1U},
32 // x = 0x1.4fcp-12, exp2m1f16(x) = 0x1.d14p-13 (RZ)
33 {0x0d3fU, 0x0b45U, 1U, 0U, 1U},
34 // x = 0x1.63p-11, exp2m1f16(x) = 0x1.ec4p-12 (RZ)
35 {0x118cU, 0x0fb1U, 1U, 0U, 0U},
36 // x = 0x1.6fp-7, exp2m1f16(x) = 0x1.fe8p-8 (RZ)
37 {0x21bcU, 0x1ffaU, 1U, 0U, 1U},
38 // x = -0x1.c6p-10, exp2m1f16(x) = -0x1.3a8p-10 (RZ)
39 {0x9718U, 0x94eaU, 0U, 1U, 0U},
40 // x = -0x1.cfcp-10, exp2m1f16(x) = -0x1.414p-10 (RZ)
41 {0x973fU, 0x9505U, 0U, 1U, 0U},
42}};
43
44#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
45static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 6;
46#else
47static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 7;
48#endif
49
50static constexpr fputil::ExceptValues<float16, N_EXP2M1F16_EXCEPTS_HI>
51 EXP2M1F16_EXCEPTS_HI = {{
52 // (input, RZ output, RU offset, RD offset, RN offset)
53 // x = 0x1.e58p-3, exp2m1f16(x) = 0x1.6dcp-3 (RZ)
54 {0x3396U, 0x31b7U, 1U, 0U, 0U},
55#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
56 // x = 0x1.2e8p-2, exp2m1f16(x) = 0x1.d14p-3 (RZ)
57 {0x34baU, 0x3345U, 1U, 0U, 0U},
58#endif
59 // x = 0x1.ad8p-2, exp2m1f16(x) = 0x1.598p-2 (RZ)
60 {0x36b6U, 0x3566U, 1U, 0U, 0U},
61#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
62 // x = 0x1.edcp-2, exp2m1f16(x) = 0x1.964p-2 (RZ)
63 {0x37b7U, 0x3659U, 1U, 0U, 1U},
64#endif
65 // x = -0x1.804p-3, exp2m1f16(x) = -0x1.f34p-4 (RZ)
66 {0xb201U, 0xafcdU, 0U, 1U, 1U},
67 // x = -0x1.f3p-3, exp2m1f16(x) = -0x1.3e4p-3 (RZ)
68 {0xb3ccU, 0xb0f9U, 0U, 1U, 0U},
69 // x = -0x1.294p-1, exp2m1f16(x) = -0x1.53p-2 (RZ)
70 {0xb8a5U, 0xb54cU, 0U, 1U, 1U},
71#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
72 // x = -0x1.a34p-1, exp2m1f16(x) = -0x1.bb4p-2 (RZ)
73 {0xba8dU, 0xb6edU, 0U, 1U, 1U},
74#endif
75 }};
76#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
77
78LLVM_LIBC_FUNCTION(float16, exp2m1f16, (float16 x)) {
79 using FPBits = fputil::FPBits<float16>;
80 FPBits x_bits(x);
81
82 uint16_t x_u = x_bits.uintval();
83 uint16_t x_abs = x_u & 0x7fffU;
84
85 // When |x| <= 2^(-3), or |x| >= 11, or x is NaN.
86 if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x4980U)) {
87 // exp2m1(NaN) = NaN
88 if (x_bits.is_nan()) {
89 if (x_bits.is_signaling_nan()) {
90 fputil::raise_except_if_required(FE_INVALID);
91 return FPBits::quiet_nan().get_val();
92 }
93
94 return x;
95 }
96
97 // When x >= 16.
98 if (x_u >= 0x4c00 && x_bits.is_pos()) {
99 // exp2m1(+inf) = +inf
100 if (x_bits.is_inf())
101 return FPBits::inf().get_val();
102
103 switch (fputil::quick_get_round()) {
104 case FE_TONEAREST:
105 case FE_UPWARD:
106 fputil::set_errno_if_required(ERANGE);
107 fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
108 return FPBits::inf().get_val();
109 default:
110 return FPBits::max_normal().get_val();
111 }
112 }
113
114 // When x < -11.
115 if (x_u > 0xc980U) {
116 // exp2m1(-inf) = -1
117 if (x_bits.is_inf())
118 return FPBits::one(Sign::NEG).get_val();
119
120 // When -12 < x < -11, round(2^x - 1, HP, RN) = -0x1.ffcp-1.
121 if (x_u < 0xca00U)
122 return fputil::round_result_slightly_down(
123 fputil::cast<float16>(-0x1.ffcp-1));
124
125 // When x <= -12, round(2^x - 1, HP, RN) = -1.
126 switch (fputil::quick_get_round()) {
127 case FE_TONEAREST:
128 case FE_DOWNWARD:
129 return FPBits::one(Sign::NEG).get_val();
130 default:
131 return fputil::cast<float16>(-0x1.ffcp-1);
132 }
133 }
134
135 // When |x| <= 2^(-3).
136 if (x_abs <= 0x3000U) {
137#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
138 if (auto r = EXP2M1F16_EXCEPTS_LO.lookup(x_u);
139 LIBC_UNLIKELY(r.has_value()))
140 return r.value();
141#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
142
143 float xf = x;
144 // Degree-5 minimax polynomial generated by Sollya with the following
145 // commands:
146 // > display = hexadecimal;
147 // > P = fpminimax((2^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]);
148 // > x * P;
149 return fputil::cast<float16>(
150 xf * fputil::polyeval(xf, 0x1.62e43p-1f, 0x1.ebfbdep-3f,
151 0x1.c6af88p-5f, 0x1.3b45d6p-7f,
152 0x1.641e7cp-10f));
153 }
154 }
155
156#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
157 if (auto r = EXP2M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
158 return r.value();
159#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
160
161 // exp2(x) = exp2(hi + mid) * exp2(lo)
162 auto [exp2_hi_mid, exp2_lo] = exp2_range_reduction(x);
163 // exp2m1(x) = exp2(hi + mid) * exp2(lo) - 1
164 return fputil::cast<float16>(
165 fputil::multiply_add(exp2_hi_mid, exp2_lo, -1.0f));
166}
167
168} // namespace LIBC_NAMESPACE_DECL
169

source code of libc/src/math/generic/exp2m1f16.cpp