1 //===-- Add and subtract IEEE 754 floating-point numbers --------*- 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_FPUTIL_GENERIC_ADD_SUB_H
10 #define LLVM_LIBC_SRC___SUPPORT_FPUTIL_GENERIC_ADD_SUB_H
11
12 #include "hdr/fenv_macros.h"
13 #include "src/__support/CPP/algorithm.h"
14 #include "src/__support/CPP/bit.h"
15 #include "src/__support/CPP/type_traits.h"
16 #include "src/__support/FPUtil/BasicOperations.h"
17 #include "src/__support/FPUtil/FEnvImpl.h"
18 #include "src/__support/FPUtil/FPBits.h"
19 #include "src/__support/FPUtil/cast.h"
20 #include "src/__support/FPUtil/dyadic_float.h"
21 #include "src/__support/FPUtil/rounding_mode.h"
22 #include "src/__support/macros/attributes.h"
23 #include "src/__support/macros/config.h"
24 #include "src/__support/macros/optimization.h"
25
26 namespace LIBC_NAMESPACE_DECL {
27 namespace fputil::generic {
28
29 template <bool IsSub, typename OutType, typename InType>
30 LIBC_INLINE cpp::enable_if_t<cpp::is_floating_point_v<OutType> &&
31 cpp::is_floating_point_v<InType> &&
32 sizeof(OutType) <= sizeof(InType),
33 OutType>
add_or_sub(InType x,InType y)34 add_or_sub(InType x, InType y) {
35 using OutFPBits = FPBits<OutType>;
36 using OutStorageType = typename OutFPBits::StorageType;
37 using InFPBits = FPBits<InType>;
38 using InStorageType = typename InFPBits::StorageType;
39
40 constexpr int GUARD_BITS_LEN = 3;
41 constexpr int RESULT_FRACTION_LEN = InFPBits::FRACTION_LEN + GUARD_BITS_LEN;
42 constexpr int RESULT_MANTISSA_LEN = RESULT_FRACTION_LEN + 1;
43
44 using DyadicFloat =
45 DyadicFloat<cpp::bit_ceil(static_cast<size_t>(RESULT_MANTISSA_LEN))>;
46
47 InFPBits x_bits(x);
48 InFPBits y_bits(y);
49
50 bool is_effectively_add = (x_bits.sign() == y_bits.sign()) != IsSub;
51
52 if (LIBC_UNLIKELY(x_bits.is_inf_or_nan() || y_bits.is_inf_or_nan() ||
53 x_bits.is_zero() || y_bits.is_zero())) {
54 if (x_bits.is_nan() || y_bits.is_nan()) {
55 if (x_bits.is_signaling_nan() || y_bits.is_signaling_nan())
56 raise_except_if_required(FE_INVALID);
57
58 if (x_bits.is_quiet_nan()) {
59 InStorageType x_payload = x_bits.get_mantissa();
60 x_payload >>= InFPBits::FRACTION_LEN - OutFPBits::FRACTION_LEN;
61 return OutFPBits::quiet_nan(x_bits.sign(),
62 static_cast<OutStorageType>(x_payload))
63 .get_val();
64 }
65
66 if (y_bits.is_quiet_nan()) {
67 InStorageType y_payload = y_bits.get_mantissa();
68 y_payload >>= InFPBits::FRACTION_LEN - OutFPBits::FRACTION_LEN;
69 return OutFPBits::quiet_nan(y_bits.sign(),
70 static_cast<OutStorageType>(y_payload))
71 .get_val();
72 }
73
74 return OutFPBits::quiet_nan().get_val();
75 }
76
77 if (x_bits.is_inf()) {
78 if (y_bits.is_inf()) {
79 if (!is_effectively_add) {
80 raise_except_if_required(FE_INVALID);
81 return OutFPBits::quiet_nan().get_val();
82 }
83
84 return OutFPBits::inf(x_bits.sign()).get_val();
85 }
86
87 return OutFPBits::inf(x_bits.sign()).get_val();
88 }
89
90 if (y_bits.is_inf())
91 return OutFPBits::inf(y_bits.sign()).get_val();
92
93 if (x_bits.is_zero()) {
94 if (y_bits.is_zero()) {
95 switch (quick_get_round()) {
96 case FE_DOWNWARD:
97 return OutFPBits::zero(Sign::NEG).get_val();
98 default:
99 return OutFPBits::zero(Sign::POS).get_val();
100 }
101 }
102
103 // volatile prevents Clang from converting tmp to OutType and then
104 // immediately back to InType before negating it, resulting in double
105 // rounding.
106 volatile InType tmp = y;
107 if constexpr (IsSub)
108 tmp = -tmp;
109 return cast<OutType>(tmp);
110 }
111
112 if (y_bits.is_zero())
113 return cast<OutType>(x);
114 }
115
116 InType x_abs = x_bits.abs().get_val();
117 InType y_abs = y_bits.abs().get_val();
118
119 if (x_abs == y_abs && !is_effectively_add) {
120 switch (quick_get_round()) {
121 case FE_DOWNWARD:
122 return OutFPBits::zero(Sign::NEG).get_val();
123 default:
124 return OutFPBits::zero(Sign::POS).get_val();
125 }
126 }
127
128 Sign result_sign = Sign::POS;
129
130 if (x_abs > y_abs) {
131 result_sign = x_bits.sign();
132 } else if (x_abs < y_abs) {
133 if (is_effectively_add)
134 result_sign = y_bits.sign();
135 else if (y_bits.is_pos())
136 result_sign = Sign::NEG;
137 } else if (is_effectively_add) {
138 result_sign = x_bits.sign();
139 }
140
141 InFPBits max_bits(cpp::max(x_abs, y_abs));
142 InFPBits min_bits(cpp::min(x_abs, y_abs));
143
144 InStorageType result_mant;
145
146 if (max_bits.is_subnormal()) {
147 // min_bits must be subnormal too.
148
149 if (is_effectively_add)
150 result_mant = max_bits.get_mantissa() + min_bits.get_mantissa();
151 else
152 result_mant = max_bits.get_mantissa() - min_bits.get_mantissa();
153
154 result_mant <<= GUARD_BITS_LEN;
155 } else {
156 InStorageType max_mant = max_bits.get_explicit_mantissa() << GUARD_BITS_LEN;
157 InStorageType min_mant = min_bits.get_explicit_mantissa() << GUARD_BITS_LEN;
158
159 int alignment = (max_bits.get_biased_exponent() - max_bits.is_normal()) -
160 (min_bits.get_biased_exponent() - min_bits.is_normal());
161
162 InStorageType aligned_min_mant =
163 min_mant >> cpp::min(alignment, RESULT_MANTISSA_LEN);
164 bool aligned_min_mant_sticky;
165
166 if (alignment <= GUARD_BITS_LEN)
167 aligned_min_mant_sticky = false;
168 else if (alignment > InFPBits::FRACTION_LEN + GUARD_BITS_LEN)
169 aligned_min_mant_sticky = true;
170 else
171 aligned_min_mant_sticky =
172 (static_cast<InStorageType>(
173 min_mant << (InFPBits::STORAGE_LEN - alignment))) != 0;
174
175 InStorageType min_mant_sticky(static_cast<int>(aligned_min_mant_sticky));
176
177 if (is_effectively_add)
178 result_mant = max_mant + (aligned_min_mant | min_mant_sticky);
179 else
180 result_mant = max_mant - (aligned_min_mant | min_mant_sticky);
181 }
182
183 int result_exp = max_bits.get_explicit_exponent() - RESULT_FRACTION_LEN;
184 DyadicFloat result(result_sign, result_exp, result_mant);
185 return result.template as<OutType, /*ShouldSignalExceptions=*/true>();
186 }
187
188 template <typename OutType, typename InType>
189 LIBC_INLINE cpp::enable_if_t<cpp::is_floating_point_v<OutType> &&
190 cpp::is_floating_point_v<InType> &&
191 sizeof(OutType) <= sizeof(InType),
192 OutType>
add(InType x,InType y)193 add(InType x, InType y) {
194 return add_or_sub</*IsSub=*/false, OutType>(x, y);
195 }
196
197 template <typename OutType, typename InType>
198 LIBC_INLINE cpp::enable_if_t<cpp::is_floating_point_v<OutType> &&
199 cpp::is_floating_point_v<InType> &&
200 sizeof(OutType) <= sizeof(InType),
201 OutType>
sub(InType x,InType y)202 sub(InType x, InType y) {
203 return add_or_sub</*IsSub=*/true, OutType>(x, y);
204 }
205
206 } // namespace fputil::generic
207 } // namespace LIBC_NAMESPACE_DECL
208
209 #endif // LLVM_LIBC_SRC___SUPPORT_FPUTIL_GENERIC_ADD_SUB_H
210