1//===----- lib/fp_add_impl.inc - floaing point addition -----------*- 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// This file implements soft-float addition with the IEEE-754 default rounding
10// (to nearest, ties to even).
11//
12//===----------------------------------------------------------------------===//
13
14#include "fp_lib.h"
15#include "fp_mode.h"
16
17static __inline fp_t __addXf3__(fp_t a, fp_t b) {
18 rep_t aRep = toRep(x: a);
19 rep_t bRep = toRep(x: b);
20 const rep_t aAbs = aRep & absMask;
21 const rep_t bAbs = bRep & absMask;
22
23 // Detect if a or b is zero, infinity, or NaN.
24 if (aAbs - REP_C(1) >= infRep - REP_C(1) ||
25 bAbs - REP_C(1) >= infRep - REP_C(1)) {
26 // NaN + anything = qNaN
27 if (aAbs > infRep)
28 return fromRep(x: toRep(x: a) | quietBit);
29 // anything + NaN = qNaN
30 if (bAbs > infRep)
31 return fromRep(x: toRep(x: b) | quietBit);
32
33 if (aAbs == infRep) {
34 // +/-infinity + -/+infinity = qNaN
35 if ((toRep(x: a) ^ toRep(x: b)) == signBit)
36 return fromRep(qnanRep);
37 // +/-infinity + anything remaining = +/- infinity
38 else
39 return a;
40 }
41
42 // anything remaining + +/-infinity = +/-infinity
43 if (bAbs == infRep)
44 return b;
45
46 // zero + anything = anything
47 if (!aAbs) {
48 // We need to get the sign right for zero + zero.
49 if (!bAbs)
50 return fromRep(x: toRep(x: a) & toRep(x: b));
51 else
52 return b;
53 }
54
55 // anything + zero = anything
56 if (!bAbs)
57 return a;
58 }
59
60 // Swap a and b if necessary so that a has the larger absolute value.
61 if (bAbs > aAbs) {
62 const rep_t temp = aRep;
63 aRep = bRep;
64 bRep = temp;
65 }
66
67 // Extract the exponent and significand from the (possibly swapped) a and b.
68 int aExponent = aRep >> significandBits & maxExponent;
69 int bExponent = bRep >> significandBits & maxExponent;
70 rep_t aSignificand = aRep & significandMask;
71 rep_t bSignificand = bRep & significandMask;
72
73 // Normalize any denormals, and adjust the exponent accordingly.
74 if (aExponent == 0)
75 aExponent = normalize(significand: &aSignificand);
76 if (bExponent == 0)
77 bExponent = normalize(significand: &bSignificand);
78
79 // The sign of the result is the sign of the larger operand, a. If they
80 // have opposite signs, we are performing a subtraction. Otherwise, we
81 // perform addition.
82 const rep_t resultSign = aRep & signBit;
83 const bool subtraction = (aRep ^ bRep) & signBit;
84
85 // Shift the significands to give us round, guard and sticky, and set the
86 // implicit significand bit. If we fell through from the denormal path it
87 // was already set by normalize( ), but setting it twice won't hurt
88 // anything.
89 aSignificand = (aSignificand | implicitBit) << 3;
90 bSignificand = (bSignificand | implicitBit) << 3;
91
92 // Shift the significand of b by the difference in exponents, with a sticky
93 // bottom bit to get rounding correct.
94 const unsigned int align = (unsigned int)(aExponent - bExponent);
95 if (align) {
96 if (align < typeWidth) {
97 const bool sticky = (bSignificand << (typeWidth - align)) != 0;
98 bSignificand = bSignificand >> align | sticky;
99 } else {
100 bSignificand = 1; // Set the sticky bit. b is known to be non-zero.
101 }
102 }
103 if (subtraction) {
104 aSignificand -= bSignificand;
105 // If a == -b, return +zero.
106 if (aSignificand == 0)
107 return fromRep(x: 0);
108
109 // If partial cancellation occured, we need to left-shift the result
110 // and adjust the exponent.
111 if (aSignificand < implicitBit << 3) {
112 const int shift = rep_clz(a: aSignificand) - rep_clz(implicitBit << 3);
113 aSignificand <<= shift;
114 aExponent -= shift;
115 }
116 } else /* addition */ {
117 aSignificand += bSignificand;
118
119 // If the addition carried up, we need to right-shift the result and
120 // adjust the exponent.
121 if (aSignificand & implicitBit << 4) {
122 const bool sticky = aSignificand & 1;
123 aSignificand = aSignificand >> 1 | sticky;
124 aExponent += 1;
125 }
126 }
127
128 // If we have overflowed the type, return +/- infinity.
129 if (aExponent >= maxExponent)
130 return fromRep(infRep | resultSign);
131
132 if (aExponent <= 0) {
133 // The result is denormal before rounding. The exponent is zero and we
134 // need to shift the significand.
135 const int shift = 1 - aExponent;
136 const bool sticky = (aSignificand << (typeWidth - shift)) != 0;
137 aSignificand = aSignificand >> shift | sticky;
138 aExponent = 0;
139 }
140
141 // Low three bits are round, guard, and sticky.
142 const int roundGuardSticky = aSignificand & 0x7;
143
144 // Shift the significand into place, and mask off the implicit bit.
145 rep_t result = aSignificand >> 3 & significandMask;
146
147 // Insert the exponent and sign.
148 result |= (rep_t)aExponent << significandBits;
149 result |= resultSign;
150
151 // Perform the final rounding. The result may overflow to infinity, but
152 // that is the correct result in that case.
153 switch (__fe_getround()) {
154 case CRT_FE_TONEAREST:
155 if (roundGuardSticky > 0x4)
156 result++;
157 if (roundGuardSticky == 0x4)
158 result += result & 1;
159 break;
160 case CRT_FE_DOWNWARD:
161 if (resultSign && roundGuardSticky) result++;
162 break;
163 case CRT_FE_UPWARD:
164 if (!resultSign && roundGuardSticky) result++;
165 break;
166 case CRT_FE_TOWARDZERO:
167 break;
168 }
169 if (roundGuardSticky)
170 __fe_raise_inexact();
171 return fromRep(x: result);
172}
173

source code of compiler-rt/lib/builtins/fp_add_impl.inc