1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
|
//===-- lib/addsf3.c - Single-precision addition ------------------*- C -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file implements single-precision soft-float addition with the IEEE-754
// default rounding (to nearest, ties to even).
//
//===----------------------------------------------------------------------===//
#include "abi.h"
#define SINGLE_PRECISION
#include "fp_lib.h"
ARM_EABI_FNALIAS(fadd, addsf3);
fp_t __addsf3(fp_t a, fp_t b) {
rep_t aRep = toRep(a);
rep_t bRep = toRep(b);
const rep_t aAbs = aRep & absMask;
const rep_t bAbs = bRep & absMask;
// Detect if a or b is zero, infinity, or NaN.
if (aAbs - 1U >= infRep - 1U || bAbs - 1U >= infRep - 1U) {
// NaN + anything = qNaN
if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
// anything + NaN = qNaN
if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
if (aAbs == infRep) {
// +/-infinity + -/+infinity = qNaN
if ((toRep(a) ^ toRep(b)) == signBit) return fromRep(qnanRep);
// +/-infinity + anything remaining = +/- infinity
else return a;
}
// anything remaining + +/-infinity = +/-infinity
if (bAbs == infRep) return b;
// zero + anything = anything
if (!aAbs) {
// but we need to get the sign right for zero + zero
if (!bAbs) return fromRep(toRep(a) & toRep(b));
else return b;
}
// anything + zero = anything
if (!bAbs) return a;
}
// Swap a and b if necessary so that a has the larger absolute value.
if (bAbs > aAbs) {
const rep_t temp = aRep;
aRep = bRep;
bRep = temp;
}
// Extract the exponent and significand from the (possibly swapped) a and b.
int aExponent = aRep >> significandBits & maxExponent;
int bExponent = bRep >> significandBits & maxExponent;
rep_t aSignificand = aRep & significandMask;
rep_t bSignificand = bRep & significandMask;
// Normalize any denormals, and adjust the exponent accordingly.
if (aExponent == 0) aExponent = normalize(&aSignificand);
if (bExponent == 0) bExponent = normalize(&bSignificand);
// The sign of the result is the sign of the larger operand, a. If they
// have opposite signs, we are performing a subtraction; otherwise addition.
const rep_t resultSign = aRep & signBit;
const bool subtraction = (aRep ^ bRep) & signBit;
// Shift the significands to give us round, guard and sticky, and or in the
// implicit significand bit. (If we fell through from the denormal path it
// was already set by normalize( ), but setting it twice won't hurt
// anything.)
aSignificand = (aSignificand | implicitBit) << 3;
bSignificand = (bSignificand | implicitBit) << 3;
// Shift the significand of b by the difference in exponents, with a sticky
// bottom bit to get rounding correct.
const int align = aExponent - bExponent;
if (align) {
if (align < typeWidth) {
const bool sticky = bSignificand << (typeWidth - align);
bSignificand = bSignificand >> align | sticky;
} else {
bSignificand = 1; // sticky; b is known to be non-zero.
}
}
if (subtraction) {
aSignificand -= bSignificand;
// If a == -b, return +zero.
if (aSignificand == 0) return fromRep(0);
// If partial cancellation occured, we need to left-shift the result
// and adjust the exponent:
if (aSignificand < implicitBit << 3) {
const int shift = rep_clz(aSignificand) - rep_clz(implicitBit << 3);
aSignificand <<= shift;
aExponent -= shift;
}
}
else /* addition */ {
aSignificand += bSignificand;
// If the addition carried up, we need to right-shift the result and
// adjust the exponent:
if (aSignificand & implicitBit << 4) {
const bool sticky = aSignificand & 1;
aSignificand = aSignificand >> 1 | sticky;
aExponent += 1;
}
}
// If we have overflowed the type, return +/- infinity:
if (aExponent >= maxExponent) return fromRep(infRep | resultSign);
if (aExponent <= 0) {
// Result is denormal before rounding; the exponent is zero and we
// need to shift the significand.
const int shift = 1 - aExponent;
const bool sticky = aSignificand << (typeWidth - shift);
aSignificand = aSignificand >> shift | sticky;
aExponent = 0;
}
// Low three bits are round, guard, and sticky.
const int roundGuardSticky = aSignificand & 0x7;
// Shift the significand into place, and mask off the implicit bit.
rep_t result = aSignificand >> 3 & significandMask;
// Insert the exponent and sign.
result |= (rep_t)aExponent << significandBits;
result |= resultSign;
// Final rounding. The result may overflow to infinity, but that is the
// correct result in that case.
if (roundGuardSticky > 0x4) result++;
if (roundGuardSticky == 0x4) result += result & 1;
return fromRep(result);
}
|
