blob: b3f8f44badd3325f900e82170bacc7b53269fe2f (
plain)
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
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
|
//===-- Utility class to manipulate wide floats. ----------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "FPBits.h"
#include "NormalFloat.h"
#include "src/__support/UInt.h"
#include <stdint.h>
namespace __llvm_libc {
namespace fputil {
// Store and manipulate positive double precision numbers at |Precision| bits.
template <size_t Precision> class XFloat {
static constexpr uint64_t OneMask = (uint64_t(1) << 63);
UInt<Precision> man;
static constexpr uint64_t WORDCOUNT = Precision / 64;
int exp;
size_t bit_width(uint64_t x) {
if (x == 0)
return 0;
size_t shift = 0;
while ((OneMask & x) == 0) {
++shift;
x <<= 1;
}
return 64 - shift;
}
public:
XFloat() : exp(0) {
for (int i = 0; i < WORDCOUNT; ++i)
man[i] = 0;
}
XFloat(const XFloat &other) : exp(other.exp) {
for (int i = 0; i < WORDCOUNT; ++i)
man[i] = other.man[i];
}
explicit XFloat(double x) {
auto xn = NormalFloat<double>(x);
exp = xn.exponent;
man[WORDCOUNT - 1] = xn.mantissa << 11;
for (int i = 0; i < WORDCOUNT - 1; ++i)
man[i] = 0;
}
XFloat(int e, const UInt<Precision> &bits) : exp(e) {
for (size_t i = 0; i < WORDCOUNT; ++i)
man[i] = bits[i];
}
// Multiply this number with x and store the result in this number.
void mul(double x) {
auto xn = NormalFloat<double>(x);
exp += xn.exponent;
uint64_t carry = man.mul(xn.mantissa << 11);
size_t carry_width = bit_width(carry);
carry_width = (carry_width == 64 ? 64 : 63);
man.shift_right(carry_width);
man[WORDCOUNT - 1] = man[WORDCOUNT - 1] + (carry << (64 - carry_width));
exp += carry_width == 64 ? 1 : 0;
normalize();
}
void drop_int() {
if (exp < 0)
return;
if (exp > int(Precision - 1)) {
for (size_t i = 0; i < WORDCOUNT; ++i)
man[i] = 0;
return;
}
man.shift_left(exp + 1);
man.shift_right(exp + 1);
normalize();
}
double mul(const XFloat<Precision> &other) {
constexpr size_t row_words = 2 * WORDCOUNT + 1;
constexpr size_t row_precision = row_words * 64;
constexpr size_t result_bits = 2 * Precision;
UInt<row_precision> rows[WORDCOUNT];
for (size_t r = 0; r < WORDCOUNT; ++r) {
for (size_t i = 0; i < row_words; ++i) {
if (i < WORDCOUNT)
rows[r][i] = man[i];
else
rows[r][i] = 0;
}
rows[r].mul(other.man[r]);
rows[r].shift_left(r * 64);
}
for (size_t r = 1; r < WORDCOUNT; ++r) {
rows[0].add(rows[r]);
}
int result_exp = exp + other.exp;
uint64_t carry = rows[0][row_words - 1];
if (carry) {
size_t carry_width = bit_width(carry);
rows[0].shift_right(carry_width);
rows[0][row_words - 2] =
rows[0][row_words - 2] + (carry << (64 - carry_width));
result_exp += carry_width;
}
if (rows[0][row_words - 2] & OneMask) {
++result_exp;
} else {
rows[0].shift_left(1);
}
UInt<result_bits> result_man;
for (size_t i = 0; i < result_bits / 64; ++i)
result_man[i] = rows[0][i];
XFloat<result_bits> result(result_exp, result_man);
result.normalize();
return double(result);
}
explicit operator double() {
normalize();
constexpr uint64_t one = uint64_t(1) << 10;
constexpr uint64_t excess_mask = (one << 1) - 1;
uint64_t excess = man[WORDCOUNT - 1] & excess_mask;
uint64_t new_man = man[WORDCOUNT - 1] >> 11;
if (excess > one) {
// We have to round up.
++new_man;
} else if (excess == one) {
bool greater_than_one = false;
for (size_t i = 0; i < WORDCOUNT - 1; ++i) {
greater_than_one = (man[i] != 0);
if (greater_than_one)
break;
}
if (greater_than_one || (new_man & 1) != 0) {
++new_man;
}
}
if (new_man == (uint64_t(1) << 53))
++exp;
// We use NormalFloat as it can produce subnormal numbers or underflow to 0
// if necessary.
NormalFloat<double> d(exp, new_man, 0);
return double(d);
}
// Normalizes this number.
void normalize() {
uint64_t man_bits = 0;
for (size_t i = 0; i < WORDCOUNT; ++i)
man_bits |= man[i];
if (man_bits == 0)
return;
while ((man[WORDCOUNT - 1] & OneMask) == 0) {
man.shift_left(1);
--exp;
}
}
};
} // namespace fputil
} // namespace __llvm_libc
|
