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
181
182
183
184
185
186
187
188
189
190
191
|
/*============================================================================
This C source file is part of the SoftPosit Posit Arithmetic Package
by S. H. Leong (Cerlane).
Copyright 2017, 2018 A*STAR. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions, and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the University nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
=============================================================================*/
#include <math.h>
#include "platform.h"
#include "internals.h"
posit_2_t qX2_to_pX2(quire_2_t qA, int x){
union ui512_qX2 uZ;
union ui32_pX2 uA;
uint_fast32_t fracA = 0, shift=0, regime;
uint_fast64_t frac64A;
bool sign, regSA=0, bitNPlusOne=0, bitsMore=0;
int_fast32_t regA, expA = 0;
int i;
if (isQX2Zero(qA)){
uA.ui=0;
return uA.p;
}
//handle NaR
else if (isNaRQX2(qA)){
uA.ui=0x80000000;
return uA.p;
}
uZ.q = qA;
sign = uZ.ui[0]>>63;
if(sign){
for (i=7; i>=0; i--){
if (uZ.ui[i]>0){
uZ.ui[i] = - uZ.ui[i];
i--;
while(i>=0){
uZ.ui[i] = ~uZ.ui[i];
i--;
}
break;
}
}
}
//minpos and maxpos
int noLZ =0;
for (i=0; i<8; i++){
if (uZ.ui[i]==0){
noLZ+=64;
}
else{
uint_fast64_t tmp = uZ.ui[i];
int noLZtmp = 0;
while (!(tmp>>63)){
noLZtmp++;
tmp= (tmp<<1);
}
noLZ+=noLZtmp;
frac64A = tmp;
if (i!=7 && noLZtmp!=0){
frac64A+= ( uZ.ui[i+1]>>(64-noLZtmp) );
if( uZ.ui[i+1] & (((uint64_t)0x1<<(64-noLZtmp))-1) )
bitsMore=1;
i++;
}
i++;
while(i<8){
if (uZ.ui[i]>0){
bitsMore = 1;;
break;
}
i++;
}
break;
}
}
//default dot is between bit 271 and 272, extreme left bit is bit 0. Last right bit is bit 511.
//Equations derived from quire32_mult last_pos = 271 - (kA<<2) - expA and first_pos = last_pos - frac_len
int kA=(271-noLZ) >> 2;
expA = 271 - noLZ - (kA<<2) ;
if(kA<0){
//regA = (-kA & 0xFFFF);
regA = -kA;
regSA = 0;
regime = 0x40000000>>regA;
}
else{
regA = kA+1;
regSA=1;
regime = 0x7FFFFFFF - (0x7FFFFFFF>>regA);
}
if(regA>(x-2)){
//max or min pos. exp and frac does not matter.
uA.ui=(regSA) ? (0x7FFFFFFF & ((int32_t)0x80000000>>(x-1)) ): (0x1 << (32-x));
}
else{
//remove hidden bit
frac64A&=0x7FFFFFFFFFFFFFFF;
shift = regA+35; //2 es bit, 1 sign bit and 1 r terminating bit , 31+4
fracA = ((uint32_t) (frac64A>>shift));
//regime length is smaller than length of posit
if (regA<x){
if (regA<=(x-4)){
bitNPlusOne = (frac64A>>(shift+31-x)) & 0x1;
if ((frac64A<<(33-shift+x)) !=0) bitsMore=1;
}
else {
if (regA==(x-2)){
bitNPlusOne = expA&0x2;
bitsMore = (expA&0x1);
expA = 0;
}
else if (regA==(x-3)){
bitNPlusOne = expA&0x1;
//expA>>=1; //taken care of by the pack algo
expA &=0x2;
}
if (frac64A>0){
fracA=0;
bitsMore =1;
}
}
}
else{
regime=(regSA) ? (regime & ((int32_t)0x80000000>>(x-1)) ): (regime << (32-x));
expA=0;
fracA=0;
}
expA <<= (28-regA);
uA.ui = packToP32UI(regime, expA, fracA) & ((int32_t)0x80000000>>(x-1));
if (bitNPlusOne)
uA.ui += (((uA.ui>>(32-x)) &0x1) | (uint32_t)bitsMore )<< (32-x);
}
if (sign) uA.ui = -uA.ui & 0xFFFFFFFF;
return uA.p;
}
|
