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
192
193
194
195
196
197
198
199
|
/*
* Copyright (C) 2014 Andreas Steffen
* HSR Hochschule fuer Technik Rapperswil
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation; either version 2 of the License, or (at your
* option) any later version. See <http://www.fsf.org/copyleft/gpl.txt>.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* for more details.
*/
#include "bliss_fft.h"
typedef struct private_bliss_fft_t private_bliss_fft_t;
/**
* Private data structure for bliss_fft_t object
*/
struct private_bliss_fft_t {
/**
* Public interface.
*/
bliss_fft_t public;
/**
* FFT parameter set used as constants
*/
bliss_fft_params_t *p;
};
METHOD(bliss_fft_t, get_size, uint16_t,
private_bliss_fft_t *this)
{
return this->p->n;
}
METHOD(bliss_fft_t, get_modulus, uint16_t,
private_bliss_fft_t *this)
{
return this->p->q;
}
/**
* Do an FFT butterfly operation
*
* x[i1] ---|+|------- x[i1]
* \/
* /\ w[iw]
* x[i2] ---|-|--|*|-- x[i2]
*
*/
static void butterfly(private_bliss_fft_t *this, uint32_t *x, int i1,int i2,
int iw)
{
uint32_t xp, xm;
xp = x[i1] + x[i2];
xm = x[i1] + (this->p->q - x[i2]);
if (xp >= this->p->q)
{
xp -= this->p->q;
}
x[i1] = xp;
x[i2] = (xm * this->p->w[iw]) % this->p->q;
}
/**
* Trivial butterfly operation of last FFT stage
*/
static void butterfly_last(private_bliss_fft_t *this, uint32_t *x, int i1)
{
uint32_t xp, xm;
int i2 = i1 + 1;
xp = x[i1] + x[i2];
xm = x[i1] + (this->p->q - x[i2]);
if (xp >= this->p->q)
{
xp -= this->p->q;
}
if (xm >= this->p->q)
{
xm -= this->p->q;
}
x[i1] = xp;
x[i2] = xm;
}
METHOD(bliss_fft_t, transform, void,
private_bliss_fft_t *this, uint32_t *a, uint32_t *b, bool inverse)
{
int stage, i, j, k, m, n, t, iw, i_rev;
uint16_t q;
uint32_t tmp;
/* we are going to use the transform size n and the modulus q a lot */
n = this->p->n;
q = this->p->q;
if (!inverse)
{
/* apply linear phase needed for negative wrapped convolution */
for (i = 0; i < n; i++)
{
b[i] = (a[i] * this->p->w[i]) % q;
}
}
else if (a != b)
{
/* copy if input and output array are not the same */
for (i = 0; i < n; i++)
{
b[i] = a[i];
}
}
m = n;
k = 1;
for (stage = this->p->stages; stage > 0; stage--)
{
m >>= 1;
t = 0;
for (j = 0; j < k; j++)
{
if (stage == 1)
{
butterfly_last(this, b, t);
}
else
{
for (i = 0; i < m; i++)
{
iw = 2 * (inverse ? (n - i * k) : (i * k));
butterfly(this, b, t + i, t + i + m, iw);
}
}
t += 2*m;
}
k <<= 1;
}
/* Sort output in bit-reverse order */
for (i = 0; i < n; i++)
{
i_rev = this->p->rev[i];
if (i_rev > i)
{
tmp = b[i];
b[i] = b[i_rev];
b[i_rev] = tmp;
}
}
/**
* Compensate the linear phase needed for negative wrapped convolution
* and normalize the output array with 1/n mod q after the inverse FFT.
*/
if (inverse)
{
for (i = 0; i < n; i++)
{
b[i] = (((b[i] * this->p->w[2*n - i]) % q) * this->p->n_inv) % q;
}
}
}
METHOD(bliss_fft_t, destroy, void,
private_bliss_fft_t *this)
{
free(this);
}
/**
* See header.
*/
bliss_fft_t *bliss_fft_create(bliss_fft_params_t *params)
{
private_bliss_fft_t *this;
INIT(this,
.public = {
.get_size = _get_size,
.get_modulus = _get_modulus,
.transform = _transform,
.destroy = _destroy,
},
.p = params,
);
return &this->public;
}
|
