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
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
|
/* Default code for GPU */
/* A compute capability of 2.0 at least is required */
__device__ void Cuda_Fully_Normalize (biguint_t A, bigint_t cy)
{
carry_t cytemp;
unsigned int thm1;
while(__any(cy[threadIdx.x])!=0)
{
thm1 = (threadIdx.x - 1) % ECM_GPU_NB_DIGITS;
cytemp = cy[thm1];
__add_cc(A[threadIdx.x], A[threadIdx.x], cytemp);
if (cytemp >= 0)
__addcy(cy[threadIdx.x]);
else /* if (cytemp < 0) */
__subcy(cy[threadIdx.x]);
}
}
/* Compute Rmod <- A + B */
/* Input: 0 <= A, B < 3*N */
/* Ouput: 0 <= Rmod < 6*N */
__device__ void Cuda_Add_mod
(biguint_t Rmod, bigint_t cy, const biguint_t A, const biguint_t B)
{
unsigned int thp1 = (threadIdx.x + 1) % ECM_GPU_NB_DIGITS;
__add_cc (Rmod[threadIdx.x], A[threadIdx.x], B[threadIdx.x]);
__addcy2(Rmod[thp1]);
__addcy (cy[thp1]);
Cuda_Fully_Normalize (Rmod, cy);
}
/* Compute Rmod <- Rmod + B */
/* Input: 0 <= Rmod, B < 3*N */
/* (except when it follows Cuda_Mulint_mod, 0 <= Rmod < 3*N, 0 < B < 7*N ) */
/* Ouput: 0 <= Rmod < 6*N */
/* (except when it follows Cuda_Mulint_mod, 0 <= Rmod < 10*N) */
__device__ void Cuda_Add_mod
(biguint_t Rmod, bigint_t cy, const biguint_t A)
{
unsigned int thp1 = (threadIdx.x + 1) % ECM_GPU_NB_DIGITS;
__add_cc (Rmod[threadIdx.x], Rmod[threadIdx.x], A[threadIdx.x]);
//__addcy (cy[threadIdx.x]);
__addcy2(Rmod[thp1]);
__addcy (cy[thp1]);
Cuda_Fully_Normalize (Rmod, cy);
}
/* Compute Rmod <- Rmod - B */
/* Input: 0 <= Rmod, B < 3*N */
/* Ouput: 0 <= Rmod < 6*N */
__device__ void Cuda_Sub_mod
(biguint_t Rmod, bigint_t cy, const biguint_t B, const digit_t N3thdx)
{
digit_t reg_Rmod = Rmod[threadIdx.x];
carry_t reg_cy = 0;
__add_cc (reg_Rmod, reg_Rmod, N3thdx);
__addcy (reg_cy);
__sub_cc (reg_Rmod, reg_Rmod, B[threadIdx.x]);
__subcy2 (reg_cy);
Rmod[threadIdx.x] = reg_Rmod;
cy[threadIdx.x] = reg_cy;
Cuda_Fully_Normalize (Rmod, cy);
}
/* Perform one step of REDC */
__device__ void Cuda_Mulmod_step
(biguint_t r, bigint_t cy, digit_t a, digit_t b, const digit_t Nthdx,
const digit_t invN)
{
digit_t t;
digit_t reg_hi = 0;
unsigned int thp1= (threadIdx.x + 1) % ECM_GPU_NB_DIGITS;
carry_t reg_cy = cy[thp1];
__mad_lo_cc(r[threadIdx.x],a,b);
__madc_hi_cc(reg_hi,a,b);
__addcy2(reg_cy);
__mul_lo(t, invN, r[0]);
__mad_lo_cc(r[threadIdx.x],t,Nthdx);
__madc_hi_cc(reg_hi,t,Nthdx);
__addcy2(reg_cy);
/* make one round of normalize + a right shift at the same time */
__add_cc(r[threadIdx.x],r[thp1],reg_hi);
__addc_cc(r[thp1],r[thp1],reg_cy);
__addcy(cy[thp1]);
}
/* Compute r <- 2*a */
/* Input: 0 <= a < 3*N */
/* Ouput: 0 <= r < 3*N */
__device__ void Cuda_Dbl_mod
(biguint_t r, biguint_t a)
{
unsigned int thp1= (threadIdx.x + 1) % ECM_GPU_NB_DIGITS;
asm ("add.cc.u32 %0, %1, %1;" : "=r"(r[threadIdx.x]) : "r"(a[threadIdx.x]));
__addcy2(r[thp1]);
}
/* Compute r <- A*b */
/* Input: 0 < b < 2^SIZE_DIGIT, 0 <= A < 6*N */
/* Ouput: 0 <= r < 7*N */
__device__ void Cuda_Mulint_mod
(biguint_t r, bigint_t cy, biguint_t A, digit_t b, const digit_t Nthdx,
const digit_t invN)
{
digit_t t;
digit_t reg_hi;
unsigned int thp1= (threadIdx.x + 1) % ECM_GPU_NB_DIGITS;
digit_t reg_A = A[threadIdx.x];
carry_t reg_cy;
__mul_lo(r[threadIdx.x],reg_A,b);
__mul_hi(reg_hi,reg_A,b);
__mul_lo(t, invN, r[0]);
__mad_lo_cc(r[threadIdx.x],t,Nthdx);
__madc_hi_cc(reg_hi,t,Nthdx);
__addcy(reg_cy);
/* make one round of normalize + a right shift at the same time */
__add_cc(r[threadIdx.x],r[thp1],reg_hi);
__addc_cc(r[thp1],r[thp1],reg_cy);
__addcy(cy[thp1]);
Cuda_Fully_Normalize(r,cy);
}
/* Compute r <- A*B */
/* Input: 0 <= A, B < 6*N */
/* (except when it follows Cuda_Mulint_mod, 0 <= A < 6*N, 0 < B < 10*N ) */
/* Ouput: 0 <= r < 3*N */
__device__ void Cuda_Mul_mod
(biguint_t mul, bigint_t cy, const biguint_t A, const biguint_t B, biguint_t r,
const digit_t Nthdx, const digit_t invN)
{
int i;
digit_t temp=A[threadIdx.x];
r[threadIdx.x]=0;
for (i=0; i<ECM_GPU_NB_DIGITS; i++)
Cuda_Mulmod_step (r, cy, temp, B[i], Nthdx, invN);
Cuda_Fully_Normalize (r, cy);
mul[threadIdx.x]=r[threadIdx.x];
}
__device__ void Cuda_Square_mod
(biguint_t mul, bigint_t cy, const biguint_t A, biguint_t r,
const digit_t Nthdx, const digit_t invN)
{
Cuda_Mul_mod (mul, cy, A, A, r, Nthdx, invN);
}
/*
Compute silmutaneously:
(xarg : zarg ) <- [2](xarg : zarg)
(xarg2 : zarg2 ) <- (xarg : zarg) + (xarg2 : zarg2)
*/
__global__ void
Cuda_Ell_DblAdd (biguint_t *xAarg, biguint_t *zAarg, biguint_t *xBarg,
biguint_t *zBarg, unsigned int firstinvd)
{
__shared__ VOL digit_t b_temp_r[ECM_GPU_CURVES_BY_BLOCK][ECM_GPU_NB_DIGITS];
__shared__ VOL carry_t b_cy[ECM_GPU_CURVES_BY_BLOCK][ECM_GPU_NB_DIGITS];
__shared__ VOL digit_t b_t[ECM_GPU_CURVES_BY_BLOCK][ECM_GPU_NB_DIGITS];
__shared__ VOL digit_t b_u[ECM_GPU_CURVES_BY_BLOCK][ECM_GPU_NB_DIGITS];
__shared__ VOL digit_t b_v[ECM_GPU_CURVES_BY_BLOCK][ECM_GPU_NB_DIGITS];
__shared__ VOL digit_t b_w[ECM_GPU_CURVES_BY_BLOCK][ECM_GPU_NB_DIGITS];
VOL digit_t *t=b_t[threadIdx.y];
VOL digit_t *u=b_u[threadIdx.y];
VOL digit_t *v=b_v[threadIdx.y];
VOL digit_t *w=b_w[threadIdx.y];
VOL digit_t *temp_r=b_temp_r[threadIdx.y];
VOL carry_t *cy=b_cy[threadIdx.y];
/* Init of shared variables */
const unsigned int idx1=blockIdx.x*blockDim.y+threadIdx.y;
//unsigned int t1=threadIdx.x+1;
cy[threadIdx.x]=0;
w[threadIdx.x]=xBarg[idx1][threadIdx.x];
v[threadIdx.x]=zBarg[idx1][threadIdx.x];
temp_r[threadIdx.x]=xAarg[idx1][threadIdx.x];
u[threadIdx.x]=zAarg[idx1][threadIdx.x];
const digit_t Nthdx = d_Ncst[threadIdx.x];
const digit_t N3thdx = d_3Ncst[threadIdx.x];
const digit_t invN = d_invNcst;
Cuda_Add_mod(t, cy, v, w); /* C=zB+xB */
Cuda_Sub_mod(v, cy, w, N3thdx); /* D=zB-xB */
Cuda_Add_mod(w, cy, u, temp_r); /* A=zA+xA */
Cuda_Sub_mod(u, cy, temp_r, N3thdx); /* B=zA-xA */
Cuda_Mul_mod(t, cy, t, u, temp_r, Nthdx, invN); /* CB=C*B=(zB+xB)(zA-xA) */
Cuda_Mul_mod(v, cy, v, w, temp_r, Nthdx, invN); /* DA=D*A=(zB-xB)(zA+xA) */
Cuda_Square_mod(w, cy, w, temp_r, Nthdx, invN); /* AA=A^2 */
Cuda_Square_mod(u, cy, u, temp_r, Nthdx, invN); /* BB=B^2 */
Cuda_Mul_mod(temp_r, cy, u, w, temp_r, Nthdx, invN); /* AA*BB */
xAarg[idx1][threadIdx.x]=temp_r[threadIdx.x];
Cuda_Sub_mod (w, cy, u, N3thdx); /* K= AA-BB */
Cuda_Mulint_mod (temp_r, cy, w, idx1 + firstinvd, Nthdx, invN); /* d*K */
Cuda_Add_mod (u, cy, temp_r); /* BB+d*K */
Cuda_Mul_mod (w, cy, w, u, temp_r, Nthdx, invN); /* K*(BB+d*K) */
zAarg[idx1][threadIdx.x]=w[threadIdx.x];
Cuda_Add_mod(w, cy, v, t); /* DA+CB mod N */
Cuda_Sub_mod(v, cy, t, N3thdx); /* DA-CB mod N */
Cuda_Square_mod(w, cy, w, temp_r, Nthdx, invN); /* (DA+CB)^2 mod N */
Cuda_Square_mod(v, cy, v, temp_r, Nthdx, invN); /* (DA-CB)^2 mod N */
/* z0=1 so there is nothing to compute for z0*(DA+CB)^2 */
Cuda_Dbl_mod(temp_r, v); /* x0=2 x0*(DA-CB)^2 */
xBarg[idx1][threadIdx.x]=w[threadIdx.x];
zBarg[idx1][threadIdx.x]=temp_r[threadIdx.x];
}
|
