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
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
|
#!/usr/bin/python
import re
import sys
def offaddr(addr, offset):
if offset == 0:
return "("+addr+")"
else:
return str(offset)+"("+addr+")"
# Generate asm for addmul1_k
# src and dst are pointers (stored in regs) + offsets
# multiplier is in a register
# rax, rbx, rcx, rdx are free for use.
def addmul1_k(src, off_src, dst, off_dst, mult, k):
init = "### addmul1: src[0] is " + offaddr(src, off_src) + "\n"
init = init + "### dst[0] is " + offaddr(dst, off_dst) + "\n"
init = init + "### mult is " + mult + "\n"
init = init + "### k is " + str(k) + "\n"
init = init + "### kills %rax, %rbx, %rcx, %rdx\n"
init = init + "### dst[0,k[ += mult*src[0,k[ plus carry put in rcx or rbx\n"
init = init + " movq " + offaddr(src, off_src) + ", %rax\n"
init = init + " mulq " + mult + "\n"
init = init + " movq %rax, %rbx\n"
init = init + " movq %rdx, %rcx\n"
block = """
movq __xii__, %rax
mulq __mult__
addq __cylo__, __zi__
adcq %rax, __cyhi__
movq %rdx, __cylo__
adcq $0, __cylo__
"""
code = init
cylo = "%rbx"
cyhi = "%rcx"
for i in range(0,k-1):
blocki = re.sub('__cylo__', cylo, block)
blocki = re.sub('__cyhi__', cyhi, blocki)
blocki = re.sub('__xii__', offaddr(src, off_src+(i+1)*8), blocki)
blocki = re.sub('__zi__', offaddr(dst, off_dst+i*8), blocki)
blocki = re.sub('__mult__', mult, blocki)
code = code + blocki
tmp = cylo
cylo = cyhi
cyhi = tmp
final = " addq " + cylo + ", " + offaddr(dst, off_dst+8*(k-1)) + "\n"
final = final + " adcq $0, " + cyhi + "\n"
final = final + "### carry limb is in " + cyhi + "\n"
code = code + final
return code, cyhi
######## TODO: improve this code!!!!
def mul1_k(src, off_src, dst, off_dst, mult, k):
init = "### mul1: src[0] is " + offaddr(src, off_src) + "\n"
init = init + "### dst[0] is " + offaddr(dst, off_dst) + "\n"
init = init + "### mult is " + mult + "\n"
init = init + "### k is " + str(k) + "\n"
init = init + "### kills %rax, %rbx, %rcx, %rdx\n"
init = init + "### dst[0,k[ = mult*src[0,k[ plus carry put in rcx or rbx\n"
init = init + " movq " + offaddr(src, off_src) + ", %rax\n"
init = init + " mulq " + mult + "\n"
init = init + " movq %rax, %rbx\n"
init = init + " movq %rdx, %rcx\n"
block = """
movq __xii__, %rax
mulq __mult__
movq __cylo__, __zi__
addq %rax, __cyhi__
movq %rdx, __cylo__
adcq $0, __cylo__
"""
code = init
cylo = "%rbx"
cyhi = "%rcx"
for i in range(0,k-1):
blocki = re.sub('__cylo__', cylo, block)
blocki = re.sub('__cyhi__', cyhi, blocki)
blocki = re.sub('__xii__', offaddr(src, off_src+(i+1)*8), blocki)
blocki = re.sub('__zi__', offaddr(dst, off_dst+i*8), blocki)
blocki = re.sub('__mult__', mult, blocki)
code = code + blocki
tmp = cylo
cylo = cyhi
cyhi = tmp
final = " movq " + cylo + ", " + offaddr(dst, off_dst+8*(k-1)) + "\n"
final = final + "### carry limb is in " + cyhi + "\n"
code = code + final
return code
def mulredc_k_rolled(k):
header = """# mp_limb_t mulredc__k(mp_limb_t * z, const mp_limb_t * x, const mp_limb_t * y,
# const mp_limb_t *m, mp_limb_t inv_m);
#
include(`config.m4')
TEXT
GLOBL GSYM_PREFIX`'mulredc__k
TYPE(GSYM_PREFIX`'mulredc__k,`function')
GSYM_PREFIX`'mulredc__k:
"""
init = re.sub("__k", str(k), header)
init = init + """ movq %rdx, %r11
movq %rcx, %r10
pushq %rbx
pushq %rbp
"""
init = init + " subq $" + str(8*(2*k+1)) + ", %rsp\n"
init = init + """# %r8 : inv_m
# %r10 : m
# %r11 : y
# %rsi : x
# %rdi : z
# %rsp : tmp
# Free registers
# %rax, %rbx, %rcx, %rdx, %r9
### set tmp[0..2k+1[ to 0
"""
for i in range(0,2*k+1):
init = init + " movq $0, " + offaddr("%rsp", 8*i) + "\n"
code = init
middle_code = "###########################################\n"
middle_code = middle_code + " movq $" + str(k) + ", %rbp\n"
middle_code = middle_code + """
.align 64
Loop:
## compute u and store in %r9
movq (%rsi), %rax
mulq (%r11)
addq (%rsp), %rax
mulq %r8
movq %rax, %r9
"""
codeaddmul, carry = addmul1_k("%r10", 0, "%rsp", 0, "%r9", k)
middle_code = middle_code + codeaddmul
middle_code = middle_code + " addq " + carry + ", " + offaddr("%rsp", 8*k) + "\n"
middle_code = middle_code + " adcq $0, " + offaddr("%rsp", 8*(k+1)) + "\n"
middle_code = middle_code + " movq (%rsi), %r9\n"
codeaddmul, carry = addmul1_k("%r11", 0, "%rsp", 0, "%r9", k)
middle_code = middle_code + codeaddmul
middle_code = middle_code + " addq " + carry + ", " + offaddr("%rsp", 8*k) + "\n"
middle_code = middle_code + " adcq $0, " + offaddr("%rsp", 8*(k+1)) + "\n\n"
middle_code = middle_code + """
addq $8, %rsi
addq $8, %rsp
decq %rbp
jnz Loop
"""
code = code + middle_code
final = "###########################################\n"
final = final + "### Copy result in z\n"
for i in range(0,k):
final = final + " movq " + offaddr("%rsp", 8*i) + ", %rax\n"
final = final + " movq %rax, " + offaddr("%rdi", 8*i) + "\n"
final = final + " movq " + offaddr("%rsp", 8*k) + ", %rax # carry\n"
final = final + " addq $" + str(8*(k+1)) + ", %rsp\n"
final = final + " popq %rbp\n"
final = final + " popq %rbx\n"
final = final + " ret\n"
code = code + final
return code
def mulredc_k(k):
header = """# mp_limb_t mulredc__k(mp_limb_t * z, const mp_limb_t * x, const mp_limb_t * y,
# const mp_limb_t *m, mp_limb_t inv_m);
#
include(`config.m4')
TEXT
GLOBL GSYM_PREFIX`'mulredc__k
TYPE(GSYM_PREFIX`'mulredc__k,`function')
GSYM_PREFIX`'mulredc__k:
"""
init = re.sub("__k", str(k), header)
init = init + """ movq %rdx, %r11
movq %rcx, %r10
pushq %rbx
"""
init = init + " subq $" + str(8*(2*k+1)) + ", %rsp\n"
init = init + """# %r8 : inv_m
# %r10 : m
# %r11 : y
# %rsi : x
# %rdi : z
# %rsp : tmp
# Free registers
# %rax, %rbx, %rcx, %rdx, %r9
### set tmp[0..2k+1[ to 0
"""
for i in range(0,2*k+1):
init = init + " movq $0, " + offaddr("%rsp", 8*i) + "\n"
code = init
for i in range(0,k):
blocki = "###########################################\n"
blocki = blocki + "### Step " + str(i) + "\n"
blocki = blocki + "### Compute u and store in %r9\n"
blocki = blocki + " movq " + offaddr("%rsi", 8*i) + ", %rax\n"
blocki = blocki + " mulq (%r11)\n"
blocki = blocki + " addq " + offaddr("%rsp", 8*i) + ", %rax\n"
blocki = blocki + " mulq %r8\n"
blocki = blocki + " movq %rax, %r9\n"
blocki = blocki + "### tmp[i,i+k] += x[i]*y + u*m\n"
codeaddmul, carry = addmul1_k("%r10", 0, "%rsp", 8*i, "%r9", k)
blocki = blocki + codeaddmul
blocki = blocki + " addq " + carry + ", " + offaddr("%rsp", 8*(k+i)) + "\n"
blocki = blocki + " adcq $0, " + offaddr("%rsp", 8*(k+i+1)) + "\n"
blocki = blocki + " movq " + offaddr("%rsi", 8*i) + ", %r9\n"
codeaddmul, carry = addmul1_k("%r11", 0, "%rsp", 8*i, "%r9", k)
blocki = blocki + codeaddmul
blocki = blocki + " addq " + carry + ", " + offaddr("%rsp", 8*(k+i)) + "\n"
blocki = blocki + " adcq $0, " + offaddr("%rsp", 8*(k+i+1)) + "\n"
code = code + blocki
final = "###########################################\n"
final = final + "### Copy result in z\n"
for i in range(0,k):
final = final + " movq " + offaddr("%rsp", 8*(k+i)) + ", %rax\n"
final = final + " movq %rax, " + offaddr("%rdi", 8*i) + "\n"
final = final + " movq " + offaddr("%rsp", 16*k) + ", %rax # carry\n"
final = final + " addq $" + str(8*(2*k+1)) + ", %rsp\n"
final = final + " popq %rbx\n"
final = final + " ret\n"
code = code + final
return code
##print addmul1_k("%rsi", 0, "%dsi", 0, "%r9", 3)
k = int(sys.argv[1])
if k == 1:
print """#
# mp_limb_t mulredc1(mp_limb_t * z, const mp_limb_t x, const mp_limb_t y,
# const mp_limb_t m, mp_limb_t inv_m)
#
# Compute z := x*y mod m, in Montgomery representation, where x, y < m
# and m is n limb wide. inv_m is the less significant limb of the
# inverse of m modulo 2^(n*GMP_LIMB_BITS)
#
# The result might be unreduced (larger than m) but becomes reduced
# after subtracting m. The calling function should take care of that.
#
# We use a temporary space for unreduced product on the stack.
# Therefore, this can not be used for large integers (anyway, the
# algorithm is quadratic).
#
# WARNING: z is only n limbs but since it might be unreduced, there
# could be a carry that does not fit in z. This carry is returned.
include(`config.m4')
TEXT
GLOBL GSYM_PREFIX`'mulredc1
TYPE(GSYM_PREFIX`'mulredc1,`function')
GSYM_PREFIX`'mulredc1:
# %r8 : inv_m
# %rcx : m
# %rdx : y
# %rsi : x
# %rdi : z
movq %rdx, %rax
mulq %rsi
movq %rdx, %r10
movq %rax, %r9 # store xy in [r9:r10]
mulq %r8 # compute u
mulq %rcx # compute u*m
addq %r9, %rax # rax is 0, now (carry is important)
adcq %r10, %rdx
movq %rdx, (%rdi)
adcq $0, %rax
ret
"""
else:
print mulredc_k_rolled(k)
|
