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[/] [pairing/] [trunk/] [rtl/] [f3m.v] - Blame information for rev 10

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Line No. Rev Author Line
1 2 homer.xing 
`include "inc.v"
2 
`define MOST 2*`M+1:2*`M
3 
 
4 3 homer.xing 
// out = (v1 & l1) | (v2 & l2) | (v3 & l3)
5 
module f3m_mux3(v1, l1, v2, l2, v3, l3, out);
6 
    input [`WIDTH:0] v1, v2, v3;
7 
    input l1, l2, l3;
8 
    output [`WIDTH:0] out;
9 
    genvar i;
10 
    generate
11 
        for(i=0;i<=`WIDTH;i=i+1)
12 
          begin : label
13 
            assign out[i] = (v1[i] & l1) | (v2[i] & l2) | (v3[i] & l3);
14 
          end
15 
    endgenerate
16 
endmodule
17 
 
18 
// out = (v0 & l0) | (v1 & l1) | (v2 & l2) | ... | (v5 & l5)
19 
module f3m_mux6(v0, v1, v2, v3, v4, v5, l0, l1, l2, l3, l4, l5, out);
20 
    input l0, l1, l2, l3, l4, l5;
21 
    input [`WIDTH:0] v0, v1, v2, v3, v4, v5;
22 
    output reg [`WIDTH:0] out;
23 
    always @ (l0,l1,l2,l3,l4,l5,v0,v1,v2,v3,v4,v5)
24 
      case ({l0,l1,l2,l3,l4,l5})
25 
        6'b100000: out = v0;
26 
        6'b010000: out = v1;
27 
        6'b001000: out = v2;
28 
        6'b000100: out = v3;
29 
        6'b000010: out = v4;
30 
        6'b000001: out = v5;
31 
        default: out = 0;
32 
      endcase
33 
endmodule
34 
 
35 2 homer.xing 
// f3m_add: C = A + B, in field F_{3^M}
36 
module f3m_add(A, B, C);
37 
    input [`WIDTH : 0] A, B;
38 
    output [`WIDTH : 0] C;
39 
    genvar i;
40 
    generate
41 
        for(i=0; i<`M; i=i+1) begin: aa
42 
            f3_add aa(A[(2*i+1) : 2*i], B[(2*i+1) : 2*i], C[(2*i+1) : 2*i]);
43 
        end
44 
    endgenerate
45 
endmodule
46 
 
47 3 homer.xing 
// f3m_add3: c == a0+a1+a2, in field GF(3^M)
48 
module f3m_add3(a0, a1, a2, c);
49 
    input [`WIDTH:0] a0,a1,a2;
50 
    output [`WIDTH:0] c;
51 
    wire [`WIDTH:0] v;
52 
    f3m_add
53 
        ins1 (a0,a1,v), // v == a0+a1
54 
        ins2 (v,a2,c);  // c == v+a2 == a0+a1+a2
55 
endmodule
56 
 
57 
// f3m_add4: c == a0+a1+a2+a3, in field GF(3^M)
58 
module f3m_add4(a0, a1, a2, a3, c);
59 
    input [`WIDTH:0] a0,a1,a2,a3;
60 
    output [`WIDTH:0] c;
61 
    wire [`WIDTH:0] v1,v2;
62 
    f3m_add
63 
        ins1 (a0,a1,v1), // v1 == a0+a1
64 
        ins2 (a2,a3,v2), // v2 == a2+a3
65 
        ins3 (v1,v2,c);  // c == v1+v2 == a0+a1+a2+a3
66 
endmodule
67 
 
68 2 homer.xing 
// f3m_neg: c == -a in GF(3^M)
69 
module f3m_neg(a, c);
70 
    input [`WIDTH:0] a;
71 
    output [`WIDTH:0] c;
72 
    genvar i;
73 
    generate
74 
        for(i=0;i<=`WIDTH;i=i+2)
75 
          begin:label
76 
            assign c[i+1:i] = {a[i],a[i+1]};
77 
          end
78 
    endgenerate
79 
endmodule
80 
 
81 
// f3m_sub: C = A - B, in field F_{3^M}
82 
module f3m_sub(A, B, C);
83 
    input [`WIDTH : 0] A, B;
84 
    output [`WIDTH : 0] C;
85 
    genvar i;
86 
    generate
87 
        for(i=0; i<`M; i=i+1) begin: aa
88 
            f3_sub aa(A[(2*i+1) : 2*i], B[(2*i+1) : 2*i], C[(2*i+1) : 2*i]);
89 
        end
90 
    endgenerate
91 
endmodule
92 
 
93 
// f3m_mult: C = A * B, in field GF(3^M)
94 
module f3m_mult(clk, reset, A, B, C, done);
95 
    input [`WIDTH : 0] A, B;
96 
    input clk;
97 
    input reset;
98 
    output reg [`WIDTH : 0] C;
99 
    output reg done;
100 
    reg [`WIDTH : 0] x, y, z;
101 
    wire [`WIDTH : 0] z1, z2, z4;
102 
    wire [`WIDTH+2 : 0] z3;
103 8 homer.xing 
    reg [`M : 0] i;
104 2 homer.xing 
    wire done1;
105 
    wire [1:0] dummy;
106 
 
107 
    func4
108 
        ins1 ({2'b0,x}, y[1:0], {dummy,z1}); // z1 == A * B[0]
109 
    f3m_add
110 
        ins2 (z1, z, z2); // z2 == z1 + z == A*B[0] + z
111 
    assign z4 = {2'd0, y[`WIDTH:2]}; // z4 == y >> 2
112 
    func3
113 
        ins3 ({2'd0,x}, z3); // z3 == X*x mod p(x)
114 8 homer.xing 
    assign done1 = i[0];
115 2 homer.xing 
 
116 
    always @ (posedge clk)
117 
        if (done1)
118 
            C <= z;
119 
 
120 
    always @ (posedge clk)
121 
        if (reset)
122 
            done <= 0;
123 
        else if (done1)
124 
            done <= 1;
125 
 
126 
    always @ (posedge clk)
127 
      begin
128 
        if (reset)
129 
          begin
130 8 homer.xing 
            x <= A; y <= B; z <= 0; i <= {1'b1,{`M{1'b0}}};
131 2 homer.xing 
          end
132 
        else
133 
          begin
134 8 homer.xing 
            x <= z3[`WIDTH:0]; y <= z4; z <= z2; i <= i >> 1;
135 2 homer.xing 
          end
136 
      end
137 
endmodule
138 
 
139 7 homer.xing 
// c0 == a0*b0; c1 == a1*b1; c2 == a2*b2; all in GF(3^M)
140 
module f3m_mult3(clk, reset,
141 
                 a0, b0, c0,
142 
                 a1, b1, c1,
143 
                 a2, b2, c2,
144 
                 done);
145 
    input clk, reset;
146 
    input [`WIDTH:0] a0, b0, a1, b1, a2, b2;
147 
    output reg [`WIDTH:0] c0, c1, c2;
148 
    output reg done;
149 
    reg [3:0] K;
150 
    reg mult_reset, delay1, delay2;
151 
    wire e1, e2, e3, mult_done, delay3, rst;
152 
    wire [`WIDTH:0] in1, in2, o;
153 
 
154 
    assign rst = delay2;
155 
    assign {e1,e2,e3} = K[3:1];
156 
 
157 
    f3m_mux3
158 
        ins9 (a0, e1, a1, e2, a2, e3, in1),
159 
        ins10 (b0, e1, b1, e2, b2, e3, in2);
160 
    f3m_mult
161 
        ins11 (clk, mult_reset, in1, in2, o, mult_done); // o == in1 * in2 in GF(3^m)
162 
    func6
163 8 homer.xing 
        ins12 (clk, reset, mult_done, delay3);
164 7 homer.xing 
 
165 
    always @ (posedge clk)
166 
      begin
167 
        if (e1) c0 <= o;
168 
        if (e2) c1 <= o;
169 
        if (e3) c2 <= o;
170 
      end
171 
 
172 
    always @ (posedge clk)
173 
        if (reset) K <= 4'b1000;
174 8 homer.xing 
        else if (delay3 | K[0]) K <= {1'b0,K[3:1]};
175 7 homer.xing 
 
176 
    always @ (posedge clk)
177 
      begin
178 
        if (rst) mult_reset <= 1;
179 
        else if (mult_done) mult_reset <= 1;
180 
        else mult_reset <= 0;
181 
      end
182 
 
183 
    always @ (posedge clk)
184 
        if (reset)     done <= 0;
185 
        else if (K[0]) done <= 1;
186 
 
187 
    always @ (posedge clk)
188 
      begin
189 
        delay2 <= delay1; delay1 <= reset;
190 
      end
191 
endmodule
192 
 
193 2 homer.xing 
/* out == in^3 mod p(x) */
194 
/* p(x) == x^97 + x^12 + 2 */
195 
module f3m_cubic(input [193:0] in, output [193:0] out);
196 
wire [1:0] w0; f3_add a0(in[131:130], in[139:138], w0);
197 
wire [1:0] w1; f3_add a1(in[133:132], in[141:140], w1);
198 
wire [1:0] w2; f3_add a2(in[135:134], in[143:142], w2);
199 
wire [1:0] w3; f3_add a3(in[137:136], in[145:144], w3);
200 
wire [1:0] w4; f3_add a4(in[147:146], in[155:154], w4);
201 
wire [1:0] w5; f3_add a5(in[149:148], in[157:156], w5);
202 
wire [1:0] w6; f3_add a6(in[151:150], in[159:158], w6);
203 
wire [1:0] w7; f3_add a7(in[153:152], in[161:160], w7);
204 
wire [1:0] w8; f3_add a8(in[163:162], in[171:170], w8);
205 
wire [1:0] w9; f3_add a9(in[165:164], in[173:172], w9);
206 
wire [1:0] w10; f3_add a10(in[167:166], in[175:174], w10);
207 
wire [1:0] w11; f3_add a11(in[169:168], in[177:176], w11);
208 
wire [1:0] w12; f3_add a12(in[179:178], in[187:186], w12);
209 
wire [1:0] w13; f3_add a13(in[181:180], in[189:188], w13);
210 
wire [1:0] w14; f3_add a14(in[183:182], in[191:190], w14);
211 
wire [1:0] w15; f3_add a15(in[185:184], in[193:192], w15);
212 
wire [1:0] w16;
213 
f3_add a16(in[1:0], w12, w16);
214 
assign out[1:0] = w16;
215 
wire [1:0] w17;
216 
f3_add a17({in[122],in[123]}, in[131:130], w17);
217 
assign out[3:2] = w17;
218 
assign out[5:4] = in[67:66];
219 
wire [1:0] w18;
220 
f3_add a18(in[3:2], w13, w18);
221 
assign out[7:6] = w18;
222 
wire [1:0] w19;
223 
f3_add a19({in[124],in[125]}, in[133:132], w19);
224 
assign out[9:8] = w19;
225 
assign out[11:10] = in[69:68];
226 
wire [1:0] w20;
227 
f3_add a20(in[5:4], w14, w20);
228 
assign out[13:12] = w20;
229 
wire [1:0] w21;
230 
f3_add a21({in[126],in[127]}, in[135:134], w21);
231 
assign out[15:14] = w21;
232 
assign out[17:16] = in[71:70];
233 
wire [1:0] w22;
234 
f3_add a22(in[7:6], w15, w22);
235 
assign out[19:18] = w22;
236 
wire [1:0] w23;
237 
f3_add a23({in[128],in[129]}, in[137:136], w23);
238 
assign out[21:20] = w23;
239 
assign out[23:22] = in[73:72];
240 
wire [1:0] w24;
241 
f3_add a24(in[9:8], {in[178],in[179]}, w24);
242 
assign out[25:24] = w24;
243 
wire [1:0] w25;
244 
f3_add a25(in[123:122], w0, w25);
245 
assign out[27:26] = w25;
246 
wire [1:0] w26;
247 
f3_add a26({in[66],in[67]}, in[75:74], w26);
248 
assign out[29:28] = w26;
249 
wire [1:0] w27;
250 
f3_add a27(in[11:10], {in[180],in[181]}, w27);
251 
assign out[31:30] = w27;
252 
wire [1:0] w28;
253 
f3_add a28(in[125:124], w1, w28);
254 
assign out[33:32] = w28;
255 
wire [1:0] w29;
256 
f3_add a29({in[68],in[69]}, in[77:76], w29);
257 
assign out[35:34] = w29;
258 
wire [1:0] w30;
259 
f3_add a30(in[13:12], {in[182],in[183]}, w30);
260 
assign out[37:36] = w30;
261 
wire [1:0] w31;
262 
f3_add a31(in[127:126], w2, w31);
263 
assign out[39:38] = w31;
264 
wire [1:0] w32;
265 
f3_add a32({in[70],in[71]}, in[79:78], w32);
266 
assign out[41:40] = w32;
267 
wire [1:0] w33;
268 
f3_add a33(in[15:14], {in[184],in[185]}, w33);
269 
assign out[43:42] = w33;
270 
wire [1:0] w34;
271 
f3_add a34(in[129:128], w3, w34);
272 
assign out[45:44] = w34;
273 
wire [1:0] w35;
274 
f3_add a35({in[72],in[73]}, in[81:80], w35);
275 
assign out[47:46] = w35;
276 
wire [1:0] w36;
277 
f3_add a36(in[17:16], {in[186],in[187]}, w36);
278 
assign out[49:48] = w36;
279 
wire [1:0] w37;
280 
f3_add a37(in[147:146], w0, w37);
281 
assign out[51:50] = w37;
282 
wire [1:0] w38;
283 
f3_add a38({in[74],in[75]}, in[83:82], w38);
284 
assign out[53:52] = w38;
285 
wire [1:0] w39;
286 
f3_add a39(in[19:18], {in[188],in[189]}, w39);
287 
assign out[55:54] = w39;
288 
wire [1:0] w40;
289 
f3_add a40(in[149:148], w1, w40);
290 
assign out[57:56] = w40;
291 
wire [1:0] w41;
292 
f3_add a41({in[76],in[77]}, in[85:84], w41);
293 
assign out[59:58] = w41;
294 
wire [1:0] w42;
295 
f3_add a42(in[21:20], {in[190],in[191]}, w42);
296 
assign out[61:60] = w42;
297 
wire [1:0] w43;
298 
f3_add a43(in[151:150], w2, w43);
299 
assign out[63:62] = w43;
300 
wire [1:0] w44;
301 
f3_add a44({in[78],in[79]}, in[87:86], w44);
302 
assign out[65:64] = w44;
303 
wire [1:0] w45;
304 
f3_add a45(in[23:22], {in[192],in[193]}, w45);
305 
assign out[67:66] = w45;
306 
wire [1:0] w46;
307 
f3_add a46(in[153:152], w3, w46);
308 
assign out[69:68] = w46;
309 
wire [1:0] w47;
310 
f3_add a47({in[80],in[81]}, in[89:88], w47);
311 
assign out[71:70] = w47;
312 
assign out[73:72] = in[25:24];
313 
wire [1:0] w48;
314 
f3_add a48(in[139:138], w4, w48);
315 
assign out[75:74] = w48;
316 
wire [1:0] w49;
317 
f3_add a49({in[82],in[83]}, in[91:90], w49);
318 
assign out[77:76] = w49;
319 
assign out[79:78] = in[27:26];
320 
wire [1:0] w50;
321 
f3_add a50(in[141:140], w5, w50);
322 
assign out[81:80] = w50;
323 
wire [1:0] w51;
324 
f3_add a51({in[84],in[85]}, in[93:92], w51);
325 
assign out[83:82] = w51;
326 
assign out[85:84] = in[29:28];
327 
wire [1:0] w52;
328 
f3_add a52(in[143:142], w6, w52);
329 
assign out[87:86] = w52;
330 
wire [1:0] w53;
331 
f3_add a53({in[86],in[87]}, in[95:94], w53);
332 
assign out[89:88] = w53;
333 
assign out[91:90] = in[31:30];
334 
wire [1:0] w54;
335 
f3_add a54(in[145:144], w7, w54);
336 
assign out[93:92] = w54;
337 
wire [1:0] w55;
338 
f3_add a55({in[88],in[89]}, in[97:96], w55);
339 
assign out[95:94] = w55;
340 
assign out[97:96] = in[33:32];
341 
wire [1:0] w56;
342 
f3_add a56(in[163:162], w4, w56);
343 
assign out[99:98] = w56;
344 
wire [1:0] w57;
345 
f3_add a57({in[90],in[91]}, in[99:98], w57);
346 
assign out[101:100] = w57;
347 
assign out[103:102] = in[35:34];
348 
wire [1:0] w58;
349 
f3_add a58(in[165:164], w5, w58);
350 
assign out[105:104] = w58;
351 
wire [1:0] w59;
352 
f3_add a59({in[92],in[93]}, in[101:100], w59);
353 
assign out[107:106] = w59;
354 
assign out[109:108] = in[37:36];
355 
wire [1:0] w60;
356 
f3_add a60(in[167:166], w6, w60);
357 
assign out[111:110] = w60;
358 
wire [1:0] w61;
359 
f3_add a61({in[94],in[95]}, in[103:102], w61);
360 
assign out[113:112] = w61;
361 
assign out[115:114] = in[39:38];
362 
wire [1:0] w62;
363 
f3_add a62(in[169:168], w7, w62);
364 
assign out[117:116] = w62;
365 
wire [1:0] w63;
366 
f3_add a63({in[96],in[97]}, in[105:104], w63);
367 
assign out[119:118] = w63;
368 
assign out[121:120] = in[41:40];
369 
wire [1:0] w64;
370 
f3_add a64(in[155:154], w8, w64);
371 
assign out[123:122] = w64;
372 
wire [1:0] w65;
373 
f3_add a65({in[98],in[99]}, in[107:106], w65);
374 
assign out[125:124] = w65;
375 
assign out[127:126] = in[43:42];
376 
wire [1:0] w66;
377 
f3_add a66(in[157:156], w9, w66);
378 
assign out[129:128] = w66;
379 
wire [1:0] w67;
380 
f3_add a67({in[100],in[101]}, in[109:108], w67);
381 
assign out[131:130] = w67;
382 
assign out[133:132] = in[45:44];
383 
wire [1:0] w68;
384 
f3_add a68(in[159:158], w10, w68);
385 
assign out[135:134] = w68;
386 
wire [1:0] w69;
387 
f3_add a69({in[102],in[103]}, in[111:110], w69);
388 
assign out[137:136] = w69;
389 
assign out[139:138] = in[47:46];
390 
wire [1:0] w70;
391 
f3_add a70(in[161:160], w11, w70);
392 
assign out[141:140] = w70;
393 
wire [1:0] w71;
394 
f3_add a71({in[104],in[105]}, in[113:112], w71);
395 
assign out[143:142] = w71;
396 
assign out[145:144] = in[49:48];
397 
wire [1:0] w72;
398 
f3_add a72(in[179:178], w8, w72);
399 
assign out[147:146] = w72;
400 
wire [1:0] w73;
401 
f3_add a73({in[106],in[107]}, in[115:114], w73);
402 
assign out[149:148] = w73;
403 
assign out[151:150] = in[51:50];
404 
wire [1:0] w74;
405 
f3_add a74(in[181:180], w9, w74);
406 
assign out[153:152] = w74;
407 
wire [1:0] w75;
408 
f3_add a75({in[108],in[109]}, in[117:116], w75);
409 
assign out[155:154] = w75;
410 
assign out[157:156] = in[53:52];
411 
wire [1:0] w76;
412 
f3_add a76(in[183:182], w10, w76);
413 
assign out[159:158] = w76;
414 
wire [1:0] w77;
415 
f3_add a77({in[110],in[111]}, in[119:118], w77);
416 
assign out[161:160] = w77;
417 
assign out[163:162] = in[55:54];
418 
wire [1:0] w78;
419 
f3_add a78(in[185:184], w11, w78);
420 
assign out[165:164] = w78;
421 
wire [1:0] w79;
422 
f3_add a79({in[112],in[113]}, in[121:120], w79);
423 
assign out[167:166] = w79;
424 
assign out[169:168] = in[57:56];
425 
wire [1:0] w80;
426 
f3_add a80(in[171:170], w12, w80);
427 
assign out[171:170] = w80;
428 
wire [1:0] w81;
429 
f3_add a81({in[114],in[115]}, in[123:122], w81);
430 
assign out[173:172] = w81;
431 
assign out[175:174] = in[59:58];
432 
wire [1:0] w82;
433 
f3_add a82(in[173:172], w13, w82);
434 
assign out[177:176] = w82;
435 
wire [1:0] w83;
436 
f3_add a83({in[116],in[117]}, in[125:124], w83);
437 
assign out[179:178] = w83;
438 
assign out[181:180] = in[61:60];
439 
wire [1:0] w84;
440 
f3_add a84(in[175:174], w14, w84);
441 
assign out[183:182] = w84;
442 
wire [1:0] w85;
443 
f3_add a85({in[118],in[119]}, in[127:126], w85);
444 
assign out[185:184] = w85;
445 
assign out[187:186] = in[63:62];
446 
wire [1:0] w86;
447 
f3_add a86(in[177:176], w15, w86);
448 
assign out[189:188] = w86;
449 
wire [1:0] w87;
450 
f3_add a87({in[120],in[121]}, in[129:128], w87);
451 
assign out[191:190] = w87;
452 
assign out[193:192] = in[65:64];
453 
endmodule
454 
 
455 
/* nine square in GF(3^m), out = in^9 mod p(x) */
456 
/* p(x) == x^97 + x^12 + 2 */
457 
module f3m_nine(clk, in, out);
458 
    input clk;
459 
    input [`WIDTH:0] in;
460 
    output reg [`WIDTH:0] out;
461 
    wire [`WIDTH:0] a,b;
462 
    f3m_cubic
463 
        ins1 (in, a), // a == in^3
464 
        ins2 (a, b);  // b == a^3 == in^9
465 
    always @ (posedge clk)
466 
        out <= b;
467 
endmodule
468 
 
469 
// inversion in GF(3^m). C = A^(-1)
470 7 homer.xing 
module f3m_inv(clk, reset, A, C, done);
471 2 homer.xing 
        input [`WIDTH:0] A;
472 
        input clk;
473 
        input reset;
474 
        output reg [`WIDTH:0] C;
475 7 homer.xing 
    output reg done;
476 2 homer.xing 
 
477 8 homer.xing 
        reg [`WIDTH+2:0] S, R, U, V, d;
478 
        reg [2*`M:0] i;
479 2 homer.xing 
        wire [1:0] q;
480 
        wire [`WIDTH+2:0] S1, S2,
481 
                          R1,
482 
                          U1, U2, U3,
483 
                          V1, V2,
484 8 homer.xing 
                          d1, d2;
485 7 homer.xing 
        wire don;
486 2 homer.xing 
 
487 
        assign d1 = {d[`WIDTH+1:0], 1'b1}; // d1 == d+1
488 
        assign d2 = {1'b0, d[`WIDTH+2:1]}; // d2 == d-1
489 8 homer.xing 
        assign don = i[0];
490 2 homer.xing 
 
491 
        f3_mult
492 
            q1(S[`MOST], R[`MOST], q); // q = s_m / r_m
493 
        func1
494 
            ins1(S, R, q, S1), // S1 = S - q*R
495 
            ins2(V, U, q, V1); // V1 = V - q*U
496 
        func2
497 
            ins3(S1, S2), // S2 = x*S1 = x*(S-q*R)
498 
            ins4(R, R1); // R1 = x*R
499 
        func3
500 
            ins5(U, U1), // U1 = x*U mod p
501 
            ins6(V1, V2); // V2 = x*V1 mod p = x*(V-qU) mod p
502 
    func4
503 
        ins7(U, R[`MOST], U2); // U2 = U/r_m
504 
    func5
505 
        ins8(U, U3); // U3 = (U/x) mod p
506 
 
507 8 homer.xing 
        always @ (posedge clk)
508 
        if (reset)
509 
            done <= 0;
510 
            else if (don)
511 
          begin
512 
                done <= 1; C <= U2[`WIDTH:0];
513 
          end
514 
 
515 2 homer.xing 
    always @ (posedge clk)
516 
        if (reset)
517 8 homer.xing 
            i <= {1'b1, {(2*`M){1'b0}}};
518 2 homer.xing 
        else
519 8 homer.xing 
            i <= i >> 1;
520 2 homer.xing 
 
521 
    always @ (posedge clk)
522 
        if (reset)
523 
          begin
524 
            S<=`PX; R<=A; U<=1; V<=0; d<=0;
525 
          end
526 
        else if (R[`MOST] == 2'b0)
527 
          begin
528 
            R<=R1; U<=U1; d<=d1;
529 
          end
530 
        else if (d[0] == 1'b0) // d == 0
531 
          begin
532 
            R<=S2; S<=R; U<=V2; V<=U; d<=d1;
533 
          end
534 
        else // d != 0
535 
          begin
536 
            S<=S2; V<=V1; U<=U3; d<=d2;
537 
          end
538 
endmodule
539 
 
540 3 homer.xing 
// put func1~5 here for breaking circular dependency in "f3m", "fun"
541 
 
542 
// out = S - q*R
543 
module func1(S, R, q, out);
544 
    input [`WIDTH+2:0] S, R;
545 
    input [1:0] q;
546 
    output [`WIDTH+2:0] out;
547 
    wire [`WIDTH+2:0] t;
548 
    func4 f(R, q, t); // t == q*R
549 
    genvar i;
550 
    generate for(i=0; i<=`WIDTH+2; i=i+2) begin: label
551 
        f3_sub s1(S[i+1:i], t[i+1:i], out[i+1:i]); // out == S - t
552 
    end endgenerate
553 
endmodule
554 
 
555 
// out = x*A
556 
module func2(A, out);
557 
    input [`WIDTH+2:0] A;
558 
    output [`WIDTH+2:0] out;
559 
    assign out = {A[`WIDTH:0], 2'd0};
560 
endmodule
561 
 
562 
// C = (x*B mod p(x))
563 
module func3(B, C);
564 
    input [`WIDTH+2:0] B;
565 
    output [`WIDTH+2:0] C;
566 
    wire [`WIDTH+2:0] A;
567 
    assign A = {B[`WIDTH:0], 2'd0}; // A == B*x
568 
    wire [1:0] w0;
569 
    f3_mult m0 (A[195:194], 2'd2, w0);
570 
    f3_sub s0 (A[1:0], w0, C[1:0]);
571 
    assign C[23:2] = A[23:2];
572 
    wire [1:0] w12;
573 
    f3_mult m12 (A[195:194], 2'd1, w12);
574 
    f3_sub s12 (A[25:24], w12, C[25:24]);
575 
    assign C[193:26] = A[193:26];
576 
    assign C[195:194] = 0;
577 
endmodule
578 
 
579 
// C = a * A; A,C \in GF(3^m); a \in GF(3)
580 
module func4(A, aa, C);
581 
    input [`WIDTH+2:0] A;
582 
    input [1:0] aa;
583 
    output [`WIDTH+2:0] C;
584 
    genvar i;
585 
    generate
586 
      for(i=0; i<=`WIDTH+2; i=i+2)
587 
      begin: label
588 
        f3_mult m(A[i+1:i], aa, C[i+1:i]);
589 
      end
590 
    endgenerate
591 
endmodule
592 
 
593 
// C = (A/x) mod p, \in GF(3^m)
594 
module func5(A, C);
595 
    input [`WIDTH+2:0] A;
596 
    output [`WIDTH+2:0] C;
597 
    assign C[195:194] = 0;
598 
    assign C[193:192] = A[1:0];
599 
    assign C[191:24] = A[193:26];
600 
    f3_add a11 (A[25:24], A[1:0], C[23:22]);
601 
    assign C[21:0] = A[23:2];
602 
endmodule

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