1 /* TomsFastMath, a fast ISO C bignum library.
3 * This project is meant to fill in where LibTomMath
4 * falls short. That is speed ;-)
6 * This project is public domain and free for all purposes.
8 * Tom St Denis, tomstdenis@gmail.com
10 #include <tfm_private.h>
12 /******************************************************************/
13 #if defined(TFM_X86) && !defined(TFM_SSE2)
24 "movl %5,%%eax \n\t" \
26 "addl %1,%%eax \n\t" \
27 "adcl $0,%%edx \n\t" \
28 "addl %%eax,%0 \n\t" \
29 "adcl $0,%%edx \n\t" \
30 "movl %%edx,%1 \n\t" \
31 :"=g"(_c[LO]), "=r"(cy) \
32 :"0"(_c[LO]), "1"(cy), "r"(mu), "r"(*tmpm++) \
33 : "%eax", "%edx", "cc")
39 "movzbl %%al,%1 \n\t" \
40 :"=g"(_c[LO]), "=r"(cy) \
41 :"0"(_c[LO]), "1"(cy) \
44 /******************************************************************/
45 #elif defined(TFM_X86_64)
56 "movq %5,%%rax \n\t" \
58 "addq %1,%%rax \n\t" \
59 "adcq $0,%%rdx \n\t" \
60 "addq %%rax,%0 \n\t" \
61 "adcq $0,%%rdx \n\t" \
62 "movq %%rdx,%1 \n\t" \
63 :"=g"(_c[LO]), "=r"(cy) \
64 :"0"(_c[LO]), "1"(cy), "r"(mu), "r"(*tmpm++) \
65 : "%rax", "%rdx", "cc")
69 "movq 0(%5),%%rax \n\t" \
70 "movq 0(%2),%%r10 \n\t" \
71 "movq 0x8(%5),%%r11 \n\t" \
73 "addq %%r10,%%rax \n\t" \
74 "adcq $0,%%rdx \n\t" \
75 "movq 0x8(%2),%%r10 \n\t" \
76 "addq %3,%%rax \n\t" \
77 "adcq $0,%%rdx \n\t" \
78 "movq %%rax,0(%0) \n\t" \
79 "movq %%rdx,%1 \n\t" \
81 "movq %%r11,%%rax \n\t" \
82 "movq 0x10(%5),%%r11 \n\t" \
84 "addq %%r10,%%rax \n\t" \
85 "adcq $0,%%rdx \n\t" \
86 "movq 0x10(%2),%%r10 \n\t" \
87 "addq %3,%%rax \n\t" \
88 "adcq $0,%%rdx \n\t" \
89 "movq %%rax,0x8(%0) \n\t" \
90 "movq %%rdx,%1 \n\t" \
92 "movq %%r11,%%rax \n\t" \
93 "movq 0x18(%5),%%r11 \n\t" \
95 "addq %%r10,%%rax \n\t" \
96 "adcq $0,%%rdx \n\t" \
97 "movq 0x18(%2),%%r10 \n\t" \
98 "addq %3,%%rax \n\t" \
99 "adcq $0,%%rdx \n\t" \
100 "movq %%rax,0x10(%0) \n\t" \
101 "movq %%rdx,%1 \n\t" \
103 "movq %%r11,%%rax \n\t" \
104 "movq 0x20(%5),%%r11 \n\t" \
106 "addq %%r10,%%rax \n\t" \
107 "adcq $0,%%rdx \n\t" \
108 "movq 0x20(%2),%%r10 \n\t" \
109 "addq %3,%%rax \n\t" \
110 "adcq $0,%%rdx \n\t" \
111 "movq %%rax,0x18(%0) \n\t" \
112 "movq %%rdx,%1 \n\t" \
114 "movq %%r11,%%rax \n\t" \
115 "movq 0x28(%5),%%r11 \n\t" \
117 "addq %%r10,%%rax \n\t" \
118 "adcq $0,%%rdx \n\t" \
119 "movq 0x28(%2),%%r10 \n\t" \
120 "addq %3,%%rax \n\t" \
121 "adcq $0,%%rdx \n\t" \
122 "movq %%rax,0x20(%0) \n\t" \
123 "movq %%rdx,%1 \n\t" \
125 "movq %%r11,%%rax \n\t" \
126 "movq 0x30(%5),%%r11 \n\t" \
128 "addq %%r10,%%rax \n\t" \
129 "adcq $0,%%rdx \n\t" \
130 "movq 0x30(%2),%%r10 \n\t" \
131 "addq %3,%%rax \n\t" \
132 "adcq $0,%%rdx \n\t" \
133 "movq %%rax,0x28(%0) \n\t" \
134 "movq %%rdx,%1 \n\t" \
136 "movq %%r11,%%rax \n\t" \
137 "movq 0x38(%5),%%r11 \n\t" \
139 "addq %%r10,%%rax \n\t" \
140 "adcq $0,%%rdx \n\t" \
141 "movq 0x38(%2),%%r10 \n\t" \
142 "addq %3,%%rax \n\t" \
143 "adcq $0,%%rdx \n\t" \
144 "movq %%rax,0x30(%0) \n\t" \
145 "movq %%rdx,%1 \n\t" \
147 "movq %%r11,%%rax \n\t" \
149 "addq %%r10,%%rax \n\t" \
150 "adcq $0,%%rdx \n\t" \
151 "addq %3,%%rax \n\t" \
152 "adcq $0,%%rdx \n\t" \
153 "movq %%rax,0x38(%0) \n\t" \
154 "movq %%rdx,%1 \n\t" \
156 :"=r"(_c), "=r"(cy) \
157 : "0"(_c), "1"(cy), "g"(mu), "r"(tmpm)\
158 : "%rax", "%rdx", "%r10", "%r11", "cc")
165 "movzbq %%al,%1 \n\t" \
166 :"=g"(_c[LO]), "=r"(cy) \
167 :"0"(_c[LO]), "1"(cy) \
170 /******************************************************************/
171 #elif defined(TFM_SSE2)
172 /* SSE2 code (assumes 32-bit fp_digits) */
173 /* XMM register assignments:
174 * xmm0 *tmpm++, then Mu * (*tmpm++)
182 asm("movd %0,%%mm2"::"g"(mp))
189 "movd %0,%%mm1 \n\t" \
190 "pxor %%mm3,%%mm3 \n\t" \
191 "pmuludq %%mm2,%%mm1 \n\t" \
194 /* pmuludq on mmx registers does a 32x32->64 multiply. */
197 "movd %1,%%mm4 \n\t" \
198 "movd %2,%%mm0 \n\t" \
199 "paddq %%mm4,%%mm3 \n\t" \
200 "pmuludq %%mm1,%%mm0 \n\t" \
201 "paddq %%mm0,%%mm3 \n\t" \
202 "movd %%mm3,%0 \n\t" \
203 "psrlq $32, %%mm3 \n\t" \
204 :"=g"(_c[LO]) : "0"(_c[LO]), "g"(*tmpm++) );
208 "movd 0(%1),%%mm4 \n\t" \
209 "movd 0(%2),%%mm0 \n\t" \
210 "paddq %%mm4,%%mm3 \n\t" \
211 "pmuludq %%mm1,%%mm0 \n\t" \
212 "movd 4(%2),%%mm5 \n\t" \
213 "paddq %%mm0,%%mm3 \n\t" \
214 "movd 4(%1),%%mm6 \n\t" \
215 "movd %%mm3,0(%0) \n\t" \
216 "psrlq $32, %%mm3 \n\t" \
218 "paddq %%mm6,%%mm3 \n\t" \
219 "pmuludq %%mm1,%%mm5 \n\t" \
220 "movd 8(%2),%%mm6 \n\t" \
221 "paddq %%mm5,%%mm3 \n\t" \
222 "movd 8(%1),%%mm7 \n\t" \
223 "movd %%mm3,4(%0) \n\t" \
224 "psrlq $32, %%mm3 \n\t" \
226 "paddq %%mm7,%%mm3 \n\t" \
227 "pmuludq %%mm1,%%mm6 \n\t" \
228 "movd 12(%2),%%mm7 \n\t" \
229 "paddq %%mm6,%%mm3 \n\t" \
230 "movd 12(%1),%%mm5 \n\t" \
231 "movd %%mm3,8(%0) \n\t" \
232 "psrlq $32, %%mm3 \n\t" \
234 "paddq %%mm5,%%mm3 \n\t" \
235 "pmuludq %%mm1,%%mm7 \n\t" \
236 "movd 16(%2),%%mm5 \n\t" \
237 "paddq %%mm7,%%mm3 \n\t" \
238 "movd 16(%1),%%mm6 \n\t" \
239 "movd %%mm3,12(%0) \n\t" \
240 "psrlq $32, %%mm3 \n\t" \
242 "paddq %%mm6,%%mm3 \n\t" \
243 "pmuludq %%mm1,%%mm5 \n\t" \
244 "movd 20(%2),%%mm6 \n\t" \
245 "paddq %%mm5,%%mm3 \n\t" \
246 "movd 20(%1),%%mm7 \n\t" \
247 "movd %%mm3,16(%0) \n\t" \
248 "psrlq $32, %%mm3 \n\t" \
250 "paddq %%mm7,%%mm3 \n\t" \
251 "pmuludq %%mm1,%%mm6 \n\t" \
252 "movd 24(%2),%%mm7 \n\t" \
253 "paddq %%mm6,%%mm3 \n\t" \
254 "movd 24(%1),%%mm5 \n\t" \
255 "movd %%mm3,20(%0) \n\t" \
256 "psrlq $32, %%mm3 \n\t" \
258 "paddq %%mm5,%%mm3 \n\t" \
259 "pmuludq %%mm1,%%mm7 \n\t" \
260 "movd 28(%2),%%mm5 \n\t" \
261 "paddq %%mm7,%%mm3 \n\t" \
262 "movd 28(%1),%%mm6 \n\t" \
263 "movd %%mm3,24(%0) \n\t" \
264 "psrlq $32, %%mm3 \n\t" \
266 "paddq %%mm6,%%mm3 \n\t" \
267 "pmuludq %%mm1,%%mm5 \n\t" \
268 "paddq %%mm5,%%mm3 \n\t" \
269 "movd %%mm3,28(%0) \n\t" \
270 "psrlq $32, %%mm3 \n\t" \
271 :"=r"(_c) : "0"(_c), "g"(tmpm) );
274 asm( "movd %%mm3,%0 \n" :"=r"(cy))
280 "movzbl %%al,%1 \n\t" \
281 :"=g"(_c[LO]), "=r"(cy) \
282 :"0"(_c[LO]), "1"(cy) \
285 /******************************************************************/
286 #elif defined(TFM_ARM)
298 " ADDS r0,r0,%0 \n\t" \
299 " MOVCS %0,#1 \n\t" \
300 " MOVCC %0,#0 \n\t" \
301 " UMLAL r0,%0,%3,%4 \n\t" \
303 :"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(*tmpm++),"1"(_c[0]):"r0","cc");
308 " ADDS r0,r0,%0 \n\t" \
310 " MOVCS %0,#1 \n\t" \
311 " MOVCC %0,#0 \n\t" \
312 :"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"r0","cc");
314 /******************************************************************/
315 #elif defined(TFM_PPC32)
326 " mullw 16,%3,%4 \n\t" \
327 " mulhwu 17,%3,%4 \n\t" \
328 " addc 16,16,%2 \n\t" \
329 " addze 17,17 \n\t" \
330 " addc %1,16,%5 \n\t" \
331 " addze %0,17 \n\t" \
332 :"=r"(cy),"=r"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"16", "17", "cc"); ++tmpm;
336 " addc %1,%3,%2 \n\t" \
337 " xor %0,%2,%2 \n\t" \
338 " addze %0,%2 \n\t" \
339 :"=r"(cy),"=r"(_c[0]):"0"(cy),"1"(_c[0]):"cc");
341 /******************************************************************/
342 #elif defined(TFM_PPC64)
353 " mulld r16,%3,%4 \n\t" \
354 " mulhdu r17,%3,%4 \n\t" \
355 " addc r16,16,%0 \n\t" \
356 " addze r17,r17 \n\t" \
357 " ldx r18,0,%1 \n\t" \
358 " addc r16,r16,r18 \n\t" \
359 " addze %0,r17 \n\t" \
360 " sdx r16,0,%1 \n\t" \
361 :"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"r16", "r17", "r18","cc"); ++tmpm;
365 " ldx r16,0,%1 \n\t" \
366 " addc r16,r16,%0 \n\t" \
367 " sdx r16,0,%1 \n\t" \
368 " xor %0,%0,%0 \n\t" \
369 " addze %0,%0 \n\t" \
370 :"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"r16","cc");
372 /******************************************************************/
373 #elif defined(TFM_AVR32)
388 " macu.d r2,%3,%4 \n\t" \
391 :"=r"(cy),"=r"(_c):"0"(cy),"r"(mu),"r"(*tmpm++),"1"(_c):"r2","r3");
400 :"=r"(cy),"=r"(&_c[0]):"0"(cy),"1"(&_c[0]):"r2","cc");
402 /******************************************************************/
403 #elif defined(TFM_MIPS)
414 " multu %3,%4 \n\t" \
417 " addu $12,$12,%0 \n\t" \
418 " sltu $10,$12,%0 \n\t" \
419 " addu $13,$13,$10 \n\t" \
421 " addu $12,$12,$10 \n\t" \
422 " sltu $10,$12,$10 \n\t" \
423 " addu %0,$13,$10 \n\t" \
425 :"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"$10","$12","$13"); ++tmpm;
430 " addu $10,$10,%0 \n\t" \
432 " sltu %0,$10,%0 \n\t" \
433 :"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"$10");
435 /******************************************************************/
447 _c[0] = t = ((fp_word)_c[0] + (fp_word)cy) + \
448 (((fp_word)mu) * ((fp_word)*tmpm++)); \
449 cy = (t >> DIGIT_BIT); \
453 do { fp_digit t = _c[0] += cy; cy = (t < cy); } while (0)
456 /******************************************************************/
461 #ifdef TFM_SMALL_MONT_SET
462 #include "fp_mont_small.i"
465 /* computes x/R == x (mod N) via Montgomery Reduction */
466 void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
468 fp_digit c[FP_SIZE], *_c, *tmpm, mu;
469 int oldused, x, y, pa;
471 /* bail if too large */
472 if (m->used > (FP_SIZE/2)) {
476 #ifdef TFM_SMALL_MONT_SET
478 fp_montgomery_reduce_small(a, m, mp);
483 #if defined(USE_MEMSET)
484 /* now zero the buff */
485 memset(c, 0, sizeof c);
491 for (x = 0; x < oldused; x++) {
494 #if !defined(USE_MEMSET)
495 for (; x < 2*pa+1; x++) {
501 for (x = 0; x < pa; x++) {
503 /* get Mu for this round */
508 #if defined(INNERMUL8)
509 for (; y < (pa & ~7); y += 8) {
516 for (; y < pa; y++) {
530 for (x = 0; x < pa+1; x++) {
534 for (; x < oldused; x++) {
543 /* if A >= m then A = A - m */
544 if (fp_cmp_mag (a, m) != FP_LT) {