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266efb73 MW |
1 | /* -*-c-*- |
2 | * | |
3 | * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1) | |
4 | * | |
5 | * (c) 2017 Straylight/Edgeware | |
6 | */ | |
7 | ||
8 | /*----- Licensing notice --------------------------------------------------* | |
9 | * | |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
16 | * | |
17 | * Catacomb is distributed in the hope that it will be useful, | |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
21 | * | |
22 | * You should have received a copy of the GNU Library General Public | |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
28 | /*----- Header files ------------------------------------------------------*/ | |
29 | ||
30 | #include "config.h" | |
31 | ||
1bc00e2a | 32 | #include "ct.h" |
266efb73 MW |
33 | #include "fgoldi.h" |
34 | ||
35 | /*----- Basic setup -------------------------------------------------------* | |
36 | * | |
37 | * Let φ = 2^224; then p = φ^2 - φ - 1, and, in GF(p), we have φ^2 = φ + 1 | |
38 | * (hence the name). | |
39 | */ | |
40 | ||
f521d4c7 MW |
41 | typedef fgoldi_piece piece; |
42 | ||
266efb73 MW |
43 | #if FGOLDI_IMPL == 28 |
44 | /* We represent an element of GF(p) as 16 28-bit signed integer pieces x_i: | |
45 | * x = SUM_{0<=i<16} x_i 2^(28i). | |
46 | */ | |
47 | ||
f521d4c7 | 48 | typedef int64 dblpiece; |
266efb73 MW |
49 | typedef uint32 upiece; typedef uint64 udblpiece; |
50 | #define PIECEWD(i) 28 | |
51 | #define NPIECE 16 | |
52 | #define P p28 | |
53 | ||
266efb73 MW |
54 | #define B27 0x08000000u |
55 | #define M28 0x0fffffffu | |
266efb73 MW |
56 | #define M32 0xffffffffu |
57 | ||
58 | #elif FGOLDI_IMPL == 12 | |
59 | /* We represent an element of GF(p) as 40 signed integer pieces x_i: x = | |
60 | * SUM_{0<=i<40} x_i 2^ceil(224i/20). Pieces i with i == 0 (mod 5) are 12 | |
61 | * bits wide; the others are 11 bits wide, so they form eight groups of 56 | |
62 | * bits. | |
63 | */ | |
64 | ||
f521d4c7 | 65 | typedef int32 dblpiece; |
266efb73 MW |
66 | typedef uint16 upiece; typedef uint32 udblpiece; |
67 | #define PIECEWD(i) ((i)%5 ? 11 : 12) | |
68 | #define NPIECE 40 | |
69 | #define P p12 | |
70 | ||
266efb73 MW |
71 | #define B11 0x0800u |
72 | #define B10 0x0400u | |
73 | #define M12 0xfffu | |
74 | #define M11 0x7ffu | |
266efb73 MW |
75 | #define M8 0xffu |
76 | ||
77 | #endif | |
78 | ||
79 | /*----- Debugging machinery -----------------------------------------------*/ | |
80 | ||
81 | #if defined(FGOLDI_DEBUG) || defined(TEST_RIG) | |
82 | ||
83 | #include <stdio.h> | |
84 | ||
85 | #include "mp.h" | |
86 | #include "mptext.h" | |
87 | ||
88 | static mp *get_pgoldi(void) | |
89 | { | |
90 | mp *p = MP_NEW, *t = MP_NEW; | |
91 | ||
92 | p = mp_setbit(p, MP_ZERO, 448); | |
93 | t = mp_setbit(t, MP_ZERO, 224); | |
94 | p = mp_sub(p, p, t); | |
95 | p = mp_sub(p, p, MP_ONE); | |
96 | mp_drop(t); | |
97 | return (p); | |
98 | } | |
99 | ||
100 | DEF_FDUMP(fdump, piece, PIECEWD, NPIECE, 56, get_pgoldi()) | |
101 | ||
102 | #endif | |
103 | ||
104 | /*----- Loading and storing -----------------------------------------------*/ | |
105 | ||
106 | /* --- @fgoldi_load@ --- * | |
107 | * | |
108 | * Arguments: @fgoldi *z@ = where to store the result | |
109 | * @const octet xv[56]@ = source to read | |
110 | * | |
111 | * Returns: --- | |
112 | * | |
113 | * Use: Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in | |
114 | * external representation from @xv@ and stores it in @z@. | |
115 | * | |
116 | * External representation is little-endian base-256. Some | |
117 | * elements have multiple encodings, which are not produced by | |
118 | * correct software; use of noncanonical encodings is not an | |
119 | * error, and toleration of them is considered a performance | |
120 | * feature. | |
121 | */ | |
122 | ||
123 | void fgoldi_load(fgoldi *z, const octet xv[56]) | |
124 | { | |
125 | #if FGOLDI_IMPL == 28 | |
126 | ||
127 | unsigned i; | |
128 | uint32 xw[14]; | |
129 | piece b, c; | |
130 | ||
131 | /* First, read the input value as words. */ | |
132 | for (i = 0; i < 14; i++) xw[i] = LOAD32_L(xv + 4*i); | |
133 | ||
134 | /* Extract unsigned 28-bit pieces from the words. */ | |
135 | z->P[ 0] = (xw[ 0] >> 0)&M28; | |
136 | z->P[ 7] = (xw[ 6] >> 4)&M28; | |
137 | z->P[ 8] = (xw[ 7] >> 0)&M28; | |
138 | z->P[15] = (xw[13] >> 4)&M28; | |
139 | for (i = 1; i < 7; i++) { | |
140 | z->P[i + 0] = ((xw[i + 0] << (4*i)) | (xw[i - 1] >> (32 - 4*i)))&M28; | |
141 | z->P[i + 8] = ((xw[i + 7] << (4*i)) | (xw[i + 6] >> (32 - 4*i)))&M28; | |
142 | } | |
143 | ||
144 | /* Convert the nonnegative pieces into a balanced signed representation, so | |
145 | * each piece ends up in the interval |z_i| <= 2^27. For each piece, if | |
146 | * its top bit is set, lend a bit leftwards; in the case of z_15, reduce | |
147 | * this bit by adding it onto z_0 and z_8, since this is the φ^2 bit, and | |
148 | * φ^2 = φ + 1. We delay this carry until after all of the pieces have | |
149 | * been balanced. If we don't do this, then we have to do a more expensive | |
150 | * test for nonzeroness to decide whether to lend a bit leftwards rather | |
151 | * than just testing a single bit. | |
152 | * | |
153 | * Note that we don't try for a canonical representation here: both upper | |
154 | * and lower bounds are achievable. | |
155 | */ | |
156 | b = z->P[15]&B27; z->P[15] -= b << 1; c = b >> 27; | |
157 | for (i = NPIECE - 1; i--; ) | |
158 | { b = z->P[i]&B27; z->P[i] -= b << 1; z->P[i + 1] += b >> 27; } | |
159 | z->P[0] += c; z->P[8] += c; | |
160 | ||
161 | #elif FGOLDI_IMPL == 12 | |
162 | ||
163 | unsigned i, j, n, w, b; | |
164 | uint32 a; | |
165 | int c; | |
166 | ||
167 | /* First, convert the bytes into nonnegative pieces. */ | |
168 | for (i = j = a = n = 0, w = PIECEWD(0); i < 56; i++) { | |
169 | a |= (uint32)xv[i] << n; n += 8; | |
170 | if (n >= w) { | |
171 | z->P[j++] = a&MASK(w); | |
172 | a >>= w; n -= w; w = PIECEWD(j); | |
173 | } | |
174 | } | |
175 | ||
176 | /* Convert the nonnegative pieces into a balanced signed representation, so | |
177 | * each piece ends up in the interval |z_i| <= 2^11 + 1. | |
178 | */ | |
179 | b = z->P[39]&B10; z->P[39] -= b << 1; c = b >> 10; | |
180 | for (i = NPIECE - 1; i--; ) { | |
181 | w = PIECEWD(i) - 1; | |
182 | b = z->P[i]&BIT(w); | |
183 | z->P[i] -= b << 1; | |
184 | z->P[i + 1] += b >> w; | |
185 | } | |
186 | z->P[0] += c; z->P[20] += c; | |
187 | ||
188 | #endif | |
189 | } | |
190 | ||
191 | /* --- @fgoldi_store@ --- * | |
192 | * | |
193 | * Arguments: @octet zv[56]@ = where to write the result | |
194 | * @const fgoldi *x@ = the field element to write | |
195 | * | |
196 | * Returns: --- | |
197 | * | |
198 | * Use: Stores a field element in the given octet vector in external | |
199 | * representation. A canonical encoding is always stored. | |
200 | */ | |
201 | ||
202 | void fgoldi_store(octet zv[56], const fgoldi *x) | |
203 | { | |
204 | #if FGOLDI_IMPL == 28 | |
205 | ||
206 | piece y[NPIECE], yy[NPIECE], c, d; | |
207 | uint32 u, v; | |
208 | mask32 m; | |
209 | unsigned i; | |
210 | ||
211 | for (i = 0; i < NPIECE; i++) y[i] = x->P[i]; | |
212 | ||
213 | /* First, propagate the carries. By the end of this, we'll have all of the | |
214 | * the pieces canonically sized and positive, and maybe there'll be | |
215 | * (signed) carry out. The carry c is in { -1, 0, +1 }, and the remaining | |
216 | * value will be in the half-open interval [0, φ^2). The whole represented | |
217 | * value is then y + φ^2 c. | |
218 | * | |
219 | * Assume that we start out with |y_i| <= 2^30. We start off by cutting | |
220 | * off and reducing the carry c_15 from the topmost piece, y_15. This | |
221 | * leaves 0 <= y_15 < 2^28; and we'll have |c_15| <= 4. We'll add this | |
222 | * onto y_0 and y_8, and propagate the carries. It's very clear that we'll | |
223 | * end up with |y + (φ + 1) c_15 - φ^2/2| << φ^2. | |
224 | * | |
225 | * Here, the y_i are signed, so we must be cautious about bithacking them. | |
226 | */ | |
227 | c = ASR(piece, y[15], 28); y[15] = (upiece)y[15]&M28; y[8] += c; | |
228 | for (i = 0; i < NPIECE; i++) | |
229 | { y[i] += c; c = ASR(piece, y[i], 28); y[i] = (upiece)y[i]&M28; } | |
230 | ||
231 | /* Now we have a slightly fiddly job to do. If c = +1, or if c = 0 and | |
232 | * y >= p, then we should subtract p from the whole value; if c = -1 then | |
233 | * we should add p; and otherwise we should do nothing. | |
234 | * | |
235 | * But conditional behaviour is bad, m'kay. So here's what we do instead. | |
236 | * | |
237 | * The first job is to sort out what we wanted to do. If c = -1 then we | |
238 | * want to (a) invert the constant addend and (b) feed in a carry-in; | |
239 | * otherwise, we don't. | |
240 | */ | |
241 | m = SIGN(c)&M28; | |
242 | d = m&1; | |
243 | ||
244 | /* Now do the addition/subtraction. Remember that all of the y_i are | |
245 | * nonnegative, so shifting and masking are safe and easy. | |
246 | */ | |
247 | d += y[0] + (1 ^ m); yy[0] = d&M28; d >>= 28; | |
248 | for (i = 1; i < 8; i++) | |
249 | { d += y[i] + m; yy[i] = d&M28; d >>= 28; } | |
250 | d += y[8] + (1 ^ m); yy[8] = d&M28; d >>= 28; | |
251 | for (i = 9; i < 16; i++) | |
252 | { d += y[i] + m; yy[i] = d&M28; d >>= 28; } | |
253 | ||
254 | /* The final carry-out is in d; since we only did addition, and the y_i are | |
255 | * nonnegative, then d is in { 0, 1 }. We want to keep y', rather than y, | |
256 | * if (a) c /= 0 (in which case we know that the old value was | |
257 | * unsatisfactory), or (b) if d = 1 (in which case, if c = 0, we know that | |
258 | * the subtraction didn't cause a borrow, so we must be in the case where | |
259 | * p <= y < φ^2. | |
260 | */ | |
261 | m = NONZEROP(c) | ~NONZEROP(d - 1); | |
262 | for (i = 0; i < NPIECE; i++) y[i] = (yy[i]&m) | (y[i]&~m); | |
263 | ||
264 | /* Extract 32-bit words from the value. */ | |
265 | for (i = 0; i < 7; i++) { | |
266 | u = ((y[i + 0] >> (4*i)) | ((uint32)y[i + 1] << (28 - 4*i)))&M32; | |
267 | v = ((y[i + 8] >> (4*i)) | ((uint32)y[i + 9] << (28 - 4*i)))&M32; | |
268 | STORE32_L(zv + 4*i, u); | |
269 | STORE32_L(zv + 4*i + 28, v); | |
270 | } | |
271 | ||
272 | #elif FGOLDI_IMPL == 12 | |
273 | ||
274 | piece y[NPIECE], yy[NPIECE], c, d; | |
275 | uint32 a; | |
276 | mask32 m, mm; | |
277 | unsigned i, j, n, w; | |
278 | ||
279 | for (i = 0; i < NPIECE; i++) y[i] = x->P[i]; | |
280 | ||
281 | /* First, propagate the carries. By the end of this, we'll have all of the | |
282 | * the pieces canonically sized and positive, and maybe there'll be | |
283 | * (signed) carry out. The carry c is in { -1, 0, +1 }, and the remaining | |
284 | * value will be in the half-open interval [0, φ^2). The whole represented | |
285 | * value is then y + φ^2 c. | |
286 | * | |
287 | * Assume that we start out with |y_i| <= 2^14. We start off by cutting | |
288 | * off and reducing the carry c_39 from the topmost piece, y_39. This | |
289 | * leaves 0 <= y_39 < 2^11; and we'll have |c_39| <= 16. We'll add this | |
290 | * onto y_0 and y_20, and propagate the carries. It's very clear that | |
291 | * we'll end up with |y + (φ + 1) c_39 - φ^2/2| << φ^2. | |
292 | * | |
293 | * Here, the y_i are signed, so we must be cautious about bithacking them. | |
294 | */ | |
295 | c = ASR(piece, y[39], 11); y[39] = (piece)y[39]&M11; y[20] += c; | |
296 | for (i = 0; i < NPIECE; i++) { | |
297 | w = PIECEWD(i); m = (1 << w) - 1; | |
298 | y[i] += c; c = ASR(piece, y[i], w); y[i] = (upiece)y[i]&m; | |
299 | } | |
300 | ||
301 | /* Now we have a slightly fiddly job to do. If c = +1, or if c = 0 and | |
302 | * y >= p, then we should subtract p from the whole value; if c = -1 then | |
303 | * we should add p; and otherwise we should do nothing. | |
304 | * | |
305 | * But conditional behaviour is bad, m'kay. So here's what we do instead. | |
306 | * | |
307 | * The first job is to sort out what we wanted to do. If c = -1 then we | |
308 | * want to (a) invert the constant addend and (b) feed in a carry-in; | |
309 | * otherwise, we don't. | |
310 | */ | |
311 | mm = SIGN(c); | |
312 | d = m&1; | |
313 | ||
314 | /* Now do the addition/subtraction. Remember that all of the y_i are | |
315 | * nonnegative, so shifting and masking are safe and easy. | |
316 | */ | |
317 | d += y[ 0] + (1 ^ (mm&M12)); yy[ 0] = d&M12; d >>= 12; | |
318 | for (i = 1; i < 20; i++) { | |
319 | w = PIECEWD(i); m = MASK(w); | |
320 | d += y[ i] + (mm&m); yy[ i] = d&m; d >>= w; | |
321 | } | |
322 | d += y[20] + (1 ^ (mm&M12)); yy[20] = d&M12; d >>= 12; | |
323 | for (i = 21; i < 40; i++) { | |
324 | w = PIECEWD(i); m = MASK(w); | |
325 | d += y[ i] + (mm&m); yy[ i] = d&m; d >>= w; | |
326 | } | |
327 | ||
328 | /* The final carry-out is in d; since we only did addition, and the y_i are | |
329 | * nonnegative, then d is in { 0, 1 }. We want to keep y', rather than y, | |
330 | * if (a) c /= 0 (in which case we know that the old value was | |
331 | * unsatisfactory), or (b) if d = 1 (in which case, if c = 0, we know that | |
332 | * the subtraction didn't cause a borrow, so we must be in the case where | |
333 | * p <= y < φ^2. | |
334 | */ | |
335 | m = NONZEROP(c) | ~NONZEROP(d - 1); | |
336 | for (i = 0; i < NPIECE; i++) y[i] = (yy[i]&m) | (y[i]&~m); | |
337 | ||
338 | /* Convert that back into octets. */ | |
339 | for (i = j = a = n = 0; i < NPIECE; i++) { | |
340 | a |= (uint32)y[i] << n; n += PIECEWD(i); | |
341 | while (n >= 8) { zv[j++] = a&M8; a >>= 8; n -= 8; } | |
342 | } | |
343 | ||
344 | #endif | |
345 | } | |
346 | ||
347 | /* --- @fgoldi_set@ --- * | |
348 | * | |
349 | * Arguments: @fgoldi *z@ = where to write the result | |
350 | * @int a@ = a small-ish constant | |
351 | * | |
352 | * Returns: --- | |
353 | * | |
354 | * Use: Sets @z@ to equal @a@. | |
355 | */ | |
356 | ||
357 | void fgoldi_set(fgoldi *x, int a) | |
358 | { | |
359 | unsigned i; | |
360 | ||
361 | x->P[0] = a; | |
362 | for (i = 1; i < NPIECE; i++) x->P[i] = 0; | |
363 | } | |
364 | ||
365 | /*----- Basic arithmetic --------------------------------------------------*/ | |
366 | ||
367 | /* --- @fgoldi_add@ --- * | |
368 | * | |
369 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) | |
370 | * @const fgoldi *x, *y@ = two operands | |
371 | * | |
372 | * Returns: --- | |
373 | * | |
374 | * Use: Set @z@ to the sum %$x + y$%. | |
375 | */ | |
376 | ||
377 | void fgoldi_add(fgoldi *z, const fgoldi *x, const fgoldi *y) | |
378 | { | |
379 | unsigned i; | |
380 | for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] + y->P[i]; | |
381 | } | |
382 | ||
383 | /* --- @fgoldi_sub@ --- * | |
384 | * | |
385 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) | |
386 | * @const fgoldi *x, *y@ = two operands | |
387 | * | |
388 | * Returns: --- | |
389 | * | |
390 | * Use: Set @z@ to the difference %$x - y$%. | |
391 | */ | |
392 | ||
393 | void fgoldi_sub(fgoldi *z, const fgoldi *x, const fgoldi *y) | |
394 | { | |
395 | unsigned i; | |
396 | for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] - y->P[i]; | |
397 | } | |
398 | ||
1bc00e2a MW |
399 | /* --- @fgoldi_neg@ --- * |
400 | * | |
401 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) | |
402 | * @const fgoldi *x@ = an operand | |
403 | * | |
404 | * Returns: --- | |
405 | * | |
406 | * Use: Set @z = -x@. | |
407 | */ | |
408 | ||
409 | void fgoldi_neg(fgoldi *z, const fgoldi *x) | |
410 | { | |
411 | unsigned i; | |
412 | for (i = 0; i < NPIECE; i++) z->P[i] = -x->P[i]; | |
413 | } | |
414 | ||
266efb73 MW |
415 | /*----- Constant-time utilities -------------------------------------------*/ |
416 | ||
1bc00e2a MW |
417 | /* --- @fgoldi_pick2@ --- * |
418 | * | |
419 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) | |
420 | * @const fgoldi *x, *y@ = two operands | |
421 | * @uint32 m@ = a mask | |
422 | * | |
423 | * Returns: --- | |
424 | * | |
425 | * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set | |
426 | * @z = x@. If @m@ has some other value, then scramble @z@ in | |
427 | * an unhelpful way. | |
428 | */ | |
429 | ||
430 | void fgoldi_pick2(fgoldi *z, const fgoldi *x, const fgoldi *y, uint32 m) | |
431 | { | |
432 | mask32 mm = FIX_MASK32(m); | |
433 | unsigned i; | |
434 | for (i = 0; i < NPIECE; i++) z->P[i] = PICK2(x->P[i], y->P[i], mm); | |
435 | } | |
436 | ||
437 | /* --- @fgoldi_pickn@ --- * | |
438 | * | |
439 | * Arguments: @fgoldi *z@ = where to put the result | |
440 | * @const fgoldi *v@ = a table of entries | |
441 | * @size_t n@ = the number of entries in @v@ | |
442 | * @size_t i@ = an index | |
443 | * | |
444 | * Returns: --- | |
445 | * | |
446 | * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then | |
447 | * do something unhelpful; otherwise, if @i >= n@ then set @z@ | |
448 | * to zero. | |
449 | */ | |
450 | ||
451 | void fgoldi_pickn(fgoldi *z, const fgoldi *v, size_t n, size_t i) | |
452 | { | |
453 | uint32 b = (uint32)1 << (31 - i); | |
454 | mask32 m; | |
455 | unsigned j; | |
456 | ||
457 | for (j = 0; j < NPIECE; j++) z->P[j] = 0; | |
458 | while (n--) { | |
459 | m = SIGN(b); | |
460 | for (j = 0; j < NPIECE; j++) CONDPICK(z->P[j], v->P[j], m); | |
461 | v++; b <<= 1; | |
462 | } | |
463 | } | |
464 | ||
266efb73 MW |
465 | /* --- @fgoldi_condswap@ --- * |
466 | * | |
467 | * Arguments: @fgoldi *x, *y@ = two operands | |
468 | * @uint32 m@ = a mask | |
469 | * | |
470 | * Returns: --- | |
471 | * | |
472 | * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then | |
473 | * exchange @x@ and @y@. If @m@ has some other value, then | |
474 | * scramble @x@ and @y@ in an unhelpful way. | |
475 | */ | |
476 | ||
477 | void fgoldi_condswap(fgoldi *x, fgoldi *y, uint32 m) | |
478 | { | |
479 | unsigned i; | |
480 | mask32 mm = FIX_MASK32(m); | |
481 | ||
482 | for (i = 0; i < NPIECE; i++) CONDSWAP(x->P[i], y->P[i], mm); | |
483 | } | |
484 | ||
1bc00e2a MW |
485 | /* --- @fgoldi_condneg@ --- * |
486 | * | |
487 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) | |
488 | * @const fgoldi *x@ = an operand | |
489 | * @uint32 m@ = a mask | |
490 | * | |
491 | * Returns: --- | |
492 | * | |
493 | * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set | |
494 | * @z = -x@. If @m@ has some other value then scramble @z@ in | |
495 | * an unhelpful way. | |
496 | */ | |
497 | ||
498 | void fgoldi_condneg(fgoldi *z, const fgoldi *x, uint32 m) | |
499 | { | |
500 | #ifdef NEG_TWOC | |
501 | mask32 m_xor = FIX_MASK32(m); | |
502 | piece m_add = m&1; | |
503 | # define CONDNEG(x) (((x) ^ m_xor) + m_add) | |
504 | #else | |
505 | int s = PICK2(-1, +1, m); | |
506 | # define CONDNEG(x) (s*(x)) | |
507 | #endif | |
508 | ||
509 | unsigned i; | |
510 | for (i = 0; i < NPIECE; i++) z->P[i] = CONDNEG(x->P[i]); | |
511 | ||
512 | #undef CONDNEG | |
513 | } | |
514 | ||
266efb73 MW |
515 | /*----- Multiplication ----------------------------------------------------*/ |
516 | ||
517 | #if FGOLDI_IMPL == 28 | |
518 | ||
519 | /* Let B = 2^63 - 1 be the largest value such that +B and -B can be | |
520 | * represented in a double-precision piece. On entry, it must be the case | |
521 | * that |X_i| <= M <= B - 2^27 for some M. If this is the case, then, on | |
522 | * exit, we will have |Z_i| <= 2^27 + M/2^27. | |
523 | */ | |
524 | #define CARRY_REDUCE(z, x) do { \ | |
525 | dblpiece _t[NPIECE], _c; \ | |
526 | unsigned _i; \ | |
527 | \ | |
528 | /* Bias the input pieces. This keeps the carries and so on centred \ | |
529 | * around zero rather than biased positive. \ | |
530 | */ \ | |
531 | for (_i = 0; _i < NPIECE; _i++) _t[_i] = (x)[_i] + B27; \ | |
532 | \ | |
533 | /* Calculate the reduced pieces. Careful with the bithacking. */ \ | |
534 | _c = ASR(dblpiece, _t[15], 28); \ | |
535 | (z)[0] = (dblpiece)((udblpiece)_t[0]&M28) - B27 + _c; \ | |
536 | for (_i = 1; _i < NPIECE; _i++) { \ | |
537 | (z)[_i] = (dblpiece)((udblpiece)_t[_i]&M28) - B27 + \ | |
538 | ASR(dblpiece, _t[_i - 1], 28); \ | |
539 | } \ | |
540 | (z)[8] += _c; \ | |
541 | } while (0) | |
542 | ||
543 | #elif FGOLDI_IMPL == 12 | |
544 | ||
545 | static void carry_reduce(dblpiece x[NPIECE]) | |
546 | { | |
547 | /* Initial bounds: we assume |x_i| < 2^31 - 2^27. */ | |
548 | ||
549 | unsigned i, j; | |
550 | dblpiece c; | |
551 | ||
552 | /* The result is nearly canonical, because we do sequential carry | |
553 | * propagation, because smaller processors are more likely to prefer the | |
554 | * smaller working set than the instruction-level parallelism. | |
555 | * | |
556 | * Start at x_37; truncate it to 10 bits, and propagate the carry to x_38. | |
557 | * Truncate x_38 to 10 bits, and add the carry onto x_39. Truncate x_39 to | |
558 | * 10 bits, and add the carry onto x_0 and x_20. And so on. | |
559 | * | |
560 | * Once we reach x_37 for the second time, we start with |x_37| <= 2^10. | |
561 | * The carry into x_37 is at most 2^21; so the carry out into x_38 has | |
562 | * magnitude at most 2^10. In turn, |x_38| <= 2^10 before the carry, so is | |
563 | * now no more than 2^11 in magnitude, and the carry out into x_39 is at | |
564 | * most 1. This leaves |x_39| <= 2^10 + 1 after carry propagation. | |
565 | * | |
566 | * Be careful with the bit hacking because the quantities involved are | |
567 | * signed. | |
568 | */ | |
569 | ||
570 | /* For each piece, we bias it so that floor division (as done by an | |
571 | * arithmetic right shift) and modulus (as done by bitwise-AND) does the | |
572 | * right thing. | |
573 | */ | |
574 | #define CARRY(i, wd, b, m) do { \ | |
575 | x[i] += (b); \ | |
576 | c = ASR(dblpiece, x[i], (wd)); \ | |
577 | x[i] = (dblpiece)((udblpiece)x[i]&(m)) - (b); \ | |
578 | } while (0) | |
579 | ||
580 | { CARRY(37, 11, B10, M11); } | |
581 | { x[38] += c; CARRY(38, 11, B10, M11); } | |
582 | { x[39] += c; CARRY(39, 11, B10, M11); } | |
583 | x[20] += c; | |
584 | for (i = 0; i < 35; ) { | |
585 | { x[i] += c; CARRY( i, 12, B11, M12); i++; } | |
586 | for (j = i + 4; i < j; ) { x[i] += c; CARRY( i, 11, B10, M11); i++; } | |
587 | } | |
588 | { x[i] += c; CARRY( i, 12, B11, M12); i++; } | |
589 | while (i < 39) { x[i] += c; CARRY( i, 11, B10, M11); i++; } | |
590 | x[39] += c; | |
591 | } | |
592 | ||
593 | #endif | |
594 | ||
595 | /* --- @fgoldi_mulconst@ --- * | |
596 | * | |
597 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) | |
598 | * @const fgoldi *x@ = an operand | |
599 | * @long a@ = a small-ish constant; %$|a| < 2^{20}$%. | |
600 | * | |
601 | * Returns: --- | |
602 | * | |
603 | * Use: Set @z@ to the product %$a x$%. | |
604 | */ | |
605 | ||
606 | void fgoldi_mulconst(fgoldi *z, const fgoldi *x, long a) | |
607 | { | |
608 | unsigned i; | |
609 | dblpiece zz[NPIECE], aa = a; | |
610 | ||
611 | for (i = 0; i < NPIECE; i++) zz[i] = aa*x->P[i]; | |
612 | #if FGOLDI_IMPL == 28 | |
613 | CARRY_REDUCE(z->P, zz); | |
614 | #elif FGOLDI_IMPL == 12 | |
615 | carry_reduce(zz); | |
616 | for (i = 0; i < NPIECE; i++) z->P[i] = zz[i]; | |
617 | #endif | |
618 | } | |
619 | ||
620 | /* --- @fgoldi_mul@ --- * | |
621 | * | |
622 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) | |
623 | * @const fgoldi *x, *y@ = two operands | |
624 | * | |
625 | * Returns: --- | |
626 | * | |
627 | * Use: Set @z@ to the product %$x y$%. | |
628 | */ | |
629 | ||
630 | void fgoldi_mul(fgoldi *z, const fgoldi *x, const fgoldi *y) | |
631 | { | |
632 | dblpiece zz[NPIECE], u[NPIECE]; | |
633 | piece ab[NPIECE/2], cd[NPIECE/2]; | |
634 | const piece | |
635 | *a = x->P + NPIECE/2, *b = x->P, | |
636 | *c = y->P + NPIECE/2, *d = y->P; | |
637 | unsigned i, j; | |
638 | ||
639 | #if FGOLDI_IMPL == 28 | |
640 | ||
641 | # define M(x,i, y,j) ((dblpiece)(x)[i]*(y)[j]) | |
642 | ||
643 | #elif FGOLDI_IMPL == 12 | |
644 | ||
645 | static const unsigned short off[39] = { | |
646 | 0, 12, 23, 34, 45, 56, 68, 79, 90, 101, | |
647 | 112, 124, 135, 146, 157, 168, 180, 191, 202, 213, | |
648 | 224, 236, 247, 258, 269, 280, 292, 303, 314, 325, | |
649 | 336, 348, 359, 370, 381, 392, 404, 415, 426 | |
650 | }; | |
651 | ||
652 | #define M(x,i, y,j) \ | |
653 | (((dblpiece)(x)[i]*(y)[j]) << (off[i] + off[j] - off[(i) + (j)])) | |
654 | ||
655 | #endif | |
656 | ||
657 | /* Behold the magic. | |
658 | * | |
659 | * Write x = a φ + b, and y = c φ + d. Then x y = a c φ^2 + | |
660 | * (a d + b c) φ + b d. Karatsuba and Ofman observed that a d + b c = | |
661 | * (a + b) (c + d) - a c - b d, saving a multiplication, and Hamburg chose | |
662 | * the prime p so that φ^2 = φ + 1. So | |
663 | * | |
664 | * x y = ((a + b) (c + d) - b d) φ + a c + b d | |
665 | */ | |
666 | ||
667 | for (i = 0; i < NPIECE; i++) zz[i] = 0; | |
668 | ||
669 | /* Our first job will be to calculate (1 - φ) b d, and write the result | |
670 | * into z. As we do this, an interesting thing will happen. Write | |
671 | * b d = u φ + v; then (1 - φ) b d = u φ + v - u φ^2 - v φ = (1 - φ) v - u. | |
672 | * So, what we do is to write the product end-swapped and negated, and then | |
673 | * we'll subtract the (negated, remember) high half from the low half. | |
674 | */ | |
675 | for (i = 0; i < NPIECE/2; i++) { | |
676 | for (j = 0; j < NPIECE/2 - i; j++) | |
677 | zz[i + j + NPIECE/2] -= M(b,i, d,j); | |
678 | for (; j < NPIECE/2; j++) | |
679 | zz[i + j - NPIECE/2] -= M(b,i, d,j); | |
680 | } | |
681 | for (i = 0; i < NPIECE/2; i++) | |
682 | zz[i] -= zz[i + NPIECE/2]; | |
683 | ||
684 | /* Next, we add on a c. There are no surprises here. */ | |
685 | for (i = 0; i < NPIECE/2; i++) | |
686 | for (j = 0; j < NPIECE/2; j++) | |
687 | zz[i + j] += M(a,i, c,j); | |
688 | ||
689 | /* Now, calculate a + b and c + d. */ | |
690 | for (i = 0; i < NPIECE/2; i++) | |
691 | { ab[i] = a[i] + b[i]; cd[i] = c[i] + d[i]; } | |
692 | ||
693 | /* Finally (for the multiplication) we must add on (a + b) (c + d) φ. | |
694 | * Write (a + b) (c + d) as u φ + v; then we actually want u φ^2 + v φ = | |
695 | * v φ + (1 + φ) u. We'll store u in a temporary place and add it on | |
696 | * twice. | |
697 | */ | |
698 | for (i = 0; i < NPIECE; i++) u[i] = 0; | |
699 | for (i = 0; i < NPIECE/2; i++) { | |
700 | for (j = 0; j < NPIECE/2 - i; j++) | |
701 | zz[i + j + NPIECE/2] += M(ab,i, cd,j); | |
702 | for (; j < NPIECE/2; j++) | |
703 | u[i + j - NPIECE/2] += M(ab,i, cd,j); | |
704 | } | |
705 | for (i = 0; i < NPIECE/2; i++) | |
706 | { zz[i] += u[i]; zz[i + NPIECE/2] += u[i]; } | |
707 | ||
708 | #undef M | |
709 | ||
710 | #if FGOLDI_IMPL == 28 | |
711 | /* That wraps it up for the multiplication. Let's figure out some bounds. | |
712 | * Fortunately, Karatsuba is a polynomial identity, so all of the pieces | |
713 | * end up the way they'd be if we'd done the thing the easy way, which | |
714 | * simplifies the analysis. Suppose we started with |x_i|, |y_i| <= 9/5 | |
715 | * 2^28. The overheads in the result are given by the coefficients of | |
716 | * | |
717 | * ((u^16 - 1)/(u - 1))^2 mod u^16 - u^8 - 1 | |
718 | * | |
719 | * the greatest of which is 38. So |z_i| <= 38*81/25*2^56 < 2^63. | |
720 | * | |
721 | * Anyway, a round of `CARRY_REDUCE' will leave us with |z_i| < 2^27 + | |
722 | * 2^36; and a second round will leave us with |z_i| < 2^27 + 512. | |
723 | */ | |
724 | for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz); | |
725 | for (i = 0; i < NPIECE; i++) z->P[i] = zz[i]; | |
726 | #elif FGOLDI_IMPL == 12 | |
727 | carry_reduce(zz); | |
728 | for (i = 0; i < NPIECE; i++) z->P[i] = zz[i]; | |
729 | #endif | |
730 | } | |
731 | ||
732 | /* --- @fgoldi_sqr@ --- * | |
733 | * | |
734 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) | |
735 | * @const fgoldi *x@ = an operand | |
736 | * | |
737 | * Returns: --- | |
738 | * | |
739 | * Use: Set @z@ to the square %$x^2$%. | |
740 | */ | |
741 | ||
742 | void fgoldi_sqr(fgoldi *z, const fgoldi *x) | |
743 | { | |
744 | #if FGOLDI_IMPL == 28 | |
745 | ||
746 | dblpiece zz[NPIECE], u[NPIECE]; | |
747 | piece ab[NPIECE]; | |
748 | const piece *a = x->P + NPIECE/2, *b = x->P; | |
749 | unsigned i, j; | |
750 | ||
751 | # define M(x,i, y,j) ((dblpiece)(x)[i]*(y)[j]) | |
752 | ||
753 | /* The magic is basically the same as `fgoldi_mul' above. We write | |
754 | * x = a φ + b and use Karatsuba and the special prime shape. This time, | |
755 | * we have | |
756 | * | |
757 | * x^2 = ((a + b)^2 - b^2) φ + a^2 + b^2 | |
758 | */ | |
759 | ||
760 | for (i = 0; i < NPIECE; i++) zz[i] = 0; | |
761 | ||
762 | /* Our first job will be to calculate (1 - φ) b^2, and write the result | |
763 | * into z. Again, this interacts pleasantly with the prime shape. | |
764 | */ | |
765 | for (i = 0; i < NPIECE/4; i++) { | |
766 | zz[2*i + NPIECE/2] -= M(b,i, b,i); | |
767 | for (j = i + 1; j < NPIECE/2 - i; j++) | |
768 | zz[i + j + NPIECE/2] -= 2*M(b,i, b,j); | |
769 | for (; j < NPIECE/2; j++) | |
770 | zz[i + j - NPIECE/2] -= 2*M(b,i, b,j); | |
771 | } | |
772 | for (; i < NPIECE/2; i++) { | |
773 | zz[2*i - NPIECE/2] -= M(b,i, b,i); | |
774 | for (j = i + 1; j < NPIECE/2; j++) | |
775 | zz[i + j - NPIECE/2] -= 2*M(b,i, b,j); | |
776 | } | |
777 | for (i = 0; i < NPIECE/2; i++) | |
778 | zz[i] -= zz[i + NPIECE/2]; | |
779 | ||
780 | /* Next, we add on a^2. There are no surprises here. */ | |
781 | for (i = 0; i < NPIECE/2; i++) { | |
782 | zz[2*i] += M(a,i, a,i); | |
783 | for (j = i + 1; j < NPIECE/2; j++) | |
784 | zz[i + j] += 2*M(a,i, a,j); | |
785 | } | |
786 | ||
787 | /* Now, calculate a + b. */ | |
788 | for (i = 0; i < NPIECE/2; i++) | |
789 | ab[i] = a[i] + b[i]; | |
790 | ||
791 | /* Finally (for the multiplication) we must add on (a + b)^2 φ. | |
792 | * Write (a + b)^2 as u φ + v; then we actually want (u + v) φ + u. We'll | |
793 | * store u in a temporary place and add it on twice. | |
794 | */ | |
795 | for (i = 0; i < NPIECE; i++) u[i] = 0; | |
796 | for (i = 0; i < NPIECE/4; i++) { | |
797 | zz[2*i + NPIECE/2] += M(ab,i, ab,i); | |
798 | for (j = i + 1; j < NPIECE/2 - i; j++) | |
799 | zz[i + j + NPIECE/2] += 2*M(ab,i, ab,j); | |
800 | for (; j < NPIECE/2; j++) | |
801 | u[i + j - NPIECE/2] += 2*M(ab,i, ab,j); | |
802 | } | |
803 | for (; i < NPIECE/2; i++) { | |
804 | u[2*i - NPIECE/2] += M(ab,i, ab,i); | |
805 | for (j = i + 1; j < NPIECE/2; j++) | |
806 | u[i + j - NPIECE/2] += 2*M(ab,i, ab,j); | |
807 | } | |
808 | for (i = 0; i < NPIECE/2; i++) | |
809 | { zz[i] += u[i]; zz[i + NPIECE/2] += u[i]; } | |
810 | ||
811 | #undef M | |
812 | ||
813 | /* Finally, carrying. */ | |
814 | for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz); | |
815 | for (i = 0; i < NPIECE; i++) z->P[i] = zz[i]; | |
816 | ||
817 | #elif FGOLDI_IMPL == 12 | |
818 | fgoldi_mul(z, x, x); | |
819 | #endif | |
820 | } | |
821 | ||
822 | /*----- More advanced operations ------------------------------------------*/ | |
823 | ||
824 | /* --- @fgoldi_inv@ --- * | |
825 | * | |
826 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) | |
827 | * @const fgoldi *x@ = an operand | |
828 | * | |
829 | * Returns: --- | |
830 | * | |
831 | * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If | |
832 | * %$x = 0$% then @z@ is set to zero. This is considered a | |
833 | * feature. | |
834 | */ | |
835 | ||
836 | void fgoldi_inv(fgoldi *z, const fgoldi *x) | |
837 | { | |
838 | fgoldi t, u; | |
839 | unsigned i; | |
840 | ||
841 | #define SQRN(z, x, n) do { \ | |
842 | fgoldi_sqr((z), (x)); \ | |
843 | for (i = 1; i < (n); i++) fgoldi_sqr((z), (z)); \ | |
844 | } while (0) | |
845 | ||
846 | /* Calculate x^-1 = x^(p - 2) = x^(2^448 - 2^224 - 3), which also handles | |
847 | * x = 0 as intended. The addition chain is home-made. | |
848 | */ /* step | value */ | |
849 | fgoldi_sqr(&u, x); /* 1 | 2 */ | |
850 | fgoldi_mul(&t, &u, x); /* 2 | 3 */ | |
851 | SQRN(&u, &t, 2); /* 4 | 12 */ | |
852 | fgoldi_mul(&t, &u, &t); /* 5 | 15 */ | |
853 | SQRN(&u, &t, 4); /* 9 | 240 */ | |
854 | fgoldi_mul(&u, &u, &t); /* 10 | 255 = 2^8 - 1 */ | |
855 | SQRN(&u, &u, 4); /* 14 | 2^12 - 16 */ | |
856 | fgoldi_mul(&t, &u, &t); /* 15 | 2^12 - 1 */ | |
857 | SQRN(&u, &t, 12); /* 27 | 2^24 - 2^12 */ | |
858 | fgoldi_mul(&u, &u, &t); /* 28 | 2^24 - 1 */ | |
859 | SQRN(&u, &u, 12); /* 40 | 2^36 - 2^12 */ | |
860 | fgoldi_mul(&t, &u, &t); /* 41 | 2^36 - 1 */ | |
861 | fgoldi_sqr(&t, &t); /* 42 | 2^37 - 2 */ | |
862 | fgoldi_mul(&t, &t, x); /* 43 | 2^37 - 1 */ | |
863 | SQRN(&u, &t, 37); /* 80 | 2^74 - 2^37 */ | |
864 | fgoldi_mul(&u, &u, &t); /* 81 | 2^74 - 1 */ | |
865 | SQRN(&u, &u, 37); /* 118 | 2^111 - 2^37 */ | |
866 | fgoldi_mul(&t, &u, &t); /* 119 | 2^111 - 1 */ | |
867 | SQRN(&u, &t, 111); /* 230 | 2^222 - 2^111 */ | |
868 | fgoldi_mul(&t, &u, &t); /* 231 | 2^222 - 1 */ | |
869 | fgoldi_sqr(&u, &t); /* 232 | 2^223 - 2 */ | |
870 | fgoldi_mul(&u, &u, x); /* 233 | 2^223 - 1 */ | |
871 | SQRN(&u, &u, 223); /* 456 | 2^446 - 2^223 */ | |
872 | fgoldi_mul(&t, &u, &t); /* 457 | 2^446 - 2^222 - 1 */ | |
873 | SQRN(&t, &t, 2); /* 459 | 2^448 - 2^224 - 4 */ | |
874 | fgoldi_mul(z, &t, x); /* 460 | 2^448 - 2^224 - 3 */ | |
875 | ||
876 | #undef SQRN | |
877 | } | |
878 | ||
1bc00e2a MW |
879 | /* --- @fgoldi_quosqrt@ --- * |
880 | * | |
881 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) | |
882 | * @const fgoldi *x, *y@ = two operands | |
883 | * | |
884 | * Returns: Zero if successful, @-1@ if %$x/y$% is not a square. | |
885 | * | |
886 | * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%. | |
887 | * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x | |
888 | * \ne 0$% then the operation fails. If you wanted a specific | |
889 | * square root then you'll have to pick it yourself. | |
890 | */ | |
891 | ||
892 | int fgoldi_quosqrt(fgoldi *z, const fgoldi *x, const fgoldi *y) | |
893 | { | |
894 | fgoldi t, u, v; | |
895 | octet xb[56], b0[56]; | |
896 | int32 rc = -1; | |
897 | mask32 m; | |
898 | unsigned i; | |
899 | ||
900 | #define SQRN(z, x, n) do { \ | |
901 | fgoldi_sqr((z), (x)); \ | |
902 | for (i = 1; i < (n); i++) fgoldi_sqr((z), (z)); \ | |
903 | } while (0) | |
904 | ||
905 | /* This is, fortunately, significantly easier than the equivalent problem | |
906 | * in GF(2^255 - 19), since p == 3 (mod 4). | |
907 | * | |
908 | * If x/y is square, then so is v = y^2 x/y = x y, and therefore u has | |
909 | * order r = (p - 1)/2. Let w = v^{(p-3)/4}. Then w^2 = v^{(p-3)/2} = | |
910 | * u^{r-1} = 1/v = 1/x y. Clearly, then, (x w)^2 = x^2/x y = x/y, so x w | |
911 | * is one of the square roots we seek. | |
912 | * | |
913 | * The addition chain, then, is a prefix of the previous one. | |
914 | */ | |
915 | fgoldi_mul(&v, x, y); | |
916 | ||
917 | fgoldi_sqr(&u, &v); /* 1 | 2 */ | |
918 | fgoldi_mul(&t, &u, &v); /* 2 | 3 */ | |
919 | SQRN(&u, &t, 2); /* 4 | 12 */ | |
920 | fgoldi_mul(&t, &u, &t); /* 5 | 15 */ | |
921 | SQRN(&u, &t, 4); /* 9 | 240 */ | |
922 | fgoldi_mul(&u, &u, &t); /* 10 | 255 = 2^8 - 1 */ | |
923 | SQRN(&u, &u, 4); /* 14 | 2^12 - 16 */ | |
924 | fgoldi_mul(&t, &u, &t); /* 15 | 2^12 - 1 */ | |
925 | SQRN(&u, &t, 12); /* 27 | 2^24 - 2^12 */ | |
926 | fgoldi_mul(&u, &u, &t); /* 28 | 2^24 - 1 */ | |
927 | SQRN(&u, &u, 12); /* 40 | 2^36 - 2^12 */ | |
928 | fgoldi_mul(&t, &u, &t); /* 41 | 2^36 - 1 */ | |
929 | fgoldi_sqr(&t, &t); /* 42 | 2^37 - 2 */ | |
930 | fgoldi_mul(&t, &t, &v); /* 43 | 2^37 - 1 */ | |
931 | SQRN(&u, &t, 37); /* 80 | 2^74 - 2^37 */ | |
932 | fgoldi_mul(&u, &u, &t); /* 81 | 2^74 - 1 */ | |
933 | SQRN(&u, &u, 37); /* 118 | 2^111 - 2^37 */ | |
934 | fgoldi_mul(&t, &u, &t); /* 119 | 2^111 - 1 */ | |
935 | SQRN(&u, &t, 111); /* 230 | 2^222 - 2^111 */ | |
936 | fgoldi_mul(&t, &u, &t); /* 231 | 2^222 - 1 */ | |
937 | fgoldi_sqr(&u, &t); /* 232 | 2^223 - 2 */ | |
938 | fgoldi_mul(&u, &u, &v); /* 233 | 2^223 - 1 */ | |
939 | SQRN(&u, &u, 223); /* 456 | 2^446 - 2^223 */ | |
940 | fgoldi_mul(&t, &u, &t); /* 457 | 2^446 - 2^222 - 1 */ | |
941 | ||
942 | #undef SQRN | |
943 | ||
944 | /* Now we must decide whether the answer was right. We should have z^2 = | |
945 | * x/y, so y z^2 = x. | |
946 | * | |
947 | * The easiest way to compare is to encode. This isn't as wasteful as it | |
948 | * sounds: the hard part is normalizing the representations, which we have | |
949 | * to do anyway. | |
950 | */ | |
951 | fgoldi_mul(z, x, &t); | |
952 | fgoldi_sqr(&t, z); | |
953 | fgoldi_mul(&t, &t, y); | |
954 | fgoldi_store(xb, x); | |
955 | fgoldi_store(b0, &t); | |
956 | m = -ct_memeq(xb, b0, 56); | |
957 | rc = PICK2(0, rc, m); | |
958 | return (rc); | |
959 | } | |
960 | ||
266efb73 MW |
961 | /*----- Test rig ----------------------------------------------------------*/ |
962 | ||
963 | #ifdef TEST_RIG | |
964 | ||
141c1284 | 965 | #include <mLib/macros.h> |
266efb73 MW |
966 | #include <mLib/report.h> |
967 | #include <mLib/str.h> | |
968 | #include <mLib/testrig.h> | |
969 | ||
970 | static void fixdstr(dstr *d) | |
971 | { | |
972 | if (d->len > 56) | |
973 | die(1, "invalid length for fgoldi"); | |
974 | else if (d->len < 56) { | |
975 | dstr_ensure(d, 56); | |
976 | memset(d->buf + d->len, 0, 56 - d->len); | |
977 | d->len = 56; | |
978 | } | |
979 | } | |
980 | ||
981 | static void cvt_fgoldi(const char *buf, dstr *d) | |
982 | { | |
983 | dstr dd = DSTR_INIT; | |
984 | ||
985 | type_hex.cvt(buf, &dd); fixdstr(&dd); | |
986 | dstr_ensure(d, sizeof(fgoldi)); d->len = sizeof(fgoldi); | |
987 | fgoldi_load((fgoldi *)d->buf, (const octet *)dd.buf); | |
988 | dstr_destroy(&dd); | |
989 | } | |
990 | ||
991 | static void dump_fgoldi(dstr *d, FILE *fp) | |
992 | { fdump(stderr, "???", (const piece *)d->buf); } | |
993 | ||
994 | static void cvt_fgoldi_ref(const char *buf, dstr *d) | |
995 | { type_hex.cvt(buf, d); fixdstr(d); } | |
996 | ||
997 | static void dump_fgoldi_ref(dstr *d, FILE *fp) | |
998 | { | |
999 | fgoldi x; | |
1000 | ||
1001 | fgoldi_load(&x, (const octet *)d->buf); | |
1002 | fdump(stderr, "???", x.P); | |
1003 | } | |
1004 | ||
1005 | static int eq(const fgoldi *x, dstr *d) | |
141c1284 | 1006 | { octet b[56]; fgoldi_store(b, x); return (MEMCMP(b, ==, d->buf, 56)); } |
266efb73 MW |
1007 | |
1008 | static const test_type | |
1009 | type_fgoldi = { cvt_fgoldi, dump_fgoldi }, | |
1010 | type_fgoldi_ref = { cvt_fgoldi_ref, dump_fgoldi_ref }; | |
1011 | ||
1012 | #define TEST_UNOP(op) \ | |
1013 | static int vrf_##op(dstr dv[]) \ | |
1014 | { \ | |
1015 | fgoldi *x = (fgoldi *)dv[0].buf; \ | |
1016 | fgoldi z, zz; \ | |
1017 | int ok = 1; \ | |
1018 | \ | |
1019 | fgoldi_##op(&z, x); \ | |
1020 | if (!eq(&z, &dv[1])) { \ | |
1021 | ok = 0; \ | |
1022 | fprintf(stderr, "failed!\n"); \ | |
1023 | fdump(stderr, "x", x->P); \ | |
1024 | fdump(stderr, "calc", z.P); \ | |
1025 | fgoldi_load(&zz, (const octet *)dv[1].buf); \ | |
1026 | fdump(stderr, "z", zz.P); \ | |
1027 | } \ | |
1028 | \ | |
1029 | return (ok); \ | |
1030 | } | |
1031 | ||
1032 | TEST_UNOP(sqr) | |
1033 | TEST_UNOP(inv) | |
1bc00e2a | 1034 | TEST_UNOP(neg) |
266efb73 MW |
1035 | |
1036 | #define TEST_BINOP(op) \ | |
1037 | static int vrf_##op(dstr dv[]) \ | |
1038 | { \ | |
1039 | fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf; \ | |
1040 | fgoldi z, zz; \ | |
1041 | int ok = 1; \ | |
1042 | \ | |
1043 | fgoldi_##op(&z, x, y); \ | |
1044 | if (!eq(&z, &dv[2])) { \ | |
1045 | ok = 0; \ | |
1046 | fprintf(stderr, "failed!\n"); \ | |
1047 | fdump(stderr, "x", x->P); \ | |
1048 | fdump(stderr, "y", y->P); \ | |
1049 | fdump(stderr, "calc", z.P); \ | |
1050 | fgoldi_load(&zz, (const octet *)dv[2].buf); \ | |
1051 | fdump(stderr, "z", zz.P); \ | |
1052 | } \ | |
1053 | \ | |
1054 | return (ok); \ | |
1055 | } | |
1056 | ||
1057 | TEST_BINOP(add) | |
1058 | TEST_BINOP(sub) | |
1059 | TEST_BINOP(mul) | |
1060 | ||
1061 | static int vrf_mulc(dstr dv[]) | |
1062 | { | |
1063 | fgoldi *x = (fgoldi *)dv[0].buf; | |
1064 | long a = *(const long *)dv[1].buf; | |
1065 | fgoldi z, zz; | |
1066 | int ok = 1; | |
1067 | ||
1068 | fgoldi_mulconst(&z, x, a); | |
1069 | if (!eq(&z, &dv[2])) { | |
1070 | ok = 0; | |
1071 | fprintf(stderr, "failed!\n"); | |
1072 | fdump(stderr, "x", x->P); | |
1073 | fprintf(stderr, "a = %ld\n", a); | |
1074 | fdump(stderr, "calc", z.P); | |
1075 | fgoldi_load(&zz, (const octet *)dv[2].buf); | |
1076 | fdump(stderr, "z", zz.P); | |
1077 | } | |
1078 | ||
1079 | return (ok); | |
1080 | } | |
1081 | ||
1bc00e2a MW |
1082 | static int vrf_condneg(dstr dv[]) |
1083 | { | |
1084 | fgoldi *x = (fgoldi *)dv[0].buf; | |
1085 | uint32 m = *(uint32 *)dv[1].buf; | |
1086 | fgoldi z; | |
1087 | int ok = 1; | |
1088 | ||
1089 | fgoldi_condneg(&z, x, m); | |
1090 | if (!eq(&z, &dv[2])) { | |
1091 | ok = 0; | |
1092 | fprintf(stderr, "failed!\n"); | |
1093 | fdump(stderr, "x", x->P); | |
1094 | fprintf(stderr, "m = 0x%08lx\n", (unsigned long)m); | |
1095 | fdump(stderr, "calc z", z.P); | |
1096 | fgoldi_load(&z, (const octet *)dv[1].buf); | |
1097 | fdump(stderr, "want z", z.P); | |
1098 | } | |
1099 | ||
1100 | return (ok); | |
1101 | } | |
1102 | ||
1103 | static int vrf_pick2(dstr dv[]) | |
1104 | { | |
1105 | fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf; | |
1106 | uint32 m = *(uint32 *)dv[2].buf; | |
1107 | fgoldi z; | |
1108 | int ok = 1; | |
1109 | ||
1110 | fgoldi_pick2(&z, x, y, m); | |
1111 | if (!eq(&z, &dv[3])) { | |
1112 | ok = 0; | |
1113 | fprintf(stderr, "failed!\n"); | |
1114 | fdump(stderr, "x", x->P); | |
1115 | fdump(stderr, "y", y->P); | |
1116 | fprintf(stderr, "m = 0x%08lx\n", (unsigned long)m); | |
1117 | fdump(stderr, "calc z", z.P); | |
1118 | fgoldi_load(&z, (const octet *)dv[3].buf); | |
1119 | fdump(stderr, "want z", z.P); | |
1120 | } | |
1121 | ||
1122 | return (ok); | |
1123 | } | |
1124 | ||
1125 | static int vrf_pickn(dstr dv[]) | |
1126 | { | |
1127 | dstr d = DSTR_INIT; | |
1128 | fgoldi v[32], z; | |
1129 | size_t i = *(uint32 *)dv[1].buf, j, n; | |
1130 | const char *p; | |
1131 | char *q; | |
1132 | int ok = 1; | |
1133 | ||
1134 | for (q = dv[0].buf, n = 0; (p = str_qword(&q, 0)) != 0; n++) | |
1135 | { cvt_fgoldi(p, &d); v[n] = *(fgoldi *)d.buf; } | |
1136 | ||
1137 | fgoldi_pickn(&z, v, n, i); | |
1138 | if (!eq(&z, &dv[2])) { | |
1139 | ok = 0; | |
1140 | fprintf(stderr, "failed!\n"); | |
1141 | for (j = 0; j < n; j++) { | |
1142 | fprintf(stderr, "v[%2u]", (unsigned)j); | |
1143 | fdump(stderr, "", v[j].P); | |
1144 | } | |
1145 | fprintf(stderr, "i = %u\n", (unsigned)i); | |
1146 | fdump(stderr, "calc z", z.P); | |
1147 | fgoldi_load(&z, (const octet *)dv[2].buf); | |
1148 | fdump(stderr, "want z", z.P); | |
1149 | } | |
1150 | ||
1151 | dstr_destroy(&d); | |
1152 | return (ok); | |
1153 | } | |
1154 | ||
266efb73 MW |
1155 | static int vrf_condswap(dstr dv[]) |
1156 | { | |
1157 | fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf; | |
1158 | fgoldi xx = *x, yy = *y; | |
1159 | uint32 m = *(uint32 *)dv[2].buf; | |
1160 | int ok = 1; | |
1161 | ||
1162 | fgoldi_condswap(&xx, &yy, m); | |
1163 | if (!eq(&xx, &dv[3]) || !eq(&yy, &dv[4])) { | |
1164 | ok = 0; | |
1165 | fprintf(stderr, "failed!\n"); | |
1166 | fdump(stderr, "x", x->P); | |
1167 | fdump(stderr, "y", y->P); | |
1168 | fprintf(stderr, "m = 0x%08lx\n", (unsigned long)m); | |
1169 | fdump(stderr, "calc xx", xx.P); | |
1170 | fdump(stderr, "calc yy", yy.P); | |
1171 | fgoldi_load(&xx, (const octet *)dv[3].buf); | |
1172 | fgoldi_load(&yy, (const octet *)dv[4].buf); | |
1173 | fdump(stderr, "want xx", xx.P); | |
1174 | fdump(stderr, "want yy", yy.P); | |
1175 | } | |
1176 | ||
1177 | return (ok); | |
1178 | } | |
1179 | ||
1bc00e2a MW |
1180 | static int vrf_quosqrt(dstr dv[]) |
1181 | { | |
1182 | fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf; | |
1183 | fgoldi z, zz; | |
1184 | int rc; | |
1185 | int ok = 1; | |
1186 | ||
1187 | if (dv[2].len) { fixdstr(&dv[2]); fixdstr(&dv[3]); } | |
1188 | rc = fgoldi_quosqrt(&z, x, y); | |
1189 | if (!dv[2].len ? !rc : (rc || (!eq(&z, &dv[2]) && !eq(&z, &dv[3])))) { | |
1190 | ok = 0; | |
1191 | fprintf(stderr, "failed!\n"); | |
1192 | fdump(stderr, "x", x->P); | |
1193 | fdump(stderr, "y", y->P); | |
1194 | if (rc) fprintf(stderr, "calc: FAIL\n"); | |
1195 | else fdump(stderr, "calc", z.P); | |
1196 | if (!dv[2].len) | |
1197 | fprintf(stderr, "exp: FAIL\n"); | |
1198 | else { | |
1199 | fgoldi_load(&zz, (const octet *)dv[2].buf); | |
1200 | fdump(stderr, "z", zz.P); | |
1201 | fgoldi_load(&zz, (const octet *)dv[3].buf); | |
1202 | fdump(stderr, "z'", zz.P); | |
1203 | } | |
1204 | } | |
1205 | ||
1206 | return (ok); | |
1207 | } | |
1208 | ||
266efb73 MW |
1209 | static int vrf_sub_mulc_add_sub_mul(dstr dv[]) |
1210 | { | |
1211 | fgoldi *u = (fgoldi *)dv[0].buf, *v = (fgoldi *)dv[1].buf, | |
1212 | *w = (fgoldi *)dv[3].buf, *x = (fgoldi *)dv[4].buf, | |
1213 | *y = (fgoldi *)dv[5].buf; | |
1214 | long a = *(const long *)dv[2].buf; | |
1215 | fgoldi umv, aumv, wpaumv, xmy, z, zz; | |
1216 | int ok = 1; | |
1217 | ||
1218 | fgoldi_sub(&umv, u, v); | |
1219 | fgoldi_mulconst(&aumv, &umv, a); | |
1220 | fgoldi_add(&wpaumv, w, &aumv); | |
1221 | fgoldi_sub(&xmy, x, y); | |
1222 | fgoldi_mul(&z, &wpaumv, &xmy); | |
1223 | ||
1224 | if (!eq(&z, &dv[6])) { | |
1225 | ok = 0; | |
1226 | fprintf(stderr, "failed!\n"); | |
1227 | fdump(stderr, "u", u->P); | |
1228 | fdump(stderr, "v", v->P); | |
1229 | fdump(stderr, "u - v", umv.P); | |
1230 | fprintf(stderr, "a = %ld\n", a); | |
1231 | fdump(stderr, "a (u - v)", aumv.P); | |
1232 | fdump(stderr, "w + a (u - v)", wpaumv.P); | |
1233 | fdump(stderr, "x", x->P); | |
1234 | fdump(stderr, "y", y->P); | |
1235 | fdump(stderr, "x - y", xmy.P); | |
1236 | fdump(stderr, "(x - y) (w + a (u - v))", z.P); | |
1237 | fgoldi_load(&zz, (const octet *)dv[6].buf); fdump(stderr, "z", zz.P); | |
1238 | } | |
1239 | ||
1240 | return (ok); | |
1241 | } | |
1242 | ||
1243 | static test_chunk tests[] = { | |
1244 | { "add", vrf_add, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } }, | |
1245 | { "sub", vrf_sub, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } }, | |
1bc00e2a MW |
1246 | { "neg", vrf_neg, { &type_fgoldi, &type_fgoldi_ref } }, |
1247 | { "condneg", vrf_condneg, | |
1248 | { &type_fgoldi, &type_uint32, &type_fgoldi_ref } }, | |
266efb73 MW |
1249 | { "mul", vrf_mul, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } }, |
1250 | { "mulconst", vrf_mulc, { &type_fgoldi, &type_long, &type_fgoldi_ref } }, | |
1bc00e2a MW |
1251 | { "pick2", vrf_pick2, |
1252 | { &type_fgoldi, &type_fgoldi, &type_uint32, &type_fgoldi_ref } }, | |
1253 | { "pickn", vrf_pickn, | |
1254 | { &type_string, &type_uint32, &type_fgoldi_ref } }, | |
266efb73 MW |
1255 | { "condswap", vrf_condswap, |
1256 | { &type_fgoldi, &type_fgoldi, &type_uint32, | |
1257 | &type_fgoldi_ref, &type_fgoldi_ref } }, | |
1258 | { "sqr", vrf_sqr, { &type_fgoldi, &type_fgoldi_ref } }, | |
1259 | { "inv", vrf_inv, { &type_fgoldi, &type_fgoldi_ref } }, | |
1bc00e2a MW |
1260 | { "quosqrt", vrf_quosqrt, |
1261 | { &type_fgoldi, &type_fgoldi, &type_hex, &type_hex } }, | |
266efb73 MW |
1262 | { "sub-mulc-add-sub-mul", vrf_sub_mulc_add_sub_mul, |
1263 | { &type_fgoldi, &type_fgoldi, &type_long, &type_fgoldi, | |
1264 | &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } }, | |
1265 | { 0, 0, { 0 } } | |
1266 | }; | |
1267 | ||
1268 | int main(int argc, char *argv[]) | |
1269 | { | |
1270 | test_run(argc, argv, tests, SRCDIR "/t/fgoldi"); | |
1271 | return (0); | |
1272 | } | |
1273 | ||
1274 | #endif | |
1275 | ||
1276 | /*----- That's all, folks -------------------------------------------------*/ |