1 #include <string.h>
2 
3 #include "private/common.h"
4 #include "utils.h"
5 
6 /*
7  h = 0
8  */
9 
10 static inline void
11 fe25519_0(fe25519 h)
12 {
13     memset(&h[0], 0, 10 * sizeof h[0]);
14 }
15 
16 /*
17  h = 1
18  */
19 
20 static inline void
21 fe25519_1(fe25519 h)
22 {
23     h[0] = 1;
24     h[1] = 0;
25     memset(&h[2], 0, 8 * sizeof h[0]);
26 }
27 
28 /*
29  h = f + g
30  Can overlap h with f or g.
31  *
32  Preconditions:
33  |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
34  |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
35  *
36  Postconditions:
37  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
38  */
39 
40 static inline void
41 fe25519_add(fe25519 h, const fe25519 f, const fe25519 g)
42 {
43     int32_t h0 = f[0] + g[0];
44     int32_t h1 = f[1] + g[1];
45     int32_t h2 = f[2] + g[2];
46     int32_t h3 = f[3] + g[3];
47     int32_t h4 = f[4] + g[4];
48     int32_t h5 = f[5] + g[5];
49     int32_t h6 = f[6] + g[6];
50     int32_t h7 = f[7] + g[7];
51     int32_t h8 = f[8] + g[8];
52     int32_t h9 = f[9] + g[9];
53 
54     h[0] = h0;
55     h[1] = h1;
56     h[2] = h2;
57     h[3] = h3;
58     h[4] = h4;
59     h[5] = h5;
60     h[6] = h6;
61     h[7] = h7;
62     h[8] = h8;
63     h[9] = h9;
64 }
65 
66 /*
67  h = f - g
68  Can overlap h with f or g.
69  *
70  Preconditions:
71  |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
72  |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
73  *
74  Postconditions:
75  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
76  */
77 
78 static void
79 fe25519_sub(fe25519 h, const fe25519 f, const fe25519 g)
80 {
81     int32_t h0 = f[0] - g[0];
82     int32_t h1 = f[1] - g[1];
83     int32_t h2 = f[2] - g[2];
84     int32_t h3 = f[3] - g[3];
85     int32_t h4 = f[4] - g[4];
86     int32_t h5 = f[5] - g[5];
87     int32_t h6 = f[6] - g[6];
88     int32_t h7 = f[7] - g[7];
89     int32_t h8 = f[8] - g[8];
90     int32_t h9 = f[9] - g[9];
91 
92     h[0] = h0;
93     h[1] = h1;
94     h[2] = h2;
95     h[3] = h3;
96     h[4] = h4;
97     h[5] = h5;
98     h[6] = h6;
99     h[7] = h7;
100     h[8] = h8;
101     h[9] = h9;
102 }
103 
104 /*
105  h = -f
106  *
107  Preconditions:
108  |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
109  *
110  Postconditions:
111  |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
112  */
113 
114 static inline void
115 fe25519_neg(fe25519 h, const fe25519 f)
116 {
117     int32_t h0 = -f[0];
118     int32_t h1 = -f[1];
119     int32_t h2 = -f[2];
120     int32_t h3 = -f[3];
121     int32_t h4 = -f[4];
122     int32_t h5 = -f[5];
123     int32_t h6 = -f[6];
124     int32_t h7 = -f[7];
125     int32_t h8 = -f[8];
126     int32_t h9 = -f[9];
127 
128     h[0] = h0;
129     h[1] = h1;
130     h[2] = h2;
131     h[3] = h3;
132     h[4] = h4;
133     h[5] = h5;
134     h[6] = h6;
135     h[7] = h7;
136     h[8] = h8;
137     h[9] = h9;
138 }
139 
140 /*
141  Replace (f,g) with (g,g) if b == 1;
142  replace (f,g) with (f,g) if b == 0.
143  *
144  Preconditions: b in {0,1}.
145  */
146 
147 static void
148 fe25519_cmov(fe25519 f, const fe25519 g, unsigned int b)
149 {
150     const uint32_t mask = (uint32_t) (-(int32_t) b);
151 
152     int32_t f0 = f[0];
153     int32_t f1 = f[1];
154     int32_t f2 = f[2];
155     int32_t f3 = f[3];
156     int32_t f4 = f[4];
157     int32_t f5 = f[5];
158     int32_t f6 = f[6];
159     int32_t f7 = f[7];
160     int32_t f8 = f[8];
161     int32_t f9 = f[9];
162 
163     int32_t x0 = f0 ^ g[0];
164     int32_t x1 = f1 ^ g[1];
165     int32_t x2 = f2 ^ g[2];
166     int32_t x3 = f3 ^ g[3];
167     int32_t x4 = f4 ^ g[4];
168     int32_t x5 = f5 ^ g[5];
169     int32_t x6 = f6 ^ g[6];
170     int32_t x7 = f7 ^ g[7];
171     int32_t x8 = f8 ^ g[8];
172     int32_t x9 = f9 ^ g[9];
173 
174     x0 &= mask;
175     x1 &= mask;
176     x2 &= mask;
177     x3 &= mask;
178     x4 &= mask;
179     x5 &= mask;
180     x6 &= mask;
181     x7 &= mask;
182     x8 &= mask;
183     x9 &= mask;
184 
185     f[0] = f0 ^ x0;
186     f[1] = f1 ^ x1;
187     f[2] = f2 ^ x2;
188     f[3] = f3 ^ x3;
189     f[4] = f4 ^ x4;
190     f[5] = f5 ^ x5;
191     f[6] = f6 ^ x6;
192     f[7] = f7 ^ x7;
193     f[8] = f8 ^ x8;
194     f[9] = f9 ^ x9;
195 }
196 
197 static void
198 fe25519_cswap(fe25519 f, fe25519 g, unsigned int b)
199 {
200     const uint32_t mask = (uint32_t) (-(int64_t) b);
201 
202     int32_t f0 = f[0];
203     int32_t f1 = f[1];
204     int32_t f2 = f[2];
205     int32_t f3 = f[3];
206     int32_t f4 = f[4];
207     int32_t f5 = f[5];
208     int32_t f6 = f[6];
209     int32_t f7 = f[7];
210     int32_t f8 = f[8];
211     int32_t f9 = f[9];
212 
213     int32_t g0 = g[0];
214     int32_t g1 = g[1];
215     int32_t g2 = g[2];
216     int32_t g3 = g[3];
217     int32_t g4 = g[4];
218     int32_t g5 = g[5];
219     int32_t g6 = g[6];
220     int32_t g7 = g[7];
221     int32_t g8 = g[8];
222     int32_t g9 = g[9];
223 
224     int32_t x0 = f0 ^ g0;
225     int32_t x1 = f1 ^ g1;
226     int32_t x2 = f2 ^ g2;
227     int32_t x3 = f3 ^ g3;
228     int32_t x4 = f4 ^ g4;
229     int32_t x5 = f5 ^ g5;
230     int32_t x6 = f6 ^ g6;
231     int32_t x7 = f7 ^ g7;
232     int32_t x8 = f8 ^ g8;
233     int32_t x9 = f9 ^ g9;
234 
235     x0 &= mask;
236     x1 &= mask;
237     x2 &= mask;
238     x3 &= mask;
239     x4 &= mask;
240     x5 &= mask;
241     x6 &= mask;
242     x7 &= mask;
243     x8 &= mask;
244     x9 &= mask;
245 
246     f[0] = f0 ^ x0;
247     f[1] = f1 ^ x1;
248     f[2] = f2 ^ x2;
249     f[3] = f3 ^ x3;
250     f[4] = f4 ^ x4;
251     f[5] = f5 ^ x5;
252     f[6] = f6 ^ x6;
253     f[7] = f7 ^ x7;
254     f[8] = f8 ^ x8;
255     f[9] = f9 ^ x9;
256 
257     g[0] = g0 ^ x0;
258     g[1] = g1 ^ x1;
259     g[2] = g2 ^ x2;
260     g[3] = g3 ^ x3;
261     g[4] = g4 ^ x4;
262     g[5] = g5 ^ x5;
263     g[6] = g6 ^ x6;
264     g[7] = g7 ^ x7;
265     g[8] = g8 ^ x8;
266     g[9] = g9 ^ x9;
267 }
268 
269 /*
270  h = f
271  */
272 
273 static inline void
274 fe25519_copy(fe25519 h, const fe25519 f)
275 {
276     int32_t f0 = f[0];
277     int32_t f1 = f[1];
278     int32_t f2 = f[2];
279     int32_t f3 = f[3];
280     int32_t f4 = f[4];
281     int32_t f5 = f[5];
282     int32_t f6 = f[6];
283     int32_t f7 = f[7];
284     int32_t f8 = f[8];
285     int32_t f9 = f[9];
286 
287     h[0] = f0;
288     h[1] = f1;
289     h[2] = f2;
290     h[3] = f3;
291     h[4] = f4;
292     h[5] = f5;
293     h[6] = f6;
294     h[7] = f7;
295     h[8] = f8;
296     h[9] = f9;
297 }
298 
299 /*
300  return 1 if f is in {1,3,5,...,q-2}
301  return 0 if f is in {0,2,4,...,q-1}
302 
303  Preconditions:
304  |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
305  */
306 
307 static inline int
308 fe25519_isnegative(const fe25519 f)
309 {
310     unsigned char s[32];
311 
312     fe25519_tobytes(s, f);
313 
314     return s[0] & 1;
315 }
316 
317 /*
318  return 1 if f == 0
319  return 0 if f != 0
320 
321  Preconditions:
322  |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
323  */
324 
325 static inline int
326 fe25519_iszero(const fe25519 f)
327 {
328     unsigned char s[32];
329 
330     fe25519_tobytes(s, f);
331 
332     return sodium_is_zero(s, 32);
333 }
334 
335 /*
336  h = f * g
337  Can overlap h with f or g.
338  *
339  Preconditions:
340  |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
341  |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
342  *
343  Postconditions:
344  |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
345  */
346 
347 /*
348  Notes on implementation strategy:
349  *
350  Using schoolbook multiplication.
351  Karatsuba would save a little in some cost models.
352  *
353  Most multiplications by 2 and 19 are 32-bit precomputations;
354  cheaper than 64-bit postcomputations.
355  *
356  There is one remaining multiplication by 19 in the carry chain;
357  one *19 precomputation can be merged into this,
358  but the resulting data flow is considerably less clean.
359  *
360  There are 12 carries below.
361  10 of them are 2-way parallelizable and vectorizable.
362  Can get away with 11 carries, but then data flow is much deeper.
363  *
364  With tighter constraints on inputs can squeeze carries into int32.
365  */
366 
367 static void
368 fe25519_mul(fe25519 h, const fe25519 f, const fe25519 g)
369 {
370     int32_t f0 = f[0];
371     int32_t f1 = f[1];
372     int32_t f2 = f[2];
373     int32_t f3 = f[3];
374     int32_t f4 = f[4];
375     int32_t f5 = f[5];
376     int32_t f6 = f[6];
377     int32_t f7 = f[7];
378     int32_t f8 = f[8];
379     int32_t f9 = f[9];
380 
381     int32_t g0 = g[0];
382     int32_t g1 = g[1];
383     int32_t g2 = g[2];
384     int32_t g3 = g[3];
385     int32_t g4 = g[4];
386     int32_t g5 = g[5];
387     int32_t g6 = g[6];
388     int32_t g7 = g[7];
389     int32_t g8 = g[8];
390     int32_t g9 = g[9];
391 
392     int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
393     int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
394     int32_t g3_19 = 19 * g3;
395     int32_t g4_19 = 19 * g4;
396     int32_t g5_19 = 19 * g5;
397     int32_t g6_19 = 19 * g6;
398     int32_t g7_19 = 19 * g7;
399     int32_t g8_19 = 19 * g8;
400     int32_t g9_19 = 19 * g9;
401     int32_t f1_2  = 2 * f1;
402     int32_t f3_2  = 2 * f3;
403     int32_t f5_2  = 2 * f5;
404     int32_t f7_2  = 2 * f7;
405     int32_t f9_2  = 2 * f9;
406 
407     int64_t f0g0    = f0 * (int64_t) g0;
408     int64_t f0g1    = f0 * (int64_t) g1;
409     int64_t f0g2    = f0 * (int64_t) g2;
410     int64_t f0g3    = f0 * (int64_t) g3;
411     int64_t f0g4    = f0 * (int64_t) g4;
412     int64_t f0g5    = f0 * (int64_t) g5;
413     int64_t f0g6    = f0 * (int64_t) g6;
414     int64_t f0g7    = f0 * (int64_t) g7;
415     int64_t f0g8    = f0 * (int64_t) g8;
416     int64_t f0g9    = f0 * (int64_t) g9;
417     int64_t f1g0    = f1 * (int64_t) g0;
418     int64_t f1g1_2  = f1_2 * (int64_t) g1;
419     int64_t f1g2    = f1 * (int64_t) g2;
420     int64_t f1g3_2  = f1_2 * (int64_t) g3;
421     int64_t f1g4    = f1 * (int64_t) g4;
422     int64_t f1g5_2  = f1_2 * (int64_t) g5;
423     int64_t f1g6    = f1 * (int64_t) g6;
424     int64_t f1g7_2  = f1_2 * (int64_t) g7;
425     int64_t f1g8    = f1 * (int64_t) g8;
426     int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
427     int64_t f2g0    = f2 * (int64_t) g0;
428     int64_t f2g1    = f2 * (int64_t) g1;
429     int64_t f2g2    = f2 * (int64_t) g2;
430     int64_t f2g3    = f2 * (int64_t) g3;
431     int64_t f2g4    = f2 * (int64_t) g4;
432     int64_t f2g5    = f2 * (int64_t) g5;
433     int64_t f2g6    = f2 * (int64_t) g6;
434     int64_t f2g7    = f2 * (int64_t) g7;
435     int64_t f2g8_19 = f2 * (int64_t) g8_19;
436     int64_t f2g9_19 = f2 * (int64_t) g9_19;
437     int64_t f3g0    = f3 * (int64_t) g0;
438     int64_t f3g1_2  = f3_2 * (int64_t) g1;
439     int64_t f3g2    = f3 * (int64_t) g2;
440     int64_t f3g3_2  = f3_2 * (int64_t) g3;
441     int64_t f3g4    = f3 * (int64_t) g4;
442     int64_t f3g5_2  = f3_2 * (int64_t) g5;
443     int64_t f3g6    = f3 * (int64_t) g6;
444     int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
445     int64_t f3g8_19 = f3 * (int64_t) g8_19;
446     int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
447     int64_t f4g0    = f4 * (int64_t) g0;
448     int64_t f4g1    = f4 * (int64_t) g1;
449     int64_t f4g2    = f4 * (int64_t) g2;
450     int64_t f4g3    = f4 * (int64_t) g3;
451     int64_t f4g4    = f4 * (int64_t) g4;
452     int64_t f4g5    = f4 * (int64_t) g5;
453     int64_t f4g6_19 = f4 * (int64_t) g6_19;
454     int64_t f4g7_19 = f4 * (int64_t) g7_19;
455     int64_t f4g8_19 = f4 * (int64_t) g8_19;
456     int64_t f4g9_19 = f4 * (int64_t) g9_19;
457     int64_t f5g0    = f5 * (int64_t) g0;
458     int64_t f5g1_2  = f5_2 * (int64_t) g1;
459     int64_t f5g2    = f5 * (int64_t) g2;
460     int64_t f5g3_2  = f5_2 * (int64_t) g3;
461     int64_t f5g4    = f5 * (int64_t) g4;
462     int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
463     int64_t f5g6_19 = f5 * (int64_t) g6_19;
464     int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
465     int64_t f5g8_19 = f5 * (int64_t) g8_19;
466     int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
467     int64_t f6g0    = f6 * (int64_t) g0;
468     int64_t f6g1    = f6 * (int64_t) g1;
469     int64_t f6g2    = f6 * (int64_t) g2;
470     int64_t f6g3    = f6 * (int64_t) g3;
471     int64_t f6g4_19 = f6 * (int64_t) g4_19;
472     int64_t f6g5_19 = f6 * (int64_t) g5_19;
473     int64_t f6g6_19 = f6 * (int64_t) g6_19;
474     int64_t f6g7_19 = f6 * (int64_t) g7_19;
475     int64_t f6g8_19 = f6 * (int64_t) g8_19;
476     int64_t f6g9_19 = f6 * (int64_t) g9_19;
477     int64_t f7g0    = f7 * (int64_t) g0;
478     int64_t f7g1_2  = f7_2 * (int64_t) g1;
479     int64_t f7g2    = f7 * (int64_t) g2;
480     int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
481     int64_t f7g4_19 = f7 * (int64_t) g4_19;
482     int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
483     int64_t f7g6_19 = f7 * (int64_t) g6_19;
484     int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
485     int64_t f7g8_19 = f7 * (int64_t) g8_19;
486     int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
487     int64_t f8g0    = f8 * (int64_t) g0;
488     int64_t f8g1    = f8 * (int64_t) g1;
489     int64_t f8g2_19 = f8 * (int64_t) g2_19;
490     int64_t f8g3_19 = f8 * (int64_t) g3_19;
491     int64_t f8g4_19 = f8 * (int64_t) g4_19;
492     int64_t f8g5_19 = f8 * (int64_t) g5_19;
493     int64_t f8g6_19 = f8 * (int64_t) g6_19;
494     int64_t f8g7_19 = f8 * (int64_t) g7_19;
495     int64_t f8g8_19 = f8 * (int64_t) g8_19;
496     int64_t f8g9_19 = f8 * (int64_t) g9_19;
497     int64_t f9g0    = f9 * (int64_t) g0;
498     int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
499     int64_t f9g2_19 = f9 * (int64_t) g2_19;
500     int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
501     int64_t f9g4_19 = f9 * (int64_t) g4_19;
502     int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
503     int64_t f9g6_19 = f9 * (int64_t) g6_19;
504     int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
505     int64_t f9g8_19 = f9 * (int64_t) g8_19;
506     int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
507 
508     int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 +
509                  f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
510     int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 +
511                  f7g4_19 + f8g3_19 + f9g2_19;
512     int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 +
513                  f7g5_38 + f8g4_19 + f9g3_38;
514     int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 +
515                  f7g6_19 + f8g5_19 + f9g4_19;
516     int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 +
517                  f7g7_38 + f8g6_19 + f9g5_38;
518     int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 +
519                  f8g7_19 + f9g6_19;
520     int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 +
521                  f7g9_38 + f8g8_19 + f9g7_38;
522     int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 +
523                  f8g9_19 + f9g8_19;
524     int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 +
525                  f8g0 + f9g9_38;
526     int64_t h9 =
527         f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
528 
529     int64_t carry0;
530     int64_t carry1;
531     int64_t carry2;
532     int64_t carry3;
533     int64_t carry4;
534     int64_t carry5;
535     int64_t carry6;
536     int64_t carry7;
537     int64_t carry8;
538     int64_t carry9;
539 
540     /*
541      |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
542      i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
543      |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
544      i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
545      */
546 
547     carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
548     h1 += carry0;
549     h0 -= carry0 * ((uint64_t) 1L << 26);
550     carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
551     h5 += carry4;
552     h4 -= carry4 * ((uint64_t) 1L << 26);
553     /* |h0| <= 2^25 */
554     /* |h4| <= 2^25 */
555     /* |h1| <= 1.71*2^59 */
556     /* |h5| <= 1.71*2^59 */
557 
558     carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
559     h2 += carry1;
560     h1 -= carry1 * ((uint64_t) 1L << 25);
561     carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
562     h6 += carry5;
563     h5 -= carry5 * ((uint64_t) 1L << 25);
564     /* |h1| <= 2^24; from now on fits into int32 */
565     /* |h5| <= 2^24; from now on fits into int32 */
566     /* |h2| <= 1.41*2^60 */
567     /* |h6| <= 1.41*2^60 */
568 
569     carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
570     h3 += carry2;
571     h2 -= carry2 * ((uint64_t) 1L << 26);
572     carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
573     h7 += carry6;
574     h6 -= carry6 * ((uint64_t) 1L << 26);
575     /* |h2| <= 2^25; from now on fits into int32 unchanged */
576     /* |h6| <= 2^25; from now on fits into int32 unchanged */
577     /* |h3| <= 1.71*2^59 */
578     /* |h7| <= 1.71*2^59 */
579 
580     carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
581     h4 += carry3;
582     h3 -= carry3 * ((uint64_t) 1L << 25);
583     carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
584     h8 += carry7;
585     h7 -= carry7 * ((uint64_t) 1L << 25);
586     /* |h3| <= 2^24; from now on fits into int32 unchanged */
587     /* |h7| <= 2^24; from now on fits into int32 unchanged */
588     /* |h4| <= 1.72*2^34 */
589     /* |h8| <= 1.41*2^60 */
590 
591     carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
592     h5 += carry4;
593     h4 -= carry4 * ((uint64_t) 1L << 26);
594     carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
595     h9 += carry8;
596     h8 -= carry8 * ((uint64_t) 1L << 26);
597     /* |h4| <= 2^25; from now on fits into int32 unchanged */
598     /* |h8| <= 2^25; from now on fits into int32 unchanged */
599     /* |h5| <= 1.01*2^24 */
600     /* |h9| <= 1.71*2^59 */
601 
602     carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
603     h0 += carry9 * 19;
604     h9 -= carry9 * ((uint64_t) 1L << 25);
605     /* |h9| <= 2^24; from now on fits into int32 unchanged */
606     /* |h0| <= 1.1*2^39 */
607 
608     carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
609     h1 += carry0;
610     h0 -= carry0 * ((uint64_t) 1L << 26);
611     /* |h0| <= 2^25; from now on fits into int32 unchanged */
612     /* |h1| <= 1.01*2^24 */
613 
614     h[0] = (int32_t) h0;
615     h[1] = (int32_t) h1;
616     h[2] = (int32_t) h2;
617     h[3] = (int32_t) h3;
618     h[4] = (int32_t) h4;
619     h[5] = (int32_t) h5;
620     h[6] = (int32_t) h6;
621     h[7] = (int32_t) h7;
622     h[8] = (int32_t) h8;
623     h[9] = (int32_t) h9;
624 }
625 
626 /*
627  h = f * f
628  Can overlap h with f.
629  *
630  Preconditions:
631  |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
632  *
633  Postconditions:
634  |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
635  */
636 
637 static void
638 fe25519_sq(fe25519 h, const fe25519 f)
639 {
640     int32_t f0 = f[0];
641     int32_t f1 = f[1];
642     int32_t f2 = f[2];
643     int32_t f3 = f[3];
644     int32_t f4 = f[4];
645     int32_t f5 = f[5];
646     int32_t f6 = f[6];
647     int32_t f7 = f[7];
648     int32_t f8 = f[8];
649     int32_t f9 = f[9];
650 
651     int32_t f0_2  = 2 * f0;
652     int32_t f1_2  = 2 * f1;
653     int32_t f2_2  = 2 * f2;
654     int32_t f3_2  = 2 * f3;
655     int32_t f4_2  = 2 * f4;
656     int32_t f5_2  = 2 * f5;
657     int32_t f6_2  = 2 * f6;
658     int32_t f7_2  = 2 * f7;
659     int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
660     int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
661     int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
662     int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
663     int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
664 
665     int64_t f0f0    = f0 * (int64_t) f0;
666     int64_t f0f1_2  = f0_2 * (int64_t) f1;
667     int64_t f0f2_2  = f0_2 * (int64_t) f2;
668     int64_t f0f3_2  = f0_2 * (int64_t) f3;
669     int64_t f0f4_2  = f0_2 * (int64_t) f4;
670     int64_t f0f5_2  = f0_2 * (int64_t) f5;
671     int64_t f0f6_2  = f0_2 * (int64_t) f6;
672     int64_t f0f7_2  = f0_2 * (int64_t) f7;
673     int64_t f0f8_2  = f0_2 * (int64_t) f8;
674     int64_t f0f9_2  = f0_2 * (int64_t) f9;
675     int64_t f1f1_2  = f1_2 * (int64_t) f1;
676     int64_t f1f2_2  = f1_2 * (int64_t) f2;
677     int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
678     int64_t f1f4_2  = f1_2 * (int64_t) f4;
679     int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
680     int64_t f1f6_2  = f1_2 * (int64_t) f6;
681     int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
682     int64_t f1f8_2  = f1_2 * (int64_t) f8;
683     int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
684     int64_t f2f2    = f2 * (int64_t) f2;
685     int64_t f2f3_2  = f2_2 * (int64_t) f3;
686     int64_t f2f4_2  = f2_2 * (int64_t) f4;
687     int64_t f2f5_2  = f2_2 * (int64_t) f5;
688     int64_t f2f6_2  = f2_2 * (int64_t) f6;
689     int64_t f2f7_2  = f2_2 * (int64_t) f7;
690     int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
691     int64_t f2f9_38 = f2 * (int64_t) f9_38;
692     int64_t f3f3_2  = f3_2 * (int64_t) f3;
693     int64_t f3f4_2  = f3_2 * (int64_t) f4;
694     int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
695     int64_t f3f6_2  = f3_2 * (int64_t) f6;
696     int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
697     int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
698     int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
699     int64_t f4f4    = f4 * (int64_t) f4;
700     int64_t f4f5_2  = f4_2 * (int64_t) f5;
701     int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
702     int64_t f4f7_38 = f4 * (int64_t) f7_38;
703     int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
704     int64_t f4f9_38 = f4 * (int64_t) f9_38;
705     int64_t f5f5_38 = f5 * (int64_t) f5_38;
706     int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
707     int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
708     int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
709     int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
710     int64_t f6f6_19 = f6 * (int64_t) f6_19;
711     int64_t f6f7_38 = f6 * (int64_t) f7_38;
712     int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
713     int64_t f6f9_38 = f6 * (int64_t) f9_38;
714     int64_t f7f7_38 = f7 * (int64_t) f7_38;
715     int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
716     int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
717     int64_t f8f8_19 = f8 * (int64_t) f8_19;
718     int64_t f8f9_38 = f8 * (int64_t) f9_38;
719     int64_t f9f9_38 = f9 * (int64_t) f9_38;
720 
721     int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
722     int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
723     int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
724     int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
725     int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
726     int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
727     int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
728     int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
729     int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
730     int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
731 
732     int64_t carry0;
733     int64_t carry1;
734     int64_t carry2;
735     int64_t carry3;
736     int64_t carry4;
737     int64_t carry5;
738     int64_t carry6;
739     int64_t carry7;
740     int64_t carry8;
741     int64_t carry9;
742 
743     carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
744     h1 += carry0;
745     h0 -= carry0 * ((uint64_t) 1L << 26);
746     carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
747     h5 += carry4;
748     h4 -= carry4 * ((uint64_t) 1L << 26);
749 
750     carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
751     h2 += carry1;
752     h1 -= carry1 * ((uint64_t) 1L << 25);
753     carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
754     h6 += carry5;
755     h5 -= carry5 * ((uint64_t) 1L << 25);
756 
757     carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
758     h3 += carry2;
759     h2 -= carry2 * ((uint64_t) 1L << 26);
760     carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
761     h7 += carry6;
762     h6 -= carry6 * ((uint64_t) 1L << 26);
763 
764     carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
765     h4 += carry3;
766     h3 -= carry3 * ((uint64_t) 1L << 25);
767     carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
768     h8 += carry7;
769     h7 -= carry7 * ((uint64_t) 1L << 25);
770 
771     carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
772     h5 += carry4;
773     h4 -= carry4 * ((uint64_t) 1L << 26);
774     carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
775     h9 += carry8;
776     h8 -= carry8 * ((uint64_t) 1L << 26);
777 
778     carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
779     h0 += carry9 * 19;
780     h9 -= carry9 * ((uint64_t) 1L << 25);
781 
782     carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
783     h1 += carry0;
784     h0 -= carry0 * ((uint64_t) 1L << 26);
785 
786     h[0] = (int32_t) h0;
787     h[1] = (int32_t) h1;
788     h[2] = (int32_t) h2;
789     h[3] = (int32_t) h3;
790     h[4] = (int32_t) h4;
791     h[5] = (int32_t) h5;
792     h[6] = (int32_t) h6;
793     h[7] = (int32_t) h7;
794     h[8] = (int32_t) h8;
795     h[9] = (int32_t) h9;
796 }
797 
798 /*
799  h = 2 * f * f
800  Can overlap h with f.
801  *
802  Preconditions:
803  |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
804  *
805  Postconditions:
806  |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
807  */
808 
809 static void
810 fe25519_sq2(fe25519 h, const fe25519 f)
811 {
812     int32_t f0 = f[0];
813     int32_t f1 = f[1];
814     int32_t f2 = f[2];
815     int32_t f3 = f[3];
816     int32_t f4 = f[4];
817     int32_t f5 = f[5];
818     int32_t f6 = f[6];
819     int32_t f7 = f[7];
820     int32_t f8 = f[8];
821     int32_t f9 = f[9];
822 
823     int32_t f0_2  = 2 * f0;
824     int32_t f1_2  = 2 * f1;
825     int32_t f2_2  = 2 * f2;
826     int32_t f3_2  = 2 * f3;
827     int32_t f4_2  = 2 * f4;
828     int32_t f5_2  = 2 * f5;
829     int32_t f6_2  = 2 * f6;
830     int32_t f7_2  = 2 * f7;
831     int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
832     int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
833     int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
834     int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
835     int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
836 
837     int64_t f0f0    = f0 * (int64_t) f0;
838     int64_t f0f1_2  = f0_2 * (int64_t) f1;
839     int64_t f0f2_2  = f0_2 * (int64_t) f2;
840     int64_t f0f3_2  = f0_2 * (int64_t) f3;
841     int64_t f0f4_2  = f0_2 * (int64_t) f4;
842     int64_t f0f5_2  = f0_2 * (int64_t) f5;
843     int64_t f0f6_2  = f0_2 * (int64_t) f6;
844     int64_t f0f7_2  = f0_2 * (int64_t) f7;
845     int64_t f0f8_2  = f0_2 * (int64_t) f8;
846     int64_t f0f9_2  = f0_2 * (int64_t) f9;
847     int64_t f1f1_2  = f1_2 * (int64_t) f1;
848     int64_t f1f2_2  = f1_2 * (int64_t) f2;
849     int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
850     int64_t f1f4_2  = f1_2 * (int64_t) f4;
851     int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
852     int64_t f1f6_2  = f1_2 * (int64_t) f6;
853     int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
854     int64_t f1f8_2  = f1_2 * (int64_t) f8;
855     int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
856     int64_t f2f2    = f2 * (int64_t) f2;
857     int64_t f2f3_2  = f2_2 * (int64_t) f3;
858     int64_t f2f4_2  = f2_2 * (int64_t) f4;
859     int64_t f2f5_2  = f2_2 * (int64_t) f5;
860     int64_t f2f6_2  = f2_2 * (int64_t) f6;
861     int64_t f2f7_2  = f2_2 * (int64_t) f7;
862     int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
863     int64_t f2f9_38 = f2 * (int64_t) f9_38;
864     int64_t f3f3_2  = f3_2 * (int64_t) f3;
865     int64_t f3f4_2  = f3_2 * (int64_t) f4;
866     int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
867     int64_t f3f6_2  = f3_2 * (int64_t) f6;
868     int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
869     int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
870     int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
871     int64_t f4f4    = f4 * (int64_t) f4;
872     int64_t f4f5_2  = f4_2 * (int64_t) f5;
873     int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
874     int64_t f4f7_38 = f4 * (int64_t) f7_38;
875     int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
876     int64_t f4f9_38 = f4 * (int64_t) f9_38;
877     int64_t f5f5_38 = f5 * (int64_t) f5_38;
878     int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
879     int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
880     int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
881     int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
882     int64_t f6f6_19 = f6 * (int64_t) f6_19;
883     int64_t f6f7_38 = f6 * (int64_t) f7_38;
884     int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
885     int64_t f6f9_38 = f6 * (int64_t) f9_38;
886     int64_t f7f7_38 = f7 * (int64_t) f7_38;
887     int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
888     int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
889     int64_t f8f8_19 = f8 * (int64_t) f8_19;
890     int64_t f8f9_38 = f8 * (int64_t) f9_38;
891     int64_t f9f9_38 = f9 * (int64_t) f9_38;
892 
893     int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
894     int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
895     int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
896     int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
897     int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
898     int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
899     int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
900     int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
901     int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
902     int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
903 
904     int64_t carry0;
905     int64_t carry1;
906     int64_t carry2;
907     int64_t carry3;
908     int64_t carry4;
909     int64_t carry5;
910     int64_t carry6;
911     int64_t carry7;
912     int64_t carry8;
913     int64_t carry9;
914 
915     h0 += h0;
916     h1 += h1;
917     h2 += h2;
918     h3 += h3;
919     h4 += h4;
920     h5 += h5;
921     h6 += h6;
922     h7 += h7;
923     h8 += h8;
924     h9 += h9;
925 
926     carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
927     h1 += carry0;
928     h0 -= carry0 * ((uint64_t) 1L << 26);
929     carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
930     h5 += carry4;
931     h4 -= carry4 * ((uint64_t) 1L << 26);
932 
933     carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
934     h2 += carry1;
935     h1 -= carry1 * ((uint64_t) 1L << 25);
936     carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
937     h6 += carry5;
938     h5 -= carry5 * ((uint64_t) 1L << 25);
939 
940     carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
941     h3 += carry2;
942     h2 -= carry2 * ((uint64_t) 1L << 26);
943     carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
944     h7 += carry6;
945     h6 -= carry6 * ((uint64_t) 1L << 26);
946 
947     carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
948     h4 += carry3;
949     h3 -= carry3 * ((uint64_t) 1L << 25);
950     carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
951     h8 += carry7;
952     h7 -= carry7 * ((uint64_t) 1L << 25);
953 
954     carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
955     h5 += carry4;
956     h4 -= carry4 * ((uint64_t) 1L << 26);
957     carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
958     h9 += carry8;
959     h8 -= carry8 * ((uint64_t) 1L << 26);
960 
961     carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
962     h0 += carry9 * 19;
963     h9 -= carry9 * ((uint64_t) 1L << 25);
964 
965     carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
966     h1 += carry0;
967     h0 -= carry0 * ((uint64_t) 1L << 26);
968 
969     h[0] = (int32_t) h0;
970     h[1] = (int32_t) h1;
971     h[2] = (int32_t) h2;
972     h[3] = (int32_t) h3;
973     h[4] = (int32_t) h4;
974     h[5] = (int32_t) h5;
975     h[6] = (int32_t) h6;
976     h[7] = (int32_t) h7;
977     h[8] = (int32_t) h8;
978     h[9] = (int32_t) h9;
979 }
980 
981 static void
982 fe25519_scalar_product(fe25519 h, const fe25519 f, uint32_t n)
983 {
984     int64_t sn = (int64_t) n;
985     int32_t f0 = f[0];
986     int32_t f1 = f[1];
987     int32_t f2 = f[2];
988     int32_t f3 = f[3];
989     int32_t f4 = f[4];
990     int32_t f5 = f[5];
991     int32_t f6 = f[6];
992     int32_t f7 = f[7];
993     int32_t f8 = f[8];
994     int32_t f9 = f[9];
995     int64_t h0 = f0 * sn;
996     int64_t h1 = f1 * sn;
997     int64_t h2 = f2 * sn;
998     int64_t h3 = f3 * sn;
999     int64_t h4 = f4 * sn;
1000     int64_t h5 = f5 * sn;
1001     int64_t h6 = f6 * sn;
1002     int64_t h7 = f7 * sn;
1003     int64_t h8 = f8 * sn;
1004     int64_t h9 = f9 * sn;
1005     int64_t carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7,
1006             carry8, carry9;
1007 
1008     carry9 = (h9 + ((int64_t) 1 << 24)) >> 25;
1009     h0 += carry9 * 19;
1010     h9 -= carry9 * ((int64_t) 1 << 25);
1011     carry1 = (h1 + ((int64_t) 1 << 24)) >> 25;
1012     h2 += carry1;
1013     h1 -= carry1 * ((int64_t) 1 << 25);
1014     carry3 = (h3 + ((int64_t) 1 << 24)) >> 25;
1015     h4 += carry3;
1016     h3 -= carry3 * ((int64_t) 1 << 25);
1017     carry5 = (h5 + ((int64_t) 1 << 24)) >> 25;
1018     h6 += carry5;
1019     h5 -= carry5 * ((int64_t) 1 << 25);
1020     carry7 = (h7 + ((int64_t) 1 << 24)) >> 25;
1021     h8 += carry7;
1022     h7 -= carry7 * ((int64_t) 1 << 25);
1023 
1024     carry0 = (h0 + ((int64_t) 1 << 25)) >> 26;
1025     h1 += carry0;
1026     h0 -= carry0 * ((int64_t) 1 << 26);
1027     carry2 = (h2 + ((int64_t) 1 << 25)) >> 26;
1028     h3 += carry2;
1029     h2 -= carry2 * ((int64_t) 1 << 26);
1030     carry4 = (h4 + ((int64_t) 1 << 25)) >> 26;
1031     h5 += carry4;
1032     h4 -= carry4 * ((int64_t) 1 << 26);
1033     carry6 = (h6 + ((int64_t) 1 << 25)) >> 26;
1034     h7 += carry6;
1035     h6 -= carry6 * ((int64_t) 1 << 26);
1036     carry8 = (h8 + ((int64_t) 1 << 25)) >> 26;
1037     h9 += carry8;
1038     h8 -= carry8 * ((int64_t) 1 << 26);
1039 
1040     h[0] = (int32_t) h0;
1041     h[1] = (int32_t) h1;
1042     h[2] = (int32_t) h2;
1043     h[3] = (int32_t) h3;
1044     h[4] = (int32_t) h4;
1045     h[5] = (int32_t) h5;
1046     h[6] = (int32_t) h6;
1047     h[7] = (int32_t) h7;
1048     h[8] = (int32_t) h8;
1049     h[9] = (int32_t) h9;
1050 }
1051