Home | History | Annotate | Line # | Download | only in private 
      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