text: /*
  * Ed25519 field element
  * (C) 2017 Ribose Inc
  *
  * Based on the public domain code from SUPERCOP ref10 by
  * Peter Schwabe, Daniel J. Bernstein, Niels Duif, Tanja Lange, Bo-Yin Yang
  *
  * Botan is released under the Simplified BSD License (see license.txt)
  */
  
  #include <botan/internal/ed25519_fe.h>
  #include <botan/internal/ed25519_internal.h>
  
  namespace Botan {
  
  //static
  FE_25519 FE_25519::invert(const FE_25519& z)
     {
     fe t0;
     fe t1;
     fe t2;
     fe t3;
  
     fe_sq(t0, z);
     fe_sq_iter(t1, t0, 2);
     fe_mul(t1, z, t1);
     fe_mul(t0, t0, t1);
     fe_sq(t2, t0);
     fe_mul(t1, t1, t2);
     fe_sq_iter(t2, t1, 5);
     fe_mul(t1, t2, t1);
     fe_sq_iter(t2, t1, 10);
     fe_mul(t2, t2, t1);
     fe_sq_iter(t3, t2, 20);
     fe_mul(t2, t3, t2);
     fe_sq_iter(t2, t2, 10);
     fe_mul(t1, t2, t1);
     fe_sq_iter(t2, t1, 50);
     fe_mul(t2, t2, t1);
     fe_sq_iter(t3, t2, 100);
     fe_mul(t2, t3, t2);
     fe_sq_iter(t2, t2, 50);
     fe_mul(t1, t2, t1);
     fe_sq_iter(t1, t1, 5);
  
     fe_mul(t0, t1, t0);
     return t0;
     }
  
  FE_25519 FE_25519::pow_22523(const fe& z)
     {
     fe t0;
     fe t1;
     fe t2;
  
     fe_sq(t0, z);
     fe_sq_iter(t1, t0, 2);
     fe_mul(t1, z, t1);
     fe_mul(t0, t0, t1);
     fe_sq(t0, t0);
     fe_mul(t0, t1, t0);
     fe_sq_iter(t1, t0, 5);
     fe_mul(t0, t1, t0);
     fe_sq_iter(t1, t0, 10);
     fe_mul(t1, t1, t0);
     fe_sq_iter(t2, t1, 20);
     fe_mul(t1, t2, t1);
     fe_sq_iter(t1, t1, 10);
     fe_mul(t0, t1, t0);
     fe_sq_iter(t1, t0, 50);
     fe_mul(t1, t1, t0);
     fe_sq_iter(t2, t1, 100);
     fe_mul(t1, t2, t1);
     fe_sq_iter(t1, t1, 50);
     fe_mul(t0, t1, t0);
     fe_sq_iter(t0, t0, 2);
  
     fe_mul(t0, t0, z);
     return t0;
     }
  
  /*
  h = f * g
  Can overlap h with f or g.
  
  Preconditions:
  |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
  |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
  
  Postconditions:
  |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
  */
  
  /*
  Notes on implementation strategy:
  
  Using schoolbook multiplication.
  Karatsuba would save a little in some cost models.
  
  Most multiplications by 2 and 19 are 32-bit precomputations;
  cheaper than 64-bit postcomputations.
  
  There is one remaining multiplication by 19 in the carry chain;
  one *19 precomputation can be merged into this,
  but the resulting data flow is considerably less clean.
  
  There are 12 carries below.
  10 of them are 2-way parallelizable and vectorizable.
  Can get away with 11 carries, but then data flow is much deeper.
  
  With tighter constraints on inputs can squeeze carries into int32.
  */
  
  //static
  FE_25519 FE_25519::mul(const FE_25519& f, const FE_25519& g)
     {
     const int32_t f0 = f[0];
     const int32_t f1 = f[1];
     const int32_t f2 = f[2];
     const int32_t f3 = f[3];
     const int32_t f4 = f[4];
     const int32_t f5 = f[5];
     const int32_t f6 = f[6];
     const int32_t f7 = f[7];
     const int32_t f8 = f[8];
     const int32_t f9 = f[9];
  
     const int32_t g0 = g[0];
     const int32_t g1 = g[1];
     const int32_t g2 = g[2];
     const int32_t g3 = g[3];
     const int32_t g4 = g[4];
     const int32_t g5 = g[5];
     const int32_t g6 = g[6];
     const int32_t g7 = g[7];
     const int32_t g8 = g[8];
     const int32_t g9 = g[9];
  
     const int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
     const int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
     const int32_t g3_19 = 19 * g3;
     const int32_t g4_19 = 19 * g4;
     const int32_t g5_19 = 19 * g5;
     const int32_t g6_19 = 19 * g6;
     const int32_t g7_19 = 19 * g7;
     const int32_t g8_19 = 19 * g8;
     const int32_t g9_19 = 19 * g9;
     const int32_t f1_2 = 2 * f1;
     const int32_t f3_2 = 2 * f3;
     const int32_t f5_2 = 2 * f5;
     const int32_t f7_2 = 2 * f7;
     const int32_t f9_2 = 2 * f9;
  
     const int64_t f0g0    = f0   * static_cast<int64_t>(g0);
     const int64_t f0g1    = f0   * static_cast<int64_t>(g1);
     const int64_t f0g2    = f0   * static_cast<int64_t>(g2);
     const int64_t f0g3    = f0   * static_cast<int64_t>(g3);
     const int64_t f0g4    = f0   * static_cast<int64_t>(g4);
     const int64_t f0g5    = f0   * static_cast<int64_t>(g5);
     const int64_t f0g6    = f0   * static_cast<int64_t>(g6);
     const int64_t f0g7    = f0   * static_cast<int64_t>(g7);
     const int64_t f0g8    = f0   * static_cast<int64_t>(g8);
     const int64_t f0g9    = f0   * static_cast<int64_t>(g9);
     const int64_t f1g0    = f1   * static_cast<int64_t>(g0);
     const int64_t f1g1_2  = f1_2 * static_cast<int64_t>(g1);
     const int64_t f1g2    = f1   * static_cast<int64_t>(g2);
     const int64_t f1g3_2  = f1_2 * static_cast<int64_t>(g3);
     const int64_t f1g4    = f1   * static_cast<int64_t>(g4);
     const int64_t f1g5_2  = f1_2 * static_cast<int64_t>(g5);
     const int64_t f1g6    = f1   * static_cast<int64_t>(g6);
     const int64_t f1g7_2  = f1_2 * static_cast<int64_t>(g7);
     const int64_t f1g8    = f1   * static_cast<int64_t>(g8);
     const int64_t f1g9_38 = f1_2 * static_cast<int64_t>(g9_19);
     const int64_t f2g0    = f2   * static_cast<int64_t>(g0);
     const int64_t f2g1    = f2   * static_cast<int64_t>(g1);
     const int64_t f2g2    = f2   * static_cast<int64_t>(g2);
     const int64_t f2g3    = f2   * static_cast<int64_t>(g3);
     const int64_t f2g4    = f2   * static_cast<int64_t>(g4);
     const int64_t f2g5    = f2   * static_cast<int64_t>(g5);
     const int64_t f2g6    = f2   * static_cast<int64_t>(g6);
     const int64_t f2g7    = f2   * static_cast<int64_t>(g7);
     const int64_t f2g8_19 = f2   * static_cast<int64_t>(g8_19);
     const int64_t f2g9_19 = f2   * static_cast<int64_t>(g9_19);
     const int64_t f3g0    = f3   * static_cast<int64_t>(g0);
     const int64_t f3g1_2  = f3_2 * static_cast<int64_t>(g1);
     const int64_t f3g2    = f3   * static_cast<int64_t>(g2);
     const int64_t f3g3_2  = f3_2 * static_cast<int64_t>(g3);
     const int64_t f3g4    = f3   * static_cast<int64_t>(g4);
     const int64_t f3g5_2  = f3_2 * static_cast<int64_t>(g5);
     const int64_t f3g6    = f3   * static_cast<int64_t>(g6);
     const int64_t f3g7_38 = f3_2 * static_cast<int64_t>(g7_19);
     const int64_t f3g8_19 = f3   * static_cast<int64_t>(g8_19);
     const int64_t f3g9_38 = f3_2 * static_cast<int64_t>(g9_19);
     const int64_t f4g0    = f4   * static_cast<int64_t>(g0);
     const int64_t f4g1    = f4   * static_cast<int64_t>(g1);
     const int64_t f4g2    = f4   * static_cast<int64_t>(g2);
     const int64_t f4g3    = f4   * static_cast<int64_t>(g3);
     const int64_t f4g4    = f4   * static_cast<int64_t>(g4);
     const int64_t f4g5    = f4   * static_cast<int64_t>(g5);
     const int64_t f4g6_19 = f4   * static_cast<int64_t>(g6_19);
     const int64_t f4g7_19 = f4   * static_cast<int64_t>(g7_19);
     const int64_t f4g8_19 = f4   * static_cast<int64_t>(g8_19);
     const int64_t f4g9_19 = f4   * static_cast<int64_t>(g9_19);
     const int64_t f5g0    = f5   * static_cast<int64_t>(g0);
     const int64_t f5g1_2  = f5_2 * static_cast<int64_t>(g1);
     const int64_t f5g2    = f5   * static_cast<int64_t>(g2);
     const int64_t f5g3_2  = f5_2 * static_cast<int64_t>(g3);
     const int64_t f5g4    = f5   * static_cast<int64_t>(g4);
     const int64_t f5g5_38 = f5_2 * static_cast<int64_t>(g5_19);
     const int64_t f5g6_19 = f5   * static_cast<int64_t>(g6_19);
     const int64_t f5g7_38 = f5_2 * static_cast<int64_t>(g7_19);
     const int64_t f5g8_19 = f5   * static_cast<int64_t>(g8_19);
     const int64_t f5g9_38 = f5_2 * static_cast<int64_t>(g9_19);
     const int64_t f6g0    = f6   * static_cast<int64_t>(g0);
     const int64_t f6g1    = f6   * static_cast<int64_t>(g1);
     const int64_t f6g2    = f6   * static_cast<int64_t>(g2);
     const int64_t f6g3    = f6   * static_cast<int64_t>(g3);
     const int64_t f6g4_19 = f6   * static_cast<int64_t>(g4_19);
     const int64_t f6g5_19 = f6   * static_cast<int64_t>(g5_19);
     const int64_t f6g6_19 = f6   * static_cast<int64_t>(g6_19);
     const int64_t f6g7_19 = f6   * static_cast<int64_t>(g7_19);
     const int64_t f6g8_19 = f6   * static_cast<int64_t>(g8_19);
     const int64_t f6g9_19 = f6   * static_cast<int64_t>(g9_19);
     const int64_t f7g0    = f7   * static_cast<int64_t>(g0);
     const int64_t f7g1_2  = f7_2 * static_cast<int64_t>(g1);
     const int64_t f7g2    = f7   * static_cast<int64_t>(g2);
     const int64_t f7g3_38 = f7_2 * static_cast<int64_t>(g3_19);
     const int64_t f7g4_19 = f7   * static_cast<int64_t>(g4_19);
     const int64_t f7g5_38 = f7_2 * static_cast<int64_t>(g5_19);
     const int64_t f7g6_19 = f7   * static_cast<int64_t>(g6_19);
     const int64_t f7g7_38 = f7_2 * static_cast<int64_t>(g7_19);
     const int64_t f7g8_19 = f7   * static_cast<int64_t>(g8_19);
     const int64_t f7g9_38 = f7_2 * static_cast<int64_t>(g9_19);
     const int64_t f8g0    = f8   * static_cast<int64_t>(g0);
     const int64_t f8g1    = f8   * static_cast<int64_t>(g1);
     const int64_t f8g2_19 = f8   * static_cast<int64_t>(g2_19);
     const int64_t f8g3_19 = f8   * static_cast<int64_t>(g3_19);
     const int64_t f8g4_19 = f8   * static_cast<int64_t>(g4_19);
     const int64_t f8g5_19 = f8   * static_cast<int64_t>(g5_19);
     const int64_t f8g6_19 = f8   * static_cast<int64_t>(g6_19);
     const int64_t f8g7_19 = f8   * static_cast<int64_t>(g7_19);
     const int64_t f8g8_19 = f8   * static_cast<int64_t>(g8_19);
     const int64_t f8g9_19 = f8   * static_cast<int64_t>(g9_19);
     const int64_t f9g0    = f9   * static_cast<int64_t>(g0);
     const int64_t f9g1_38 = f9_2 * static_cast<int64_t>(g1_19);
     const int64_t f9g2_19 = f9   * static_cast<int64_t>(g2_19);
     const int64_t f9g3_38 = f9_2 * static_cast<int64_t>(g3_19);
     const int64_t f9g4_19 = f9   * static_cast<int64_t>(g4_19);
     const int64_t f9g5_38 = f9_2 * static_cast<int64_t>(g5_19);
     const int64_t f9g6_19 = f9   * static_cast<int64_t>(g6_19);
     const int64_t f9g7_38 = f9_2 * static_cast<int64_t>(g7_19);
     const int64_t f9g8_19 = f9   * static_cast<int64_t>(g8_19);
     const int64_t f9g9_38 = f9_2 * static_cast<int64_t>(g9_19);
  
     int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
     int64_t h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
     int64_t h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
     int64_t h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
     int64_t h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
     int64_t h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
     int64_t h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
     int64_t h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
     int64_t h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
     int64_t h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
  
     /*
     |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
     i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
     |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
     i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
     */
     carry<26>(h0, h1);
     carry<26>(h4, h5);
  
     /* |h0| <= 2^25 */
     /* |h4| <= 2^25 */
     /* |h1| <= 1.71*2^59 */
     /* |h5| <= 1.71*2^59 */
  
     carry<25>(h1, h2);
     carry<25>(h5, h6);
  
     /* |h1| <= 2^24; from now on fits into int32 */
     /* |h5| <= 2^24; from now on fits into int32 */
     /* |h2| <= 1.41*2^60 */
     /* |h6| <= 1.41*2^60 */
  
     carry<26>(h2, h3);
     carry<26>(h6, h7);
     /* |h2| <= 2^25; from now on fits into int32 unchanged */
     /* |h6| <= 2^25; from now on fits into int32 unchanged */
     /* |h3| <= 1.71*2^59 */
     /* |h7| <= 1.71*2^59 */
  
     carry<25>(h3, h4);
     carry<25>(h7, h8);
     /* |h3| <= 2^24; from now on fits into int32 unchanged */
     /* |h7| <= 2^24; from now on fits into int32 unchanged */
     /* |h4| <= 1.72*2^34 */
     /* |h8| <= 1.41*2^60 */
  
     carry<26>(h4, h5);
     carry<26>(h8, h9);
     /* |h4| <= 2^25; from now on fits into int32 unchanged */
     /* |h8| <= 2^25; from now on fits into int32 unchanged */
     /* |h5| <= 1.01*2^24 */
     /* |h9| <= 1.71*2^59 */
  
     carry<25, 19>(h9, h0);
  
     /* |h9| <= 2^24; from now on fits into int32 unchanged */
     /* |h0| <= 1.1*2^39 */
  
     carry<26>(h0, h1);
     /* |h0| <= 2^25; from now on fits into int32 unchanged */
     /* |h1| <= 1.01*2^24 */
  
     return FE_25519(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9);
     }
  
  /*
  h = f * f
  Can overlap h with f.
  
  Preconditions:
  |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
  
  Postconditions:
  |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
  */
  
  /*
  See fe_mul.c for discussion of implementation strategy.
  */
  
  //static
  FE_25519 FE_25519::sqr_iter(const FE_25519& f, size_t iter)
     {
     int32_t f0 = f[0];
     int32_t f1 = f[1];
     int32_t f2 = f[2];
     int32_t f3 = f[3];
     int32_t f4 = f[4];
     int32_t f5 = f[5];
     int32_t f6 = f[6];
     int32_t f7 = f[7];
     int32_t f8 = f[8];
     int32_t f9 = f[9];
  
     for(size_t i = 0; i != iter; ++i)
        {
        const int32_t f0_2 = 2 * f0;
        const int32_t f1_2 = 2 * f1;
        const int32_t f2_2 = 2 * f2;
        const int32_t f3_2 = 2 * f3;
        const int32_t f4_2 = 2 * f4;
        const int32_t f5_2 = 2 * f5;
        const int32_t f6_2 = 2 * f6;
        const int32_t f7_2 = 2 * f7;
        const int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
        const int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
        const int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
        const int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
        const int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
  
        const int64_t f0f0    = f0   * static_cast<int64_t>(f0);
        const int64_t f0f1_2  = f0_2 * static_cast<int64_t>(f1);
        const int64_t f0f2_2  = f0_2 * static_cast<int64_t>(f2);
        const int64_t f0f3_2  = f0_2 * static_cast<int64_t>(f3);
        const int64_t f0f4_2  = f0_2 * static_cast<int64_t>(f4);
        const int64_t f0f5_2  = f0_2 * static_cast<int64_t>(f5);
        const int64_t f0f6_2  = f0_2 * static_cast<int64_t>(f6);
        const int64_t f0f7_2  = f0_2 * static_cast<int64_t>(f7);
        const int64_t f0f8_2  = f0_2 * static_cast<int64_t>(f8);
        const int64_t f0f9_2  = f0_2 * static_cast<int64_t>(f9);
        const int64_t f1f1_2  = f1_2 * static_cast<int64_t>(f1);
        const int64_t f1f2_2  = f1_2 * static_cast<int64_t>(f2);
        const int64_t f1f3_4  = f1_2 * static_cast<int64_t>(f3_2);
        const int64_t f1f4_2  = f1_2 * static_cast<int64_t>(f4);
        const int64_t f1f5_4  = f1_2 * static_cast<int64_t>(f5_2);
        const int64_t f1f6_2  = f1_2 * static_cast<int64_t>(f6);
        const int64_t f1f7_4  = f1_2 * static_cast<int64_t>(f7_2);
        const int64_t f1f8_2  = f1_2 * static_cast<int64_t>(f8);
        const int64_t f1f9_76 = f1_2 * static_cast<int64_t>(f9_38);
        const int64_t f2f2    = f2   * static_cast<int64_t>(f2);
        const int64_t f2f3_2  = f2_2 * static_cast<int64_t>(f3);
        const int64_t f2f4_2  = f2_2 * static_cast<int64_t>(f4);
        const int64_t f2f5_2  = f2_2 * static_cast<int64_t>(f5);
        const int64_t f2f6_2  = f2_2 * static_cast<int64_t>(f6);
        const int64_t f2f7_2  = f2_2 * static_cast<int64_t>(f7);
        const int64_t f2f8_38 = f2_2 * static_cast<int64_t>(f8_19);
        const int64_t f2f9_38 = f2   * static_cast<int64_t>(f9_38);
        const int64_t f3f3_2  = f3_2 * static_cast<int64_t>(f3);
        const int64_t f3f4_2  = f3_2 * static_cast<int64_t>(f4);
        const int64_t f3f5_4  = f3_2 * static_cast<int64_t>(f5_2);
        const int64_t f3f6_2  = f3_2 * static_cast<int64_t>(f6);
        const int64_t f3f7_76 = f3_2 * static_cast<int64_t>(f7_38);
        const int64_t f3f8_38 = f3_2 * static_cast<int64_t>(f8_19);
        const int64_t f3f9_76 = f3_2 * static_cast<int64_t>(f9_38);
        const int64_t f4f4    = f4   * static_cast<int64_t>(f4);
        const int64_t f4f5_2  = f4_2 * static_cast<int64_t>(f5);
        const int64_t f4f6_38 = f4_2 * static_cast<int64_t>(f6_19);
        const int64_t f4f7_38 = f4   * static_cast<int64_t>(f7_38);
        const int64_t f4f8_38 = f4_2 * static_cast<int64_t>(f8_19);
        const int64_t f4f9_38 = f4   * static_cast<int64_t>(f9_38);
        const int64_t f5f5_38 = f5   * static_cast<int64_t>(f5_38);
        const int64_t f5f6_38 = f5_2 * static_cast<int64_t>(f6_19);
        const int64_t f5f7_76 = f5_2 * static_cast<int64_t>(f7_38);
        const int64_t f5f8_38 = f5_2 * static_cast<int64_t>(f8_19);
        const int64_t f5f9_76 = f5_2 * static_cast<int64_t>(f9_38);
        const int64_t f6f6_19 = f6   * static_cast<int64_t>(f6_19);
        const int64_t f6f7_38 = f6   * static_cast<int64_t>(f7_38);
        const int64_t f6f8_38 = f6_2 * static_cast<int64_t>(f8_19);
        const int64_t f6f9_38 = f6   * static_cast<int64_t>(f9_38);
        const int64_t f7f7_38 = f7   * static_cast<int64_t>(f7_38);
        const int64_t f7f8_38 = f7_2 * static_cast<int64_t>(f8_19);
        const int64_t f7f9_76 = f7_2 * static_cast<int64_t>(f9_38);
        const int64_t f8f8_19 = f8   * static_cast<int64_t>(f8_19);
        const int64_t f8f9_38 = f8   * static_cast<int64_t>(f9_38);
        const int64_t f9f9_38 = f9   * static_cast<int64_t>(f9_38);
  
        int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
        int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
        int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
        int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
        int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
        int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
        int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
        int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
        int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
        int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
  
        carry<26>(h0, h1);
        carry<26>(h4, h5);
        carry<25>(h1, h2);
        carry<25>(h5, h6);
        carry<26>(h2, h3);
        carry<26>(h6, h7);
  
        carry<25>(h3, h4);
        carry<25>(h7, h8);
  
        carry<26>(h4, h5);
        carry<26>(h8, h9);
        carry<25,19>(h9, h0);
        carry<26>(h0, h1);
  
        f0 = static_cast<int32_t>(h0);
        f1 = static_cast<int32_t>(h1);
        f2 = static_cast<int32_t>(h2);
        f3 = static_cast<int32_t>(h3);
        f4 = static_cast<int32_t>(h4);
        f5 = static_cast<int32_t>(h5);
        f6 = static_cast<int32_t>(h6);
        f7 = static_cast<int32_t>(h7);
        f8 = static_cast<int32_t>(h8);
        f9 = static_cast<int32_t>(h9);
        }
  
     return FE_25519(f0, f1, f2, f3, f4, f5, f6, f7, f8, f9);
     }
  
  /*
  h = 2 * f * f
  Can overlap h with f.
  
  Preconditions:
  |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
  
  Postconditions:
  |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
  */
  
  /*
  See fe_mul.c for discussion of implementation strategy.
  */
  
  //static
  FE_25519 FE_25519::sqr2(const FE_25519& f)
     {
     const int32_t f0 = f[0];
     const int32_t f1 = f[1];
     const int32_t f2 = f[2];
     const int32_t f3 = f[3];
     const int32_t f4 = f[4];
     const int32_t f5 = f[5];
     const int32_t f6 = f[6];
     const int32_t f7 = f[7];
     const int32_t f8 = f[8];
     const int32_t f9 = f[9];
     const int32_t f0_2 = 2 * f0;
     const int32_t f1_2 = 2 * f1;
     const int32_t f2_2 = 2 * f2;
     const int32_t f3_2 = 2 * f3;
     const int32_t f4_2 = 2 * f4;
     const int32_t f5_2 = 2 * f5;
     const int32_t f6_2 = 2 * f6;
     const int32_t f7_2 = 2 * f7;
     const int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
     const int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
     const int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
     const int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
     const int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
     const int64_t f0f0    = f0   * static_cast<int64_t>(f0);
     const int64_t f0f1_2  = f0_2 * static_cast<int64_t>(f1);
     const int64_t f0f2_2  = f0_2 * static_cast<int64_t>(f2);
     const int64_t f0f3_2  = f0_2 * static_cast<int64_t>(f3);
     const int64_t f0f4_2  = f0_2 * static_cast<int64_t>(f4);
     const int64_t f0f5_2  = f0_2 * static_cast<int64_t>(f5);
     const int64_t f0f6_2  = f0_2 * static_cast<int64_t>(f6);
     const int64_t f0f7_2  = f0_2 * static_cast<int64_t>(f7);
     const int64_t f0f8_2  = f0_2 * static_cast<int64_t>(f8);
     const int64_t f0f9_2  = f0_2 * static_cast<int64_t>(f9);
     const int64_t f1f1_2  = f1_2 * static_cast<int64_t>(f1);
     const int64_t f1f2_2  = f1_2 * static_cast<int64_t>(f2);
     const int64_t f1f3_4  = f1_2 * static_cast<int64_t>(f3_2);
     const int64_t f1f4_2  = f1_2 * static_cast<int64_t>(f4);
     const int64_t f1f5_4  = f1_2 * static_cast<int64_t>(f5_2);
     const int64_t f1f6_2  = f1_2 * static_cast<int64_t>(f6);
     const int64_t f1f7_4  = f1_2 * static_cast<int64_t>(f7_2);
     const int64_t f1f8_2  = f1_2 * static_cast<int64_t>(f8);
     const int64_t f1f9_76 = f1_2 * static_cast<int64_t>(f9_38);
     const int64_t f2f2    = f2   * static_cast<int64_t>(f2);
     const int64_t f2f3_2  = f2_2 * static_cast<int64_t>(f3);
     const int64_t f2f4_2  = f2_2 * static_cast<int64_t>(f4);
     const int64_t f2f5_2  = f2_2 * static_cast<int64_t>(f5);
     const int64_t f2f6_2  = f2_2 * static_cast<int64_t>(f6);
     const int64_t f2f7_2  = f2_2 * static_cast<int64_t>(f7);
     const int64_t f2f8_38 = f2_2 * static_cast<int64_t>(f8_19);
     const int64_t f2f9_38 = f2   * static_cast<int64_t>(f9_38);
     const int64_t f3f3_2  = f3_2 * static_cast<int64_t>(f3);
     const int64_t f3f4_2  = f3_2 * static_cast<int64_t>(f4);
     const int64_t f3f5_4  = f3_2 * static_cast<int64_t>(f5_2);
     const int64_t f3f6_2  = f3_2 * static_cast<int64_t>(f6);
     const int64_t f3f7_76 = f3_2 * static_cast<int64_t>(f7_38);
     const int64_t f3f8_38 = f3_2 * static_cast<int64_t>(f8_19);
     const int64_t f3f9_76 = f3_2 * static_cast<int64_t>(f9_38);
     const int64_t f4f4    = f4   * static_cast<int64_t>(f4);
     const int64_t f4f5_2  = f4_2 * static_cast<int64_t>(f5);
     const int64_t f4f6_38 = f4_2 * static_cast<int64_t>(f6_19);
     const int64_t f4f7_38 = f4   * static_cast<int64_t>(f7_38);
     const int64_t f4f8_38 = f4_2 * static_cast<int64_t>(f8_19);
     const int64_t f4f9_38 = f4   * static_cast<int64_t>(f9_38);
     const int64_t f5f5_38 = f5   * static_cast<int64_t>(f5_38);
     const int64_t f5f6_38 = f5_2 * static_cast<int64_t>(f6_19);
     const int64_t f5f7_76 = f5_2 * static_cast<int64_t>(f7_38);
     const int64_t f5f8_38 = f5_2 * static_cast<int64_t>(f8_19);
     const int64_t f5f9_76 = f5_2 * static_cast<int64_t>(f9_38);
     const int64_t f6f6_19 = f6   * static_cast<int64_t>(f6_19);
     const int64_t f6f7_38 = f6   * static_cast<int64_t>(f7_38);
     const int64_t f6f8_38 = f6_2 * static_cast<int64_t>(f8_19);
     const int64_t f6f9_38 = f6   * static_cast<int64_t>(f9_38);
     const int64_t f7f7_38 = f7   * static_cast<int64_t>(f7_38);
     const int64_t f7f8_38 = f7_2 * static_cast<int64_t>(f8_19);
     const int64_t f7f9_76 = f7_2 * static_cast<int64_t>(f9_38);
     const int64_t f8f8_19 = f8   * static_cast<int64_t>(f8_19);
     const int64_t f8f9_38 = f8   * static_cast<int64_t>(f9_38);
     const int64_t f9f9_38 = f9   * static_cast<int64_t>(f9_38);
  
     int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
     int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
     int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
     int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
     int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
     int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
     int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
     int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
     int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
     int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
  
     h0 += h0;
     h1 += h1;
     h2 += h2;
     h3 += h3;
     h4 += h4;
     h5 += h5;
     h6 += h6;
     h7 += h7;
     h8 += h8;
     h9 += h9;
  
     carry<26>(h0, h1);
     carry<26>(h4, h5);
  
     carry<25>(h1, h2);
     carry<25>(h5, h6);
  
     carry<26>(h2, h3);
     carry<26>(h6, h7);
  
     carry<25>(h3, h4);
     carry<25>(h7, h8);
     carry<26>(h4, h5);
     carry<26>(h8, h9);
     carry<25,19>(h9, h0);
     carry<26>(h0, h1);
  
     return FE_25519(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9);
     }
  
  /*
  Ignores top bit of h.
  */
  
  void FE_25519::from_bytes(const uint8_t s[32])
     {
     int64_t h0 = load_4(s);
     int64_t h1 = load_3(s + 4) << 6;
     int64_t h2 = load_3(s + 7) << 5;
     int64_t h3 = load_3(s + 10) << 3;
     int64_t h4 = load_3(s + 13) << 2;
     int64_t h5 = load_4(s + 16);
     int64_t h6 = load_3(s + 20) << 7;
     int64_t h7 = load_3(s + 23) << 5;
     int64_t h8 = load_3(s + 26) << 4;
     int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
  
     carry<25,19>(h9, h0);
     carry<25>(h1, h2);
     carry<25>(h3, h4);
     carry<25>(h5, h6);
     carry<25>(h7, h8);
  
     carry<26>(h0, h1);
     carry<26>(h2, h3);
     carry<26>(h4, h5);
     carry<26>(h6, h7);
     carry<26>(h8, h9);
  
     m_fe[0] = static_cast<int32_t>(h0);
     m_fe[1] = static_cast<int32_t>(h1);
     m_fe[2] = static_cast<int32_t>(h2);
     m_fe[3] = static_cast<int32_t>(h3);
     m_fe[4] = static_cast<int32_t>(h4);
     m_fe[5] = static_cast<int32_t>(h5);
     m_fe[6] = static_cast<int32_t>(h6);
     m_fe[7] = static_cast<int32_t>(h7);
     m_fe[8] = static_cast<int32_t>(h8);
     m_fe[9] = static_cast<int32_t>(h9);
     }
  
  /*
  Preconditions:
  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
  
  Write p=2^255-19; q=floor(h/p).
  Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
  
  Proof:
  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
  
  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
  Then 0<y<1.
  
  Write r=h-pq.
  Have 0<=r<=p-1=2^255-20.
  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
  
  Write x=r+19(2^-255)r+y.
  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
  
  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
  */
  
  void FE_25519::to_bytes(uint8_t s[32]) const
     {
     const int64_t X25 = (1 << 25);
  
     int32_t h0 = m_fe[0];
     int32_t h1 = m_fe[1];
     int32_t h2 = m_fe[2];
     int32_t h3 = m_fe[3];
     int32_t h4 = m_fe[4];
     int32_t h5 = m_fe[5];
     int32_t h6 = m_fe[6];
     int32_t h7 = m_fe[7];
     int32_t h8 = m_fe[8];
     int32_t h9 = m_fe[9];
     int32_t q;
  
     q = (19 * h9 + ((static_cast<int32_t>(1) << 24))) >> 25;
     q = (h0 + q) >> 26;
     q = (h1 + q) >> 25;
     q = (h2 + q) >> 26;
     q = (h3 + q) >> 25;
     q = (h4 + q) >> 26;
     q = (h5 + q) >> 25;
     q = (h6 + q) >> 26;
     q = (h7 + q) >> 25;
     q = (h8 + q) >> 26;
     q = (h9 + q) >> 25;
  
     /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
     h0 += 19 * q;
     /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
  
     carry0<26>(h0, h1);
     carry0<25>(h1, h2);
     carry0<26>(h2, h3);
     carry0<25>(h3, h4);
     carry0<26>(h4, h5);
     carry0<25>(h5, h6);
     carry0<26>(h6, h7);
     carry0<25>(h7, h8);
     carry0<26>(h8, h9);
  
     int32_t carry9 = h9 >> 25;
     h9 -= carry9 * X25;
     /* h10 = carry9 */
  
     /*
     Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
     Have h0+...+2^230 h9 between 0 and 2^255-1;
     evidently 2^255 h10-2^255 q = 0.
     Goal: Output h0+...+2^230 h9.
     */
  
     s[0] = h0 >> 0;
     s[1] = h0 >> 8;
     s[2] = h0 >> 16;
     s[3] = (h0 >> 24) | (h1 << 2);
     s[4] = h1 >> 6;
     s[5] = h1 >> 14;
     s[6] = (h1 >> 22) | (h2 << 3);
     s[7] = h2 >> 5;
     s[8] = h2 >> 13;
     s[9] = (h2 >> 21) | (h3 << 5);
     s[10] = h3 >> 3;
     s[11] = h3 >> 11;
     s[12] = (h3 >> 19) | (h4 << 6);
     s[13] = h4 >> 2;
     s[14] = h4 >> 10;
     s[15] = h4 >> 18;
     s[16] = h5 >> 0;
     s[17] = h5 >> 8;
     s[18] = h5 >> 16;
     s[19] = (h5 >> 24) | (h6 << 1);
     s[20] = h6 >> 7;
     s[21] = h6 >> 15;
     s[22] = (h6 >> 23) | (h7 << 3);
     s[23] = h7 >> 5;
     s[24] = h7 >> 13;
     s[25] = (h7 >> 21) | (h8 << 4);
     s[26] = h8 >> 4;
     s[27] = h8 >> 12;
     s[28] = (h8 >> 20) | (h9 << 6);
     s[29] = h9 >> 2;
     s[30] = h9 >> 10;
     s[31] = h9 >> 18;
     }
  
  }
  