/*
 * ISC License
 *
 * Copyright (c) 2013-2019
 * Frank Denis <j at pureftpd dot org>
 *
 * Permission to use, copy, modify, and/or distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

#include <roken.h>
#include <string.h>

/*
 h = 0
 */

static inline void
fe25519_0(fe25519 h)
{
    memset(&h[0], 0, 10 * sizeof h[0]);
}

/*
 h = 1
 */

static inline void
fe25519_1(fe25519 h)
{
    h[0] = 1;
    h[1] = 0;
    memset(&h[2], 0, 8 * sizeof h[0]);
}

/*
 h = f + g
 Can overlap h with f or g.
 *
 Preconditions:
 |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 *
 Postconditions:
 |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
 */

static inline void
fe25519_add(fe25519 h, const fe25519 f, const fe25519 g)
{
    int32_t h0 = f[0] + g[0];
    int32_t h1 = f[1] + g[1];
    int32_t h2 = f[2] + g[2];
    int32_t h3 = f[3] + g[3];
    int32_t h4 = f[4] + g[4];
    int32_t h5 = f[5] + g[5];
    int32_t h6 = f[6] + g[6];
    int32_t h7 = f[7] + g[7];
    int32_t h8 = f[8] + g[8];
    int32_t h9 = f[9] + g[9];

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

/*
 h = f - g
 Can overlap h with f or g.
 *
 Preconditions:
 |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 *
 Postconditions:
 |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
 */

static void
fe25519_sub(fe25519 h, const fe25519 f, const fe25519 g)
{
    int32_t h0 = f[0] - g[0];
    int32_t h1 = f[1] - g[1];
    int32_t h2 = f[2] - g[2];
    int32_t h3 = f[3] - g[3];
    int32_t h4 = f[4] - g[4];
    int32_t h5 = f[5] - g[5];
    int32_t h6 = f[6] - g[6];
    int32_t h7 = f[7] - g[7];
    int32_t h8 = f[8] - g[8];
    int32_t h9 = f[9] - g[9];

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

/*
 h = -f
 *
 Preconditions:
 |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 *
 Postconditions:
 |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 */

static inline void
fe25519_neg(fe25519 h, const fe25519 f)
{
    int32_t h0 = -f[0];
    int32_t h1 = -f[1];
    int32_t h2 = -f[2];
    int32_t h3 = -f[3];
    int32_t h4 = -f[4];
    int32_t h5 = -f[5];
    int32_t h6 = -f[6];
    int32_t h7 = -f[7];
    int32_t h8 = -f[8];
    int32_t h9 = -f[9];

    h[0] = h0;
    h[1] = h1;
    h[2] = h2;
    h[3] = h3;
    h[4] = h4;
    h[5] = h5;
    h[6] = h6;
    h[7] = h7;
    h[8] = h8;
    h[9] = h9;
}

/*
 Replace (f,g) with (g,g) if b == 1;
 replace (f,g) with (f,g) if b == 0.
 *
 Preconditions: b in {0,1}.
 */

static void
fe25519_cmov(fe25519 f, const fe25519 g, unsigned int b)
{
    const uint32_t mask = (uint32_t) (-(int32_t) b);

    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];

    int32_t x0 = f0 ^ g[0];
    int32_t x1 = f1 ^ g[1];
    int32_t x2 = f2 ^ g[2];
    int32_t x3 = f3 ^ g[3];
    int32_t x4 = f4 ^ g[4];
    int32_t x5 = f5 ^ g[5];
    int32_t x6 = f6 ^ g[6];
    int32_t x7 = f7 ^ g[7];
    int32_t x8 = f8 ^ g[8];
    int32_t x9 = f9 ^ g[9];

    x0 &= mask;
    x1 &= mask;
    x2 &= mask;
    x3 &= mask;
    x4 &= mask;
    x5 &= mask;
    x6 &= mask;
    x7 &= mask;
    x8 &= mask;
    x9 &= mask;

    f[0] = f0 ^ x0;
    f[1] = f1 ^ x1;
    f[2] = f2 ^ x2;
    f[3] = f3 ^ x3;
    f[4] = f4 ^ x4;
    f[5] = f5 ^ x5;
    f[6] = f6 ^ x6;
    f[7] = f7 ^ x7;
    f[8] = f8 ^ x8;
    f[9] = f9 ^ x9;
}

static void
fe25519_cswap(fe25519 f, fe25519 g, unsigned int b)
{
    const uint32_t mask = (uint32_t) (-(int64_t) b);

    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];

    int32_t g0 = g[0];
    int32_t g1 = g[1];
    int32_t g2 = g[2];
    int32_t g3 = g[3];
    int32_t g4 = g[4];
    int32_t g5 = g[5];
    int32_t g6 = g[6];
    int32_t g7 = g[7];
    int32_t g8 = g[8];
    int32_t g9 = g[9];

    int32_t x0 = f0 ^ g0;
    int32_t x1 = f1 ^ g1;
    int32_t x2 = f2 ^ g2;
    int32_t x3 = f3 ^ g3;
    int32_t x4 = f4 ^ g4;
    int32_t x5 = f5 ^ g5;
    int32_t x6 = f6 ^ g6;
    int32_t x7 = f7 ^ g7;
    int32_t x8 = f8 ^ g8;
    int32_t x9 = f9 ^ g9;

    x0 &= mask;
    x1 &= mask;
    x2 &= mask;
    x3 &= mask;
    x4 &= mask;
    x5 &= mask;
    x6 &= mask;
    x7 &= mask;
    x8 &= mask;
    x9 &= mask;

    f[0] = f0 ^ x0;
    f[1] = f1 ^ x1;
    f[2] = f2 ^ x2;
    f[3] = f3 ^ x3;
    f[4] = f4 ^ x4;
    f[5] = f5 ^ x5;
    f[6] = f6 ^ x6;
    f[7] = f7 ^ x7;
    f[8] = f8 ^ x8;
    f[9] = f9 ^ x9;

    g[0] = g0 ^ x0;
    g[1] = g1 ^ x1;
    g[2] = g2 ^ x2;
    g[3] = g3 ^ x3;
    g[4] = g4 ^ x4;
    g[5] = g5 ^ x5;
    g[6] = g6 ^ x6;
    g[7] = g7 ^ x7;
    g[8] = g8 ^ x8;
    g[9] = g9 ^ x9;
}

/*
 h = f
 */

static inline void
fe25519_copy(fe25519 h, const fe25519 f)
{
    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];

    h[0] = f0;
    h[1] = f1;
    h[2] = f2;
    h[3] = f3;
    h[4] = f4;
    h[5] = f5;
    h[6] = f6;
    h[7] = f7;
    h[8] = f8;
    h[9] = f9;
}

/*
 return 1 if f is in {1,3,5,...,q-2}
 return 0 if f is in {0,2,4,...,q-1}

 Preconditions:
 |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
 */

static inline int
fe25519_isnegative(const fe25519 f)
{
    unsigned char s[32];

    fe25519_tobytes(s, f);

    return s[0] & 1;
}

/*
 return 1 if f == 0
 return 0 if f != 0

 Preconditions:
 |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
 */

static inline int
fe25519_iszero(const fe25519 f)
{
    unsigned char s[32];

    fe25519_tobytes(s, f);

    return sodium_is_zero(s, 32);
}

/*
 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 void
fe25519_mul(fe25519 h, const fe25519 f, const fe25519 g)
{
    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];

    int32_t g0 = g[0];
    int32_t g1 = g[1];
    int32_t g2 = g[2];
    int32_t g3 = g[3];
    int32_t g4 = g[4];
    int32_t g5 = g[5];
    int32_t g6 = g[6];
    int32_t g7 = g[7];
    int32_t g8 = g[8];
    int32_t g9 = g[9];

    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
    int32_t g3_19 = 19 * g3;
    int32_t g4_19 = 19 * g4;
    int32_t g5_19 = 19 * g5;
    int32_t g6_19 = 19 * g6;
    int32_t g7_19 = 19 * g7;
    int32_t g8_19 = 19 * g8;
    int32_t g9_19 = 19 * g9;
    int32_t f1_2  = 2 * f1;
    int32_t f3_2  = 2 * f3;
    int32_t f5_2  = 2 * f5;
    int32_t f7_2  = 2 * f7;
    int32_t f9_2  = 2 * f9;

    int64_t f0g0    = f0 * (int64_t) g0;
    int64_t f0g1    = f0 * (int64_t) g1;
    int64_t f0g2    = f0 * (int64_t) g2;
    int64_t f0g3    = f0 * (int64_t) g3;
    int64_t f0g4    = f0 * (int64_t) g4;
    int64_t f0g5    = f0 * (int64_t) g5;
    int64_t f0g6    = f0 * (int64_t) g6;
    int64_t f0g7    = f0 * (int64_t) g7;
    int64_t f0g8    = f0 * (int64_t) g8;
    int64_t f0g9    = f0 * (int64_t) g9;
    int64_t f1g0    = f1 * (int64_t) g0;
    int64_t f1g1_2  = f1_2 * (int64_t) g1;
    int64_t f1g2    = f1 * (int64_t) g2;
    int64_t f1g3_2  = f1_2 * (int64_t) g3;
    int64_t f1g4    = f1 * (int64_t) g4;
    int64_t f1g5_2  = f1_2 * (int64_t) g5;
    int64_t f1g6    = f1 * (int64_t) g6;
    int64_t f1g7_2  = f1_2 * (int64_t) g7;
    int64_t f1g8    = f1 * (int64_t) g8;
    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
    int64_t f2g0    = f2 * (int64_t) g0;
    int64_t f2g1    = f2 * (int64_t) g1;
    int64_t f2g2    = f2 * (int64_t) g2;
    int64_t f2g3    = f2 * (int64_t) g3;
    int64_t f2g4    = f2 * (int64_t) g4;
    int64_t f2g5    = f2 * (int64_t) g5;
    int64_t f2g6    = f2 * (int64_t) g6;
    int64_t f2g7    = f2 * (int64_t) g7;
    int64_t f2g8_19 = f2 * (int64_t) g8_19;
    int64_t f2g9_19 = f2 * (int64_t) g9_19;
    int64_t f3g0    = f3 * (int64_t) g0;
    int64_t f3g1_2  = f3_2 * (int64_t) g1;
    int64_t f3g2    = f3 * (int64_t) g2;
    int64_t f3g3_2  = f3_2 * (int64_t) g3;
    int64_t f3g4    = f3 * (int64_t) g4;
    int64_t f3g5_2  = f3_2 * (int64_t) g5;
    int64_t f3g6    = f3 * (int64_t) g6;
    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
    int64_t f3g8_19 = f3 * (int64_t) g8_19;
    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
    int64_t f4g0    = f4 * (int64_t) g0;
    int64_t f4g1    = f4 * (int64_t) g1;
    int64_t f4g2    = f4 * (int64_t) g2;
    int64_t f4g3    = f4 * (int64_t) g3;
    int64_t f4g4    = f4 * (int64_t) g4;
    int64_t f4g5    = f4 * (int64_t) g5;
    int64_t f4g6_19 = f4 * (int64_t) g6_19;
    int64_t f4g7_19 = f4 * (int64_t) g7_19;
    int64_t f4g8_19 = f4 * (int64_t) g8_19;
    int64_t f4g9_19 = f4 * (int64_t) g9_19;
    int64_t f5g0    = f5 * (int64_t) g0;
    int64_t f5g1_2  = f5_2 * (int64_t) g1;
    int64_t f5g2    = f5 * (int64_t) g2;
    int64_t f5g3_2  = f5_2 * (int64_t) g3;
    int64_t f5g4    = f5 * (int64_t) g4;
    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
    int64_t f5g6_19 = f5 * (int64_t) g6_19;
    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
    int64_t f5g8_19 = f5 * (int64_t) g8_19;
    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
    int64_t f6g0    = f6 * (int64_t) g0;
    int64_t f6g1    = f6 * (int64_t) g1;
    int64_t f6g2    = f6 * (int64_t) g2;
    int64_t f6g3    = f6 * (int64_t) g3;
    int64_t f6g4_19 = f6 * (int64_t) g4_19;
    int64_t f6g5_19 = f6 * (int64_t) g5_19;
    int64_t f6g6_19 = f6 * (int64_t) g6_19;
    int64_t f6g7_19 = f6 * (int64_t) g7_19;
    int64_t f6g8_19 = f6 * (int64_t) g8_19;
    int64_t f6g9_19 = f6 * (int64_t) g9_19;
    int64_t f7g0    = f7 * (int64_t) g0;
    int64_t f7g1_2  = f7_2 * (int64_t) g1;
    int64_t f7g2    = f7 * (int64_t) g2;
    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
    int64_t f7g4_19 = f7 * (int64_t) g4_19;
    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
    int64_t f7g6_19 = f7 * (int64_t) g6_19;
    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
    int64_t f7g8_19 = f7 * (int64_t) g8_19;
    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
    int64_t f8g0    = f8 * (int64_t) g0;
    int64_t f8g1    = f8 * (int64_t) g1;
    int64_t f8g2_19 = f8 * (int64_t) g2_19;
    int64_t f8g3_19 = f8 * (int64_t) g3_19;
    int64_t f8g4_19 = f8 * (int64_t) g4_19;
    int64_t f8g5_19 = f8 * (int64_t) g5_19;
    int64_t f8g6_19 = f8 * (int64_t) g6_19;
    int64_t f8g7_19 = f8 * (int64_t) g7_19;
    int64_t f8g8_19 = f8 * (int64_t) g8_19;
    int64_t f8g9_19 = f8 * (int64_t) g9_19;
    int64_t f9g0    = f9 * (int64_t) g0;
    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
    int64_t f9g2_19 = f9 * (int64_t) g2_19;
    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
    int64_t f9g4_19 = f9 * (int64_t) g4_19;
    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
    int64_t f9g6_19 = f9 * (int64_t) g6_19;
    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
    int64_t f9g8_19 = f9 * (int64_t) g8_19;
    int64_t f9g9_38 = f9_2 * (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;

    int64_t carry0;
    int64_t carry1;
    int64_t carry2;
    int64_t carry3;
    int64_t carry4;
    int64_t carry5;
    int64_t carry6;
    int64_t carry7;
    int64_t carry8;
    int64_t carry9;

    /*
     |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
     */

    carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
    h1 += carry0;
    h0 -= carry0 * ((uint64_t) 1L << 26);
    carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
    h5 += carry4;
    h4 -= carry4 * ((uint64_t) 1L << 26);
    /* |h0| <= 2^25 */
    /* |h4| <= 2^25 */
    /* |h1| <= 1.71*2^59 */
    /* |h5| <= 1.71*2^59 */

    carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
    h2 += carry1;
    h1 -= carry1 * ((uint64_t) 1L << 25);
    carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
    h6 += carry5;
    h5 -= carry5 * ((uint64_t) 1L << 25);
    /* |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 */

    carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
    h3 += carry2;
    h2 -= carry2 * ((uint64_t) 1L << 26);
    carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
    h7 += carry6;
    h6 -= carry6 * ((uint64_t) 1L << 26);
    /* |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 */

    carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
    h4 += carry3;
    h3 -= carry3 * ((uint64_t) 1L << 25);
    carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
    h8 += carry7;
    h7 -= carry7 * ((uint64_t) 1L << 25);
    /* |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 */

    carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
    h5 += carry4;
    h4 -= carry4 * ((uint64_t) 1L << 26);
    carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
    h9 += carry8;
    h8 -= carry8 * ((uint64_t) 1L << 26);
    /* |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 */

    carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
    h0 += carry9 * 19;
    h9 -= carry9 * ((uint64_t) 1L << 25);
    /* |h9| <= 2^24; from now on fits into int32 unchanged */
    /* |h0| <= 1.1*2^39 */

    carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
    h1 += carry0;
    h0 -= carry0 * ((uint64_t) 1L << 26);
    /* |h0| <= 2^25; from now on fits into int32 unchanged */
    /* |h1| <= 1.01*2^24 */

    h[0] = (int32_t) h0;
    h[1] = (int32_t) h1;
    h[2] = (int32_t) h2;
    h[3] = (int32_t) h3;
    h[4] = (int32_t) h4;
    h[5] = (int32_t) h5;
    h[6] = (int32_t) h6;
    h[7] = (int32_t) h7;
    h[8] = (int32_t) h8;
    h[9] = (int32_t) 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.
 */

static void
fe25519_sq(fe25519 h, const fe25519 f)
{
    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];

    int32_t f0_2  = 2 * f0;
    int32_t f1_2  = 2 * f1;
    int32_t f2_2  = 2 * f2;
    int32_t f3_2  = 2 * f3;
    int32_t f4_2  = 2 * f4;
    int32_t f5_2  = 2 * f5;
    int32_t f6_2  = 2 * f6;
    int32_t f7_2  = 2 * f7;
    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */

    int64_t f0f0    = f0 * (int64_t) f0;
    int64_t f0f1_2  = f0_2 * (int64_t) f1;
    int64_t f0f2_2  = f0_2 * (int64_t) f2;
    int64_t f0f3_2  = f0_2 * (int64_t) f3;
    int64_t f0f4_2  = f0_2 * (int64_t) f4;
    int64_t f0f5_2  = f0_2 * (int64_t) f5;
    int64_t f0f6_2  = f0_2 * (int64_t) f6;
    int64_t f0f7_2  = f0_2 * (int64_t) f7;
    int64_t f0f8_2  = f0_2 * (int64_t) f8;
    int64_t f0f9_2  = f0_2 * (int64_t) f9;
    int64_t f1f1_2  = f1_2 * (int64_t) f1;
    int64_t f1f2_2  = f1_2 * (int64_t) f2;
    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
    int64_t f1f4_2  = f1_2 * (int64_t) f4;
    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
    int64_t f1f6_2  = f1_2 * (int64_t) f6;
    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
    int64_t f1f8_2  = f1_2 * (int64_t) f8;
    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
    int64_t f2f2    = f2 * (int64_t) f2;
    int64_t f2f3_2  = f2_2 * (int64_t) f3;
    int64_t f2f4_2  = f2_2 * (int64_t) f4;
    int64_t f2f5_2  = f2_2 * (int64_t) f5;
    int64_t f2f6_2  = f2_2 * (int64_t) f6;
    int64_t f2f7_2  = f2_2 * (int64_t) f7;
    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
    int64_t f2f9_38 = f2 * (int64_t) f9_38;
    int64_t f3f3_2  = f3_2 * (int64_t) f3;
    int64_t f3f4_2  = f3_2 * (int64_t) f4;
    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
    int64_t f3f6_2  = f3_2 * (int64_t) f6;
    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
    int64_t f4f4    = f4 * (int64_t) f4;
    int64_t f4f5_2  = f4_2 * (int64_t) f5;
    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
    int64_t f4f7_38 = f4 * (int64_t) f7_38;
    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
    int64_t f4f9_38 = f4 * (int64_t) f9_38;
    int64_t f5f5_38 = f5 * (int64_t) f5_38;
    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
    int64_t f6f6_19 = f6 * (int64_t) f6_19;
    int64_t f6f7_38 = f6 * (int64_t) f7_38;
    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
    int64_t f6f9_38 = f6 * (int64_t) f9_38;
    int64_t f7f7_38 = f7 * (int64_t) f7_38;
    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
    int64_t f8f8_19 = f8 * (int64_t) f8_19;
    int64_t f8f9_38 = f8 * (int64_t) f9_38;
    int64_t f9f9_38 = f9 * (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;

    int64_t carry0;
    int64_t carry1;
    int64_t carry2;
    int64_t carry3;
    int64_t carry4;
    int64_t carry5;
    int64_t carry6;
    int64_t carry7;
    int64_t carry8;
    int64_t carry9;

    carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
    h1 += carry0;
    h0 -= carry0 * ((uint64_t) 1L << 26);
    carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
    h5 += carry4;
    h4 -= carry4 * ((uint64_t) 1L << 26);

    carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
    h2 += carry1;
    h1 -= carry1 * ((uint64_t) 1L << 25);
    carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
    h6 += carry5;
    h5 -= carry5 * ((uint64_t) 1L << 25);

    carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
    h3 += carry2;
    h2 -= carry2 * ((uint64_t) 1L << 26);
    carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
    h7 += carry6;
    h6 -= carry6 * ((uint64_t) 1L << 26);

    carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
    h4 += carry3;
    h3 -= carry3 * ((uint64_t) 1L << 25);
    carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
    h8 += carry7;
    h7 -= carry7 * ((uint64_t) 1L << 25);

    carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
    h5 += carry4;
    h4 -= carry4 * ((uint64_t) 1L << 26);
    carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
    h9 += carry8;
    h8 -= carry8 * ((uint64_t) 1L << 26);

    carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
    h0 += carry9 * 19;
    h9 -= carry9 * ((uint64_t) 1L << 25);

    carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
    h1 += carry0;
    h0 -= carry0 * ((uint64_t) 1L << 26);

    h[0] = (int32_t) h0;
    h[1] = (int32_t) h1;
    h[2] = (int32_t) h2;
    h[3] = (int32_t) h3;
    h[4] = (int32_t) h4;
    h[5] = (int32_t) h5;
    h[6] = (int32_t) h6;
    h[7] = (int32_t) h7;
    h[8] = (int32_t) h8;
    h[9] = (int32_t) h9;
}

/*
 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.
 */

static void
fe25519_sq2(fe25519 h, const fe25519 f)
{
    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];

    int32_t f0_2  = 2 * f0;
    int32_t f1_2  = 2 * f1;
    int32_t f2_2  = 2 * f2;
    int32_t f3_2  = 2 * f3;
    int32_t f4_2  = 2 * f4;
    int32_t f5_2  = 2 * f5;
    int32_t f6_2  = 2 * f6;
    int32_t f7_2  = 2 * f7;
    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */

    int64_t f0f0    = f0 * (int64_t) f0;
    int64_t f0f1_2  = f0_2 * (int64_t) f1;
    int64_t f0f2_2  = f0_2 * (int64_t) f2;
    int64_t f0f3_2  = f0_2 * (int64_t) f3;
    int64_t f0f4_2  = f0_2 * (int64_t) f4;
    int64_t f0f5_2  = f0_2 * (int64_t) f5;
    int64_t f0f6_2  = f0_2 * (int64_t) f6;
    int64_t f0f7_2  = f0_2 * (int64_t) f7;
    int64_t f0f8_2  = f0_2 * (int64_t) f8;
    int64_t f0f9_2  = f0_2 * (int64_t) f9;
    int64_t f1f1_2  = f1_2 * (int64_t) f1;
    int64_t f1f2_2  = f1_2 * (int64_t) f2;
    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
    int64_t f1f4_2  = f1_2 * (int64_t) f4;
    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
    int64_t f1f6_2  = f1_2 * (int64_t) f6;
    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
    int64_t f1f8_2  = f1_2 * (int64_t) f8;
    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
    int64_t f2f2    = f2 * (int64_t) f2;
    int64_t f2f3_2  = f2_2 * (int64_t) f3;
    int64_t f2f4_2  = f2_2 * (int64_t) f4;
    int64_t f2f5_2  = f2_2 * (int64_t) f5;
    int64_t f2f6_2  = f2_2 * (int64_t) f6;
    int64_t f2f7_2  = f2_2 * (int64_t) f7;
    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
    int64_t f2f9_38 = f2 * (int64_t) f9_38;
    int64_t f3f3_2  = f3_2 * (int64_t) f3;
    int64_t f3f4_2  = f3_2 * (int64_t) f4;
    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
    int64_t f3f6_2  = f3_2 * (int64_t) f6;
    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
    int64_t f4f4    = f4 * (int64_t) f4;
    int64_t f4f5_2  = f4_2 * (int64_t) f5;
    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
    int64_t f4f7_38 = f4 * (int64_t) f7_38;
    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
    int64_t f4f9_38 = f4 * (int64_t) f9_38;
    int64_t f5f5_38 = f5 * (int64_t) f5_38;
    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
    int64_t f6f6_19 = f6 * (int64_t) f6_19;
    int64_t f6f7_38 = f6 * (int64_t) f7_38;
    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
    int64_t f6f9_38 = f6 * (int64_t) f9_38;
    int64_t f7f7_38 = f7 * (int64_t) f7_38;
    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
    int64_t f8f8_19 = f8 * (int64_t) f8_19;
    int64_t f8f9_38 = f8 * (int64_t) f9_38;
    int64_t f9f9_38 = f9 * (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;

    int64_t carry0;
    int64_t carry1;
    int64_t carry2;
    int64_t carry3;
    int64_t carry4;
    int64_t carry5;
    int64_t carry6;
    int64_t carry7;
    int64_t carry8;
    int64_t carry9;

    h0 += h0;
    h1 += h1;
    h2 += h2;
    h3 += h3;
    h4 += h4;
    h5 += h5;
    h6 += h6;
    h7 += h7;
    h8 += h8;
    h9 += h9;

    carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
    h1 += carry0;
    h0 -= carry0 * ((uint64_t) 1L << 26);
    carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
    h5 += carry4;
    h4 -= carry4 * ((uint64_t) 1L << 26);

    carry1 = (h1 + (int64_t)(1L << 24)) >> 25;
    h2 += carry1;
    h1 -= carry1 * ((uint64_t) 1L << 25);
    carry5 = (h5 + (int64_t)(1L << 24)) >> 25;
    h6 += carry5;
    h5 -= carry5 * ((uint64_t) 1L << 25);

    carry2 = (h2 + (int64_t)(1L << 25)) >> 26;
    h3 += carry2;
    h2 -= carry2 * ((uint64_t) 1L << 26);
    carry6 = (h6 + (int64_t)(1L << 25)) >> 26;
    h7 += carry6;
    h6 -= carry6 * ((uint64_t) 1L << 26);

    carry3 = (h3 + (int64_t)(1L << 24)) >> 25;
    h4 += carry3;
    h3 -= carry3 * ((uint64_t) 1L << 25);
    carry7 = (h7 + (int64_t)(1L << 24)) >> 25;
    h8 += carry7;
    h7 -= carry7 * ((uint64_t) 1L << 25);

    carry4 = (h4 + (int64_t)(1L << 25)) >> 26;
    h5 += carry4;
    h4 -= carry4 * ((uint64_t) 1L << 26);
    carry8 = (h8 + (int64_t)(1L << 25)) >> 26;
    h9 += carry8;
    h8 -= carry8 * ((uint64_t) 1L << 26);

    carry9 = (h9 + (int64_t)(1L << 24)) >> 25;
    h0 += carry9 * 19;
    h9 -= carry9 * ((uint64_t) 1L << 25);

    carry0 = (h0 + (int64_t)(1L << 25)) >> 26;
    h1 += carry0;
    h0 -= carry0 * ((uint64_t) 1L << 26);

    h[0] = (int32_t) h0;
    h[1] = (int32_t) h1;
    h[2] = (int32_t) h2;
    h[3] = (int32_t) h3;
    h[4] = (int32_t) h4;
    h[5] = (int32_t) h5;
    h[6] = (int32_t) h6;
    h[7] = (int32_t) h7;
    h[8] = (int32_t) h8;
    h[9] = (int32_t) h9;
}

static void
fe25519_scalar_product(fe25519 h, const fe25519 f, uint32_t n)
{
    int64_t sn = (int64_t) n;
    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];
    int64_t h0 = f0 * sn;
    int64_t h1 = f1 * sn;
    int64_t h2 = f2 * sn;
    int64_t h3 = f3 * sn;
    int64_t h4 = f4 * sn;
    int64_t h5 = f5 * sn;
    int64_t h6 = f6 * sn;
    int64_t h7 = f7 * sn;
    int64_t h8 = f8 * sn;
    int64_t h9 = f9 * sn;
    int64_t carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7,
            carry8, carry9;

    carry9 = (h9 + ((int64_t) 1 << 24)) >> 25;
    h0 += carry9 * 19;
    h9 -= carry9 * ((int64_t) 1 << 25);
    carry1 = (h1 + ((int64_t) 1 << 24)) >> 25;
    h2 += carry1;
    h1 -= carry1 * ((int64_t) 1 << 25);
    carry3 = (h3 + ((int64_t) 1 << 24)) >> 25;
    h4 += carry3;
    h3 -= carry3 * ((int64_t) 1 << 25);
    carry5 = (h5 + ((int64_t) 1 << 24)) >> 25;
    h6 += carry5;
    h5 -= carry5 * ((int64_t) 1 << 25);
    carry7 = (h7 + ((int64_t) 1 << 24)) >> 25;
    h8 += carry7;
    h7 -= carry7 * ((int64_t) 1 << 25);

    carry0 = (h0 + ((int64_t) 1 << 25)) >> 26;
    h1 += carry0;
    h0 -= carry0 * ((int64_t) 1 << 26);
    carry2 = (h2 + ((int64_t) 1 << 25)) >> 26;
    h3 += carry2;
    h2 -= carry2 * ((int64_t) 1 << 26);
    carry4 = (h4 + ((int64_t) 1 << 25)) >> 26;
    h5 += carry4;
    h4 -= carry4 * ((int64_t) 1 << 26);
    carry6 = (h6 + ((int64_t) 1 << 25)) >> 26;
    h7 += carry6;
    h6 -= carry6 * ((int64_t) 1 << 26);
    carry8 = (h8 + ((int64_t) 1 << 25)) >> 26;
    h9 += carry8;
    h8 -= carry8 * ((int64_t) 1 << 26);

    h[0] = (int32_t) h0;
    h[1] = (int32_t) h1;
    h[2] = (int32_t) h2;
    h[3] = (int32_t) h3;
    h[4] = (int32_t) h4;
    h[5] = (int32_t) h5;
    h[6] = (int32_t) h6;
    h[7] = (int32_t) h7;
    h[8] = (int32_t) h8;
    h[9] = (int32_t) h9;
}