third_party/fiat/curve25519.c

// The MIT License (MIT)
//
// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.

// Some of this code is taken from the ref10 version of Ed25519 in SUPERCOP
// 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
// public domain but parts have been replaced with code generated by Fiat
// (https://github.com/mit-plv/fiat-crypto), which is MIT licensed.
//
// The field functions are shared by Ed25519 and X25519 where possible.

#include <openssl/curve25519.h>

#include <assert.h>
#include <string.h>

#include <openssl/cpu.h>
#include <openssl/mem.h>
#include <openssl/rand.h>
#include <openssl/sha.h>
#include <openssl/type_check.h>

#include "internal.h"
#include "../../crypto/internal.h"


// Various pre-computed constants.
#include "./curve25519_tables.h"


// Low-level intrinsic operations (hand-written).

static uint64_t load_3(const uint8_t *in) {
  uint64_t result;
  result = (uint64_t)in[0];
  result |= ((uint64_t)in[1]) << 8;
  result |= ((uint64_t)in[2]) << 16;
  return result;
}

static uint64_t load_4(const uint8_t *in) {
  uint64_t result;
  result = (uint64_t)in[0];
  result |= ((uint64_t)in[1]) << 8;
  result |= ((uint64_t)in[2]) << 16;
  result |= ((uint64_t)in[3]) << 24;
  return result;
}

#if defined(BORINGSSL_CURVE25519_64BIT)
static uint64_t load_8(const uint8_t *in) {
  uint64_t result;
  result = (uint64_t)in[0];
  result |= ((uint64_t)in[1]) << 8;
  result |= ((uint64_t)in[2]) << 16;
  result |= ((uint64_t)in[3]) << 24;
  result |= ((uint64_t)in[4]) << 32;
  result |= ((uint64_t)in[5]) << 40;
  result |= ((uint64_t)in[6]) << 48;
  result |= ((uint64_t)in[7]) << 56;
  return result;
}

static uint8_t /*bool*/ addcarryx_u51(uint8_t /*bool*/ c, uint64_t a,
                                      uint64_t b, uint64_t *low) {
  // This function extracts 51 bits of result and 1 bit of carry (52 total), so
  // a 64-bit intermediate is sufficient.
  uint64_t x = a + b + c;
  *low = x & ((UINT64_C(1) << 51) - 1);
  return (x >> 51) & 1;
}

static uint8_t /*bool*/ subborrow_u51(uint8_t /*bool*/ c, uint64_t a,
                                      uint64_t b, uint64_t *low) {
  // This function extracts 51 bits of result and 1 bit of borrow (52 total), so
  // a 64-bit intermediate is sufficient.
  uint64_t x = a - b - c;
  *low = x & ((UINT64_C(1) << 51) - 1);
  return x >> 63;
}

static uint64_t cmovznz64(uint64_t t, uint64_t z, uint64_t nz) {
  t = -!!t; // all set if nonzero, 0 if 0
  return (t&nz) | ((~t)&z);
}

#else

static uint8_t /*bool*/ addcarryx_u25(uint8_t /*bool*/ c, uint32_t a,
                                      uint32_t b, uint32_t *low) {
  // This function extracts 25 bits of result and 1 bit of carry (26 total), so
  // a 32-bit intermediate is sufficient.
  uint32_t x = a + b + c;
  *low = x & ((1 << 25) - 1);
  return (x >> 25) & 1;
}

static uint8_t /*bool*/ addcarryx_u26(uint8_t /*bool*/ c, uint32_t a,
                                      uint32_t b, uint32_t *low) {
  // This function extracts 26 bits of result and 1 bit of carry (27 total), so
  // a 32-bit intermediate is sufficient.
  uint32_t x = a + b + c;
  *low = x & ((1 << 26) - 1);
  return (x >> 26) & 1;
}

static uint8_t /*bool*/ subborrow_u25(uint8_t /*bool*/ c, uint32_t a,
                                      uint32_t b, uint32_t *low) {
  // This function extracts 25 bits of result and 1 bit of borrow (26 total), so
  // a 32-bit intermediate is sufficient.
  uint32_t x = a - b - c;
  *low = x & ((1 << 25) - 1);
  return x >> 31;
}

static uint8_t /*bool*/ subborrow_u26(uint8_t /*bool*/ c, uint32_t a,
                                      uint32_t b, uint32_t *low) {
  // This function extracts 26 bits of result and 1 bit of borrow (27 total), so
  // a 32-bit intermediate is sufficient.
  uint32_t x = a - b - c;
  *low = x & ((1 << 26) - 1);
  return x >> 31;
}

static uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz) {
  t = -!!t; // all set if nonzero, 0 if 0
  return (t&nz) | ((~t)&z);
}

#endif


// Field operations.

#if defined(BORINGSSL_CURVE25519_64BIT)

#define assert_fe(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < 1.125*(UINT64_C(1)<<51)); \
  } \
} while (0)

#define assert_fe_loose(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < 3.375*(UINT64_C(1)<<51)); \
  } \
} while (0)

#define assert_fe_frozen(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < (UINT64_C(1)<<51)); \
  } \
} while (0)

static void fe_frombytes_impl(uint64_t h[5], const uint8_t *s) {
  // Ignores top bit of s.
  uint64_t a0 = load_8(s);
  uint64_t a1 = load_8(s+8);
  uint64_t a2 = load_8(s+16);
  uint64_t a3 = load_8(s+24);
  // Use 51 bits, 64-51 = 13 left.
  h[0] = a0 & ((UINT64_C(1) << 51) - 1);
  // (64-51) + 38 = 13 + 38 = 51
  h[1] = (a0 >> 51) | ((a1 & ((UINT64_C(1) << 38) - 1)) << 13);
  // (64-38) + 25 = 26 + 25 = 51
  h[2] = (a1 >> 38) | ((a2 & ((UINT64_C(1) << 25) - 1)) << 26);
  // (64-25) + 12 = 39 + 12 = 51
  h[3] = (a2 >> 25) | ((a3 & ((UINT64_C(1) << 12) - 1)) << 39);
  // (64-12) = 52, ignore top bit
  h[4] = (a3 >> 12) & ((UINT64_C(1) << 51) - 1);
  assert_fe(h);
}

static void fe_frombytes(fe *h, const uint8_t *s) {
  fe_frombytes_impl(h->v, s);
}

static void fe_freeze(uint64_t out[5], const uint64_t in1[5]) {
  { const uint64_t x7 = in1[4];
  { const uint64_t x8 = in1[3];
  { const uint64_t x6 = in1[2];
  { const uint64_t x4 = in1[1];
  { const uint64_t x2 = in1[0];
  { uint64_t x10; uint8_t/*bool*/ x11 = subborrow_u51(0x0, x2, 0x7ffffffffffed, &x10);
  { uint64_t x13; uint8_t/*bool*/ x14 = subborrow_u51(x11, x4, 0x7ffffffffffff, &x13);
  { uint64_t x16; uint8_t/*bool*/ x17 = subborrow_u51(x14, x6, 0x7ffffffffffff, &x16);
  { uint64_t x19; uint8_t/*bool*/ x20 = subborrow_u51(x17, x8, 0x7ffffffffffff, &x19);
  { uint64_t x22; uint8_t/*bool*/ x23 = subborrow_u51(x20, x7, 0x7ffffffffffff, &x22);
  { uint64_t x24 = cmovznz64(x23, 0x0, 0xffffffffffffffffL);
  { uint64_t x25 = (x24 & 0x7ffffffffffed);
  { uint64_t x27; uint8_t/*bool*/ x28 = addcarryx_u51(0x0, x10, x25, &x27);
  { uint64_t x29 = (x24 & 0x7ffffffffffff);
  { uint64_t x31; uint8_t/*bool*/ x32 = addcarryx_u51(x28, x13, x29, &x31);
  { uint64_t x33 = (x24 & 0x7ffffffffffff);
  { uint64_t x35; uint8_t/*bool*/ x36 = addcarryx_u51(x32, x16, x33, &x35);
  { uint64_t x37 = (x24 & 0x7ffffffffffff);
  { uint64_t x39; uint8_t/*bool*/ x40 = addcarryx_u51(x36, x19, x37, &x39);
  { uint64_t x41 = (x24 & 0x7ffffffffffff);
  { uint64_t x43; addcarryx_u51(x40, x22, x41, &x43);
  out[0] = x27;
  out[1] = x31;
  out[2] = x35;
  out[3] = x39;
  out[4] = x43;
  }}}}}}}}}}}}}}}}}}}}}
}

static void fe_tobytes(uint8_t s[32], const fe *f) {
  assert_fe(f->v);
  uint64_t h[5];
  fe_freeze(h, f->v);
  assert_fe_frozen(h);

  s[0] = h[0] >> 0;
  s[1] = h[0] >> 8;
  s[2] = h[0] >> 16;
  s[3] = h[0] >> 24;
  s[4] = h[0] >> 32;
  s[5] = h[0] >> 40;
  s[6] = (h[0] >> 48) | (h[1] << 3);
  s[7] = h[1] >> 5;
  s[8] = h[1] >> 13;
  s[9] = h[1] >> 21;
  s[10] = h[1] >> 29;
  s[11] = h[1] >> 37;
  s[12] = (h[1] >> 45) | (h[2] << 6);
  s[13] = h[2] >> 2;
  s[14] = h[2] >> 10;
  s[15] = h[2] >> 18;
  s[16] = h[2] >> 26;
  s[17] = h[2] >> 34;
  s[18] = h[2] >> 42;
  s[19] = (h[2] >> 50) | (h[3] << 1);
  s[20] = h[3] >> 7;
  s[21] = h[3] >> 15;
  s[22] = h[3] >> 23;
  s[23] = h[3] >> 31;
  s[24] = h[3] >> 39;
  s[25] = (h[3] >> 47) | (h[4] << 4);
  s[26] = h[4] >> 4;
  s[27] = h[4] >> 12;
  s[28] = h[4] >> 20;
  s[29] = h[4] >> 28;
  s[30] = h[4] >> 36;
  s[31] = h[4] >> 44;
}

// h = 0
static void fe_0(fe *h) {
  OPENSSL_memset(h, 0, sizeof(fe));
}

static void fe_loose_0(fe_loose *h) {
  OPENSSL_memset(h, 0, sizeof(fe_loose));
}

// h = 1
static void fe_1(fe *h) {
  OPENSSL_memset(h, 0, sizeof(fe));
  h->v[0] = 1;
}

static void fe_loose_1(fe_loose *h) {
  OPENSSL_memset(h, 0, sizeof(fe_loose));
  h->v[0] = 1;
}

static void fe_add_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) {
  { const uint64_t x10 = in1[4];
  { const uint64_t x11 = in1[3];
  { const uint64_t x9 = in1[2];
  { const uint64_t x7 = in1[1];
  { const uint64_t x5 = in1[0];
  { const uint64_t x18 = in2[4];
  { const uint64_t x19 = in2[3];
  { const uint64_t x17 = in2[2];
  { const uint64_t x15 = in2[1];
  { const uint64_t x13 = in2[0];
  out[0] = (x5 + x13);
  out[1] = (x7 + x15);
  out[2] = (x9 + x17);
  out[3] = (x11 + x19);
  out[4] = (x10 + x18);
  }}}}}}}}}}
}

// h = f + g
// Can overlap h with f or g.
static void fe_add(fe_loose *h, const fe *f, const fe *g) {
  assert_fe(f->v);
  assert_fe(g->v);
  fe_add_impl(h->v, f->v, g->v);
  assert_fe_loose(h->v);
}

static void fe_sub_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) {
  { const uint64_t x10 = in1[4];
  { const uint64_t x11 = in1[3];
  { const uint64_t x9 = in1[2];
  { const uint64_t x7 = in1[1];
  { const uint64_t x5 = in1[0];
  { const uint64_t x18 = in2[4];
  { const uint64_t x19 = in2[3];
  { const uint64_t x17 = in2[2];
  { const uint64_t x15 = in2[1];
  { const uint64_t x13 = in2[0];
  out[0] = ((0xfffffffffffda + x5) - x13);
  out[1] = ((0xffffffffffffe + x7) - x15);
  out[2] = ((0xffffffffffffe + x9) - x17);
  out[3] = ((0xffffffffffffe + x11) - x19);
  out[4] = ((0xffffffffffffe + x10) - x18);
  }}}}}}}}}}
}

// h = f - g
// Can overlap h with f or g.
static void fe_sub(fe_loose *h, const fe *f, const fe *g) {
  assert_fe(f->v);
  assert_fe(g->v);
  fe_sub_impl(h->v, f->v, g->v);
  assert_fe_loose(h->v);
}

static void fe_carry_impl(uint64_t out[5], const uint64_t in1[5]) {
  { const uint64_t x7 = in1[4];
  { const uint64_t x8 = in1[3];
  { const uint64_t x6 = in1[2];
  { const uint64_t x4 = in1[1];
  { const uint64_t x2 = in1[0];
  { uint64_t x9 = (x2 >> 0x33);
  { uint64_t x10 = (x2 & 0x7ffffffffffff);
  { uint64_t x11 = (x9 + x4);
  { uint64_t x12 = (x11 >> 0x33);
  { uint64_t x13 = (x11 & 0x7ffffffffffff);
  { uint64_t x14 = (x12 + x6);
  { uint64_t x15 = (x14 >> 0x33);
  { uint64_t x16 = (x14 & 0x7ffffffffffff);
  { uint64_t x17 = (x15 + x8);
  { uint64_t x18 = (x17 >> 0x33);
  { uint64_t x19 = (x17 & 0x7ffffffffffff);
  { uint64_t x20 = (x18 + x7);
  { uint64_t x21 = (x20 >> 0x33);
  { uint64_t x22 = (x20 & 0x7ffffffffffff);
  { uint64_t x23 = (x10 + (0x13 * x21));
  { uint64_t x24 = (x23 >> 0x33);
  { uint64_t x25 = (x23 & 0x7ffffffffffff);
  { uint64_t x26 = (x24 + x13);
  { uint64_t x27 = (x26 >> 0x33);
  { uint64_t x28 = (x26 & 0x7ffffffffffff);
  out[0] = x25;
  out[1] = x28;
  out[2] = (x27 + x16);
  out[3] = x19;
  out[4] = x22;
  }}}}}}}}}}}}}}}}}}}}}}}}}
}

static void fe_carry(fe *h, const fe_loose* f) {
  assert_fe_loose(f->v);
  fe_carry_impl(h->v, f->v);
  assert_fe(h->v);
}

static void fe_mul_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) {
  assert_fe_loose(in1);
  assert_fe_loose(in2);
  { const uint64_t x10 = in1[4];
  { const uint64_t x11 = in1[3];
  { const uint64_t x9 = in1[2];
  { const uint64_t x7 = in1[1];
  { const uint64_t x5 = in1[0];
  { const uint64_t x18 = in2[4];
  { const uint64_t x19 = in2[3];
  { const uint64_t x17 = in2[2];
  { const uint64_t x15 = in2[1];
  { const uint64_t x13 = in2[0];
  { uint128_t x20 = ((uint128_t)x5 * x13);
  { uint128_t x21 = (((uint128_t)x5 * x15) + ((uint128_t)x7 * x13));
  { uint128_t x22 = ((((uint128_t)x5 * x17) + ((uint128_t)x9 * x13)) + ((uint128_t)x7 * x15));
  { uint128_t x23 = (((((uint128_t)x5 * x19) + ((uint128_t)x11 * x13)) + ((uint128_t)x7 * x17)) + ((uint128_t)x9 * x15));
  { uint128_t x24 = ((((((uint128_t)x5 * x18) + ((uint128_t)x10 * x13)) + ((uint128_t)x11 * x15)) + ((uint128_t)x7 * x19)) + ((uint128_t)x9 * x17));
  { uint64_t x25 = (x10 * 0x13);
  { uint64_t x26 = (x7 * 0x13);
  { uint64_t x27 = (x9 * 0x13);
  { uint64_t x28 = (x11 * 0x13);
  { uint128_t x29 = ((((x20 + ((uint128_t)x25 * x15)) + ((uint128_t)x26 * x18)) + ((uint128_t)x27 * x19)) + ((uint128_t)x28 * x17));
  { uint128_t x30 = (((x21 + ((uint128_t)x25 * x17)) + ((uint128_t)x27 * x18)) + ((uint128_t)x28 * x19));
  { uint128_t x31 = ((x22 + ((uint128_t)x25 * x19)) + ((uint128_t)x28 * x18));
  { uint128_t x32 = (x23 + ((uint128_t)x25 * x18));
  { uint64_t x33 = (uint64_t) (x29 >> 0x33);
  { uint64_t x34 = ((uint64_t)x29 & 0x7ffffffffffff);
  { uint128_t x35 = (x33 + x30);
  { uint64_t x36 = (uint64_t) (x35 >> 0x33);
  { uint64_t x37 = ((uint64_t)x35 & 0x7ffffffffffff);
  { uint128_t x38 = (x36 + x31);
  { uint64_t x39 = (uint64_t) (x38 >> 0x33);
  { uint64_t x40 = ((uint64_t)x38 & 0x7ffffffffffff);
  { uint128_t x41 = (x39 + x32);
  { uint64_t x42 = (uint64_t) (x41 >> 0x33);
  { uint64_t x43 = ((uint64_t)x41 & 0x7ffffffffffff);
  { uint128_t x44 = (x42 + x24);
  { uint64_t x45 = (uint64_t) (x44 >> 0x33);
  { uint64_t x46 = ((uint64_t)x44 & 0x7ffffffffffff);
  { uint64_t x47 = (x34 + (0x13 * x45));
  { uint64_t x48 = (x47 >> 0x33);
  { uint64_t x49 = (x47 & 0x7ffffffffffff);
  { uint64_t x50 = (x48 + x37);
  { uint64_t x51 = (x50 >> 0x33);
  { uint64_t x52 = (x50 & 0x7ffffffffffff);
  out[0] = x49;
  out[1] = x52;
  out[2] = (x51 + x40);
  out[3] = x43;
  out[4] = x46;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_ttt(fe *h, const fe *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_sqr_impl(uint64_t out[5], const uint64_t in1[5]) {
  assert_fe_loose(in1);
  { const uint64_t x7 = in1[4];
  { const uint64_t x8 = in1[3];
  { const uint64_t x6 = in1[2];
  { const uint64_t x4 = in1[1];
  { const uint64_t x2 = in1[0];
  { uint64_t x9 = (x2 * 0x2);
  { uint64_t x10 = (x4 * 0x2);
  { uint64_t x11 = ((x6 * 0x2) * 0x13);
  { uint64_t x12 = (x7 * 0x13);
  { uint64_t x13 = (x12 * 0x2);
  { uint128_t x14 = ((((uint128_t)x2 * x2) + ((uint128_t)x13 * x4)) + ((uint128_t)x11 * x8));
  { uint128_t x15 = ((((uint128_t)x9 * x4) + ((uint128_t)x13 * x6)) + ((uint128_t)x8 * (x8 * 0x13)));
  { uint128_t x16 = ((((uint128_t)x9 * x6) + ((uint128_t)x4 * x4)) + ((uint128_t)x13 * x8));
  { uint128_t x17 = ((((uint128_t)x9 * x8) + ((uint128_t)x10 * x6)) + ((uint128_t)x7 * x12));
  { uint128_t x18 = ((((uint128_t)x9 * x7) + ((uint128_t)x10 * x8)) + ((uint128_t)x6 * x6));
  { uint64_t x19 = (uint64_t) (x14 >> 0x33);
  { uint64_t x20 = ((uint64_t)x14 & 0x7ffffffffffff);
  { uint128_t x21 = (x19 + x15);
  { uint64_t x22 = (uint64_t) (x21 >> 0x33);
  { uint64_t x23 = ((uint64_t)x21 & 0x7ffffffffffff);
  { uint128_t x24 = (x22 + x16);
  { uint64_t x25 = (uint64_t) (x24 >> 0x33);
  { uint64_t x26 = ((uint64_t)x24 & 0x7ffffffffffff);
  { uint128_t x27 = (x25 + x17);
  { uint64_t x28 = (uint64_t) (x27 >> 0x33);
  { uint64_t x29 = ((uint64_t)x27 & 0x7ffffffffffff);
  { uint128_t x30 = (x28 + x18);
  { uint64_t x31 = (uint64_t) (x30 >> 0x33);
  { uint64_t x32 = ((uint64_t)x30 & 0x7ffffffffffff);
  { uint64_t x33 = (x20 + (0x13 * x31));
  { uint64_t x34 = (x33 >> 0x33);
  { uint64_t x35 = (x33 & 0x7ffffffffffff);
  { uint64_t x36 = (x34 + x23);
  { uint64_t x37 = (x36 >> 0x33);
  { uint64_t x38 = (x36 & 0x7ffffffffffff);
  out[0] = x35;
  out[1] = x38;
  out[2] = (x37 + x26);
  out[3] = x29;
  out[4] = x32;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_sq_tl(fe *h, const fe_loose *f) {
  fe_sqr_impl(h->v, f->v);
}

static void fe_sq_tt(fe *h, const fe *f) {
  fe_sqr_impl(h->v, f->v);
}

// Replace (f,g) with (g,f) if b == 1;
// replace (f,g) with (f,g) if b == 0.
//
// Preconditions: b in {0,1}.
static void fe_cswap(fe *f, fe *g, uint64_t b) {
  b = 0-b;
  for (unsigned i = 0; i < 5; i++) {
    uint64_t x = f->v[i] ^ g->v[i];
    x &= b;
    f->v[i] ^= x;
    g->v[i] ^= x;
  }
}

// NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0..
static void fe_mul_121666_impl(uint64_t out[5], const uint64_t in1[5]) {
  { const uint64_t x10 = in1[4];
  { const uint64_t x11 = in1[3];
  { const uint64_t x9 = in1[2];
  { const uint64_t x7 = in1[1];
  { const uint64_t x5 = in1[0];
  { const uint64_t x18 = 0;
  { const uint64_t x19 = 0;
  { const uint64_t x17 = 0;
  { const uint64_t x15 = 0;
  { const uint64_t x13 = 121666;
  { uint128_t x20 = ((uint128_t)x5 * x13);
  { uint128_t x21 = (((uint128_t)x5 * x15) + ((uint128_t)x7 * x13));
  { uint128_t x22 = ((((uint128_t)x5 * x17) + ((uint128_t)x9 * x13)) + ((uint128_t)x7 * x15));
  { uint128_t x23 = (((((uint128_t)x5 * x19) + ((uint128_t)x11 * x13)) + ((uint128_t)x7 * x17)) + ((uint128_t)x9 * x15));
  { uint128_t x24 = ((((((uint128_t)x5 * x18) + ((uint128_t)x10 * x13)) + ((uint128_t)x11 * x15)) + ((uint128_t)x7 * x19)) + ((uint128_t)x9 * x17));
  { uint64_t x25 = (x10 * 0x13);
  { uint64_t x26 = (x7 * 0x13);
  { uint64_t x27 = (x9 * 0x13);
  { uint64_t x28 = (x11 * 0x13);
  { uint128_t x29 = ((((x20 + ((uint128_t)x25 * x15)) + ((uint128_t)x26 * x18)) + ((uint128_t)x27 * x19)) + ((uint128_t)x28 * x17));
  { uint128_t x30 = (((x21 + ((uint128_t)x25 * x17)) + ((uint128_t)x27 * x18)) + ((uint128_t)x28 * x19));
  { uint128_t x31 = ((x22 + ((uint128_t)x25 * x19)) + ((uint128_t)x28 * x18));
  { uint128_t x32 = (x23 + ((uint128_t)x25 * x18));
  { uint64_t x33 = (uint64_t) (x29 >> 0x33);
  { uint64_t x34 = ((uint64_t)x29 & 0x7ffffffffffff);
  { uint128_t x35 = (x33 + x30);
  { uint64_t x36 = (uint64_t) (x35 >> 0x33);
  { uint64_t x37 = ((uint64_t)x35 & 0x7ffffffffffff);
  { uint128_t x38 = (x36 + x31);
  { uint64_t x39 = (uint64_t) (x38 >> 0x33);
  { uint64_t x40 = ((uint64_t)x38 & 0x7ffffffffffff);
  { uint128_t x41 = (x39 + x32);
  { uint64_t x42 = (uint64_t) (x41 >> 0x33);
  { uint64_t x43 = ((uint64_t)x41 & 0x7ffffffffffff);
  { uint128_t x44 = (x42 + x24);
  { uint64_t x45 = (uint64_t) (x44 >> 0x33);
  { uint64_t x46 = ((uint64_t)x44 & 0x7ffffffffffff);
  { uint64_t x47 = (x34 + (0x13 * x45));
  { uint64_t x48 = (x47 >> 0x33);
  { uint64_t x49 = (x47 & 0x7ffffffffffff);
  { uint64_t x50 = (x48 + x37);
  { uint64_t x51 = (x50 >> 0x33);
  { uint64_t x52 = (x50 & 0x7ffffffffffff);
  out[0] = x49;
  out[1] = x52;
  out[2] = (x51 + x40);
  out[3] = x43;
  out[4] = x46;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
}

static void fe_mul121666(fe *h, const fe_loose *f) {
  assert_fe_loose(f->v);
  fe_mul_121666_impl(h->v, f->v);
  assert_fe(h->v);
}

// Adapted from Fiat-synthesized |fe_sub_impl| with |out| = 0.
static void fe_neg_impl(uint64_t out[5], const uint64_t in2[5]) {
  { const uint64_t x10 = 0;
  { const uint64_t x11 = 0;
  { const uint64_t x9 = 0;
  { const uint64_t x7 = 0;
  { const uint64_t x5 = 0;
  { const uint64_t x18 = in2[4];
  { const uint64_t x19 = in2[3];
  { const uint64_t x17 = in2[2];
  { const uint64_t x15 = in2[1];
  { const uint64_t x13 = in2[0];
  out[0] = ((0xfffffffffffda + x5) - x13);
  out[1] = ((0xffffffffffffe + x7) - x15);
  out[2] = ((0xffffffffffffe + x9) - x17);
  out[3] = ((0xffffffffffffe + x11) - x19);
  out[4] = ((0xffffffffffffe + x10) - x18);
  }}}}}}}}}}
}

// h = -f
static void fe_neg(fe_loose *h, const fe *f) {
  assert_fe(f->v);
  fe_neg_impl(h->v, f->v);
  assert_fe_loose(h->v);
}

// 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 fe_cmov(fe_loose *f, const fe_loose *g, uint64_t b) {
  b = 0-b;
  for (unsigned i = 0; i < 5; i++) {
    uint64_t x = f->v[i] ^ g->v[i];
    x &= b;
    f->v[i] ^= x;
  }
}

#else

#define assert_fe(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < 1.125*(1<<(26-(_assert_fe_i&1)))); \
  } \
} while (0)

#define assert_fe_loose(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < 3.375*(1<<(26-(_assert_fe_i&1)))); \
  } \
} while (0)

#define assert_fe_frozen(f) do { \
  for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
    assert(f[_assert_fe_i] < (1u<<(26-(_assert_fe_i&1)))); \
  } \
} while (0)

static void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) {
  // Ignores top bit of s.
  uint32_t a0 = load_4(s);
  uint32_t a1 = load_4(s+4);
  uint32_t a2 = load_4(s+8);
  uint32_t a3 = load_4(s+12);
  uint32_t a4 = load_4(s+16);
  uint32_t a5 = load_4(s+20);
  uint32_t a6 = load_4(s+24);
  uint32_t a7 = load_4(s+28);
  h[0] = a0&((1<<26)-1);                    // 26 used, 32-26 left.   26
  h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); // (32-26) + 19 =  6+19 = 25
  h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); // (32-19) + 13 = 13+13 = 26
  h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); // (32-13) +  6 = 19+ 6 = 25
  h[4] = (a3>> 6);                          // (32- 6)              = 26
  h[5] = a4&((1<<25)-1);                    //                        25
  h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); // (32-25) + 19 =  7+19 = 26
  h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); // (32-19) + 12 = 13+12 = 25
  h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); // (32-12) +  6 = 20+ 6 = 26
  h[9] = (a7>> 6)&((1<<25)-1); //                                     25
  assert_fe(h);
}

static void fe_frombytes(fe *h, const uint8_t *s) {
  fe_frombytes_impl(h->v, s);
}

static void fe_freeze(uint32_t out[10], const uint32_t in1[10]) {
  { const uint32_t x17 = in1[9];
  { const uint32_t x18 = in1[8];
  { const uint32_t x16 = in1[7];
  { const uint32_t x14 = in1[6];
  { const uint32_t x12 = in1[5];
  { const uint32_t x10 = in1[4];
  { const uint32_t x8 = in1[3];
  { const uint32_t x6 = in1[2];
  { const uint32_t x4 = in1[1];
  { const uint32_t x2 = in1[0];
  { uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
  { uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
  { uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
  { uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
  { uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
  { uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
  { uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
  { uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
  { uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
  { uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
  { uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff);
  { uint32_t x50 = (x49 & 0x3ffffed);
  { uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
  { uint32_t x54 = (x49 & 0x1ffffff);
  { uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
  { uint32_t x58 = (x49 & 0x3ffffff);
  { uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
  { uint32_t x62 = (x49 & 0x1ffffff);
  { uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
  { uint32_t x66 = (x49 & 0x3ffffff);
  { uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
  { uint32_t x70 = (x49 & 0x1ffffff);
  { uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
  { uint32_t x74 = (x49 & 0x3ffffff);
  { uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
  { uint32_t x78 = (x49 & 0x1ffffff);
  { uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
  { uint32_t x82 = (x49 & 0x3ffffff);
  { uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
  { uint32_t x86 = (x49 & 0x1ffffff);
  { uint32_t x88; addcarryx_u25(x85, x47, x86, &x88);
  out[0] = x52;
  out[1] = x56;
  out[2] = x60;
  out[3] = x64;
  out[4] = x68;
  out[5] = x72;
  out[6] = x76;
  out[7] = x80;
  out[8] = x84;
  out[9] = x88;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
}

static void fe_tobytes(uint8_t s[32], const fe *f) {
  assert_fe(f->v);
  uint32_t h[10];
  fe_freeze(h, f->v);
  assert_fe_frozen(h);

  s[0] = h[0] >> 0;
  s[1] = h[0] >> 8;
  s[2] = h[0] >> 16;
  s[3] = (h[0] >> 24) | (h[1] << 2);
  s[4] = h[1] >> 6;
  s[5] = h[1] >> 14;
  s[6] = (h[1] >> 22) | (h[2] << 3);
  s[7] = h[2] >> 5;
  s[8] = h[2] >> 13;
  s[9] = (h[2] >> 21) | (h[3] << 5);
  s[10] = h[3] >> 3;
  s[11] = h[3] >> 11;
  s[12] = (h[3] >> 19) | (h[4] << 6);
  s[13] = h[4] >> 2;
  s[14] = h[4] >> 10;
  s[15] = h[4] >> 18;
  s[16] = h[5] >> 0;
  s[17] = h[5] >> 8;
  s[18] = h[5] >> 16;
  s[19] = (h[5] >> 24) | (h[6] << 1);
  s[20] = h[6] >> 7;
  s[21] = h[6] >> 15;
  s[22] = (h[6] >> 23) | (h[7] << 3);
  s[23] = h[7] >> 5;
  s[24] = h[7] >> 13;
  s[25] = (h[7] >> 21) | (h[8] << 4);
  s[26] = h[8] >> 4;
  s[27] = h[8] >> 12;
  s[28] = (h[8] >> 20) | (h[9] << 6);
  s[29] = h[9] >> 2;
  s[30] = h[9] >> 10;
  s[31] = h[9] >> 18;
}

// h = 0
static void fe_0(fe *h) {
  OPENSSL_memset(h, 0, sizeof(fe));
}

static void fe_loose_0(fe_loose *h) {
  OPENSSL_memset(h, 0, sizeof(fe_loose));
}

// h = 1
static void fe_1(fe *h) {
  OPENSSL_memset(h, 0, sizeof(fe));
  h->v[0] = 1;
}

static void fe_loose_1(fe_loose *h) {
  OPENSSL_memset(h, 0, sizeof(fe_loose));
  h->v[0] = 1;
}

static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  out[0] = (x5 + x23);
  out[1] = (x7 + x25);
  out[2] = (x9 + x27);
  out[3] = (x11 + x29);
  out[4] = (x13 + x31);
  out[5] = (x15 + x33);
  out[6] = (x17 + x35);
  out[7] = (x19 + x37);
  out[8] = (x21 + x39);
  out[9] = (x20 + x38);
  }}}}}}}}}}}}}}}}}}}}
}

// h = f + g
// Can overlap h with f or g.
static void fe_add(fe_loose *h, const fe *f, const fe *g) {
  assert_fe(f->v);
  assert_fe(g->v);
  fe_add_impl(h->v, f->v, g->v);
  assert_fe_loose(h->v);
}

static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  out[0] = ((0x7ffffda + x5) - x23);
  out[1] = ((0x3fffffe + x7) - x25);
  out[2] = ((0x7fffffe + x9) - x27);
  out[3] = ((0x3fffffe + x11) - x29);
  out[4] = ((0x7fffffe + x13) - x31);
  out[5] = ((0x3fffffe + x15) - x33);
  out[6] = ((0x7fffffe + x17) - x35);
  out[7] = ((0x3fffffe + x19) - x37);
  out[8] = ((0x7fffffe + x21) - x39);
  out[9] = ((0x3fffffe + x20) - x38);
  }}}}}}}}}}}}}}}}}}}}
}

// h = f - g
// Can overlap h with f or g.
static void fe_sub(fe_loose *h, const fe *f, const fe *g) {
  assert_fe(f->v);
  assert_fe(g->v);
  fe_sub_impl(h->v, f->v, g->v);
  assert_fe_loose(h->v);
}

static void fe_carry_impl(uint32_t out[10], const uint32_t in1[10]) {
  { const uint32_t x17 = in1[9];
  { const uint32_t x18 = in1[8];
  { const uint32_t x16 = in1[7];
  { const uint32_t x14 = in1[6];
  { const uint32_t x12 = in1[5];
  { const uint32_t x10 = in1[4];
  { const uint32_t x8 = in1[3];
  { const uint32_t x6 = in1[2];
  { const uint32_t x4 = in1[1];
  { const uint32_t x2 = in1[0];
  { uint32_t x19 = (x2 >> 0x1a);
  { uint32_t x20 = (x2 & 0x3ffffff);
  { uint32_t x21 = (x19 + x4);
  { uint32_t x22 = (x21 >> 0x19);
  { uint32_t x23 = (x21 & 0x1ffffff);
  { uint32_t x24 = (x22 + x6);
  { uint32_t x25 = (x24 >> 0x1a);
  { uint32_t x26 = (x24 & 0x3ffffff);
  { uint32_t x27 = (x25 + x8);
  { uint32_t x28 = (x27 >> 0x19);
  { uint32_t x29 = (x27 & 0x1ffffff);
  { uint32_t x30 = (x28 + x10);
  { uint32_t x31 = (x30 >> 0x1a);
  { uint32_t x32 = (x30 & 0x3ffffff);
  { uint32_t x33 = (x31 + x12);
  { uint32_t x34 = (x33 >> 0x19);
  { uint32_t x35 = (x33 & 0x1ffffff);
  { uint32_t x36 = (x34 + x14);
  { uint32_t x37 = (x36 >> 0x1a);
  { uint32_t x38 = (x36 & 0x3ffffff);
  { uint32_t x39 = (x37 + x16);
  { uint32_t x40 = (x39 >> 0x19);
  { uint32_t x41 = (x39 & 0x1ffffff);
  { uint32_t x42 = (x40 + x18);
  { uint32_t x43 = (x42 >> 0x1a);
  { uint32_t x44 = (x42 & 0x3ffffff);
  { uint32_t x45 = (x43 + x17);
  { uint32_t x46 = (x45 >> 0x19);
  { uint32_t x47 = (x45 & 0x1ffffff);
  { uint32_t x48 = (x20 + (0x13 * x46));
  { uint32_t x49 = (x48 >> 0x1a);
  { uint32_t x50 = (x48 & 0x3ffffff);
  { uint32_t x51 = (x49 + x23);
  { uint32_t x52 = (x51 >> 0x19);
  { uint32_t x53 = (x51 & 0x1ffffff);
  out[0] = x50;
  out[1] = x53;
  out[2] = (x52 + x26);
  out[3] = x29;
  out[4] = x32;
  out[5] = x35;
  out[6] = x38;
  out[7] = x41;
  out[8] = x44;
  out[9] = x47;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
}

static void fe_carry(fe *h, const fe_loose* f) {
  assert_fe_loose(f->v);
  fe_carry_impl(h->v, f->v);
  assert_fe(h->v);
}

static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
  assert_fe_loose(in1);
  assert_fe_loose(in2);
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  { uint64_t x40 = ((uint64_t)x23 * x5);
  { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
  { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
  { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
  { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
  { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
  { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
  { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
  { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
  { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
  { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
  { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
  { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
  { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
  { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
  { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
  { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
  { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
  { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
  { uint64_t x59 = (x48 + (x58 << 0x4));
  { uint64_t x60 = (x59 + (x58 << 0x1));
  { uint64_t x61 = (x60 + x58);
  { uint64_t x62 = (x47 + (x57 << 0x4));
  { uint64_t x63 = (x62 + (x57 << 0x1));
  { uint64_t x64 = (x63 + x57);
  { uint64_t x65 = (x46 + (x56 << 0x4));
  { uint64_t x66 = (x65 + (x56 << 0x1));
  { uint64_t x67 = (x66 + x56);
  { uint64_t x68 = (x45 + (x55 << 0x4));
  { uint64_t x69 = (x68 + (x55 << 0x1));
  { uint64_t x70 = (x69 + x55);
  { uint64_t x71 = (x44 + (x54 << 0x4));
  { uint64_t x72 = (x71 + (x54 << 0x1));
  { uint64_t x73 = (x72 + x54);
  { uint64_t x74 = (x43 + (x53 << 0x4));
  { uint64_t x75 = (x74 + (x53 << 0x1));
  { uint64_t x76 = (x75 + x53);
  { uint64_t x77 = (x42 + (x52 << 0x4));
  { uint64_t x78 = (x77 + (x52 << 0x1));
  { uint64_t x79 = (x78 + x52);
  { uint64_t x80 = (x41 + (x51 << 0x4));
  { uint64_t x81 = (x80 + (x51 << 0x1));
  { uint64_t x82 = (x81 + x51);
  { uint64_t x83 = (x40 + (x50 << 0x4));
  { uint64_t x84 = (x83 + (x50 << 0x1));
  { uint64_t x85 = (x84 + x50);
  { uint64_t x86 = (x85 >> 0x1a);
  { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
  { uint64_t x88 = (x86 + x82);
  { uint64_t x89 = (x88 >> 0x19);
  { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
  { uint64_t x91 = (x89 + x79);
  { uint64_t x92 = (x91 >> 0x1a);
  { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
  { uint64_t x94 = (x92 + x76);
  { uint64_t x95 = (x94 >> 0x19);
  { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
  { uint64_t x97 = (x95 + x73);
  { uint64_t x98 = (x97 >> 0x1a);
  { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
  { uint64_t x100 = (x98 + x70);
  { uint64_t x101 = (x100 >> 0x19);
  { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
  { uint64_t x103 = (x101 + x67);
  { uint64_t x104 = (x103 >> 0x1a);
  { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
  { uint64_t x106 = (x104 + x64);
  { uint64_t x107 = (x106 >> 0x19);
  { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
  { uint64_t x109 = (x107 + x61);
  { uint64_t x110 = (x109 >> 0x1a);
  { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
  { uint64_t x112 = (x110 + x49);
  { uint64_t x113 = (x112 >> 0x19);
  { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
  { uint64_t x115 = (x87 + (0x13 * x113));
  { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
  { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
  { uint32_t x118 = (x116 + x90);
  { uint32_t x119 = (x118 >> 0x19);
  { uint32_t x120 = (x118 & 0x1ffffff);
  out[0] = x117;
  out[1] = x120;
  out[2] = (x119 + x93);
  out[3] = x96;
  out[4] = x99;
  out[5] = x102;
  out[6] = x105;
  out[7] = x108;
  out[8] = x111;
  out[9] = x114;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_ttt(fe *h, const fe *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) {
  fe_mul_impl(h->v, f->v, g->v);
}

static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) {
  assert_fe_loose(in1);
  { const uint32_t x17 = in1[9];
  { const uint32_t x18 = in1[8];
  { const uint32_t x16 = in1[7];
  { const uint32_t x14 = in1[6];
  { const uint32_t x12 = in1[5];
  { const uint32_t x10 = in1[4];
  { const uint32_t x8 = in1[3];
  { const uint32_t x6 = in1[2];
  { const uint32_t x4 = in1[1];
  { const uint32_t x2 = in1[0];
  { uint64_t x19 = ((uint64_t)x2 * x2);
  { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
  { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
  { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
  { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
  { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
  { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
  { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
  { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
  { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
  { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
  { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
  { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
  { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
  { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
  { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
  { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
  { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
  { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
  { uint64_t x38 = (x27 + (x37 << 0x4));
  { uint64_t x39 = (x38 + (x37 << 0x1));
  { uint64_t x40 = (x39 + x37);
  { uint64_t x41 = (x26 + (x36 << 0x4));
  { uint64_t x42 = (x41 + (x36 << 0x1));
  { uint64_t x43 = (x42 + x36);
  { uint64_t x44 = (x25 + (x35 << 0x4));
  { uint64_t x45 = (x44 + (x35 << 0x1));
  { uint64_t x46 = (x45 + x35);
  { uint64_t x47 = (x24 + (x34 << 0x4));
  { uint64_t x48 = (x47 + (x34 << 0x1));
  { uint64_t x49 = (x48 + x34);
  { uint64_t x50 = (x23 + (x33 << 0x4));
  { uint64_t x51 = (x50 + (x33 << 0x1));
  { uint64_t x52 = (x51 + x33);
  { uint64_t x53 = (x22 + (x32 << 0x4));
  { uint64_t x54 = (x53 + (x32 << 0x1));
  { uint64_t x55 = (x54 + x32);
  { uint64_t x56 = (x21 + (x31 << 0x4));
  { uint64_t x57 = (x56 + (x31 << 0x1));
  { uint64_t x58 = (x57 + x31);
  { uint64_t x59 = (x20 + (x30 << 0x4));
  { uint64_t x60 = (x59 + (x30 << 0x1));
  { uint64_t x61 = (x60 + x30);
  { uint64_t x62 = (x19 + (x29 << 0x4));
  { uint64_t x63 = (x62 + (x29 << 0x1));
  { uint64_t x64 = (x63 + x29);
  { uint64_t x65 = (x64 >> 0x1a);
  { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
  { uint64_t x67 = (x65 + x61);
  { uint64_t x68 = (x67 >> 0x19);
  { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
  { uint64_t x70 = (x68 + x58);
  { uint64_t x71 = (x70 >> 0x1a);
  { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
  { uint64_t x73 = (x71 + x55);
  { uint64_t x74 = (x73 >> 0x19);
  { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
  { uint64_t x76 = (x74 + x52);
  { uint64_t x77 = (x76 >> 0x1a);
  { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
  { uint64_t x79 = (x77 + x49);
  { uint64_t x80 = (x79 >> 0x19);
  { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
  { uint64_t x82 = (x80 + x46);
  { uint64_t x83 = (x82 >> 0x1a);
  { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
  { uint64_t x85 = (x83 + x43);
  { uint64_t x86 = (x85 >> 0x19);
  { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
  { uint64_t x88 = (x86 + x40);
  { uint64_t x89 = (x88 >> 0x1a);
  { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
  { uint64_t x91 = (x89 + x28);
  { uint64_t x92 = (x91 >> 0x19);
  { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
  { uint64_t x94 = (x66 + (0x13 * x92));
  { uint32_t x95 = (uint32_t) (x94 >> 0x1a);
  { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
  { uint32_t x97 = (x95 + x69);
  { uint32_t x98 = (x97 >> 0x19);
  { uint32_t x99 = (x97 & 0x1ffffff);
  out[0] = x96;
  out[1] = x99;
  out[2] = (x98 + x72);
  out[3] = x75;
  out[4] = x78;
  out[5] = x81;
  out[6] = x84;
  out[7] = x87;
  out[8] = x90;
  out[9] = x93;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  assert_fe(out);
}

static void fe_sq_tl(fe *h, const fe_loose *f) {
  fe_sqr_impl(h->v, f->v);
}

static void fe_sq_tt(fe *h, const fe *f) {
  fe_sqr_impl(h->v, f->v);
}

// Replace (f,g) with (g,f) if b == 1;
// replace (f,g) with (f,g) if b == 0.
//
// Preconditions: b in {0,1}.
static void fe_cswap(fe *f, fe *g, unsigned int b) {
  b = 0-b;
  unsigned i;
  for (i = 0; i < 10; i++) {
    uint32_t x = f->v[i] ^ g->v[i];
    x &= b;
    f->v[i] ^= x;
    g->v[i] ^= x;
  }
}

// NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0..
static void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) {
  { const uint32_t x20 = in1[9];
  { const uint32_t x21 = in1[8];
  { const uint32_t x19 = in1[7];
  { const uint32_t x17 = in1[6];
  { const uint32_t x15 = in1[5];
  { const uint32_t x13 = in1[4];
  { const uint32_t x11 = in1[3];
  { const uint32_t x9 = in1[2];
  { const uint32_t x7 = in1[1];
  { const uint32_t x5 = in1[0];
  { const uint32_t x38 = 0;
  { const uint32_t x39 = 0;
  { const uint32_t x37 = 0;
  { const uint32_t x35 = 0;
  { const uint32_t x33 = 0;
  { const uint32_t x31 = 0;
  { const uint32_t x29 = 0;
  { const uint32_t x27 = 0;
  { const uint32_t x25 = 0;
  { const uint32_t x23 = 121666;
  { uint64_t x40 = ((uint64_t)x23 * x5);
  { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
  { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
  { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
  { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
  { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
  { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
  { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
  { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
  { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
  { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
  { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
  { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
  { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
  { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
  { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
  { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
  { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
  { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
  { uint64_t x59 = (x48 + (x58 << 0x4));
  { uint64_t x60 = (x59 + (x58 << 0x1));
  { uint64_t x61 = (x60 + x58);
  { uint64_t x62 = (x47 + (x57 << 0x4));
  { uint64_t x63 = (x62 + (x57 << 0x1));
  { uint64_t x64 = (x63 + x57);
  { uint64_t x65 = (x46 + (x56 << 0x4));
  { uint64_t x66 = (x65 + (x56 << 0x1));
  { uint64_t x67 = (x66 + x56);
  { uint64_t x68 = (x45 + (x55 << 0x4));
  { uint64_t x69 = (x68 + (x55 << 0x1));
  { uint64_t x70 = (x69 + x55);
  { uint64_t x71 = (x44 + (x54 << 0x4));
  { uint64_t x72 = (x71 + (x54 << 0x1));
  { uint64_t x73 = (x72 + x54);
  { uint64_t x74 = (x43 + (x53 << 0x4));
  { uint64_t x75 = (x74 + (x53 << 0x1));
  { uint64_t x76 = (x75 + x53);
  { uint64_t x77 = (x42 + (x52 << 0x4));
  { uint64_t x78 = (x77 + (x52 << 0x1));
  { uint64_t x79 = (x78 + x52);
  { uint64_t x80 = (x41 + (x51 << 0x4));
  { uint64_t x81 = (x80 + (x51 << 0x1));
  { uint64_t x82 = (x81 + x51);
  { uint64_t x83 = (x40 + (x50 << 0x4));
  { uint64_t x84 = (x83 + (x50 << 0x1));
  { uint64_t x85 = (x84 + x50);
  { uint64_t x86 = (x85 >> 0x1a);
  { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
  { uint64_t x88 = (x86 + x82);
  { uint64_t x89 = (x88 >> 0x19);
  { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
  { uint64_t x91 = (x89 + x79);
  { uint64_t x92 = (x91 >> 0x1a);
  { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
  { uint64_t x94 = (x92 + x76);
  { uint64_t x95 = (x94 >> 0x19);
  { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
  { uint64_t x97 = (x95 + x73);
  { uint64_t x98 = (x97 >> 0x1a);
  { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
  { uint64_t x100 = (x98 + x70);
  { uint64_t x101 = (x100 >> 0x19);
  { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
  { uint64_t x103 = (x101 + x67);
  { uint64_t x104 = (x103 >> 0x1a);
  { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
  { uint64_t x106 = (x104 + x64);
  { uint64_t x107 = (x106 >> 0x19);
  { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
  { uint64_t x109 = (x107 + x61);
  { uint64_t x110 = (x109 >> 0x1a);
  { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
  { uint64_t x112 = (x110 + x49);
  { uint64_t x113 = (x112 >> 0x19);
  { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
  { uint64_t x115 = (x87 + (0x13 * x113));
  { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
  { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
  { uint32_t x118 = (x116 + x90);
  { uint32_t x119 = (x118 >> 0x19);
  { uint32_t x120 = (x118 & 0x1ffffff);
  out[0] = x117;
  out[1] = x120;
  out[2] = (x119 + x93);
  out[3] = x96;
  out[4] = x99;
  out[5] = x102;
  out[6] = x105;
  out[7] = x108;
  out[8] = x111;
  out[9] = x114;
  }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
}

static void fe_mul121666(fe *h, const fe_loose *f) {
  assert_fe_loose(f->v);
  fe_mul_121666_impl(h->v, f->v);
  assert_fe(h->v);
}

// Adapted from Fiat-synthesized |fe_sub_impl| with |out| = 0.
static void fe_neg_impl(uint32_t out[10], const uint32_t in2[10]) {
  { const uint32_t x20 = 0;
  { const uint32_t x21 = 0;
  { const uint32_t x19 = 0;
  { const uint32_t x17 = 0;
  { const uint32_t x15 = 0;
  { const uint32_t x13 = 0;
  { const uint32_t x11 = 0;
  { const uint32_t x9 = 0;
  { const uint32_t x7 = 0;
  { const uint32_t x5 = 0;
  { const uint32_t x38 = in2[9];
  { const uint32_t x39 = in2[8];
  { const uint32_t x37 = in2[7];
  { const uint32_t x35 = in2[6];
  { const uint32_t x33 = in2[5];
  { const uint32_t x31 = in2[4];
  { const uint32_t x29 = in2[3];
  { const uint32_t x27 = in2[2];
  { const uint32_t x25 = in2[1];
  { const uint32_t x23 = in2[0];
  out[0] = ((0x7ffffda + x5) - x23);
  out[1] = ((0x3fffffe + x7) - x25);
  out[2] = ((0x7fffffe + x9) - x27);
  out[3] = ((0x3fffffe + x11) - x29);
  out[4] = ((0x7fffffe + x13) - x31);
  out[5] = ((0x3fffffe + x15) - x33);
  out[6] = ((0x7fffffe + x17) - x35);
  out[7] = ((0x3fffffe + x19) - x37);
  out[8] = ((0x7fffffe + x21) - x39);
  out[9] = ((0x3fffffe + x20) - x38);
  }}}}}}}}}}}}}}}}}}}}
}

// h = -f
static void fe_neg(fe_loose *h, const fe *f) {
  assert_fe(f->v);
  fe_neg_impl(h->v, f->v);
  assert_fe_loose(h->v);
}

// 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 fe_cmov(fe_loose *f, const fe_loose *g, unsigned b) {
  b = 0-b;
  unsigned i;
  for (i = 0; i < 10; i++) {
    uint32_t x = f->v[i] ^ g->v[i];
    x &= b;
    f->v[i] ^= x;
  }
}

#endif  // BORINGSSL_CURVE25519_64BIT

// h = f
static void fe_copy(fe *h, const fe *f) {
  OPENSSL_memmove(h, f, sizeof(fe));
}

static void fe_copy_lt(fe_loose *h, const fe *f) {
  OPENSSL_STATIC_ASSERT(sizeof(fe_loose) == sizeof(fe),
                        "fe and fe_loose mismatch");
  OPENSSL_memmove(h, f, sizeof(fe));
}
#if !defined(OPENSSL_SMALL)
static void fe_copy_ll(fe_loose *h, const fe_loose *f) {
  OPENSSL_memmove(h, f, sizeof(fe_loose));
}
#endif // !defined(OPENSSL_SMALL)

static void fe_loose_invert(fe *out, const fe_loose *z) {
  fe t0;
  fe t1;
  fe t2;
  fe t3;
  int i;

  fe_sq_tl(&t0, z);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 2; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_tlt(&t1, z, &t1);
  fe_mul_ttt(&t0, &t0, &t1);
  fe_sq_tt(&t2, &t0);
  fe_mul_ttt(&t1, &t1, &t2);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 5; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t2, &t2, &t1);
  fe_sq_tt(&t3, &t2);
  for (i = 1; i < 20; ++i) {
    fe_sq_tt(&t3, &t3);
  }
  fe_mul_ttt(&t2, &t3, &t2);
  fe_sq_tt(&t2, &t2);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t2, &t2, &t1);
  fe_sq_tt(&t3, &t2);
  for (i = 1; i < 100; ++i) {
    fe_sq_tt(&t3, &t3);
  }
  fe_mul_ttt(&t2, &t3, &t2);
  fe_sq_tt(&t2, &t2);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t1, &t1);
  for (i = 1; i < 5; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(out, &t1, &t0);
}

static void fe_invert(fe *out, const fe *z) {
  fe_loose l;
  fe_copy_lt(&l, z);
  fe_loose_invert(out, &l);
}

// return 0 if f == 0
// return 1 if f != 0
static int fe_isnonzero(const fe_loose *f) {
  fe tight;
  fe_carry(&tight, f);
  uint8_t s[32];
  fe_tobytes(s, &tight);

  static const uint8_t zero[32] = {0};
  return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
}

// return 1 if f is in {1,3,5,...,q-2}
// return 0 if f is in {0,2,4,...,q-1}
static int fe_isnegative(const fe *f) {
  uint8_t s[32];
  fe_tobytes(s, f);
  return s[0] & 1;
}

static void fe_sq2_tt(fe *h, const fe *f) {
  // h = f^2
  fe_sq_tt(h, f);

  // h = h + h
  fe_loose tmp;
  fe_add(&tmp, h, h);
  fe_carry(h, &tmp);
}

static void fe_pow22523(fe *out, const fe *z) {
  fe t0;
  fe t1;
  fe t2;
  int i;

  fe_sq_tt(&t0, z);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 2; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t1, z, &t1);
  fe_mul_ttt(&t0, &t0, &t1);
  fe_sq_tt(&t0, &t0);
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 5; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t1, &t1, &t0);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 20; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t1, &t1);
  for (i = 1; i < 10; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t1, &t0);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t1, &t1, &t0);
  fe_sq_tt(&t2, &t1);
  for (i = 1; i < 100; ++i) {
    fe_sq_tt(&t2, &t2);
  }
  fe_mul_ttt(&t1, &t2, &t1);
  fe_sq_tt(&t1, &t1);
  for (i = 1; i < 50; ++i) {
    fe_sq_tt(&t1, &t1);
  }
  fe_mul_ttt(&t0, &t1, &t0);
  fe_sq_tt(&t0, &t0);
  for (i = 1; i < 2; ++i) {
    fe_sq_tt(&t0, &t0);
  }
  fe_mul_ttt(out, &t0, z);
}


// Group operations.

void x25519_ge_tobytes(uint8_t s[32], const ge_p2 *h) {
  fe recip;
  fe x;
  fe y;

  fe_invert(&recip, &h->Z);
  fe_mul_ttt(&x, &h->X, &recip);
  fe_mul_ttt(&y, &h->Y, &recip);
  fe_tobytes(s, &y);
  s[31] ^= fe_isnegative(&x) << 7;
}

static void ge_p3_tobytes(uint8_t s[32], const ge_p3 *h) {
  fe recip;
  fe x;
  fe y;

  fe_invert(&recip, &h->Z);
  fe_mul_ttt(&x, &h->X, &recip);
  fe_mul_ttt(&y, &h->Y, &recip);
  fe_tobytes(s, &y);
  s[31] ^= fe_isnegative(&x) << 7;
}

int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
  fe u;
  fe_loose v;
  fe v3;
  fe vxx;
  fe_loose check;

  fe_frombytes(&h->Y, s);
  fe_1(&h->Z);
  fe_sq_tt(&v3, &h->Y);
  fe_mul_ttt(&vxx, &v3, &d);
  fe_sub(&v, &v3, &h->Z);  // u = y^2-1
  fe_carry(&u, &v);
  fe_add(&v, &vxx, &h->Z);  // v = dy^2+1

  fe_sq_tl(&v3, &v);
  fe_mul_ttl(&v3, &v3, &v);  // v3 = v^3
  fe_sq_tt(&h->X, &v3);
  fe_mul_ttl(&h->X, &h->X, &v);
  fe_mul_ttt(&h->X, &h->X, &u);  // x = uv^7

  fe_pow22523(&h->X, &h->X);  // x = (uv^7)^((q-5)/8)
  fe_mul_ttt(&h->X, &h->X, &v3);
  fe_mul_ttt(&h->X, &h->X, &u);  // x = uv^3(uv^7)^((q-5)/8)

  fe_sq_tt(&vxx, &h->X);
  fe_mul_ttl(&vxx, &vxx, &v);
  fe_sub(&check, &vxx, &u);
  if (fe_isnonzero(&check)) {
    fe_add(&check, &vxx, &u);
    if (fe_isnonzero(&check)) {
      return 0;
    }
    fe_mul_ttt(&h->X, &h->X, &sqrtm1);
  }

  if (fe_isnegative(&h->X) != (s[31] >> 7)) {
    fe_loose t;
    fe_neg(&t, &h->X);
    fe_carry(&h->X, &t);
  }

  fe_mul_ttt(&h->T, &h->X, &h->Y);
  return 1;
}

static void ge_p2_0(ge_p2 *h) {
  fe_0(&h->X);
  fe_1(&h->Y);
  fe_1(&h->Z);
}

static void ge_p3_0(ge_p3 *h) {
  fe_0(&h->X);
  fe_1(&h->Y);
  fe_1(&h->Z);
  fe_0(&h->T);
}

static void ge_cached_0(ge_cached *h) {
  fe_loose_1(&h->YplusX);
  fe_loose_1(&h->YminusX);
  fe_loose_1(&h->Z);
  fe_loose_0(&h->T2d);
}

static void ge_precomp_0(ge_precomp *h) {
  fe_loose_1(&h->yplusx);
  fe_loose_1(&h->yminusx);
  fe_loose_0(&h->xy2d);
}

// r = p
static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
  fe_copy(&r->X, &p->X);
  fe_copy(&r->Y, &p->Y);
  fe_copy(&r->Z, &p->Z);
}

// r = p
void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
  fe_add(&r->YplusX, &p->Y, &p->X);
  fe_sub(&r->YminusX, &p->Y, &p->X);
  fe_copy_lt(&r->Z, &p->Z);
  fe_mul_ltt(&r->T2d, &p->T, &d2);
}

// r = p
void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
  fe_mul_tll(&r->X, &p->X, &p->T);
  fe_mul_tll(&r->Y, &p->Y, &p->Z);
  fe_mul_tll(&r->Z, &p->Z, &p->T);
}

// r = p
void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
  fe_mul_tll(&r->X, &p->X, &p->T);
  fe_mul_tll(&r->Y, &p->Y, &p->Z);
  fe_mul_tll(&r->Z, &p->Z, &p->T);
  fe_mul_tll(&r->T, &p->X, &p->Y);
}

// r = p
static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) {
  ge_p3 t;
  x25519_ge_p1p1_to_p3(&t, p);
  x25519_ge_p3_to_cached(r, &t);
}

// r = 2 * p
static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
  fe trX, trZ, trT;
  fe t0;

  fe_sq_tt(&trX, &p->X);
  fe_sq_tt(&trZ, &p->Y);
  fe_sq2_tt(&trT, &p->Z);
  fe_add(&r->Y, &p->X, &p->Y);
  fe_sq_tl(&t0, &r->Y);

  fe_add(&r->Y, &trZ, &trX);
  fe_sub(&r->Z, &trZ, &trX);
  fe_carry(&trZ, &r->Y);
  fe_sub(&r->X, &t0, &trZ);
  fe_carry(&trZ, &r->Z);
  fe_sub(&r->T, &trT, &trZ);
}

// r = 2 * p
static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
  ge_p2 q;
  ge_p3_to_p2(&q, p);
  ge_p2_dbl(r, &q);
}

// r = p + q
static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
  fe trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->yplusx);
  fe_mul_tll(&trY, &r->Y, &q->yminusx);
  fe_mul_tlt(&trT, &q->xy2d, &p->T);
  fe_add(&r->T, &p->Z, &p->Z);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_add(&r->Z, &trZ, &trT);
  fe_sub(&r->T, &trZ, &trT);
}

// r = p - q
static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
  fe trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->yminusx);
  fe_mul_tll(&trY, &r->Y, &q->yplusx);
  fe_mul_tlt(&trT, &q->xy2d, &p->T);
  fe_add(&r->T, &p->Z, &p->Z);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_sub(&r->Z, &trZ, &trT);
  fe_add(&r->T, &trZ, &trT);
}

// r = p + q
void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
  fe trX, trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->YplusX);
  fe_mul_tll(&trY, &r->Y, &q->YminusX);
  fe_mul_tlt(&trT, &q->T2d, &p->T);
  fe_mul_ttl(&trX, &p->Z, &q->Z);
  fe_add(&r->T, &trX, &trX);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_add(&r->Z, &trZ, &trT);
  fe_sub(&r->T, &trZ, &trT);
}

// r = p - q
void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
  fe trX, trY, trZ, trT;

  fe_add(&r->X, &p->Y, &p->X);
  fe_sub(&r->Y, &p->Y, &p->X);
  fe_mul_tll(&trZ, &r->X, &q->YminusX);
  fe_mul_tll(&trY, &r->Y, &q->YplusX);
  fe_mul_tlt(&trT, &q->T2d, &p->T);
  fe_mul_ttl(&trX, &p->Z, &q->Z);
  fe_add(&r->T, &trX, &trX);
  fe_sub(&r->X, &trZ, &trY);
  fe_add(&r->Y, &trZ, &trY);
  fe_carry(&trZ, &r->T);
  fe_sub(&r->Z, &trZ, &trT);
  fe_add(&r->T, &trZ, &trT);
}

static uint8_t equal(signed char b, signed char c) {
  uint8_t ub = b;
  uint8_t uc = c;
  uint8_t x = ub ^ uc;  // 0: yes; 1..255: no
  uint32_t y = x;       // 0: yes; 1..255: no
  y -= 1;               // 4294967295: yes; 0..254: no
  y >>= 31;             // 1: yes; 0: no
  return y;
}

static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
  fe_cmov(&t->yplusx, &u->yplusx, b);
  fe_cmov(&t->yminusx, &u->yminusx, b);
  fe_cmov(&t->xy2d, &u->xy2d, b);
}

void x25519_ge_scalarmult_small_precomp(
    ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) {
  // precomp_table is first expanded into matching |ge_precomp|
  // elements.
  ge_precomp multiples[15];

  unsigned i;
  for (i = 0; i < 15; i++) {
    const uint8_t *bytes = &precomp_table[i*(2 * 32)];
    fe x, y;
    fe_frombytes(&x, bytes);
    fe_frombytes(&y, bytes + 32);

    ge_precomp *out = &multiples[i];
    fe_add(&out->yplusx, &y, &x);
    fe_sub(&out->yminusx, &y, &x);
    fe_mul_ltt(&out->xy2d, &x, &y);
    fe_mul_llt(&out->xy2d, &out->xy2d, &d2);
  }

  // See the comment above |k25519SmallPrecomp| about the structure of the
  // precomputed elements. This loop does 64 additions and 64 doublings to
  // calculate the result.
  ge_p3_0(h);

  for (i = 63; i < 64; i--) {
    unsigned j;
    signed char index = 0;

    for (j = 0; j < 4; j++) {
      const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
      index |= (bit << j);
    }

    ge_precomp e;
    ge_precomp_0(&e);

    for (j = 1; j < 16; j++) {
      cmov(&e, &multiples[j-1], equal(index, j));
    }

    ge_cached cached;
    ge_p1p1 r;
    x25519_ge_p3_to_cached(&cached, h);
    x25519_ge_add(&r, h, &cached);
    x25519_ge_p1p1_to_p3(h, &r);

    ge_madd(&r, h, &e);
    x25519_ge_p1p1_to_p3(h, &r);
  }
}

#if defined(OPENSSL_SMALL)

void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
  x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp);
}

#else

static uint8_t negative(signed char b) {
  uint32_t x = b;
  x >>= 31;  // 1: yes; 0: no
  return x;
}

static void table_select(ge_precomp *t, int pos, signed char b) {
  ge_precomp minust;
  uint8_t bnegative = negative(b);
  uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);

  ge_precomp_0(t);
  cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
  cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
  cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
  cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
  cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
  cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
  cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
  cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
  fe_copy_ll(&minust.yplusx, &t->yminusx);
  fe_copy_ll(&minust.yminusx, &t->yplusx);

  // NOTE: the input table is canonical, but types don't encode it
  fe tmp;
  fe_carry(&tmp, &t->xy2d);
  fe_neg(&minust.xy2d, &tmp);

  cmov(t, &minust, bnegative);
}

// h = a * B
// where a = a[0]+256*a[1]+...+256^31 a[31]
// B is the Ed25519 base point (x,4/5) with x positive.
//
// Preconditions:
//   a[31] <= 127
void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
  signed char e[64];
  signed char carry;
  ge_p1p1 r;
  ge_p2 s;
  ge_precomp t;
  int i;

  for (i = 0; i < 32; ++i) {
    e[2 * i + 0] = (a[i] >> 0) & 15;
    e[2 * i + 1] = (a[i] >> 4) & 15;
  }
  // each e[i] is between 0 and 15
  // e[63] is between 0 and 7

  carry = 0;
  for (i = 0; i < 63; ++i) {
    e[i] += carry;
    carry = e[i] + 8;
    carry >>= 4;
    e[i] -= carry << 4;
  }
  e[63] += carry;
  // each e[i] is between -8 and 8

  ge_p3_0(h);
  for (i = 1; i < 64; i += 2) {
    table_select(&t, i / 2, e[i]);
    ge_madd(&r, h, &t);
    x25519_ge_p1p1_to_p3(h, &r);
  }

  ge_p3_dbl(&r, h);
  x25519_ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s);
  x25519_ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s);
  x25519_ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s);
  x25519_ge_p1p1_to_p3(h, &r);

  for (i = 0; i < 64; i += 2) {
    table_select(&t, i / 2, e[i]);
    ge_madd(&r, h, &t);
    x25519_ge_p1p1_to_p3(h, &r);
  }
}

#endif

static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) {
  fe_cmov(&t->YplusX, &u->YplusX, b);
  fe_cmov(&t->YminusX, &u->YminusX, b);
  fe_cmov(&t->Z, &u->Z, b);
  fe_cmov(&t->T2d, &u->T2d, b);
}

// r = scalar * A.
// where a = a[0]+256*a[1]+...+256^31 a[31].
void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) {
  ge_p2 Ai_p2[8];
  ge_cached Ai[16];
  ge_p1p1 t;

  ge_cached_0(&Ai[0]);
  x25519_ge_p3_to_cached(&Ai[1], A);
  ge_p3_to_p2(&Ai_p2[1], A);

  unsigned i;
  for (i = 2; i < 16; i += 2) {
    ge_p2_dbl(&t, &Ai_p2[i / 2]);
    ge_p1p1_to_cached(&Ai[i], &t);
    if (i < 8) {
      x25519_ge_p1p1_to_p2(&Ai_p2[i], &t);
    }
    x25519_ge_add(&t, A, &Ai[i]);
    ge_p1p1_to_cached(&Ai[i + 1], &t);
    if (i < 7) {
      x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t);
    }
  }

  ge_p2_0(r);
  ge_p3 u;

  for (i = 0; i < 256; i += 4) {
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    x25519_ge_p1p1_to_p3(&u, &t);

    uint8_t index = scalar[31 - i/8];
    index >>= 4 - (i & 4);
    index &= 0xf;

    unsigned j;
    ge_cached selected;
    ge_cached_0(&selected);
    for (j = 0; j < 16; j++) {
      cmov_cached(&selected, &Ai[j], equal(j, index));
    }

    x25519_ge_add(&t, &u, &selected);
    x25519_ge_p1p1_to_p2(r, &t);
  }
}

static void slide(signed char *r, const uint8_t *a) {
  int i;
  int b;
  int k;

  for (i = 0; i < 256; ++i) {
    r[i] = 1 & (a[i >> 3] >> (i & 7));
  }

  for (i = 0; i < 256; ++i) {
    if (r[i]) {
      for (b = 1; b <= 6 && i + b < 256; ++b) {
        if (r[i + b]) {
          if (r[i] + (r[i + b] << b) <= 15) {
            r[i] += r[i + b] << b;
            r[i + b] = 0;
          } else if (r[i] - (r[i + b] << b) >= -15) {
            r[i] -= r[i + b] << b;
            for (k = i + b; k < 256; ++k) {
              if (!r[k]) {
                r[k] = 1;
                break;
              }
              r[k] = 0;
            }
          } else {
            break;
          }
        }
      }
    }
  }
}

// r = a * A + b * B
// where a = a[0]+256*a[1]+...+256^31 a[31].
// and b = b[0]+256*b[1]+...+256^31 b[31].
// B is the Ed25519 base point (x,4/5) with x positive.
static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
                                         const ge_p3 *A, const uint8_t *b) {
  signed char aslide[256];
  signed char bslide[256];
  ge_cached Ai[8];  // A,3A,5A,7A,9A,11A,13A,15A
  ge_p1p1 t;
  ge_p3 u;
  ge_p3 A2;
  int i;

  slide(aslide, a);
  slide(bslide, b);

  x25519_ge_p3_to_cached(&Ai[0], A);
  ge_p3_dbl(&t, A);
  x25519_ge_p1p1_to_p3(&A2, &t);
  x25519_ge_add(&t, &A2, &Ai[0]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[1], &u);
  x25519_ge_add(&t, &A2, &Ai[1]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[2], &u);
  x25519_ge_add(&t, &A2, &Ai[2]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[3], &u);
  x25519_ge_add(&t, &A2, &Ai[3]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[4], &u);
  x25519_ge_add(&t, &A2, &Ai[4]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[5], &u);
  x25519_ge_add(&t, &A2, &Ai[5]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[6], &u);
  x25519_ge_add(&t, &A2, &Ai[6]);
  x25519_ge_p1p1_to_p3(&u, &t);
  x25519_ge_p3_to_cached(&Ai[7], &u);

  ge_p2_0(r);

  for (i = 255; i >= 0; --i) {
    if (aslide[i] || bslide[i]) {
      break;
    }
  }

  for (; i >= 0; --i) {
    ge_p2_dbl(&t, r);

    if (aslide[i] > 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]);
    } else if (aslide[i] < 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
    }

    if (bslide[i] > 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      ge_madd(&t, &u, &Bi[bslide[i] / 2]);
    } else if (bslide[i] < 0) {
      x25519_ge_p1p1_to_p3(&u, &t);
      ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
    }

    x25519_ge_p1p1_to_p2(r, &t);
  }
}

// The set of scalars is \Z/l
// where l = 2^252 + 27742317777372353535851937790883648493.

// Input:
//   s[0]+256*s[1]+...+256^63*s[63] = s
//
// Output:
//   s[0]+256*s[1]+...+256^31*s[31] = s mod l
//   where l = 2^252 + 27742317777372353535851937790883648493.
//   Overwrites s in place.
void x25519_sc_reduce(uint8_t s[64]) {
  int64_t s0 = 2097151 & load_3(s);
  int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
  int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
  int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
  int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
  int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
  int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
  int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
  int64_t s8 = 2097151 & load_3(s + 21);
  int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
  int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
  int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
  int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
  int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
  int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
  int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
  int64_t s16 = 2097151 & load_3(s + 42);
  int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
  int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
  int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
  int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
  int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
  int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
  int64_t s23 = (load_4(s + 60) >> 3);
  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;
  int64_t carry10;
  int64_t carry11;
  int64_t carry12;
  int64_t carry13;
  int64_t carry14;
  int64_t carry15;
  int64_t carry16;

  s11 += s23 * 666643;
  s12 += s23 * 470296;
  s13 += s23 * 654183;
  s14 -= s23 * 997805;
  s15 += s23 * 136657;
  s16 -= s23 * 683901;
  s23 = 0;

  s10 += s22 * 666643;
  s11 += s22 * 470296;
  s12 += s22 * 654183;
  s13 -= s22 * 997805;
  s14 += s22 * 136657;
  s15 -= s22 * 683901;
  s22 = 0;

  s9 += s21 * 666643;
  s10 += s21 * 470296;
  s11 += s21 * 654183;
  s12 -= s21 * 997805;
  s13 += s21 * 136657;
  s14 -= s21 * 683901;
  s21 = 0;

  s8 += s20 * 666643;
  s9 += s20 * 470296;
  s10 += s20 * 654183;
  s11 -= s20 * 997805;
  s12 += s20 * 136657;
  s13 -= s20 * 683901;
  s20 = 0;

  s7 += s19 * 666643;
  s8 += s19 * 470296;
  s9 += s19 * 654183;
  s10 -= s19 * 997805;
  s11 += s19 * 136657;
  s12 -= s19 * 683901;
  s19 = 0;

  s6 += s18 * 666643;
  s7 += s18 * 470296;
  s8 += s18 * 654183;
  s9 -= s18 * 997805;
  s10 += s18 * 136657;
  s11 -= s18 * 683901;
  s18 = 0;

  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry12 = (s12 + (1 << 20)) >> 21;
  s13 += carry12;
  s12 -= carry12 << 21;
  carry14 = (s14 + (1 << 20)) >> 21;
  s15 += carry14;
  s14 -= carry14 << 21;
  carry16 = (s16 + (1 << 20)) >> 21;
  s17 += carry16;
  s16 -= carry16 << 21;

  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;
  carry13 = (s13 + (1 << 20)) >> 21;
  s14 += carry13;
  s13 -= carry13 << 21;
  carry15 = (s15 + (1 << 20)) >> 21;
  s16 += carry15;
  s15 -= carry15 << 21;

  s5 += s17 * 666643;
  s6 += s17 * 470296;
  s7 += s17 * 654183;
  s8 -= s17 * 997805;
  s9 += s17 * 136657;
  s10 -= s17 * 683901;
  s17 = 0;

  s4 += s16 * 666643;
  s5 += s16 * 470296;
  s6 += s16 * 654183;
  s7 -= s16 * 997805;
  s8 += s16 * 136657;
  s9 -= s16 * 683901;
  s16 = 0;

  s3 += s15 * 666643;
  s4 += s15 * 470296;
  s5 += s15 * 654183;
  s6 -= s15 * 997805;
  s7 += s15 * 136657;
  s8 -= s15 * 683901;
  s15 = 0;

  s2 += s14 * 666643;
  s3 += s14 * 470296;
  s4 += s14 * 654183;
  s5 -= s14 * 997805;
  s6 += s14 * 136657;
  s7 -= s14 * 683901;
  s14 = 0;

  s1 += s13 * 666643;
  s2 += s13 * 470296;
  s3 += s13 * 654183;
  s4 -= s13 * 997805;
  s5 += s13 * 136657;
  s6 -= s13 * 683901;
  s13 = 0;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = (s0 + (1 << 20)) >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry2 = (s2 + (1 << 20)) >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry4 = (s4 + (1 << 20)) >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  carry1 = (s1 + (1 << 20)) >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry3 = (s3 + (1 << 20)) >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry5 = (s5 + (1 << 20)) >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry11 = s11 >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  s[0] = s0 >> 0;
  s[1] = s0 >> 8;
  s[2] = (s0 >> 16) | (s1 << 5);
  s[3] = s1 >> 3;
  s[4] = s1 >> 11;
  s[5] = (s1 >> 19) | (s2 << 2);
  s[6] = s2 >> 6;
  s[7] = (s2 >> 14) | (s3 << 7);
  s[8] = s3 >> 1;
  s[9] = s3 >> 9;
  s[10] = (s3 >> 17) | (s4 << 4);
  s[11] = s4 >> 4;
  s[12] = s4 >> 12;
  s[13] = (s4 >> 20) | (s5 << 1);
  s[14] = s5 >> 7;
  s[15] = (s5 >> 15) | (s6 << 6);
  s[16] = s6 >> 2;
  s[17] = s6 >> 10;
  s[18] = (s6 >> 18) | (s7 << 3);
  s[19] = s7 >> 5;
  s[20] = s7 >> 13;
  s[21] = s8 >> 0;
  s[22] = s8 >> 8;
  s[23] = (s8 >> 16) | (s9 << 5);
  s[24] = s9 >> 3;
  s[25] = s9 >> 11;
  s[26] = (s9 >> 19) | (s10 << 2);
  s[27] = s10 >> 6;
  s[28] = (s10 >> 14) | (s11 << 7);
  s[29] = s11 >> 1;
  s[30] = s11 >> 9;
  s[31] = s11 >> 17;
}

// Input:
//   a[0]+256*a[1]+...+256^31*a[31] = a
//   b[0]+256*b[1]+...+256^31*b[31] = b
//   c[0]+256*c[1]+...+256^31*c[31] = c
//
// Output:
//   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
//   where l = 2^252 + 27742317777372353535851937790883648493.
static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
                      const uint8_t *c) {
  int64_t a0 = 2097151 & load_3(a);
  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
  int64_t a8 = 2097151 & load_3(a + 21);
  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
  int64_t a11 = (load_4(a + 28) >> 7);
  int64_t b0 = 2097151 & load_3(b);
  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
  int64_t b8 = 2097151 & load_3(b + 21);
  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
  int64_t b11 = (load_4(b + 28) >> 7);
  int64_t c0 = 2097151 & load_3(c);
  int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
  int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
  int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
  int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
  int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
  int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
  int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
  int64_t c8 = 2097151 & load_3(c + 21);
  int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
  int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
  int64_t c11 = (load_4(c + 28) >> 7);
  int64_t s0;
  int64_t s1;
  int64_t s2;
  int64_t s3;
  int64_t s4;
  int64_t s5;
  int64_t s6;
  int64_t s7;
  int64_t s8;
  int64_t s9;
  int64_t s10;
  int64_t s11;
  int64_t s12;
  int64_t s13;
  int64_t s14;
  int64_t s15;
  int64_t s16;
  int64_t s17;
  int64_t s18;
  int64_t s19;
  int64_t s20;
  int64_t s21;
  int64_t s22;
  int64_t s23;
  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;
  int64_t carry10;
  int64_t carry11;
  int64_t carry12;
  int64_t carry13;
  int64_t carry14;
  int64_t carry15;
  int64_t carry16;
  int64_t carry17;
  int64_t carry18;
  int64_t carry19;
  int64_t carry20;
  int64_t carry21;
  int64_t carry22;

  s0 = c0 + a0 * b0;
  s1 = c1 + a0 * b1 + a1 * b0;
  s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
  s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
  s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
  s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
  s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
  s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
       a6 * b1 + a7 * b0;
  s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
       a6 * b2 + a7 * b1 + a8 * b0;
  s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
       a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
  s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
        a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
  s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
        a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
  s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
        a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
  s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
        a9 * b4 + a10 * b3 + a11 * b2;
  s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
        a10 * b4 + a11 * b3;
  s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
        a11 * b4;
  s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
  s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
  s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
  s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
  s20 = a9 * b11 + a10 * b10 + a11 * b9;
  s21 = a10 * b11 + a11 * b10;
  s22 = a11 * b11;
  s23 = 0;

  carry0 = (s0 + (1 << 20)) >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry2 = (s2 + (1 << 20)) >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry4 = (s4 + (1 << 20)) >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry12 = (s12 + (1 << 20)) >> 21;
  s13 += carry12;
  s12 -= carry12 << 21;
  carry14 = (s14 + (1 << 20)) >> 21;
  s15 += carry14;
  s14 -= carry14 << 21;
  carry16 = (s16 + (1 << 20)) >> 21;
  s17 += carry16;
  s16 -= carry16 << 21;
  carry18 = (s18 + (1 << 20)) >> 21;
  s19 += carry18;
  s18 -= carry18 << 21;
  carry20 = (s20 + (1 << 20)) >> 21;
  s21 += carry20;
  s20 -= carry20 << 21;
  carry22 = (s22 + (1 << 20)) >> 21;
  s23 += carry22;
  s22 -= carry22 << 21;

  carry1 = (s1 + (1 << 20)) >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry3 = (s3 + (1 << 20)) >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry5 = (s5 + (1 << 20)) >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;
  carry13 = (s13 + (1 << 20)) >> 21;
  s14 += carry13;
  s13 -= carry13 << 21;
  carry15 = (s15 + (1 << 20)) >> 21;
  s16 += carry15;
  s15 -= carry15 << 21;
  carry17 = (s17 + (1 << 20)) >> 21;
  s18 += carry17;
  s17 -= carry17 << 21;
  carry19 = (s19 + (1 << 20)) >> 21;
  s20 += carry19;
  s19 -= carry19 << 21;
  carry21 = (s21 + (1 << 20)) >> 21;
  s22 += carry21;
  s21 -= carry21 << 21;

  s11 += s23 * 666643;
  s12 += s23 * 470296;
  s13 += s23 * 654183;
  s14 -= s23 * 997805;
  s15 += s23 * 136657;
  s16 -= s23 * 683901;
  s23 = 0;

  s10 += s22 * 666643;
  s11 += s22 * 470296;
  s12 += s22 * 654183;
  s13 -= s22 * 997805;
  s14 += s22 * 136657;
  s15 -= s22 * 683901;
  s22 = 0;

  s9 += s21 * 666643;
  s10 += s21 * 470296;
  s11 += s21 * 654183;
  s12 -= s21 * 997805;
  s13 += s21 * 136657;
  s14 -= s21 * 683901;
  s21 = 0;

  s8 += s20 * 666643;
  s9 += s20 * 470296;
  s10 += s20 * 654183;
  s11 -= s20 * 997805;
  s12 += s20 * 136657;
  s13 -= s20 * 683901;
  s20 = 0;

  s7 += s19 * 666643;
  s8 += s19 * 470296;
  s9 += s19 * 654183;
  s10 -= s19 * 997805;
  s11 += s19 * 136657;
  s12 -= s19 * 683901;
  s19 = 0;

  s6 += s18 * 666643;
  s7 += s18 * 470296;
  s8 += s18 * 654183;
  s9 -= s18 * 997805;
  s10 += s18 * 136657;
  s11 -= s18 * 683901;
  s18 = 0;

  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry12 = (s12 + (1 << 20)) >> 21;
  s13 += carry12;
  s12 -= carry12 << 21;
  carry14 = (s14 + (1 << 20)) >> 21;
  s15 += carry14;
  s14 -= carry14 << 21;
  carry16 = (s16 + (1 << 20)) >> 21;
  s17 += carry16;
  s16 -= carry16 << 21;

  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;
  carry13 = (s13 + (1 << 20)) >> 21;
  s14 += carry13;
  s13 -= carry13 << 21;
  carry15 = (s15 + (1 << 20)) >> 21;
  s16 += carry15;
  s15 -= carry15 << 21;

  s5 += s17 * 666643;
  s6 += s17 * 470296;
  s7 += s17 * 654183;
  s8 -= s17 * 997805;
  s9 += s17 * 136657;
  s10 -= s17 * 683901;
  s17 = 0;

  s4 += s16 * 666643;
  s5 += s16 * 470296;
  s6 += s16 * 654183;
  s7 -= s16 * 997805;
  s8 += s16 * 136657;
  s9 -= s16 * 683901;
  s16 = 0;

  s3 += s15 * 666643;
  s4 += s15 * 470296;
  s5 += s15 * 654183;
  s6 -= s15 * 997805;
  s7 += s15 * 136657;
  s8 -= s15 * 683901;
  s15 = 0;

  s2 += s14 * 666643;
  s3 += s14 * 470296;
  s4 += s14 * 654183;
  s5 -= s14 * 997805;
  s6 += s14 * 136657;
  s7 -= s14 * 683901;
  s14 = 0;

  s1 += s13 * 666643;
  s2 += s13 * 470296;
  s3 += s13 * 654183;
  s4 -= s13 * 997805;
  s5 += s13 * 136657;
  s6 -= s13 * 683901;
  s13 = 0;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = (s0 + (1 << 20)) >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry2 = (s2 + (1 << 20)) >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry4 = (s4 + (1 << 20)) >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry6 = (s6 + (1 << 20)) >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry8 = (s8 + (1 << 20)) >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry10 = (s10 + (1 << 20)) >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  carry1 = (s1 + (1 << 20)) >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry3 = (s3 + (1 << 20)) >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry5 = (s5 + (1 << 20)) >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry7 = (s7 + (1 << 20)) >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry9 = (s9 + (1 << 20)) >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry11 = (s11 + (1 << 20)) >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;
  carry11 = s11 >> 21;
  s12 += carry11;
  s11 -= carry11 << 21;

  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  carry0 = s0 >> 21;
  s1 += carry0;
  s0 -= carry0 << 21;
  carry1 = s1 >> 21;
  s2 += carry1;
  s1 -= carry1 << 21;
  carry2 = s2 >> 21;
  s3 += carry2;
  s2 -= carry2 << 21;
  carry3 = s3 >> 21;
  s4 += carry3;
  s3 -= carry3 << 21;
  carry4 = s4 >> 21;
  s5 += carry4;
  s4 -= carry4 << 21;
  carry5 = s5 >> 21;
  s6 += carry5;
  s5 -= carry5 << 21;
  carry6 = s6 >> 21;
  s7 += carry6;
  s6 -= carry6 << 21;
  carry7 = s7 >> 21;
  s8 += carry7;
  s7 -= carry7 << 21;
  carry8 = s8 >> 21;
  s9 += carry8;
  s8 -= carry8 << 21;
  carry9 = s9 >> 21;
  s10 += carry9;
  s9 -= carry9 << 21;
  carry10 = s10 >> 21;
  s11 += carry10;
  s10 -= carry10 << 21;

  s[0] = s0 >> 0;
  s[1] = s0 >> 8;
  s[2] = (s0 >> 16) | (s1 << 5);
  s[3] = s1 >> 3;
  s[4] = s1 >> 11;
  s[5] = (s1 >> 19) | (s2 << 2);
  s[6] = s2 >> 6;
  s[7] = (s2 >> 14) | (s3 << 7);
  s[8] = s3 >> 1;
  s[9] = s3 >> 9;
  s[10] = (s3 >> 17) | (s4 << 4);
  s[11] = s4 >> 4;
  s[12] = s4 >> 12;
  s[13] = (s4 >> 20) | (s5 << 1);
  s[14] = s5 >> 7;
  s[15] = (s5 >> 15) | (s6 << 6);
  s[16] = s6 >> 2;
  s[17] = s6 >> 10;
  s[18] = (s6 >> 18) | (s7 << 3);
  s[19] = s7 >> 5;
  s[20] = s7 >> 13;
  s[21] = s8 >> 0;
  s[22] = s8 >> 8;
  s[23] = (s8 >> 16) | (s9 << 5);
  s[24] = s9 >> 3;
  s[25] = s9 >> 11;
  s[26] = (s9 >> 19) | (s10 << 2);
  s[27] = s10 >> 6;
  s[28] = (s10 >> 14) | (s11 << 7);
  s[29] = s11 >> 1;
  s[30] = s11 >> 9;
  s[31] = s11 >> 17;
}

void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
  uint8_t seed[32];
  RAND_bytes(seed, 32);
  ED25519_keypair_from_seed(out_public_key, out_private_key, seed);
}

int ED25519_sign(uint8_t out_sig[64], const uint8_t *message,
                 size_t message_len, const uint8_t private_key[64]) {
  // NOTE: The documentation on this function says that it returns zero on
  // allocation failure. While that can't happen with the current
  // implementation, we want to reserve the ability to allocate in this
  // implementation in the future.

  uint8_t az[SHA512_DIGEST_LENGTH];
  SHA512(private_key, 32, az);

  az[0] &= 248;
  az[31] &= 63;
  az[31] |= 64;

  SHA512_CTX hash_ctx;
  SHA512_Init(&hash_ctx);
  SHA512_Update(&hash_ctx, az + 32, 32);
  SHA512_Update(&hash_ctx, message, message_len);
  uint8_t nonce[SHA512_DIGEST_LENGTH];
  SHA512_Final(nonce, &hash_ctx);

  x25519_sc_reduce(nonce);
  ge_p3 R;
  x25519_ge_scalarmult_base(&R, nonce);
  ge_p3_tobytes(out_sig, &R);

  SHA512_Init(&hash_ctx);
  SHA512_Update(&hash_ctx, out_sig, 32);
  SHA512_Update(&hash_ctx, private_key + 32, 32);
  SHA512_Update(&hash_ctx, message, message_len);
  uint8_t hram[SHA512_DIGEST_LENGTH];
  SHA512_Final(hram, &hash_ctx);

  x25519_sc_reduce(hram);
  sc_muladd(out_sig + 32, hram, az, nonce);

  return 1;
}

int ED25519_verify(const uint8_t *message, size_t message_len,
                   const uint8_t signature[64], const uint8_t public_key[32]) {
  ge_p3 A;
  if ((signature[63] & 224) != 0 ||
      !x25519_ge_frombytes_vartime(&A, public_key)) {
    return 0;
  }

  fe_loose t;
  fe_neg(&t, &A.X);
  fe_carry(&A.X, &t);
  fe_neg(&t, &A.T);
  fe_carry(&A.T, &t);

  uint8_t pkcopy[32];
  OPENSSL_memcpy(pkcopy, public_key, 32);
  uint8_t rcopy[32];
  OPENSSL_memcpy(rcopy, signature, 32);
  union {
    uint64_t u64[4];
    uint8_t u8[32];
  } scopy;
  OPENSSL_memcpy(&scopy.u8[0], signature + 32, 32);

  // https://tools.ietf.org/html/rfc8032#section-5.1.7 requires that s be in
  // the range [0, order) in order to prevent signature malleability.

  // kOrder is the order of Curve25519 in little-endian form.
  static const uint64_t kOrder[4] = {
    UINT64_C(0x5812631a5cf5d3ed),
    UINT64_C(0x14def9dea2f79cd6),
    0,
    UINT64_C(0x1000000000000000),
  };
  for (size_t i = 3;; i--) {
    if (scopy.u64[i] > kOrder[i]) {
      return 0;
    } else if (scopy.u64[i] < kOrder[i]) {
      break;
    } else if (i == 0) {
      return 0;
    }
  }

  SHA512_CTX hash_ctx;
  SHA512_Init(&hash_ctx);
  SHA512_Update(&hash_ctx, signature, 32);
  SHA512_Update(&hash_ctx, public_key, 32);
  SHA512_Update(&hash_ctx, message, message_len);
  uint8_t h[SHA512_DIGEST_LENGTH];
  SHA512_Final(h, &hash_ctx);

  x25519_sc_reduce(h);

  ge_p2 R;
  ge_double_scalarmult_vartime(&R, h, &A, scopy.u8);

  uint8_t rcheck[32];
  x25519_ge_tobytes(rcheck, &R);

  return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
}

void ED25519_keypair_from_seed(uint8_t out_public_key[32],
                               uint8_t out_private_key[64],
                               const uint8_t seed[32]) {
  uint8_t az[SHA512_DIGEST_LENGTH];
  SHA512(seed, 32, az);

  az[0] &= 248;
  az[31] &= 127;
  az[31] |= 64;

  ge_p3 A;
  x25519_ge_scalarmult_base(&A, az);
  ge_p3_tobytes(out_public_key, &A);

  OPENSSL_memcpy(out_private_key, seed, 32);
  OPENSSL_memcpy(out_private_key + 32, out_public_key, 32);
}


static void x25519_scalar_mult_generic(uint8_t out[32],
                                       const uint8_t scalar[32],
                                       const uint8_t point[32]) {
  fe x1, x2, z2, x3, z3, tmp0, tmp1;
  fe_loose x2l, z2l, x3l, tmp0l, tmp1l;

  uint8_t e[32];
  OPENSSL_memcpy(e, scalar, 32);
  e[0] &= 248;
  e[31] &= 127;
  e[31] |= 64;

  // The following implementation was transcribed to Coq and proven to
  // correspond to unary scalar multiplication in affine coordinates given that
  // x1 != 0 is the x coordinate of some point on the curve. It was also checked
  // in Coq that doing a ladderstep with x1 = x3 = 0 gives z2' = z3' = 0, and z2
  // = z3 = 0 gives z2' = z3' = 0. The statement was quantified over the
  // underlying field, so it applies to Curve25519 itself and the quadratic
  // twist of Curve25519. It was not proven in Coq that prime-field arithmetic
  // correctly simulates extension-field arithmetic on prime-field values.
  // The decoding of the byte array representation of e was not considered.
  // Specification of Montgomery curves in affine coordinates:
  // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
  // Proof that these form a group that is isomorphic to a Weierstrass curve:
  // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
  // Coq transcription and correctness proof of the loop (where scalarbits=255):
  // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
  // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
  // preconditions: 0 <= e < 2^255 (not necessarily e < order), fe_invert(0) = 0
  fe_frombytes(&x1, point);
  fe_1(&x2);
  fe_0(&z2);
  fe_copy(&x3, &x1);
  fe_1(&z3);

  unsigned swap = 0;
  int pos;
  for (pos = 254; pos >= 0; --pos) {
    // loop invariant as of right before the test, for the case where x1 != 0:
    //   pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 is nonzero
    //   let r := e >> (pos+1) in the following equalities of projective points:
    //   to_xz (r*P)     === if swap then (x3, z3) else (x2, z2)
    //   to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
    //   x1 is the nonzero x coordinate of the nonzero point (r*P-(r+1)*P)
    unsigned b = 1 & (e[pos / 8] >> (pos & 7));
    swap ^= b;
    fe_cswap(&x2, &x3, swap);
    fe_cswap(&z2, &z3, swap);
    swap = b;
    // Coq transcription of ladderstep formula (called from transcribed loop):
    // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
    // <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
    // x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
    // x1  = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
    fe_sub(&tmp0l, &x3, &z3);
    fe_sub(&tmp1l, &x2, &z2);
    fe_add(&x2l, &x2, &z2);
    fe_add(&z2l, &x3, &z3);
    fe_mul_tll(&z3, &tmp0l, &x2l);
    fe_mul_tll(&z2, &z2l, &tmp1l);
    fe_sq_tl(&tmp0, &tmp1l);
    fe_sq_tl(&tmp1, &x2l);
    fe_add(&x3l, &z3, &z2);
    fe_sub(&z2l, &z3, &z2);
    fe_mul_ttt(&x2, &tmp1, &tmp0);
    fe_sub(&tmp1l, &tmp1, &tmp0);
    fe_sq_tl(&z2, &z2l);
    fe_mul121666(&z3, &tmp1l);
    fe_sq_tl(&x3, &x3l);
    fe_add(&tmp0l, &tmp0, &z3);
    fe_mul_ttt(&z3, &x1, &z2);
    fe_mul_tll(&z2, &tmp1l, &tmp0l);
  }
  // here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) else (x2, z2)
  fe_cswap(&x2, &x3, swap);
  fe_cswap(&z2, &z3, swap);

  fe_invert(&z2, &z2);
  fe_mul_ttt(&x2, &x2, &z2);
  fe_tobytes(out, &x2);
}

static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
                               const uint8_t point[32]) {
#if defined(BORINGSSL_X25519_NEON)
  if (CRYPTO_is_NEON_capable()) {
    x25519_NEON(out, scalar, point);
    return;
  }
#endif

  x25519_scalar_mult_generic(out, scalar, point);
}

void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
  RAND_bytes(out_private_key, 32);

  // All X25519 implementations should decode scalars correctly (see
  // https://tools.ietf.org/html/rfc7748#section-5). However, if an
  // implementation doesn't then it might interoperate with random keys a
  // fraction of the time because they'll, randomly, happen to be correctly
  // formed.
  //
  // Thus we do the opposite of the masking here to make sure that our private
  // keys are never correctly masked and so, hopefully, any incorrect
  // implementations are deterministically broken.
  //
  // This does not affect security because, although we're throwing away
  // entropy, a valid implementation of scalarmult should throw away the exact
  // same bits anyway.
  out_private_key[0] |= ~248;
  out_private_key[31] &= ~64;
  out_private_key[31] |= ~127;

  X25519_public_from_private(out_public_value, out_private_key);
}

int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
           const uint8_t peer_public_value[32]) {
  static const uint8_t kZeros[32] = {0};
  x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
  // The all-zero output results when the input is a point of small order.
  return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
}

void X25519_public_from_private(uint8_t out_public_value[32],
                                const uint8_t private_key[32]) {
#if defined(BORINGSSL_X25519_NEON)
  if (CRYPTO_is_NEON_capable()) {
    static const uint8_t kMongomeryBasePoint[32] = {9};
    x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
    return;
  }
#endif

  uint8_t e[32];
  OPENSSL_memcpy(e, private_key, 32);
  e[0] &= 248;
  e[31] &= 127;
  e[31] |= 64;

  ge_p3 A;
  x25519_ge_scalarmult_base(&A, e);

  // We only need the u-coordinate of the curve25519 point. The map is
  // u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y).
  fe_loose zplusy, zminusy;
  fe zminusy_inv;
  fe_add(&zplusy, &A.Z, &A.Y);
  fe_sub(&zminusy, &A.Z, &A.Y);
  fe_loose_invert(&zminusy_inv, &zminusy);
  fe_mul_tlt(&zminusy_inv, &zplusy, &zminusy_inv);
  fe_tobytes(out_public_value, &zminusy_inv);
}