wownero/src/crypto/crypto_ops_builder/crypto-ops-old.c

// Copyright (c) 2014-2018, The Monero Project
// 
// All rights reserved.
// 
// Redistribution and use in source and binary forms, with or without modification, are
// permitted provided that the following conditions are met:
// 
// 1. Redistributions of source code must retain the above copyright notice, this list of
//    conditions and the following disclaimer.
// 
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
//    of conditions and the following disclaimer in the documentation and/or other
//    materials provided with the distribution.
// 
// 3. Neither the name of the copyright holder nor the names of its contributors may be
//    used to endorse or promote products derived from this software without specific
//    prior written permission.
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers


#include <stdint.h> //standard
#include <assert.h> //standard

//#include "warnings.h" //where is this??
#include "crypto-ops.h" //fine

//DISABLE_VS_WARNINGS(4146 4244)

/* Predeclarations */

static void fe_mul(fe, const fe, const fe);
static void fe_sq(fe, const fe);
static void fe_tobytes(unsigned char *, const fe);
static void ge_madd(ge_p1p1 *, const ge_p3 *, const ge_precomp *);
static void ge_msub(ge_p1p1 *, const ge_p3 *, const ge_precomp *);
static void ge_p2_0(ge_p2 *);
static void ge_p3_dbl(ge_p1p1 *, const ge_p3 *);
static void ge_sub(ge_p1p1 *, const ge_p3 *, const ge_cached *);
static void fe_divpowm1(fe, const fe, const fe);

/* Common functions */

//x 
//u
static uint64_t load_3(const unsigned char *in) {
  uint64_t result;
  result = (uint64_t) in[0];
  result |= ((uint64_t) in[1]) << 8;
  result |= ((uint64_t) in[2]) << 16;
  return result;
}

//x 
//u
static uint64_t load_4(const unsigned char *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;
}

/* From fe_0.c */

/*
h = 0
*/

//x
static void fe_0(fe h) {
  h[0] = 0;
  h[1] = 0;
  h[2] = 0;
  h[3] = 0;
  h[4] = 0;
  h[5] = 0;
  h[6] = 0;
  h[7] = 0;
  h[8] = 0;
  h[9] = 0;
}

/* From fe_1.c */

/*
h = 1
*/

//x
static void fe_1(fe h) {
  h[0] = 1;
  h[1] = 0;
  h[2] = 0;
  h[3] = 0;
  h[4] = 0;
  h[5] = 0;
  h[6] = 0;
  h[7] = 0;
  h[8] = 0;
  h[9] = 0;
}

/* From fe_add.c */

/*
h = f + g
Can overlap h with f or g.

Preconditions:
   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Postconditions:
   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/

static void fe_add(fe h, const fe f, const fe g) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t h0 = f0 + g0;
  int32_t h1 = f1 + g1;
  int32_t h2 = f2 + g2;
  int32_t h3 = f3 + g3;
  int32_t h4 = f4 + g4;
  int32_t h5 = f5 + g5;
  int32_t h6 = f6 + g6;
  int32_t h7 = f7 + g7;
  int32_t h8 = f8 + g8;
  int32_t h9 = f9 + g9;
  h[0] = h0;
  h[1] = h1;
  h[2] = h2;
  h[3] = h3;
  h[4] = h4;
  h[5] = h5;
  h[6] = h6;
  h[7] = h7;
  h[8] = h8;
  h[9] = h9;
}

/* From fe_cmov.c */

/*
Replace (f,g) with (g,g) if b == 1;
replace (f,g) with (f,g) if b == 0.

Preconditions: b in {0,1}.
*/

//x
static void fe_cmov(fe f, const fe g, unsigned int b) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t x0 = f0 ^ g0;
  int32_t x1 = f1 ^ g1;
  int32_t x2 = f2 ^ g2;
  int32_t x3 = f3 ^ g3;
  int32_t x4 = f4 ^ g4;
  int32_t x5 = f5 ^ g5;
  int32_t x6 = f6 ^ g6;
  int32_t x7 = f7 ^ g7;
  int32_t x8 = f8 ^ g8;
  int32_t x9 = f9 ^ g9;
  assert((((b - 1) & ~b) | ((b - 2) & ~(b - 1))) == (unsigned int) -1);
  b = -b;
  x0 &= b;
  x1 &= b;
  x2 &= b;
  x3 &= b;
  x4 &= b;
  x5 &= b;
  x6 &= b;
  x7 &= b;
  x8 &= b;
  x9 &= b;
  f[0] = f0 ^ x0;
  f[1] = f1 ^ x1;
  f[2] = f2 ^ x2;
  f[3] = f3 ^ x3;
  f[4] = f4 ^ x4;
  f[5] = f5 ^ x5;
  f[6] = f6 ^ x6;
  f[7] = f7 ^ x7;
  f[8] = f8 ^ x8;
  f[9] = f9 ^ x9;
}

/* From fe_copy.c */

/*
h = f
*/

//x
static void fe_copy(fe h, const fe f) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  h[0] = f0;
  h[1] = f1;
  h[2] = f2;
  h[3] = f3;
  h[4] = f4;
  h[5] = f5;
  h[6] = f6;
  h[7] = f7;
  h[8] = f8;
  h[9] = f9;
}

/* From fe_invert.c */

//x using fermat
static void fe_invert(fe out, const fe z) {
  fe t0;
  fe t1;
  fe t2;
  fe t3;
  int i;

  fe_sq(t0, z);
  fe_sq(t1, t0);
  fe_sq(t1, t1);
  fe_mul(t1, z, t1);
  fe_mul(t0, t0, t1);
  fe_sq(t2, t0);
  fe_mul(t1, t1, t2);
  fe_sq(t2, t1);
  for (i = 0; i < 4; ++i) {
    fe_sq(t2, t2);
  }
  fe_mul(t1, t2, t1);
  fe_sq(t2, t1);
  for (i = 0; i < 9; ++i) {
    fe_sq(t2, t2);
  }
  fe_mul(t2, t2, t1);
  fe_sq(t3, t2);
  for (i = 0; i < 19; ++i) {
    fe_sq(t3, t3);
  }
  fe_mul(t2, t3, t2);
  fe_sq(t2, t2);
  for (i = 0; i < 9; ++i) {
    fe_sq(t2, t2);
  }
  fe_mul(t1, t2, t1);
  fe_sq(t2, t1);
  for (i = 0; i < 49; ++i) {
    fe_sq(t2, t2);
  }
  fe_mul(t2, t2, t1);
  fe_sq(t3, t2);
  for (i = 0; i < 99; ++i) {
    fe_sq(t3, t3);
  }
  fe_mul(t2, t3, t2);
  fe_sq(t2, t2);
  for (i = 0; i < 49; ++i) {
    fe_sq(t2, t2);
  }
  fe_mul(t1, t2, t1);
  fe_sq(t1, t1);
  for (i = 0; i < 4; ++i) {
    fe_sq(t1, t1);
  }
  fe_mul(out, t1, t0);

  return;
}

/* From fe_isnegative.c */

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

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

//x
static int fe_isnegative(const fe f) {
  unsigned char s[32];
  fe_tobytes(s, f);
  return s[0] & 1;
}

/* From fe_isnonzero.c, modified */

//x
static int fe_isnonzero(const fe f) {
  unsigned char s[32];
  fe_tobytes(s, f);
  return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] |
    s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] |
    s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
    s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1;
}

/* From fe_mul.c */

/*
h = f * g
Can overlap h with f or g.

Preconditions:
   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
   |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.

Postconditions:
   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/

/*
Notes on implementation strategy:

Using schoolbook multiplication.
Karatsuba would save a little in some cost models.

Most multiplications by 2 and 19 are 32-bit precomputations;
cheaper than 64-bit postcomputations.

There is one remaining multiplication by 19 in the carry chain;
one *19 precomputation can be merged into this,
but the resulting data flow is considerably less clean.

There are 12 carries below.
10 of them are 2-way parallelizable and vectorizable.
Can get away with 11 carries, but then data flow is much deeper.

With tighter constraints on inputs can squeeze carries into int32.
*/

static void fe_mul(fe h, const fe f, const fe g) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
  int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
  int32_t g3_19 = 19 * g3;
  int32_t g4_19 = 19 * g4;
  int32_t g5_19 = 19 * g5;
  int32_t g6_19 = 19 * g6;
  int32_t g7_19 = 19 * g7;
  int32_t g8_19 = 19 * g8;
  int32_t g9_19 = 19 * g9;
  int32_t f1_2 = 2 * f1;
  int32_t f3_2 = 2 * f3;
  int32_t f5_2 = 2 * f5;
  int32_t f7_2 = 2 * f7;
  int32_t f9_2 = 2 * f9;
  int64_t f0g0    = f0   * (int64_t) g0;
  int64_t f0g1    = f0   * (int64_t) g1;
  int64_t f0g2    = f0   * (int64_t) g2;
  int64_t f0g3    = f0   * (int64_t) g3;
  int64_t f0g4    = f0   * (int64_t) g4;
  int64_t f0g5    = f0   * (int64_t) g5;
  int64_t f0g6    = f0   * (int64_t) g6;
  int64_t f0g7    = f0   * (int64_t) g7;
  int64_t f0g8    = f0   * (int64_t) g8;
  int64_t f0g9    = f0   * (int64_t) g9;
  int64_t f1g0    = f1   * (int64_t) g0;
  int64_t f1g1_2  = f1_2 * (int64_t) g1;
  int64_t f1g2    = f1   * (int64_t) g2;
  int64_t f1g3_2  = f1_2 * (int64_t) g3;
  int64_t f1g4    = f1   * (int64_t) g4;
  int64_t f1g5_2  = f1_2 * (int64_t) g5;
  int64_t f1g6    = f1   * (int64_t) g6;
  int64_t f1g7_2  = f1_2 * (int64_t) g7;
  int64_t f1g8    = f1   * (int64_t) g8;
  int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
  int64_t f2g0    = f2   * (int64_t) g0;
  int64_t f2g1    = f2   * (int64_t) g1;
  int64_t f2g2    = f2   * (int64_t) g2;
  int64_t f2g3    = f2   * (int64_t) g3;
  int64_t f2g4    = f2   * (int64_t) g4;
  int64_t f2g5    = f2   * (int64_t) g5;
  int64_t f2g6    = f2   * (int64_t) g6;
  int64_t f2g7    = f2   * (int64_t) g7;
  int64_t f2g8_19 = f2   * (int64_t) g8_19;
  int64_t f2g9_19 = f2   * (int64_t) g9_19;
  int64_t f3g0    = f3   * (int64_t) g0;
  int64_t f3g1_2  = f3_2 * (int64_t) g1;
  int64_t f3g2    = f3   * (int64_t) g2;
  int64_t f3g3_2  = f3_2 * (int64_t) g3;
  int64_t f3g4    = f3   * (int64_t) g4;
  int64_t f3g5_2  = f3_2 * (int64_t) g5;
  int64_t f3g6    = f3   * (int64_t) g6;
  int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
  int64_t f3g8_19 = f3   * (int64_t) g8_19;
  int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
  int64_t f4g0    = f4   * (int64_t) g0;
  int64_t f4g1    = f4   * (int64_t) g1;
  int64_t f4g2    = f4   * (int64_t) g2;
  int64_t f4g3    = f4   * (int64_t) g3;
  int64_t f4g4    = f4   * (int64_t) g4;
  int64_t f4g5    = f4   * (int64_t) g5;
  int64_t f4g6_19 = f4   * (int64_t) g6_19;
  int64_t f4g7_19 = f4   * (int64_t) g7_19;
  int64_t f4g8_19 = f4   * (int64_t) g8_19;
  int64_t f4g9_19 = f4   * (int64_t) g9_19;
  int64_t f5g0    = f5   * (int64_t) g0;
  int64_t f5g1_2  = f5_2 * (int64_t) g1;
  int64_t f5g2    = f5   * (int64_t) g2;
  int64_t f5g3_2  = f5_2 * (int64_t) g3;
  int64_t f5g4    = f5   * (int64_t) g4;
  int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
  int64_t f5g6_19 = f5   * (int64_t) g6_19;
  int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
  int64_t f5g8_19 = f5   * (int64_t) g8_19;
  int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
  int64_t f6g0    = f6   * (int64_t) g0;
  int64_t f6g1    = f6   * (int64_t) g1;
  int64_t f6g2    = f6   * (int64_t) g2;
  int64_t f6g3    = f6   * (int64_t) g3;
  int64_t f6g4_19 = f6   * (int64_t) g4_19;
  int64_t f6g5_19 = f6   * (int64_t) g5_19;
  int64_t f6g6_19 = f6   * (int64_t) g6_19;
  int64_t f6g7_19 = f6   * (int64_t) g7_19;
  int64_t f6g8_19 = f6   * (int64_t) g8_19;
  int64_t f6g9_19 = f6   * (int64_t) g9_19;
  int64_t f7g0    = f7   * (int64_t) g0;
  int64_t f7g1_2  = f7_2 * (int64_t) g1;
  int64_t f7g2    = f7   * (int64_t) g2;
  int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
  int64_t f7g4_19 = f7   * (int64_t) g4_19;
  int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
  int64_t f7g6_19 = f7   * (int64_t) g6_19;
  int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
  int64_t f7g8_19 = f7   * (int64_t) g8_19;
  int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
  int64_t f8g0    = f8   * (int64_t) g0;
  int64_t f8g1    = f8   * (int64_t) g1;
  int64_t f8g2_19 = f8   * (int64_t) g2_19;
  int64_t f8g3_19 = f8   * (int64_t) g3_19;
  int64_t f8g4_19 = f8   * (int64_t) g4_19;
  int64_t f8g5_19 = f8   * (int64_t) g5_19;
  int64_t f8g6_19 = f8   * (int64_t) g6_19;
  int64_t f8g7_19 = f8   * (int64_t) g7_19;
  int64_t f8g8_19 = f8   * (int64_t) g8_19;
  int64_t f8g9_19 = f8   * (int64_t) g9_19;
  int64_t f9g0    = f9   * (int64_t) g0;
  int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
  int64_t f9g2_19 = f9   * (int64_t) g2_19;
  int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
  int64_t f9g4_19 = f9   * (int64_t) g4_19;
  int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
  int64_t f9g6_19 = f9   * (int64_t) g6_19;
  int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
  int64_t f9g8_19 = f9   * (int64_t) g8_19;
  int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
  int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
  int64_t h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
  int64_t h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
  int64_t h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
  int64_t h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
  int64_t h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
  int64_t h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
  int64_t h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
  int64_t h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
  int64_t h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

  /*
  |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
    i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
  |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
    i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
  */

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

  carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
  carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
  /* |h1| <= 2^24; from now on fits into int32 */
  /* |h5| <= 2^24; from now on fits into int32 */
  /* |h2| <= 1.41*2^60 */
  /* |h6| <= 1.41*2^60 */

  carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
  carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
  /* |h2| <= 2^25; from now on fits into int32 unchanged */
  /* |h6| <= 2^25; from now on fits into int32 unchanged */
  /* |h3| <= 1.71*2^59 */
  /* |h7| <= 1.71*2^59 */

  carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
  carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
  /* |h3| <= 2^24; from now on fits into int32 unchanged */
  /* |h7| <= 2^24; from now on fits into int32 unchanged */
  /* |h4| <= 1.72*2^34 */
  /* |h8| <= 1.41*2^60 */

  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
  carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
  /* |h4| <= 2^25; from now on fits into int32 unchanged */
  /* |h8| <= 2^25; from now on fits into int32 unchanged */
  /* |h5| <= 1.01*2^24 */
  /* |h9| <= 1.71*2^59 */

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

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

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

/* From fe_neg.c */

/*
h = -f

Preconditions:
   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

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

//x
static void fe_neg(fe h, const fe f) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t h0 = -f0;
  int32_t h1 = -f1;
  int32_t h2 = -f2;
  int32_t h3 = -f3;
  int32_t h4 = -f4;
  int32_t h5 = -f5;
  int32_t h6 = -f6;
  int32_t h7 = -f7;
  int32_t h8 = -f8;
  int32_t h9 = -f9;
  h[0] = h0;
  h[1] = h1;
  h[2] = h2;
  h[3] = h3;
  h[4] = h4;
  h[5] = h5;
  h[6] = h6;
  h[7] = h7;
  h[8] = h8;
  h[9] = h9;
}

/* From fe_sq.c */

/*
h = f * f
Can overlap h with f.

Preconditions:
   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.

Postconditions:
   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/

/*
See fe_mul.c for discussion of implementation strategy.
*/

static void fe_sq(fe h, const fe f) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t f0_2 = 2 * f0;
  int32_t f1_2 = 2 * f1;
  int32_t f2_2 = 2 * f2;
  int32_t f3_2 = 2 * f3;
  int32_t f4_2 = 2 * f4;
  int32_t f5_2 = 2 * f5;
  int32_t f6_2 = 2 * f6;
  int32_t f7_2 = 2 * f7;
  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
  int64_t f0f0    = f0   * (int64_t) f0;
  int64_t f0f1_2  = f0_2 * (int64_t) f1;
  int64_t f0f2_2  = f0_2 * (int64_t) f2;
  int64_t f0f3_2  = f0_2 * (int64_t) f3;
  int64_t f0f4_2  = f0_2 * (int64_t) f4;
  int64_t f0f5_2  = f0_2 * (int64_t) f5;
  int64_t f0f6_2  = f0_2 * (int64_t) f6;
  int64_t f0f7_2  = f0_2 * (int64_t) f7;
  int64_t f0f8_2  = f0_2 * (int64_t) f8;
  int64_t f0f9_2  = f0_2 * (int64_t) f9;
  int64_t f1f1_2  = f1_2 * (int64_t) f1;
  int64_t f1f2_2  = f1_2 * (int64_t) f2;
  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
  int64_t f1f4_2  = f1_2 * (int64_t) f4;
  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
  int64_t f1f6_2  = f1_2 * (int64_t) f6;
  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
  int64_t f1f8_2  = f1_2 * (int64_t) f8;
  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
  int64_t f2f2    = f2   * (int64_t) f2;
  int64_t f2f3_2  = f2_2 * (int64_t) f3;
  int64_t f2f4_2  = f2_2 * (int64_t) f4;
  int64_t f2f5_2  = f2_2 * (int64_t) f5;
  int64_t f2f6_2  = f2_2 * (int64_t) f6;
  int64_t f2f7_2  = f2_2 * (int64_t) f7;
  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
  int64_t f2f9_38 = f2   * (int64_t) f9_38;
  int64_t f3f3_2  = f3_2 * (int64_t) f3;
  int64_t f3f4_2  = f3_2 * (int64_t) f4;
  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
  int64_t f3f6_2  = f3_2 * (int64_t) f6;
  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
  int64_t f4f4    = f4   * (int64_t) f4;
  int64_t f4f5_2  = f4_2 * (int64_t) f5;
  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
  int64_t f4f7_38 = f4   * (int64_t) f7_38;
  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
  int64_t f4f9_38 = f4   * (int64_t) f9_38;
  int64_t f5f5_38 = f5   * (int64_t) f5_38;
  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
  int64_t f6f6_19 = f6   * (int64_t) f6_19;
  int64_t f6f7_38 = f6   * (int64_t) f7_38;
  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
  int64_t f6f9_38 = f6   * (int64_t) f9_38;
  int64_t f7f7_38 = f7   * (int64_t) f7_38;
  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
  int64_t f8f8_19 = f8   * (int64_t) f8_19;
  int64_t f8f9_38 = f8   * (int64_t) f9_38;
  int64_t f9f9_38 = f9   * (int64_t) f9_38;
  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

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

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

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

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

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

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

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

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

/* From fe_sq2.c */

/*
h = 2 * f * f
Can overlap h with f.

Preconditions:
   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.

Postconditions:
   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/

/*
See fe_mul.c for discussion of implementation strategy.
*/

static void fe_sq2(fe h, const fe f) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t f0_2 = 2 * f0;
  int32_t f1_2 = 2 * f1;
  int32_t f2_2 = 2 * f2;
  int32_t f3_2 = 2 * f3;
  int32_t f4_2 = 2 * f4;
  int32_t f5_2 = 2 * f5;
  int32_t f6_2 = 2 * f6;
  int32_t f7_2 = 2 * f7;
  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
  int64_t f0f0    = f0   * (int64_t) f0;
  int64_t f0f1_2  = f0_2 * (int64_t) f1;
  int64_t f0f2_2  = f0_2 * (int64_t) f2;
  int64_t f0f3_2  = f0_2 * (int64_t) f3;
  int64_t f0f4_2  = f0_2 * (int64_t) f4;
  int64_t f0f5_2  = f0_2 * (int64_t) f5;
  int64_t f0f6_2  = f0_2 * (int64_t) f6;
  int64_t f0f7_2  = f0_2 * (int64_t) f7;
  int64_t f0f8_2  = f0_2 * (int64_t) f8;
  int64_t f0f9_2  = f0_2 * (int64_t) f9;
  int64_t f1f1_2  = f1_2 * (int64_t) f1;
  int64_t f1f2_2  = f1_2 * (int64_t) f2;
  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
  int64_t f1f4_2  = f1_2 * (int64_t) f4;
  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
  int64_t f1f6_2  = f1_2 * (int64_t) f6;
  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
  int64_t f1f8_2  = f1_2 * (int64_t) f8;
  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
  int64_t f2f2    = f2   * (int64_t) f2;
  int64_t f2f3_2  = f2_2 * (int64_t) f3;
  int64_t f2f4_2  = f2_2 * (int64_t) f4;
  int64_t f2f5_2  = f2_2 * (int64_t) f5;
  int64_t f2f6_2  = f2_2 * (int64_t) f6;
  int64_t f2f7_2  = f2_2 * (int64_t) f7;
  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
  int64_t f2f9_38 = f2   * (int64_t) f9_38;
  int64_t f3f3_2  = f3_2 * (int64_t) f3;
  int64_t f3f4_2  = f3_2 * (int64_t) f4;
  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
  int64_t f3f6_2  = f3_2 * (int64_t) f6;
  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
  int64_t f4f4    = f4   * (int64_t) f4;
  int64_t f4f5_2  = f4_2 * (int64_t) f5;
  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
  int64_t f4f7_38 = f4   * (int64_t) f7_38;
  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
  int64_t f4f9_38 = f4   * (int64_t) f9_38;
  int64_t f5f5_38 = f5   * (int64_t) f5_38;
  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
  int64_t f6f6_19 = f6   * (int64_t) f6_19;
  int64_t f6f7_38 = f6   * (int64_t) f7_38;
  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
  int64_t f6f9_38 = f6   * (int64_t) f9_38;
  int64_t f7f7_38 = f7   * (int64_t) f7_38;
  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
  int64_t f8f8_19 = f8   * (int64_t) f8_19;
  int64_t f8f9_38 = f8   * (int64_t) f9_38;
  int64_t f9f9_38 = f9   * (int64_t) f9_38;
  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

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

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

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

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

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

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

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

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

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

/* From fe_sub.c */

/*
h = f - g
Can overlap h with f or g.

Preconditions:
   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Postconditions:
   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/

//x
static void fe_sub(fe h, const fe f, const fe g) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t h0 = f0 - g0;
  int32_t h1 = f1 - g1;
  int32_t h2 = f2 - g2;
  int32_t h3 = f3 - g3;
  int32_t h4 = f4 - g4;
  int32_t h5 = f5 - g5;
  int32_t h6 = f6 - g6;
  int32_t h7 = f7 - g7;
  int32_t h8 = f8 - g8;
  int32_t h9 = f9 - g9;
  h[0] = h0;
  h[1] = h1;
  h[2] = h2;
  h[3] = h3;
  h[4] = h4;
  h[5] = h5;
  h[6] = h6;
  h[7] = h7;
  h[8] = h8;
  h[9] = h9;
}

/* From fe_tobytes.c */

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

Write p=2^255-19; q=floor(h/p).
Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).

Proof:
  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.

  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
  Then 0<y<1.

  Write r=h-pq.
  Have 0<=r<=p-1=2^255-20.
  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.

  Write x=r+19(2^-255)r+y.
  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.

  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
*/

static void fe_tobytes(unsigned char *s, const fe h) {
  int32_t h0 = h[0];
  int32_t h1 = h[1];
  int32_t h2 = h[2];
  int32_t h3 = h[3];
  int32_t h4 = h[4];
  int32_t h5 = h[5];
  int32_t h6 = h[6];
  int32_t h7 = h[7];
  int32_t h8 = h[8];
  int32_t h9 = h[9];
  int32_t q;
  int32_t carry0;
  int32_t carry1;
  int32_t carry2;
  int32_t carry3;
  int32_t carry4;
  int32_t carry5;
  int32_t carry6;
  int32_t carry7;
  int32_t carry8;
  int32_t carry9;

  q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
  q = (h0 + q) >> 26;
  q = (h1 + q) >> 25;
  q = (h2 + q) >> 26;
  q = (h3 + q) >> 25;
  q = (h4 + q) >> 26;
  q = (h5 + q) >> 25;
  q = (h6 + q) >> 26;
  q = (h7 + q) >> 25;
  q = (h8 + q) >> 26;
  q = (h9 + q) >> 25;

  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
  h0 += 19 * q;
  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */

  carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
  carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
  carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
  carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
  carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
  carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
  carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
  carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
  carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
  carry9 = h9 >> 25;               h9 -= carry9 << 25;
                  /* h10 = carry9 */

  /*
  Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
  Have h0+...+2^230 h9 between 0 and 2^255-1;
  evidently 2^255 h10-2^255 q = 0.
  Goal: Output h0+...+2^230 h9.
  */

  s[0] = h0 >> 0;
  s[1] = h0 >> 8;
  s[2] = h0 >> 16;
  s[3] = (h0 >> 24) | (h1 << 2);
  s[4] = h1 >> 6;
  s[5] = h1 >> 14;
  s[6] = (h1 >> 22) | (h2 << 3);
  s[7] = h2 >> 5;
  s[8] = h2 >> 13;
  s[9] = (h2 >> 21) | (h3 << 5);
  s[10] = h3 >> 3;
  s[11] = h3 >> 11;
  s[12] = (h3 >> 19) | (h4 << 6);
  s[13] = h4 >> 2;
  s[14] = h4 >> 10;
  s[15] = h4 >> 18;
  s[16] = h5 >> 0;
  s[17] = h5 >> 8;
  s[18] = h5 >> 16;
  s[19] = (h5 >> 24) | (h6 << 1);
  s[20] = h6 >> 7;
  s[21] = h6 >> 15;
  s[22] = (h6 >> 23) | (h7 << 3);
  s[23] = h7 >> 5;
  s[24] = h7 >> 13;
  s[25] = (h7 >> 21) | (h8 << 4);
  s[26] = h8 >> 4;
  s[27] = h8 >> 12;
  s[28] = (h8 >> 20) | (h9 << 6);
  s[29] = h9 >> 2;
  s[30] = h9 >> 10;
  s[31] = h9 >> 18;
}

/* From ge_add.c */

//x
void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
  fe t0;
  fe_add(r->X, p->Y, p->X);
  fe_sub(r->Y, p->Y, p->X);
  fe_mul(r->Z, r->X, q->YplusX);
  fe_mul(r->Y, r->Y, q->YminusX);
  fe_mul(r->T, q->T2d, p->T);
  fe_mul(r->X, p->Z, q->Z);
  fe_add(t0, r->X, r->X);
  fe_sub(r->X, r->Z, r->Y);
  fe_add(r->Y, r->Z, r->Y);
  fe_add(r->Z, t0, r->T);
  fe_sub(r->T, t0, r->T);
}

/* From ge_double_scalarmult.c, modified */

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

  //this loop just makes a binary string out of a 
  //e.g. a = {3, 0, 0, ...} then r = 110000....
  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;
        }
      }
    }
  }
}

//double scalar mult precomp
void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s) {
  ge_p1p1 t;
  ge_p3 s2, u;
  ge_p3_to_cached(&r[0], s);
  ge_p3_dbl(&t, s); ge_p1p1_to_p3(&s2, &t);
  ge_add(&t, &s2, &r[0]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[1], &u);
  ge_add(&t, &s2, &r[1]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[2], &u);
  ge_add(&t, &s2, &r[2]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[3], &u);
  ge_add(&t, &s2, &r[3]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[4], &u);
  ge_add(&t, &s2, &r[4]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[5], &u);
  ge_add(&t, &s2, &r[5]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[6], &u);
  ge_add(&t, &s2, &r[6]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[7], &u);
}

/*
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.
*/

//this is a really simple alg. actually
void ge_double_scalarmult_base_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
  signed char aslide[256];
  signed char bslide[256];
  ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */
  ge_p1p1 t;
  ge_p3 u;
  int i;

  slide(aslide, a);
  slide(bslide, b);
  ge_dsm_precomp(Ai, A);/* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */

  ge_p2_0(r);

  for (i = 255; i >= 0; --i) {
      //so this gets us to the highest i such that both have a nonzero
    if (aslide[i] || bslide[i]) break;
  }

  for (; i >= 0; --i) {
    ge_p2_dbl(&t, r);//simple double and add

    if (aslide[i] > 0) {
      ge_p1p1_to_p3(&u, &t);
      ge_add(&t, &u, &Ai[aslide[i]/2]);
    } else if (aslide[i] < 0) {
      ge_p1p1_to_p3(&u, &t);
      ge_sub(&t, &u, &Ai[(-aslide[i])/2]);
    }

    if (bslide[i] > 0) {
      ge_p1p1_to_p3(&u, &t);
      ge_madd(&t, &u, &ge_Bi[bslide[i]/2]);
    } else if (bslide[i] < 0) {
      ge_p1p1_to_p3(&u, &t);
      ge_msub(&t, &u, &ge_Bi[(-bslide[i])/2]);
    }

    ge_p1p1_to_p2(r, &t);
  }
}

/* From ge_frombytes.c, modified */
//this is like xrecover .. 
//x
int ge_frombytes_vartime(ge_p3 *h, const unsigned char *s) {
  fe u;
  fe v;
  fe vxx;
  fe check;

  /* From fe_frombytes.c */

  int64_t h0 = load_4(s);
  int64_t h1 = load_3(s + 4) << 6;
  int64_t h2 = load_3(s + 7) << 5;
  int64_t h3 = load_3(s + 10) << 3;
  int64_t h4 = load_3(s + 13) << 2;
  int64_t h5 = load_4(s + 16);
  int64_t h6 = load_3(s + 20) << 7;
  int64_t h7 = load_3(s + 23) << 5;
  int64_t h8 = load_3(s + 26) << 4;
  int64_t h9 = (load_3(s + 29) & 8388607) << 2;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

  /* Validate the number to be canonical */
  if (h9 == 33554428 && h8 == 268435440 && h7 == 536870880 && h6 == 2147483520 &&
    h5 == 4294967295 && h4 == 67108860 && h3 == 134217720 && h2 == 536870880 &&
    h1 == 1073741760 && h0 >= 4294967277) {
    return -1;
  }

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

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

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

  /* End fe_frombytes.c */

  fe_1(h->Z);
  fe_sq(u, h->Y);
  fe_mul(v, u, fe_d);
  fe_sub(u, u, h->Z);       /* u = y^2-1 */
  fe_add(v, v, h->Z);       /* v = dy^2+1 */

  fe_divpowm1(h->X, u, v); /* x = uv^3(uv^7)^((q-5)/8) */

  fe_sq(vxx, h->X);
  fe_mul(vxx, vxx, v);
  fe_sub(check, vxx, u);    /* vx^2-u */
  if (fe_isnonzero(check)) {
    fe_add(check, vxx, u);  /* vx^2+u */
    if (fe_isnonzero(check)) {
      return -1;
    }
    fe_mul(h->X, h->X, fe_sqrtm1); //this is mapping X to X * sqrt(-1) c.f. 3.1 in hisil, dong, etc. 
  }

  if (fe_isnegative(h->X) != (s[31] >> 7)) {
    /* If x = 0, the sign must be positive */
    if (!fe_isnonzero(h->X)) {
      return -1;
    }
    fe_neg(h->X, h->X);
  }

  fe_mul(h->T, h->X, h->Y);
  return 0;
}

/* From ge_madd.c */

/*
r = p + q
*/

//x
static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
  fe t0;
  fe_add(r->X, p->Y, p->X);
  fe_sub(r->Y, p->Y, p->X);
  fe_mul(r->Z, r->X, q->yplusx);
  fe_mul(r->Y, r->Y, q->yminusx);
  fe_mul(r->T, q->xy2d, p->T);
  fe_add(t0, p->Z, p->Z);
  fe_sub(r->X, r->Z, r->Y);
  fe_add(r->Y, r->Z, r->Y);
  fe_add(r->Z, t0, r->T);
  fe_sub(r->T, t0, r->T);
}

/* From ge_msub.c */

/*
r = p - q
*/

//x
static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
  fe t0;
  fe_add(r->X, p->Y, p->X);
  fe_sub(r->Y, p->Y, p->X);
  fe_mul(r->Z, r->X, q->yminusx);
  fe_mul(r->Y, r->Y, q->yplusx);
  fe_mul(r->T, q->xy2d, p->T);
  fe_add(t0, p->Z, p->Z);
  fe_sub(r->X, r->Z, r->Y);
  fe_add(r->Y, r->Z, r->Y);
  fe_sub(r->Z, t0, r->T);
  fe_add(r->T, t0, r->T);
}

/* From ge_p1p1_to_p2.c */

/*
r = p
*/

//x
void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
  fe_mul(r->X, p->X, p->T);
  fe_mul(r->Y, p->Y, p->Z);
  fe_mul(r->Z, p->Z, p->T);
}

/* From ge_p1p1_to_p3.c */

/*
r = p
*/

//x
void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
  fe_mul(r->X, p->X, p->T);
  fe_mul(r->Y, p->Y, p->Z);
  fe_mul(r->Z, p->Z, p->T);
  fe_mul(r->T, p->X, p->Y);
}

/* From ge_p2_0.c */

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

/* From ge_p2_dbl.c */

/*
r = 2 * p
*/

//x
void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
  fe t0;
  fe_sq(r->X, p->X);
  fe_sq(r->Z, p->Y);
  fe_sq2(r->T, p->Z);
  fe_add(r->Y, p->X, p->Y);
  fe_sq(t0, r->Y);
  fe_add(r->Y, r->Z, r->X);
  fe_sub(r->Z, r->Z, r->X);
  fe_sub(r->X, t0, r->Y);
  fe_sub(r->T, r->T, r->Z);
}

/* From ge_p3_0.c */

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

/* From ge_p3_dbl.c */

/*
r = 2 * p
*/

//x
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);
}

/* From ge_p3_to_cached.c */

/*
r = p
*/

//x
void 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(r->Z, p->Z);
  fe_mul(r->T2d, p->T, fe_d2);
}

/* From ge_p3_to_p2.c */

/*
r = p
*/

//x
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);
}

/* From ge_p3_tobytes.c */

//x
void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) {
  fe recip;
  fe x;
  fe y;

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

/* From ge_precomp_0.c */

//x
static void ge_precomp_0(ge_precomp *h) {
  fe_1(h->yplusx);
  fe_1(h->yminusx);
  fe_0(h->xy2d);
}

/* From ge_scalarmult_base.c */

//x
static unsigned char equal(signed char b, signed char c) {
  unsigned char ub = b;
  unsigned char uc = c;
  unsigned char 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 unsigned char negative(signed char b) {
  unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
  x >>= 63; /* 1: yes; 0: no */
  return x;
}

static void ge_precomp_cmov(ge_precomp *t, const ge_precomp *u, unsigned char b) {
  fe_cmov(t->yplusx, u->yplusx, b);
  fe_cmov(t->yminusx, u->yminusx, b);
  fe_cmov(t->xy2d, u->xy2d, b);
}

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

  ge_precomp_0(t);
  ge_precomp_cmov(t, &ge_base[pos][0], equal(babs, 1));
  ge_precomp_cmov(t, &ge_base[pos][1], equal(babs, 2));
  ge_precomp_cmov(t, &ge_base[pos][2], equal(babs, 3));
  ge_precomp_cmov(t, &ge_base[pos][3], equal(babs, 4));
  ge_precomp_cmov(t, &ge_base[pos][4], equal(babs, 5));
  ge_precomp_cmov(t, &ge_base[pos][5], equal(babs, 6));
  ge_precomp_cmov(t, &ge_base[pos][6], equal(babs, 7));
  ge_precomp_cmov(t, &ge_base[pos][7], equal(babs, 8));
  fe_copy(minust.yplusx, t->yminusx);
  fe_copy(minust.yminusx, t->yplusx);
  fe_neg(minust.xy2d, t->xy2d);
  ge_precomp_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 ge_scalarmult_base(ge_p3 *h, const unsigned char *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);
  //note, these are indexing from 1, 3, 5, etc. 
  for (i = 1; i < 64; i += 2) {
    select(&t, i / 2, e[i]); //here's where you grab multiples of the basepoint .. 
    //so must be doing e P = (e[0] (2^4)^0 P + e[1] (2^4)^1 P + e[2] (2^4)^2 P + ...)
    //except, probably writing in big-endian to make more sense..
    //and the e[i] P are going to be pre-computed...
    //so have to wonder if by precomputing more, if can save time??
    ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r);
  }

  ge_p3_dbl(&r, h);  ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r);
  ge_p2_dbl(&r, &s); ge_p1p1_to_p3(h, &r);

  //note, these are indexing from 0, 2, 4, etc. 
  for (i = 0; i < 64; i += 2) {
    select(&t, i / 2, e[i]);
    ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r);
  }
}

/* From ge_sub.c */

/*
r = p - q
*/

//x
static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
  fe t0;
  fe_add(r->X, p->Y, p->X);
  fe_sub(r->Y, p->Y, p->X);
  fe_mul(r->Z, r->X, q->YminusX);
  fe_mul(r->Y, r->Y, q->YplusX);
  fe_mul(r->T, q->T2d, p->T);
  fe_mul(r->X, p->Z, q->Z);
  fe_add(t0, r->X, r->X);
  fe_sub(r->X, r->Z, r->Y);
  fe_add(r->Y, r->Z, r->Y);
  fe_sub(r->Z, t0, r->T);
  fe_add(r->T, t0, r->T);
}

/* From ge_tobytes.c */

//x
void ge_tobytes(unsigned char *s, const ge_p2 *h) {
  fe recip;
  fe x;
  fe y;

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

/* From sc_reduce.c */

/*
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.
*/

//x
void sc_reduce(unsigned char *s) {
  //the point is to load in 21 bits at a time..
  //Mininero should give you the ints 2097151, the shifts below, and either load 3 or 4
  int64_t s0 = 2097151 & load_3(s); //2097151 is 21 1's in binary, so there are possible 5 bits left over.. 
  int64_t s1 = 2097151 & (load_4(s + 2) >> 5); //now you start at 2^16, so you have to move right 5 bits to 2^21.., the 2 comes from the fact that you loaded 3 last time..
  int64_t s2 = 2097151 & (load_3(s + 5) >> 2); //in last one you had bits 22 ->42, you are starting at (2^8)^5 = 2^40, so need to move right 2 bits...
  int64_t s3 = 2097151 & (load_4(s + 7) >> 7); //etc...
  int64_t s4 = 2097151 & (load_4(s + 10) >> 4); //ahh, these are "int 64;s"
  int64_t s5 = 2097151 & (load_3(s + 13) >> 1); //not uint 64s
  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); //note no &2097151 here .. 
                                       //so rather than doing 24 = 512 
                                       //we've done 23 = 504 
                                       //so curve size rather than
                                       //size of s
                                       //this should be handled
                                       //at the end with those
                                       //two extra reductions
  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;
  //17 carries because 11, 12, ... 16 = #digits in l

  //reduce first 105 bits.. to go from 504 to 399
  //Note that 683901 * 2^(5*21) - 136657 * 2^(4 * 21) + ... - 66643 = 27742317777372353535851937790883648493, which is c in the curve order..
  s11 += s23 * 666643; // =1430509 - 2 ^ 21  //note there is a 12 step difference, 12^21 = 252
                                             //so you subtract q 12^21 and then add c at each step..
                                             //just have to be careful of the carries .. 
                                             //If you are using unsigned int's, you had better carry at each step
                                             //so the first step is to factorize 252 and whatever radix
                                             //must be in those factors.. 
  s12 += s23 * 470296; // = 1626855 - 2^21 - 1
  s13 += s23 * 654183; // = 1442968 - 2 ^ 21 - 1?
  s14 -= s23 * 997805; //note the negative ones are same as result from toDigits
  s15 += s23 * 136657; // 1960495 - 2 ** 21
  s16 -= s23 * 683901; //note negative ones are same 

  s10 += s22 * 666643; //22 - 10 = 12, 12 * 21 = 252 
  s11 += s22 * 470296;
  s12 += s22 * 654183;
  s13 -= s22 * 997805;
  s14 += s22 * 136657;
  s15 -= s22 * 683901;

  s9 += s21 * 666643; //21 - 9 = 12
  s10 += s21 * 470296;
  s11 += s21 * 654183;
  s12 -= s21 * 997805;
  s13 += s21 * 136657;
  s14 -= s21 * 683901;

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

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

  s6 += s18 * 666643;
  s7 += s18 * 470296;
  s8 += s18 * 654183;
  s9 -= s18 * 997805;
  s10 += s18 * 136657;
  s11 -= s18 * 683901;
  //so we repeat this until we get down to s11
  //note that 11 * 21 = 231

  //1st carry...
  //note span = 6 here
  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;//take parts that are more than 21 bits in new s6 and add to s7..
  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;

  //span = 5 here
  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;

  //reduce 105 bits to go from 399 to 294
  s5 += s17 * 666643; //17 - 5 = 12 = 252/21
  s6 += s17 * 470296;
  s7 += s17 * 654183;
  s8 -= s17 * 997805;
  s9 += s17 * 136657;
  s10 -= s17 * 683901;

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

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

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

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

  s0 += s12 * 666643; //12 - 0 = 12..
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  //2nd carry
  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;

  //reduce another 21 bits... go from 294 to 273
  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;
  s12 = 0;

  //3rd carry
  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;

  //reduce last 21 bits to go from 273 to get to 2^252..
  s0 += s12 * 666643;
  s1 += s12 * 470296;
  s2 += s12 * 654183;
  s3 -= s12 * 997805;
  s4 += s12 * 136657;
  s5 -= s12 * 683901;

  //carry
  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;

  //go from 2^[256/12]'s to 2^[256/32]'s 
  s[0] = s0 >> 0;
  s[1] = s0 >> 8;
  s[2] = (s0 >> 16) | (s1 << 5); // | since there is no overlap
  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;
}

/* New code */
/* (u / v)^(m + 1) */
static void fe_divpowm1(fe r, const fe u, const fe v) {
  fe v3, uv7, t0, t1, t2;
  int i;

  fe_sq(v3, v);
  fe_mul(v3, v3, v); /* v3 = v^3 */
  fe_sq(uv7, v3);
  fe_mul(uv7, uv7, v);
  fe_mul(uv7, uv7, u); /* uv7 = uv^7 */

  /*fe_pow22523(uv7, uv7);*/

  /* From fe_pow22523.c */

  fe_sq(t0, uv7);
  fe_sq(t1, t0);
  fe_sq(t1, t1);
  fe_mul(t1, uv7, t1);
  fe_mul(t0, t0, t1);
  fe_sq(t0, t0);
  fe_mul(t0, t1, t0);
  fe_sq(t1, t0);
  for (i = 0; i < 4; ++i) {
    fe_sq(t1, t1);
  }
  fe_mul(t0, t1, t0);
  fe_sq(t1, t0);
  for (i = 0; i < 9; ++i) {
    fe_sq(t1, t1);
  }
  fe_mul(t1, t1, t0);
  fe_sq(t2, t1);
  for (i = 0; i < 19; ++i) {
    fe_sq(t2, t2);
  }
  fe_mul(t1, t2, t1);
  for (i = 0; i < 10; ++i) {
    fe_sq(t1, t1);
  }
  fe_mul(t0, t1, t0);
  fe_sq(t1, t0);
  for (i = 0; i < 49; ++i) {
    fe_sq(t1, t1);
  }
  fe_mul(t1, t1, t0);
  fe_sq(t2, t1);
  for (i = 0; i < 99; ++i) {
    fe_sq(t2, t2);
  }
  fe_mul(t1, t2, t1);
  for (i = 0; i < 50; ++i) {
    fe_sq(t1, t1);
  }
  fe_mul(t0, t1, t0);
  fe_sq(t0, t0);
  fe_sq(t0, t0);
  fe_mul(t0, t0, uv7);

  /* End fe_pow22523.c */
  /* t0 = (uv^7)^((q-5)/8) */
  fe_mul(t0, t0, v3);
  fe_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */
}

static void ge_cached_0(ge_cached *r) {
  fe_1(r->YplusX);
  fe_1(r->YminusX);
  fe_1(r->Z);
  fe_0(r->T2d);
}

static void ge_cached_cmov(ge_cached *t, const ge_cached *u, unsigned char 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);
}

/* Assumes that a[31] <= 127 */
void ge_scalarmult(ge_p2 *r, const unsigned char *a, const ge_p3 *A) {
  signed char e[64];
  int carry, carry2, i;
  ge_cached Ai[8]; /* 1 * A, 2 * A, ..., 8 * A */
  ge_p1p1 t;
  ge_p3 u;

  carry = 0; /* 0..1 */
  for (i = 0; i < 31; i++) {
    carry += a[i]; /* 0..256 */
    carry2 = (carry + 8) >> 4; /* 0..16 */
    e[2 * i] = carry - (carry2 << 4); /* -8..7 */
    carry = (carry2 + 8) >> 4; /* 0..1 */
    e[2 * i + 1] = carry2 - (carry << 4); /* -8..7 */
  }
  carry += a[31]; /* 0..128 */
  carry2 = (carry + 8) >> 4; /* 0..8 */
  e[62] = carry - (carry2 << 4); /* -8..7 */
  e[63] = carry2; /* 0..8 */

  ge_p3_to_cached(&Ai[0], A);
  for (i = 0; i < 7; i++) {
    ge_add(&t, A, &Ai[i]);
    ge_p1p1_to_p3(&u, &t);
    ge_p3_to_cached(&Ai[i + 1], &u);
  }

  ge_p2_0(r);
  for (i = 63; i >= 0; i--) {
    signed char b = e[i];
    unsigned char bnegative = negative(b);
    unsigned char babs = b - (((-bnegative) & b) << 1);
    ge_cached cur, minuscur;
    ge_p2_dbl(&t, r);
    ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    ge_p1p1_to_p2(r, &t);
    ge_p2_dbl(&t, r);
    ge_p1p1_to_p3(&u, &t);
    ge_cached_0(&cur);
    ge_cached_cmov(&cur, &Ai[0], equal(babs, 1));
    ge_cached_cmov(&cur, &Ai[1], equal(babs, 2));
    ge_cached_cmov(&cur, &Ai[2], equal(babs, 3));
    ge_cached_cmov(&cur, &Ai[3], equal(babs, 4));
    ge_cached_cmov(&cur, &Ai[4], equal(babs, 5));
    ge_cached_cmov(&cur, &Ai[5], equal(babs, 6));
    ge_cached_cmov(&cur, &Ai[6], equal(babs, 7));
    ge_cached_cmov(&cur, &Ai[7], equal(babs, 8));
    fe_copy(minuscur.YplusX, cur.YminusX);
    fe_copy(minuscur.YminusX, cur.YplusX);
    fe_copy(minuscur.Z, cur.Z);
    fe_neg(minuscur.T2d, cur.T2d);
    ge_cached_cmov(&cur, &minuscur, bnegative);
    ge_add(&t, &u, &cur);
    ge_p1p1_to_p2(r, &t);
  }
}

//assume Bi has precomputed multiples
void ge_double_scalarmult_precomp_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b, const ge_dsmp Bi) {
  signed char aslide[256];
  signed char bslide[256];
  ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ //precomps
  ge_p1p1 t;
  ge_p3 u;
  int i;

  slide(aslide, a);
  slide(bslide, b);
  ge_dsm_precomp(Ai, A);

  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) {
      ge_p1p1_to_p3(&u, &t);
      ge_add(&t, &u, &Ai[aslide[i]/2]);
    } else if (aslide[i] < 0) {
      ge_p1p1_to_p3(&u, &t);
      ge_sub(&t, &u, &Ai[(-aslide[i])/2]);
    }

    if (bslide[i] > 0) {
      ge_p1p1_to_p3(&u, &t);
      ge_add(&t, &u, &Bi[bslide[i]/2]);
    } else if (bslide[i] < 0) {
      ge_p1p1_to_p3(&u, &t);
      ge_sub(&t, &u, &Bi[(-bslide[i])/2]);
    }

    ge_p1p1_to_p2(r, &t);
  }
}

//x
void ge_mul8(ge_p1p1 *r, const ge_p2 *t) {
  ge_p2 u;
  ge_p2_dbl(r, t);
  ge_p1p1_to_p2(&u, r);
  ge_p2_dbl(r, &u);
  ge_p1p1_to_p2(&u, r);
  ge_p2_dbl(r, &u);
}

//x
void ge_fromfe_frombytes_vartime(ge_p2 *r, const unsigned char *s) {
  fe u, v, w, x, y, z;
  unsigned char sign;

  /* From fe_frombytes.c */

  int64_t h0 = load_4(s);
  int64_t h1 = load_3(s + 4) << 6;
  int64_t h2 = load_3(s + 7) << 5;
  int64_t h3 = load_3(s + 10) << 3;
  int64_t h4 = load_3(s + 13) << 2;
  int64_t h5 = load_4(s + 16);
  int64_t h6 = load_3(s + 20) << 7;
  int64_t h7 = load_3(s + 23) << 5;
  int64_t h8 = load_3(s + 26) << 4;
  int64_t h9 = load_3(s + 29) << 2;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

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

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

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

  /* End fe_frombytes.c */

  fe_sq2(v, u); /* 2 * u^2 */
  fe_1(w);
  fe_add(w, v, w); /* w = 2 * u^2 + 1 */
  fe_sq(x, w); /* w^2 */
  fe_mul(y, fe_ma2, v); /* -2 * A^2 * u^2 */
  fe_add(x, x, y); /* x = w^2 - 2 * A^2 * u^2 */
  fe_divpowm1(r->X, w, x); /* (w / x)^(m + 1) */
  fe_sq(y, r->X);
  fe_mul(x, y, x);
  fe_sub(y, w, x);
  fe_copy(z, fe_ma);
  if (fe_isnonzero(y)) {
    fe_add(y, w, x);
    if (fe_isnonzero(y)) {
      goto negative;
    } else {
      fe_mul(r->X, r->X, fe_fffb1);
    }
  } else {
    fe_mul(r->X, r->X, fe_fffb2);
  }
  fe_mul(r->X, r->X, u); /* u * sqrt(2 * A * (A + 2) * w / x) */
  fe_mul(z, z, v); /* -2 * A * u^2 */
  sign = 0;
  goto setsign;
negative:
  fe_mul(x, x, fe_sqrtm1);
  fe_sub(y, w, x);
  if (fe_isnonzero(y)) {
    assert((fe_add(y, w, x), !fe_isnonzero(y)));
    fe_mul(r->X, r->X, fe_fffb3);
  } else {
    fe_mul(r->X, r->X, fe_fffb4);
  }
  /* r->X = sqrt(A * (A + 2) * w / x) */
  /* z = -A */
  sign = 1;
setsign:
  if (fe_isnegative(r->X) != sign) {
    assert(fe_isnonzero(r->X));
    fe_neg(r->X, r->X);
  }
  fe_add(r->Z, z, w);
  fe_sub(r->Y, z, w);
  fe_mul(r->X, r->X, r->Z);
#if !defined(NDEBUG)
  {
    fe check_x, check_y, check_iz, check_v;
    fe_invert(check_iz, r->Z);
    fe_mul(check_x, r->X, check_iz);
    fe_mul(check_y, r->Y, check_iz);
    fe_sq(check_x, check_x);
    fe_sq(check_y, check_y);
    fe_mul(check_v, check_x, check_y);
    fe_mul(check_v, fe_d, check_v);
    fe_add(check_v, check_v, check_x);
    fe_sub(check_v, check_v, check_y);
    fe_1(check_x);
    fe_add(check_v, check_v, check_x);
    assert(!fe_isnonzero(check_v));
  }
#endif
}

//x
void sc_0(unsigned char *s) {
  int i;
  for (i = 0; i < 32; i++) {
    s[i] = 0;
  }
}

//x
void sc_reduce32(unsigned char *s) {
  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 = (load_4(s + 28) >> 7);
  int64_t s12 = 0;
  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;

  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;

  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;
}

//x
void sc_add(unsigned char *s, const unsigned char *a, const unsigned char *b) {
  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 s0 = a0 + b0;
  int64_t s1 = a1 + b1;
  int64_t s2 = a2 + b2;
  int64_t s3 = a3 + b3;
  int64_t s4 = a4 + b4;
  int64_t s5 = a5 + b5;
  int64_t s6 = a6 + b6;
  int64_t s7 = a7 + b7;
  int64_t s8 = a8 + b8;
  int64_t s9 = a9 + b9;
  int64_t s10 = a10 + b10;
  int64_t s11 = a11 + b11;
  int64_t s12 = 0;
  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;

  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;

  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;
}

//x
void sc_sub(unsigned char *s, const unsigned char *a, const unsigned char *b) {
  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 s0 = a0 - b0;
  int64_t s1 = a1 - b1;
  int64_t s2 = a2 - b2;
  int64_t s3 = a3 - b3;
  int64_t s4 = a4 - b4;
  int64_t s5 = a5 - b5;
  int64_t s6 = a6 - b6;
  int64_t s7 = a7 - b7;
  int64_t s8 = a8 - b8;
  int64_t s9 = a9 - b9;
  int64_t s10 = a10 - b10;
  int64_t s11 = a11 - b11;
  int64_t s12 = 0;
  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;

  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;

  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] = (c-ab) mod l
  where l = 2^252 + 27742317777372353535851937790883648493.
*/

//x
void sc_mulsub(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *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;

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

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

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

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

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

  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;

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

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

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

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

  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;

  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;
}

/* Assumes that a != INT64_MIN */
//x c.f. lt in 32 bit ref
static int64_t signum(int64_t a) {
  return (a >> 63) - ((-a) >> 63);
}

//x
int sc_check(const unsigned char *s) {
  int64_t s0 = load_4(s);
  int64_t s1 = load_4(s + 4);
  int64_t s2 = load_4(s + 8);
  int64_t s3 = load_4(s + 12);
  int64_t s4 = load_4(s + 16);
  int64_t s5 = load_4(s + 20);
  int64_t s6 = load_4(s + 24);
  int64_t s7 = load_4(s + 28);
  return (signum(1559614444 - s0) + (signum(1477600026 - s1) << 1) + (signum(2734136534 - s2) << 2) + (signum(350157278 - s3) << 3) + (signum(-s4) << 4) + (signum(-s5) << 5) + (signum(-s6) << 6) + (signum(268435456 - s7) << 7)) >> 8;
}

//x
int sc_isnonzero(const unsigned char *s) {
  return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] |
    s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] |
    s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
    s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1;
}