text: /*************************************************************************/
  /*  ed25519_fe.cpp                                                       */
  /*************************************************************************/
  /*                     This file is part of the                          */
  /*             Maria and Mysql database connection module                */
  /*                    for use in the Godot Engine                        */
  /*                           GODOT ENGINE                                */
  /*                      https://godotengine.org                          */
  /* This file was derived from information found at                       */
  /* https://tools.ietf.org/html/rfc8032#page-44                           */
  /*************************************************************************/
  /* Copyright (c) 2021 Shawn Shipton. https://vikingtinkerer.com          */
  /*                                                                       */
  /* 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.                */
  /*************************************************************************/
  
  #include "ed25519_fe.h"
  
  #include <algorithm>
  #include <cassert>
  #include <vector>
  
  static uint64_t bytes_to_u64(const uint8_t *src, size_t byte_count) {
  	uint64_t result = 0;
  	assert(byte_count <= 8);
  
  	for (size_t i = 0; i < byte_count; ++i)
  		result |= static_cast<uint64_t>(src[i] << (i * 8));
  	return result;
  }
  
  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;
  }
  
  /*
      h = 1
  */
  
  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;
  }
  
  /*
      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.
  */
  
  void fe_add(fe h, const fe f, const fe g) {
  	for (size_t i = 0; i < 10; ++i)
  		h[i] = f[i] + g[i];
  }
  
  /*
      Replace (f,g) with (g,g) if b == 1;
      replace (f,g) with (f,g) if b == 0.
  
      Preconditions: b in {0,1}.
  */
  
  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;
  
  	b = (unsigned int)(-(int)b); /* silence warning */
  	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;
  }
  
  /*
      Replace (f,g) with (g,f) if b == 1;
      replace (f,g) with (f,g) if b == 0.
  
      Preconditions: b in {0,1}.
  */
  
  void fe_cswap(fe f, 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;
  	b = (unsigned int)(-(int)b); /* silence warning */
  	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;
  	g[0] = g0 ^ x0;
  	g[1] = g1 ^ x1;
  	g[2] = g2 ^ x2;
  	g[3] = g3 ^ x3;
  	g[4] = g4 ^ x4;
  	g[5] = g5 ^ x5;
  	g[6] = g6 ^ x6;
  	g[7] = g7 ^ x7;
  	g[8] = g8 ^ x8;
  	g[9] = g9 ^ x9;
  }
  
  /*
      h = f
  */
  
  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;
  }
  
  /*
      Ignores top bit of h.
  */
  void fe_frombytes(fe h, const uint8_t *s) {
  	int64_t h0 = bytes_to_u64(s, 4);
  	int64_t h1 = bytes_to_u64(s + 4, 3) << 6;
  	int64_t h2 = bytes_to_u64(s + 7, 3) << 5;
  	int64_t h3 = bytes_to_u64(s + 10, 3) << 3;
  	int64_t h4 = bytes_to_u64(s + 13, 3) << 2;
  	int64_t h5 = bytes_to_u64(s + 16, 4);
  	int64_t h6 = bytes_to_u64(s + 20, 3) << 7;
  	int64_t h7 = bytes_to_u64(s + 23, 3) << 5;
  	int64_t h8 = bytes_to_u64(s + 26, 3) << 4;
  	int64_t h9 = (bytes_to_u64(s + 29, 3) & 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;
  
  	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[0] = (int32_t)h0;
  	h[1] = (int32_t)h1;
  	h[2] = (int32_t)h2;
  	h[3] = (int32_t)h3;
  	h[4] = (int32_t)h4;
  	h[5] = (int32_t)h5;
  	h[6] = (int32_t)h6;
  	h[7] = (int32_t)h7;
  	h[8] = (int32_t)h8;
  	h[9] = (int32_t)h9;
  }
  
  void fe_invert(fe out, const fe z) {
  	fe t0;
  	fe t1;
  	fe t2;
  	fe t3;
  	int i;
  
  	fe_sq(t0, z);
  
  	for (i = 1; i < 1; ++i) {
  		fe_sq(t0, t0);
  	}
  
  	fe_sq(t1, t0);
  
  	for (i = 1; i < 2; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(t1, z, t1);
  	fe_mul(t0, t0, t1);
  	fe_sq(t2, t0);
  
  	for (i = 1; i < 1; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t1, t1, t2);
  	fe_sq(t2, t1);
  
  	for (i = 1; i < 5; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t1, t2, t1);
  	fe_sq(t2, t1);
  
  	for (i = 1; i < 10; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t2, t2, t1);
  	fe_sq(t3, t2);
  
  	for (i = 1; i < 20; ++i) {
  		fe_sq(t3, t3);
  	}
  
  	fe_mul(t2, t3, t2);
  	fe_sq(t2, t2);
  
  	for (i = 1; i < 10; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t1, t2, t1);
  	fe_sq(t2, t1);
  
  	for (i = 1; i < 50; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t2, t2, t1);
  	fe_sq(t3, t2);
  
  	for (i = 1; i < 100; ++i) {
  		fe_sq(t3, t3);
  	}
  
  	fe_mul(t2, t3, t2);
  	fe_sq(t2, t2);
  
  	for (i = 1; i < 50; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t1, t2, t1);
  	fe_sq(t1, t1);
  
  	for (i = 1; i < 5; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(out, t1, t0);
  }
  
  /*
      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.
  */
  
  int fe_isnegative(const fe f) {
  	uint8_t s[32];
  
  	fe_tobytes(s, f);
  
  	return s[0] & 1;
  }
  
  /*
      return 1 if f == 0
      return 0 if f != 0
  
      Preconditions:
         |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
  */
  
  int fe_isnonzero(const fe f) {
  	uint8_t s[32];
  	uint8_t r;
  
  	fe_tobytes(s, f);
  	r = s[0];
  
  	for (size_t i = 1; i < 32; ++i)
  		r |= s[i];
  
  	return r != 0;
  }
  
  /*
      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.
  */
  
  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;
  
  	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] = (int32_t)h0;
  	h[1] = (int32_t)h1;
  	h[2] = (int32_t)h2;
  	h[3] = (int32_t)h3;
  	h[4] = (int32_t)h4;
  	h[5] = (int32_t)h5;
  	h[6] = (int32_t)h6;
  	h[7] = (int32_t)h7;
  	h[8] = (int32_t)h8;
  	h[9] = (int32_t)h9;
  }
  
  /*
  h = f * 121666
  Can overlap h with f.
  
  Preconditions:
     |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
  
  Postconditions:
     |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
  */
  
  void fe_mul121666(fe h, 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];
  	int64_t h0 = f0 * (int64_t)121666;
  	int64_t h1 = f1 * (int64_t)121666;
  	int64_t h2 = f2 * (int64_t)121666;
  	int64_t h3 = f3 * (int64_t)121666;
  	int64_t h4 = f4 * (int64_t)121666;
  	int64_t h5 = f5 * (int64_t)121666;
  	int64_t h6 = f6 * (int64_t)121666;
  	int64_t h7 = f7 * (int64_t)121666;
  	int64_t h8 = f8 * (int64_t)121666;
  	int64_t h9 = f9 * (int64_t)121666;
  	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;
  
  	h[0] = (int32_t)h0;
  	h[1] = (int32_t)h1;
  	h[2] = (int32_t)h2;
  	h[3] = (int32_t)h3;
  	h[4] = (int32_t)h4;
  	h[5] = (int32_t)h5;
  	h[6] = (int32_t)h6;
  	h[7] = (int32_t)h7;
  	h[8] = (int32_t)h8;
  	h[9] = (int32_t)h9;
  }
  
  /*
  h = -f
  
  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.
  */
  
  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;
  }
  
  void fe_pow22523(fe out, const fe z) {
  	fe t0;
  	fe t1;
  	fe t2;
  	int i;
  	fe_sq(t0, z);
  
  	for (i = 1; i < 1; ++i) {
  		fe_sq(t0, t0);
  	}
  
  	fe_sq(t1, t0);
  
  	for (i = 1; i < 2; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(t1, z, t1);
  	fe_mul(t0, t0, t1);
  	fe_sq(t0, t0);
  
  	for (i = 1; i < 1; ++i) {
  		fe_sq(t0, t0);
  	}
  
  	fe_mul(t0, t1, t0);
  	fe_sq(t1, t0);
  
  	for (i = 1; i < 5; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(t0, t1, t0);
  	fe_sq(t1, t0);
  
  	for (i = 1; i < 10; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(t1, t1, t0);
  	fe_sq(t2, t1);
  
  	for (i = 1; i < 20; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t1, t2, t1);
  	fe_sq(t1, t1);
  
  	for (i = 1; i < 10; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(t0, t1, t0);
  	fe_sq(t1, t0);
  
  	for (i = 1; i < 50; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(t1, t1, t0);
  	fe_sq(t2, t1);
  
  	for (i = 1; i < 100; ++i) {
  		fe_sq(t2, t2);
  	}
  
  	fe_mul(t1, t2, t1);
  	fe_sq(t1, t1);
  
  	for (i = 1; i < 50; ++i) {
  		fe_sq(t1, t1);
  	}
  
  	fe_mul(t0, t1, t0);
  	fe_sq(t0, t0);
  
  	for (i = 1; i < 2; ++i) {
  		fe_sq(t0, t0);
  	}
  
  	fe_mul(out, t0, z);
  	return;
  }
  
  /*
  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.
  */
  
  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] = (int32_t)h0;
  	h[1] = (int32_t)h1;
  	h[2] = (int32_t)h2;
  	h[3] = (int32_t)h3;
  	h[4] = (int32_t)h4;
  	h[5] = (int32_t)h5;
  	h[6] = (int32_t)h6;
  	h[7] = (int32_t)h7;
  	h[8] = (int32_t)h8;
  	h[9] = (int32_t)h9;
  }
  
  /*
  h = 2 * f * f
  Can overlap h with f.
  
  Preconditions:
     |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
  
  Postconditions:
     |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
  */
  
  /*
  See fe_mul.c for discussion of implementation strategy.
  */
  
  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] = (int32_t)h0;
  	h[1] = (int32_t)h1;
  	h[2] = (int32_t)h2;
  	h[3] = (int32_t)h3;
  	h[4] = (int32_t)h4;
  	h[5] = (int32_t)h5;
  	h[6] = (int32_t)h6;
  	h[7] = (int32_t)h7;
  	h[8] = (int32_t)h8;
  	h[9] = (int32_t)h9;
  }
  
  /*
  h = f - 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.
  */
  
  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;
  }
  
  /*
  Preconditions:
    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
  
  Write p=2^255-19; q=floor(h/p).
  Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
  
  Proof:
    Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
    Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
  
    Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
    Then 0<y<1.
  
    Write r=h-pq.
    Have 0<=r<=p-1=2^255-20.
    Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
  
    Write x=r+19(2^-255)r+y.
    Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
  
    Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
    so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
  */
  
  void fe_tobytes(uint8_t *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] = (uint8_t)(h0 >> 0);
  	s[1] = (uint8_t)(h0 >> 8);
  	s[2] = (uint8_t)(h0 >> 16);
  	s[3] = (uint8_t)((h0 >> 24) | (h1 << 2));
  	s[4] = (uint8_t)(h1 >> 6);
  	s[5] = (uint8_t)(h1 >> 14);
  	s[6] = (uint8_t)((h1 >> 22) | (h2 << 3));
  	s[7] = (uint8_t)(h2 >> 5);
  	s[8] = (uint8_t)(h2 >> 13);
  	s[9] = (uint8_t)((h2 >> 21) | (h3 << 5));
  	s[10] = (uint8_t)(h3 >> 3);
  	s[11] = (uint8_t)(h3 >> 11);
  	s[12] = (uint8_t)((h3 >> 19) | (h4 << 6));
  	s[13] = (uint8_t)(h4 >> 2);
  	s[14] = (uint8_t)(h4 >> 10);
  	s[15] = (uint8_t)(h4 >> 18);
  	s[16] = (uint8_t)(h5 >> 0);
  	s[17] = (uint8_t)(h5 >> 8);
  	s[18] = (uint8_t)(h5 >> 16);
  	s[19] = (uint8_t)((h5 >> 24) | (h6 << 1));
  	s[20] = (uint8_t)(h6 >> 7);
  	s[21] = (uint8_t)(h6 >> 15);
  	s[22] = (uint8_t)((h6 >> 23) | (h7 << 3));
  	s[23] = (uint8_t)(h7 >> 5);
  	s[24] = (uint8_t)(h7 >> 13);
  	s[25] = (uint8_t)((h7 >> 21) | (h8 << 4));
  	s[26] = (uint8_t)(h8 >> 4);
  	s[27] = (uint8_t)(h8 >> 12);
  	s[28] = (uint8_t)((h8 >> 20) | (h9 << 6));
  	s[29] = (uint8_t)(h9 >> 2);
  	s[30] = (uint8_t)(h9 >> 10);
  	s[31] = (uint8_t)(h9 >> 18);
  }
  