tor

ed25519-ref10.c (171009B)

---

#include <stdint.h>
#include <stddef.h>
#include <string.h>

static int crypto_verify_32(const unsigned char *x,const unsigned char *y)
{
 unsigned int differentbits = 0;
#define F(i) differentbits |= x[i] ^ y[i];
 F(0)
 F(1)
 F(2)
 F(3)
 F(4)
 F(5)
 F(6)
 F(7)
 F(8)
 F(9)
 F(10)
 F(11)
 F(12)
 F(13)
 F(14)
 F(15)
 F(16)
 F(17)
 F(18)
 F(19)
 F(20)
 F(21)
 F(22)
 F(23)
 F(24)
 F(25)
 F(26)
 F(27)
 F(28)
 F(29)
 F(30)
 F(31)
 return (1 & ((differentbits - 1) >> 8)) - 1;
}

#if defined(ED25519_REFHASH)

/* reference/slow SHA-512. really, do not use this */

#define HASH_BLOCK_SIZE 128
#define HASH_DIGEST_SIZE 64

typedef struct sha512_state_t {
uint64_t H[8];
uint64_t T[2];
uint32_t leftover;
uint8_t buffer[HASH_BLOCK_SIZE];
} sha512_state;

typedef sha512_state ed25519_hash_context;

static const uint64_t sha512_constants[80] = {
0x428a2f98d728ae22ull, 0x7137449123ef65cdull, 0xb5c0fbcfec4d3b2full, 0xe9b5dba58189dbbcull,
0x3956c25bf348b538ull, 0x59f111f1b605d019ull, 0x923f82a4af194f9bull, 0xab1c5ed5da6d8118ull,
0xd807aa98a3030242ull, 0x12835b0145706fbeull, 0x243185be4ee4b28cull, 0x550c7dc3d5ffb4e2ull,
0x72be5d74f27b896full, 0x80deb1fe3b1696b1ull, 0x9bdc06a725c71235ull, 0xc19bf174cf692694ull,
0xe49b69c19ef14ad2ull, 0xefbe4786384f25e3ull, 0x0fc19dc68b8cd5b5ull, 0x240ca1cc77ac9c65ull,
0x2de92c6f592b0275ull, 0x4a7484aa6ea6e483ull, 0x5cb0a9dcbd41fbd4ull, 0x76f988da831153b5ull,
0x983e5152ee66dfabull, 0xa831c66d2db43210ull, 0xb00327c898fb213full, 0xbf597fc7beef0ee4ull,
0xc6e00bf33da88fc2ull, 0xd5a79147930aa725ull, 0x06ca6351e003826full, 0x142929670a0e6e70ull,
0x27b70a8546d22ffcull, 0x2e1b21385c26c926ull, 0x4d2c6dfc5ac42aedull, 0x53380d139d95b3dfull,
0x650a73548baf63deull, 0x766a0abb3c77b2a8ull, 0x81c2c92e47edaee6ull, 0x92722c851482353bull,
0xa2bfe8a14cf10364ull, 0xa81a664bbc423001ull, 0xc24b8b70d0f89791ull, 0xc76c51a30654be30ull,
0xd192e819d6ef5218ull, 0xd69906245565a910ull, 0xf40e35855771202aull, 0x106aa07032bbd1b8ull,
0x19a4c116b8d2d0c8ull, 0x1e376c085141ab53ull, 0x2748774cdf8eeb99ull, 0x34b0bcb5e19b48a8ull,
0x391c0cb3c5c95a63ull, 0x4ed8aa4ae3418acbull, 0x5b9cca4f7763e373ull, 0x682e6ff3d6b2b8a3ull,
0x748f82ee5defb2fcull, 0x78a5636f43172f60ull, 0x84c87814a1f0ab72ull, 0x8cc702081a6439ecull,
0x90befffa23631e28ull, 0xa4506cebde82bde9ull, 0xbef9a3f7b2c67915ull, 0xc67178f2e372532bull,
0xca273eceea26619cull, 0xd186b8c721c0c207ull, 0xeada7dd6cde0eb1eull, 0xf57d4f7fee6ed178ull,
0x06f067aa72176fbaull, 0x0a637dc5a2c898a6ull, 0x113f9804bef90daeull, 0x1b710b35131c471bull,
0x28db77f523047d84ull, 0x32caab7b40c72493ull, 0x3c9ebe0a15c9bebcull, 0x431d67c49c100d4cull,
0x4cc5d4becb3e42b6ull, 0x597f299cfc657e2aull, 0x5fcb6fab3ad6faecull, 0x6c44198c4a475817ull
};

static uint64_t
sha512_ROTR64(uint64_t x, int k) {
return (x >> k) | (x << (64 - k));
}

static uint64_t
sha512_LOAD64_BE(const uint8_t *p) {
return 
	((uint64_t)p[0] << 56) |
	((uint64_t)p[1] << 48) |
	((uint64_t)p[2] << 40) |
	((uint64_t)p[3] << 32) |
	((uint64_t)p[4] << 24) |
	((uint64_t)p[5] << 16) |
	((uint64_t)p[6] <<  8) |
	((uint64_t)p[7]      );
}

static void
sha512_STORE64_BE(uint8_t *p, uint64_t v) {
p[0] = (uint8_t)(v >> 56);
p[1] = (uint8_t)(v >> 48);
p[2] = (uint8_t)(v >> 40);
p[3] = (uint8_t)(v >> 32);
p[4] = (uint8_t)(v >> 24);
p[5] = (uint8_t)(v >> 16);
p[6] = (uint8_t)(v >>  8);
p[7] = (uint8_t)(v      );
}

#define Ch(x,y,z)  (z ^ (x & (y ^ z)))
#define Maj(x,y,z) (((x | y) & z) | (x & y))
#define S0(x)      (sha512_ROTR64(x, 28) ^ sha512_ROTR64(x, 34) ^ sha512_ROTR64(x, 39))
#define S1(x)      (sha512_ROTR64(x, 14) ^ sha512_ROTR64(x, 18) ^ sha512_ROTR64(x, 41))
#define G0(x)      (sha512_ROTR64(x,  1) ^ sha512_ROTR64(x,  8) ^ (x >>  7))
#define G1(x)      (sha512_ROTR64(x, 19) ^ sha512_ROTR64(x, 61) ^ (x >>  6))
#define W0(in,i)   (sha512_LOAD64_BE(&in[i * 8]))
#define W1(i)      (G1(w[i - 2]) + w[i - 7] + G0(w[i - 15]) + w[i - 16])
#define STEP(i) \
t1 = S0(r[0]) + Maj(r[0], r[1], r[2]); \
t0 = r[7] + S1(r[4]) + Ch(r[4], r[5], r[6]) + sha512_constants[i] + w[i]; \
r[7] = r[6]; \
r[6] = r[5]; \
r[5] = r[4]; \
r[4] = r[3] + t0; \
r[3] = r[2]; \
r[2] = r[1]; \
r[1] = r[0]; \
r[0] = t0 + t1;

static void
sha512_blocks(sha512_state *S, const uint8_t *in, size_t blocks) {
uint64_t r[8], w[80], t0, t1;
size_t i;

for (i = 0; i < 8; i++) r[i] = S->H[i];

while (blocks--) {
	for (i =  0; i < 16; i++) { w[i] = W0(in, i); }
	for (i = 16; i < 80; i++) { w[i] = W1(i); }
	for (i =  0; i < 80; i++) { STEP(i); }
	for (i =  0; i <  8; i++) { r[i] += S->H[i]; S->H[i] = r[i]; }
	S->T[0] += HASH_BLOCK_SIZE * 8;
	S->T[1] += (!S->T[0]) ? 1 : 0;
	in += HASH_BLOCK_SIZE;
}
}

static void
ed25519_hash_init(sha512_state *S) {
S->H[0] = 0x6a09e667f3bcc908ull;
S->H[1] = 0xbb67ae8584caa73bull;
S->H[2] = 0x3c6ef372fe94f82bull;
S->H[3] = 0xa54ff53a5f1d36f1ull;
S->H[4] = 0x510e527fade682d1ull;
S->H[5] = 0x9b05688c2b3e6c1full;
S->H[6] = 0x1f83d9abfb41bd6bull;
S->H[7] = 0x5be0cd19137e2179ull;
S->T[0] = 0;
S->T[1] = 0;
S->leftover = 0;
}

static void
ed25519_hash_update(sha512_state *S, const uint8_t *in, size_t inlen) {
size_t blocks, want;

/* handle the previous data */
if (S->leftover) {
	want = (HASH_BLOCK_SIZE - S->leftover);
	want = (want < inlen) ? want : inlen;
	memcpy(S->buffer + S->leftover, in, want);
	S->leftover += (uint32_t)want;
	if (S->leftover < HASH_BLOCK_SIZE)
		return;
	in += want;
	inlen -= want;
	sha512_blocks(S, S->buffer, 1);
}

/* handle the current data */
blocks = (inlen & ~(HASH_BLOCK_SIZE - 1));
S->leftover = (uint32_t)(inlen - blocks);
if (blocks) {
	sha512_blocks(S, in, blocks / HASH_BLOCK_SIZE);
	in += blocks;
}

/* handle leftover data */
if (S->leftover)
	memcpy(S->buffer, in, S->leftover);
}

static void
ed25519_hash_final(sha512_state *S, uint8_t *hash) {
uint64_t t0 = S->T[0] + (S->leftover * 8), t1 = S->T[1];

S->buffer[S->leftover] = 0x80;
if (S->leftover <= 111) {
	memset(S->buffer + S->leftover + 1, 0, 111 - S->leftover);
} else {
	memset(S->buffer + S->leftover + 1, 0, 127 - S->leftover);
	sha512_blocks(S, S->buffer, 1);
	memset(S->buffer, 0, 112);
}

sha512_STORE64_BE(S->buffer + 112, t1);
sha512_STORE64_BE(S->buffer + 120, t0);
sha512_blocks(S, S->buffer, 1);

sha512_STORE64_BE(&hash[ 0], S->H[0]);
sha512_STORE64_BE(&hash[ 8], S->H[1]);
sha512_STORE64_BE(&hash[16], S->H[2]);
sha512_STORE64_BE(&hash[24], S->H[3]);
sha512_STORE64_BE(&hash[32], S->H[4]);
sha512_STORE64_BE(&hash[40], S->H[5]);
sha512_STORE64_BE(&hash[48], S->H[6]);
sha512_STORE64_BE(&hash[56], S->H[7]);
}

static void
crypto_hash_sha512(unsigned char *hash, const unsigned char *in, size_t inlen) {
ed25519_hash_context ctx;
ed25519_hash_init(&ctx);
ed25519_hash_update(&ctx, in, inlen);
ed25519_hash_final(&ctx, hash);
}

#else

#include <openssl/sha.h>

static void
crypto_hash_sha512(unsigned char *hash, const unsigned char *in, size_t inlen) {
SHA512(in, inlen, hash);
}

#endif




typedef int32_t crypto_int32;
typedef uint32_t crypto_uint32;
typedef int64_t crypto_int64;
typedef uint64_t crypto_uint64;

typedef crypto_int32 fe[10];

/*
h = 0
*/

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;
}

/*
h = 1
*/

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;
}

/*
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)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 f9 = f[9];
 crypto_int32 g0 = g[0];
 crypto_int32 g1 = g[1];
 crypto_int32 g2 = g[2];
 crypto_int32 g3 = g[3];
 crypto_int32 g4 = g[4];
 crypto_int32 g5 = g[5];
 crypto_int32 g6 = g[6];
 crypto_int32 g7 = g[7];
 crypto_int32 g8 = g[8];
 crypto_int32 g9 = g[9];
 crypto_int32 h0 = f0 + g0;
 crypto_int32 h1 = f1 + g1;
 crypto_int32 h2 = f2 + g2;
 crypto_int32 h3 = f3 + g3;
 crypto_int32 h4 = f4 + g4;
 crypto_int32 h5 = f5 + g5;
 crypto_int32 h6 = f6 + g6;
 crypto_int32 h7 = f7 + g7;
 crypto_int32 h8 = f8 + g8;
 crypto_int32 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;
}


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

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

static void fe_cmov(fe f,const fe g,unsigned int b)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 f9 = f[9];
 crypto_int32 g0 = g[0];
 crypto_int32 g1 = g[1];
 crypto_int32 g2 = g[2];
 crypto_int32 g3 = g[3];
 crypto_int32 g4 = g[4];
 crypto_int32 g5 = g[5];
 crypto_int32 g6 = g[6];
 crypto_int32 g7 = g[7];
 crypto_int32 g8 = g[8];
 crypto_int32 g9 = g[9];
 crypto_int32 x0 = f0 ^ g0;
 crypto_int32 x1 = f1 ^ g1;
 crypto_int32 x2 = f2 ^ g2;
 crypto_int32 x3 = f3 ^ g3;
 crypto_int32 x4 = f4 ^ g4;
 crypto_int32 x5 = f5 ^ g5;
 crypto_int32 x6 = f6 ^ g6;
 crypto_int32 x7 = f7 ^ g7;
 crypto_int32 x8 = f8 ^ g8;
 crypto_int32 x9 = f9 ^ g9;
 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;
}


/*
h = f
*/

static void fe_copy(fe h,const fe f)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 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;
}


static crypto_uint64 load_3(const unsigned char *in)
{
 crypto_uint64 result;
 result = (crypto_uint64) in[0];
 result |= ((crypto_uint64) in[1]) << 8;
 result |= ((crypto_uint64) in[2]) << 16;
 return result;
}

static crypto_uint64 load_4(const unsigned char *in)
{
 crypto_uint64 result;
 result = (crypto_uint64) in[0];
 result |= ((crypto_uint64) in[1]) << 8;
 result |= ((crypto_uint64) in[2]) << 16;
 result |= ((crypto_uint64) in[3]) << 24;
 return result;
}

/*
Ignores top bit of h.
*/

static void fe_frombytes(fe h,const unsigned char *s)
{
 crypto_int64 h0 = load_4(s);
 crypto_int64 h1 = load_3(s + 4) << 6;
 crypto_int64 h2 = load_3(s + 7) << 5;
 crypto_int64 h3 = load_3(s + 10) << 3;
 crypto_int64 h4 = load_3(s + 13) << 2;
 crypto_int64 h5 = load_4(s + 16);
 crypto_int64 h6 = load_3(s + 20) << 7;
 crypto_int64 h7 = load_3(s + 23) << 5;
 crypto_int64 h8 = load_3(s + 26) << 4;
 crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2;
 crypto_int64 carry0;
 crypto_int64 carry1;
 crypto_int64 carry2;
 crypto_int64 carry3;
 crypto_int64 carry4;
 crypto_int64 carry5;
 crypto_int64 carry6;
 crypto_int64 carry7;
 crypto_int64 carry8;
 crypto_int64 carry9;

 carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
 carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
 carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
 carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
 carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;

 carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
 carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
 carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
 carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
 carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 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;
}

/*
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)
{
 crypto_int32 h0 = h[0];
 crypto_int32 h1 = h[1];
 crypto_int32 h2 = h[2];
 crypto_int32 h3 = h[3];
 crypto_int32 h4 = h[4];
 crypto_int32 h5 = h[5];
 crypto_int32 h6 = h[6];
 crypto_int32 h7 = h[7];
 crypto_int32 h8 = h[8];
 crypto_int32 h9 = h[9];
 crypto_int32 q;
 crypto_int32 carry0;
 crypto_int32 carry1;
 crypto_int32 carry2;
 crypto_int32 carry3;
 crypto_int32 carry4;
 crypto_int32 carry5;
 crypto_int32 carry6;
 crypto_int32 carry7;
 crypto_int32 carry8;
 crypto_int32 carry9;

 q = (19 * h9 + (((crypto_int32) 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;
}


/*
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_sub(fe h,const fe f,const fe g)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 f9 = f[9];
 crypto_int32 g0 = g[0];
 crypto_int32 g1 = g[1];
 crypto_int32 g2 = g[2];
 crypto_int32 g3 = g[3];
 crypto_int32 g4 = g[4];
 crypto_int32 g5 = g[5];
 crypto_int32 g6 = g[6];
 crypto_int32 g7 = g[7];
 crypto_int32 g8 = g[8];
 crypto_int32 g9 = g[9];
 crypto_int32 h0 = f0 - g0;
 crypto_int32 h1 = f1 - g1;
 crypto_int32 h2 = f2 - g2;
 crypto_int32 h3 = f3 - g3;
 crypto_int32 h4 = f4 - g4;
 crypto_int32 h5 = f5 - g5;
 crypto_int32 h6 = f6 - g6;
 crypto_int32 h7 = f7 - g7;
 crypto_int32 h8 = f8 - g8;
 crypto_int32 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;
}


/*
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)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 f9 = f[9];
 crypto_int32 f0_2 = 2 * f0;
 crypto_int32 f1_2 = 2 * f1;
 crypto_int32 f2_2 = 2 * f2;
 crypto_int32 f3_2 = 2 * f3;
 crypto_int32 f4_2 = 2 * f4;
 crypto_int32 f5_2 = 2 * f5;
 crypto_int32 f6_2 = 2 * f6;
 crypto_int32 f7_2 = 2 * f7;
 crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
 crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
 crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
 crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
 crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
 crypto_int64 f0f0    = f0   * (crypto_int64) f0;
 crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
 crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
 crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
 crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
 crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
 crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
 crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
 crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
 crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
 crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
 crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
 crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
 crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
 crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
 crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
 crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
 crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
 crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
 crypto_int64 f2f2    = f2   * (crypto_int64) f2;
 crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
 crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
 crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
 crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
 crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
 crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
 crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
 crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
 crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
 crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
 crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
 crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
 crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
 crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
 crypto_int64 f4f4    = f4   * (crypto_int64) f4;
 crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
 crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
 crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
 crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
 crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
 crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
 crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
 crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
 crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
 crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
 crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
 crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
 crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
 crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
 crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
 crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
 crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
 crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
 crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
 crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
 crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
 crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
 crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
 crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
 crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
 crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
 crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
 crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
 crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
 crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
 crypto_int64 carry0;
 crypto_int64 carry1;
 crypto_int64 carry2;
 crypto_int64 carry3;
 crypto_int64 carry4;
 crypto_int64 carry5;
 crypto_int64 carry6;
 crypto_int64 carry7;
 crypto_int64 carry8;
 crypto_int64 carry9;

 carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
 carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;

 carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
 carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;

 carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
 carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;

 carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
 carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;

 carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
 carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;

 carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;

 carry0 = (h0 + (crypto_int64) (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;
}

/*
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)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 f9 = f[9];
 crypto_int32 f0_2 = 2 * f0;
 crypto_int32 f1_2 = 2 * f1;
 crypto_int32 f2_2 = 2 * f2;
 crypto_int32 f3_2 = 2 * f3;
 crypto_int32 f4_2 = 2 * f4;
 crypto_int32 f5_2 = 2 * f5;
 crypto_int32 f6_2 = 2 * f6;
 crypto_int32 f7_2 = 2 * f7;
 crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
 crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
 crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
 crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
 crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
 crypto_int64 f0f0    = f0   * (crypto_int64) f0;
 crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
 crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
 crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
 crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
 crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
 crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
 crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
 crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
 crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
 crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
 crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
 crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
 crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
 crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
 crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
 crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
 crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
 crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
 crypto_int64 f2f2    = f2   * (crypto_int64) f2;
 crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
 crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
 crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
 crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
 crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
 crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
 crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
 crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
 crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
 crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
 crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
 crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
 crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
 crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
 crypto_int64 f4f4    = f4   * (crypto_int64) f4;
 crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
 crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
 crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
 crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
 crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
 crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
 crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
 crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
 crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
 crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
 crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
 crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
 crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
 crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
 crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
 crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
 crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
 crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
 crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
 crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
 crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
 crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
 crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
 crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
 crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
 crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
 crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
 crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
 crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
 crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
 crypto_int64 carry0;
 crypto_int64 carry1;
 crypto_int64 carry2;
 crypto_int64 carry3;
 crypto_int64 carry4;
 crypto_int64 carry5;
 crypto_int64 carry6;
 crypto_int64 carry7;
 crypto_int64 carry8;
 crypto_int64 carry9;

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

 carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
 carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;

 carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
 carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;

 carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
 carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;

 carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
 carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;

 carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
 carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;

 carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;

 carry0 = (h0 + (crypto_int64) (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;
}

/*
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)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 f9 = f[9];
 crypto_int32 g0 = g[0];
 crypto_int32 g1 = g[1];
 crypto_int32 g2 = g[2];
 crypto_int32 g3 = g[3];
 crypto_int32 g4 = g[4];
 crypto_int32 g5 = g[5];
 crypto_int32 g6 = g[6];
 crypto_int32 g7 = g[7];
 crypto_int32 g8 = g[8];
 crypto_int32 g9 = g[9];
 crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
 crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
 crypto_int32 g3_19 = 19 * g3;
 crypto_int32 g4_19 = 19 * g4;
 crypto_int32 g5_19 = 19 * g5;
 crypto_int32 g6_19 = 19 * g6;
 crypto_int32 g7_19 = 19 * g7;
 crypto_int32 g8_19 = 19 * g8;
 crypto_int32 g9_19 = 19 * g9;
 crypto_int32 f1_2 = 2 * f1;
 crypto_int32 f3_2 = 2 * f3;
 crypto_int32 f5_2 = 2 * f5;
 crypto_int32 f7_2 = 2 * f7;
 crypto_int32 f9_2 = 2 * f9;
 crypto_int64 f0g0    = f0   * (crypto_int64) g0;
 crypto_int64 f0g1    = f0   * (crypto_int64) g1;
 crypto_int64 f0g2    = f0   * (crypto_int64) g2;
 crypto_int64 f0g3    = f0   * (crypto_int64) g3;
 crypto_int64 f0g4    = f0   * (crypto_int64) g4;
 crypto_int64 f0g5    = f0   * (crypto_int64) g5;
 crypto_int64 f0g6    = f0   * (crypto_int64) g6;
 crypto_int64 f0g7    = f0   * (crypto_int64) g7;
 crypto_int64 f0g8    = f0   * (crypto_int64) g8;
 crypto_int64 f0g9    = f0   * (crypto_int64) g9;
 crypto_int64 f1g0    = f1   * (crypto_int64) g0;
 crypto_int64 f1g1_2  = f1_2 * (crypto_int64) g1;
 crypto_int64 f1g2    = f1   * (crypto_int64) g2;
 crypto_int64 f1g3_2  = f1_2 * (crypto_int64) g3;
 crypto_int64 f1g4    = f1   * (crypto_int64) g4;
 crypto_int64 f1g5_2  = f1_2 * (crypto_int64) g5;
 crypto_int64 f1g6    = f1   * (crypto_int64) g6;
 crypto_int64 f1g7_2  = f1_2 * (crypto_int64) g7;
 crypto_int64 f1g8    = f1   * (crypto_int64) g8;
 crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
 crypto_int64 f2g0    = f2   * (crypto_int64) g0;
 crypto_int64 f2g1    = f2   * (crypto_int64) g1;
 crypto_int64 f2g2    = f2   * (crypto_int64) g2;
 crypto_int64 f2g3    = f2   * (crypto_int64) g3;
 crypto_int64 f2g4    = f2   * (crypto_int64) g4;
 crypto_int64 f2g5    = f2   * (crypto_int64) g5;
 crypto_int64 f2g6    = f2   * (crypto_int64) g6;
 crypto_int64 f2g7    = f2   * (crypto_int64) g7;
 crypto_int64 f2g8_19 = f2   * (crypto_int64) g8_19;
 crypto_int64 f2g9_19 = f2   * (crypto_int64) g9_19;
 crypto_int64 f3g0    = f3   * (crypto_int64) g0;
 crypto_int64 f3g1_2  = f3_2 * (crypto_int64) g1;
 crypto_int64 f3g2    = f3   * (crypto_int64) g2;
 crypto_int64 f3g3_2  = f3_2 * (crypto_int64) g3;
 crypto_int64 f3g4    = f3   * (crypto_int64) g4;
 crypto_int64 f3g5_2  = f3_2 * (crypto_int64) g5;
 crypto_int64 f3g6    = f3   * (crypto_int64) g6;
 crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
 crypto_int64 f3g8_19 = f3   * (crypto_int64) g8_19;
 crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
 crypto_int64 f4g0    = f4   * (crypto_int64) g0;
 crypto_int64 f4g1    = f4   * (crypto_int64) g1;
 crypto_int64 f4g2    = f4   * (crypto_int64) g2;
 crypto_int64 f4g3    = f4   * (crypto_int64) g3;
 crypto_int64 f4g4    = f4   * (crypto_int64) g4;
 crypto_int64 f4g5    = f4   * (crypto_int64) g5;
 crypto_int64 f4g6_19 = f4   * (crypto_int64) g6_19;
 crypto_int64 f4g7_19 = f4   * (crypto_int64) g7_19;
 crypto_int64 f4g8_19 = f4   * (crypto_int64) g8_19;
 crypto_int64 f4g9_19 = f4   * (crypto_int64) g9_19;
 crypto_int64 f5g0    = f5   * (crypto_int64) g0;
 crypto_int64 f5g1_2  = f5_2 * (crypto_int64) g1;
 crypto_int64 f5g2    = f5   * (crypto_int64) g2;
 crypto_int64 f5g3_2  = f5_2 * (crypto_int64) g3;
 crypto_int64 f5g4    = f5   * (crypto_int64) g4;
 crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
 crypto_int64 f5g6_19 = f5   * (crypto_int64) g6_19;
 crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
 crypto_int64 f5g8_19 = f5   * (crypto_int64) g8_19;
 crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
 crypto_int64 f6g0    = f6   * (crypto_int64) g0;
 crypto_int64 f6g1    = f6   * (crypto_int64) g1;
 crypto_int64 f6g2    = f6   * (crypto_int64) g2;
 crypto_int64 f6g3    = f6   * (crypto_int64) g3;
 crypto_int64 f6g4_19 = f6   * (crypto_int64) g4_19;
 crypto_int64 f6g5_19 = f6   * (crypto_int64) g5_19;
 crypto_int64 f6g6_19 = f6   * (crypto_int64) g6_19;
 crypto_int64 f6g7_19 = f6   * (crypto_int64) g7_19;
 crypto_int64 f6g8_19 = f6   * (crypto_int64) g8_19;
 crypto_int64 f6g9_19 = f6   * (crypto_int64) g9_19;
 crypto_int64 f7g0    = f7   * (crypto_int64) g0;
 crypto_int64 f7g1_2  = f7_2 * (crypto_int64) g1;
 crypto_int64 f7g2    = f7   * (crypto_int64) g2;
 crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
 crypto_int64 f7g4_19 = f7   * (crypto_int64) g4_19;
 crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
 crypto_int64 f7g6_19 = f7   * (crypto_int64) g6_19;
 crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
 crypto_int64 f7g8_19 = f7   * (crypto_int64) g8_19;
 crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
 crypto_int64 f8g0    = f8   * (crypto_int64) g0;
 crypto_int64 f8g1    = f8   * (crypto_int64) g1;
 crypto_int64 f8g2_19 = f8   * (crypto_int64) g2_19;
 crypto_int64 f8g3_19 = f8   * (crypto_int64) g3_19;
 crypto_int64 f8g4_19 = f8   * (crypto_int64) g4_19;
 crypto_int64 f8g5_19 = f8   * (crypto_int64) g5_19;
 crypto_int64 f8g6_19 = f8   * (crypto_int64) g6_19;
 crypto_int64 f8g7_19 = f8   * (crypto_int64) g7_19;
 crypto_int64 f8g8_19 = f8   * (crypto_int64) g8_19;
 crypto_int64 f8g9_19 = f8   * (crypto_int64) g9_19;
 crypto_int64 f9g0    = f9   * (crypto_int64) g0;
 crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
 crypto_int64 f9g2_19 = f9   * (crypto_int64) g2_19;
 crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
 crypto_int64 f9g4_19 = f9   * (crypto_int64) g4_19;
 crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
 crypto_int64 f9g6_19 = f9   * (crypto_int64) g6_19;
 crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
 crypto_int64 f9g8_19 = f9   * (crypto_int64) g8_19;
 crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
 crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
 crypto_int64 h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
 crypto_int64 h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
 crypto_int64 h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
 crypto_int64 h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
 crypto_int64 h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
 crypto_int64 h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
 crypto_int64 h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
 crypto_int64 h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
 crypto_int64 h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
 crypto_int64 carry0;
 crypto_int64 carry1;
 crypto_int64 carry2;
 crypto_int64 carry3;
 crypto_int64 carry4;
 crypto_int64 carry5;
 crypto_int64 carry6;
 crypto_int64 carry7;
 crypto_int64 carry8;
 crypto_int64 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 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
 carry4 = (h4 + (crypto_int64) (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 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
 carry5 = (h5 + (crypto_int64) (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 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
 carry6 = (h6 + (crypto_int64) (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 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
 carry7 = (h7 + (crypto_int64) (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 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
 carry8 = (h8 + (crypto_int64) (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 + (crypto_int64) (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 + (crypto_int64) (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;
}


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

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

static int fe_isnegative(const fe f)
{
 unsigned char 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.
*/

static const unsigned char zero[32] = {0};

static int fe_isnonzero(const fe f)
{
 unsigned char s[32];
 fe_tobytes(s,f);
 return crypto_verify_32(s,zero);
}

/*
h = -f

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

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

static void fe_neg(fe h,const fe f)
{
 crypto_int32 f0 = f[0];
 crypto_int32 f1 = f[1];
 crypto_int32 f2 = f[2];
 crypto_int32 f3 = f[3];
 crypto_int32 f4 = f[4];
 crypto_int32 f5 = f[5];
 crypto_int32 f6 = f[6];
 crypto_int32 f7 = f[7];
 crypto_int32 f8 = f[8];
 crypto_int32 f9 = f[9];
 crypto_int32 h0 = -f0;
 crypto_int32 h1 = -f1;
 crypto_int32 h2 = -f2;
 crypto_int32 h3 = -f3;
 crypto_int32 h4 = -f4;
 crypto_int32 h5 = -f5;
 crypto_int32 h6 = -f6;
 crypto_int32 h7 = -f7;
 crypto_int32 h8 = -f8;
 crypto_int32 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;
}

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


/* qhasm: fe z1 */

/* qhasm: fe z2 */

/* qhasm: fe z8 */

/* qhasm: fe z9 */

/* qhasm: fe z11 */

/* qhasm: fe z22 */

/* qhasm: fe z_5_0 */

/* qhasm: fe z_10_5 */

/* qhasm: fe z_10_0 */

/* qhasm: fe z_20_10 */

/* qhasm: fe z_20_0 */

/* qhasm: fe z_40_20 */

/* qhasm: fe z_40_0 */

/* qhasm: fe z_50_10 */

/* qhasm: fe z_50_0 */

/* qhasm: fe z_100_50 */

/* qhasm: fe z_100_0 */

/* qhasm: fe z_200_100 */

/* qhasm: fe z_200_0 */

/* qhasm: fe z_250_50 */

/* qhasm: fe z_250_0 */

/* qhasm: fe z_255_5 */

/* qhasm: fe z_255_21 */

/* qhasm: enter pow225521 */

/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);

/* qhasm: z8 = z2^2^2 */
/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);

/* qhasm: z9 = z1*z8 */
/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
fe_mul(t1,z,t1);

/* qhasm: z11 = z2*z9 */
/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
fe_mul(t0,t0,t1);

/* qhasm: z22 = z11^2^1 */
/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);

/* qhasm: z_5_0 = z9*z22 */
/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
fe_mul(t1,t1,t2);

/* qhasm: z_10_5 = z_5_0^2^5 */
/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);

/* qhasm: z_10_0 = z_10_5*z_5_0 */
/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
fe_mul(t1,t2,t1);

/* qhasm: z_20_10 = z_10_0^2^10 */
/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);

/* qhasm: z_20_0 = z_20_10*z_10_0 */
/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
fe_mul(t2,t2,t1);

/* qhasm: z_40_20 = z_20_0^2^20 */
/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);

/* qhasm: z_40_0 = z_40_20*z_20_0 */
/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
fe_mul(t2,t3,t2);

/* qhasm: z_50_10 = z_40_0^2^10 */
/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);

/* qhasm: z_50_0 = z_50_10*z_10_0 */
/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
fe_mul(t1,t2,t1);

/* qhasm: z_100_50 = z_50_0^2^50 */
/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);

/* qhasm: z_100_0 = z_100_50*z_50_0 */
/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
fe_mul(t2,t2,t1);

/* qhasm: z_200_100 = z_100_0^2^100 */
/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);

/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
fe_mul(t2,t3,t2);

/* qhasm: z_250_50 = z_200_0^2^50 */
/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);

/* qhasm: z_250_0 = z_250_50*z_50_0 */
/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
fe_mul(t1,t2,t1);

/* qhasm: z_255_5 = z_250_0^2^5 */
/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);

/* qhasm: z_255_21 = z_255_5*z11 */
/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
fe_mul(out,t1,t0);

/* qhasm: return */

 return;
}


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


/* qhasm: fe z1 */

/* qhasm: fe z2 */

/* qhasm: fe z8 */

/* qhasm: fe z9 */

/* qhasm: fe z11 */

/* qhasm: fe z22 */

/* qhasm: fe z_5_0 */

/* qhasm: fe z_10_5 */

/* qhasm: fe z_10_0 */

/* qhasm: fe z_20_10 */

/* qhasm: fe z_20_0 */

/* qhasm: fe z_40_20 */

/* qhasm: fe z_40_0 */

/* qhasm: fe z_50_10 */

/* qhasm: fe z_50_0 */

/* qhasm: fe z_100_50 */

/* qhasm: fe z_100_0 */

/* qhasm: fe z_200_100 */

/* qhasm: fe z_200_0 */

/* qhasm: fe z_250_50 */

/* qhasm: fe z_250_0 */

/* qhasm: fe z_252_2 */

/* qhasm: fe z_252_3 */

/* qhasm: enter pow22523 */

/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);

/* qhasm: z8 = z2^2^2 */
/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);

/* qhasm: z9 = z1*z8 */
/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
fe_mul(t1,z,t1);

/* qhasm: z11 = z2*z9 */
/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
fe_mul(t0,t0,t1);

/* qhasm: z22 = z11^2^1 */
/* asm 1: fe_sq(>z22=fe#1,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#1,>z22=fe#1); */
/* asm 2: fe_sq(>z22=t0,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t0,>z22=t0); */
fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0);

/* qhasm: z_5_0 = z9*z22 */
/* asm 1: fe_mul(>z_5_0=fe#1,<z9=fe#2,<z22=fe#1); */
/* asm 2: fe_mul(>z_5_0=t0,<z9=t1,<z22=t0); */
fe_mul(t0,t1,t0);

/* qhasm: z_10_5 = z_5_0^2^5 */
/* asm 1: fe_sq(>z_10_5=fe#2,<z_5_0=fe#1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#2,>z_10_5=fe#2); */
/* asm 2: fe_sq(>z_10_5=t1,<z_5_0=t0); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t1,>z_10_5=t1); */
fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1);

/* qhasm: z_10_0 = z_10_5*z_5_0 */
/* asm 1: fe_mul(>z_10_0=fe#1,<z_10_5=fe#2,<z_5_0=fe#1); */
/* asm 2: fe_mul(>z_10_0=t0,<z_10_5=t1,<z_5_0=t0); */
fe_mul(t0,t1,t0);

/* qhasm: z_20_10 = z_10_0^2^10 */
/* asm 1: fe_sq(>z_20_10=fe#2,<z_10_0=fe#1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#2,>z_20_10=fe#2); */
/* asm 2: fe_sq(>z_20_10=t1,<z_10_0=t0); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t1,>z_20_10=t1); */
fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1);

/* qhasm: z_20_0 = z_20_10*z_10_0 */
/* asm 1: fe_mul(>z_20_0=fe#2,<z_20_10=fe#2,<z_10_0=fe#1); */
/* asm 2: fe_mul(>z_20_0=t1,<z_20_10=t1,<z_10_0=t0); */
fe_mul(t1,t1,t0);

/* qhasm: z_40_20 = z_20_0^2^20 */
/* asm 1: fe_sq(>z_40_20=fe#3,<z_20_0=fe#2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#3,>z_40_20=fe#3); */
/* asm 2: fe_sq(>z_40_20=t2,<z_20_0=t1); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t2,>z_40_20=t2); */
fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2);

/* qhasm: z_40_0 = z_40_20*z_20_0 */
/* asm 1: fe_mul(>z_40_0=fe#2,<z_40_20=fe#3,<z_20_0=fe#2); */
/* asm 2: fe_mul(>z_40_0=t1,<z_40_20=t2,<z_20_0=t1); */
fe_mul(t1,t2,t1);

/* qhasm: z_50_10 = z_40_0^2^10 */
/* asm 1: fe_sq(>z_50_10=fe#2,<z_40_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#2,>z_50_10=fe#2); */
/* asm 2: fe_sq(>z_50_10=t1,<z_40_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t1,>z_50_10=t1); */
fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1);

/* qhasm: z_50_0 = z_50_10*z_10_0 */
/* asm 1: fe_mul(>z_50_0=fe#1,<z_50_10=fe#2,<z_10_0=fe#1); */
/* asm 2: fe_mul(>z_50_0=t0,<z_50_10=t1,<z_10_0=t0); */
fe_mul(t0,t1,t0);

/* qhasm: z_100_50 = z_50_0^2^50 */
/* asm 1: fe_sq(>z_100_50=fe#2,<z_50_0=fe#1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#2,>z_100_50=fe#2); */
/* asm 2: fe_sq(>z_100_50=t1,<z_50_0=t0); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t1,>z_100_50=t1); */
fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1);

/* qhasm: z_100_0 = z_100_50*z_50_0 */
/* asm 1: fe_mul(>z_100_0=fe#2,<z_100_50=fe#2,<z_50_0=fe#1); */
/* asm 2: fe_mul(>z_100_0=t1,<z_100_50=t1,<z_50_0=t0); */
fe_mul(t1,t1,t0);

/* qhasm: z_200_100 = z_100_0^2^100 */
/* asm 1: fe_sq(>z_200_100=fe#3,<z_100_0=fe#2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#3,>z_200_100=fe#3); */
/* asm 2: fe_sq(>z_200_100=t2,<z_100_0=t1); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t2,>z_200_100=t2); */
fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2);

/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#2,<z_200_100=fe#3,<z_100_0=fe#2); */
/* asm 2: fe_mul(>z_200_0=t1,<z_200_100=t2,<z_100_0=t1); */
fe_mul(t1,t2,t1);

/* qhasm: z_250_50 = z_200_0^2^50 */
/* asm 1: fe_sq(>z_250_50=fe#2,<z_200_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#2,>z_250_50=fe#2); */
/* asm 2: fe_sq(>z_250_50=t1,<z_200_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t1,>z_250_50=t1); */
fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1);

/* qhasm: z_250_0 = z_250_50*z_50_0 */
/* asm 1: fe_mul(>z_250_0=fe#1,<z_250_50=fe#2,<z_50_0=fe#1); */
/* asm 2: fe_mul(>z_250_0=t0,<z_250_50=t1,<z_50_0=t0); */
fe_mul(t0,t1,t0);

/* qhasm: z_252_2 = z_250_0^2^2 */
/* asm 1: fe_sq(>z_252_2=fe#1,<z_250_0=fe#1); for (i = 1;i < 2;++i) fe_sq(>z_252_2=fe#1,>z_252_2=fe#1); */
/* asm 2: fe_sq(>z_252_2=t0,<z_250_0=t0); for (i = 1;i < 2;++i) fe_sq(>z_252_2=t0,>z_252_2=t0); */
fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0);

/* qhasm: z_252_3 = z_252_2*z1 */
/* asm 1: fe_mul(>z_252_3=fe#12,<z_252_2=fe#1,<z1=fe#11); */
/* asm 2: fe_mul(>z_252_3=out,<z_252_2=t0,<z1=z); */
fe_mul(out,t0,z);

/* qhasm: return */


 return;
}


/*
ge means group element.

Here the group is the set of pairs (x,y) of field elements (see fe.h)
satisfying -x^2 + y^2 = 1 + d x^2y^2
where d = -121665/121666.

Representations:
 ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
 ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
 ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
 ge_precomp (Duif): (y+x,y-x,2dxy)
*/

typedef struct {
 fe X;
 fe Y;
 fe Z;
} ge_p2;

typedef struct {
 fe X;
 fe Y;
 fe Z;
 fe T;
} ge_p3;

typedef struct {
 fe X;
 fe Y;
 fe Z;
 fe T;
} ge_p1p1;

typedef struct {
 fe yplusx;
 fe yminusx;
 fe xy2d;
} ge_precomp;

typedef struct {
 fe YplusX;
 fe YminusX;
 fe Z;
 fe T2d;
} ge_cached;

static const fe d = {
-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116
} ;

static const fe sqrtm1 = {
-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482
} ;

static const fe d2 = {
-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199
} ;

static ge_precomp Bi[8] = {
{
 { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
 { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
 { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
},
{
 { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
 { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
 { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
},
{
 { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
 { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
 { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
},
{
 { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
 { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
 { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
},
{
 { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 },
 { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 },
 { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 },
},
{
 { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 },
 { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 },
 { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 },
},
{
 { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 },
 { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 },
 { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 },
},
{
 { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 },
 { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 },
 { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 },
},
} ;


/* base[i][j] = (j+1)*256^i*B */
static ge_precomp base[32][8] = {
{
{
 { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
 { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
 { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
},
{
 { -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 },
 { -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 },
 { 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 },
},
{
 { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
 { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
 { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
},
{
 { -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 },
 { 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 },
 { 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 },
},
{
 { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
 { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
 { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
},
{
 { -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 },
 { -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 },
 { -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 },
},
{
 { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
 { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
 { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
},
{
 { 14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726 },
 { -7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955 },
 { 27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425 },
},
},
{
{
 { -13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171 },
 { 27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510 },
 { 17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660 },
},
{
 { -10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639 },
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 { -28017847,9834845,18617207,-2681312,-3401956,-13307506,8205540,13585437,-17127465,15115439 },
 { 23711543,-672915,31206561,-8362711,6164647,-9709987,-33535882,-1426096,8236921,16492939 },
 { -23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424 },
},
{
 { 2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310 },
 { 3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608 },
 { -32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079 },
},
{
 { -23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101 },
 { 21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418 },
 { 18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576 },
},
{
 { 30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356 },
 { 9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996 },
 { -26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099 },
},
},
{
{
 { -26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728 },
 { -13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658 },
 { -10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242 },
},
{
 { -21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001 },
 { -4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766 },
 { 18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373 },
},
{
 { 26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458 },
 { -17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628 },
 { -13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657 },
},
{
 { -23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062 },
 { 25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616 },
 { 31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014 },
},
{
 { 24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383 },
 { -25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814 },
 { -20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718 },
},
{
 { 30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417 },
 { 2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222 },
 { 33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444 },
},
{
 { -20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597 },
 { 23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970 },
 { 1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799 },
},
{
 { -5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647 },
 { 13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511 },
 { -29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032 },
},
},
{
{
 { 9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834 },
 { -23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461 },
 { 29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062 },
},
{
 { -25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516 },
 { -20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547 },
 { -24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240 },
},
{
 { -17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038 },
 { -33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741 },
 { 16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103 },
},
{
 { -19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747 },
 { -1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323 },
 { 31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016 },
},
{
 { -14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373 },
 { 15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228 },
 { -2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141 },
},
{
 { 16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399 },
 { 11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831 },
 { -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 },
},
{
 { -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 },
 { -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 },
 { -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 },
},
{
 { -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 },
 { 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 },
 { -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 },
},
},
} ;

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

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

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

/*
r = p
*/

static 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);
}

/*
r = p
*/

static 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);
}

/*
r = p
*/

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


/*
r = 2 * p
*/

static void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
{
 fe t0;
/* qhasm: enter ge_p2_dbl */

/* qhasm: fe X1 */

/* qhasm: fe Y1 */

/* qhasm: fe Z1 */

/* qhasm: fe A */

/* qhasm: fe AA */

/* qhasm: fe XX */

/* qhasm: fe YY */

/* qhasm: fe B */

/* qhasm: fe X3 */

/* qhasm: fe Y3 */

/* qhasm: fe Z3 */

/* qhasm: fe T3 */

/* qhasm: XX=X1^2 */
/* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */
/* asm 2: fe_sq(>XX=r->X,<X1=p->X); */
fe_sq(r->X,p->X);

/* qhasm: YY=Y1^2 */
/* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */
/* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */
fe_sq(r->Z,p->Y);

/* qhasm: B=2*Z1^2 */
/* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */
/* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */
fe_sq2(r->T,p->Z);

/* qhasm: A=X1+Y1 */
/* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */
/* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */
fe_add(r->Y,p->X,p->Y);

/* qhasm: AA=A^2 */
/* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */
/* asm 2: fe_sq(>AA=t0,<A=r->Y); */
fe_sq(t0,r->Y);

/* qhasm: Y3=YY+XX */
/* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */
/* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */
fe_add(r->Y,r->Z,r->X);

/* qhasm: Z3=YY-XX */
/* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */
/* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */
fe_sub(r->Z,r->Z,r->X);

/* qhasm: X3=AA-Y3 */
/* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */
fe_sub(r->X,t0,r->Y);

/* qhasm: T3=B-Z3 */
/* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */
/* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */
fe_sub(r->T,r->T,r->Z);

/* qhasm: return */
}


/*
r = 2 * p
*/

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


/*
r = p
*/

static 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,d2);
}

/*
r = p + q
*/

static void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
 fe t0;
/* qhasm: enter ge_add */

/* qhasm: fe X1 */

/* qhasm: fe Y1 */

/* qhasm: fe Z1 */

/* qhasm: fe Z2 */

/* qhasm: fe T1 */

/* qhasm: fe ZZ */

/* qhasm: fe YpX2 */

/* qhasm: fe YmX2 */

/* qhasm: fe T2d2 */

/* qhasm: fe X3 */

/* qhasm: fe Y3 */

/* qhasm: fe Z3 */

/* qhasm: fe T3 */

/* qhasm: fe YpX1 */

/* qhasm: fe YmX1 */

/* qhasm: fe A */

/* qhasm: fe B */

/* qhasm: fe C */

/* qhasm: fe D */

/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);

/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);

/* qhasm: A = YpX1*YpX2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */
fe_mul(r->Z,r->X,q->YplusX);

/* qhasm: B = YmX1*YmX2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */
fe_mul(r->Y,r->Y,q->YminusX);

/* qhasm: C = T2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
fe_mul(r->T,q->T2d,p->T);

/* qhasm: ZZ = Z1*Z2 */
/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
fe_mul(r->X,p->Z,q->Z);

/* qhasm: D = 2*ZZ */
/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
fe_add(t0,r->X,r->X);

/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);

/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);

/* qhasm: Z3 = D+C */
/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
fe_add(r->Z,t0,r->T);

/* qhasm: T3 = D-C */
/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
fe_sub(r->T,t0,r->T);

/* qhasm: return */
}


/*
r = p - q
*/

static void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
 fe t0;
/* qhasm: enter ge_sub */

/* qhasm: fe X1 */

/* qhasm: fe Y1 */

/* qhasm: fe Z1 */

/* qhasm: fe Z2 */

/* qhasm: fe T1 */

/* qhasm: fe ZZ */

/* qhasm: fe YpX2 */

/* qhasm: fe YmX2 */

/* qhasm: fe T2d2 */

/* qhasm: fe X3 */

/* qhasm: fe Y3 */

/* qhasm: fe Z3 */

/* qhasm: fe T3 */

/* qhasm: fe YpX1 */

/* qhasm: fe YmX1 */

/* qhasm: fe A */

/* qhasm: fe B */

/* qhasm: fe C */

/* qhasm: fe D */

/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);

/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);

/* qhasm: A = YpX1*YmX2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */
fe_mul(r->Z,r->X,q->YminusX);

/* qhasm: B = YmX1*YpX2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */
fe_mul(r->Y,r->Y,q->YplusX);

/* qhasm: C = T2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
fe_mul(r->T,q->T2d,p->T);

/* qhasm: ZZ = Z1*Z2 */
/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
fe_mul(r->X,p->Z,q->Z);

/* qhasm: D = 2*ZZ */
/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
fe_add(t0,r->X,r->X);

/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);

/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);

/* qhasm: Z3 = D-C */
/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
fe_sub(r->Z,t0,r->T);

/* qhasm: T3 = D+C */
/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
fe_add(r->T,t0,r->T);

/* qhasm: return */
}


/*
r = p + q
*/

static void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
 fe t0;
/* qhasm: enter ge_madd */

/* qhasm: fe X1 */

/* qhasm: fe Y1 */

/* qhasm: fe Z1 */

/* qhasm: fe T1 */

/* qhasm: fe ypx2 */

/* qhasm: fe ymx2 */

/* qhasm: fe xy2d2 */

/* qhasm: fe X3 */

/* qhasm: fe Y3 */

/* qhasm: fe Z3 */

/* qhasm: fe T3 */

/* qhasm: fe YpX1 */

/* qhasm: fe YmX1 */

/* qhasm: fe A */

/* qhasm: fe B */

/* qhasm: fe C */

/* qhasm: fe D */

/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);

/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);

/* qhasm: A = YpX1*ypx2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ypx2=fe#15); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ypx2=q->yplusx); */
fe_mul(r->Z,r->X,q->yplusx);

/* qhasm: B = YmX1*ymx2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ymx2=fe#16); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ymx2=q->yminusx); */
fe_mul(r->Y,r->Y,q->yminusx);

/* qhasm: C = xy2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
fe_mul(r->T,q->xy2d,p->T);

/* qhasm: D = 2*Z1 */
/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
fe_add(t0,p->Z,p->Z);

/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);

/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);

/* qhasm: Z3 = D+C */
/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
fe_add(r->Z,t0,r->T);

/* qhasm: T3 = D-C */
/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
fe_sub(r->T,t0,r->T);

/* qhasm: return */
}


/*
r = p - q
*/

static void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
 fe t0;
/* qhasm: enter ge_msub */

/* qhasm: fe X1 */

/* qhasm: fe Y1 */

/* qhasm: fe Z1 */

/* qhasm: fe T1 */

/* qhasm: fe ypx2 */

/* qhasm: fe ymx2 */

/* qhasm: fe xy2d2 */

/* qhasm: fe X3 */

/* qhasm: fe Y3 */

/* qhasm: fe Z3 */

/* qhasm: fe T3 */

/* qhasm: fe YpX1 */

/* qhasm: fe YmX1 */

/* qhasm: fe A */

/* qhasm: fe B */

/* qhasm: fe C */

/* qhasm: fe D */

/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);

/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);

/* qhasm: A = YpX1*ymx2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */
fe_mul(r->Z,r->X,q->yminusx);

/* qhasm: B = YmX1*ypx2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */
fe_mul(r->Y,r->Y,q->yplusx);

/* qhasm: C = xy2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
fe_mul(r->T,q->xy2d,p->T);

/* qhasm: D = 2*Z1 */
/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
fe_add(t0,p->Z,p->Z);

/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);

/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);

/* qhasm: Z3 = D-C */
/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
fe_sub(r->Z,t0,r->T);

/* qhasm: T3 = D+C */
/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
fe_add(r->T,t0,r->T);

/* qhasm: return */
}


static 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;
}

static 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;
}

static int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s)
{
 fe u;
 fe v;
 fe v3;
 fe vxx;
 fe check;

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

 fe_sq(v3,v);
 fe_mul(v3,v3,v);        /* v3 = v^3 */
 fe_sq(h->X,v3);
 fe_mul(h->X,h->X,v);
 fe_mul(h->X,h->X,u);    /* x = uv^7 */

 fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
 fe_mul(h->X,h->X,v3);
 fe_mul(h->X,h->X,u);    /* 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,sqrtm1);
 }

 if (fe_isnegative(h->X) == (s[31] >> 7))
   fe_neg(h->X,h->X);

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


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

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

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

}


/*
r = a * A + b * B
where a = a[0]+256*a[1]+...+256^31 a[31].
and b = b[0]+256*b[1]+...+256^31 b[31].
B is the Ed25519 base point (x,4/5) with x positive.
*/

static void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b)
{
 signed char aslide[256];
 signed char bslide[256];
 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
 ge_p1p1 t;
 ge_p3 u;
 ge_p3 A2;
 int i;

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

 ge_p3_to_cached(&Ai[0],A);
 ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t);
 ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u);
 ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u);
 ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u);
 ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u);
 ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u);
 ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u);
 ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u);

 ge_p2_0(r);

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

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

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

   ge_p1p1_to_p2(r,&t);
 }
}

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 */
 crypto_uint32 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 cmov(ge_precomp *t,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);
 cmov(t,&base[pos][0],equal(babs,1));
 cmov(t,&base[pos][1],equal(babs,2));
 cmov(t,&base[pos][2],equal(babs,3));
 cmov(t,&base[pos][3],equal(babs,4));
 cmov(t,&base[pos][4],equal(babs,5));
 cmov(t,&base[pos][5],equal(babs,6));
 cmov(t,&base[pos][6],equal(babs,7));
 cmov(t,&base[pos][7],equal(babs,8));
 fe_copy(minust.yplusx,t->yminusx);
 fe_copy(minust.yminusx,t->yplusx);
 fe_neg(minust.xy2d,t->xy2d);
 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
*/

static 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);
 for (i = 1;i < 64;i += 2) {
   select(&t,i / 2,e[i]);
   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);

 for (i = 0;i < 64;i += 2) {
   select(&t,i / 2,e[i]);
   ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
 }
}

/*
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.
*/

static void sc_reduce(unsigned char *s)
{
 crypto_int64 s0 = 2097151 & load_3(s);
 crypto_int64 s1 = 2097151 & (load_4(s + 2) >> 5);
 crypto_int64 s2 = 2097151 & (load_3(s + 5) >> 2);
 crypto_int64 s3 = 2097151 & (load_4(s + 7) >> 7);
 crypto_int64 s4 = 2097151 & (load_4(s + 10) >> 4);
 crypto_int64 s5 = 2097151 & (load_3(s + 13) >> 1);
 crypto_int64 s6 = 2097151 & (load_4(s + 15) >> 6);
 crypto_int64 s7 = 2097151 & (load_3(s + 18) >> 3);
 crypto_int64 s8 = 2097151 & load_3(s + 21);
 crypto_int64 s9 = 2097151 & (load_4(s + 23) >> 5);
 crypto_int64 s10 = 2097151 & (load_3(s + 26) >> 2);
 crypto_int64 s11 = 2097151 & (load_4(s + 28) >> 7);
 crypto_int64 s12 = 2097151 & (load_4(s + 31) >> 4);
 crypto_int64 s13 = 2097151 & (load_3(s + 34) >> 1);
 crypto_int64 s14 = 2097151 & (load_4(s + 36) >> 6);
 crypto_int64 s15 = 2097151 & (load_3(s + 39) >> 3);
 crypto_int64 s16 = 2097151 & load_3(s + 42);
 crypto_int64 s17 = 2097151 & (load_4(s + 44) >> 5);
 crypto_int64 s18 = 2097151 & (load_3(s + 47) >> 2);
 crypto_int64 s19 = 2097151 & (load_4(s + 49) >> 7);
 crypto_int64 s20 = 2097151 & (load_4(s + 52) >> 4);
 crypto_int64 s21 = 2097151 & (load_3(s + 55) >> 1);
 crypto_int64 s22 = 2097151 & (load_4(s + 57) >> 6);
 crypto_int64 s23 = (load_4(s + 60) >> 3);
 crypto_int64 carry0;
 crypto_int64 carry1;
 crypto_int64 carry2;
 crypto_int64 carry3;
 crypto_int64 carry4;
 crypto_int64 carry5;
 crypto_int64 carry6;
 crypto_int64 carry7;
 crypto_int64 carry8;
 crypto_int64 carry9;
 crypto_int64 carry10;
 crypto_int64 carry11;
 crypto_int64 carry12;
 crypto_int64 carry13;
 crypto_int64 carry14;
 crypto_int64 carry15;
 crypto_int64 carry16;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

/*
Input:
 a[0]+256*a[1]+...+256^31*a[31] = a
 b[0]+256*b[1]+...+256^31*b[31] = b
 c[0]+256*c[1]+...+256^31*c[31] = c

Output:
 s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
 where l = 2^252 + 27742317777372353535851937790883648493.
*/

static void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c)
{
 crypto_int64 a0 = 2097151 & load_3(a);
 crypto_int64 a1 = 2097151 & (load_4(a + 2) >> 5);
 crypto_int64 a2 = 2097151 & (load_3(a + 5) >> 2);
 crypto_int64 a3 = 2097151 & (load_4(a + 7) >> 7);
 crypto_int64 a4 = 2097151 & (load_4(a + 10) >> 4);
 crypto_int64 a5 = 2097151 & (load_3(a + 13) >> 1);
 crypto_int64 a6 = 2097151 & (load_4(a + 15) >> 6);
 crypto_int64 a7 = 2097151 & (load_3(a + 18) >> 3);
 crypto_int64 a8 = 2097151 & load_3(a + 21);
 crypto_int64 a9 = 2097151 & (load_4(a + 23) >> 5);
 crypto_int64 a10 = 2097151 & (load_3(a + 26) >> 2);
 crypto_int64 a11 = (load_4(a + 28) >> 7);
 crypto_int64 b0 = 2097151 & load_3(b);
 crypto_int64 b1 = 2097151 & (load_4(b + 2) >> 5);
 crypto_int64 b2 = 2097151 & (load_3(b + 5) >> 2);
 crypto_int64 b3 = 2097151 & (load_4(b + 7) >> 7);
 crypto_int64 b4 = 2097151 & (load_4(b + 10) >> 4);
 crypto_int64 b5 = 2097151 & (load_3(b + 13) >> 1);
 crypto_int64 b6 = 2097151 & (load_4(b + 15) >> 6);
 crypto_int64 b7 = 2097151 & (load_3(b + 18) >> 3);
 crypto_int64 b8 = 2097151 & load_3(b + 21);
 crypto_int64 b9 = 2097151 & (load_4(b + 23) >> 5);
 crypto_int64 b10 = 2097151 & (load_3(b + 26) >> 2);
 crypto_int64 b11 = (load_4(b + 28) >> 7);
 crypto_int64 c0 = 2097151 & load_3(c);
 crypto_int64 c1 = 2097151 & (load_4(c + 2) >> 5);
 crypto_int64 c2 = 2097151 & (load_3(c + 5) >> 2);
 crypto_int64 c3 = 2097151 & (load_4(c + 7) >> 7);
 crypto_int64 c4 = 2097151 & (load_4(c + 10) >> 4);
 crypto_int64 c5 = 2097151 & (load_3(c + 13) >> 1);
 crypto_int64 c6 = 2097151 & (load_4(c + 15) >> 6);
 crypto_int64 c7 = 2097151 & (load_3(c + 18) >> 3);
 crypto_int64 c8 = 2097151 & load_3(c + 21);
 crypto_int64 c9 = 2097151 & (load_4(c + 23) >> 5);
 crypto_int64 c10 = 2097151 & (load_3(c + 26) >> 2);
 crypto_int64 c11 = (load_4(c + 28) >> 7);
 crypto_int64 s0;
 crypto_int64 s1;
 crypto_int64 s2;
 crypto_int64 s3;
 crypto_int64 s4;
 crypto_int64 s5;
 crypto_int64 s6;
 crypto_int64 s7;
 crypto_int64 s8;
 crypto_int64 s9;
 crypto_int64 s10;
 crypto_int64 s11;
 crypto_int64 s12;
 crypto_int64 s13;
 crypto_int64 s14;
 crypto_int64 s15;
 crypto_int64 s16;
 crypto_int64 s17;
 crypto_int64 s18;
 crypto_int64 s19;
 crypto_int64 s20;
 crypto_int64 s21;
 crypto_int64 s22;
 crypto_int64 s23;
 crypto_int64 carry0;
 crypto_int64 carry1;
 crypto_int64 carry2;
 crypto_int64 carry3;
 crypto_int64 carry4;
 crypto_int64 carry5;
 crypto_int64 carry6;
 crypto_int64 carry7;
 crypto_int64 carry8;
 crypto_int64 carry9;
 crypto_int64 carry10;
 crypto_int64 carry11;
 crypto_int64 carry12;
 crypto_int64 carry13;
 crypto_int64 carry14;
 crypto_int64 carry15;
 crypto_int64 carry16;
 crypto_int64 carry17;
 crypto_int64 carry18;
 crypto_int64 carry19;
 crypto_int64 carry20;
 crypto_int64 carry21;
 crypto_int64 carry22;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

/*
int crypto_sign_keypair(unsigned char *pk,unsigned char *sk)
{
 unsigned char h[64];
 ge_p3 A;
 int i;

 randombytes(sk,32);
 crypto_hash_sha512(h,sk,32);
 h[0] &= 248;
 h[31] &= 63;
 h[31] |= 64;

 ge_scalarmult_base(&A,h);
 ge_p3_tobytes(pk,&A);

 for (i = 0;i < 32;++i) sk[32 + i] = pk[i];
 return 0;
}
*/

int crypto_sign_pk_ref10(unsigned char *pk,unsigned char *sk)
{
 unsigned char h[64];
 ge_p3 A;
 int i;

 crypto_hash_sha512(h,sk,32);
 h[0] &= 248;
 h[31] &= 63;
 h[31] |= 64;

 ge_scalarmult_base(&A,h);
 ge_p3_tobytes(pk,&A);

 for (i = 0;i < 32;++i) sk[32 + i] = pk[i];
 return 0;
}

int crypto_sign_ref10(
 unsigned char *sm,unsigned long long *smlen,
 const unsigned char *m,unsigned long long mlen,
 const unsigned char *sk
)
{
 unsigned char az[64];
 unsigned char r[64];
 unsigned char hram[64];
 ge_p3 R;
 unsigned long long i;

 crypto_hash_sha512(az,sk,32);
 az[0] &= 248;
 az[31] &= 63;
 az[31] |= 64;

 *smlen = mlen + 64;
 for (i = 0;i < mlen;++i) sm[64 + i] = m[i];
 for (i = 0;i < 32;++i) sm[32 + i] = az[32 + i];
 crypto_hash_sha512(r,sm + 32,mlen + 32);
 for (i = 0;i < 32;++i) sm[32 + i] = sk[32 + i];

 sc_reduce(r);
 ge_scalarmult_base(&R,r);
 ge_p3_tobytes(sm,&R);

 crypto_hash_sha512(hram,sm,mlen + 64);
 sc_reduce(hram);
 sc_muladd(sm + 32,hram,az,r);

 return 0;
}

int crypto_sign_open_ref10(
 unsigned char *m,unsigned long long *mlen,
 const unsigned char *sm,unsigned long long smlen,
 const unsigned char *pk
)
{
 unsigned char h[64];
 unsigned char checkr[32];
 ge_p3 A;
 ge_p2 R;
 unsigned long long i;

 *mlen = -1;
 if (smlen < 64) return -1;
 if (sm[63] & 224) return -1;
 if (ge_frombytes_negate_vartime(&A,pk) != 0) return -1;

 for (i = 0;i < smlen;++i) m[i] = sm[i];
 for (i = 0;i < 32;++i) m[32 + i] = pk[i];
 crypto_hash_sha512(h,m,smlen);
 sc_reduce(h);

 ge_double_scalarmult_vartime(&R,h,&A,sm + 32);
 ge_tobytes(checkr,&R);
 if (crypto_verify_32(checkr,sm) != 0) {
   for (i = 0;i < smlen;++i) m[i] = 0;
   return -1;
 }

 for (i = 0;i < smlen - 64;++i) m[i] = sm[64 + i];
 for (i = smlen - 64;i < smlen;++i) m[i] = 0;
 *mlen = smlen - 64;
 return 0;
}