/* ge_operations.c
 *
 * Copyright (C) 2006-2015 wolfSSL Inc.
 *
 * This file is part of wolfSSL. (formerly known as CyaSSL)
 *
 * wolfSSL is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * wolfSSL is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
 */

 /* Based On Daniel J Bernstein's ed25519 Public Domain ref10 work. */


#ifdef HAVE_CONFIG_H
    #include <config.h>
#endif

#include <wolfssl/wolfcrypt/settings.h>

#ifdef HAVE_ED25519

#include <wolfssl/wolfcrypt/ge_operations.h>
#include <wolfssl/wolfcrypt/error-crypt.h>
#ifdef NO_INLINE
    #include <wolfssl/wolfcrypt/misc.h>
#else
    #include <wolfcrypt/src/misc.c>
#endif

/*
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)
*/


/*
Input:
  s[0]+256*s[1]+...+256^63*s[63] = s

Output:
  s[0]+256*s[1]+...+256^31*s[31] = s mod l
  where l = 2^252 + 27742317777372353535851937790883648493.
  Overwrites s in place.
*/
void sc_reduce(byte* s)
{
  int64_t s0 = 2097151 & load_3(s);
  int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
  int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
  int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
  int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
  int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
  int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
  int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
  int64_t s8 = 2097151 & load_3(s + 21);
  int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
  int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
  int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
  int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
  int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
  int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
  int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
  int64_t s16 = 2097151 & load_3(s + 42);
  int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
  int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
  int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
  int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
  int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
  int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
  int64_t s23 = (load_4(s + 60) >> 3);
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;
  int64_t carry10;
  int64_t carry11;
  int64_t carry12;
  int64_t carry13;
  int64_t carry14;
  int64_t carry15;
  int64_t carry16;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  /* hush warnings after setting values to 0 */
  (void)s12;
  (void)s13;
  (void)s14;
  (void)s15;
  (void)s16;
  (void)s17;
  (void)s18;
  (void)s19;
  (void)s20;
  (void)s21;
  (void)s22;
  (void)s23;
}


/*
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.
*/
void sc_muladd(byte* s, const byte* a, const byte* b, const byte* c)
{
  int64_t a0 = 2097151 & load_3(a);
  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
  int64_t a8 = 2097151 & load_3(a + 21);
  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
  int64_t a11 = (load_4(a + 28) >> 7);
  int64_t b0 = 2097151 & load_3(b);
  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
  int64_t b8 = 2097151 & load_3(b + 21);
  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
  int64_t b11 = (load_4(b + 28) >> 7);
  int64_t c0 = 2097151 & load_3(c);
  int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
  int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
  int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
  int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
  int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
  int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
  int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
  int64_t c8 = 2097151 & load_3(c + 21);
  int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
  int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
  int64_t c11 = (load_4(c + 28) >> 7);
  int64_t s0;
  int64_t s1;
  int64_t s2;
  int64_t s3;
  int64_t s4;
  int64_t s5;
  int64_t s6;
  int64_t s7;
  int64_t s8;
  int64_t s9;
  int64_t s10;
  int64_t s11;
  int64_t s12;
  int64_t s13;
  int64_t s14;
  int64_t s15;
  int64_t s16;
  int64_t s17;
  int64_t s18;
  int64_t s19;
  int64_t s20;
  int64_t s21;
  int64_t s22;
  int64_t s23;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;
  int64_t carry10;
  int64_t carry11;
  int64_t carry12;
  int64_t carry13;
  int64_t carry14;
  int64_t carry15;
  int64_t carry16;
  int64_t carry17;
  int64_t carry18;
  int64_t carry19;
  int64_t carry20;
  int64_t carry21;
  int64_t carry22;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  /* hush warnings after setting values to 0 */
  (void)s12;
  (void)s13;
  (void)s14;
  (void)s15;
  (void)s16;
  (void)s17;
  (void)s18;
  (void)s19;
  (void)s20;
  (void)s21;
  (void)s22;
  (void)s23;
}


int ge_compress_key(byte* out, const byte* xIn, const byte* yIn, word32 keySz)
{
    fe     x,y,z;
    ge_p3  g;
    byte   bArray[keySz];
    word32 i;

    fe_0(x);
    fe_0(y);
    fe_1(z);
    fe_frombytes(x, xIn);
    fe_frombytes(y, yIn);

    fe_copy(g.X, x);
    fe_copy(g.Y, y);
    fe_copy(g.Z, z);

    ge_p3_tobytes(bArray, &g);

    for (i = 0; i < keySz; i++) {
        out[keySz - 1 - i] = bArray[i];
    }

    return 0;
}


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


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


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


static void 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);
}


/* 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 },
  { 29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963 },
  { 5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950 },
 },
 {
  { -27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568 },
  { 12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335 },
  { 25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628 },
 },
 {
  { -26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007 },
  { -2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772 },
  { -22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653 },
 },
 {
  { 2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567 },
  { 13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686 },
  { 21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372 },
 },
 {
  { -13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887 },
  { -23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954 },
  { -29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953 },
 },
 {
  { 24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833 },
  { -16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532 },
  { -22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876 },
 },
 {
  { 2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268 },
  { 33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214 },
  { 1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038 },
 },
},
{
 {
  { 6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800 },
  { 4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645 },
  { -4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664 },
 },
 {
  { 1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933 },
  { -25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182 },
  { -17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222 },
 },
 {
  { -18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991 },
  { 20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880 },
  { 9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092 },
 },
 {
  { -16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295 },
  { 19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788 },
  { 8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553 },
 },
 {
  { -15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026 },
  { 11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347 },
  { -18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033 },
 },
 {
  { -23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395 },
  { -27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278 },
  { 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 },
 },
 {
  { 32173121,-16129311,24896207,3921497,22579056,-3410854,19270449,12217473,17789017,-3395995 },
  { -30552961,-2228401,-15578829,-10147201,13243889,517024,15479401,-3853233,30460520,1052596 },
  { -11614875,13323618,32618793,8175907,-15230173,12596687,27491595,-4612359,3179268,-9478891 },
 },
 {
  { 31947069,-14366651,-4640583,-15339921,-15125977,-6039709,-14756777,-16411740,19072640,-9511060 },
  { 11685058,11822410,3158003,-13952594,33402194,-4165066,5977896,-5215017,473099,5040608 },
  { -20290863,8198642,-27410132,11602123,1290375,-2799760,28326862,1721092,-19558642,-3131606 },
 },
},
{
 {
  { 7881532,10687937,7578723,7738378,-18951012,-2553952,21820786,8076149,-27868496,11538389 },
  { -19935666,3899861,18283497,-6801568,-15728660,-11249211,8754525,7446702,-5676054,5797016 },
  { -11295600,-3793569,-15782110,-7964573,12708869,-8456199,2014099,-9050574,-2369172,-5877341 },
 },
 {
  { -22472376,-11568741,-27682020,1146375,18956691,16640559,1192730,-3714199,15123619,10811505 },
  { 14352098,-3419715,-18942044,10822655,32750596,4699007,-70363,15776356,-28886779,-11974553 },
  { -28241164,-8072475,-4978962,-5315317,29416931,1847569,-20654173,-16484855,4714547,-9600655 },
 },
 {
  { 15200332,8368572,19679101,15970074,-31872674,1959451,24611599,-4543832,-11745876,12340220 },
  { 12876937,-10480056,33134381,6590940,-6307776,14872440,9613953,8241152,15370987,9608631 },
  { -4143277,-12014408,8446281,-391603,4407738,13629032,-7724868,15866074,-28210621,-8814099 },
 },
 {
  { 26660628,-15677655,8393734,358047,-7401291,992988,-23904233,858697,20571223,8420556 },
  { 14620715,13067227,-15447274,8264467,14106269,15080814,33531827,12516406,-21574435,-12476749 },
  { 236881,10476226,57258,-14677024,6472998,2466984,17258519,7256740,8791136,15069930 },
 },
 {
  { 1276410,-9371918,22949635,-16322807,-23493039,-5702186,14711875,4874229,-30663140,-2331391 },
  { 5855666,4990204,-13711848,7294284,-7804282,1924647,-1423175,-7912378,-33069337,9234253 },
  { 20590503,-9018988,31529744,-7352666,-2706834,10650548,31559055,-11609587,18979186,13396066 },
 },
 {
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  { -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_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
*/
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) {
    ge_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) {
    ge_select(&t,i / 2,e[i]);
    ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
  }
}


/* ge double scalar mult */
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;
        }
      }
    }
}


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 },
 },
} ;


/*
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.
*/
int 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);
  }

  return 0;
}


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
} ;


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;
}


/* ge madd */
/*
r = p + q
*/

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


/* ge msub */

/*
r = p - q
*/

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


/* ge p1p1 to p2 */
/*
r = p
*/

extern 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);
}


/* ge p1p1 to p3 */

/*
r = p
*/

extern 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);
}


/* ge p2 0 */

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


/* ge p2 dbl */

/*
r = 2 * p
*/

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


/* ge p3 0 */

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


/* ge p3 dble */

/*
r = 2 * p
*/

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);
}


/* ge p3 to cached */

/*
r = p
*/

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


extern 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);
}


/* ge p3 to p2 */
/*
r = p
*/

extern 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);
}


/* ge p3 tobytes */
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;
}


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


/* ge_sub */
/*
r = p - q
*/

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


/* ge tobytes */
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;
}
#endif /* HAVE_ED25519 */