text: /**********************************************************************
   * Copyright (c) 2013, 2014 Pieter Wuille                             *
   * Distributed under the MIT software license, see the accompanying   *
   * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
   **********************************************************************/
  
  #ifndef SECP256K1_FIELD_INNER5X52_IMPL_H
  #define SECP256K1_FIELD_INNER5X52_IMPL_H
  
  #include <stdint.h>
  
  #ifdef VERIFY
  #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
  #else
  #define VERIFY_BITS(x, n) do { } while(0)
  #endif
  
  SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
      uint128_t c, d;
      uint64_t t3, t4, tx, u0;
      uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
      const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
  
      VERIFY_BITS(a[0], 56);
      VERIFY_BITS(a[1], 56);
      VERIFY_BITS(a[2], 56);
      VERIFY_BITS(a[3], 56);
      VERIFY_BITS(a[4], 52);
      VERIFY_BITS(b[0], 56);
      VERIFY_BITS(b[1], 56);
      VERIFY_BITS(b[2], 56);
      VERIFY_BITS(b[3], 56);
      VERIFY_BITS(b[4], 52);
      VERIFY_CHECK(r != b);
  
      /*  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
       *  px is a shorthand for sum(a[i]*b[x-i], i=0..x).
       *  Note that [x 0 0 0 0 0] = [x*R].
       */
  
      d  = (uint128_t)a0 * b[3]
         + (uint128_t)a1 * b[2]
         + (uint128_t)a2 * b[1]
         + (uint128_t)a3 * b[0];
      VERIFY_BITS(d, 114);
      /* [d 0 0 0] = [p3 0 0 0] */
      c  = (uint128_t)a4 * b[4];
      VERIFY_BITS(c, 112);
      /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
      d += (c & M) * R; c >>= 52;
      VERIFY_BITS(d, 115);
      VERIFY_BITS(c, 60);
      /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
      t3 = d & M; d >>= 52;
      VERIFY_BITS(t3, 52);
      VERIFY_BITS(d, 63);
      /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
  
      d += (uint128_t)a0 * b[4]
         + (uint128_t)a1 * b[3]
         + (uint128_t)a2 * b[2]
         + (uint128_t)a3 * b[1]
         + (uint128_t)a4 * b[0];
      VERIFY_BITS(d, 115);
      /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
      d += c * R;
      VERIFY_BITS(d, 116);
      /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
      t4 = d & M; d >>= 52;
      VERIFY_BITS(t4, 52);
      VERIFY_BITS(d, 64);
      /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
      tx = (t4 >> 48); t4 &= (M >> 4);
      VERIFY_BITS(tx, 4);
      VERIFY_BITS(t4, 48);
      /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
  
      c  = (uint128_t)a0 * b[0];
      VERIFY_BITS(c, 112);
      /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
      d += (uint128_t)a1 * b[4]
         + (uint128_t)a2 * b[3]
         + (uint128_t)a3 * b[2]
         + (uint128_t)a4 * b[1];
      VERIFY_BITS(d, 115);
      /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      u0 = d & M; d >>= 52;
      VERIFY_BITS(u0, 52);
      VERIFY_BITS(d, 63);
      /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      u0 = (u0 << 4) | tx;
      VERIFY_BITS(u0, 56);
      /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      c += (uint128_t)u0 * (R >> 4);
      VERIFY_BITS(c, 115);
      /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      r[0] = c & M; c >>= 52;
      VERIFY_BITS(r[0], 52);
      VERIFY_BITS(c, 61);
      /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
  
      c += (uint128_t)a0 * b[1]
         + (uint128_t)a1 * b[0];
      VERIFY_BITS(c, 114);
      /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
      d += (uint128_t)a2 * b[4]
         + (uint128_t)a3 * b[3]
         + (uint128_t)a4 * b[2];
      VERIFY_BITS(d, 114);
      /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
      c += (d & M) * R; d >>= 52;
      VERIFY_BITS(c, 115);
      VERIFY_BITS(d, 62);
      /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
      r[1] = c & M; c >>= 52;
      VERIFY_BITS(r[1], 52);
      VERIFY_BITS(c, 63);
      /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
  
      c += (uint128_t)a0 * b[2]
         + (uint128_t)a1 * b[1]
         + (uint128_t)a2 * b[0];
      VERIFY_BITS(c, 114);
      /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint128_t)a3 * b[4]
         + (uint128_t)a4 * b[3];
      VERIFY_BITS(d, 114);
      /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      c += (d & M) * R; d >>= 52;
      VERIFY_BITS(c, 115);
      VERIFY_BITS(d, 62);
      /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[2] = c & M; c >>= 52;
      VERIFY_BITS(r[2], 52);
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      c   += d * R + t3;
      VERIFY_BITS(c, 100);
      /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[3] = c & M; c >>= 52;
      VERIFY_BITS(r[3], 52);
      VERIFY_BITS(c, 48);
      /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      c   += t4;
      VERIFY_BITS(c, 49);
      /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[4] = c;
      VERIFY_BITS(r[4], 49);
      /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  }
  
  SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
      uint128_t c, d;
      uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
      int64_t t3, t4, tx, u0;
      const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
  
      VERIFY_BITS(a[0], 56);
      VERIFY_BITS(a[1], 56);
      VERIFY_BITS(a[2], 56);
      VERIFY_BITS(a[3], 56);
      VERIFY_BITS(a[4], 52);
  
      /**  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
       *  px is a shorthand for sum(a[i]*a[x-i], i=0..x).
       *  Note that [x 0 0 0 0 0] = [x*R].
       */
  
      d  = (uint128_t)(a0*2) * a3
         + (uint128_t)(a1*2) * a2;
      VERIFY_BITS(d, 114);
      /* [d 0 0 0] = [p3 0 0 0] */
      c  = (uint128_t)a4 * a4;
      VERIFY_BITS(c, 112);
      /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
      d += (c & M) * R; c >>= 52;
      VERIFY_BITS(d, 115);
      VERIFY_BITS(c, 60);
      /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
      t3 = d & M; d >>= 52;
      VERIFY_BITS(t3, 52);
      VERIFY_BITS(d, 63);
      /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
  
      a4 *= 2;
      d += (uint128_t)a0 * a4
         + (uint128_t)(a1*2) * a3
         + (uint128_t)a2 * a2;
      VERIFY_BITS(d, 115);
      /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
      d += c * R;
      VERIFY_BITS(d, 116);
      /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
      t4 = d & M; d >>= 52;
      VERIFY_BITS(t4, 52);
      VERIFY_BITS(d, 64);
      /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
      tx = (t4 >> 48); t4 &= (M >> 4);
      VERIFY_BITS(tx, 4);
      VERIFY_BITS(t4, 48);
      /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
  
      c  = (uint128_t)a0 * a0;
      VERIFY_BITS(c, 112);
      /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
      d += (uint128_t)a1 * a4
         + (uint128_t)(a2*2) * a3;
      VERIFY_BITS(d, 114);
      /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      u0 = d & M; d >>= 52;
      VERIFY_BITS(u0, 52);
      VERIFY_BITS(d, 62);
      /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      u0 = (u0 << 4) | tx;
      VERIFY_BITS(u0, 56);
      /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      c += (uint128_t)u0 * (R >> 4);
      VERIFY_BITS(c, 113);
      /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
      r[0] = c & M; c >>= 52;
      VERIFY_BITS(r[0], 52);
      VERIFY_BITS(c, 61);
      /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
  
      a0 *= 2;
      c += (uint128_t)a0 * a1;
      VERIFY_BITS(c, 114);
      /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
      d += (uint128_t)a2 * a4
         + (uint128_t)a3 * a3;
      VERIFY_BITS(d, 114);
      /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
      c += (d & M) * R; d >>= 52;
      VERIFY_BITS(c, 115);
      VERIFY_BITS(d, 62);
      /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
      r[1] = c & M; c >>= 52;
      VERIFY_BITS(r[1], 52);
      VERIFY_BITS(c, 63);
      /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
  
      c += (uint128_t)a0 * a2
         + (uint128_t)a1 * a1;
      VERIFY_BITS(c, 114);
      /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint128_t)a3 * a4;
      VERIFY_BITS(d, 114);
      /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      c += (d & M) * R; d >>= 52;
      VERIFY_BITS(c, 115);
      VERIFY_BITS(d, 62);
      /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[2] = c & M; c >>= 52;
      VERIFY_BITS(r[2], 52);
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      c   += d * R + t3;
      VERIFY_BITS(c, 100);
      /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[3] = c & M; c >>= 52;
      VERIFY_BITS(r[3], 52);
      VERIFY_BITS(c, 48);
      /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      c   += t4;
      VERIFY_BITS(c, 49);
      /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[4] = c;
      VERIFY_BITS(r[4], 49);
      /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  }
  
  #endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */
  