text: /**********************************************************************
   * Copyright (c) 2013, 2014 Pieter Wuille                             *
   * Distributed under the MIT software license, see the accompanying   *
   * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
   **********************************************************************/
  
  #ifndef _SECP256K1_FIELD_REPR_IMPL_H_
  #define _SECP256K1_FIELD_REPR_IMPL_H_
  
  #include <stdio.h>
  #include <string.h>
  #include "util.h"
  #include "num.h"
  #include "field.h"
  
  #ifdef VERIFY
  static void secp256k1_fe_verify(const secp256k1_fe *a) {
      const uint32_t *d = a->n;
      int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
      r &= (d[0] <= 0x3FFFFFFUL * m);
      r &= (d[1] <= 0x3FFFFFFUL * m);
      r &= (d[2] <= 0x3FFFFFFUL * m);
      r &= (d[3] <= 0x3FFFFFFUL * m);
      r &= (d[4] <= 0x3FFFFFFUL * m);
      r &= (d[5] <= 0x3FFFFFFUL * m);
      r &= (d[6] <= 0x3FFFFFFUL * m);
      r &= (d[7] <= 0x3FFFFFFUL * m);
      r &= (d[8] <= 0x3FFFFFFUL * m);
      r &= (d[9] <= 0x03FFFFFUL * m);
      r &= (a->magnitude >= 0);
      r &= (a->magnitude <= 32);
      if (a->normalized) {
          r &= (a->magnitude <= 1);
          if (r && (d[9] == 0x03FFFFFUL)) {
              uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
              if (mid == 0x3FFFFFFUL) {
                  r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
              }
          }
      }
      VERIFY_CHECK(r == 1);
  }
  #else
  static void secp256k1_fe_verify(const secp256k1_fe *a) {
      (void)a;
  }
  #endif
  
  static void secp256k1_fe_normalize(secp256k1_fe *r) {
      uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
               t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
  
      /* Reduce t9 at the start so there will be at most a single carry from the first pass */
      uint32_t m;
      uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
  
      /* The first pass ensures the magnitude is 1, ... */
      t0 += x * 0x3D1UL; t1 += (x << 6);
      t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
      t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
      t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
      t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
      t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
      t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
      t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
      t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
      t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
  
      /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
      VERIFY_CHECK(t9 >> 23 == 0);
  
      /* At most a single final reduction is needed; check if the value is >= the field characteristic */
      x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
          & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
  
      /* Apply the final reduction (for constant-time behaviour, we do it always) */
      t0 += x * 0x3D1UL; t1 += (x << 6);
      t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
      t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
      t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
      t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
      t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
      t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
      t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
      t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
      t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
  
      /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
      VERIFY_CHECK(t9 >> 22 == x);
  
      /* Mask off the possible multiple of 2^256 from the final reduction */
      t9 &= 0x03FFFFFUL;
  
      r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
      r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
  
  #ifdef VERIFY
      r->magnitude = 1;
      r->normalized = 1;
      secp256k1_fe_verify(r);
  #endif
  }
  
  static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
      uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
               t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
  
      /* Reduce t9 at the start so there will be at most a single carry from the first pass */
      uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
  
      /* The first pass ensures the magnitude is 1, ... */
      t0 += x * 0x3D1UL; t1 += (x << 6);
      t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
      t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
      t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
      t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
      t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
      t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
      t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
      t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
      t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
  
      /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
      VERIFY_CHECK(t9 >> 23 == 0);
  
      r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
      r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
  
  #ifdef VERIFY
      r->magnitude = 1;
      secp256k1_fe_verify(r);
  #endif
  }
  
  static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
      uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
               t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
  
      /* Reduce t9 at the start so there will be at most a single carry from the first pass */
      uint32_t m;
      uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
  
      /* The first pass ensures the magnitude is 1, ... */
      t0 += x * 0x3D1UL; t1 += (x << 6);
      t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
      t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
      t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
      t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
      t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
      t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
      t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
      t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
      t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
  
      /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
      VERIFY_CHECK(t9 >> 23 == 0);
  
      /* At most a single final reduction is needed; check if the value is >= the field characteristic */
      x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
          & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
  
      if (x) {
          t0 += 0x3D1UL; t1 += (x << 6);
          t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
          t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
          t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
          t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
          t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
          t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
          t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
          t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
          t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
  
          /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
          VERIFY_CHECK(t9 >> 22 == x);
  
          /* Mask off the possible multiple of 2^256 from the final reduction */
          t9 &= 0x03FFFFFUL;
      }
  
      r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
      r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
  
  #ifdef VERIFY
      r->magnitude = 1;
      r->normalized = 1;
      secp256k1_fe_verify(r);
  #endif
  }
  
  static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
      uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
               t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
  
      /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
      uint32_t z0, z1;
  
      /* Reduce t9 at the start so there will be at most a single carry from the first pass */
      uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
  
      /* The first pass ensures the magnitude is 1, ... */
      t0 += x * 0x3D1UL; t1 += (x << 6);
      t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0  = t0; z1  = t0 ^ 0x3D0UL;
      t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
      t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
      t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
      t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
      t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
      t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
      t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
      t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
                                           z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
  
      /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
      VERIFY_CHECK(t9 >> 23 == 0);
  
      return (z0 == 0) | (z1 == 0x3FFFFFFUL);
  }
  
  static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
      uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
      uint32_t z0, z1;
      uint32_t x;
  
      t0 = r->n[0];
      t9 = r->n[9];
  
      /* Reduce t9 at the start so there will be at most a single carry from the first pass */
      x = t9 >> 22;
  
      /* The first pass ensures the magnitude is 1, ... */
      t0 += x * 0x3D1UL;
  
      /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
      z0 = t0 & 0x3FFFFFFUL;
      z1 = z0 ^ 0x3D0UL;
  
      /* Fast return path should catch the majority of cases */
      if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) {
          return 0;
      }
  
      t1 = r->n[1];
      t2 = r->n[2];
      t3 = r->n[3];
      t4 = r->n[4];
      t5 = r->n[5];
      t6 = r->n[6];
      t7 = r->n[7];
      t8 = r->n[8];
  
      t9 &= 0x03FFFFFUL;
      t1 += (x << 6);
  
      t1 += (t0 >> 26);
      t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
      t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
      t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
      t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
      t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
      t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
      t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
      t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
                                           z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
  
      /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
      VERIFY_CHECK(t9 >> 23 == 0);
  
      return (z0 == 0) | (z1 == 0x3FFFFFFUL);
  }
  
  SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
      r->n[0] = a;
      r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
  #ifdef VERIFY
      r->magnitude = 1;
      r->normalized = 1;
      secp256k1_fe_verify(r);
  #endif
  }
  
  SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
      const uint32_t *t = a->n;
  #ifdef VERIFY
      VERIFY_CHECK(a->normalized);
      secp256k1_fe_verify(a);
  #endif
      return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
  }
  
  SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
  #ifdef VERIFY
      VERIFY_CHECK(a->normalized);
      secp256k1_fe_verify(a);
  #endif
      return a->n[0] & 1;
  }
  
  SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
      int i;
  #ifdef VERIFY
      a->magnitude = 0;
      a->normalized = 1;
  #endif
      for (i=0; i<10; i++) {
          a->n[i] = 0;
      }
  }
  
  static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
      int i;
  #ifdef VERIFY
      VERIFY_CHECK(a->normalized);
      VERIFY_CHECK(b->normalized);
      secp256k1_fe_verify(a);
      secp256k1_fe_verify(b);
  #endif
      for (i = 9; i >= 0; i--) {
          if (a->n[i] > b->n[i]) {
              return 1;
          }
          if (a->n[i] < b->n[i]) {
              return -1;
          }
      }
      return 0;
  }
  
  static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
      int i;
      r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
      r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
      for (i=0; i<32; i++) {
          int j;
          for (j=0; j<4; j++) {
              int limb = (8*i+2*j)/26;
              int shift = (8*i+2*j)%26;
              r->n[limb] |= (uint32_t)((a[31-i] >> (2*j)) & 0x3) << shift;
          }
      }
      if (r->n[9] == 0x3FFFFFUL && (r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL && (r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL) {
          return 0;
      }
  #ifdef VERIFY
      r->magnitude = 1;
      r->normalized = 1;
      secp256k1_fe_verify(r);
  #endif
      return 1;
  }
  
  /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
  static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
      int i;
  #ifdef VERIFY
      VERIFY_CHECK(a->normalized);
      secp256k1_fe_verify(a);
  #endif
      for (i=0; i<32; i++) {
          int j;
          int c = 0;
          for (j=0; j<4; j++) {
              int limb = (8*i+2*j)/26;
              int shift = (8*i+2*j)%26;
              c |= ((a->n[limb] >> shift) & 0x3) << (2 * j);
          }
          r[31-i] = c;
      }
  }
  
  SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
  #ifdef VERIFY
      VERIFY_CHECK(a->magnitude <= m);
      secp256k1_fe_verify(a);
  #endif
      r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
      r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
      r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
      r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
      r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
      r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
      r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
      r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
      r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
      r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
  #ifdef VERIFY
      r->magnitude = m + 1;
      r->normalized = 0;
      secp256k1_fe_verify(r);
  #endif
  }
  
  SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
      r->n[0] *= a;
      r->n[1] *= a;
      r->n[2] *= a;
      r->n[3] *= a;
      r->n[4] *= a;
      r->n[5] *= a;
      r->n[6] *= a;
      r->n[7] *= a;
      r->n[8] *= a;
      r->n[9] *= a;
  #ifdef VERIFY
      r->magnitude *= a;
      r->normalized = 0;
      secp256k1_fe_verify(r);
  #endif
  }
  
  SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
  #ifdef VERIFY
      secp256k1_fe_verify(a);
  #endif
      r->n[0] += a->n[0];
      r->n[1] += a->n[1];
      r->n[2] += a->n[2];
      r->n[3] += a->n[3];
      r->n[4] += a->n[4];
      r->n[5] += a->n[5];
      r->n[6] += a->n[6];
      r->n[7] += a->n[7];
      r->n[8] += a->n[8];
      r->n[9] += a->n[9];
  #ifdef VERIFY
      r->magnitude += a->magnitude;
      r->normalized = 0;
      secp256k1_fe_verify(r);
  #endif
  }
  
  #if defined(USE_EXTERNAL_ASM)
  
  /* External assembler implementation */
  void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
  void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
  
  #else
  
  #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(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
      uint64_t c, d;
      uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
      uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
      const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
  
      VERIFY_BITS(a[0], 30);
      VERIFY_BITS(a[1], 30);
      VERIFY_BITS(a[2], 30);
      VERIFY_BITS(a[3], 30);
      VERIFY_BITS(a[4], 30);
      VERIFY_BITS(a[5], 30);
      VERIFY_BITS(a[6], 30);
      VERIFY_BITS(a[7], 30);
      VERIFY_BITS(a[8], 30);
      VERIFY_BITS(a[9], 26);
      VERIFY_BITS(b[0], 30);
      VERIFY_BITS(b[1], 30);
      VERIFY_BITS(b[2], 30);
      VERIFY_BITS(b[3], 30);
      VERIFY_BITS(b[4], 30);
      VERIFY_BITS(b[5], 30);
      VERIFY_BITS(b[6], 30);
      VERIFY_BITS(b[7], 30);
      VERIFY_BITS(b[8], 30);
      VERIFY_BITS(b[9], 26);
  
      /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + 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 0 0 0 0 0] = [x*R1 x*R0].
       */
  
      d  = (uint64_t)a[0] * b[9]
         + (uint64_t)a[1] * b[8]
         + (uint64_t)a[2] * b[7]
         + (uint64_t)a[3] * b[6]
         + (uint64_t)a[4] * b[5]
         + (uint64_t)a[5] * b[4]
         + (uint64_t)a[6] * b[3]
         + (uint64_t)a[7] * b[2]
         + (uint64_t)a[8] * b[1]
         + (uint64_t)a[9] * b[0];
      /* VERIFY_BITS(d, 64); */
      /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
      t9 = d & M; d >>= 26;
      VERIFY_BITS(t9, 26);
      VERIFY_BITS(d, 38);
      /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
  
      c  = (uint64_t)a[0] * b[0];
      VERIFY_BITS(c, 60);
      /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
      d += (uint64_t)a[1] * b[9]
         + (uint64_t)a[2] * b[8]
         + (uint64_t)a[3] * b[7]
         + (uint64_t)a[4] * b[6]
         + (uint64_t)a[5] * b[5]
         + (uint64_t)a[6] * b[4]
         + (uint64_t)a[7] * b[3]
         + (uint64_t)a[8] * b[2]
         + (uint64_t)a[9] * b[1];
      VERIFY_BITS(d, 63);
      /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
      u0 = d & M; d >>= 26; c += u0 * R0;
      VERIFY_BITS(u0, 26);
      VERIFY_BITS(d, 37);
      VERIFY_BITS(c, 61);
      /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
      t0 = c & M; c >>= 26; c += u0 * R1;
      VERIFY_BITS(t0, 26);
      VERIFY_BITS(c, 37);
      /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
      /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
  
      c += (uint64_t)a[0] * b[1]
         + (uint64_t)a[1] * b[0];
      VERIFY_BITS(c, 62);
      /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
      d += (uint64_t)a[2] * b[9]
         + (uint64_t)a[3] * b[8]
         + (uint64_t)a[4] * b[7]
         + (uint64_t)a[5] * b[6]
         + (uint64_t)a[6] * b[5]
         + (uint64_t)a[7] * b[4]
         + (uint64_t)a[8] * b[3]
         + (uint64_t)a[9] * b[2];
      VERIFY_BITS(d, 63);
      /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
      u1 = d & M; d >>= 26; c += u1 * R0;
      VERIFY_BITS(u1, 26);
      VERIFY_BITS(d, 37);
      VERIFY_BITS(c, 63);
      /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
      t1 = c & M; c >>= 26; c += u1 * R1;
      VERIFY_BITS(t1, 26);
      VERIFY_BITS(c, 38);
      /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
      /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
  
      c += (uint64_t)a[0] * b[2]
         + (uint64_t)a[1] * b[1]
         + (uint64_t)a[2] * b[0];
      VERIFY_BITS(c, 62);
      /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      d += (uint64_t)a[3] * b[9]
         + (uint64_t)a[4] * b[8]
         + (uint64_t)a[5] * b[7]
         + (uint64_t)a[6] * b[6]
         + (uint64_t)a[7] * b[5]
         + (uint64_t)a[8] * b[4]
         + (uint64_t)a[9] * b[3];
      VERIFY_BITS(d, 63);
      /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      u2 = d & M; d >>= 26; c += u2 * R0;
      VERIFY_BITS(u2, 26);
      VERIFY_BITS(d, 37);
      VERIFY_BITS(c, 63);
      /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      t2 = c & M; c >>= 26; c += u2 * R1;
      VERIFY_BITS(t2, 26);
      VERIFY_BITS(c, 38);
      /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
  
      c += (uint64_t)a[0] * b[3]
         + (uint64_t)a[1] * b[2]
         + (uint64_t)a[2] * b[1]
         + (uint64_t)a[3] * b[0];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      d += (uint64_t)a[4] * b[9]
         + (uint64_t)a[5] * b[8]
         + (uint64_t)a[6] * b[7]
         + (uint64_t)a[7] * b[6]
         + (uint64_t)a[8] * b[5]
         + (uint64_t)a[9] * b[4];
      VERIFY_BITS(d, 63);
      /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      u3 = d & M; d >>= 26; c += u3 * R0;
      VERIFY_BITS(u3, 26);
      VERIFY_BITS(d, 37);
      /* VERIFY_BITS(c, 64); */
      /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      t3 = c & M; c >>= 26; c += u3 * R1;
      VERIFY_BITS(t3, 26);
      VERIFY_BITS(c, 39);
      /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
  
      c += (uint64_t)a[0] * b[4]
         + (uint64_t)a[1] * b[3]
         + (uint64_t)a[2] * b[2]
         + (uint64_t)a[3] * b[1]
         + (uint64_t)a[4] * b[0];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      d += (uint64_t)a[5] * b[9]
         + (uint64_t)a[6] * b[8]
         + (uint64_t)a[7] * b[7]
         + (uint64_t)a[8] * b[6]
         + (uint64_t)a[9] * b[5];
      VERIFY_BITS(d, 62);
      /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      u4 = d & M; d >>= 26; c += u4 * R0;
      VERIFY_BITS(u4, 26);
      VERIFY_BITS(d, 36);
      /* VERIFY_BITS(c, 64); */
      /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      t4 = c & M; c >>= 26; c += u4 * R1;
      VERIFY_BITS(t4, 26);
      VERIFY_BITS(c, 39);
      /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)a[0] * b[5]
         + (uint64_t)a[1] * b[4]
         + (uint64_t)a[2] * b[3]
         + (uint64_t)a[3] * b[2]
         + (uint64_t)a[4] * b[1]
         + (uint64_t)a[5] * b[0];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)a[6] * b[9]
         + (uint64_t)a[7] * b[8]
         + (uint64_t)a[8] * b[7]
         + (uint64_t)a[9] * b[6];
      VERIFY_BITS(d, 62);
      /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      u5 = d & M; d >>= 26; c += u5 * R0;
      VERIFY_BITS(u5, 26);
      VERIFY_BITS(d, 36);
      /* VERIFY_BITS(c, 64); */
      /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      t5 = c & M; c >>= 26; c += u5 * R1;
      VERIFY_BITS(t5, 26);
      VERIFY_BITS(c, 39);
      /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)a[0] * b[6]
         + (uint64_t)a[1] * b[5]
         + (uint64_t)a[2] * b[4]
         + (uint64_t)a[3] * b[3]
         + (uint64_t)a[4] * b[2]
         + (uint64_t)a[5] * b[1]
         + (uint64_t)a[6] * b[0];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)a[7] * b[9]
         + (uint64_t)a[8] * b[8]
         + (uint64_t)a[9] * b[7];
      VERIFY_BITS(d, 61);
      /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      u6 = d & M; d >>= 26; c += u6 * R0;
      VERIFY_BITS(u6, 26);
      VERIFY_BITS(d, 35);
      /* VERIFY_BITS(c, 64); */
      /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      t6 = c & M; c >>= 26; c += u6 * R1;
      VERIFY_BITS(t6, 26);
      VERIFY_BITS(c, 39);
      /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)a[0] * b[7]
         + (uint64_t)a[1] * b[6]
         + (uint64_t)a[2] * b[5]
         + (uint64_t)a[3] * b[4]
         + (uint64_t)a[4] * b[3]
         + (uint64_t)a[5] * b[2]
         + (uint64_t)a[6] * b[1]
         + (uint64_t)a[7] * b[0];
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x8000007C00000007ULL);
      /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)a[8] * b[9]
         + (uint64_t)a[9] * b[8];
      VERIFY_BITS(d, 58);
      /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      u7 = d & M; d >>= 26; c += u7 * R0;
      VERIFY_BITS(u7, 26);
      VERIFY_BITS(d, 32);
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
      /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      t7 = c & M; c >>= 26; c += u7 * R1;
      VERIFY_BITS(t7, 26);
      VERIFY_BITS(c, 38);
      /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)a[0] * b[8]
         + (uint64_t)a[1] * b[7]
         + (uint64_t)a[2] * b[6]
         + (uint64_t)a[3] * b[5]
         + (uint64_t)a[4] * b[4]
         + (uint64_t)a[5] * b[3]
         + (uint64_t)a[6] * b[2]
         + (uint64_t)a[7] * b[1]
         + (uint64_t)a[8] * b[0];
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x9000007B80000008ULL);
      /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)a[9] * b[9];
      VERIFY_BITS(d, 57);
      /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      u8 = d & M; d >>= 26; c += u8 * R0;
      VERIFY_BITS(u8, 26);
      VERIFY_BITS(d, 31);
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      r[3] = t3;
      VERIFY_BITS(r[3], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[4] = t4;
      VERIFY_BITS(r[4], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[5] = t5;
      VERIFY_BITS(r[5], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[6] = t6;
      VERIFY_BITS(r[6], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[7] = t7;
      VERIFY_BITS(r[7], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      r[8] = c & M; c >>= 26; c += u8 * R1;
      VERIFY_BITS(r[8], 26);
      VERIFY_BITS(c, 39);
      /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      c   += d * R0 + t9;
      VERIFY_BITS(c, 45);
      /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
      VERIFY_BITS(r[9], 22);
      VERIFY_BITS(c, 46);
      /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      d    = c * (R0 >> 4) + t0;
      VERIFY_BITS(d, 56);
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[0] = d & M; d >>= 26;
      VERIFY_BITS(r[0], 26);
      VERIFY_BITS(d, 30);
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      d   += c * (R1 >> 4) + t1;
      VERIFY_BITS(d, 53);
      VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[1] = d & M; d >>= 26;
      VERIFY_BITS(r[1], 26);
      VERIFY_BITS(d, 27);
      VERIFY_CHECK(d <= 0x4000000ULL);
      /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      d   += t2;
      VERIFY_BITS(d, 27);
      /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[2] = d;
      VERIFY_BITS(r[2], 27);
      /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  }
  
  SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
      uint64_t c, d;
      uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
      uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
      const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
  
      VERIFY_BITS(a[0], 30);
      VERIFY_BITS(a[1], 30);
      VERIFY_BITS(a[2], 30);
      VERIFY_BITS(a[3], 30);
      VERIFY_BITS(a[4], 30);
      VERIFY_BITS(a[5], 30);
      VERIFY_BITS(a[6], 30);
      VERIFY_BITS(a[7], 30);
      VERIFY_BITS(a[8], 30);
      VERIFY_BITS(a[9], 26);
  
      /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + 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 0 0 0 0 0] = [x*R1 x*R0].
       */
  
      d  = (uint64_t)(a[0]*2) * a[9]
         + (uint64_t)(a[1]*2) * a[8]
         + (uint64_t)(a[2]*2) * a[7]
         + (uint64_t)(a[3]*2) * a[6]
         + (uint64_t)(a[4]*2) * a[5];
      /* VERIFY_BITS(d, 64); */
      /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
      t9 = d & M; d >>= 26;
      VERIFY_BITS(t9, 26);
      VERIFY_BITS(d, 38);
      /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
  
      c  = (uint64_t)a[0] * a[0];
      VERIFY_BITS(c, 60);
      /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
      d += (uint64_t)(a[1]*2) * a[9]
         + (uint64_t)(a[2]*2) * a[8]
         + (uint64_t)(a[3]*2) * a[7]
         + (uint64_t)(a[4]*2) * a[6]
         + (uint64_t)a[5] * a[5];
      VERIFY_BITS(d, 63);
      /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
      u0 = d & M; d >>= 26; c += u0 * R0;
      VERIFY_BITS(u0, 26);
      VERIFY_BITS(d, 37);
      VERIFY_BITS(c, 61);
      /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
      t0 = c & M; c >>= 26; c += u0 * R1;
      VERIFY_BITS(t0, 26);
      VERIFY_BITS(c, 37);
      /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
      /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
  
      c += (uint64_t)(a[0]*2) * a[1];
      VERIFY_BITS(c, 62);
      /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
      d += (uint64_t)(a[2]*2) * a[9]
         + (uint64_t)(a[3]*2) * a[8]
         + (uint64_t)(a[4]*2) * a[7]
         + (uint64_t)(a[5]*2) * a[6];
      VERIFY_BITS(d, 63);
      /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
      u1 = d & M; d >>= 26; c += u1 * R0;
      VERIFY_BITS(u1, 26);
      VERIFY_BITS(d, 37);
      VERIFY_BITS(c, 63);
      /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
      t1 = c & M; c >>= 26; c += u1 * R1;
      VERIFY_BITS(t1, 26);
      VERIFY_BITS(c, 38);
      /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
      /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
  
      c += (uint64_t)(a[0]*2) * a[2]
         + (uint64_t)a[1] * a[1];
      VERIFY_BITS(c, 62);
      /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      d += (uint64_t)(a[3]*2) * a[9]
         + (uint64_t)(a[4]*2) * a[8]
         + (uint64_t)(a[5]*2) * a[7]
         + (uint64_t)a[6] * a[6];
      VERIFY_BITS(d, 63);
      /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      u2 = d & M; d >>= 26; c += u2 * R0;
      VERIFY_BITS(u2, 26);
      VERIFY_BITS(d, 37);
      VERIFY_BITS(c, 63);
      /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      t2 = c & M; c >>= 26; c += u2 * R1;
      VERIFY_BITS(t2, 26);
      VERIFY_BITS(c, 38);
      /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
      /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
  
      c += (uint64_t)(a[0]*2) * a[3]
         + (uint64_t)(a[1]*2) * a[2];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      d += (uint64_t)(a[4]*2) * a[9]
         + (uint64_t)(a[5]*2) * a[8]
         + (uint64_t)(a[6]*2) * a[7];
      VERIFY_BITS(d, 63);
      /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      u3 = d & M; d >>= 26; c += u3 * R0;
      VERIFY_BITS(u3, 26);
      VERIFY_BITS(d, 37);
      /* VERIFY_BITS(c, 64); */
      /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      t3 = c & M; c >>= 26; c += u3 * R1;
      VERIFY_BITS(t3, 26);
      VERIFY_BITS(c, 39);
      /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
      /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
  
      c += (uint64_t)(a[0]*2) * a[4]
         + (uint64_t)(a[1]*2) * a[3]
         + (uint64_t)a[2] * a[2];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      d += (uint64_t)(a[5]*2) * a[9]
         + (uint64_t)(a[6]*2) * a[8]
         + (uint64_t)a[7] * a[7];
      VERIFY_BITS(d, 62);
      /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      u4 = d & M; d >>= 26; c += u4 * R0;
      VERIFY_BITS(u4, 26);
      VERIFY_BITS(d, 36);
      /* VERIFY_BITS(c, 64); */
      /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      t4 = c & M; c >>= 26; c += u4 * R1;
      VERIFY_BITS(t4, 26);
      VERIFY_BITS(c, 39);
      /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)(a[0]*2) * a[5]
         + (uint64_t)(a[1]*2) * a[4]
         + (uint64_t)(a[2]*2) * a[3];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)(a[6]*2) * a[9]
         + (uint64_t)(a[7]*2) * a[8];
      VERIFY_BITS(d, 62);
      /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      u5 = d & M; d >>= 26; c += u5 * R0;
      VERIFY_BITS(u5, 26);
      VERIFY_BITS(d, 36);
      /* VERIFY_BITS(c, 64); */
      /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      t5 = c & M; c >>= 26; c += u5 * R1;
      VERIFY_BITS(t5, 26);
      VERIFY_BITS(c, 39);
      /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)(a[0]*2) * a[6]
         + (uint64_t)(a[1]*2) * a[5]
         + (uint64_t)(a[2]*2) * a[4]
         + (uint64_t)a[3] * a[3];
      VERIFY_BITS(c, 63);
      /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)(a[7]*2) * a[9]
         + (uint64_t)a[8] * a[8];
      VERIFY_BITS(d, 61);
      /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      u6 = d & M; d >>= 26; c += u6 * R0;
      VERIFY_BITS(u6, 26);
      VERIFY_BITS(d, 35);
      /* VERIFY_BITS(c, 64); */
      /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      t6 = c & M; c >>= 26; c += u6 * R1;
      VERIFY_BITS(t6, 26);
      VERIFY_BITS(c, 39);
      /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)(a[0]*2) * a[7]
         + (uint64_t)(a[1]*2) * a[6]
         + (uint64_t)(a[2]*2) * a[5]
         + (uint64_t)(a[3]*2) * a[4];
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x8000007C00000007ULL);
      /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)(a[8]*2) * a[9];
      VERIFY_BITS(d, 58);
      /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      u7 = d & M; d >>= 26; c += u7 * R0;
      VERIFY_BITS(u7, 26);
      VERIFY_BITS(d, 32);
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
      /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      t7 = c & M; c >>= 26; c += u7 * R1;
      VERIFY_BITS(t7, 26);
      VERIFY_BITS(c, 38);
      /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      c += (uint64_t)(a[0]*2) * a[8]
         + (uint64_t)(a[1]*2) * a[7]
         + (uint64_t)(a[2]*2) * a[6]
         + (uint64_t)(a[3]*2) * a[5]
         + (uint64_t)a[4] * a[4];
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x9000007B80000008ULL);
      /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      d += (uint64_t)a[9] * a[9];
      VERIFY_BITS(d, 57);
      /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      u8 = d & M; d >>= 26; c += u8 * R0;
      VERIFY_BITS(u8, 26);
      VERIFY_BITS(d, 31);
      /* VERIFY_BITS(c, 64); */
      VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      r[3] = t3;
      VERIFY_BITS(r[3], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[4] = t4;
      VERIFY_BITS(r[4], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[5] = t5;
      VERIFY_BITS(r[5], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[6] = t6;
      VERIFY_BITS(r[6], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[7] = t7;
      VERIFY_BITS(r[7], 26);
      /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      r[8] = c & M; c >>= 26; c += u8 * R1;
      VERIFY_BITS(r[8], 26);
      VERIFY_BITS(c, 39);
      /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      c   += d * R0 + t9;
      VERIFY_BITS(c, 45);
      /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
      VERIFY_BITS(r[9], 22);
      VERIFY_BITS(c, 46);
      /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  
      d    = c * (R0 >> 4) + t0;
      VERIFY_BITS(d, 56);
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[0] = d & M; d >>= 26;
      VERIFY_BITS(r[0], 26);
      VERIFY_BITS(d, 30);
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      d   += c * (R1 >> 4) + t1;
      VERIFY_BITS(d, 53);
      VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
      /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[1] = d & M; d >>= 26;
      VERIFY_BITS(r[1], 26);
      VERIFY_BITS(d, 27);
      VERIFY_CHECK(d <= 0x4000000ULL);
      /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      d   += t2;
      VERIFY_BITS(d, 27);
      /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
      r[2] = d;
      VERIFY_BITS(r[2], 27);
      /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
  }
  #endif
  
  static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
  #ifdef VERIFY
      VERIFY_CHECK(a->magnitude <= 8);
      VERIFY_CHECK(b->magnitude <= 8);
      secp256k1_fe_verify(a);
      secp256k1_fe_verify(b);
      VERIFY_CHECK(r != b);
  #endif
      secp256k1_fe_mul_inner(r->n, a->n, b->n);
  #ifdef VERIFY
      r->magnitude = 1;
      r->normalized = 0;
      secp256k1_fe_verify(r);
  #endif
  }
  
  static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
  #ifdef VERIFY
      VERIFY_CHECK(a->magnitude <= 8);
      secp256k1_fe_verify(a);
  #endif
      secp256k1_fe_sqr_inner(r->n, a->n);
  #ifdef VERIFY
      r->magnitude = 1;
      r->normalized = 0;
      secp256k1_fe_verify(r);
  #endif
  }
  
  static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
      uint32_t mask0, mask1;
      mask0 = flag + ~((uint32_t)0);
      mask1 = ~mask0;
      r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
      r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
      r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
      r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
      r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
      r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
      r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
      r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
      r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
      r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
  #ifdef VERIFY
      if (a->magnitude > r->magnitude) {
          r->magnitude = a->magnitude;
      }
      r->normalized &= a->normalized;
  #endif
  }
  
  static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
      uint32_t mask0, mask1;
      mask0 = flag + ~((uint32_t)0);
      mask1 = ~mask0;
      r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
      r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
      r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
      r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
      r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
      r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
      r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
      r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
  }
  
  static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
  #ifdef VERIFY
      VERIFY_CHECK(a->normalized);
  #endif
      r->n[0] = a->n[0] | a->n[1] << 26;
      r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
      r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
      r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
      r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
      r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
      r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
      r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
  }
  
  static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
      r->n[0] = a->n[0] & 0x3FFFFFFUL;
      r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
      r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
      r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
      r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
      r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
      r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
      r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
      r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
      r->n[9] = a->n[7] >> 10;
  #ifdef VERIFY
      r->magnitude = 1;
      r->normalized = 1;
  #endif
  }
  
  #endif
  