text: /************************************************************************
   * Copyright (c) 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_SCALAR_REPR_IMPL_H
  #define SECP256K1_SCALAR_REPR_IMPL_H
  
  /* Limbs of the secp256k1 order. */
  #define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
  #define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
  #define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
  #define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
  #define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
  #define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
  #define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
  #define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
  
  /* Limbs of 2^256 minus the secp256k1 order. */
  #define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
  #define SECP256K1_N_C_1 (~SECP256K1_N_1)
  #define SECP256K1_N_C_2 (~SECP256K1_N_2)
  #define SECP256K1_N_C_3 (~SECP256K1_N_3)
  #define SECP256K1_N_C_4 (1)
  
  /* Limbs of half the secp256k1 order. */
  #define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
  #define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
  #define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
  #define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
  #define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
  #define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
  #define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
  #define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
  
  SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
      r->d[0] = 0;
      r->d[1] = 0;
      r->d[2] = 0;
      r->d[3] = 0;
      r->d[4] = 0;
      r->d[5] = 0;
      r->d[6] = 0;
      r->d[7] = 0;
  }
  
  SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
      r->d[0] = v;
      r->d[1] = 0;
      r->d[2] = 0;
      r->d[3] = 0;
      r->d[4] = 0;
      r->d[5] = 0;
      r->d[6] = 0;
      r->d[7] = 0;
  }
  
  SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
      VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
      return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
  }
  
  SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
      VERIFY_CHECK(count < 32);
      VERIFY_CHECK(offset + count <= 256);
      if ((offset + count - 1) >> 5 == offset >> 5) {
          return secp256k1_scalar_get_bits(a, offset, count);
      } else {
          VERIFY_CHECK((offset >> 5) + 1 < 8);
          return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
      }
  }
  
  SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
      int yes = 0;
      int no = 0;
      no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
      no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
      no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
      no |= (a->d[4] < SECP256K1_N_4);
      yes |= (a->d[4] > SECP256K1_N_4) & ~no;
      no |= (a->d[3] < SECP256K1_N_3) & ~yes;
      yes |= (a->d[3] > SECP256K1_N_3) & ~no;
      no |= (a->d[2] < SECP256K1_N_2) & ~yes;
      yes |= (a->d[2] > SECP256K1_N_2) & ~no;
      no |= (a->d[1] < SECP256K1_N_1) & ~yes;
      yes |= (a->d[1] > SECP256K1_N_1) & ~no;
      yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
      return yes;
  }
  
  SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
      uint64_t t;
      VERIFY_CHECK(overflow <= 1);
      t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
      r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
      t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
      r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
      t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
      r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
      t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
      r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
      t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
      r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
      t += (uint64_t)r->d[5];
      r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
      t += (uint64_t)r->d[6];
      r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
      t += (uint64_t)r->d[7];
      r->d[7] = t & 0xFFFFFFFFUL;
      return overflow;
  }
  
  static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
      int overflow;
      uint64_t t = (uint64_t)a->d[0] + b->d[0];
      r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)a->d[1] + b->d[1];
      r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)a->d[2] + b->d[2];
      r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)a->d[3] + b->d[3];
      r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)a->d[4] + b->d[4];
      r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)a->d[5] + b->d[5];
      r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)a->d[6] + b->d[6];
      r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)a->d[7] + b->d[7];
      r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
      overflow = t + secp256k1_scalar_check_overflow(r);
      VERIFY_CHECK(overflow == 0 || overflow == 1);
      secp256k1_scalar_reduce(r, overflow);
      return overflow;
  }
  
  static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
      uint64_t t;
      VERIFY_CHECK(bit < 256);
      bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 5) > 7 makes this a noop */
      t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
      r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
      r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
      r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
      r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
      r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
      r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
      r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
      t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
      r->d[7] = t & 0xFFFFFFFFULL;
  #ifdef VERIFY
      VERIFY_CHECK((t >> 32) == 0);
      VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
  #endif
  }
  
  static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
      int over;
      r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
      r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
      r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24;
      r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24;
      r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24;
      r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24;
      r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24;
      r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24;
      over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
      if (overflow) {
          *overflow = over;
      }
  }
  
  static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
      bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
      bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
      bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
      bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4];
      bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3];
      bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2];
      bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1];
      bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
  }
  
  SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
      return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
  }
  
  static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
      uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
      uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
      r->d[0] = t & nonzero; t >>= 32;
      t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
      r->d[1] = t & nonzero; t >>= 32;
      t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
      r->d[2] = t & nonzero; t >>= 32;
      t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
      r->d[3] = t & nonzero; t >>= 32;
      t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
      r->d[4] = t & nonzero; t >>= 32;
      t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
      r->d[5] = t & nonzero; t >>= 32;
      t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
      r->d[6] = t & nonzero; t >>= 32;
      t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
      r->d[7] = t & nonzero;
  }
  
  SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
      return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
  }
  
  static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
      int yes = 0;
      int no = 0;
      no |= (a->d[7] < SECP256K1_N_H_7);
      yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
      no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
      no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
      no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
      no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
      yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
      no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
      yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
      no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
      yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
      yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
      return yes;
  }
  
  static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
      /* If we are flag = 0, mask = 00...00 and this is a no-op;
       * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
      uint32_t mask = !flag - 1;
      uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
      uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
      r->d[0] = t & nonzero; t >>= 32;
      t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
      r->d[1] = t & nonzero; t >>= 32;
      t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
      r->d[2] = t & nonzero; t >>= 32;
      t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
      r->d[3] = t & nonzero; t >>= 32;
      t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
      r->d[4] = t & nonzero; t >>= 32;
      t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
      r->d[5] = t & nonzero; t >>= 32;
      t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
      r->d[6] = t & nonzero; t >>= 32;
      t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
      r->d[7] = t & nonzero;
      return 2 * (mask == 0) - 1;
  }
  
  
  /* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
  
  /** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
  #define muladd(a,b) { \
      uint32_t tl, th; \
      { \
          uint64_t t = (uint64_t)a * b; \
          th = t >> 32;         /* at most 0xFFFFFFFE */ \
          tl = t; \
      } \
      c0 += tl;                 /* overflow is handled on the next line */ \
      th += (c0 < tl);          /* at most 0xFFFFFFFF */ \
      c1 += th;                 /* overflow is handled on the next line */ \
      c2 += (c1 < th);          /* never overflows by contract (verified in the next line) */ \
      VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
  }
  
  /** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
  #define muladd_fast(a,b) { \
      uint32_t tl, th; \
      { \
          uint64_t t = (uint64_t)a * b; \
          th = t >> 32;         /* at most 0xFFFFFFFE */ \
          tl = t; \
      } \
      c0 += tl;                 /* overflow is handled on the next line */ \
      th += (c0 < tl);          /* at most 0xFFFFFFFF */ \
      c1 += th;                 /* never overflows by contract (verified in the next line) */ \
      VERIFY_CHECK(c1 >= th); \
  }
  
  /** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
  #define muladd2(a,b) { \
      uint32_t tl, th, th2, tl2; \
      { \
          uint64_t t = (uint64_t)a * b; \
          th = t >> 32;               /* at most 0xFFFFFFFE */ \
          tl = t; \
      } \
      th2 = th + th;                  /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \
      c2 += (th2 < th);               /* never overflows by contract (verified the next line) */ \
      VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
      tl2 = tl + tl;                  /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \
      th2 += (tl2 < tl);              /* at most 0xFFFFFFFF */ \
      c0 += tl2;                      /* overflow is handled on the next line */ \
      th2 += (c0 < tl2);              /* second overflow is handled on the next line */ \
      c2 += (c0 < tl2) & (th2 == 0);  /* never overflows by contract (verified the next line) */ \
      VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
      c1 += th2;                      /* overflow is handled on the next line */ \
      c2 += (c1 < th2);               /* never overflows by contract (verified the next line) */ \
      VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
  }
  
  /** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
  #define sumadd(a) { \
      unsigned int over; \
      c0 += (a);                  /* overflow is handled on the next line */ \
      over = (c0 < (a)); \
      c1 += over;                 /* overflow is handled on the next line */ \
      c2 += (c1 < over);          /* never overflows by contract */ \
  }
  
  /** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
  #define sumadd_fast(a) { \
      c0 += (a);                 /* overflow is handled on the next line */ \
      c1 += (c0 < (a));          /* never overflows by contract (verified the next line) */ \
      VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
      VERIFY_CHECK(c2 == 0); \
  }
  
  /** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */
  #define extract(n) { \
      (n) = c0; \
      c0 = c1; \
      c1 = c2; \
      c2 = 0; \
  }
  
  /** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */
  #define extract_fast(n) { \
      (n) = c0; \
      c0 = c1; \
      c1 = 0; \
      VERIFY_CHECK(c2 == 0); \
  }
  
  static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
      uint64_t c;
      uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
      uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
      uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
  
      /* 96 bit accumulator. */
      uint32_t c0, c1, c2;
  
      /* Reduce 512 bits into 385. */
      /* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
      c0 = l[0]; c1 = 0; c2 = 0;
      muladd_fast(n0, SECP256K1_N_C_0);
      extract_fast(m0);
      sumadd_fast(l[1]);
      muladd(n1, SECP256K1_N_C_0);
      muladd(n0, SECP256K1_N_C_1);
      extract(m1);
      sumadd(l[2]);
      muladd(n2, SECP256K1_N_C_0);
      muladd(n1, SECP256K1_N_C_1);
      muladd(n0, SECP256K1_N_C_2);
      extract(m2);
      sumadd(l[3]);
      muladd(n3, SECP256K1_N_C_0);
      muladd(n2, SECP256K1_N_C_1);
      muladd(n1, SECP256K1_N_C_2);
      muladd(n0, SECP256K1_N_C_3);
      extract(m3);
      sumadd(l[4]);
      muladd(n4, SECP256K1_N_C_0);
      muladd(n3, SECP256K1_N_C_1);
      muladd(n2, SECP256K1_N_C_2);
      muladd(n1, SECP256K1_N_C_3);
      sumadd(n0);
      extract(m4);
      sumadd(l[5]);
      muladd(n5, SECP256K1_N_C_0);
      muladd(n4, SECP256K1_N_C_1);
      muladd(n3, SECP256K1_N_C_2);
      muladd(n2, SECP256K1_N_C_3);
      sumadd(n1);
      extract(m5);
      sumadd(l[6]);
      muladd(n6, SECP256K1_N_C_0);
      muladd(n5, SECP256K1_N_C_1);
      muladd(n4, SECP256K1_N_C_2);
      muladd(n3, SECP256K1_N_C_3);
      sumadd(n2);
      extract(m6);
      sumadd(l[7]);
      muladd(n7, SECP256K1_N_C_0);
      muladd(n6, SECP256K1_N_C_1);
      muladd(n5, SECP256K1_N_C_2);
      muladd(n4, SECP256K1_N_C_3);
      sumadd(n3);
      extract(m7);
      muladd(n7, SECP256K1_N_C_1);
      muladd(n6, SECP256K1_N_C_2);
      muladd(n5, SECP256K1_N_C_3);
      sumadd(n4);
      extract(m8);
      muladd(n7, SECP256K1_N_C_2);
      muladd(n6, SECP256K1_N_C_3);
      sumadd(n5);
      extract(m9);
      muladd(n7, SECP256K1_N_C_3);
      sumadd(n6);
      extract(m10);
      sumadd_fast(n7);
      extract_fast(m11);
      VERIFY_CHECK(c0 <= 1);
      m12 = c0;
  
      /* Reduce 385 bits into 258. */
      /* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
      c0 = m0; c1 = 0; c2 = 0;
      muladd_fast(m8, SECP256K1_N_C_0);
      extract_fast(p0);
      sumadd_fast(m1);
      muladd(m9, SECP256K1_N_C_0);
      muladd(m8, SECP256K1_N_C_1);
      extract(p1);
      sumadd(m2);
      muladd(m10, SECP256K1_N_C_0);
      muladd(m9, SECP256K1_N_C_1);
      muladd(m8, SECP256K1_N_C_2);
      extract(p2);
      sumadd(m3);
      muladd(m11, SECP256K1_N_C_0);
      muladd(m10, SECP256K1_N_C_1);
      muladd(m9, SECP256K1_N_C_2);
      muladd(m8, SECP256K1_N_C_3);
      extract(p3);
      sumadd(m4);
      muladd(m12, SECP256K1_N_C_0);
      muladd(m11, SECP256K1_N_C_1);
      muladd(m10, SECP256K1_N_C_2);
      muladd(m9, SECP256K1_N_C_3);
      sumadd(m8);
      extract(p4);
      sumadd(m5);
      muladd(m12, SECP256K1_N_C_1);
      muladd(m11, SECP256K1_N_C_2);
      muladd(m10, SECP256K1_N_C_3);
      sumadd(m9);
      extract(p5);
      sumadd(m6);
      muladd(m12, SECP256K1_N_C_2);
      muladd(m11, SECP256K1_N_C_3);
      sumadd(m10);
      extract(p6);
      sumadd_fast(m7);
      muladd_fast(m12, SECP256K1_N_C_3);
      sumadd_fast(m11);
      extract_fast(p7);
      p8 = c0 + m12;
      VERIFY_CHECK(p8 <= 2);
  
      /* Reduce 258 bits into 256. */
      /* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
      c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
      r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
      c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
      r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
      c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
      r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
      c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
      r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
      c += p4 + (uint64_t)p8;
      r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
      c += p5;
      r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
      c += p6;
      r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
      c += p7;
      r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
  
      /* Final reduction of r. */
      secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
  }
  
  static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
      /* 96 bit accumulator. */
      uint32_t c0 = 0, c1 = 0, c2 = 0;
  
      /* l[0..15] = a[0..7] * b[0..7]. */
      muladd_fast(a->d[0], b->d[0]);
      extract_fast(l[0]);
      muladd(a->d[0], b->d[1]);
      muladd(a->d[1], b->d[0]);
      extract(l[1]);
      muladd(a->d[0], b->d[2]);
      muladd(a->d[1], b->d[1]);
      muladd(a->d[2], b->d[0]);
      extract(l[2]);
      muladd(a->d[0], b->d[3]);
      muladd(a->d[1], b->d[2]);
      muladd(a->d[2], b->d[1]);
      muladd(a->d[3], b->d[0]);
      extract(l[3]);
      muladd(a->d[0], b->d[4]);
      muladd(a->d[1], b->d[3]);
      muladd(a->d[2], b->d[2]);
      muladd(a->d[3], b->d[1]);
      muladd(a->d[4], b->d[0]);
      extract(l[4]);
      muladd(a->d[0], b->d[5]);
      muladd(a->d[1], b->d[4]);
      muladd(a->d[2], b->d[3]);
      muladd(a->d[3], b->d[2]);
      muladd(a->d[4], b->d[1]);
      muladd(a->d[5], b->d[0]);
      extract(l[5]);
      muladd(a->d[0], b->d[6]);
      muladd(a->d[1], b->d[5]);
      muladd(a->d[2], b->d[4]);
      muladd(a->d[3], b->d[3]);
      muladd(a->d[4], b->d[2]);
      muladd(a->d[5], b->d[1]);
      muladd(a->d[6], b->d[0]);
      extract(l[6]);
      muladd(a->d[0], b->d[7]);
      muladd(a->d[1], b->d[6]);
      muladd(a->d[2], b->d[5]);
      muladd(a->d[3], b->d[4]);
      muladd(a->d[4], b->d[3]);
      muladd(a->d[5], b->d[2]);
      muladd(a->d[6], b->d[1]);
      muladd(a->d[7], b->d[0]);
      extract(l[7]);
      muladd(a->d[1], b->d[7]);
      muladd(a->d[2], b->d[6]);
      muladd(a->d[3], b->d[5]);
      muladd(a->d[4], b->d[4]);
      muladd(a->d[5], b->d[3]);
      muladd(a->d[6], b->d[2]);
      muladd(a->d[7], b->d[1]);
      extract(l[8]);
      muladd(a->d[2], b->d[7]);
      muladd(a->d[3], b->d[6]);
      muladd(a->d[4], b->d[5]);
      muladd(a->d[5], b->d[4]);
      muladd(a->d[6], b->d[3]);
      muladd(a->d[7], b->d[2]);
      extract(l[9]);
      muladd(a->d[3], b->d[7]);
      muladd(a->d[4], b->d[6]);
      muladd(a->d[5], b->d[5]);
      muladd(a->d[6], b->d[4]);
      muladd(a->d[7], b->d[3]);
      extract(l[10]);
      muladd(a->d[4], b->d[7]);
      muladd(a->d[5], b->d[6]);
      muladd(a->d[6], b->d[5]);
      muladd(a->d[7], b->d[4]);
      extract(l[11]);
      muladd(a->d[5], b->d[7]);
      muladd(a->d[6], b->d[6]);
      muladd(a->d[7], b->d[5]);
      extract(l[12]);
      muladd(a->d[6], b->d[7]);
      muladd(a->d[7], b->d[6]);
      extract(l[13]);
      muladd_fast(a->d[7], b->d[7]);
      extract_fast(l[14]);
      VERIFY_CHECK(c1 == 0);
      l[15] = c0;
  }
  
  static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
      /* 96 bit accumulator. */
      uint32_t c0 = 0, c1 = 0, c2 = 0;
  
      /* l[0..15] = a[0..7]^2. */
      muladd_fast(a->d[0], a->d[0]);
      extract_fast(l[0]);
      muladd2(a->d[0], a->d[1]);
      extract(l[1]);
      muladd2(a->d[0], a->d[2]);
      muladd(a->d[1], a->d[1]);
      extract(l[2]);
      muladd2(a->d[0], a->d[3]);
      muladd2(a->d[1], a->d[2]);
      extract(l[3]);
      muladd2(a->d[0], a->d[4]);
      muladd2(a->d[1], a->d[3]);
      muladd(a->d[2], a->d[2]);
      extract(l[4]);
      muladd2(a->d[0], a->d[5]);
      muladd2(a->d[1], a->d[4]);
      muladd2(a->d[2], a->d[3]);
      extract(l[5]);
      muladd2(a->d[0], a->d[6]);
      muladd2(a->d[1], a->d[5]);
      muladd2(a->d[2], a->d[4]);
      muladd(a->d[3], a->d[3]);
      extract(l[6]);
      muladd2(a->d[0], a->d[7]);
      muladd2(a->d[1], a->d[6]);
      muladd2(a->d[2], a->d[5]);
      muladd2(a->d[3], a->d[4]);
      extract(l[7]);
      muladd2(a->d[1], a->d[7]);
      muladd2(a->d[2], a->d[6]);
      muladd2(a->d[3], a->d[5]);
      muladd(a->d[4], a->d[4]);
      extract(l[8]);
      muladd2(a->d[2], a->d[7]);
      muladd2(a->d[3], a->d[6]);
      muladd2(a->d[4], a->d[5]);
      extract(l[9]);
      muladd2(a->d[3], a->d[7]);
      muladd2(a->d[4], a->d[6]);
      muladd(a->d[5], a->d[5]);
      extract(l[10]);
      muladd2(a->d[4], a->d[7]);
      muladd2(a->d[5], a->d[6]);
      extract(l[11]);
      muladd2(a->d[5], a->d[7]);
      muladd(a->d[6], a->d[6]);
      extract(l[12]);
      muladd2(a->d[6], a->d[7]);
      extract(l[13]);
      muladd_fast(a->d[7], a->d[7]);
      extract_fast(l[14]);
      VERIFY_CHECK(c1 == 0);
      l[15] = c0;
  }
  
  #undef sumadd
  #undef sumadd_fast
  #undef muladd
  #undef muladd_fast
  #undef muladd2
  #undef extract
  #undef extract_fast
  
  static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
      uint32_t l[16];
      secp256k1_scalar_mul_512(l, a, b);
      secp256k1_scalar_reduce_512(r, l);
  }
  
  static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
      int ret;
      VERIFY_CHECK(n > 0);
      VERIFY_CHECK(n < 16);
      ret = r->d[0] & ((1 << n) - 1);
      r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
      r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
      r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
      r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
      r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
      r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
      r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
      r->d[7] = (r->d[7] >> n);
      return ret;
  }
  
  static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
      uint32_t l[16];
      secp256k1_scalar_sqr_512(l, a);
      secp256k1_scalar_reduce_512(r, l);
  }
  
  static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) {
      r1->d[0] = k->d[0];
      r1->d[1] = k->d[1];
      r1->d[2] = k->d[2];
      r1->d[3] = k->d[3];
      r1->d[4] = 0;
      r1->d[5] = 0;
      r1->d[6] = 0;
      r1->d[7] = 0;
      r2->d[0] = k->d[4];
      r2->d[1] = k->d[5];
      r2->d[2] = k->d[6];
      r2->d[3] = k->d[7];
      r2->d[4] = 0;
      r2->d[5] = 0;
      r2->d[6] = 0;
      r2->d[7] = 0;
  }
  
  SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
      return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
  }
  
  SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
      uint32_t l[16];
      unsigned int shiftlimbs;
      unsigned int shiftlow;
      unsigned int shifthigh;
      VERIFY_CHECK(shift >= 256);
      secp256k1_scalar_mul_512(l, a, b);
      shiftlimbs = shift >> 5;
      shiftlow = shift & 0x1F;
      shifthigh = 32 - shiftlow;
      r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
      r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
      r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
      r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
      r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
      r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
      r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
      r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow)  : 0;
      secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
  }
  
  static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) {
      uint32_t mask0, mask1;
      VG_CHECK_VERIFY(r->d, sizeof(r->d));
      mask0 = flag + ~((uint32_t)0);
      mask1 = ~mask0;
      r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1);
      r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1);
      r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1);
      r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1);
      r->d[4] = (r->d[4] & mask0) | (a->d[4] & mask1);
      r->d[5] = (r->d[5] & mask0) | (a->d[5] & mask1);
      r->d[6] = (r->d[6] & mask0) | (a->d[6] & mask1);
      r->d[7] = (r->d[7] & mask0) | (a->d[7] & mask1);
  }
  
  #endif /* SECP256K1_SCALAR_REPR_IMPL_H */
  