text: /* crypto/bn/bn_nist.c */
  /*
   * Written by Nils Larsch for the OpenSSL project
   */
  /* ====================================================================
   * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. All advertising materials mentioning features or use of this
   *    software must display the following acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
   *
   * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
   *    endorse or promote products derived from this software without
   *    prior written permission. For written permission, please contact
   *    openssl-core@openssl.org.
   *
   * 5. Products derived from this software may not be called "OpenSSL"
   *    nor may "OpenSSL" appear in their names without prior written
   *    permission of the OpenSSL Project.
   *
   * 6. Redistributions of any form whatsoever must retain the following
   *    acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
   *
   * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
   * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
   * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
   * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
   * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
   * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
   * OF THE POSSIBILITY OF SUCH DAMAGE.
   * ====================================================================
   *
   * This product includes cryptographic software written by Eric Young
   * (eay@cryptsoft.com).  This product includes software written by Tim
   * Hudson (tjh@cryptsoft.com).
   *
   */
  
  #include "bn_lcl.h"
  #include "cryptlib.h"
  
  #define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2
  #define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2
  #define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2
  #define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2
  #define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2
  
  /* pre-computed tables are "carry-less" values of modulus*(i+1) */
  #if BN_BITS2 == 64
  static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
      {0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFFULL},
      {0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL},
      {0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFCULL, 0xFFFFFFFFFFFFFFFFULL}
  };
  
  static const BN_ULONG _nist_p_192_sqr[] = {
      0x0000000000000001ULL, 0x0000000000000002ULL, 0x0000000000000001ULL,
      0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL
  };
  
  static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
      {0x0000000000000001ULL, 0xFFFFFFFF00000000ULL,
       0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL},
      {0x0000000000000002ULL, 0xFFFFFFFE00000000ULL,
       0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFFULL} /* this one is
                                                      * "carry-full" */
  };
  
  static const BN_ULONG _nist_p_224_sqr[] = {
      0x0000000000000001ULL, 0xFFFFFFFE00000000ULL,
      0xFFFFFFFFFFFFFFFFULL, 0x0000000200000000ULL,
      0x0000000000000000ULL, 0xFFFFFFFFFFFFFFFEULL,
      0xFFFFFFFFFFFFFFFFULL
  };
  
  static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
      {0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL,
       0x0000000000000000ULL, 0xFFFFFFFF00000001ULL},
      {0xFFFFFFFFFFFFFFFEULL, 0x00000001FFFFFFFFULL,
       0x0000000000000000ULL, 0xFFFFFFFE00000002ULL},
      {0xFFFFFFFFFFFFFFFDULL, 0x00000002FFFFFFFFULL,
       0x0000000000000000ULL, 0xFFFFFFFD00000003ULL},
      {0xFFFFFFFFFFFFFFFCULL, 0x00000003FFFFFFFFULL,
       0x0000000000000000ULL, 0xFFFFFFFC00000004ULL},
      {0xFFFFFFFFFFFFFFFBULL, 0x00000004FFFFFFFFULL,
       0x0000000000000000ULL, 0xFFFFFFFB00000005ULL},
  };
  
  static const BN_ULONG _nist_p_256_sqr[] = {
      0x0000000000000001ULL, 0xFFFFFFFE00000000ULL,
      0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFEULL,
      0x00000001FFFFFFFEULL, 0x00000001FFFFFFFEULL,
      0xFFFFFFFE00000001ULL, 0xFFFFFFFE00000002ULL
  };
  
  static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
      {0x00000000FFFFFFFFULL, 0xFFFFFFFF00000000ULL, 0xFFFFFFFFFFFFFFFEULL,
       0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
      {0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL,
       0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
      {0x00000002FFFFFFFDULL, 0xFFFFFFFD00000000ULL, 0xFFFFFFFFFFFFFFFCULL,
       0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
      {0x00000003FFFFFFFCULL, 0xFFFFFFFC00000000ULL, 0xFFFFFFFFFFFFFFFBULL,
       0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
      {0x00000004FFFFFFFBULL, 0xFFFFFFFB00000000ULL, 0xFFFFFFFFFFFFFFFAULL,
       0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL},
  };
  
  static const BN_ULONG _nist_p_384_sqr[] = {
      0xFFFFFFFE00000001ULL, 0x0000000200000000ULL, 0xFFFFFFFE00000000ULL,
      0x0000000200000000ULL, 0x0000000000000001ULL, 0x0000000000000000ULL,
      0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL,
      0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL
  };
  
  static const BN_ULONG _nist_p_521[] =
      { 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
      0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
      0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
      0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
      0x00000000000001FFULL
  };
  
  static const BN_ULONG _nist_p_521_sqr[] = {
      0x0000000000000001ULL, 0x0000000000000000ULL, 0x0000000000000000ULL,
      0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL,
      0x0000000000000000ULL, 0x0000000000000000ULL, 0xFFFFFFFFFFFFFC00ULL,
      0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
      0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL,
      0xFFFFFFFFFFFFFFFFULL, 0x000000000003FFFFULL
  };
  #elif BN_BITS2 == 32
  static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
      {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
      {0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
      {0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
  };
  
  static const BN_ULONG _nist_p_192_sqr[] = {
      0x00000001, 0x00000000, 0x00000002, 0x00000000, 0x00000001, 0x00000000,
      0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF
  };
  
  static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
      {0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF,
       0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
      {0x00000002, 0x00000000, 0x00000000, 0xFFFFFFFE,
       0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
  };
  
  static const BN_ULONG _nist_p_224_sqr[] = {
      0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE,
      0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000002,
      0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF,
      0xFFFFFFFF, 0xFFFFFFFF
  };
  
  static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
      {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000,
       0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF},
      {0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001,
       0x00000000, 0x00000000, 0x00000002, 0xFFFFFFFE},
      {0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000002,
       0x00000000, 0x00000000, 0x00000003, 0xFFFFFFFD},
      {0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000003,
       0x00000000, 0x00000000, 0x00000004, 0xFFFFFFFC},
      {0xFFFFFFFB, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000004,
       0x00000000, 0x00000000, 0x00000005, 0xFFFFFFFB},
  };
  
  static const BN_ULONG _nist_p_256_sqr[] = {
      0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE,
      0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0x00000001,
      0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001,
      0x00000001, 0xFFFFFFFE, 0x00000002, 0xFFFFFFFE
  };
  
  static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
      {0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF,
       0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
      {0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF,
       0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
      {0xFFFFFFFD, 0x00000002, 0x00000000, 0xFFFFFFFD, 0xFFFFFFFC, 0xFFFFFFFF,
       0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
      {0xFFFFFFFC, 0x00000003, 0x00000000, 0xFFFFFFFC, 0xFFFFFFFB, 0xFFFFFFFF,
       0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
      {0xFFFFFFFB, 0x00000004, 0x00000000, 0xFFFFFFFB, 0xFFFFFFFA, 0xFFFFFFFF,
       0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF},
  };
  
  static const BN_ULONG _nist_p_384_sqr[] = {
      0x00000001, 0xFFFFFFFE, 0x00000000, 0x00000002, 0x00000000, 0xFFFFFFFE,
      0x00000000, 0x00000002, 0x00000001, 0x00000000, 0x00000000, 0x00000000,
      0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF,
      0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF
  };
  
  static const BN_ULONG _nist_p_521[] = { 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
      0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
      0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
      0xFFFFFFFF, 0x000001FF
  };
  
  static const BN_ULONG _nist_p_521_sqr[] = {
      0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
      0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xFFFFFC00, 0xFFFFFFFF,
      0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
      0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
      0xFFFFFFFF, 0xFFFFFFFF, 0x0003FFFF
  };
  #else
  # error "unsupported BN_BITS2"
  #endif
  
  static const BIGNUM _bignum_nist_p_192 = {
      (BN_ULONG *)_nist_p_192[0],
      BN_NIST_192_TOP,
      BN_NIST_192_TOP,
      0,
      BN_FLG_STATIC_DATA
  };
  
  static const BIGNUM _bignum_nist_p_224 = {
      (BN_ULONG *)_nist_p_224[0],
      BN_NIST_224_TOP,
      BN_NIST_224_TOP,
      0,
      BN_FLG_STATIC_DATA
  };
  
  static const BIGNUM _bignum_nist_p_256 = {
      (BN_ULONG *)_nist_p_256[0],
      BN_NIST_256_TOP,
      BN_NIST_256_TOP,
      0,
      BN_FLG_STATIC_DATA
  };
  
  static const BIGNUM _bignum_nist_p_384 = {
      (BN_ULONG *)_nist_p_384[0],
      BN_NIST_384_TOP,
      BN_NIST_384_TOP,
      0,
      BN_FLG_STATIC_DATA
  };
  
  static const BIGNUM _bignum_nist_p_521 = {
      (BN_ULONG *)_nist_p_521,
      BN_NIST_521_TOP,
      BN_NIST_521_TOP,
      0,
      BN_FLG_STATIC_DATA
  };
  
  const BIGNUM *BN_get0_nist_prime_192(void)
  {
      return &_bignum_nist_p_192;
  }
  
  const BIGNUM *BN_get0_nist_prime_224(void)
  {
      return &_bignum_nist_p_224;
  }
  
  const BIGNUM *BN_get0_nist_prime_256(void)
  {
      return &_bignum_nist_p_256;
  }
  
  const BIGNUM *BN_get0_nist_prime_384(void)
  {
      return &_bignum_nist_p_384;
  }
  
  const BIGNUM *BN_get0_nist_prime_521(void)
  {
      return &_bignum_nist_p_521;
  }
  
  static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
  {
      int i;
      BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
  
  #ifdef BN_DEBUG
      OPENSSL_assert(top <= max);
  #endif
      for (i = (top); i != 0; i--)
          *_tmp1++ = *_tmp2++;
      for (i = (max) - (top); i != 0; i--)
          *_tmp1++ = (BN_ULONG)0;
  }
  
  static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
  {
      int i;
      BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
      for (i = (top); i != 0; i--)
          *_tmp1++ = *_tmp2++;
  }
  
  #if BN_BITS2 == 64
  # define bn_cp_64(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
  # define bn_64_set_0(to, n)              (to)[n] = (BN_ULONG)0;
  /*
   * two following macros are implemented under assumption that they
   * are called in a sequence with *ascending* n, i.e. as they are...
   */
  # define bn_cp_32_naked(to, n, from, m)  (((n)&1)?(to[(n)/2]|=((m)&1)?(from[(m)/2]&BN_MASK2h):(from[(m)/2]<<32))\
                                                  :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
  # define bn_32_set_0(to, n)              (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
  # define bn_cp_32(to,n,from,m)           ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
  #else
  # define bn_cp_64(to, n, from, m) \
          { \
          bn_cp_32(to, (n)*2, from, (m)*2); \
          bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
          }
  # define bn_64_set_0(to, n) \
          { \
          bn_32_set_0(to, (n)*2); \
          bn_32_set_0(to, (n)*2+1); \
          }
  # if BN_BITS2 == 32
  #  define bn_cp_32(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
  #  define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
  # endif
  #endif                          /* BN_BITS2 != 64 */
  
  #define nist_set_192(to, from, a1, a2, a3) \
          { \
          bn_cp_64(to, 0, from, (a3) - 3) \
          bn_cp_64(to, 1, from, (a2) - 3) \
          bn_cp_64(to, 2, from, (a1) - 3) \
          }
  
  int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
                      BN_CTX *ctx)
  {
      int top = a->top, i;
      int carry;
      register BN_ULONG *r_d, *a_d = a->d;
      BN_ULONG t_d[BN_NIST_192_TOP],
          buf[BN_NIST_192_TOP], c_d[BN_NIST_192_TOP], *res;
      size_t mask;
      static const BIGNUM _bignum_nist_p_192_sqr = {
          (BN_ULONG *)_nist_p_192_sqr,
          sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]),
          sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]),
          0, BN_FLG_STATIC_DATA
      };
  
      field = &_bignum_nist_p_192; /* just to make sure */
  
      if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_192_sqr) >= 0)
          return BN_nnmod(r, a, field, ctx);
  
      i = BN_ucmp(field, a);
      if (i == 0) {
          BN_zero(r);
          return 1;
      } else if (i > 0)
          return (r == a) ? 1 : (BN_copy(r, a) != NULL);
  
      if (r != a) {
          if (!bn_wexpand(r, BN_NIST_192_TOP))
              return 0;
          r_d = r->d;
          nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
      } else
          r_d = a_d;
  
      nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP,
                   BN_NIST_192_TOP);
  
      nist_set_192(t_d, buf, 0, 3, 3);
      carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
      nist_set_192(t_d, buf, 4, 4, 0);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
      nist_set_192(t_d, buf, 5, 5, 5)
          carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
  
      if (carry > 0)
          carry =
              (int)bn_sub_words(r_d, r_d, _nist_p_192[carry - 1],
                                BN_NIST_192_TOP);
      else
          carry = 1;
  
      /*
       * we need 'if (carry==0 || result>=modulus) result-=modulus;'
       * as comparison implies subtraction, we can write
       * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
       * this is what happens below, but without explicit if:-) a.
       */
      mask =
          0 - (size_t)bn_sub_words(c_d, r_d, _nist_p_192[0], BN_NIST_192_TOP);
      mask &= 0 - (size_t)carry;
      res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
      nist_cp_bn(r_d, res, BN_NIST_192_TOP);
      r->top = BN_NIST_192_TOP;
      bn_correct_top(r);
  
      return 1;
  }
  
  typedef BN_ULONG (*bn_addsub_f) (BN_ULONG *, const BN_ULONG *,
                                   const BN_ULONG *, int);
  
  #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
          { \
          bn_cp_32(to, 0, from, (a7) - 7) \
          bn_cp_32(to, 1, from, (a6) - 7) \
          bn_cp_32(to, 2, from, (a5) - 7) \
          bn_cp_32(to, 3, from, (a4) - 7) \
          bn_cp_32(to, 4, from, (a3) - 7) \
          bn_cp_32(to, 5, from, (a2) - 7) \
          bn_cp_32(to, 6, from, (a1) - 7) \
          }
  
  int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
                      BN_CTX *ctx)
  {
      int top = a->top, i;
      int carry;
      BN_ULONG *r_d, *a_d = a->d;
      BN_ULONG t_d[BN_NIST_224_TOP],
          buf[BN_NIST_224_TOP], c_d[BN_NIST_224_TOP], *res;
      size_t mask;
      union {
          bn_addsub_f f;
          size_t p;
      } u;
      static const BIGNUM _bignum_nist_p_224_sqr = {
          (BN_ULONG *)_nist_p_224_sqr,
          sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]),
          sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]),
          0, BN_FLG_STATIC_DATA
      };
  
      field = &_bignum_nist_p_224; /* just to make sure */
  
      if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_224_sqr) >= 0)
          return BN_nnmod(r, a, field, ctx);
  
      i = BN_ucmp(field, a);
      if (i == 0) {
          BN_zero(r);
          return 1;
      } else if (i > 0)
          return (r == a) ? 1 : (BN_copy(r, a) != NULL);
  
      if (r != a) {
          if (!bn_wexpand(r, BN_NIST_224_TOP))
              return 0;
          r_d = r->d;
          nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
      } else
          r_d = a_d;
  
  #if BN_BITS2==64
      /* copy upper 256 bits of 448 bit number ... */
      nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP - 1),
                   top - (BN_NIST_224_TOP - 1), BN_NIST_224_TOP);
      /* ... and right shift by 32 to obtain upper 224 bits */
      nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
      /* truncate lower part to 224 bits too */
      r_d[BN_NIST_224_TOP - 1] &= BN_MASK2l;
  #else
      nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP,
                   BN_NIST_224_TOP);
  #endif
      nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
      carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
      nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
      nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
      nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
  
  #if BN_BITS2==64
      carry = (int)(r_d[BN_NIST_224_TOP - 1] >> 32);
  #endif
      u.f = bn_sub_words;
      if (carry > 0) {
          carry =
              (int)bn_sub_words(r_d, r_d, _nist_p_224[carry - 1],
                                BN_NIST_224_TOP);
  #if BN_BITS2==64
          carry = (int)(~(r_d[BN_NIST_224_TOP - 1] >> 32)) & 1;
  #endif
      } else if (carry < 0) {
          /*
           * it's a bit more comlicated logic in this case. if bn_add_words
           * yields no carry, then result has to be adjusted by unconditionally
           * *adding* the modulus. but if it does, then result has to be
           * compared to the modulus and conditionally adjusted by
           * *subtracting* the latter.
           */
          carry =
              (int)bn_add_words(r_d, r_d, _nist_p_224[-carry - 1],
                                BN_NIST_224_TOP);
          mask = 0 - (size_t)carry;
          u.p = ((size_t)bn_sub_words & mask) | ((size_t)bn_add_words & ~mask);
      } else
          carry = 1;
  
      /* otherwise it's effectively same as in BN_nist_mod_192... */
      mask = 0 - (size_t)(*u.f) (c_d, r_d, _nist_p_224[0], BN_NIST_224_TOP);
      mask &= 0 - (size_t)carry;
      res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
      nist_cp_bn(r_d, res, BN_NIST_224_TOP);
      r->top = BN_NIST_224_TOP;
      bn_correct_top(r);
  
      return 1;
  }
  
  #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
          { \
          bn_cp_32(to, 0, from, (a8) - 8) \
          bn_cp_32(to, 1, from, (a7) - 8) \
          bn_cp_32(to, 2, from, (a6) - 8) \
          bn_cp_32(to, 3, from, (a5) - 8) \
          bn_cp_32(to, 4, from, (a4) - 8) \
          bn_cp_32(to, 5, from, (a3) - 8) \
          bn_cp_32(to, 6, from, (a2) - 8) \
          bn_cp_32(to, 7, from, (a1) - 8) \
          }
  
  int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
                      BN_CTX *ctx)
  {
      int i, top = a->top;
      int carry = 0;
      register BN_ULONG *a_d = a->d, *r_d;
      BN_ULONG t_d[BN_NIST_256_TOP],
          buf[BN_NIST_256_TOP], c_d[BN_NIST_256_TOP], *res;
      size_t mask;
      union {
          bn_addsub_f f;
          size_t p;
      } u;
      static const BIGNUM _bignum_nist_p_256_sqr = {
          (BN_ULONG *)_nist_p_256_sqr,
          sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]),
          sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]),
          0, BN_FLG_STATIC_DATA
      };
  
      field = &_bignum_nist_p_256; /* just to make sure */
  
      if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_256_sqr) >= 0)
          return BN_nnmod(r, a, field, ctx);
  
      i = BN_ucmp(field, a);
      if (i == 0) {
          BN_zero(r);
          return 1;
      } else if (i > 0)
          return (r == a) ? 1 : (BN_copy(r, a) != NULL);
  
      if (r != a) {
          if (!bn_wexpand(r, BN_NIST_256_TOP))
              return 0;
          r_d = r->d;
          nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
      } else
          r_d = a_d;
  
      nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP,
                   BN_NIST_256_TOP);
  
      /*
       * S1
       */
      nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
      /*
       * S2
       */
      nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
      carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
      /* left shift */
      {
          register BN_ULONG *ap, t, c;
          ap = t_d;
          c = 0;
          for (i = BN_NIST_256_TOP; i != 0; --i) {
              t = *ap;
              *(ap++) = ((t << 1) | c) & BN_MASK2;
              c = (t & BN_TBIT) ? 1 : 0;
          }
          carry <<= 1;
          carry |= c;
      }
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
      /*
       * S3
       */
      nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
      /*
       * S4
       */
      nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
      /*
       * D1
       */
      nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
      /*
       * D2
       */
      nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
      /*
       * D3
       */
      nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
      /*
       * D4
       */
      nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
  
      /* see BN_nist_mod_224 for explanation */
      u.f = bn_sub_words;
      if (carry > 0)
          carry =
              (int)bn_sub_words(r_d, r_d, _nist_p_256[carry - 1],
                                BN_NIST_256_TOP);
      else if (carry < 0) {
          carry =
              (int)bn_add_words(r_d, r_d, _nist_p_256[-carry - 1],
                                BN_NIST_256_TOP);
          mask = 0 - (size_t)carry;
          u.p = ((size_t)bn_sub_words & mask) | ((size_t)bn_add_words & ~mask);
      } else
          carry = 1;
  
      mask = 0 - (size_t)(*u.f) (c_d, r_d, _nist_p_256[0], BN_NIST_256_TOP);
      mask &= 0 - (size_t)carry;
      res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
      nist_cp_bn(r_d, res, BN_NIST_256_TOP);
      r->top = BN_NIST_256_TOP;
      bn_correct_top(r);
  
      return 1;
  }
  
  #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
          { \
          bn_cp_32(to, 0, from,  (a12) - 12) \
          bn_cp_32(to, 1, from,  (a11) - 12) \
          bn_cp_32(to, 2, from,  (a10) - 12) \
          bn_cp_32(to, 3, from,  (a9) - 12)  \
          bn_cp_32(to, 4, from,  (a8) - 12)  \
          bn_cp_32(to, 5, from,  (a7) - 12)  \
          bn_cp_32(to, 6, from,  (a6) - 12)  \
          bn_cp_32(to, 7, from,  (a5) - 12)  \
          bn_cp_32(to, 8, from,  (a4) - 12)  \
          bn_cp_32(to, 9, from,  (a3) - 12)  \
          bn_cp_32(to, 10, from, (a2) - 12)  \
          bn_cp_32(to, 11, from, (a1) - 12)  \
          }
  
  int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
                      BN_CTX *ctx)
  {
      int i, top = a->top;
      int carry = 0;
      register BN_ULONG *r_d, *a_d = a->d;
      BN_ULONG t_d[BN_NIST_384_TOP],
          buf[BN_NIST_384_TOP], c_d[BN_NIST_384_TOP], *res;
      size_t mask;
      union {
          bn_addsub_f f;
          size_t p;
      } u;
      static const BIGNUM _bignum_nist_p_384_sqr = {
          (BN_ULONG *)_nist_p_384_sqr,
          sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]),
          sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]),
          0, BN_FLG_STATIC_DATA
      };
  
      field = &_bignum_nist_p_384; /* just to make sure */
  
      if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_384_sqr) >= 0)
          return BN_nnmod(r, a, field, ctx);
  
      i = BN_ucmp(field, a);
      if (i == 0) {
          BN_zero(r);
          return 1;
      } else if (i > 0)
          return (r == a) ? 1 : (BN_copy(r, a) != NULL);
  
      if (r != a) {
          if (!bn_wexpand(r, BN_NIST_384_TOP))
              return 0;
          r_d = r->d;
          nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
      } else
          r_d = a_d;
  
      nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP,
                   BN_NIST_384_TOP);
  
      /*
       * S1
       */
      nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23 - 4, 22 - 4, 21 - 4);
      /* left shift */
      {
          register BN_ULONG *ap, t, c;
          ap = t_d;
          c = 0;
          for (i = 3; i != 0; --i) {
              t = *ap;
              *(ap++) = ((t << 1) | c) & BN_MASK2;
              c = (t & BN_TBIT) ? 1 : 0;
          }
          *ap = c;
      }
      carry = (int)bn_add_words(r_d + (128 / BN_BITS2), r_d + (128 / BN_BITS2),
                                t_d, BN_NIST_256_TOP);
      /*
       * S2
       */
      carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
      /*
       * S3
       */
      nist_set_384(t_d, buf, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
      /*
       * S4
       */
      nist_set_384(t_d, buf, 19, 18, 17, 16, 15, 14, 13, 12, 20, 0, 23, 0);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
      /*
       * S5
       */
      nist_set_384(t_d, buf, 0, 0, 0, 0, 23, 22, 21, 20, 0, 0, 0, 0);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
      /*
       * S6
       */
      nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 23, 22, 21, 0, 0, 20);
      carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
      /*
       * D1
       */
      nist_set_384(t_d, buf, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
      /*
       * D2
       */
      nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 22, 21, 20, 0);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
      /*
       * D3
       */
      nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 23, 0, 0, 0);
      carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
  
      /* see BN_nist_mod_224 for explanation */
      u.f = bn_sub_words;
      if (carry > 0)
          carry =
              (int)bn_sub_words(r_d, r_d, _nist_p_384[carry - 1],
                                BN_NIST_384_TOP);
      else if (carry < 0) {
          carry =
              (int)bn_add_words(r_d, r_d, _nist_p_384[-carry - 1],
                                BN_NIST_384_TOP);
          mask = 0 - (size_t)carry;
          u.p = ((size_t)bn_sub_words & mask) | ((size_t)bn_add_words & ~mask);
      } else
          carry = 1;
  
      mask = 0 - (size_t)(*u.f) (c_d, r_d, _nist_p_384[0], BN_NIST_384_TOP);
      mask &= 0 - (size_t)carry;
      res = (BN_ULONG *)(((size_t)c_d & ~mask) | ((size_t)r_d & mask));
      nist_cp_bn(r_d, res, BN_NIST_384_TOP);
      r->top = BN_NIST_384_TOP;
      bn_correct_top(r);
  
      return 1;
  }
  
  #define BN_NIST_521_RSHIFT      (521%BN_BITS2)
  #define BN_NIST_521_LSHIFT      (BN_BITS2-BN_NIST_521_RSHIFT)
  #define BN_NIST_521_TOP_MASK    ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
  
  int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
                      BN_CTX *ctx)
  {
      int top = a->top, i;
      BN_ULONG *r_d, *a_d = a->d, t_d[BN_NIST_521_TOP], val, tmp, *res;
      size_t mask;
      static const BIGNUM _bignum_nist_p_521_sqr = {
          (BN_ULONG *)_nist_p_521_sqr,
          sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]),
          sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]),
          0, BN_FLG_STATIC_DATA
      };
  
      field = &_bignum_nist_p_521; /* just to make sure */
  
      if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_521_sqr) >= 0)
          return BN_nnmod(r, a, field, ctx);
  
      i = BN_ucmp(field, a);
      if (i == 0) {
          BN_zero(r);
          return 1;
      } else if (i > 0)
          return (r == a) ? 1 : (BN_copy(r, a) != NULL);
  
      if (r != a) {
          if (!bn_wexpand(r, BN_NIST_521_TOP))
              return 0;
          r_d = r->d;
          nist_cp_bn(r_d, a_d, BN_NIST_521_TOP);
      } else
          r_d = a_d;
  
      /* upper 521 bits, copy ... */
      nist_cp_bn_0(t_d, a_d + (BN_NIST_521_TOP - 1),
                   top - (BN_NIST_521_TOP - 1), BN_NIST_521_TOP);
      /* ... and right shift */
      for (val = t_d[0], i = 0; i < BN_NIST_521_TOP - 1; i++) {
          tmp = val >> BN_NIST_521_RSHIFT;
          val = t_d[i + 1];
          t_d[i] = (tmp | val << BN_NIST_521_LSHIFT) & BN_MASK2;
      }
      t_d[i] = val >> BN_NIST_521_RSHIFT;
      /* lower 521 bits */
      r_d[i] &= BN_NIST_521_TOP_MASK;
  
      bn_add_words(r_d, r_d, t_d, BN_NIST_521_TOP);
      mask = 0 - (size_t)bn_sub_words(t_d, r_d, _nist_p_521, BN_NIST_521_TOP);
      res = (BN_ULONG *)(((size_t)t_d & ~mask) | ((size_t)r_d & mask));
      nist_cp_bn(r_d, res, BN_NIST_521_TOP);
      r->top = BN_NIST_521_TOP;
      bn_correct_top(r);
  
      return 1;
  }
  