text: /* LibTomMath, multiple-precision integer library -- Tom St Denis */
  /* SPDX-License-Identifier: Unlicense */
  
  #ifndef BN_H_
  #define BN_H_
  
  #include <stdlib.h>
  #include <stdint.h>
  #include <limits.h>
  
  #ifndef LTM_NO_FILE
  #  include <stdio.h>
  #endif
  
  #include "tommath_class.h"
  
  #ifdef __cplusplus
  extern "C" {
  #endif
  
  /* MS Visual C++ doesn't have a 128bit type for words, so fall back to 32bit MPI's (where words are 64bit) */
  #if defined(_MSC_VER) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__)
  #   define MP_32BIT
  #endif
  
  /* detect 64-bit mode if possible */
  #if defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || \
      defined(__powerpc64__) || defined(__ppc64__) || defined(__PPC64__) || \
      defined(__s390x__) || defined(__arch64__) || defined(__aarch64__) || \
      defined(__sparcv9) || defined(__sparc_v9__) || defined(__sparc64__) || \
      defined(__ia64) || defined(__ia64__) || defined(__itanium__) || defined(_M_IA64) || \
      defined(__LP64__) || defined(_LP64) || defined(__64BIT__)
  #   if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
  #      if defined(__GNUC__)
  /* we support 128bit integers only via: __attribute__((mode(TI))) */
  #         define MP_64BIT
  #      else
  /* otherwise we fall back to MP_32BIT even on 64bit platforms */
  #         define MP_32BIT
  #      endif
  #   endif
  #endif
  
  /* some default configurations.
   *
   * A "mp_digit" must be able to hold MP_DIGIT_BIT + 1 bits
   * A "mp_word" must be able to hold 2*MP_DIGIT_BIT + 1 bits
   *
   * At the very least a mp_digit must be able to hold 7 bits
   * [any size beyond that is ok provided it doesn't overflow the data type]
   */
  #ifdef MP_8BIT
  typedef uint8_t              mp_digit;
  typedef uint16_t             mp_word;
  #   define MP_SIZEOF_MP_DIGIT 1
  #   ifdef MP_DIGIT_BIT
  #      error You must not define MP_DIGIT_BIT when using MP_8BIT
  #   endif
  #elif defined(MP_16BIT)
  typedef uint16_t             mp_digit;
  typedef uint32_t             mp_word;
  #   define MP_SIZEOF_MP_DIGIT 2
  #   ifdef MP_DIGIT_BIT
  #      error You must not define MP_DIGIT_BIT when using MP_16BIT
  #   endif
  #elif defined(MP_64BIT)
  /* for GCC only on supported platforms */
  typedef uint64_t mp_digit;
  typedef unsigned long        mp_word __attribute__((mode(TI)));
  #   define MP_DIGIT_BIT 60
  #else
  /* this is the default case, 28-bit digits */
  
  /* this is to make porting into LibTomCrypt easier :-) */
  typedef uint32_t             mp_digit;
  typedef uint64_t             mp_word;
  
  #   ifdef MP_31BIT
  /* this is an extension that uses 31-bit digits */
  #      define MP_DIGIT_BIT 31
  #   else
  /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
  #      define MP_DIGIT_BIT 28
  #      define MP_28BIT
  #   endif
  #endif
  
  /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
  #ifndef MP_DIGIT_BIT
  #   define MP_DIGIT_BIT (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1))  /* bits per digit */
  #endif
  
  #define MP_MASK          ((((mp_digit)1)<<((mp_digit)MP_DIGIT_BIT))-((mp_digit)1))
  #define MP_DIGIT_MAX     MP_MASK
  
  /* equalities */
  #define MP_LT        -1   /* less than */
  #define MP_EQ         0   /* equal to */
  #define MP_GT         1   /* greater than */
  
  #define MP_ZPOS       0   /* positive integer */
  #define MP_NEG        1   /* negative */
  
  #define MP_OKAY       0   /* ok result */
  #define MP_MEM        -2  /* out of mem */
  #define MP_VAL        -3  /* invalid input */
  #define MP_RANGE      MP_VAL
  #define MP_ITER       -4  /* Max. iterations reached */
  
  #define MP_YES        1   /* yes response */
  #define MP_NO         0   /* no response */
  
  /* Primality generation flags */
  #define LTM_PRIME_BBS      0x0001 /* BBS style prime */
  #define LTM_PRIME_SAFE     0x0002 /* Safe prime (p-1)/2 == prime */
  #define LTM_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */
  
  typedef int           mp_err;
  
  /* you'll have to tune these... */
  extern int KARATSUBA_MUL_CUTOFF,
         KARATSUBA_SQR_CUTOFF,
         TOOM_MUL_CUTOFF,
         TOOM_SQR_CUTOFF;
  
  /* define this to use lower memory usage routines (exptmods mostly) */
  /* #define MP_LOW_MEM */
  
  /* default precision */
  #ifndef MP_PREC
  #   ifndef MP_LOW_MEM
  #      define MP_PREC 32        /* default digits of precision */
  #   else
  #      define MP_PREC 8         /* default digits of precision */
  #   endif
  #endif
  
  /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
  #define PRIVATE_MP_WARRAY (1u << (((CHAR_BIT * sizeof(mp_word)) - (2 * MP_DIGIT_BIT)) + 1))
  #define MP_WARRAY (MP_DEPRECATED_PRAGMA("MP_WARRAY is an internal macro") PRIVATE_MP_WARRAY)
  
  /* the infamous mp_int structure */
  typedef struct  {
     int used, alloc, sign;
     mp_digit *dp;
  } mp_int;
  
  /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
  typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
  
  #if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 301)
  #  define MP_DEPRECATED(x) __attribute__((deprecated("replaced by " #x)))
  #  define PRIVATE_MP_DEPRECATED_PRAGMA(s) _Pragma(#s)
  #  define MP_DEPRECATED_PRAGMA(s) PRIVATE_MP_DEPRECATED_PRAGMA(GCC warning s)
  #elif defined(_MSC_VER) && _MSC_VER >= 1500
  #  define MP_DEPRECATED(x) __declspec(deprecated("replaced by " #x))
  #  define MP_DEPRECATED_PRAGMA(s) __pragma(message(s))
  #else
  #  define MP_DEPRECATED
  #  define MP_DEPRECATED_PRAGMA(s)
  #endif
  
  #define DIGIT_BIT   (MP_DEPRECATED_PRAGMA("DIGIT_BIT macro is deprecated, MP_DIGIT_BIT instead") MP_DIGIT_BIT)
  #define USED(m)     (MP_DEPRECATED_PRAGMA("USED macro is deprecated, use z->used instead") (m)->used)
  #define DIGIT(m, k) (MP_DEPRECATED_PRAGMA("DIGIT macro is deprecated, use z->dp instead") (m)->dp[(k)])
  #define SIGN(m)     (MP_DEPRECATED_PRAGMA("SIGN macro is deprecated, use z->sign instead") (m)->sign)
  
  /* error code to char* string */
  const char *mp_error_to_string(int code);
  
  /* ---> init and deinit bignum functions <--- */
  /* init a bignum */
  int mp_init(mp_int *a);
  
  /* free a bignum */
  void mp_clear(mp_int *a);
  
  /* init a null terminated series of arguments */
  int mp_init_multi(mp_int *mp, ...);
  
  /* clear a null terminated series of arguments */
  void mp_clear_multi(mp_int *mp, ...);
  
  /* exchange two ints */
  void mp_exch(mp_int *a, mp_int *b);
  
  /* shrink ram required for a bignum */
  int mp_shrink(mp_int *a);
  
  /* grow an int to a given size */
  int mp_grow(mp_int *a, int size);
  
  /* init to a given number of digits */
  int mp_init_size(mp_int *a, int size);
  
  /* ---> Basic Manipulations <--- */
  #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
  int mp_iseven(const mp_int *a);
  int mp_isodd(const mp_int *a);
  #define mp_isneg(a)  (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)
  
  /* set to zero */
  void mp_zero(mp_int *a);
  
  /* set to a digit */
  void mp_set(mp_int *a, mp_digit b);
  
  /* set a double */
  int mp_set_double(mp_int *a, double b);
  
  /* set a 32-bit const */
  int mp_set_int(mp_int *a, unsigned long b);
  
  /* set a platform dependent unsigned long value */
  int mp_set_long(mp_int *a, unsigned long b);
  
  /* set a platform dependent unsigned long long value */
  int mp_set_long_long(mp_int *a, unsigned long long b);
  
  /* get a double */
  double mp_get_double(const mp_int *a);
  
  /* get a 32-bit value */
  unsigned long mp_get_int(const mp_int *a);
  
  /* get a platform dependent unsigned long value */
  unsigned long mp_get_long(const mp_int *a);
  
  /* get a platform dependent unsigned long long value */
  unsigned long long mp_get_long_long(const mp_int *a);
  
  /* initialize and set a digit */
  int mp_init_set(mp_int *a, mp_digit b);
  
  /* initialize and set 32-bit value */
  int mp_init_set_int(mp_int *a, unsigned long b);
  
  /* copy, b = a */
  int mp_copy(const mp_int *a, mp_int *b);
  
  /* inits and copies, a = b */
  int mp_init_copy(mp_int *a, const mp_int *b);
  
  /* trim unused digits */
  void mp_clamp(mp_int *a);
  
  /* import binary data */
  int mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, const void *op);
  
  /* export binary data */
  int mp_export(void *rop, size_t *countp, int order, size_t size, int endian, size_t nails, const mp_int *op);
  
  /* ---> digit manipulation <--- */
  
  /* right shift by "b" digits */
  void mp_rshd(mp_int *a, int b);
  
  /* left shift by "b" digits */
  int mp_lshd(mp_int *a, int b);
  
  /* c = a / 2**b, implemented as c = a >> b */
  int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
  
  /* b = a/2 */
  int mp_div_2(const mp_int *a, mp_int *b);
  
  /* c = a * 2**b, implemented as c = a << b */
  int mp_mul_2d(const mp_int *a, int b, mp_int *c);
  
  /* b = a*2 */
  int mp_mul_2(const mp_int *a, mp_int *b);
  
  /* c = a mod 2**b */
  int mp_mod_2d(const mp_int *a, int b, mp_int *c);
  
  /* computes a = 2**b */
  int mp_2expt(mp_int *a, int b);
  
  /* Counts the number of lsbs which are zero before the first zero bit */
  int mp_cnt_lsb(const mp_int *a);
  
  /* I Love Earth! */
  
  /* makes a pseudo-random mp_int of a given size */
  int mp_rand(mp_int *a, int digits);
  /* makes a pseudo-random small int of a given size */
  int mp_rand_digit(mp_digit *r);
  
  #ifdef MP_PRNG_ENABLE_LTM_RNG
  /* A last resort to provide random data on systems without any of the other
   * implemented ways to gather entropy.
   * It is compatible with `rng_get_bytes()` from libtomcrypt so you could
   * provide that one and then set `ltm_rng = rng_get_bytes;` */
  extern unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void));
  extern void (*ltm_rng_callback)(void);
  #endif
  
  /* ---> binary operations <--- */
  /* c = a XOR b  */
  int mp_xor(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = a OR b */
  int mp_or(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = a AND b */
  int mp_and(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* Checks the bit at position b and returns MP_YES
     if the bit is 1, MP_NO if it is 0 and MP_VAL
     in case of error */
  int mp_get_bit(const mp_int *a, int b);
  
  /* c = a XOR b (two complement) */
  int mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = a OR b (two complement) */
  int mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = a AND b (two complement) */
  int mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* right shift (two complement) */
  int mp_tc_div_2d(const mp_int *a, int b, mp_int *c);
  
  /* ---> Basic arithmetic <--- */
  
  /* b = ~a */
  int mp_complement(const mp_int *a, mp_int *b);
  
  /* b = -a */
  int mp_neg(const mp_int *a, mp_int *b);
  
  /* b = |a| */
  int mp_abs(const mp_int *a, mp_int *b);
  
  /* compare a to b */
  int mp_cmp(const mp_int *a, const mp_int *b);
  
  /* compare |a| to |b| */
  int mp_cmp_mag(const mp_int *a, const mp_int *b);
  
  /* c = a + b */
  int mp_add(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = a - b */
  int mp_sub(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = a * b */
  int mp_mul(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* b = a*a  */
  int mp_sqr(const mp_int *a, mp_int *b);
  
  /* a/b => cb + d == a */
  int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d);
  
  /* c = a mod b, 0 <= c < b  */
  int mp_mod(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* ---> single digit functions <--- */
  
  /* compare against a single digit */
  int mp_cmp_d(const mp_int *a, mp_digit b);
  
  /* c = a + b */
  int mp_add_d(const mp_int *a, mp_digit b, mp_int *c);
  
  /* Increment "a" by one like "a++". Changes input! */
  int mp_incr(mp_int *a);
  
  /* c = a - b */
  int mp_sub_d(const mp_int *a, mp_digit b, mp_int *c);
  
  /* Decrement "a" by one like "a--". Changes input! */
  int mp_decr(mp_int *a);
  
  /* c = a * b */
  int mp_mul_d(const mp_int *a, mp_digit b, mp_int *c);
  
  /* a/b => cb + d == a */
  int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
  
  /* a/3 => 3c + d == a */
  int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d);
  
  /* c = a**b */
  int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c);
  int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast);
  
  /* c = a mod b, 0 <= c < b  */
  int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c);
  
  /* ---> number theory <--- */
  
  /* d = a + b (mod c) */
  int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
  
  /* d = a - b (mod c) */
  int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
  
  /* d = a * b (mod c) */
  int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
  
  /* c = a * a (mod b) */
  int mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = 1/a (mod b) */
  int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* c = (a, b) */
  int mp_gcd(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* produces value such that U1*a + U2*b = U3 */
  int mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
  
  /* c = [a, b] or (a*b)/(a, b) */
  int mp_lcm(const mp_int *a, const mp_int *b, mp_int *c);
  
  /* finds one of the b'th root of a, such that |c|**b <= |a|
   *
   * returns error if a < 0 and b is even
   */
  int mp_n_root(const mp_int *a, mp_digit b, mp_int *c);
  int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast);
  
  /* special sqrt algo */
  int mp_sqrt(const mp_int *arg, mp_int *ret);
  
  /* special sqrt (mod prime) */
  int mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret);
  
  /* is number a square? */
  int mp_is_square(const mp_int *arg, int *ret);
  
  /* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
  int mp_jacobi(const mp_int *a, const mp_int *n, int *c);
  
  /* computes the Kronecker symbol c = (a | p) (like jacobi() but with {a,p} in Z */
  int mp_kronecker(const mp_int *a, const mp_int *p, int *c);
  
  /* used to setup the Barrett reduction for a given modulus b */
  int mp_reduce_setup(mp_int *a, const mp_int *b);
  
  /* Barrett Reduction, computes a (mod b) with a precomputed value c
   *
   * Assumes that 0 < x <= m*m, note if 0 > x > -(m*m) then you can merely
   * compute the reduction as -1 * mp_reduce(mp_abs(x)) [pseudo code].
   */
  int mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu);
  
  /* setups the montgomery reduction */
  int mp_montgomery_setup(const mp_int *n, mp_digit *rho);
  
  /* computes a = B**n mod b without division or multiplication useful for
   * normalizing numbers in a Montgomery system.
   */
  int mp_montgomery_calc_normalization(mp_int *a, const mp_int *b);
  
  /* computes x/R == x (mod N) via Montgomery Reduction */
  int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho);
  
  /* returns 1 if a is a valid DR modulus */
  int mp_dr_is_modulus(const mp_int *a);
  
  /* sets the value of "d" required for mp_dr_reduce */
  void mp_dr_setup(const mp_int *a, mp_digit *d);
  
  /* reduces a modulo n using the Diminished Radix method */
  int mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k);
  
  /* returns true if a can be reduced with mp_reduce_2k */
  int mp_reduce_is_2k(const mp_int *a);
  
  /* determines k value for 2k reduction */
  int mp_reduce_2k_setup(const mp_int *a, mp_digit *d);
  
  /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
  int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d);
  
  /* returns true if a can be reduced with mp_reduce_2k_l */
  int mp_reduce_is_2k_l(const mp_int *a);
  
  /* determines k value for 2k reduction */
  int mp_reduce_2k_setup_l(const mp_int *a, mp_int *d);
  
  /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
  int mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d);
  
  /* Y = G**X (mod P) */
  int mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y);
  
  /* ---> Primes <--- */
  
  /* number of primes */
  #ifdef MP_8BIT
  #  define PRIME_SIZE 31
  #else
  #  define PRIME_SIZE 256
  #endif
  
  /* table of first PRIME_SIZE primes */
  extern const mp_digit ltm_prime_tab[PRIME_SIZE];
  
  /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
  int mp_prime_is_divisible(const mp_int *a, int *result);
  
  /* performs one Fermat test of "a" using base "b".
   * Sets result to 0 if composite or 1 if probable prime
   */
  int mp_prime_fermat(const mp_int *a, const mp_int *b, int *result);
  
  /* performs one Miller-Rabin test of "a" using base "b".
   * Sets result to 0 if composite or 1 if probable prime
   */
  int mp_prime_miller_rabin(const mp_int *a, const mp_int *b, int *result);
  
  /* This gives [for a given bit size] the number of trials required
   * such that Miller-Rabin gives a prob of failure lower than 2^-96
   */
  int mp_prime_rabin_miller_trials(int size);
  
  /* performs one strong Lucas-Selfridge test of "a".
   * Sets result to 0 if composite or 1 if probable prime
   */
  int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result);
  
  /* performs one Frobenius test of "a" as described by Paul Underwood.
   * Sets result to 0 if composite or 1 if probable prime
   */
  int mp_prime_frobenius_underwood(const mp_int *N, int *result);
  
  /* performs t random rounds of Miller-Rabin on "a" additional to
   * bases 2 and 3.  Also performs an initial sieve of trial
   * division.  Determines if "a" is prime with probability
   * of error no more than (1/4)**t.
   * Both a strong Lucas-Selfridge to complete the BPSW test
   * and a separate Frobenius test are available at compile time.
   * With t<0 a deterministic test is run for primes up to
   * 318665857834031151167461. With t<13 (abs(t)-13) additional
   * tests with sequential small primes are run starting at 43.
   * Is Fips 186.4 compliant if called with t as computed by
   * mp_prime_rabin_miller_trials();
   *
   * Sets result to 1 if probably prime, 0 otherwise
   */
  int mp_prime_is_prime(const mp_int *a, int t, int *result);
  
  /* finds the next prime after the number "a" using "t" trials
   * of Miller-Rabin.
   *
   * bbs_style = 1 means the prime must be congruent to 3 mod 4
   */
  int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
  
  /* makes a truly random prime of a given size (bytes),
   * call with bbs = 1 if you want it to be congruent to 3 mod 4
   *
   * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
   * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
   * so it can be NULL
   *
   * The prime generated will be larger than 2^(8*size).
   */
  #define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
  
  /* makes a truly random prime of a given size (bits),
   *
   * Flags are as follows:
   *
   *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
   *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
   *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
   *
   * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
   * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
   * so it can be NULL
   *
   */
  int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
  
  
  /* Integer logarithm to integer base */
  int mp_ilogb(mp_int *a, mp_digit base, mp_int *c);
  
  
  /* ---> radix conversion <--- */
  int mp_count_bits(const mp_int *a);
  
  int mp_unsigned_bin_size(const mp_int *a);
  int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
  int mp_to_unsigned_bin(const mp_int *a, unsigned char *b);
  int mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen);
  
  int mp_signed_bin_size(const mp_int *a);
  int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
  int mp_to_signed_bin(const mp_int *a,  unsigned char *b);
  int mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen);
  
  int mp_read_radix(mp_int *a, const char *str, int radix);
  int mp_toradix(const mp_int *a, char *str, int radix);
  int mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen);
  int mp_radix_size(const mp_int *a, int radix, int *size);
  
  #ifndef LTM_NO_FILE
  int mp_fread(mp_int *a, int radix, FILE *stream);
  int mp_fwrite(const mp_int *a, int radix, FILE *stream);
  #endif
  
  #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
  #define mp_raw_size(mp)           mp_signed_bin_size(mp)
  #define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
  #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
  #define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
  #define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))
  
  #define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
  #define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
  #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
  #define mp_tohex(M, S)     mp_toradix((M), (S), 16)
  
  #ifdef __cplusplus
  }
  #endif
  
  #endif
  