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 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
 /* SPDX-License-Identifier: Unlicense */
 
 #ifndef BN_H_
 #define BN_H_
 
 #ifndef MODULE_SCOPE
 #define MODULE_SCOPE extern
 #endif
 
 
 
 #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(_WIN32) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__)) && !defined(MP_64BIT)
 #   define MP_32BIT
 #endif
 
 /* detect 64-bit mode if possible */
 #if defined(NEVER)
 #   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
 
 #ifdef MP_DIGIT_BIT
 #   error Defining MP_DIGIT_BIT is disallowed, use MP_8/16/31/32/64BIT
 #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
 #ifndef MP_DIGIT_DECLARED
 typedef unsigned char        mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
 #ifndef MP_WORD_DECLARED
 typedef unsigned short       private_mp_word;
 #define MP_WORD_DECLARED
 #endif
 #   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)
 #ifndef MP_DIGIT_DECLARED
 typedef unsigned short       mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
 #ifndef MP_WORD_DECLARED
 typedef unsigned int         private_mp_word;
 #define MP_WORD_DECLARED
 #endif
 #   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 */
 #ifndef MP_DIGIT_DECLARED
 typedef unsigned long long   mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
 #if defined(__GNUC__)
 typedef unsigned long        private_mp_word __attribute__((mode(TI)));
 #endif
 #   define MP_DIGIT_BIT 60
 #else
 #ifndef MP_DIGIT_DECLARED
 typedef unsigned int         mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
 #ifndef MP_WORD_DECLARED
 #ifdef _WIN32
 typedef unsigned __int64   private_mp_word;
 #else
 typedef unsigned long long   private_mp_word;
 #endif
 #define MP_WORD_DECLARED
 #endif
 
 #   ifdef MP_31BIT
 /*
  * This is an extension that uses 31-bit digits.
  * Please be aware that not all functions support this size, especially s_mp_mul_digs_fast
  * will be reduced to work on small numbers only:
  * Up to 8 limbs, 248 bits instead of up to 512 limbs, 15872 bits with MP_28BIT.
  */
 #      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
 
 /* Primality generation flags */
 #define MP_PRIME_BBS      0x0001 /* BBS style prime */
 #define MP_PRIME_SAFE     0x0002 /* Safe prime (p-1)/2 == prime */
 #define MP_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */
 
 #define LTM_PRIME_BBS      (MP_DEPRECATED_PRAGMA("LTM_PRIME_BBS has been deprecated, use MP_PRIME_BBS") MP_PRIME_BBS)
 #define LTM_PRIME_SAFE     (MP_DEPRECATED_PRAGMA("LTM_PRIME_SAFE has been deprecated, use MP_PRIME_SAFE") MP_PRIME_SAFE)
 #define LTM_PRIME_2MSB_ON  (MP_DEPRECATED_PRAGMA("LTM_PRIME_2MSB_ON has been deprecated, use MP_PRIME_2MSB_ON") MP_PRIME_2MSB_ON)
 
 #ifdef MP_USE_ENUMS
 typedef enum {
    MP_ZPOS = 0,   /* positive */
    MP_NEG = 1     /* negative */
 } mp_sign;
 typedef enum {
    MP_LT = -1,    /* less than */
    MP_EQ = 0,     /* equal */
    MP_GT = 1      /* greater than */
 } mp_ord;
 typedef enum {
    MP_NO = 0,
    MP_YES = 1
 } mp_bool;
 typedef enum {
    MP_OKAY  = 0,   /* no error */
    MP_ERR   = -1,  /* unknown error */
    MP_MEM   = -2,  /* out of mem */
    MP_VAL   = -3,  /* invalid input */
    MP_ITER  = -4,  /* maximum iterations reached */
    MP_BUF   = -5   /* buffer overflow, supplied buffer too small */
 } mp_err;
 typedef enum {
    MP_LSB_FIRST = -1,
    MP_MSB_FIRST =  1
 } mp_order;
 typedef enum {
    MP_LITTLE_ENDIAN  = -1,
    MP_NATIVE_ENDIAN  =  0,
    MP_BIG_ENDIAN     =  1
 } mp_endian;
 #else
 typedef int mp_sign;
 #define MP_ZPOS       0   /* positive integer */
 #define MP_NEG        1   /* negative */
 typedef int mp_ord;
 #define MP_LT        -1   /* less than */
 #define MP_EQ         0   /* equal to */
 #define MP_GT         1   /* greater than */
 typedef int mp_bool;
 #define MP_YES        1
 #define MP_NO         0
 typedef int mp_err;
 #define MP_OKAY       0   /* no error */
 #define MP_ERR        -1  /* unknown error */
 #define MP_MEM        -2  /* out of mem */
 #define MP_VAL        -3  /* invalid input */
 #define MP_RANGE      (MP_DEPRECATED_PRAGMA("MP_RANGE has been deprecated in favor of MP_VAL") MP_VAL)
 #define MP_ITER       -4  /* maximum iterations reached */
 #define MP_BUF        -5  /* buffer overflow, supplied buffer too small */
 typedef int mp_order;
 #define MP_LSB_FIRST -1
 #define MP_MSB_FIRST  1
 typedef int mp_endian;
 #define MP_LITTLE_ENDIAN  -1
 #define MP_NATIVE_ENDIAN  0
 #define MP_BIG_ENDIAN     1
 #endif
 
 /* tunable cutoffs */
 
 #ifndef MP_FIXED_CUTOFFS
 extern int
 KARATSUBA_MUL_CUTOFF,
 KARATSUBA_SQR_CUTOFF,
 TOOM_MUL_CUTOFF,
 TOOM_SQR_CUTOFF;
 #endif
 
 /* 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 */
 #   elif defined(MP_8BIT)
 #      define MP_PREC 16        /* 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 (int)(1 << (((CHAR_BIT * sizeof(private_mp_word)) - (2 * MP_DIGIT_BIT)) + 1))
 
 #if defined(__GNUC__) && __GNUC__ >= 4
 #   define MP_NULL_TERMINATED __attribute__((sentinel))
 #else
 #   define MP_NULL_TERMINATED
 #endif
 
 /*
  * MP_WUR - warn unused result
  * ---------------------------
  *
  * The result of functions annotated with MP_WUR must be
  * checked and cannot be ignored.
  *
  * Most functions in libtommath return an error code.
  * This error code must be checked in order to prevent crashes or invalid
  * results.
  *
  * If you still want to avoid the error checks for quick and dirty programs
  * without robustness guarantees, you can `#define MP_WUR` before including
  * tommath.h, disabling the warnings.
  */
 #ifndef MP_WUR
 #  if defined(__GNUC__) && __GNUC__ >= 4
 #     define MP_WUR __attribute__((warn_unused_result))
 #  else
 #     define MP_WUR
 #  endif
 #endif
 
 #if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 405)
 #  define MP_DEPRECATED(x) __attribute__((deprecated("replaced by " #x)))
 #elif defined(_MSC_VER) && _MSC_VER >= 1500
 #  define MP_DEPRECATED(x) __declspec(deprecated("replaced by " #x))
 #else
 #  define MP_DEPRECATED(x)
 #endif
 
 #ifndef MP_NO_DEPRECATED_PRAGMA
 #if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 301)
 #  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_PRAGMA(s) __pragma(message(s))
 #endif
 #endif
 
 #ifndef MP_DEPRECATED_PRAGMA
 #  define MP_DEPRECATED_PRAGMA(s)
 #endif
 
 #define DIGIT_BIT   MP_DIGIT_BIT
 #define USED(m)    ((m)->used)
 #define DIGIT(m,k) ((m)->dp[(k)])
 #define SIGN(m)    ((m)->sign)
 
 /* the infamous mp_int structure */
 #ifndef MP_INT_DECLARED
 #define MP_INT_DECLARED
 typedef struct mp_int mp_int;
 #endif
 struct mp_int {
    int used, alloc;
    mp_sign sign;
    mp_digit *dp;
 };
 
 /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
 typedef int private_mp_prime_callback(unsigned char *dst, int len, void *dat);
 typedef private_mp_prime_callback MP_DEPRECATED(mp_rand_source) ltm_prime_callback;
 
 /* error code to char* string */
 /*
 const char *mp_error_to_string(mp_err code) MP_WUR;
 */
 
 /* ---> init and deinit bignum functions <--- */
 /* init a bignum */
 /*
 mp_err mp_init(mp_int *a) MP_WUR;
 */
 
 /* free a bignum */
 /*
 void mp_clear(mp_int *a);
 */
 
 /* init a null terminated series of arguments */
 /*
 mp_err mp_init_multi(mp_int *mp, ...) MP_NULL_TERMINATED MP_WUR;
 */
 
 /* clear a null terminated series of arguments */
 /*
 void mp_clear_multi(mp_int *mp, ...) MP_NULL_TERMINATED;
 */
 
 /* exchange two ints */
 /*
 void mp_exch(mp_int *a, mp_int *b);
 */
 
 /* shrink ram required for a bignum */
 /*
 mp_err mp_shrink(mp_int *a) MP_WUR;
 */
 
 /* grow an int to a given size */
 /*
 mp_err mp_grow(mp_int *a, int size) MP_WUR;
 */
 
 /* init to a given number of digits */
 /*
 mp_err mp_init_size(mp_int *a, int size) MP_WUR;
 */
 
 /* ---> Basic Manipulations <--- */
 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
 #define mp_isodd(a)  (((a)->used != 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
 #define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
 #define mp_isneg(a)  (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)
 
 /* set to zero */
 /*
 void mp_zero(mp_int *a);
 */
 
 /* get and set doubles */
 /*
 double mp_get_double(const mp_int *a) MP_WUR;
 */
 /*
 mp_err mp_set_double(mp_int *a, double b) MP_WUR;
 */
 
 /* get integer, set integer and init with integer (int32_t) */
 #ifndef MP_NO_STDINT
 /*
 int32_t mp_get_i32(const mp_int *a) MP_WUR;
 */
 /*
 void mp_set_i32(mp_int *a, int32_t b);
 */
 /*
 mp_err mp_init_i32(mp_int *a, int32_t b) MP_WUR;
 */
 
 /* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint32_t) */
 #define mp_get_u32(a) ((uint32_t)mp_get_i32(a))
 /*
 void mp_set_u32(mp_int *a, uint32_t b);
 */
 /*
 mp_err mp_init_u32(mp_int *a, uint32_t b) MP_WUR;
 */
 
 /* get integer, set integer and init with integer (int64_t) */
 /*
 int64_t mp_get_i64(const mp_int *a) MP_WUR;
 */
 /*
 void mp_set_i64(mp_int *a, int64_t b);
 */
 /*
 mp_err mp_init_i64(mp_int *a, int64_t b) MP_WUR;
 */
 
 /* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint64_t) */
 #define mp_get_u64(a) ((uint64_t)mp_get_i64(a))
 /*
 void mp_set_u64(mp_int *a, uint64_t b);
 */
 /*
 mp_err mp_init_u64(mp_int *a, uint64_t b) MP_WUR;
 */
 
 /* get magnitude */
 /*
 uint32_t mp_get_mag_u32(const mp_int *a) MP_WUR;
 */
 /*
 uint64_t mp_get_mag_u64(const mp_int *a) MP_WUR;
 */
 #endif
 /*
 unsigned long mp_get_mag_ul(const mp_int *a) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_get_mag_u64) Tcl_WideUInt mp_get_mag_ull(const mp_int *a) MP_WUR;
 */
 
 /* get integer, set integer (long) */
 /*
 long mp_get_l(const mp_int *a) MP_WUR;
 */
 /*
 void mp_set_l(mp_int *a, long b);
 */
 /*
 mp_err mp_init_l(mp_int *a, long b) MP_WUR;
 */
 
 /* get integer, set integer (unsigned long) */
 #define mp_get_ul(a) ((unsigned long)mp_get_l(a))
 /*
 void mp_set_ul(mp_int *a, unsigned long b);
 */
 /*
 mp_err mp_init_ul(mp_int *a, unsigned long b) MP_WUR;
 */
 
 /* get integer, set integer (Tcl_WideInt) */
 /*
 MP_DEPRECATED(mp_get_i64) Tcl_WideInt mp_get_ll(const mp_int *a) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_set_i64) void mp_set_ll(mp_int *a, Tcl_WideInt b);
 */
 /*
 MP_DEPRECATED(mp_init_i64) mp_err mp_init_ll(mp_int *a, Tcl_WideInt b) MP_WUR;
 */
 
 /* get integer, set integer (Tcl_WideUInt) */
 /*
 #define mp_get_ull(a) (MP_DEPRECATED_PRAGMA("mp_get_ull() has been deprecated, use mp_get_u64()") ((Tcl_WideUInt)mp_get_ll(a)))
 */
 /*
 MP_DEPRECATED(mp_set_u64) void mp_set_ull(mp_int *a, Tcl_WideUInt b);
 */
 /*
 MP_DEPRECATED(mp_init_u64) mp_err mp_init_ull(mp_int *a, Tcl_WideUInt b) MP_WUR;
 */
 
 /* set to single unsigned digit, up to MP_DIGIT_MAX */
 /*
 void mp_set(mp_int *a, mp_digit b);
 */
 /*
 mp_err mp_init_set(mp_int *a, mp_digit b) MP_WUR;
 */
 
 /* get integer, set integer and init with integer (deprecated) */
 /*
 MP_DEPRECATED(mp_get_mag_u32/mp_get_u32) unsigned long mp_get_int(const mp_int *a) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_get_mag_ul/mp_get_ul) unsigned long mp_get_long(const mp_int *a) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_get_mag_u64/mp_get_u64) Tcl_WideUInt mp_get_long_long(const mp_int *a) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_set_ul) mp_err mp_set_int(mp_int *a, unsigned long b);
 */
 /*
 MP_DEPRECATED(mp_set_ul) mp_err mp_set_long(mp_int *a, unsigned long b);
 */
 /*
 MP_DEPRECATED(mp_set_ull) mp_err mp_set_long_long(mp_int *a, Tcl_WideUInt b);
 */
 /*
 MP_DEPRECATED(mp_init_ul) mp_err mp_init_set_int(mp_int *a, unsigned long b) MP_WUR;
 */
 
 /* copy, b = a */
 /*
 mp_err mp_copy(const mp_int *a, mp_int *b) MP_WUR;
 */
 
 /* inits and copies, a = b */
 /*
 mp_err mp_init_copy(mp_int *a, const mp_int *b) MP_WUR;
 */
 
 /* trim unused digits */
 /*
 void mp_clamp(mp_int *a);
 */
 
 
 /* export binary data */
 /*
 MP_DEPRECATED(mp_pack) mp_err mp_export(void *rop, size_t *countp, int order, size_t size,
                                         int endian, size_t nails, const mp_int *op) MP_WUR;
 */
 
 /* import binary data */
 /*
 MP_DEPRECATED(mp_unpack) mp_err mp_import(mp_int *rop, size_t count, int order,
       size_t size, int endian, size_t nails,
       const void *op) MP_WUR;
 */
 
 /* unpack binary data */
 /*
 mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, mp_endian endian,
                  size_t nails, const void *op) MP_WUR;
 */
 
 /* pack binary data */
 /*
 size_t mp_pack_count(const mp_int *a, size_t nails, size_t size) MP_WUR;
 */
 /*
 mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size,
                mp_endian endian, size_t nails, const mp_int *op) MP_WUR;
 */
 
 /* ---> digit manipulation <--- */
 
 /* right shift by "b" digits */
 /*
 void mp_rshd(mp_int *a, int b);
 */
 
 /* left shift by "b" digits */
 /*
 mp_err mp_lshd(mp_int *a, int b) MP_WUR;
 */
 
 /* c = a / 2**b, implemented as c = a >> b */
 /*
 mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d) MP_WUR;
 */
 
 /* b = a/2 */
 /*
 mp_err mp_div_2(const mp_int *a, mp_int *b) MP_WUR;
 */
 
 /* a/3 => 3c + d == a */
 /*
 MP_DEPRECATED(mp_div_d) mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d) MP_WUR;
 */
 
 /* c = a * 2**b, implemented as c = a << b */
 /*
 mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c) MP_WUR;
 */
 
 /* b = a*2 */
 /*
 mp_err mp_mul_2(const mp_int *a, mp_int *b) MP_WUR;
 */
 
 /* c = a mod 2**b */
 /*
 mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c) MP_WUR;
 */
 
 /* computes a = 2**b */
 /*
 mp_err mp_2expt(mp_int *a, int b) MP_WUR;
 */
 
 /* Counts the number of lsbs which are zero before the first zero bit */
 /*
 int mp_cnt_lsb(const mp_int *a) MP_WUR;
 */
 
 /* I Love Earth! */
 
 /* makes a pseudo-random mp_int of a given size */
 /*
 mp_err mp_rand(mp_int *a, int digits) MP_WUR;
 */
 /* makes a pseudo-random small int of a given size */
 /*
 MP_DEPRECATED(mp_rand) mp_err mp_rand_digit(mp_digit *r) MP_WUR;
 */
 /* use custom random data source instead of source provided the platform */
 /*
 void mp_rand_source(mp_err(*source)(void *out, size_t size));
 */
 
 #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 <--- */
 
 /* 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
  */
 /*
 MP_DEPRECATED(s_mp_get_bit) int mp_get_bit(const mp_int *a, int b) MP_WUR;
 */
 
 /* c = a XOR b (two complement) */
 /*
 MP_DEPRECATED(mp_xor) mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 /*
 mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* c = a OR b (two complement) */
 /*
 MP_DEPRECATED(mp_or) mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 /*
 mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* c = a AND b (two complement) */
 /*
 MP_DEPRECATED(mp_and) mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 /*
 mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* b = ~a (bitwise not, two complement) */
 /*
 mp_err mp_complement(const mp_int *a, mp_int *b) MP_WUR;
 */
 
 /* right shift with sign extension */
 /*
 MP_DEPRECATED(mp_signed_rsh) mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c) MP_WUR;
 */
 /*
 mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c) MP_WUR;
 */
 
 /* ---> Basic arithmetic <--- */
 
 /* b = -a */
 /*
 mp_err mp_neg(const mp_int *a, mp_int *b) MP_WUR;
 */
 
 /* b = |a| */
 /*
 mp_err mp_abs(const mp_int *a, mp_int *b) MP_WUR;
 */
 
 /* compare a to b */
 /*
 mp_ord mp_cmp(const mp_int *a, const mp_int *b) MP_WUR;
 */
 
 /* compare |a| to |b| */
 /*
 mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) MP_WUR;
 */
 
 /* c = a + b */
 /*
 mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* c = a - b */
 /*
 mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* c = a * b */
 /*
 mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* b = a*a  */
 /*
 mp_err mp_sqr(const mp_int *a, mp_int *b) MP_WUR;
 */
 
 /* a/b => cb + d == a */
 /*
 mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) MP_WUR;
 */
 
 /* c = a mod b, 0 <= c < b  */
 /*
 mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* Increment "a" by one like "a++". Changes input! */
 /*
 mp_err mp_incr(mp_int *a) MP_WUR;
 */
 
 /* Decrement "a" by one like "a--". Changes input! */
 /*
 mp_err mp_decr(mp_int *a) MP_WUR;
 */
 
 /* ---> single digit functions <--- */
 
 /* compare against a single digit */
 /*
 mp_ord mp_cmp_d(const mp_int *a, mp_digit b) MP_WUR;
 */
 
 /* c = a + b */
 /*
 mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
 */
 
 /* c = a - b */
 /*
 mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
 */
 
 /* c = a * b */
 /*
 mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
 */
 
 /* a/b => cb + d == a */
 /*
 mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d) MP_WUR;
 */
 
 /* c = a mod b, 0 <= c < b  */
 /*
 mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c) MP_WUR;
 */
 
 /* ---> number theory <--- */
 
 /* d = a + b (mod c) */
 /*
 mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR;
 */
 
 /* d = a - b (mod c) */
 /*
 mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR;
 */
 
 /* d = a * b (mod c) */
 /*
 mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR;
 */
 
 /* c = a * a (mod b) */
 /*
 mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* c = 1/a (mod b) */
 /*
 mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* c = (a, b) */
 /*
 mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* produces value such that U1*a + U2*b = U3 */
 /*
 mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) MP_WUR;
 */
 
 /* c = [a, b] or (a*b)/(a, b) */
 /*
 mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
 */
 
 /* Integer logarithm to integer base */
 /*
 mp_err mp_log_n(const mp_int *a, int base, int *c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_log_n) mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c) MP_WUR;
 */
 
 /* c = a**b */
 /*
 mp_err mp_expt_n(const mp_int *a, int b, mp_int *c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_expt_n) mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_expt_n) mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_expt_n) mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) MP_WUR;
 */
 /* finds one of the b'th root of a, such that |c|**b <= |a|
  *
  * returns error if a < 0 and b is even
  */
  /*
 mp_err mp_root_n(const mp_int *a, int b, mp_int *c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_root_n) mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_root_n) mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_root_n) mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) MP_WUR;
 */
 
 /* special sqrt algo */
 /*
 mp_err mp_sqrt(const mp_int *arg, mp_int *ret) MP_WUR;
 */
 
 /* special sqrt (mod prime) */
 /*
 mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) MP_WUR;
 */
 
 /* is number a square? */
 /*
 mp_err mp_is_square(const mp_int *arg, mp_bool *ret) MP_WUR;
 */
 
 /* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
 /*
 MP_DEPRECATED(mp_kronecker) mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c) MP_WUR;
 */
 
 /* computes the Kronecker symbol c = (a | p) (like jacobi() but with {a,p} in Z */
 /*
 mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c) MP_WUR;
 */
 
 /* used to setup the Barrett reduction for a given modulus b */
 /*
 mp_err mp_reduce_setup(mp_int *a, const mp_int *b) MP_WUR;
 */
 
 /* 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].
  */
 /*
 mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu) MP_WUR;
 */
 
 /* setups the montgomery reduction */
 /*
 mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho) MP_WUR;
 */
 
 /* computes a = B**n mod b without division or multiplication useful for
  * normalizing numbers in a Montgomery system.
  */
 /*
 mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b) MP_WUR;
 */
 
 /* computes x/R == x (mod N) via Montgomery Reduction */
 /*
 mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) MP_WUR;
 */
 
 /* returns 1 if a is a valid DR modulus */
 /*
 mp_bool mp_dr_is_modulus(const mp_int *a) MP_WUR;
 */
 
 /* 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 */
 /*
 mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k) MP_WUR;
 */
 
 /* returns true if a can be reduced with mp_reduce_2k */
 /*
 mp_bool mp_reduce_is_2k(const mp_int *a) MP_WUR;
 */
 
 /* determines k value for 2k reduction */
 /*
 mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d) MP_WUR;
 */
 
 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
 /*
 mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d) MP_WUR;
 */
 
 /* returns true if a can be reduced with mp_reduce_2k_l */
 /*
 mp_bool mp_reduce_is_2k_l(const mp_int *a) MP_WUR;
 */
 
 /* determines k value for 2k reduction */
 /*
 mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d) MP_WUR;
 */
 
 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
 /*
 mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d) MP_WUR;
 */
 
 /* Y = G**X (mod P) */
 /*
 mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y) MP_WUR;
 */
 
 /* ---> Primes <--- */
 
 /* number of primes */
 #ifdef MP_8BIT
 #  define PRIVATE_MP_PRIME_TAB_SIZE 31
 #else
 #  define PRIVATE_MP_PRIME_TAB_SIZE 256
 #endif
 #define PRIME_SIZE (MP_DEPRECATED_PRAGMA("PRIME_SIZE has been made internal") PRIVATE_MP_PRIME_TAB_SIZE)
 
 /* table of first PRIME_SIZE primes */
 #if defined(BUILD_tcl) || !defined(_WIN32)
 MODULE_SCOPE const mp_digit ltm_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE];
 #endif
 
 /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
 /*
 MP_DEPRECATED(mp_prime_is_prime) mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result) MP_WUR;
 */
 
 /* performs one Fermat test of "a" using base "b".
  * Sets result to 0 if composite or 1 if probable prime
  */
 /*
 mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result) MP_WUR;
 */
 
 /* performs one Miller-Rabin test of "a" using base "b".
  * Sets result to 0 if composite or 1 if probable prime
  */
 /*
 mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result) MP_WUR;
 */
 
 /* 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) MP_WUR;
 */
 
 /* performs one strong Lucas-Selfridge test of "a".
  * Sets result to 0 if composite or 1 if probable prime
  */
 /*
 mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result) MP_WUR;
 */
 
 /* performs one Frobenius test of "a" as described by Paul Underwood.
  * Sets result to 0 if composite or 1 if probable prime
  */
 /*
 mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result) MP_WUR;
 */
 
 /* 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
  */
 /*
 mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result) MP_WUR;
 */
 
 /* 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
  */
 /*
 mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style) MP_WUR;
 */
 
 /* 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_DEPRECATED_PRAGMA("mp_prime_random has been deprecated, use mp_prime_rand instead") mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?MP_PRIME_BBS:0, cb, dat))
 
 /* makes a truly random prime of a given size (bits),
  *
  * Flags are as follows:
  *
  *   MP_PRIME_BBS      - make prime congruent to 3 mod 4
  *   MP_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS)
  *   MP_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
  *
  */
 /*
 MP_DEPRECATED(mp_prime_rand) mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags,
       private_mp_prime_callback cb, void *dat) MP_WUR;
 */
 /*
 mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) MP_WUR;
 */
 
 /* ---> radix conversion <--- */
 /*
 int mp_count_bits(const mp_int *a) MP_WUR;
 */
 
 
 /*
 MP_DEPRECATED(mp_ubin_size) int mp_unsigned_bin_size(const mp_int *a) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_from_ubin) mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_to_ubin) mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_to_ubin) mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR;
 */
 
 /*
 MP_DEPRECATED(mp_sbin_size) int mp_signed_bin_size(const mp_int *a) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_from_sbin) mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_to_sbin) mp_err mp_to_signed_bin(const mp_int *a,  unsigned char *b) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_to_sbin) mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR;
 */
 
 /*
 size_t mp_ubin_size(const mp_int *a) MP_WUR;
 */
 /*
 mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size) MP_WUR;
 */
 /*
 mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) MP_WUR;
 */
 
 /*
 size_t mp_sbin_size(const mp_int *a) MP_WUR;
 */
 /*
 mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size) MP_WUR;
 */
 /*
 mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) MP_WUR;
 */
 
 /*
 mp_err mp_read_radix(mp_int *a, const char *str, int radix) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_to_radix) mp_err mp_toradix(const mp_int *a, char *str, int radix) MP_WUR;
 */
 /*
 MP_DEPRECATED(mp_to_radix) mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen) MP_WUR;
 */
 /*
 mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix) MP_WUR;
 */
 /*
 mp_err mp_radix_size(const mp_int *a, int radix, int *size) MP_WUR;
 */
 
 #ifndef MP_NO_FILE
 /*
 mp_err mp_fread(mp_int *a, int radix, FILE *stream) MP_WUR;
 */
 /*
 mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream) MP_WUR;
 */
 #endif
 
 #define mp_read_raw(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_signed_bin") mp_read_signed_bin((mp), (str), (len)))
 #define mp_raw_size(mp)           (MP_DEPRECATED_PRAGMA("replaced by mp_signed_bin_size") mp_signed_bin_size(mp))
 #define mp_toraw(mp, str)         (MP_DEPRECATED_PRAGMA("replaced by mp_to_signed_bin") mp_to_signed_bin((mp), (str)))
 #define mp_read_mag(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_unsigned_bin") mp_read_unsigned_bin((mp), (str), (len))
 #define mp_mag_size(mp)           (MP_DEPRECATED_PRAGMA("replaced by mp_unsigned_bin_size") mp_unsigned_bin_size(mp))
 #define mp_tomag(mp, str)         (MP_DEPRECATED_PRAGMA("replaced by mp_to_unsigned_bin") mp_to_unsigned_bin((mp), (str)))
 
 #define mp_tobinary(M, S)  (MP_DEPRECATED_PRAGMA("replaced by mp_to_binary")  mp_toradix((M), (S), 2))
 #define mp_tooctal(M, S)   (MP_DEPRECATED_PRAGMA("replaced by mp_to_octal")   mp_toradix((M), (S), 8))
 #define mp_todecimal(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_decimal") mp_toradix((M), (S), 10))
 #define mp_tohex(M, S)     (MP_DEPRECATED_PRAGMA("replaced by mp_to_hex")     mp_toradix((M), (S), 16))
 
 #define mp_to_binary(M, S, N)  mp_to_radix((M), (S), (N), NULL, 2)
 #define mp_to_octal(M, S, N)   mp_to_radix((M), (S), (N), NULL, 8)
 #define mp_to_decimal(M, S, N) mp_to_radix((M), (S), (N), NULL, 10)
 #define mp_to_hex(M, S, N)     mp_to_radix((M), (S), (N), NULL, 16)
 
 #ifdef __cplusplus
 }
 #endif
 
 #include "tclTomMathDecls.h"
 
 #endif

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