--- /dev/null
+/* 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
+typedef unsigned long private_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 :-) */
+#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)))
+# 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(s)
+# 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;
+*/
+/*
+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) */
+/*
+Tcl_WideInt mp_get_ll(const mp_int *a) MP_WUR;
+*/
+/*
+void mp_set_ll(mp_int *a, Tcl_WideInt b);
+*/
+/*
+mp_err mp_init_ll(mp_int *a, Tcl_WideInt b) MP_WUR;
+*/
+
+/* get integer, set integer (Tcl_WideUInt) */
+#define mp_get_ull(a) ((Tcl_WideUInt)mp_get_ll(a))
+/*
+void mp_set_ull(mp_int *a, Tcl_WideUInt b);
+*/
+/*
+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_ull/mp_get_ull) 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_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;
+*/
+
+/* 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_u32(const mp_int *a, unsigned int b, mp_int *c) MP_WUR;
+*/
+/*
+MP_DEPRECATED(mp_root_u32) mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
+*/
+/*
+MP_DEPRECATED(mp_root_u32) 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;
+*/
+
+/* Integer logarithm to integer base */
+/*
+mp_err mp_log_u32(const mp_int *a, unsigned int base, unsigned int *c) MP_WUR;
+*/
+
+/* c = a**b */
+/*
+mp_err mp_expt_u32(const mp_int *a, unsigned int b, mp_int *c) MP_WUR;
+*/
+/*
+MP_DEPRECATED(mp_expt_u32) mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
+*/
+/*
+MP_DEPRECATED(mp_expt_u32) mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) 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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