g_lip.h

密码大家Shoup写的数论算法c语言实现

#ifdef NTL_SINGLE_MUL
#error "do not set NTL_SINGLE_MUL when NTL_GMP_LIP is set"
#endif

#if 1

typedef void *_ntl_gbigint;

#else

/*
 * This way of defining the bigint handle type is a bit non-standard,
 * but better for debugging.
 */

struct _ntl_gbigint_is_opaque { int _x_; };
typedef struct _ntl_gbigint_is_opaque * _ntl_gbigint;

#endif

#define NTL_SP_NBITS NTL_NBITS_MAX
#define NTL_SP_BOUND (1L << NTL_SP_NBITS)
#define NTL_SP_FBOUND ((double) NTL_SP_BOUND)

#define NTL_WSP_NBITS (NTL_BITS_PER_LONG-2)
#define NTL_WSP_BOUND (1L << NTL_WSP_NBITS)

/* define the following so an error is raised */

#define NTL_RADIX ......
#define NTL_NBITSH ......
#define NTL_RADIXM ......
#define NTL_RADIXROOT ......
#define NTL_RADIXROOTM ......
#define NTL_FRADIX_INV ......




#if (defined(__cplusplus) && !defined(NTL_CXX_ONLY))
extern "C" {
#endif


/***********************************************************************

   Basic Functions

***********************************************************************/
    


    void _ntl_gsadd(_ntl_gbigint a, long d, _ntl_gbigint *b);
       /* *b = a + d */

    void _ntl_gadd(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
       /*  *c = a + b */

    void _ntl_gsub(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
       /* *c = a - b */

    void _ntl_gsubpos(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
       /* *c = a - b; assumes a >= b >= 0 */

    void _ntl_gsmul(_ntl_gbigint a, long d, _ntl_gbigint *b);
       /* *b = d * a */

    void _ntl_gmul(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
       /* *c = a * b */

    void _ntl_gsq(_ntl_gbigint a, _ntl_gbigint *c);
       /* *c = a * a */

    long _ntl_gsdiv(_ntl_gbigint a, long b, _ntl_gbigint *q);
       /* (*q) = floor(a/b) and a - floor(a/b)*(*q) is returned;
          error is raised if b == 0;
          if b does not divide a, then sign(*q) == sign(b) */

    void _ntl_gdiv(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *q, _ntl_gbigint *r);
       /* (*q) = floor(a/b) and (*r) = a - floor(a/b)*(*q);
          error is raised if b == 0;
          if b does not divide a, then sign(*q) == sign(b) */

    void _ntl_gmod(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *r);
       /* same as _ntl_gdiv, but only remainder is computed */

    long _ntl_gsmod(_ntl_gbigint a, long d);
       /* same as _ntl_gsdiv, but only remainder is computed */

    void _ntl_gquickmod(_ntl_gbigint *r, _ntl_gbigint b);
       /* *r = *r % b; 
	  The division is performed in place (but may sometimes
	  assumes b > 0 and *r >= 0;
          cause *r to grow by one digit) */

/********************************************************************

   Shifting and bit manipulation

*********************************************************************/


    void _ntl_glshift(_ntl_gbigint n, long k, _ntl_gbigint *a);
       /* *a = sign(n) * (|n| << k);
          shift is in reverse direction for negative k */

    void _ntl_grshift(_ntl_gbigint n, long k, _ntl_gbigint *a);
       /* *a = sign(n) * (|n| >> k);
          shift is in reverse direction for negative k */
    
    long _ntl_gmakeodd(_ntl_gbigint *n);
       /*
          if (n != 0)
              *n = m;
              return (k such that n == 2 ^ k * m with m odd);
          else
              return (0); 
        */

    long _ntl_gnumtwos(_ntl_gbigint n);
        /* return largest e such that 2^e divides n, or zero if n is zero */

    long _ntl_godd(_ntl_gbigint a);
       /* returns 1 if n is odd and 0 if it is even */

    long _ntl_gbit(_ntl_gbigint a, long p);
       /* returns p-th bit of a, where the low order bit is indexed by 0;
          p out of range returns 0 */

    long _ntl_gsetbit(_ntl_gbigint *a, long p);
       /* returns original value of p-th bit of |a|, and replaces
          p-th bit of a by 1 if it was zero;
          error if p < 0 */

    long _ntl_gswitchbit(_ntl_gbigint *a, long p);
       /* returns original value of p-th bit of |a|, and switches
          the value of p-th bit of a;
          p starts counting at 0;
          error if p < 0 */


     void _ntl_glowbits(_ntl_gbigint a, long k, _ntl_gbigint *b);
        /* places k low order bits of |a| in b */ 

     long _ntl_gslowbits(_ntl_gbigint a, long k);
        /* returns k low order bits of |a| */

    long _ntl_gweights(long a);
        /* returns Hamming weight of |a| */

    long _ntl_gweight(_ntl_gbigint a);
        /* returns Hamming weight of |a| */

    void _ntl_gand(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
        /* c gets bit pattern `bits of |a|` and `bits of |b|` */

    void _ntl_gor(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
        /* c gets bit pattern `bits of |a|` inclusive or `bits of |b|` */

    void _ntl_gxor(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
        /* c gets bit pattern `bits of |a|` exclusive or `bits of |b|` */




/************************************************************************

   Comparison

*************************************************************************/

    long _ntl_gcompare(_ntl_gbigint a, _ntl_gbigint b);
       /*
          if (a > b)
              return (1);
          if (a == b)
              return (0);
          if (a < b)
              return (-1);
         */

    long _ntl_gscompare(_ntl_gbigint a, long b);
       /* single-precision version of the above */

    long _ntl_giszero (_ntl_gbigint a);
       /* test for 0 */


    long _ntl_gsign(_ntl_gbigint a);
       /* 
          if (a > 0)
              return (1);
          if (a == 0)
              return (0);
          if (a < 0)
              return (-1);
        */

    void _ntl_gabs(_ntl_gbigint *a);
       /* *a = |a| */

    void _ntl_gnegate(_ntl_gbigint *a);
       /* *a = -a */

    void _ntl_gcopy(_ntl_gbigint a, _ntl_gbigint *b);
       /* *b = a;  */

    void _ntl_gswap(_ntl_gbigint *a, _ntl_gbigint *b);
       /* swap a and b (by swaping pointers) */

    long _ntl_g2log(_ntl_gbigint a);
       /* number of bits in |a|; returns 0 if a = 0 */

    long _ntl_g2logs(long a);
        /* single-precision version of the above */


/********************************************************************

   Conversion

*********************************************************************/
        
    void _ntl_gzero(_ntl_gbigint *a);
       /* *a = 0;  */

    void _ntl_gone(_ntl_gbigint *a);
       /* *a = 1 */

    void _ntl_gintoz(long d, _ntl_gbigint *a);
       /* *a = d;  */


    void _ntl_guintoz(unsigned long d, _ntl_gbigint *a);
       /* *a = d;  space is allocated  */

    long _ntl_gtoint(_ntl_gbigint a);
       /* converts a to a long;  overflow results in value
          mod 2^{NTL_BITS_PER_LONG}. */

    unsigned long _ntl_gtouint(_ntl_gbigint a);
       /* converts a to a long;  overflow results in value
          mod 2^{NTL_BITS_PER_LONG}. */

   


    double _ntl_gdoub(_ntl_gbigint n);
       /* converts a to a double;  no overflow check */

    long _ntl_ground_correction(_ntl_gbigint a, long k, long residual);
       /* k >= 1, |a| >= 2^k, and residual is 0, 1, or -1.
          The result is what we should add to (a >> k) to round
          x = a/2^k to the nearest integer using IEEE-like rounding rules
          (i.e., round to nearest, and round to even to break ties).
          The result is either 0 or sign(a).
          If residual is not zero, it is as if x were replaced by
          x' = x + residual*2^{-(k+1)}.
          This can be used to break ties when x is exactly
          half way between two integers. */

    double _ntl_glog(_ntl_gbigint a);
       /* computes log(a), protecting against overflow */

    void _ntl_gdoubtoz(double a, _ntl_gbigint *x);