lip.h

应用密码学这本书的源代码

        * c gets 0 if b <= 0
        * p starts counting at 0
        \******************************************************************/

    long zsetbit(verylong *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
        * p starts counting at 0
        \******************************************************************/

    long zswitchbit(verylong *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
        \******************************************************************/

    long zreverses(long aa);
        /******************************************************************\
        * returns the bit reverse of |a|
        * i.e., zreverses(11001010) is 1010011
        \******************************************************************/

    void zreverse(verylong a, verylong *b);
        /******************************************************************\
        * b gets the bit reverse of |a|
	* i.e., zintoz(11,&a); zlshift(a,100,&a); zreverse(a,&b);
        *       produces b with value 13
        \******************************************************************/


/******************************************************************************\
*  Comparison, signs, copying, logarithms
\******************************************************************************/

    long zscompare(verylong a, long b);
        /******************************************************************\
        * if (a > b)
        *     return (1);
        * if (a == b)
        *     return (0);
        * if (a < b)
        *     return (-1);
        \******************************************************************/

    long zcompare(verylong a, verylong b);
        /******************************************************************\
        * if (a > b)
        *     return (1);
        * if (a == b)
        *     return (0);
        * if (a < b)
        *     return (-1);
        \******************************************************************/

    long ziszero (verylong a);
        /******************************************************************\
        * if (a == 0)
        *     return (1);
        * if (a != 0)
        *     return (0);
        \******************************************************************/


    long zsign(verylong a);
        /******************************************************************\
        * if (a > 0)
        *     return (1);
        * if (a == 0)
        *     return (0);
        * if (a < 0)
        *     return (-1);
        \******************************************************************/

    void zabs(verylong *a);
        /******************************************************************\
        * *a = abs(a);
        * 
        \******************************************************************/

    void znegate(verylong *a);
        /******************************************************************\
        * *a = -a;
        * 
        * has no effect on zero a
        \******************************************************************/

    void zcopy(verylong a, verylong *b);
        /******************************************************************\
        * *b = a;
        \******************************************************************/

    void zswap(verylong *a, verylong *b);
        /******************************************************************\
        * exchange values of *a and *b
        \******************************************************************/

    long z2logs(long a);
        /******************************************************************\
        * return (1 + log2(abs(a));
        * 
        * the number of binary bits to represent a,
        * returns 0 if a = 0
        \******************************************************************/

    long z2log(verylong a);
        /******************************************************************\
        * return (1 + log2(abs(a));
        * 
        * the number of binary bits to represent a,
        * returns 0 if a = 0
        \******************************************************************/


    double zln(verylong a);
        /******************************************************************\
        * return (approximation to the natural logarithm of |a|);
        * 
        * only for a != 0
        *
        * possible error message:
        *   non-positive argument in zln
        * result undefined if error occurs
        \******************************************************************/

    double zslog(verylong a, long b);
        /******************************************************************\
        * return (approximation of the logarithm of |a|, base b);
        * 
        * only for a != 0, b >= 2
        \******************************************************************/

    double zlog(verylong a, verylong b);
        /******************************************************************\
        * return (approximation of the logarithm of |a|, base b);
        * 
        * only for a != 0, b >= 2
        \******************************************************************/

    double zdlog(verylong a, double b);
        /******************************************************************\
        * return (approximation of the logarithm of |a|, base b);
        * 
        * only for a != 0, b > 1
        \******************************************************************/


/******************************************************************************\
*  Conversion
*
*  Conversion between very long ints and ordinary longs or doubles.
*  Conversion for very long ints to arbitrary basis and back.
\******************************************************************************/
        
    void zzero(verylong *a);
        /******************************************************************\
        * *a = 0;
        * 
        * allocated zero
        \******************************************************************/

    void zone(verylong *a);
        /******************************************************************\
        * *a = 1;
        * 
        \******************************************************************/

    void zintoz(long d, verylong *a);
        /******************************************************************\
        * *a = d;
        * 
        \******************************************************************/

    void zuintoz(unsigned long d, verylong *a);
        /******************************************************************\
        * *a = d;
        * 
        \******************************************************************/

    void zultoz(unsigned long row[], long len, verylong *a);
        /******************************************************************\
        * *a = sum row[i]X^i, sum from i=0 to len-1, where
        * X = 2^{CHARL*SIZEOFLONG}
        * to convert base 2^32 (or 2^64) representation to verylong 
        * 
        \******************************************************************/

    long ztoint(verylong a);
        /******************************************************************\
        * return (attempted conversion of a`s value to long);
        * no overflow check
        * 
        \******************************************************************/

    unsigned long ztouint(verylong a);
        /******************************************************************\
        * return (attempted conversion of |a|`s value to unsigned long);
        * no overflow check
        * 
        \******************************************************************/

    long ztoul(verylong a, unsigned long row[], long *len);
        /******************************************************************\
        * sets *len to m and row[i] such that
        * |a| = sum from i = 0 to i = m - 1 of row[i] * X ^ i,
        * with 0 <= row[i] < X = 2^{CHARL*SIZEOFLONG}
        * returns 1 if m <= *len on input (which should on input be
        * the length of row[]) returns 0 if *len on input is too small to
        * represent |a| in *len blocks
        \******************************************************************/

    long zstrtozbas(char *s, long b, verylong *a);
        /******************************************************************\
        * a gets the value of s whose characters are interpreted as base |b|
        * integers, for 0<|b|<=16. First character of s may be a `-` or a `_`
        * to indicate negative number. Reads until it finds a character that
        * cannot be correctly interpreted as a base |b| digit. Returns the
        * number of characters read (excluding the sign), returns 0 for
        * b zero, or |b| > 16.
        * 
        \******************************************************************/

    long zstrtoz(char *s, verylong *a);
        /******************************************************************\
        * as zstrtozbas with b = 10
        \******************************************************************/

    double zdoub(verylong n);
        /******************************************************************\
        * return (attempted conversion of a`s value to double);
        * 
        * no overflow check
        \******************************************************************/

    void zsbastoz(long base, long row[], long len, verylong *n);
        /******************************************************************\
        * *n = sum from i = 0 to i = len - 1 of row[i] * base ^ i
        * 
        \******************************************************************/

    void zbastoz(verylong base, verylong row[], long len, verylong *n);
        /******************************************************************\
        * *n = sum from i = 0 to i = len - 1 of row[i] * base ^ i
        * 
        \******************************************************************/

    long zstobas(verylong n, long base, long row[], long *len);
        /******************************************************************\
        * sets *len to m and row[i] such that |n| equals
        * sum from i = 0 to i = m - 1 of row[i] * |base| ^ i,
        * with 0 <= row[i] < |base|
        * returns 1 if m <= *len on input
        * (which should on input be the length of row[])
        * returns 0 if *len on input is too small to represent
        * n in *len blocks or if |base| <= 1
        \******************************************************************/

    long ztobas(verylong n, verylong base, verylong row[], long *len);
        /******************************************************************\
        * same as zstobas, but with a very long int base
        * 
        \******************************************************************/

    long zstosymbas(verylong n, long base, long row[], long *len);
        /******************************************************************\
        * same as zstobas, except that |row[i]| <= |base| / 2
        * 
        \******************************************************************/

    long ztosymbas(verylong n, verylong base, verylong row[], long *len);
        /******************************************************************\
        * same as zstosymbas, but with a very long int base
        * 
        \******************************************************************/


/******************************************************************************\
*  Non-modular exponentiation 
*
*  Exponentiation, squareroots  and arbitrary roots.
\******************************************************************************/

    void zsexp(verylong a, long e, verylong *b);
        /******************************************************************\
        * *b = a ^ e;
        * 
        * arguments cannot be the same,
        * e must be >= 0 if abs(a) != 1
        \******************************************************************/

    void zexp(verylong a, verylong e, verylong *b);
        /******************************************************************\
        * *b = a ^ e;
        * 
        * arguments cannot be the same,
        * e must be >= 0 if abs(a) != 1,
        * better be sure that you know what you`re 
        * doing before you call this
        *
        * possible error message:
        *   negative exponent in zexp
        * result undefined if error occurs
        \******************************************************************/

    long zsqrts(long n);
        /******************************************************************\
        * if (n > 0)
        *     return ([sqrt(n)]);
        * else
        *     return (0);
        \******************************************************************/

    long zsqrt(verylong n, verylong *r, verylong *dif);
        /******************************************************************\
        * *r = [sqrt(n)];
        * *dif = n - r ^ 2;
        * if (n perfect square)
        *     return (1)
        * else
        *     return (0)
        * 
        * n must be >= 0
        *
        * possible error message:
        *   negative argument in zsqrt
        * result undefined if error occurs
        \******************************************************************/

    long zroot(verylong a, long n, verylong *b);
        /******************************************************************\
        * *b = nth root of a;
        * 
	* if (n perfect dth root)
	*	return 1
	* else if (no dth root)
	*	return -1
	* else
	*	return 0