#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);
/* x = floor(a); */
/************************************************************************
Square roots
*************************************************************************/
long _ntl_gsqrts(long n);
/* return floor(sqrt(n)); error raised in n < 0 */
void _ntl_gsqrt(_ntl_gbigint n, _ntl_gbigint *r);
/* *r = floor(sqrt(n)); error raised in n < 0 */
/*********************************************************************
Exponentiation
**********************************************************************/
void _ntl_gexp(_ntl_gbigint a, long e, _ntl_gbigint *b);
/* *b = a^e; error raised if e < 0 */
void _ntl_gexps(long a, long e, _ntl_gbigint *b);
/* *b = a^e; error raised if e < 0 */
/*********************************************************************
Modular Arithmetic
Addition, subtraction, multiplication, squaring division, inversion,
and exponentiation modulo a positive modulus n, where all operands
(except for the exponent in exponentiation) and results are in the
range [0, n-1].
ALIAS RESTRICTION: output parameters should not alias n
***********************************************************************/
void _ntl_gaddmod(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint n, _ntl_gbigint *c);
/* *c = (a + b) % n */
void _ntl_gsubmod(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint n, _ntl_gbigint *c);
/* *c = (a - b) % n */
void _ntl_gsmulmod(_ntl_gbigint a, long b, _ntl_gbigint n, _ntl_gbigint *c);
/* *c = (a * b) % n */
void _ntl_gmulmod(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint n, _ntl_gbigint *c);
/* *c = (a * b) % n */
void _ntl_gsqmod(_ntl_gbigint a, _ntl_gbigint n, _ntl_gbigint *c);
/* *c = (a ^ 2) % n */
void _ntl_ginvmod(_ntl_gbigint a, _ntl_gbigint n, _ntl_gbigint *c);
/* *c = (1 / a) % n; error raised if gcd(b, n) != 1 */
void _ntl_gpowermod(_ntl_gbigint g, _ntl_gbigint e, _ntl_gbigint F,
_ntl_gbigint *h);
/* *b = (a ^ e) % n; */
/**************************************************************************
Euclidean Algorithms
***************************************************************************/
void _ntl_ggcd(_ntl_gbigint m1, _ntl_gbigint m2, _ntl_gbigint *r);
/* *r = greatest common divisor of m1 and m2;
uses binary gcd algorithm */
void _ntl_gexteucl(_ntl_gbigint a, _ntl_gbigint *xa,
_ntl_gbigint b, _ntl_gbigint *xb,
_ntl_gbigint *d);
/*
*d = a * *xa + b * *xb = gcd(a, b);
sets *d, *xa and *xb given a and b;
uses Lehmer`s trick
*/
long _ntl_ginv(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *c);
/*
if (a and b coprime)
{
*c = inv;
return(0);
}
else
{
*c = gcd(a, b);
return(1);
}
where inv is such that (inv * a) == 1 mod b;
error raised if a < 0 or b <= 0
*/
long _ntl_gxxratrecon(_ntl_gbigint x, _ntl_gbigint m,
_ntl_gbigint a_bound, _ntl_gbigint b_bound,
_ntl_gbigint *a, _ntl_gbigint *b);
/* rational reconstruction: see doc in ZZ.txt */
/**********************************************************************
Storage Allocation
These routines use malloc and free.
***********************************************************************/
void _ntl_gsetlength(_ntl_gbigint *v, long len);
/* Allocates enough space to hold a len-digit number,
where each digit has NTL_NBITS bits.
If space must be allocated, space for one extra digit
is always allocated. */
void _ntl_gfree(_ntl_gbigint *x);
/* Free's space held by x, and sets x back to 0. */
/*******************************************************************
Special routines
********************************************************************/
long _ntl_gsize(_ntl_gbigint n);
long _ntl_gisone(_ntl_gbigint n);
long _ntl_gsptest(_ntl_gbigint a);
long _ntl_gwsptest(_ntl_gbigint a);
long _ntl_gcrtinrange(_ntl_gbigint g, _ntl_gbigint a);
void _ntl_gfrombytes(_ntl_gbigint *x, const unsigned char *p, long n);
void _ntl_gbytesfromz(unsigned char *p, _ntl_gbigint a, long nn);
long _ntl_gblock_construct_alloc(_ntl_gbigint *x, long d, long n);
void _ntl_gblock_construct_set(_ntl_gbigint x, _ntl_gbigint *y, long i);
long _ntl_gblock_destroy(_ntl_gbigint x);
long _ntl_gblock_storage(long d);
void _ntl_gcrt_struct_init(void **crt_struct, long n, _ntl_gbigint p,
const long *primes);
void _ntl_gcrt_struct_insert(void *crt_struct, long i, _ntl_gbigint m);
void _ntl_gcrt_struct_free(void *crt_struct);
void _ntl_gcrt_struct_eval(void *crt_struct, _ntl_gbigint *t, const long *a);
long _ntl_gcrt_struct_special(void *crt_struct);
void _ntl_grem_struct_init(void **rem_struct, long n, _ntl_gbigint p,
const long *primes);
void _ntl_grem_struct_free(void *rem_struct);
void _ntl_grem_struct_eval(void *rem_struct, long *x, _ntl_gbigint a);
#if (defined(__cplusplus) && !defined(NTL_CXX_ONLY))
}
#endif
extern int _ntl_gmp_hack;
#define NTL_crt_struct_eval _ntl_gcrt_struct_eval
#define NTL_crt_struct_free _ntl_gcrt_struct_free
#define NTL_crt_struct_init _ntl_gcrt_struct_init
#define NTL_crt_struct_insert _ntl_gcrt_struct_insert
#define NTL_crt_struct_special _ntl_gcrt_struct_special
#define NTL_rem_struct_eval _ntl_grem_struct_eval
#define NTL_rem_struct_free _ntl_grem_struct_free
#define NTL_rem_struct_init _ntl_grem_struct_init
#define NTL_verylong _ntl_gbigint
#define NTL_z2log _ntl_g2log
#define NTL_zabs _ntl_gabs
#define NTL_zadd _ntl_gadd
#define NTL_zaddmod _ntl_gaddmod
#define NTL_zand _ntl_gand
#define NTL_zbit _ntl_gbit
#define NTL_zblock_construct_alloc _ntl_gblock_construct_alloc
#define NTL_zblock_construct_set _ntl_gblock_construct_set
#define NTL_zblock_destroy _ntl_gblock_destroy
#define NTL_zblock_storage _ntl_gblock_storage
#define NTL_zbytesfromz _ntl_gbytesfromz
#define NTL_zcompare _ntl_gcompare
#define NTL_zcopy _ntl_gcopy
#define NTL_zcrtinrange _ntl_gcrtinrange
#define NTL_zdiv _ntl_gdiv
#define NTL_zdoub _ntl_gdoub
#define NTL_zdoubtoz _ntl_gdoubtoz
#define NTL_zexp _ntl_gexp
#define NTL_zexps _ntl_gexps
#define NTL_zexteucl _ntl_gexteucl
#define NTL_zfree _ntl_gfree
#define NTL_zfrombytes _ntl_gfrombytes
#define NTL_zgcd _ntl_ggcd
#define NTL_zintoz _ntl_gintoz
#define NTL_zinv _ntl_ginv
#define NTL_zinvmod _ntl_ginvmod
#define NTL_zisone _ntl_gisone
#define NTL_ziszero _ntl_giszero
#define NTL_zlog _ntl_glog
#define NTL_zlowbits _ntl_glowbits
#define NTL_zlshift _ntl_glshift
#define NTL_zmakeodd _ntl_gmakeodd
#define NTL_zmod _ntl_gmod
#define NTL_zmul _ntl_gmul
#define NTL_zmulmod _ntl_gmulmod
#define NTL_znegate _ntl_gnegate
#define NTL_znumtwos _ntl_gnumtwos
#define NTL_zodd _ntl_godd
#define NTL_zone _ntl_gone
#define NTL_zor _ntl_gor
#define NTL_zpowermod _ntl_gpowermod
#define NTL_zquickmod _ntl_gquickmod
#define NTL_zround_correction _ntl_ground_correction
#define NTL_zrshift _ntl_grshift
#define NTL_zsadd _ntl_gsadd
#define NTL_zscompare _ntl_gscompare
#define NTL_zsdiv _ntl_gsdiv
#define NTL_zsetbit _ntl_gsetbit
#define NTL_zsetlength _ntl_gsetlength
#define NTL_zsign _ntl_gsign
#define NTL_zsize _ntl_gsize
#define NTL_zslowbits _ntl_gslowbits
#define NTL_zsmod _ntl_gsmod
#define NTL_zsmul _ntl_gsmul
#define NTL_zsmulmod _ntl_gsmulmod
#define NTL_zsptest _ntl_gsptest
#define NTL_zsq _ntl_gsq
#define NTL_zsqmod _ntl_gsqmod
#define NTL_zsqrt _ntl_gsqrt
#define NTL_zsqrts _ntl_gsqrts
#define NTL_zsub _ntl_gsub
#define NTL_zsubmod _ntl_gsubmod
#define NTL_zsubpos _ntl_gsubpos
#define NTL_zswap _ntl_gswap
#define NTL_zswitchbit _ntl_gswitchbit
#define NTL_ztoint _ntl_gtoint
#define NTL_ztouint _ntl_gtouint
#define NTL_zuintoz _ntl_guintoz
#define NTL_zweight _ntl_gweight
#define NTL_zweights _ntl_gweights
#define NTL_zwsptest _ntl_gwsptest
#define NTL_zxor _ntl_gxor
#define NTL_zxxratrecon _ntl_gxxratrecon
#define NTL_zzero _ntl_gzero
#define NTL_GMP_LIP
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