imath.c File Reference

#include "postgres.h"
#include "px.h"
#include "imath.h"

Include dependency graph for imath.c:

Go to the source code of this file.

Macros
#define	assert(TEST)   Assert(TEST)
#define	TRACEABLE_CLAMP   0
#define	TRACEABLE_FREE   0
#define	MP_CAP_DIGITS   1 /* flag bit to capitalize letter digits */
#define	CHECK(TEST)   assert(TEST)
#define	NRCHECK(TEST)   assert(TEST)
#define	MP_VALUE_DIGITS(V)   ((sizeof(V)+(sizeof(mp_digit)-1))/sizeof(mp_digit))
#define	ROUND_PREC(P)   ((mp_size)(2*(((P)+1)/2)))
#define	ZERO(P, S)   do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P);memset(p__,0,i__);}while(0)
#define	COPY(P, Q, S)
#define	REV(T, A, N)   do{T *u_=(A),*v_=u_+(N)-1;while(u_<v_){T xch=*u_;*u_++=*v_;*v_--=xch;}}while(0)
#define	CLAMP(Z)
#define	MIN(A, B)   ((B)<(A)?(B):(A))
#define	MAX(A, B)   ((B)>(A)?(B):(A))
#define	SWAP(T, A, B)   do{T t_=(A);A=(B);B=t_;}while(0)
#define	TEMP(K)   (temp + (K))
#define	SETUP(E, C)   do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0)
#define	CMPZ(Z)   (((Z)->used==1&&(Z)->digits[0]==0)?0:((Z)->sign==MP_NEG)?-1:1)
#define	UMUL(X, Y, Z)
#define	USQR(X, Z)
#define	UPPER_HALF(W)   ((mp_word)((W) >> MP_DIGIT_BIT))
#define	LOWER_HALF(W)   ((mp_digit)(W))
#define	HIGH_BIT_SET(W)   ((W) >> (MP_WORD_BIT - 1))
#define	ADD_WILL_OVERFLOW(W, V)   ((MP_WORD_MAX - (V)) < (W))
#define	s_free(P)   px_free(P)

Functions
static mp_digit *	s_alloc (mp_size num)
static int	s_pad (mp_int z, mp_size min)
static void	s_fake (mp_int z, int value, mp_digit vbuf[])
static int	s_cdig (mp_digit *da, mp_digit *db, mp_size len)
static int	s_vpack (int v, mp_digit t[])
static int	s_ucmp (mp_int a, mp_int b)
static int	s_vcmp (mp_int a, int v)
static mp_digit	s_uadd (mp_digit *da, mp_digit *db, mp_digit *dc, mp_size size_a, mp_size size_b)
static void	s_usub (mp_digit *da, mp_digit *db, mp_digit *dc, mp_size size_a, mp_size size_b)
static int	s_kmul (mp_digit *da, mp_digit *db, mp_digit *dc, mp_size size_a, mp_size size_b)
static void	s_umul (mp_digit *da, mp_digit *db, mp_digit *dc, mp_size size_a, mp_size size_b)
static int	s_ksqr (mp_digit *da, mp_digit *dc, mp_size size_a)
static void	s_usqr (mp_digit *da, mp_digit *dc, mp_size size_a)
static void	s_dadd (mp_int a, mp_digit b)
static void	s_dmul (mp_int a, mp_digit b)
static void	s_dbmul (mp_digit *da, mp_digit b, mp_digit *dc, mp_size size_a)
static mp_digit	s_ddiv (mp_int a, mp_digit b)
static void	s_qdiv (mp_int z, mp_size p2)
static void	s_qmod (mp_int z, mp_size p2)
static int	s_qmul (mp_int z, mp_size p2)
static int	s_qsub (mp_int z, mp_size p2)
static int	s_dp2k (mp_int z)
static int	s_isp2 (mp_int z)
static int	s_2expt (mp_int z, int k)
static int	s_norm (mp_int a, mp_int b)
static mp_result	s_brmu (mp_int z, mp_int m)
static int	s_reduce (mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2)
static mp_result	s_embar (mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
static mp_result	s_udiv (mp_int a, mp_int b)
static int	s_outlen (mp_int z, mp_size r)
static mp_size	s_inlen (int len, mp_size r)
static int	s_ch2val (char c, int r)
static char	s_val2ch (int v, int caps)
static void	s_2comp (unsigned char *buf, int len)
static mp_result	s_tobin (mp_int z, unsigned char *buf, int *limpos, int pad)
mp_size	mp_get_default_precision (void)
void	mp_set_default_precision (mp_size s)
mp_size	mp_get_multiply_threshold (void)
void	mp_set_multiply_threshold (mp_size s)
mp_result	mp_int_init (mp_int z)
mp_int	mp_int_alloc (void)
mp_result	mp_int_init_size (mp_int z, mp_size prec)
mp_result	mp_int_init_copy (mp_int z, mp_int old)
mp_result	mp_int_init_value (mp_int z, int value)
mp_result	mp_int_set_value (mp_int z, int value)
void	mp_int_clear (mp_int z)
void	mp_int_free (mp_int z)
mp_result	mp_int_copy (mp_int a, mp_int c)
void	mp_int_swap (mp_int a, mp_int c)
void	mp_int_zero (mp_int z)
mp_result	mp_int_abs (mp_int a, mp_int c)
mp_result	mp_int_neg (mp_int a, mp_int c)
mp_result	mp_int_add (mp_int a, mp_int b, mp_int c)
mp_result	mp_int_add_value (mp_int a, int value, mp_int c)
mp_result	mp_int_sub (mp_int a, mp_int b, mp_int c)
mp_result	mp_int_sub_value (mp_int a, int value, mp_int c)
mp_result	mp_int_mul (mp_int a, mp_int b, mp_int c)
mp_result	mp_int_mul_value (mp_int a, int value, mp_int c)
mp_result	mp_int_mul_pow2 (mp_int a, int p2, mp_int c)
mp_result	mp_int_sqr (mp_int a, mp_int c)
mp_result	mp_int_div (mp_int a, mp_int b, mp_int q, mp_int r)
mp_result	mp_int_mod (mp_int a, mp_int m, mp_int c)
mp_result	mp_int_div_value (mp_int a, int value, mp_int q, int *r)
mp_result	mp_int_div_pow2 (mp_int a, int p2, mp_int q, mp_int r)
mp_result	mp_int_expt (mp_int a, int b, mp_int c)
mp_result	mp_int_expt_value (int a, int b, mp_int c)
int	mp_int_compare (mp_int a, mp_int b)
int	mp_int_compare_unsigned (mp_int a, mp_int b)
int	mp_int_compare_zero (mp_int z)
int	mp_int_compare_value (mp_int z, int value)
mp_result	mp_int_exptmod (mp_int a, mp_int b, mp_int m, mp_int c)
mp_result	mp_int_exptmod_evalue (mp_int a, int value, mp_int m, mp_int c)
mp_result	mp_int_exptmod_bvalue (int value, mp_int b, mp_int m, mp_int c)
mp_result	mp_int_exptmod_known (mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
mp_result	mp_int_redux_const (mp_int m, mp_int c)
mp_result	mp_int_invmod (mp_int a, mp_int m, mp_int c)
mp_result	mp_int_gcd (mp_int a, mp_int b, mp_int c)
mp_result	mp_int_egcd (mp_int a, mp_int b, mp_int c, mp_int x, mp_int y)
int	mp_int_divisible_value (mp_int a, int v)
int	mp_int_is_pow2 (mp_int z)
mp_result	mp_int_sqrt (mp_int a, mp_int c)
mp_result	mp_int_to_int (mp_int z, int *out)
mp_result	mp_int_to_string (mp_int z, mp_size radix, char *str, int limit)
mp_result	mp_int_string_len (mp_int z, mp_size radix)
mp_result	mp_int_read_string (mp_int z, mp_size radix, const char *str)
mp_result	mp_int_read_cstring (mp_int z, mp_size radix, const char *str, char **end)
mp_result	mp_int_count_bits (mp_int z)
mp_result	mp_int_to_binary (mp_int z, unsigned char *buf, int limit)
mp_result	mp_int_read_binary (mp_int z, unsigned char *buf, int len)
mp_result	mp_int_binary_len (mp_int z)
mp_result	mp_int_to_unsigned (mp_int z, unsigned char *buf, int limit)
mp_result	mp_int_read_unsigned (mp_int z, unsigned char *buf, int len)
mp_result	mp_int_unsigned_len (mp_int z)
const char *	mp_error_string (mp_result res)
static mp_digit *	s_realloc (mp_digit *old, mp_size num)

Variables
const mp_result	MP_OK = 0
const mp_result	MP_FALSE = 0
const mp_result	MP_TRUE = -1
const mp_result	MP_MEMORY = -2
const mp_result	MP_RANGE = -3
const mp_result	MP_UNDEF = -4
const mp_result	MP_TRUNC = -5
const mp_result	MP_BADARG = -6
const mp_sign	MP_NEG = 1
const mp_sign	MP_ZPOS = 0
static const char *	s_unknown_err = "unknown result code"
static const char *	s_error_msg []
static const double	s_log2 []
static mp_size	default_precision = 64
static mp_size	multiply_threshold = 32
static mp_word	mp_flags = MP_CAP_DIGITS

Macro Definition Documentation

#define ADD_WILL_OVERFLOW	(		W,
			V
	)		((MP_WORD_MAX - (V)) < (W))

Definition at line 162 of file imath.c.

Referenced by s_usqr().

#define assert

(

TEST

)

Assert(TEST)

Definition at line 37 of file imath.c.

Referenced by addchr(), addrange(), allocarc(), bracket(), breakconstraintloop(), brenext(), caltdissect(), cbracket(), cbrdissect(), cclass_column_index(), ccondissect(), cdissect(), cfind(), cfindloop(), changearctarget(), citerdissect(), cleanup(), clearcvec(), cloneouts(), clonesuccessorstates(), colorcomplement(), combine(), compact(), copyins(), copyouts(), createarc(), crevcondissect(), creviterdissect(), delsub(), deltraverse(), destroystate(), duptraverse(), eclass(), element(), find(), findconstraintloop(), fixconstraintloops(), fixempties(), freearc(), freecnfa(), freecolor(), freelacons(), freestate(), generate_unaccent_rules::get_plain_letter(), generate_unaccent_rules::get_plain_letters(), getladfa(), getvacant(), IncreaseBuffer(), inet_cidr_pton_ipv4(), inet_net_pton_ipv4(), initialize(), lacon(), lexescape(), lexnest(), lexstart(), makesearch(), markst(), matchuntil(), mergeins(), miss(), moresubs(), moveins(), moveouts(), mp_int_alloc(), newarc(), newcolor(), newdfa(), NewMetaString(), newstate(), newsub(), next(), nfanode(), nfatree(), nonword(), numst(), okcolors(), parse(), parsebranch(), parseqatom(), pg_reg_colorisbegin(), pg_reg_colorisend(), pg_reg_getcharacters(), pg_reg_getcolor(), pg_reg_getfinalstate(), pg_reg_getinitialstate(), pg_reg_getnumcharacters(), pg_reg_getnumcolors(), pg_reg_getnumoutarcs(), pg_reg_getnumstates(), pg_reg_getoutarcs(), pg_regcomp(), pg_regexec(), pg_regprefix(), processlacon(), pull(), pullback(), push(), pushfwd(), s_alloc(), s_embar(), s_kmul(), s_qsub(), s_realloc(), s_udiv(), s_usqr(), s_usub(), s_val2ch(), scanplain(), shortest(), skip(), sortins(), sortouts(), specialcolors(), store_match(), subcolor(), subcolorhi(), subcoloronechr(), subcoloronerange(), subre(), subset(), uncolorchain(), word(), wordchrs(), and zaptreesubs().

#define CHECK

(

TEST

)

assert(TEST)

Definition at line 74 of file imath.c.

Referenced by mp_int_abs(), mp_int_add(), mp_int_compare(), mp_int_compare_value(), mp_int_copy(), mp_int_count_bits(), mp_int_div(), mp_int_div_pow2(), mp_int_egcd(), mp_int_expt(), mp_int_expt_value(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_gcd(), mp_int_init_copy(), mp_int_init_size(), mp_int_init_value(), mp_int_invmod(), mp_int_is_pow2(), mp_int_mul(), mp_int_mul_pow2(), mp_int_neg(), mp_int_read_binary(), mp_int_read_cstring(), mp_int_read_unsigned(), mp_int_redux_const(), mp_int_set_value(), mp_int_sqr(), mp_int_sqrt(), mp_int_string_len(), mp_int_sub(), mp_int_to_binary(), mp_int_to_int(), mp_int_to_string(), and mp_int_to_unsigned().

#define CLAMP

(

Z

)

Value:

do{mp_int z_=(Z);mp_size uz_=MP_USED(z_);mp_digit *dz_=MP_DIGITS(z_)+uz_-1;\
while(uz_ > 1 && (*dz_-- == 0)) --uz_;MP_USED(z_)=uz_;}while(0)

Definition at line 131 of file imath.c.

Referenced by mp_int_add(), mp_int_mul(), mp_int_read_cstring(), mp_int_sqr(), mp_int_sub(), s_ddiv(), s_qdiv(), s_qmod(), s_qmul(), s_qsub(), and s_udiv().

#define CMPZ

(

Z

)

(((Z)->used==1&&(Z)->digits[0]==0)?0:((Z)->sign==MP_NEG)?-1:1)

Definition at line 146 of file imath.c.

Referenced by mp_int_div(), mp_int_egcd(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_gcd(), mp_int_invmod(), mp_int_mod(), mp_int_neg(), mp_int_read_cstring(), mp_int_to_string(), and s_reduce().

#define COPY	(		P,
			Q,
			S
	)

Value:

do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P),*q__=(Q);\
memcpy(q__,p__,i__);}while(0)

Definition at line 120 of file imath.c.

Referenced by mp_int_copy(), mp_int_init_copy(), s_kmul(), and s_ksqr().

#define HIGH_BIT_SET

(

W

)

((W) >> (MP_WORD_BIT - 1))

Definition at line 161 of file imath.c.

Referenced by s_usqr().

#define LOWER_HALF

(

W

)

((mp_digit)(W))

Definition at line 160 of file imath.c.

Referenced by s_dadd(), s_dbmul(), s_dmul(), s_ksqr(), s_qsub(), s_uadd(), s_umul(), s_usqr(), and s_usub().

#define MAX	(		A,
			B
	)		((B)>(A)?(B):(A))

Definition at line 139 of file imath.c.

Referenced by mp_int_add(), mp_int_init_copy(), mp_int_init_size(), mp_int_mul(), mp_int_sqr(), and mp_int_sub().

#define MIN	(		A,
			B
	)		((B)<(A)?(B):(A))

Definition at line 138 of file imath.c.

Referenced by mp_int_egcd(), and mp_int_gcd().

#define MP_CAP_DIGITS   1 /* flag bit to capitalize letter digits */

Definition at line 70 of file imath.c.

Referenced by mp_int_to_string().

#define MP_VALUE_DIGITS

(

V

)

((sizeof(V)+(sizeof(mp_digit)-1))/sizeof(mp_digit))

Definition at line 109 of file imath.c.

Referenced by mp_int_add_value(), mp_int_div_value(), mp_int_exptmod_bvalue(), mp_int_exptmod_evalue(), mp_int_mul_value(), mp_int_set_value(), mp_int_sub_value(), s_fake(), and s_vcmp().

#define NRCHECK

(

TEST

)

assert(TEST)

Definition at line 75 of file imath.c.

Referenced by mp_int_compare_unsigned(), mp_int_compare_zero(), mp_int_free(), mp_int_zero(), and mp_set_default_precision().

#define REV	(		T,
			A,
			N
	)		do{T *u_=(A),*v_=u_+(N)-1;while(u_<v_){T xch=*u_;*u_++=*v_;*v_--=xch;}}while(0)

Definition at line 125 of file imath.c.

Referenced by s_tobin(), and s_udiv().

#define ROUND_PREC

(

P

)

((mp_size)(2*(((P)+1)/2)))

Definition at line 113 of file imath.c.

Referenced by mp_int_init_size(), mp_int_mul(), mp_int_sqr(), mp_set_default_precision(), and s_pad().

#define s_free

(

P

)

px_free(P)

Definition at line 182 of file imath.c.

Referenced by mp_int_clear(), mp_int_mul(), mp_int_sqr(), and s_kmul().

#define SETUP	(		E,
			C
	)		do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0)

Definition at line 143 of file imath.c.

Referenced by mp_int_div(), mp_int_egcd(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_sqrt(), and s_embar().

#define SWAP	(		T,
			A,
			B
	)		do{T t_=(A);A=(B);B=t_;}while(0)

Definition at line 140 of file imath.c.

Referenced by s_kmul(), and s_uadd().

#define TEMP

(

K

)

(temp + (K))

Definition at line 142 of file imath.c.

Referenced by mp_int_div(), mp_int_egcd(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_invmod(), mp_int_sqrt(), and s_embar().

#define TRACEABLE_CLAMP   0

Definition at line 38 of file imath.c.

#define TRACEABLE_FREE   0

Definition at line 39 of file imath.c.

#define UMUL	(		X,
			Y,
			Z
	)

Value:

do{mp_size ua_=MP_USED(X),ub_=MP_USED(Y);mp_size o_=ua_+ub_;\
ZERO(MP_DIGITS(Z),o_);\
(void) s_kmul(MP_DIGITS(X),MP_DIGITS(Y),MP_DIGITS(Z),ua_,ub_);\
MP_USED(Z)=o_;CLAMP(Z);}while(0)

Definition at line 149 of file imath.c.

Referenced by s_embar(), and s_reduce().

#define UPPER_HALF

(

W

)

((mp_word)((W) >> MP_DIGIT_BIT))

Definition at line 159 of file imath.c.

Referenced by s_dadd(), s_dbmul(), s_dmul(), s_ksqr(), s_qsub(), s_uadd(), s_umul(), s_usqr(), and s_usub().

#define USQR	(		X,
			Z
	)

Value:

do{mp_size ua_=MP_USED(X),o_=ua_+ua_;ZERO(MP_DIGITS(Z),o_);\
(void) s_ksqr(MP_DIGITS(X),MP_DIGITS(Z),ua_);MP_USED(Z)=o_;CLAMP(Z);}while(0)

Definition at line 155 of file imath.c.

Referenced by s_embar().

#define ZERO	(		P,
			S
	)		do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P);memset(p__,0,i__);}while(0)

Definition at line 116 of file imath.c.

Referenced by mp_int_mul(), mp_int_sqr(), s_2expt(), s_embar(), s_kmul(), s_ksqr(), s_qmul(), and s_udiv().

Function Documentation

const char* mp_error_string

(

mp_result

res

)

Definition at line 2259 of file imath.c.

References NULL, s_error_msg, and s_unknown_err.

{
    int         ix;

    if (res > 0)
        return s_unknown_err;

    res = -res;
    for (ix = 0; ix < res && s_error_msg[ix] != NULL; ++ix)
        ;

    if (s_error_msg[ix] != NULL)
        return s_error_msg[ix];
    else
        return s_unknown_err;
}

mp_size mp_get_default_precision

(

void

)

Definition at line 319 of file imath.c.

References default_precision.

{
    return default_precision;
}

mp_size mp_get_multiply_threshold

(

void

)

Definition at line 341 of file imath.c.

References multiply_threshold.

{
    return multiply_threshold;
}

mp_result mp_int_abs	(	mp_int	a,
		mp_int	c
	)

Definition at line 569 of file imath.c.

References CHECK, mp_int_copy(), MP_OK, MP_SIGN, MP_ZPOS, and NULL.

Referenced by mp_int_egcd(), and mp_int_gcd().

{
    mp_result   res;

    CHECK(a != NULL && c != NULL);

    if ((res = mp_int_copy(a, c)) != MP_OK)
        return res;

    MP_SIGN(c) = MP_ZPOS;
    return MP_OK;
}

mp_result mp_int_add	(	mp_int	a,
		mp_int	b,
		mp_int	c
	)

Definition at line 607 of file imath.c.

References CHECK, CLAMP, cmp(), mpz::digits, MAX, MP_DIGITS, MP_MEMORY, MP_OK, MP_SIGN, MP_USED, NULL, s_pad(), s_uadd(), s_ucmp(), and s_usub().

Referenced by mp_int_add_value(), mp_int_egcd(), mp_int_mod(), and mp_int_sqrt().

{
    mp_size     ua,
                ub,
                uc,
                max;

    CHECK(a != NULL && b != NULL && c != NULL);

    ua = MP_USED(a);
    ub = MP_USED(b);
    uc = MP_USED(c);
    max = MAX(ua, ub);

    if (MP_SIGN(a) == MP_SIGN(b))
    {
        /* Same sign -- add magnitudes, preserve sign of addends */
        mp_digit    carry;

        if (!s_pad(c, max))
            return MP_MEMORY;

        carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
        uc = max;

        if (carry)
        {
            if (!s_pad(c, max + 1))
                return MP_MEMORY;

            c->digits[max] = carry;
            ++uc;
        }

        MP_USED(c) = uc;
        MP_SIGN(c) = MP_SIGN(a);

    }
    else
    {
        /* Different signs -- subtract magnitudes, preserve sign of greater */
        mp_int      x,
                    y;
        int         cmp = s_ucmp(a, b); /* magnitude comparison, sign ignored */

        /* Set x to max(a, b), y to min(a, b) to simplify later code */
        if (cmp >= 0)
        {
            x = a;
            y = b;
        }
        else
        {
            x = b;
            y = a;
        }

        if (!s_pad(c, MP_USED(x)))
            return MP_MEMORY;

        /* Subtract smaller from larger */
        s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y));
        MP_USED(c) = MP_USED(x);
        CLAMP(c);

        /* Give result the sign of the larger */
        MP_SIGN(c) = MP_SIGN(x);
    }

    return MP_OK;
}

mp_result mp_int_add_value	(	mp_int	a,
		int	value,
		mp_int	c
	)

Definition at line 684 of file imath.c.

References mp_int_add(), MP_VALUE_DIGITS, and s_fake().

{
    mpz_t       vtmp;
    mp_digit    vbuf[MP_VALUE_DIGITS(value)];

    s_fake(&vtmp, value, vbuf);

    return mp_int_add(a, &vtmp, c);
}

mp_int mp_int_alloc

(

void

)

Definition at line 371 of file imath.c.

References mpz::alloc, assert, mpz::digits, NULL, px_alloc, mpz::sign, and mpz::used.

Referenced by mp_new().

{
    mp_int      out = px_alloc(sizeof(mpz_t));

    assert(out != NULL);
    out->digits = NULL;
    out->used = 0;
    out->alloc = 0;
    out->sign = 0;

    return out;
}

mp_result mp_int_binary_len

(

mp_int

z

)

Definition at line 2170 of file imath.c.

References mp_int_count_bits(), and mp_int_unsigned_len().

{
    mp_result   res = mp_int_count_bits(z);
    int         bytes = mp_int_unsigned_len(z);

    if (res <= 0)
        return res;

    bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT;

    /*
     * If the highest-order bit falls exactly on a byte boundary, we need to
     * pad with an extra byte so that the sign will be read correctly when
     * reading it back in.
     */
    if (bytes * CHAR_BIT == res)
        ++bytes;

    return bytes;
}

void mp_int_clear

(

mp_int

z

)

Definition at line 478 of file imath.c.

References MP_DIGITS, NULL, and s_free.

Referenced by mp_int_div(), mp_int_div_value(), mp_int_egcd(), mp_int_expt(), mp_int_expt_value(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_free(), mp_int_gcd(), mp_int_invmod(), mp_int_mod(), mp_int_sqrt(), mp_int_to_string(), s_embar(), and s_udiv().

{
    if (z == NULL)
        return;

    if (MP_DIGITS(z) != NULL)
    {
        s_free(MP_DIGITS(z));
        MP_DIGITS(z) = NULL;
    }
}

int mp_int_compare	(	mp_int	a,
		mp_int	b
	)

Definition at line 1242 of file imath.c.

References CHECK, cmp(), MP_SIGN, MP_ZPOS, NULL, and s_ucmp().

Referenced by mp_int_egcd(), and s_reduce().

{
    mp_sign     sa;

    CHECK(a != NULL && b != NULL);

    sa = MP_SIGN(a);
    if (sa == MP_SIGN(b))
    {
        int         cmp = s_ucmp(a, b);

        /*
         * If they're both zero or positive, the normal comparison applies; if
         * both negative, the sense is reversed.
         */
        if (sa == MP_ZPOS)
            return cmp;
        else
            return -cmp;

    }
    else
    {
        if (sa == MP_ZPOS)
            return 1;
        else
            return -1;
    }
}

int mp_int_compare_unsigned	(	mp_int	a,
		mp_int	b
	)

Definition at line 1277 of file imath.c.

References NRCHECK, NULL, and s_ucmp().

Referenced by mp_int_sqrt().

{
    NRCHECK(a != NULL && b != NULL);

    return s_ucmp(a, b);
}

int mp_int_compare_value	(	mp_int	z,
		int	value
	)

Definition at line 1306 of file imath.c.

References CHECK, cmp(), MP_NEG, MP_SIGN, MP_ZPOS, NULL, and s_vcmp().

Referenced by mp_int_invmod(), and mp_int_to_int().

{
    mp_sign     vsign = (value < 0) ? MP_NEG : MP_ZPOS;
    int         cmp;

    CHECK(z != NULL);

    if (vsign == MP_SIGN(z))
    {
        cmp = s_vcmp(z, value);

        if (vsign == MP_ZPOS)
            return cmp;
        else
            return -cmp;
    }
    else
    {
        if (value < 0)
            return 1;
        else
            return -1;
    }
}

int mp_int_compare_zero

(

mp_int

z

)

Definition at line 1289 of file imath.c.

References mpz::digits, MP_SIGN, MP_USED, MP_ZPOS, NRCHECK, and NULL.

Referenced by mp_int_mul().

{
    NRCHECK(z != NULL);

    if (MP_USED(z) == 1 && z->digits[0] == 0)
        return 0;
    else if (MP_SIGN(z) == MP_ZPOS)
        return 1;
    else
        return -1;
}

mp_result mp_int_copy	(	mp_int	a,
		mp_int	c
	)

Definition at line 510 of file imath.c.

References CHECK, COPY, MP_DIGITS, MP_MEMORY, MP_OK, MP_SIGN, MP_USED, NULL, and s_pad().

Referenced by mp_int_abs(), mp_int_div(), mp_int_div_pow2(), mp_int_egcd(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_gcd(), mp_int_invmod(), mp_int_mod(), mp_int_mul_pow2(), mp_int_neg(), mp_int_sqrt(), s_embar(), s_reduce(), and s_udiv().

{
    CHECK(a != NULL && c != NULL);

    if (a != c)
    {
        mp_size     ua = MP_USED(a);
        mp_digit   *da,
                   *dc;

        if (!s_pad(c, ua))
            return MP_MEMORY;

        da = MP_DIGITS(a);
        dc = MP_DIGITS(c);
        COPY(da, dc, ua);

        MP_USED(c) = ua;
        MP_SIGN(c) = MP_SIGN(a);
    }

    return MP_OK;
}

mp_result mp_int_count_bits

(

mp_int

z

)

Definition at line 2073 of file imath.c.

References CHECK, mpz::digits, MP_DIGIT_BIT, MP_USED, and NULL.

Referenced by bn_to_mpi(), mp_int_binary_len(), mp_int_unsigned_len(), mpi_to_bn(), pgp_elgamal_encrypt(), and s_outlen().

{
    mp_size     nbits = 0,
                uz;
    mp_digit    d;

    CHECK(z != NULL);

    uz = MP_USED(z);
    if (uz == 1 && z->digits[0] == 0)
        return 1;

    --uz;
    nbits = uz * MP_DIGIT_BIT;
    d = z->digits[uz];

    while (d != 0)
    {
        d >>= 1;
        ++nbits;
    }

    return nbits;
}

mp_result mp_int_div	(	mp_int	a,
		mp_int	b,
		mp_int	q,
		mp_int	r
	)

Definition at line 955 of file imath.c.

References CHECK, cmp(), CMPZ, mpz::digits, mp_int_clear(), mp_int_copy(), mp_int_init_copy(), mp_int_zero(), MP_NEG, MP_OK, MP_SIGN, MP_UNDEF, MP_ZPOS, NULL, s_isp2(), s_qdiv(), s_qmod(), s_ucmp(), s_udiv(), SETUP, and TEMP.

Referenced by mp_int_div_value(), mp_int_mod(), mp_int_sqrt(), and s_brmu().

{
    int         cmp,
                last = 0,
                lg;
    mp_result   res = MP_OK;
    mpz_t       temp[2];
    mp_int      qout,
                rout;
    mp_sign     sa = MP_SIGN(a),
                sb = MP_SIGN(b);

    CHECK(a != NULL && b != NULL && q != r);

    if (CMPZ(b) == 0)
        return MP_UNDEF;
    else if ((cmp = s_ucmp(a, b)) < 0)
    {
        /*
         * If |a| < |b|, no division is required: q = 0, r = a
         */
        if (r && (res = mp_int_copy(a, r)) != MP_OK)
            return res;

        if (q)
            mp_int_zero(q);

        return MP_OK;
    }
    else if (cmp == 0)
    {
        /*
         * If |a| = |b|, no division is required: q = 1 or -1, r = 0
         */
        if (r)
            mp_int_zero(r);

        if (q)
        {
            mp_int_zero(q);
            q->digits[0] = 1;

            if (sa != sb)
                MP_SIGN(q) = MP_NEG;
        }

        return MP_OK;
    }

    /*
     * When |a| > |b|, real division is required.  We need someplace to store
     * quotient and remainder, but q and r are allowed to be NULL or to
     * overlap with the inputs.
     */
    if ((lg = s_isp2(b)) < 0)
    {
        if (q && b != q && (res = mp_int_copy(a, q)) == MP_OK)
        {
            qout = q;
        }
        else
        {
            qout = TEMP(last);
            SETUP(mp_int_init_copy(TEMP(last), a), last);
        }

        if (r && a != r && (res = mp_int_copy(b, r)) == MP_OK)
        {
            rout = r;
        }
        else
        {
            rout = TEMP(last);
            SETUP(mp_int_init_copy(TEMP(last), b), last);
        }

        if ((res = s_udiv(qout, rout)) != MP_OK)
            goto CLEANUP;
    }
    else
    {
        if (q && (res = mp_int_copy(a, q)) != MP_OK)
            goto CLEANUP;
        if (r && (res = mp_int_copy(a, r)) != MP_OK)
            goto CLEANUP;

        if (q)
            s_qdiv(q, (mp_size) lg);
        qout = q;
        if (r)
            s_qmod(r, (mp_size) lg);
        rout = r;
    }

    /* Recompute signs for output */
    if (rout)
    {
        MP_SIGN(rout) = sa;
        if (CMPZ(rout) == 0)
            MP_SIGN(rout) = MP_ZPOS;
    }
    if (qout)
    {
        MP_SIGN(qout) = (sa == sb) ? MP_ZPOS : MP_NEG;
        if (CMPZ(qout) == 0)
            MP_SIGN(qout) = MP_ZPOS;
    }

    if (q && (res = mp_int_copy(qout, q)) != MP_OK)
        goto CLEANUP;
    if (r && (res = mp_int_copy(rout, r)) != MP_OK)
        goto CLEANUP;

CLEANUP:
    while (--last >= 0)
        mp_int_clear(TEMP(last));

    return res;
}

mp_result mp_int_div_pow2	(	mp_int	a,
		int	p2,
		mp_int	q,
		mp_int	r
	)

Definition at line 1146 of file imath.c.

References CHECK, mp_int_copy(), MP_OK, NULL, s_qdiv(), and s_qmod().

Referenced by mp_int_sqrt().

{
    mp_result   res = MP_OK;

    CHECK(a != NULL && p2 >= 0 && q != r);

    if (q != NULL && (res = mp_int_copy(a, q)) == MP_OK)
        s_qdiv(q, (mp_size) p2);

    if (res == MP_OK && r != NULL && (res = mp_int_copy(a, r)) == MP_OK)
        s_qmod(r, (mp_size) p2);

    return res;
}

mp_result mp_int_div_value	(	mp_int	a,
		int	value,
		mp_int	q,
		int *	r
	)

Definition at line 1119 of file imath.c.

References mp_int_clear(), mp_int_div(), mp_int_init(), mp_int_to_int(), MP_OK, MP_VALUE_DIGITS, and s_fake().

Referenced by mp_int_divisible_value().

{
    mpz_t       vtmp,
                rtmp;
    mp_digit    vbuf[MP_VALUE_DIGITS(value)];
    mp_result   res;

    if ((res = mp_int_init(&rtmp)) != MP_OK)
        return res;
    s_fake(&vtmp, value, vbuf);

    if ((res = mp_int_div(a, &vtmp, q, &rtmp)) != MP_OK)
        goto CLEANUP;

    if (r)
        (void) mp_int_to_int(&rtmp, r); /* can't fail */

CLEANUP:
    mp_int_clear(&rtmp);
    return res;
}

int mp_int_divisible_value	(	mp_int	a,
		int	v
	)

Definition at line 1781 of file imath.c.

References mp_int_div_value(), MP_OK, and NULL.

{
    int         rem = 0;

    if (mp_int_div_value(a, v, NULL, &rem) != MP_OK)
        return 0;

    return rem == 0;
}

mp_result mp_int_egcd	(	mp_int	a,
		mp_int	b,
		mp_int	c,
		mp_int	x,
		mp_int	y
	)

Definition at line 1631 of file imath.c.

References CHECK, CMPZ, MIN, mp_int_abs(), mp_int_add(), mp_int_clear(), mp_int_compare(), mp_int_copy(), mp_int_init(), mp_int_init_copy(), mp_int_is_even, mp_int_is_odd, mp_int_set_value(), mp_int_sub(), mp_int_zero(), MP_MEMORY, MP_OK, MP_SIGN, MP_UNDEF, MP_ZPOS, NULL, s_dp2k(), s_qdiv(), s_qmul(), SETUP, and TEMP.

Referenced by mp_int_invmod().

{
    int         k,
                last = 0,
                ca,
                cb;
    mpz_t       temp[8];
    mp_result   res;

    CHECK(a != NULL && b != NULL && c != NULL &&
          (x != NULL || y != NULL));

    ca = CMPZ(a);
    cb = CMPZ(b);
    if (ca == 0 && cb == 0)
        return MP_UNDEF;
    else if (ca == 0)
    {
        if ((res = mp_int_abs(b, c)) != MP_OK)
            return res;
        mp_int_zero(x);
        (void) mp_int_set_value(y, 1);
        return MP_OK;
    }
    else if (cb == 0)
    {
        if ((res = mp_int_abs(a, c)) != MP_OK)
            return res;
        (void) mp_int_set_value(x, 1);
        mp_int_zero(y);
        return MP_OK;
    }

    /*
     * Initialize temporaries: A:0, B:1, C:2, D:3, u:4, v:5, ou:6, ov:7
     */
    for (last = 0; last < 4; ++last)
    {
        if ((res = mp_int_init(TEMP(last))) != MP_OK)
            goto CLEANUP;
    }
    TEMP(0)->digits[0] = 1;
    TEMP(3)->digits[0] = 1;

    SETUP(mp_int_init_copy(TEMP(4), a), last);
    SETUP(mp_int_init_copy(TEMP(5), b), last);

    /* We will work with absolute values here */
    MP_SIGN(TEMP(4)) = MP_ZPOS;
    MP_SIGN(TEMP(5)) = MP_ZPOS;

    {                           /* Divide out common factors of 2 from u and v */
        int         div2_u = s_dp2k(TEMP(4)),
                    div2_v = s_dp2k(TEMP(5));

        k = MIN(div2_u, div2_v);
        s_qdiv(TEMP(4), k);
        s_qdiv(TEMP(5), k);
    }

    SETUP(mp_int_init_copy(TEMP(6), TEMP(4)), last);
    SETUP(mp_int_init_copy(TEMP(7), TEMP(5)), last);

    for (;;)
    {
        while (mp_int_is_even(TEMP(4)))
        {
            s_qdiv(TEMP(4), 1);

            if (mp_int_is_odd(TEMP(0)) || mp_int_is_odd(TEMP(1)))
            {
                if ((res = mp_int_add(TEMP(0), TEMP(7), TEMP(0))) != MP_OK)
                    goto CLEANUP;
                if ((res = mp_int_sub(TEMP(1), TEMP(6), TEMP(1))) != MP_OK)
                    goto CLEANUP;
            }

            s_qdiv(TEMP(0), 1);
            s_qdiv(TEMP(1), 1);
        }

        while (mp_int_is_even(TEMP(5)))
        {
            s_qdiv(TEMP(5), 1);

            if (mp_int_is_odd(TEMP(2)) || mp_int_is_odd(TEMP(3)))
            {
                if ((res = mp_int_add(TEMP(2), TEMP(7), TEMP(2))) != MP_OK)
                    goto CLEANUP;
                if ((res = mp_int_sub(TEMP(3), TEMP(6), TEMP(3))) != MP_OK)
                    goto CLEANUP;
            }

            s_qdiv(TEMP(2), 1);
            s_qdiv(TEMP(3), 1);
        }

        if (mp_int_compare(TEMP(4), TEMP(5)) >= 0)
        {
            if ((res = mp_int_sub(TEMP(4), TEMP(5), TEMP(4))) != MP_OK)
                goto CLEANUP;
            if ((res = mp_int_sub(TEMP(0), TEMP(2), TEMP(0))) != MP_OK)
                goto CLEANUP;
            if ((res = mp_int_sub(TEMP(1), TEMP(3), TEMP(1))) != MP_OK)
                goto CLEANUP;
        }
        else
        {
            if ((res = mp_int_sub(TEMP(5), TEMP(4), TEMP(5))) != MP_OK)
                goto CLEANUP;
            if ((res = mp_int_sub(TEMP(2), TEMP(0), TEMP(2))) != MP_OK)
                goto CLEANUP;
            if ((res = mp_int_sub(TEMP(3), TEMP(1), TEMP(3))) != MP_OK)
                goto CLEANUP;
        }

        if (CMPZ(TEMP(4)) == 0)
        {
            if (x && (res = mp_int_copy(TEMP(2), x)) != MP_OK)
                goto CLEANUP;
            if (y && (res = mp_int_copy(TEMP(3), y)) != MP_OK)
                goto CLEANUP;
            if (c)
            {
                if (!s_qmul(TEMP(5), k))
                {
                    res = MP_MEMORY;
                    goto CLEANUP;
                }

                res = mp_int_copy(TEMP(5), c);
            }

            break;
        }
    }

CLEANUP:
    while (--last >= 0)
        mp_int_clear(TEMP(last));

    return res;
}

mp_result mp_int_expt	(	mp_int	a,
		int	b,
		mp_int	c
	)

Definition at line 1166 of file imath.c.

References CHECK, mp_int_clear(), mp_int_init_copy(), mp_int_mul(), mp_int_set_value(), mp_int_sqr(), MP_OK, and NULL.

{
    mpz_t       t;
    mp_result   res;
    unsigned int v = abs(b);

    CHECK(b >= 0 && c != NULL);

    if ((res = mp_int_init_copy(&t, a)) != MP_OK)
        return res;

    (void) mp_int_set_value(c, 1);
    while (v != 0)
    {
        if (v & 1)
        {
            if ((res = mp_int_mul(c, &t, c)) != MP_OK)
                goto CLEANUP;
        }

        v >>= 1;
        if (v == 0)
            break;

        if ((res = mp_int_sqr(&t, &t)) != MP_OK)
            goto CLEANUP;
    }

CLEANUP:
    mp_int_clear(&t);
    return res;
}

mp_result mp_int_expt_value	(	int	a,
		int	b,
		mp_int	c
	)

Definition at line 1204 of file imath.c.

References CHECK, mp_int_clear(), mp_int_init_value(), mp_int_mul(), mp_int_set_value(), mp_int_sqr(), MP_OK, and NULL.

{
    mpz_t       t;
    mp_result   res;
    unsigned int v = abs(b);

    CHECK(b >= 0 && c != NULL);

    if ((res = mp_int_init_value(&t, a)) != MP_OK)
        return res;

    (void) mp_int_set_value(c, 1);
    while (v != 0)
    {
        if (v & 1)
        {
            if ((res = mp_int_mul(c, &t, c)) != MP_OK)
                goto CLEANUP;
        }

        v >>= 1;
        if (v == 0)
            break;

        if ((res = mp_int_sqr(&t, &t)) != MP_OK)
            goto CLEANUP;
    }

CLEANUP:
    mp_int_clear(&t);
    return res;
}

mp_result mp_int_exptmod	(	mp_int	a,
		mp_int	b,
		mp_int	m,
		mp_int	c
	)

Definition at line 1336 of file imath.c.

References CHECK, CMPZ, mp_int_clear(), mp_int_copy(), mp_int_init_size(), mp_int_mod(), MP_OK, MP_RANGE, MP_UNDEF, MP_USED, NULL, s_brmu(), s_embar(), SETUP, and TEMP.

Referenced by mp_int_exptmod_bvalue(), mp_int_exptmod_evalue(), pgp_elgamal_decrypt(), pgp_elgamal_encrypt(), pgp_rsa_decrypt(), and pgp_rsa_encrypt().

{
    mp_result   res;
    mp_size     um;
    mpz_t       temp[3];
    mp_int      s;
    int         last = 0;

    CHECK(a != NULL && b != NULL && c != NULL && m != NULL);

    /* Zero moduli and negative exponents are not considered. */
    if (CMPZ(m) == 0)
        return MP_UNDEF;
    if (CMPZ(b) < 0)
        return MP_RANGE;

    um = MP_USED(m);
    SETUP(mp_int_init_size(TEMP(0), 2 * um), last);
    SETUP(mp_int_init_size(TEMP(1), 2 * um), last);

    if (c == b || c == m)
    {
        SETUP(mp_int_init_size(TEMP(2), 2 * um), last);
        s = TEMP(2);
    }
    else
    {
        s = c;
    }

    if ((res = mp_int_mod(a, m, TEMP(0))) != MP_OK)
        goto CLEANUP;

    if ((res = s_brmu(TEMP(1), m)) != MP_OK)
        goto CLEANUP;

    if ((res = s_embar(TEMP(0), b, m, TEMP(1), s)) != MP_OK)
        goto CLEANUP;

    res = mp_int_copy(s, c);

CLEANUP:
    while (--last >= 0)
        mp_int_clear(TEMP(last));

    return res;
}

mp_result mp_int_exptmod_bvalue	(	int	value,
		mp_int	b,
		mp_int	m,
		mp_int	c
	)

Definition at line 1404 of file imath.c.

References mp_int_exptmod(), MP_VALUE_DIGITS, and s_fake().

{
    mpz_t       vtmp;
    mp_digit    vbuf[MP_VALUE_DIGITS(value)];

    s_fake(&vtmp, value, vbuf);

    return mp_int_exptmod(&vtmp, b, m, c);
}

mp_result mp_int_exptmod_evalue	(	mp_int	a,
		int	value,
		mp_int	m,
		mp_int	c
	)

Definition at line 1389 of file imath.c.

References mp_int_exptmod(), MP_VALUE_DIGITS, and s_fake().

{
    mpz_t       vtmp;
    mp_digit    vbuf[MP_VALUE_DIGITS(value)];

    s_fake(&vtmp, value, vbuf);

    return mp_int_exptmod(a, &vtmp, m, c);
}

mp_result mp_int_exptmod_known	(	mp_int	a,
		mp_int	b,
		mp_int	m,
		mp_int	mu,
		mp_int	c
	)

Definition at line 1420 of file imath.c.

References CHECK, CMPZ, mp_int_clear(), mp_int_copy(), mp_int_init_size(), mp_int_mod(), MP_OK, MP_RANGE, MP_UNDEF, MP_USED, s_embar(), SETUP, and TEMP.

{
    mp_result   res;
    mp_size     um;
    mpz_t       temp[2];
    mp_int      s;
    int         last = 0;

    CHECK(a && b && m && c);

    /* Zero moduli and negative exponents are not considered. */
    if (CMPZ(m) == 0)
        return MP_UNDEF;
    if (CMPZ(b) < 0)
        return MP_RANGE;

    um = MP_USED(m);
    SETUP(mp_int_init_size(TEMP(0), 2 * um), last);

    if (c == b || c == m)
    {
        SETUP(mp_int_init_size(TEMP(1), 2 * um), last);
        s = TEMP(1);
    }
    else
    {
        s = c;
    }

    if ((res = mp_int_mod(a, m, TEMP(0))) != MP_OK)
        goto CLEANUP;

    if ((res = s_embar(TEMP(0), b, m, mu, s)) != MP_OK)
        goto CLEANUP;

    res = mp_int_copy(s, c);

CLEANUP:
    while (--last >= 0)
        mp_int_clear(TEMP(last));

    return res;
}

void mp_int_free

(

mp_int

z

)

Definition at line 495 of file imath.c.

References mpz::digits, mp_int_clear(), NRCHECK, NULL, and px_free.

Referenced by mp_clear_free().

{
    NRCHECK(z != NULL);

    if (z->digits != NULL)
        mp_int_clear(z);

    px_free(z);
}

mp_result mp_int_gcd	(	mp_int	a,
		mp_int	b,
		mp_int	c
	)

Definition at line 1536 of file imath.c.

References CHECK, CMPZ, MIN, mp_int_abs(), mp_int_clear(), mp_int_copy(), mp_int_init(), mp_int_init_copy(), mp_int_is_odd, mp_int_neg(), mp_int_sub(), MP_MEMORY, MP_OK, MP_SIGN, MP_UNDEF, MP_ZPOS, NULL, s_dp2k(), s_qdiv(), and s_qmul().

{
    int         ca,
                cb,
                k = 0;
    mpz_t       u,
                v,
                t;
    mp_result   res;

    CHECK(a != NULL && b != NULL && c != NULL);

    ca = CMPZ(a);
    cb = CMPZ(b);
    if (ca == 0 && cb == 0)
        return MP_UNDEF;
    else if (ca == 0)
        return mp_int_abs(b, c);
    else if (cb == 0)
        return mp_int_abs(a, c);

    if ((res = mp_int_init(&t)) != MP_OK)
        return res;
    if ((res = mp_int_init_copy(&u, a)) != MP_OK)
        goto U;
    if ((res = mp_int_init_copy(&v, b)) != MP_OK)
        goto V;

    MP_SIGN(&u) = MP_ZPOS;
    MP_SIGN(&v) = MP_ZPOS;

    {                           /* Divide out common factors of 2 from u and v */
        int         div2_u = s_dp2k(&u),
                    div2_v = s_dp2k(&v);

        k = MIN(div2_u, div2_v);
        s_qdiv(&u, (mp_size) k);
        s_qdiv(&v, (mp_size) k);
    }

    if (mp_int_is_odd(&u))
    {
        if ((res = mp_int_neg(&v, &t)) != MP_OK)
            goto CLEANUP;
    }
    else
    {
        if ((res = mp_int_copy(&u, &t)) != MP_OK)
            goto CLEANUP;
    }

    for (;;)
    {
        s_qdiv(&t, s_dp2k(&t));

        if (CMPZ(&t) > 0)
        {
            if ((res = mp_int_copy(&t, &u)) != MP_OK)
                goto CLEANUP;
        }
        else
        {
            if ((res = mp_int_neg(&t, &v)) != MP_OK)
                goto CLEANUP;
        }

        if ((res = mp_int_sub(&u, &v, &t)) != MP_OK)
            goto CLEANUP;

        if (CMPZ(&t) == 0)
            break;
    }

    if ((res = mp_int_abs(&u, c)) != MP_OK)
        goto CLEANUP;
    if (!s_qmul(c, (mp_size) k))
        res = MP_MEMORY;

CLEANUP:
    mp_int_clear(&v);
V:  mp_int_clear(&u);
U:  mp_int_clear(&t);

    return res;
}

mp_result mp_int_init

(

mp_int

z

)

Definition at line 361 of file imath.c.

References default_precision, and mp_int_init_size().

Referenced by mp_int_div_value(), mp_int_egcd(), mp_int_gcd(), mp_int_init_value(), mp_int_invmod(), mp_int_mod(), and mp_int_sqrt().

{
    return mp_int_init_size(z, default_precision);
}

mp_result mp_int_init_copy	(	mp_int	z,
		mp_int	old
	)

Definition at line 412 of file imath.c.

References CHECK, COPY, default_precision, MAX, MP_DIGITS, mp_int_init_size(), MP_OK, MP_SIGN, MP_USED, and NULL.

Referenced by mp_int_div(), mp_int_egcd(), mp_int_expt(), mp_int_gcd(), mp_int_sqrt(), and mp_int_to_string().

{
    mp_result   res;
    mp_size     uold,
                target;

    CHECK(z != NULL && old != NULL);

    uold = MP_USED(old);
    target = MAX(uold, default_precision);

    if ((res = mp_int_init_size(z, target)) != MP_OK)
        return res;

    MP_USED(z) = uold;
    MP_SIGN(z) = MP_SIGN(old);
    COPY(MP_DIGITS(old), MP_DIGITS(z), uold);

    return MP_OK;
}

mp_result mp_int_init_size	(	mp_int	z,
		mp_size	prec
	)

Definition at line 389 of file imath.c.

References CHECK, default_precision, mpz::digits, MAX, MP_ALLOC, MP_DIGITS, MP_MEMORY, MP_OK, MP_SIGN, MP_USED, MP_ZPOS, NULL, ROUND_PREC, and s_alloc().

Referenced by mp_int_exptmod(), mp_int_exptmod_known(), mp_int_init(), mp_int_init_copy(), mp_new(), s_embar(), and s_udiv().

{
    CHECK(z != NULL);

    prec = (mp_size) ROUND_PREC(prec);
    prec = MAX(prec, default_precision);

    if ((MP_DIGITS(z) = s_alloc(prec)) == NULL)
        return MP_MEMORY;

    z->digits[0] = 0;
    MP_USED(z) = 1;
    MP_ALLOC(z) = prec;
    MP_SIGN(z) = MP_ZPOS;

    return MP_OK;
}

mp_result mp_int_init_value	(	mp_int	z,
		int	value
	)

Definition at line 438 of file imath.c.

References CHECK, mp_int_init(), mp_int_set_value(), MP_OK, and NULL.

Referenced by mp_int_expt_value().

{
    mp_result   res;

    CHECK(z != NULL);

    if ((res = mp_int_init(z)) != MP_OK)
        return res;

    return mp_int_set_value(z, value);
}

mp_result mp_int_invmod	(	mp_int	a,
		mp_int	m,
		mp_int	c
	)

Definition at line 1481 of file imath.c.

References CHECK, CMPZ, mp_int_clear(), mp_int_compare_value(), mp_int_copy(), mp_int_egcd(), mp_int_init(), mp_int_mod(), mp_int_sub(), MP_NEG, MP_OK, MP_RANGE, MP_SIGN, MP_UNDEF, NULL, and TEMP.

Referenced by pgp_elgamal_decrypt().

{
    mp_result   res;
    mp_sign     sa;
    int         last = 0;
    mpz_t       temp[2];

    CHECK(a != NULL && m != NULL && c != NULL);

    if (CMPZ(a) == 0 || CMPZ(m) <= 0)
        return MP_RANGE;

    sa = MP_SIGN(a);            /* need this for the result later */

    for (last = 0; last < 2; ++last)
        if ((res = mp_int_init(TEMP(last))) != MP_OK)
            goto CLEANUP;

    if ((res = mp_int_egcd(a, m, TEMP(0), TEMP(1), NULL)) != MP_OK)
        goto CLEANUP;

    if (mp_int_compare_value(TEMP(0), 1) != 0)
    {
        res = MP_UNDEF;
        goto CLEANUP;
    }

    /* It is first necessary to constrain the value to the proper range */
    if ((res = mp_int_mod(TEMP(1), m, TEMP(1))) != MP_OK)
        goto CLEANUP;

    /*
     * Now, if 'a' was originally negative, the value we have is actually the
     * magnitude of the negative representative; to get the positive value we
     * have to subtract from the modulus.  Otherwise, the value is okay as it
     * stands.
     */
    if (sa == MP_NEG)
        res = mp_int_sub(m, TEMP(1), c);
    else
        res = mp_int_copy(TEMP(1), c);

CLEANUP:
    while (--last >= 0)
        mp_int_clear(TEMP(last));

    return res;
}

int mp_int_is_pow2

(

mp_int

z

)

Definition at line 1796 of file imath.c.

References CHECK, NULL, and s_isp2().

{
    CHECK(z != NULL);

    return s_isp2(z);
}

mp_result mp_int_mod	(	mp_int	a,
		mp_int	m,
		mp_int	c
	)

Definition at line 1080 of file imath.c.

References CMPZ, mp_int_add(), mp_int_clear(), mp_int_copy(), mp_int_div(), mp_int_init(), MP_OK, and NULL.

Referenced by mp_int_exptmod(), mp_int_exptmod_known(), mp_int_invmod(), and mp_modmul().

{
    mp_result   res;
    mpz_t       tmp;
    mp_int      out;

    if (m == c)
    {
        if ((res = mp_int_init(&tmp)) != MP_OK)
            return res;

        out = &tmp;
    }
    else
    {
        out = c;
    }

    if ((res = mp_int_div(a, m, NULL, out)) != MP_OK)
        goto CLEANUP;

    if (CMPZ(out) < 0)
        res = mp_int_add(out, m, c);
    else
        res = mp_int_copy(out, c);

CLEANUP:
    if (out != c)
        mp_int_clear(&tmp);

    return res;
}

mp_result mp_int_mul	(	mp_int	a,
		mp_int	b,
		mp_int	c
	)

Definition at line 794 of file imath.c.

References CHECK, CLAMP, default_precision, MAX, MP_ALLOC, MP_DIGITS, mp_int_compare_zero(), mp_int_zero(), MP_MEMORY, MP_NEG, MP_OK, MP_SIGN, MP_USED, MP_ZPOS, NULL, ROUND_PREC, s_alloc(), s_free, s_kmul(), s_pad(), and ZERO.

Referenced by mp_int_expt(), mp_int_expt_value(), mp_int_mul_value(), and mp_modmul().

{
    mp_digit   *out;
    mp_size     osize,
                ua,
                ub,
                p = 0;
    mp_sign     osign;

    CHECK(a != NULL && b != NULL && c != NULL);

    /* If either input is zero, we can shortcut multiplication */
    if (mp_int_compare_zero(a) == 0 || mp_int_compare_zero(b) == 0)
    {
        mp_int_zero(c);
        return MP_OK;
    }

    /* Output is positive if inputs have same sign, otherwise negative */
    osign = (MP_SIGN(a) == MP_SIGN(b)) ? MP_ZPOS : MP_NEG;

    /*
     * If the output is not equal to any of the inputs, we'll write the
     * results there directly; otherwise, allocate a temporary space.
     */
    ua = MP_USED(a);
    ub = MP_USED(b);
    osize = MAX(ua, ub);
    osize = 4 * ((osize + 1) / 2);

    if (c == a || c == b)
    {
        p = ROUND_PREC(osize);
        p = MAX(p, default_precision);

        if ((out = s_alloc(p)) == NULL)
            return MP_MEMORY;
    }
    else
    {
        if (!s_pad(c, osize))
            return MP_MEMORY;

        out = MP_DIGITS(c);
    }
    ZERO(out, osize);

    if (!s_kmul(MP_DIGITS(a), MP_DIGITS(b), out, ua, ub))
        return MP_MEMORY;

    /*
     * If we allocated a new buffer, get rid of whatever memory c was already
     * using, and fix up its fields to reflect that.
     */
    if (out != MP_DIGITS(c))
    {
        s_free(MP_DIGITS(c));
        MP_DIGITS(c) = out;
        MP_ALLOC(c) = p;
    }

    MP_USED(c) = osize;         /* might not be true, but we'll fix it ... */
    CLAMP(c);                   /* ... right here */
    MP_SIGN(c) = osign;

    return MP_OK;
}

mp_result mp_int_mul_pow2	(	mp_int	a,
		int	p2,
		mp_int	c
	)

Definition at line 882 of file imath.c.

References CHECK, mp_int_copy(), MP_MEMORY, MP_OK, NULL, and s_qmul().

{
    mp_result   res;

    CHECK(a != NULL && c != NULL && p2 >= 0);

    if ((res = mp_int_copy(a, c)) != MP_OK)
        return res;

    if (s_qmul(c, (mp_size) p2))
        return MP_OK;
    else
        return MP_MEMORY;
}

mp_result mp_int_mul_value	(	mp_int	a,
		int	value,
		mp_int	c
	)

Definition at line 867 of file imath.c.

References mp_int_mul(), MP_VALUE_DIGITS, and s_fake().

{
    mpz_t       vtmp;
    mp_digit    vbuf[MP_VALUE_DIGITS(value)];

    s_fake(&vtmp, value, vbuf);

    return mp_int_mul(a, &vtmp, c);
}

mp_result mp_int_neg	(	mp_int	a,
		mp_int	c
	)

Definition at line 587 of file imath.c.

References CHECK, CMPZ, mp_int_copy(), MP_OK, MP_SIGN, and NULL.

Referenced by mp_int_gcd().

{
    mp_result   res;

    CHECK(a != NULL && c != NULL);

    if ((res = mp_int_copy(a, c)) != MP_OK)
        return res;

    if (CMPZ(c) != 0)
        MP_SIGN(c) = 1 - MP_SIGN(a);

    return MP_OK;
}

mp_result mp_int_read_binary	(	mp_int	z,
		unsigned char *	buf,
		int	len
	)

Definition at line 2125 of file imath.c.

References CHECK, i, MP_DIGIT_BIT, MP_DIGITS, mp_int_zero(), MP_MEMORY, MP_NEG, MP_OK, MP_SIGN, NULL, s_2comp(), s_pad(), and s_qmul().

{
    mp_size     need,
                i;
    unsigned char *tmp;
    mp_digit   *dz;

    CHECK(z != NULL && buf != NULL && len > 0);

    /* Figure out how many digits are needed to represent this value */
    need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT;
    if (!s_pad(z, need))
        return MP_MEMORY;

    mp_int_zero(z);

    /*
     * If the high-order bit is set, take the 2's complement before reading
     * the value (it will be restored afterward)
     */
    if (buf[0] >> (CHAR_BIT - 1))
    {
        MP_SIGN(z) = MP_NEG;
        s_2comp(buf, len);
    }

    dz = MP_DIGITS(z);
    for (tmp = buf, i = len; i > 0; --i, ++tmp)
    {
        s_qmul(z, (mp_size) CHAR_BIT);
        *dz |= *tmp;
    }

    /* Restore 2's complement if we took it before */
    if (MP_SIGN(z) == MP_NEG)
        s_2comp(buf, len);

    return MP_OK;
}

mp_result mp_int_read_cstring	(	mp_int	z,
		mp_size	radix,
		const char *	str,
		char **	end
	)

Definition at line 2004 of file imath.c.

References CHECK, CLAMP, CMPZ, mpz::digits, MP_MAX_RADIX, MP_MEMORY, MP_NEG, MP_OK, MP_RANGE, MP_SIGN, MP_TRUNC, MP_USED, MP_ZPOS, NULL, s_ch2val(), s_dadd(), s_dmul(), s_inlen(), and s_pad().

Referenced by mp_int_read_string().

{
    int         ch;

    CHECK(z != NULL && str != NULL);

    if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
        return MP_RANGE;

    /* Skip leading whitespace */
    while (isspace((unsigned char) *str))
        ++str;

    /* Handle leading sign tag (+/-, positive default) */
    switch (*str)
    {
        case '-':
            MP_SIGN(z) = MP_NEG;
            ++str;
            break;
        case '+':
            ++str;              /* fallthrough */
        default:
            MP_SIGN(z) = MP_ZPOS;
            break;
    }

    /* Skip leading zeroes */
    while ((ch = s_ch2val(*str, radix)) == 0)
        ++str;

    /* Make sure there is enough space for the value */
    if (!s_pad(z, s_inlen(strlen(str), radix)))
        return MP_MEMORY;

    MP_USED(z) = 1;
    z->digits[0] = 0;

    while (*str != '\0' && ((ch = s_ch2val(*str, radix)) >= 0))
    {
        s_dmul(z, (mp_digit) radix);
        s_dadd(z, (mp_digit) ch);
        ++str;
    }

    CLAMP(z);

    /* Override sign for zero, even if negative specified. */
    if (CMPZ(z) == 0)
        MP_SIGN(z) = MP_ZPOS;

    if (end != NULL)
        *end = (char *) str;

    /*
     * Return a truncation error if the string has unprocessed characters
     * remaining, so the caller can tell if the whole string was done
     */
    if (*str != '\0')
        return MP_TRUNC;
    else
        return MP_OK;
}

mp_result mp_int_read_string	(	mp_int	z,
		mp_size	radix,
		const char *	str
	)

Definition at line 1993 of file imath.c.

References mp_int_read_cstring(), and NULL.

{
    return mp_int_read_cstring(z, radix, str, NULL);

}

mp_result mp_int_read_unsigned	(	mp_int	z,
		unsigned char *	buf,
		int	len
	)

Definition at line 2210 of file imath.c.

References CHECK, i, MP_DIGIT_BIT, MP_DIGITS, mp_int_zero(), MP_MEMORY, MP_OK, NULL, s_pad(), and s_qmul().

Referenced by mp_px_rand(), and mpi_to_bn().

{
    mp_size     need,
                i;
    unsigned char *tmp;
    mp_digit   *dz;

    CHECK(z != NULL && buf != NULL && len > 0);

    /* Figure out how many digits are needed to represent this value */
    need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT;
    if (!s_pad(z, need))
        return MP_MEMORY;

    mp_int_zero(z);

    dz = MP_DIGITS(z);
    for (tmp = buf, i = len; i > 0; --i, ++tmp)
    {
        (void) s_qmul(z, CHAR_BIT);
        *dz |= *tmp;
    }

    return MP_OK;
}

mp_result mp_int_redux_const	(	mp_int	m,
		mp_int	c
	)

Definition at line 1469 of file imath.c.

References CHECK, NULL, and s_brmu().

{
    CHECK(m != NULL && c != NULL && m != c);

    return s_brmu(c, m);
}

mp_result mp_int_set_value	(	mp_int	z,
		int	value
	)

Definition at line 455 of file imath.c.

References CHECK, MP_DIGITS, MP_MEMORY, MP_NEG, MP_OK, MP_SIGN, MP_USED, MP_VALUE_DIGITS, MP_ZPOS, NULL, s_pad(), and s_vpack().

Referenced by mp_int_egcd(), mp_int_expt(), mp_int_expt_value(), mp_int_init_value(), and s_embar().

{
    mp_size     ndig;

    CHECK(z != NULL);

    /* How many digits to copy */
    ndig = (mp_size) MP_VALUE_DIGITS(value);

    if (!s_pad(z, ndig))
        return MP_MEMORY;

    MP_USED(z) = (mp_size) s_vpack(value, MP_DIGITS(z));
    MP_SIGN(z) = (value < 0) ? MP_NEG : MP_ZPOS;

    return MP_OK;
}

mp_result mp_int_sqr	(	mp_int	a,
		mp_int	c
	)

Definition at line 902 of file imath.c.

References CHECK, CLAMP, default_precision, MAX, MP_ALLOC, MP_DIGITS, MP_MEMORY, MP_OK, MP_SIGN, MP_USED, MP_ZPOS, NULL, ROUND_PREC, s_alloc(), s_free, s_ksqr(), s_pad(), and ZERO.

Referenced by mp_int_expt(), mp_int_expt_value(), and mp_int_sqrt().

{
    mp_digit   *out;
    mp_size     osize,
                p = 0;

    CHECK(a != NULL && c != NULL);

    /* Get a temporary buffer big enough to hold the result */
    osize = (mp_size) 4 * ((MP_USED(a) + 1) / 2);

    if (a == c)
    {
        p = ROUND_PREC(osize);
        p = MAX(p, default_precision);

        if ((out = s_alloc(p)) == NULL)
            return MP_MEMORY;
    }
    else
    {
        if (!s_pad(c, osize))
            return MP_MEMORY;

        out = MP_DIGITS(c);
    }
    ZERO(out, osize);

    s_ksqr(MP_DIGITS(a), out, MP_USED(a));

    /*
     * Get rid of whatever memory c was already using, and fix up its fields
     * to reflect the new digit array it's using
     */
    if (out != MP_DIGITS(c))
    {
        s_free(MP_DIGITS(c));
        MP_DIGITS(c) = out;
        MP_ALLOC(c) = p;
    }

    MP_USED(c) = osize;         /* might not be true, but we'll fix it ... */
    CLAMP(c);                   /* ... right here */
    MP_SIGN(c) = MP_ZPOS;

    return MP_OK;
}

mp_result mp_int_sqrt	(	mp_int	a,
		mp_int	c
	)

Definition at line 1808 of file imath.c.

References CHECK, mp_int_add(), mp_int_clear(), mp_int_compare_unsigned(), mp_int_copy(), mp_int_div(), mp_int_div_pow2(), mp_int_init(), mp_int_init_copy(), mp_int_sqr(), mp_int_sub_value(), MP_NEG, MP_OK, MP_SIGN, MP_UNDEF, NULL, SETUP, and TEMP.

{
    mp_result   res = MP_OK;
    mpz_t       temp[2];
    int         last = 0;

    CHECK(a != NULL && c != NULL);

    /* The square root of a negative value does not exist in the integers. */
    if (MP_SIGN(a) == MP_NEG)
        return MP_UNDEF;

    SETUP(mp_int_init_copy(TEMP(last), a), last);
    SETUP(mp_int_init(TEMP(last)), last);

    for (;;)
    {
        if ((res = mp_int_sqr(TEMP(0), TEMP(1))) != MP_OK)
            goto CLEANUP;

        if (mp_int_compare_unsigned(a, TEMP(1)) == 0)
            break;

        if ((res = mp_int_copy(a, TEMP(1))) != MP_OK)
            goto CLEANUP;
        if ((res = mp_int_div(TEMP(1), TEMP(0), TEMP(1), NULL)) != MP_OK)
            goto CLEANUP;
        if ((res = mp_int_add(TEMP(0), TEMP(1), TEMP(1))) != MP_OK)
            goto CLEANUP;
        if ((res = mp_int_div_pow2(TEMP(1), 1, TEMP(1), NULL)) != MP_OK)
            goto CLEANUP;

        if (mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0)
            break;
        if ((res = mp_int_sub_value(TEMP(0), 1, TEMP(0))) != MP_OK)
            goto CLEANUP;
        if (mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0)
            break;

        if ((res = mp_int_copy(TEMP(1), TEMP(0))) != MP_OK)
            goto CLEANUP;
    }

    res = mp_int_copy(TEMP(0), c);

CLEANUP:
    while (--last >= 0)
        mp_int_clear(TEMP(last));

    return res;
}

mp_result mp_int_string_len	(	mp_int	z,
		mp_size	radix
	)

Definition at line 1969 of file imath.c.

References CHECK, MP_MAX_RADIX, MP_NEG, MP_RANGE, MP_SIGN, NULL, and s_outlen().

{
    int         len;

    CHECK(z != NULL);

    if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
        return MP_RANGE;

    len = s_outlen(z, radix) + 1;   /* for terminator */

    /* Allow for sign marker on negatives */
    if (MP_SIGN(z) == MP_NEG)
        len += 1;

    return len;
}

mp_result mp_int_sub	(	mp_int	a,
		mp_int	b,
		mp_int	c
	)

Definition at line 699 of file imath.c.

References CHECK, CLAMP, cmp(), mpz::digits, MAX, MP_DIGITS, MP_MEMORY, MP_NEG, MP_OK, MP_SIGN, MP_USED, MP_ZPOS, NULL, s_pad(), s_uadd(), s_ucmp(), and s_usub().

Referenced by mp_int_egcd(), mp_int_gcd(), mp_int_invmod(), mp_int_sub_value(), s_reduce(), and s_udiv().

{
    mp_size     ua,
                ub,
                uc,
                max;

    CHECK(a != NULL && b != NULL && c != NULL);

    ua = MP_USED(a);
    ub = MP_USED(b);
    uc = MP_USED(c);
    max = MAX(ua, ub);

    if (MP_SIGN(a) != MP_SIGN(b))
    {
        /* Different signs -- add magnitudes and keep sign of a */
        mp_digit    carry;

        if (!s_pad(c, max))
            return MP_MEMORY;

        carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
        uc = max;

        if (carry)
        {
            if (!s_pad(c, max + 1))
                return MP_MEMORY;

            c->digits[max] = carry;
            ++uc;
        }

        MP_USED(c) = uc;
        MP_SIGN(c) = MP_SIGN(a);

    }
    else
    {
        /* Same signs -- subtract magnitudes */
        mp_int      x,
                    y;
        mp_sign     osign;
        int         cmp = s_ucmp(a, b);

        if (!s_pad(c, max))
            return MP_MEMORY;

        if (cmp >= 0)
        {
            x = a;
            y = b;
            osign = MP_ZPOS;
        }
        else
        {
            x = b;
            y = a;
            osign = MP_NEG;
        }

        if (MP_SIGN(a) == MP_NEG && cmp != 0)
            osign = 1 - osign;

        s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y));
        MP_USED(c) = MP_USED(x);
        CLAMP(c);

        MP_SIGN(c) = osign;
    }

    return MP_OK;
}

mp_result mp_int_sub_value	(	mp_int	a,
		int	value,
		mp_int	c
	)

Definition at line 779 of file imath.c.

References mp_int_sub(), MP_VALUE_DIGITS, and s_fake().

Referenced by mp_int_sqrt().

{
    mpz_t       vtmp;
    mp_digit    vbuf[MP_VALUE_DIGITS(value)];

    s_fake(&vtmp, value, vbuf);

    return mp_int_sub(a, &vtmp, c);
}

void mp_int_swap	(	mp_int	a,
		mp_int	c
	)

Definition at line 539 of file imath.c.

{
    if (a != c)
    {
        mpz_t       tmp = *a;

        *a = *c;
        *c = tmp;
    }
}

mp_result mp_int_to_binary	(	mp_int	z,
		unsigned char *	buf,
		int	limit
	)

Definition at line 2103 of file imath.c.

References CHECK, MP_NEG, MP_SIGN, NULL, s_2comp(), and s_tobin().

{
    static const int PAD_FOR_2C = 1;

    mp_result   res;
    int         limpos = limit;

    CHECK(z != NULL && buf != NULL);

    res = s_tobin(z, buf, &limpos, PAD_FOR_2C);

    if (MP_SIGN(z) == MP_NEG)
        s_2comp(buf, limpos);

    return res;
}

mp_result mp_int_to_int	(	mp_int	z,
		int *	out
	)

Definition at line 1865 of file imath.c.

References CHECK, MP_DIGIT_BIT, MP_DIGITS, mp_int_compare_value(), MP_NEG, MP_OK, MP_RANGE, MP_SIGN, MP_USED, MP_ZPOS, and NULL.

Referenced by mp_int_div_value().

{
    unsigned int uv = 0;
    mp_size     uz;
    mp_digit   *dz;
    mp_sign     sz;

    CHECK(z != NULL);

    /* Make sure the value is representable as an int */
    sz = MP_SIGN(z);
    if ((sz == MP_ZPOS && mp_int_compare_value(z, INT_MAX) > 0) ||
        mp_int_compare_value(z, INT_MIN) < 0)
        return MP_RANGE;

    uz = MP_USED(z);
    dz = MP_DIGITS(z) + uz - 1;

    while (uz > 0)
    {
        uv <<= MP_DIGIT_BIT / 2;
        uv = (uv << (MP_DIGIT_BIT / 2)) | *dz--;
        --uz;
    }

    if (out)
        *out = (sz == MP_NEG) ? -(int) uv : (int) uv;

    return MP_OK;
}

mp_result mp_int_to_string	(	mp_int	z,
		mp_size	radix,
		char *	str,
		int	limit
	)

Definition at line 1901 of file imath.c.

References CHECK, cmp(), CMPZ, MP_CAP_DIGITS, mp_flags, mp_int_clear(), mp_int_init_copy(), MP_MAX_RADIX, MP_NEG, MP_OK, MP_RANGE, MP_SIGN, MP_TRUNC, NULL, s_ddiv(), and s_val2ch().

{
    mp_result   res;
    int         cmp = 0;

    CHECK(z != NULL && str != NULL && limit >= 2);

    if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
        return MP_RANGE;

    if (CMPZ(z) == 0)
    {
        *str++ = s_val2ch(0, mp_flags & MP_CAP_DIGITS);
    }
    else
    {
        mpz_t       tmp;
        char       *h,
                   *t;

        if ((res = mp_int_init_copy(&tmp, z)) != MP_OK)
            return res;

        if (MP_SIGN(z) == MP_NEG)
        {
            *str++ = '-';
            --limit;
        }
        h = str;

        /* Generate digits in reverse order until finished or limit reached */
        for ( /* */ ; limit > 0; --limit)
        {
            mp_digit    d;

            if ((cmp = CMPZ(&tmp)) == 0)
                break;

            d = s_ddiv(&tmp, (mp_digit) radix);
            *str++ = s_val2ch(d, mp_flags & MP_CAP_DIGITS);
        }
        t = str - 1;

        /* Put digits back in correct output order */
        while (h < t)
        {
            char        tc = *h;

            *h++ = *t;
            *t-- = tc;
        }

        mp_int_clear(&tmp);
    }

    *str = '\0';
    if (cmp == 0)
        return MP_OK;
    else
        return MP_TRUNC;
}

mp_result mp_int_to_unsigned	(	mp_int	z,
		unsigned char *	buf,
		int	limit
	)

Definition at line 2196 of file imath.c.

References CHECK, NULL, and s_tobin().

Referenced by bn_to_mpi().

{
    static const int NO_PADDING = 0;

    CHECK(z != NULL && buf != NULL);

    return s_tobin(z, buf, &limit, NO_PADDING);
}

mp_result mp_int_unsigned_len

(

mp_int

z

)

Definition at line 2241 of file imath.c.

References mp_int_count_bits().

Referenced by mp_int_binary_len().

{
    mp_result   res = mp_int_count_bits(z);
    int         bytes;

    if (res <= 0)
        return res;

    bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT;

    return bytes;
}

void mp_int_zero

(

mp_int

z

)

Definition at line 555 of file imath.c.

References mpz::digits, MP_SIGN, MP_USED, MP_ZPOS, NRCHECK, and NULL.

Referenced by mp_int_div(), mp_int_egcd(), mp_int_mul(), mp_int_read_binary(), mp_int_read_unsigned(), and s_qdiv().

{
    NRCHECK(z != NULL);

    z->digits[0] = 0;
    MP_USED(z) = 1;
    MP_SIGN(z) = MP_ZPOS;
}

void mp_set_default_precision

(

mp_size

s

)

Definition at line 329 of file imath.c.

References default_precision, NRCHECK, and ROUND_PREC.

{
    NRCHECK(s > 0);

    default_precision = (mp_size) ROUND_PREC(s);
}

void mp_set_multiply_threshold

(

mp_size

s

)

Definition at line 351 of file imath.c.

References multiply_threshold.

{
    multiply_threshold = s;
}

static void s_2comp ( unsigned char *  buf, int  len  )

static

Definition at line 3579 of file imath.c.

References i.

Referenced by mp_int_read_binary(), and mp_int_to_binary().

{
    int         i;
    unsigned short s = 1;

    for (i = len - 1; i >= 0; --i)
    {
        unsigned char c = ~buf[i];

        s = c + s;
        c = s & UCHAR_MAX;
        s >>= CHAR_BIT;

        buf[i] = c;
    }

    /* last carry out is ignored */
}

static int s_2expt ( mp_int  z, int  k  )

static

Definition at line 3175 of file imath.c.

References MP_DIGIT_BIT, MP_DIGITS, MP_USED, s_pad(), and ZERO.

Referenced by s_brmu().

{
    mp_size     ndig,
                rest;
    mp_digit   *dz;

    ndig = (k + MP_DIGIT_BIT) / MP_DIGIT_BIT;
    rest = k % MP_DIGIT_BIT;

    if (!s_pad(z, ndig))
        return 0;

    dz = MP_DIGITS(z);
    ZERO(dz, ndig);
    *(dz + ndig - 1) = (1 << rest);
    MP_USED(z) = ndig;

    return 1;
}

static mp_digit * s_alloc ( mp_size  num )

static

Definition at line 2284 of file imath.c.

References assert, NULL, and px_alloc.

Referenced by mp_int_init_size(), mp_int_mul(), mp_int_sqr(), s_kmul(), and s_ksqr().

{
    mp_digit   *out = px_alloc(num * sizeof(mp_digit));

    assert(out != NULL);        /* for debugging */

    return out;
}

static mp_result s_brmu ( mp_int  z, mp_int  m  )

static

Definition at line 3226 of file imath.c.

References MP_DIGIT_BIT, mp_int_div(), MP_MEMORY, MP_USED, NULL, s_2expt(), and s_pad().

Referenced by mp_int_exptmod(), and mp_int_redux_const().

{
    mp_size     um = MP_USED(m) * 2;

    if (!s_pad(z, um))
        return MP_MEMORY;

    s_2expt(z, MP_DIGIT_BIT * um);
    return mp_int_div(z, m, z, NULL);
}

static int s_cdig ( mp_digit *  da, mp_digit *  db, mp_size  len  )

static

Definition at line 2379 of file imath.c.

Referenced by s_ucmp(), and s_vcmp().

{
    mp_digit   *dat = da + len - 1,
               *dbt = db + len - 1;

    for ( /* */ ; len != 0; --len, --dat, --dbt)
    {
        if (*dat > *dbt)
            return 1;
        else if (*dat < *dbt)
            return -1;
    }

    return 0;
}

static int s_ch2val ( char  c, int  r  )

static

Definition at line 3538 of file imath.c.

Referenced by mp_int_read_cstring().

{
    int         out;

    if (isdigit((unsigned char) c))
        out = c - '0';
    else if (r > 10 && isalpha((unsigned char) c))
        out = toupper((unsigned char) c) - 'A' + 10;
    else
        return -1;

    return (out >= r) ? -1 : out;
}

static void s_dadd ( mp_int  a, mp_digit  b  )

static

Definition at line 2808 of file imath.c.

References LOWER_HALF, MP_DIGITS, MP_USED, and UPPER_HALF.

Referenced by mp_int_read_cstring().

{
    mp_word     w = 0;
    mp_digit   *da = MP_DIGITS(a);
    mp_size     ua = MP_USED(a);

    w = (mp_word) *da + b;
    *da++ = LOWER_HALF(w);
    w = UPPER_HALF(w);

    for (ua -= 1; ua > 0; --ua, ++da)
    {
        w = (mp_word) *da + w;

        *da = LOWER_HALF(w);
        w = UPPER_HALF(w);
    }

    if (w)
    {
        *da = (mp_digit) w;
        MP_USED(a) += 1;
    }
}

static void s_dbmul ( mp_digit *  da, mp_digit  b, mp_digit *  dc, mp_size  size_a  )

static

Definition at line 2864 of file imath.c.

References LOWER_HALF, and UPPER_HALF.

Referenced by s_udiv().

{
    mp_word     w = 0;

    while (size_a > 0)
    {
        w = (mp_word) *da++ * (mp_word) b + w;

        *dc++ = LOWER_HALF(w);
        w = UPPER_HALF(w);
        --size_a;
    }

    if (w)
        *dc = LOWER_HALF(w);
}

static mp_digit s_ddiv ( mp_int  a, mp_digit  b  )

static

Definition at line 2886 of file imath.c.

References CLAMP, MP_DIGIT_BIT, MP_DIGITS, and MP_USED.

Referenced by mp_int_to_string().

{
    mp_word     w = 0,
                qdigit;
    mp_size     ua = MP_USED(a);
    mp_digit   *da = MP_DIGITS(a) + ua - 1;

    for ( /* */ ; ua > 0; --ua, --da)
    {
        w = (w << MP_DIGIT_BIT) | *da;

        if (w >= b)
        {
            qdigit = w / b;
            w = w % b;
        }
        else
        {
            qdigit = 0;
        }

        *da = (mp_digit) qdigit;
    }

    CLAMP(a);
    return (mp_digit) w;
}

static void s_dmul ( mp_int  a, mp_digit  b  )

static

Definition at line 2838 of file imath.c.

References LOWER_HALF, MP_DIGITS, MP_USED, and UPPER_HALF.

Referenced by mp_int_read_cstring().

{
    mp_word     w = 0;
    mp_digit   *da = MP_DIGITS(a);
    mp_size     ua = MP_USED(a);

    while (ua > 0)
    {
        w = (mp_word) *da * b + w;
        *da++ = LOWER_HALF(w);
        w = UPPER_HALF(w);
        --ua;
    }

    if (w)
    {
        *da = (mp_digit) w;
        MP_USED(a) += 1;
    }
}

static int s_dp2k ( mp_int  z )

static

Definition at line 3113 of file imath.c.

References MP_DIGIT_BIT, MP_DIGITS, and MP_USED.

Referenced by mp_int_egcd(), and mp_int_gcd().

{
    int         k = 0;
    mp_digit   *dp = MP_DIGITS(z),
                d;

    if (MP_USED(z) == 1 && *dp == 0)
        return 1;

    while (*dp == 0)
    {
        k += MP_DIGIT_BIT;
        ++dp;
    }

    d = *dp;
    while ((d & 1) == 0)
    {
        d >>= 1;
        ++k;
    }

    return k;
}

static mp_result s_embar ( mp_int  a, mp_int  b, mp_int  m, mp_int  mu, mp_int  c  )

static

Definition at line 3298 of file imath.c.

References assert, i, MP_ALLOC, MP_DIGIT_BIT, MP_DIGITS, mp_int_clear(), mp_int_copy(), mp_int_init_size(), mp_int_set_value(), MP_MEMORY, MP_SIGN, MP_USED, MP_ZPOS, s_reduce(), SETUP, TEMP, UMUL, USQR, and ZERO.

Referenced by mp_int_exptmod(), and mp_int_exptmod_known().

{
    mp_digit   *db,
               *dbt,
                umu,
                d;
    mpz_t       temp[3];
    mp_result   res;
    int         last = 0;

    umu = MP_USED(mu);
    db = MP_DIGITS(b);
    dbt = db + MP_USED(b) - 1;

    while (last < 3)
    {
        SETUP(mp_int_init_size(TEMP(last), 4 * umu), last);
        ZERO(MP_DIGITS(TEMP(last - 1)), MP_ALLOC(TEMP(last - 1)));
    }

    (void) mp_int_set_value(c, 1);

    /* Take care of low-order digits */
    while (db < dbt)
    {
        int         i;

        for (d = *db, i = MP_DIGIT_BIT; i > 0; --i, d >>= 1)
        {
            if (d & 1)
            {
                /* The use of a second temporary avoids allocation */
                UMUL(c, a, TEMP(0));
                if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2)))
                {
                    res = MP_MEMORY;
                    goto CLEANUP;
                }
                mp_int_copy(TEMP(0), c);
            }


            USQR(a, TEMP(0));
            assert(MP_SIGN(TEMP(0)) == MP_ZPOS);
            if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2)))
            {
                res = MP_MEMORY;
                goto CLEANUP;
            }
            assert(MP_SIGN(TEMP(0)) == MP_ZPOS);
            mp_int_copy(TEMP(0), a);


        }

        ++db;
    }

    /* Take care of highest-order digit */
    d = *dbt;
    for (;;)
    {
        if (d & 1)
        {
            UMUL(c, a, TEMP(0));
            if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2)))
            {
                res = MP_MEMORY;
                goto CLEANUP;
            }
            mp_int_copy(TEMP(0), c);
        }

        d >>= 1;
        if (!d)
            break;

        USQR(a, TEMP(0));
        if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2)))
        {
            res = MP_MEMORY;
            goto CLEANUP;
        }
        (void) mp_int_copy(TEMP(0), a);
    }

CLEANUP:
    while (--last >= 0)
        mp_int_clear(TEMP(last));

    return res;
}

static void s_fake ( mp_int  z, int  value, mp_digit  vbuf[]  )

static

Definition at line 2364 of file imath.c.

References mpz::alloc, mpz::digits, MP_NEG, MP_VALUE_DIGITS, MP_ZPOS, s_vpack(), mpz::sign, and mpz::used.

Referenced by mp_int_add_value(), mp_int_div_value(), mp_int_exptmod_bvalue(), mp_int_exptmod_evalue(), mp_int_mul_value(), and mp_int_sub_value().

{
    mp_size     uv = (mp_size) s_vpack(value, vbuf);

    z->used = uv;
    z->alloc = MP_VALUE_DIGITS(value);
    z->sign = (value < 0) ? MP_NEG : MP_ZPOS;
    z->digits = vbuf;
}

static mp_size s_inlen ( int  len, mp_size  r  )

static

Definition at line 3525 of file imath.c.

References MP_DIGIT_BIT, and s_log2.

Referenced by mp_int_read_cstring().

{
    double      raw = (double) len / s_log2[r];
    mp_size     bits = (mp_size) (raw + 0.5);

    return (mp_size) ((bits + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT);
}

static int s_isp2 ( mp_int  z )

static

Definition at line 3143 of file imath.c.

References MP_DIGIT_BIT, MP_DIGITS, and MP_USED.

Referenced by mp_int_div(), and mp_int_is_pow2().

{
    mp_size     uz = MP_USED(z),
                k = 0;
    mp_digit   *dz = MP_DIGITS(z),
                d;

    while (uz > 1)
    {
        if (*dz++ != 0)
            return -1;
        k += MP_DIGIT_BIT;
        --uz;
    }

    d = *dz;
    while (d > 1)
    {
        if (d & 1)
            return -1;
        ++k;
        d >>= 1;
    }

    return (int) k;
}

static int s_kmul ( mp_digit *  da, mp_digit *  db, mp_digit *  dc, mp_size  size_a, mp_size  size_b  )

static

Definition at line 2541 of file imath.c.

References assert, COPY, multiply_threshold, NULL, s_alloc(), s_free, s_uadd(), s_umul(), s_usub(), SWAP, and ZERO.

Referenced by mp_int_mul(), and s_ksqr().

{
    mp_size     bot_size;

    /* Make sure b is the smaller of the two input values */
    if (size_b > size_a)
    {
        SWAP(mp_digit *, da, db);
        SWAP(mp_size, size_a, size_b);
    }

    /*
     * Insure that the bottom is the larger half in an odd-length split; the
     * code below relies on this being true.
     */
    bot_size = (size_a + 1) / 2;

    /*
     * If the values are big enough to bother with recursion, use the
     * Karatsuba algorithm to compute the product; otherwise use the normal
     * multiplication algorithm
     */
    if (multiply_threshold &&
        size_a >= multiply_threshold &&
        size_b > bot_size)
    {

        mp_digit   *t1,
                   *t2,
                   *t3,
                    carry;

        mp_digit   *a_top = da + bot_size;
        mp_digit   *b_top = db + bot_size;

        mp_size     at_size = size_a - bot_size;
        mp_size     bt_size = size_b - bot_size;
        mp_size     buf_size = 2 * bot_size;

        /*
         * Do a single allocation for all three temporary buffers needed; each
         * buffer must be big enough to hold the product of two bottom halves,
         * and one buffer needs space for the completed product; twice the
         * space is plenty.
         */
        if ((t1 = s_alloc(4 * buf_size)) == NULL)
            return 0;
        t2 = t1 + buf_size;
        t3 = t2 + buf_size;
        ZERO(t1, 4 * buf_size);

        /*
         * t1 and t2 are initially used as temporaries to compute the inner
         * product (a1 + a0)(b1 + b0) = a1b1 + a1b0 + a0b1 + a0b0
         */
        carry = s_uadd(da, a_top, t1, bot_size, at_size);   /* t1 = a1 + a0 */
        t1[bot_size] = carry;

        carry = s_uadd(db, b_top, t2, bot_size, bt_size);   /* t2 = b1 + b0 */
        t2[bot_size] = carry;

        (void) s_kmul(t1, t2, t3, bot_size + 1, bot_size + 1);  /* t3 = t1 * t2 */

        /*
         * Now we'll get t1 = a0b0 and t2 = a1b1, and subtract them out so
         * that we're left with only the pieces we want:  t3 = a1b0 + a0b1
         */
        ZERO(t1, buf_size);
        ZERO(t2, buf_size);
        (void) s_kmul(da, db, t1, bot_size, bot_size);  /* t1 = a0 * b0 */
        (void) s_kmul(a_top, b_top, t2, at_size, bt_size);  /* t2 = a1 * b1 */

        /* Subtract out t1 and t2 to get the inner product */
        s_usub(t3, t1, t3, buf_size + 2, buf_size);
        s_usub(t3, t2, t3, buf_size + 2, buf_size);

        /* Assemble the output value */
        COPY(t1, dc, buf_size);
        carry = s_uadd(t3, dc + bot_size, dc + bot_size,
                       buf_size + 1, buf_size);
        assert(carry == 0);

        carry = s_uadd(t2, dc + 2 * bot_size, dc + 2 * bot_size,
                       buf_size, buf_size);
        assert(carry == 0);

        s_free(t1);             /* note t2 and t3 are just internal pointers
                                 * to t1 */
    }
    else
    {
        s_umul(da, db, dc, size_a, size_b);
    }

    return 1;
}

static int s_ksqr ( mp_digit *  da, mp_digit *  dc, mp_size  size_a  )

static

Definition at line 2677 of file imath.c.

References COPY, i, LOWER_HALF, multiply_threshold, NULL, px_free, s_alloc(), s_kmul(), s_uadd(), s_usqr(), UPPER_HALF, and ZERO.

Referenced by mp_int_sqr().

{
    if (multiply_threshold && size_a > multiply_threshold)
    {
        mp_size     bot_size = (size_a + 1) / 2;
        mp_digit   *a_top = da + bot_size;
        mp_digit   *t1,
                   *t2,
                   *t3;
        mp_size     at_size = size_a - bot_size;
        mp_size     buf_size = 2 * bot_size;

        if ((t1 = s_alloc(4 * buf_size)) == NULL)
            return 0;
        t2 = t1 + buf_size;
        t3 = t2 + buf_size;
        ZERO(t1, 4 * buf_size);

        (void) s_ksqr(da, t1, bot_size);    /* t1 = a0 ^ 2 */
        (void) s_ksqr(a_top, t2, at_size);  /* t2 = a1 ^ 2 */

        (void) s_kmul(da, a_top, t3, bot_size, at_size);    /* t3 = a0 * a1 */

        /* Quick multiply t3 by 2, shifting left (can't overflow) */
        {
            int         i,
                        top = bot_size + at_size;
            mp_word     w,
                        save = 0;

            for (i = 0; i < top; ++i)
            {
                w = t3[i];
                w = (w << 1) | save;
                t3[i] = LOWER_HALF(w);
                save = UPPER_HALF(w);
            }
            t3[i] = LOWER_HALF(save);
        }

        /* Assemble the output value */
        COPY(t1, dc, 2 * bot_size);
        (void) s_uadd(t3, dc + bot_size, dc + bot_size,
                      buf_size + 1, buf_size + 1);

        (void) s_uadd(t2, dc + 2 * bot_size, dc + 2 * bot_size,
                      buf_size, buf_size);

        px_free(t1);            /* note that t2 and t2 are internal pointers
                                 * only */

    }
    else
    {
        s_usqr(da, dc, size_a);
    }

    return 1;
}

static int s_norm ( mp_int  a, mp_int  b  )

static

Definition at line 3200 of file imath.c.

References mpz::digits, MP_DIGIT_BIT, MP_USED, and s_qmul().

Referenced by s_udiv().

{
    mp_digit    d = b->digits[MP_USED(b) - 1];
    int         k = 0;

    while (d < (mp_digit) ((mp_digit) 1 << (MP_DIGIT_BIT - 1)))
    {                           /* d < (MP_RADIX / 2) */
        d <<= 1;
        ++k;
    }

    /* These multiplications can't fail */
    if (k != 0)
    {
        (void) s_qmul(a, (mp_size) k);
        (void) s_qmul(b, (mp_size) k);
    }

    return k;
}

static int s_outlen ( mp_int  z, mp_size  r  )

static

Definition at line 3509 of file imath.c.

References mp_int_count_bits(), and s_log2.

Referenced by mp_int_string_len().

{
    mp_result   bits;
    double      raw;

    bits = mp_int_count_bits(z);
    raw = (double) bits * s_log2[r];

    return (int) (raw + 0.999999);
}

static int s_pad ( mp_int  z, mp_size  min  )

static

Definition at line 2324 of file imath.c.

References MP_ALLOC, MP_DIGITS, NULL, ROUND_PREC, and s_realloc().

Referenced by mp_int_add(), mp_int_copy(), mp_int_mul(), mp_int_read_binary(), mp_int_read_cstring(), mp_int_read_unsigned(), mp_int_set_value(), mp_int_sqr(), mp_int_sub(), px_find_combo(), s_2expt(), s_brmu(), s_qmul(), and s_qsub().

{
    if (MP_ALLOC(z) < min)
    {
        mp_size     nsize = ROUND_PREC(min);
        mp_digit   *tmp = s_realloc(MP_DIGITS(z), nsize);

        if (tmp == NULL)
            return 0;

        MP_DIGITS(z) = tmp;
        MP_ALLOC(z) = nsize;
    }

    return 1;
}

static void s_qdiv ( mp_int  z, mp_size  p2  )

static

Definition at line 2919 of file imath.c.

References CLAMP, mpz::digits, MP_DIGIT_BIT, MP_DIGITS, mp_int_zero(), MP_SIGN, MP_USED, and MP_ZPOS.

Referenced by mp_int_div(), mp_int_div_pow2(), mp_int_egcd(), mp_int_gcd(), s_reduce(), and s_udiv().

{
    mp_size     ndig = p2 / MP_DIGIT_BIT,
                nbits = p2 % MP_DIGIT_BIT;
    mp_size     uz = MP_USED(z);

    if (ndig)
    {
        mp_size     mark;
        mp_digit   *to,
                   *from;

        if (ndig >= uz)
        {
            mp_int_zero(z);
            return;
        }

        to = MP_DIGITS(z);
        from = to + ndig;

        for (mark = ndig; mark < uz; ++mark)
            *to++ = *from++;

        MP_USED(z) = uz - ndig;
    }

    if (nbits)
    {
        mp_digit    d = 0,
                   *dz,
                    save;
        mp_size     up = MP_DIGIT_BIT - nbits;

        uz = MP_USED(z);
        dz = MP_DIGITS(z) + uz - 1;

        for ( /* */ ; uz > 0; --uz, --dz)
        {
            save = *dz;

            *dz = (*dz >> nbits) | (d << up);
            d = save;
        }

        CLAMP(z);
    }

    if (MP_USED(z) == 1 && z->digits[0] == 0)
        MP_SIGN(z) = MP_ZPOS;
}

static void s_qmod ( mp_int  z, mp_size  p2  )

static

Definition at line 2976 of file imath.c.

References CLAMP, mpz::digits, MP_DIGIT_BIT, and MP_USED.

Referenced by mp_int_div(), mp_int_div_pow2(), and s_reduce().

{
    mp_size     start = p2 / MP_DIGIT_BIT + 1,
                rest = p2 % MP_DIGIT_BIT;
    mp_size     uz = MP_USED(z);
    mp_digit    mask = (1 << rest) - 1;

    if (start <= uz)
    {
        MP_USED(z) = start;
        z->digits[start - 1] &= mask;
        CLAMP(z);
    }
}

static int s_qmul ( mp_int  z, mp_size  p2  )

static

Definition at line 2996 of file imath.c.

References CLAMP, i, MP_DIGIT_BIT, MP_DIGITS, MP_USED, s_pad(), and ZERO.

Referenced by mp_int_egcd(), mp_int_gcd(), mp_int_mul_pow2(), mp_int_read_binary(), mp_int_read_unsigned(), and s_norm().

{
    mp_size     uz,
                need,
                rest,
                extra,
                i;
    mp_digit   *from,
               *to,
                d;

    if (p2 == 0)
        return 1;

    uz = MP_USED(z);
    need = p2 / MP_DIGIT_BIT;
    rest = p2 % MP_DIGIT_BIT;

    /*
     * Figure out if we need an extra digit at the top end; this occurs if the
     * topmost `rest' bits of the high-order digit of z are not zero, meaning
     * they will be shifted off the end if not preserved
     */
    extra = 0;
    if (rest != 0)
    {
        mp_digit   *dz = MP_DIGITS(z) + uz - 1;

        if ((*dz >> (MP_DIGIT_BIT - rest)) != 0)
            extra = 1;
    }

    if (!s_pad(z, uz + need + extra))
        return 0;

    /*
     * If we need to shift by whole digits, do that in one pass, then to back
     * and shift by partial digits.
     */
    if (need > 0)
    {
        from = MP_DIGITS(z) + uz - 1;
        to = from + need;

        for (i = 0; i < uz; ++i)
            *to-- = *from--;

        ZERO(MP_DIGITS(z), need);
        uz += need;
    }

    if (rest)
    {
        d = 0;
        for (i = need, from = MP_DIGITS(z) + need; i < uz; ++i, ++from)
        {
            mp_digit    save = *from;

            *from = (*from << rest) | (d >> (MP_DIGIT_BIT - rest));
            d = save;
        }

        d >>= (MP_DIGIT_BIT - rest);
        if (d != 0)
        {
            *from = d;
            uz += extra;
        }
    }

    MP_USED(z) = uz;
    CLAMP(z);

    return 1;
}

static int s_qsub ( mp_int  z, mp_size  p2  )

static

Definition at line 3078 of file imath.c.

References assert, CLAMP, LOWER_HALF, MP_DIGIT_BIT, MP_DIGIT_MAX, MP_DIGITS, MP_SIGN, MP_ZPOS, s_pad(), and UPPER_HALF.

Referenced by s_reduce().

{
    mp_digit    hi = (1 << (p2 % MP_DIGIT_BIT)),
               *zp;
    mp_size     tdig = (p2 / MP_DIGIT_BIT),
                pos;
    mp_word     w = 0;

    if (!s_pad(z, tdig + 1))
        return 0;

    for (pos = 0, zp = MP_DIGITS(z); pos < tdig; ++pos, ++zp)
    {
        w = ((mp_word) MP_DIGIT_MAX + 1) - w - (mp_word) *zp;

        *zp = LOWER_HALF(w);
        w = UPPER_HALF(w) ? 0 : 1;
    }

    w = ((mp_word) MP_DIGIT_MAX + 1 + hi) - w - (mp_word) *zp;
    *zp = LOWER_HALF(w);

    assert(UPPER_HALF(w) != 0); /* no borrow out should be possible */

    MP_SIGN(z) = MP_ZPOS;
    CLAMP(z);

    return 1;
}

static mp_digit* s_realloc ( mp_digit *  old, mp_size  num  )

static

Definition at line 2298 of file imath.c.

References assert, NULL, and px_realloc.

Referenced by s_pad().

{
    mp_digit   *new = px_realloc(old, num * sizeof(mp_digit));

    assert(new != NULL);        /* for debugging */

    return new;
}

static int s_reduce ( mp_int  x, mp_int  m, mp_int  mu, mp_int  q1, mp_int  q2  )

static

Definition at line 3242 of file imath.c.

References CMPZ, MP_DIGIT_BIT, mp_int_compare(), mp_int_copy(), mp_int_sub(), MP_OK, MP_USED, s_qdiv(), s_qmod(), s_qsub(), and UMUL.

Referenced by s_embar().

{
    mp_size     um = MP_USED(m),
                umb_p1,
                umb_m1;

    umb_p1 = (um + 1) * MP_DIGIT_BIT;
    umb_m1 = (um - 1) * MP_DIGIT_BIT;

    if (mp_int_copy(x, q1) != MP_OK)
        return 0;

    /* Compute q2 = floor((floor(x / b^(k-1)) * mu) / b^(k+1)) */
    s_qdiv(q1, umb_m1);
    UMUL(q1, mu, q2);
    s_qdiv(q2, umb_p1);

    /* Set x = x mod b^(k+1) */
    s_qmod(x, umb_p1);

    /*
     * Now, q is a guess for the quotient a / m. Compute x - q * m mod
     * b^(k+1), replacing x.  This may be off by a factor of 2m, but no more
     * than that.
     */
    UMUL(q2, m, q1);
    s_qmod(q1, umb_p1);
    (void) mp_int_sub(x, q1, x);    /* can't fail */

    /*
     * The result may be < 0; if it is, add b^(k+1) to pin it in the proper
     * range.
     */
    if ((CMPZ(x) < 0) && !s_qsub(x, umb_p1))
        return 0;

    /*
     * If x > m, we need to back it off until it is in range. This will be
     * required at most twice.
     */
    if (mp_int_compare(x, m) >= 0)
        (void) mp_int_sub(x, m, x);
    if (mp_int_compare(x, m) >= 0)
        (void) mp_int_sub(x, m, x);

    /* At this point, x has been properly reduced. */
    return 1;
}

static mp_result s_tobin ( mp_int  z, unsigned char *  buf, int *  limpos, int  pad  )

static

Definition at line 3603 of file imath.c.

References i, MP_DIGITS, MP_OK, MP_TRUNC, MP_USED, and REV.

Referenced by mp_int_to_binary(), and mp_int_to_unsigned().

{
    mp_size     uz;
    mp_digit   *dz;
    int         pos = 0,
                limit = *limpos;

    uz = MP_USED(z);
    dz = MP_DIGITS(z);
    while (uz > 0 && pos < limit)
    {
        mp_digit    d = *dz++;
        int         i;

        for (i = sizeof(mp_digit); i > 0 && pos < limit; --i)
        {
            buf[pos++] = (unsigned char) d;
            d >>= CHAR_BIT;

            /* Don't write leading zeroes */
            if (d == 0 && uz == 1)
                i = 0;          /* exit loop without signaling truncation */
        }

        /* Detect truncation (loop exited with pos >= limit) */
        if (i > 0)
            break;

        --uz;
    }

    if (pad != 0 && (buf[pos - 1] >> (CHAR_BIT - 1)))
    {
        if (pos < limit)
            buf[pos++] = 0;
        else
            uz = 1;
    }

    /* Digits are in reverse order, fix that */
    REV(unsigned char, buf, pos);

    /* Return the number of bytes actually written */
    *limpos = pos;

    return (uz == 0) ? MP_OK : MP_TRUNC;
}

static mp_digit s_uadd ( mp_digit *  da, mp_digit *  db, mp_digit *  dc, mp_size  size_a, mp_size  size_b  )

static

Definition at line 2464 of file imath.c.

References LOWER_HALF, SWAP, and UPPER_HALF.

Referenced by mp_int_add(), mp_int_sub(), s_kmul(), and s_ksqr().

{
    mp_size     pos;
    mp_word     w = 0;

    /* Insure that da is the longer of the two to simplify later code */
    if (size_b > size_a)
    {
        SWAP(mp_digit *, da, db);
        SWAP(mp_size, size_a, size_b);
    }

    /* Add corresponding digits until the shorter number runs out */
    for (pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc)
    {
        w = w + (mp_word) *da + (mp_word) *db;
        *dc = LOWER_HALF(w);
        w = UPPER_HALF(w);
    }

    /* Propagate carries as far as necessary */
    for ( /* */ ; pos < size_a; ++pos, ++da, ++dc)
    {
        w = w + *da;

        *dc = LOWER_HALF(w);
        w = UPPER_HALF(w);
    }

    /* Return carry out */
    return (mp_digit) w;
}

static int s_ucmp ( mp_int  a, mp_int  b  )

static

Definition at line 2425 of file imath.c.

References MP_DIGITS, MP_USED, and s_cdig().

Referenced by mp_int_add(), mp_int_compare(), mp_int_compare_unsigned(), mp_int_div(), mp_int_sub(), and s_udiv().

{
    mp_size     ua = MP_USED(a),
                ub = MP_USED(b);

    if (ua > ub)
        return 1;
    else if (ub > ua)
        return -1;
    else
        return s_cdig(MP_DIGITS(a), MP_DIGITS(b), ua);
}

static mp_result s_udiv ( mp_int  a, mp_int  b  )

static

Definition at line 3399 of file imath.c.

References mpz::alloc, assert, CLAMP, mpz::digits, MP_ALLOC, MP_DIGIT_BIT, MP_DIGIT_MAX, MP_DIGITS, mp_int_clear(), mp_int_copy(), mp_int_init_size(), mp_int_sub(), MP_OK, MP_SIGN, MP_USED, MP_ZPOS, REV, s_dbmul(), s_norm(), s_qdiv(), s_ucmp(), s_usub(), mpz::sign, skip(), mpz::used, and ZERO.

Referenced by mp_int_div().

{
    mpz_t       q,
                r,
                t;
    mp_size     ua,
                ub,
                qpos = 0;
    mp_digit   *da,
                btop;
    mp_result   res = MP_OK;
    int         k,
                skip = 0;

    /* Force signs to positive */
    MP_SIGN(a) = MP_ZPOS;
    MP_SIGN(b) = MP_ZPOS;

    /* Normalize, per Knuth */
    k = s_norm(a, b);

    ua = MP_USED(a);
    ub = MP_USED(b);
    btop = b->digits[ub - 1];
    if ((res = mp_int_init_size(&q, ua)) != MP_OK)
        return res;
    if ((res = mp_int_init_size(&t, ua + 1)) != MP_OK)
        goto CLEANUP;

    da = MP_DIGITS(a);
    r.digits = da + ua - 1;     /* The contents of r are shared with a */
    r.used = 1;
    r.sign = MP_ZPOS;
    r.alloc = MP_ALLOC(a);
    ZERO(t.digits, t.alloc);

    /* Solve for quotient digits, store in q.digits in reverse order */
    while (r.digits >= da)
    {
        assert(qpos <= q.alloc);

        if (s_ucmp(b, &r) > 0)
        {
            r.digits -= 1;
            r.used += 1;

            if (++skip > 1)
                q.digits[qpos++] = 0;

            CLAMP(&r);
        }
        else
        {
            mp_word     pfx = r.digits[r.used - 1];
            mp_word     qdigit;

            if (r.used > 1 && (pfx < btop || r.digits[r.used - 2] == 0))
            {
                pfx <<= MP_DIGIT_BIT / 2;
                pfx <<= MP_DIGIT_BIT / 2;
                pfx |= r.digits[r.used - 2];
            }

            qdigit = pfx / btop;
            if (qdigit > MP_DIGIT_MAX)
                qdigit = 1;

            s_dbmul(MP_DIGITS(b), (mp_digit) qdigit, t.digits, ub);
            t.used = ub + 1;
            CLAMP(&t);
            while (s_ucmp(&t, &r) > 0)
            {
                --qdigit;
                (void) mp_int_sub(&t, b, &t);   /* cannot fail */
            }

            s_usub(r.digits, t.digits, r.digits, r.used, t.used);
            CLAMP(&r);

            q.digits[qpos++] = (mp_digit) qdigit;
            ZERO(t.digits, t.used);
            skip = 0;
        }
    }

    /* Put quotient digits in the correct order, and discard extra zeroes */
    q.used = qpos;
    REV(mp_digit, q.digits, qpos);
    CLAMP(&q);

    /* Denormalize the remainder */
    CLAMP(a);
    if (k != 0)
        s_qdiv(a, k);

    mp_int_copy(a, b);          /* ok:  0 <= r < b */
    mp_int_copy(&q, a);         /* ok:  q <= a     */

    mp_int_clear(&t);
CLEANUP:
    mp_int_clear(&q);
    return res;
}

static void s_umul ( mp_digit *  da, mp_digit *  db, mp_digit *  dc, mp_size  size_a, mp_size  size_b  )

static

Definition at line 2644 of file imath.c.

References LOWER_HALF, and UPPER_HALF.

Referenced by s_kmul().

{
    mp_size     a,
                b;
    mp_word     w;

    for (a = 0; a < size_a; ++a, ++dc, ++da)
    {
        mp_digit   *dct = dc;
        mp_digit   *dbt = db;

        if (*da == 0)
            continue;

        w = 0;
        for (b = 0; b < size_b; ++b, ++dbt, ++dct)
        {
            w = (mp_word) *da * (mp_word) *dbt + w + (mp_word) *dct;

            *dct = LOWER_HALF(w);
            w = UPPER_HALF(w);
        }

        *dct = (mp_digit) w;
    }
}

static void s_usqr ( mp_digit *  da, mp_digit *  dc, mp_size  size_a  )

static

Definition at line 2742 of file imath.c.

References ADD_WILL_OVERFLOW, assert, HIGH_BIT_SET, i, LOWER_HALF, MP_DIGIT_MAX, and UPPER_HALF.

Referenced by s_ksqr().

{
    mp_size     i,
                j;
    mp_word     w;

    for (i = 0; i < size_a; ++i, dc += 2, ++da)
    {
        mp_digit   *dct = dc,
                   *dat = da;

        if (*da == 0)
            continue;

        /* Take care of the first digit, no rollover */
        w = (mp_word) *dat * (mp_word) *dat + (mp_word) *dct;
        *dct = LOWER_HALF(w);
        w = UPPER_HALF(w);
        ++dat;
        ++dct;

        for (j = i + 1; j < size_a; ++j, ++dat, ++dct)
        {
            mp_word     t = (mp_word) *da * (mp_word) *dat;
            mp_word     u = w + (mp_word) *dct,
                        ov = 0;

            /* Check if doubling t will overflow a word */
            if (HIGH_BIT_SET(t))
                ov = 1;

            w = t + t;

            /* Check if adding u to w will overflow a word */
            if (ADD_WILL_OVERFLOW(w, u))
                ov = 1;

            w += u;

            *dct = LOWER_HALF(w);
            w = UPPER_HALF(w);
            if (ov)
            {
                w += MP_DIGIT_MAX;  /* MP_RADIX */
                ++w;
            }
        }

        w = w + *dct;
        *dct = (mp_digit) w;
        while ((w = UPPER_HALF(w)) != 0)
        {
            ++dct;
            w = w + *dct;
            *dct = LOWER_HALF(w);
        }

        assert(w == 0);
    }
}

static void s_usub ( mp_digit *  da, mp_digit *  db, mp_digit *  dc, mp_size  size_a, mp_size  size_b  )

static

Definition at line 2503 of file imath.c.

References assert, LOWER_HALF, MP_DIGIT_MAX, and UPPER_HALF.

Referenced by mp_int_add(), mp_int_sub(), s_kmul(), and s_udiv().

{
    mp_size     pos;
    mp_word     w = 0;

    /* We assume that |a| >= |b| so this should definitely hold */
    assert(size_a >= size_b);

    /* Subtract corresponding digits and propagate borrow */
    for (pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc)
    {
        w = ((mp_word) MP_DIGIT_MAX + 1 +   /* MP_RADIX */
             (mp_word) *da) - w - (mp_word) *db;

        *dc = LOWER_HALF(w);
        w = (UPPER_HALF(w) == 0);
    }

    /* Finish the subtraction for remaining upper digits of da */
    for ( /* */ ; pos < size_a; ++pos, ++da, ++dc)
    {
        w = ((mp_word) MP_DIGIT_MAX + 1 +   /* MP_RADIX */
             (mp_word) *da) - w;

        *dc = LOWER_HALF(w);
        w = (UPPER_HALF(w) == 0);
    }

    /* If there is a borrow out at the end, it violates the precondition */
    assert(w == 0);
}

static char s_val2ch ( int  v, int  caps  )

static

Definition at line 3557 of file imath.c.

References assert.

Referenced by mp_int_to_string().

{
    assert(v >= 0);

    if (v < 10)
        return v + '0';
    else
    {
        char        out = (v - 10) + 'a';

        if (caps)
            return toupper((unsigned char) out);
        else
            return out;
    }
}

static int s_vcmp ( mp_int  a, int  v  )

static

Definition at line 2443 of file imath.c.

References MP_DIGITS, MP_USED, MP_VALUE_DIGITS, s_cdig(), and s_vpack().

Referenced by mp_int_compare_value().

{
    mp_digit    vdig[MP_VALUE_DIGITS(v)];
    int         ndig = 0;
    mp_size     ua = MP_USED(a);

    ndig = s_vpack(v, vdig);

    if (ua > ndig)
        return 1;
    else if (ua < ndig)
        return -1;
    else
        return s_cdig(MP_DIGITS(a), vdig, ndig);
}

static int s_vpack ( int  v, mp_digit  t[]  )

static

Definition at line 2400 of file imath.c.

References MP_DIGIT_BIT.

Referenced by mp_int_set_value(), s_fake(), and s_vcmp().

{
    unsigned int uv = (unsigned int) ((v < 0) ? -v : v);
    int         ndig = 0;

    if (uv == 0)
        t[ndig++] = 0;
    else
    {
        while (uv != 0)
        {
            t[ndig++] = (mp_digit) uv;
            uv >>= MP_DIGIT_BIT / 2;
            uv >>= MP_DIGIT_BIT / 2;
        }
    }

    return ndig;
}

Variable Documentation

mp_size default_precision = 64

static

Definition at line 167 of file imath.c.

Referenced by mp_get_default_precision(), mp_int_init(), mp_int_init_copy(), mp_int_init_size(), mp_int_mul(), mp_int_sqr(), and mp_set_default_precision().

const mp_result MP_BADARG = -6

Definition at line 50 of file imath.c.

const mp_result MP_FALSE = 0

Definition at line 44 of file imath.c.

mp_word mp_flags = MP_CAP_DIGITS

static

Definition at line 173 of file imath.c.

Referenced by mp_int_to_string().

const mp_result MP_MEMORY = -2

Definition at line 46 of file imath.c.

Referenced by mp_int_add(), mp_int_copy(), mp_int_egcd(), mp_int_gcd(), mp_int_init_size(), mp_int_mul(), mp_int_mul_pow2(), mp_int_read_binary(), mp_int_read_cstring(), mp_int_read_unsigned(), mp_int_set_value(), mp_int_sqr(), mp_int_sub(), s_brmu(), and s_embar().

const mp_sign MP_NEG = 1

Definition at line 52 of file imath.c.

Referenced by mp_int_compare_value(), mp_int_div(), mp_int_invmod(), mp_int_mul(), mp_int_read_binary(), mp_int_read_cstring(), mp_int_set_value(), mp_int_sqrt(), mp_int_string_len(), mp_int_sub(), mp_int_to_binary(), mp_int_to_int(), mp_int_to_string(), and s_fake().

const mp_result MP_OK = 0

Definition at line 43 of file imath.c.

Referenced by mp_int_abs(), mp_int_add(), mp_int_copy(), mp_int_div(), mp_int_div_pow2(), mp_int_div_value(), mp_int_divisible_value(), mp_int_egcd(), mp_int_expt(), mp_int_expt_value(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_gcd(), mp_int_init_copy(), mp_int_init_size(), mp_int_init_value(), mp_int_invmod(), mp_int_mod(), mp_int_mul(), mp_int_mul_pow2(), mp_int_neg(), mp_int_read_binary(), mp_int_read_cstring(), mp_int_read_unsigned(), mp_int_set_value(), mp_int_sqr(), mp_int_sqrt(), mp_int_sub(), mp_int_to_int(), mp_int_to_string(), s_reduce(), s_tobin(), and s_udiv().

const mp_result MP_RANGE = -3

Definition at line 47 of file imath.c.

Referenced by mp_int_exptmod(), mp_int_exptmod_known(), mp_int_invmod(), mp_int_read_cstring(), mp_int_string_len(), mp_int_to_int(), and mp_int_to_string().

const mp_result MP_TRUE = -1

Definition at line 45 of file imath.c.

const mp_result MP_TRUNC = -5

Definition at line 49 of file imath.c.

Referenced by mp_int_read_cstring(), mp_int_to_string(), and s_tobin().

const mp_result MP_UNDEF = -4

Definition at line 48 of file imath.c.

Referenced by mp_int_div(), mp_int_egcd(), mp_int_exptmod(), mp_int_exptmod_known(), mp_int_gcd(), mp_int_invmod(), and mp_int_sqrt().

const mp_sign MP_ZPOS = 0

Definition at line 53 of file imath.c.

Referenced by mp_int_abs(), mp_int_compare(), mp_int_compare_value(), mp_int_compare_zero(), mp_int_div(), mp_int_egcd(), mp_int_gcd(), mp_int_init_size(), mp_int_mul(), mp_int_read_cstring(), mp_int_set_value(), mp_int_sqr(), mp_int_sub(), mp_int_to_int(), mp_int_zero(), s_embar(), s_fake(), s_qdiv(), s_qsub(), and s_udiv().

mp_size multiply_threshold = 32

static

Definition at line 170 of file imath.c.

Referenced by mp_get_multiply_threshold(), mp_set_multiply_threshold(), s_kmul(), and s_ksqr().

const char* s_error_msg[]

static

Initial value:

= {
    "error code 0",
    "boolean true",
    "out of memory",
    "argument out of range",
    "result undefined",
    "output truncated",
    "invalid null argument",
    NULL
}

Definition at line 56 of file imath.c.

Referenced by mp_error_string().

const double s_log2[]

static

Initial value:

= {
    0.000000000, 0.000000000, 1.000000000, 0.630929754, 
    0.500000000, 0.430676558, 0.386852807, 0.356207187, 
    0.333333333, 0.315464877, 0.301029996, 0.289064826, 
    0.278942946, 0.270238154, 0.262649535, 0.255958025, 
    0.250000000, 0.244650542, 0.239812467, 0.235408913, 
    0.231378213, 0.227670249, 0.224243824, 0.221064729, 
    0.218104292, 0.215338279, 0.212746054, 0.210309918, 
    0.208014598, 0.205846832, 0.203795047, 0.201849087, 
    0.200000000, 0.198239863, 0.196561632, 0.194959022, 
    0.193426404, 0.191958720, 0.190551412, 0.189200360, 
    0.187901825, 0.186652411, 0.185449023, 0.184288833, 
    0.183169251, 0.182087900, 0.181042597, 0.180031327, 
    0.179052232, 0.178103594, 0.177183820, 0.176291434, 
    0.175425064, 0.174583430, 0.173765343, 0.172969690, 
    0.172195434, 0.171441601, 0.170707280, 0.169991616, 
    0.169293808, 0.168613099, 0.167948779, 0.167300179, 
    0.166666667
}

Definition at line 85 of file imath.c.

Referenced by s_inlen(), and s_outlen().

const char* s_unknown_err = "unknown result code"

static

Definition at line 55 of file imath.c.

Referenced by mp_error_string().