diff options
Diffstat (limited to 'source4/heimdal/lib/hcrypto/imath/imath.c')
| -rw-r--r-- | source4/heimdal/lib/hcrypto/imath/imath.c | 3353 |
1 files changed, 0 insertions, 3353 deletions
diff --git a/source4/heimdal/lib/hcrypto/imath/imath.c b/source4/heimdal/lib/hcrypto/imath/imath.c deleted file mode 100644 index 0079bafd02..0000000000 --- a/source4/heimdal/lib/hcrypto/imath/imath.c +++ /dev/null @@ -1,3353 +0,0 @@ -/* - Name: imath.c - Purpose: Arbitrary precision integer arithmetic routines. - Author: M. J. Fromberger <http://spinning-yarns.org/michael/> - Info: $Id: imath.c 826 2009-02-11 16:21:04Z sting $ - - Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. - - Permission is hereby granted, free of charge, to any person - obtaining a copy of this software and associated documentation files - (the "Software"), to deal in the Software without restriction, - including without limitation the rights to use, copy, modify, merge, - publish, distribute, sublicense, and/or sell copies of the Software, - and to permit persons to whom the Software is furnished to do so, - subject to the following conditions: - - The above copyright notice and this permission notice shall be - included in all copies or substantial portions of the Software. - - THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, - EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF - MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND - NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS - BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN - ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN - CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE - SOFTWARE. - */ - -#include "imath.h" - -#if DEBUG -#include <stdio.h> -#endif - -#include <stdlib.h> -#include <string.h> -#include <ctype.h> - -#include <assert.h> - -#if DEBUG -#define STATIC /* public */ -#else -#define STATIC static -#endif - -/* {{{ Constants */ - -const mp_result MP_OK = 0; /* no error, all is well */ -const mp_result MP_FALSE = 0; /* boolean false */ -const mp_result MP_TRUE = -1; /* boolean true */ -const mp_result MP_MEMORY = -2; /* out of memory */ -const mp_result MP_RANGE = -3; /* argument out of range */ -const mp_result MP_UNDEF = -4; /* result undefined */ -const mp_result MP_TRUNC = -5; /* output truncated */ -const mp_result MP_BADARG = -6; /* invalid null argument */ -const mp_result MP_MINERR = -6; - -const mp_sign MP_NEG = 1; /* value is strictly negative */ -const mp_sign MP_ZPOS = 0; /* value is non-negative */ - -STATIC const char *s_unknown_err = "unknown result code"; -STATIC const char *s_error_msg[] = { - "error code 0", - "boolean true", - "out of memory", - "argument out of range", - "result undefined", - "output truncated", - "invalid argument", - NULL -}; - -/* }}} */ - -/* Argument checking macros - Use CHECK() where a return value is required; NRCHECK() elsewhere */ -#define CHECK(TEST) assert(TEST) -#define NRCHECK(TEST) assert(TEST) - -/* {{{ Logarithm table for computing output sizes */ - -/* The ith entry of this table gives the value of log_i(2). - - An integer value n requires ceil(log_i(n)) digits to be represented - in base i. Since it is easy to compute lg(n), by counting bits, we - can compute log_i(n) = lg(n) * log_i(2). - - The use of this table eliminates a dependency upon linkage against - the standard math libraries. - */ -STATIC const double s_log2[] = { - 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* 0 1 2 3 */ - 0.500000000, 0.430676558, 0.386852807, 0.356207187, /* 4 5 6 7 */ - 0.333333333, 0.315464877, 0.301029996, 0.289064826, /* 8 9 10 11 */ - 0.278942946, 0.270238154, 0.262649535, 0.255958025, /* 12 13 14 15 */ - 0.250000000, 0.244650542, 0.239812467, 0.235408913, /* 16 17 18 19 */ - 0.231378213, 0.227670249, 0.224243824, 0.221064729, /* 20 21 22 23 */ - 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */ - 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */ - 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */ - 0.193426404, /* 36 */ -}; - -/* }}} */ -/* {{{ Various macros */ - -/* Return the number of digits needed to represent a static value */ -#define MP_VALUE_DIGITS(V) \ -((sizeof(V)+(sizeof(mp_digit)-1))/sizeof(mp_digit)) - -/* Round precision P to nearest word boundary */ -#define ROUND_PREC(P) ((mp_size)(2*(((P)+1)/2))) - -/* Set array P of S digits to zero */ -#define ZERO(P, S) \ -do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P);memset(p__,0,i__);}while(0) - -/* Copy S digits from array P to array Q */ -#define COPY(P, Q, S) \ -do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P),*q__=(Q);\ -memcpy(q__,p__,i__);}while(0) - -/* Reverse N elements of type T in array A */ -#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) \ -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) - -/* Select min/max. Do not provide expressions for which multiple - evaluation would be problematic, e.g. x++ */ -#define MIN(A, B) ((B)<(A)?(B):(A)) -#define MAX(A, B) ((B)>(A)?(B):(A)) - -/* Exchange lvalues A and B of type T, e.g. - SWAP(int, x, y) where x and y are variables of type int. */ -#define SWAP(T, A, B) do{T t_=(A);A=(B);B=t_;}while(0) - -/* Used to set up and access simple temp stacks within functions. */ -#define TEMP(K) (temp + (K)) -#define SETUP(E, C) \ -do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0) - -/* Compare value to zero. */ -#define CMPZ(Z) \ -(((Z)->used==1&&(Z)->digits[0]==0)?0:((Z)->sign==MP_NEG)?-1:1) - -/* Multiply X by Y into Z, ignoring signs. Requires that Z have - enough storage preallocated to hold the result. */ -#define UMUL(X, Y, Z) \ -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) - -/* Square X into Z. Requires that Z have enough storage to hold the - result. */ -#define USQR(X, Z) \ -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) - -#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)) - -/* }}} */ -/* {{{ Default configuration settings */ - -/* Default number of digits allocated to a new mp_int */ -#if IMATH_TEST -mp_size default_precision = MP_DEFAULT_PREC; -#else -STATIC const mp_size default_precision = MP_DEFAULT_PREC; -#endif - -/* Minimum number of digits to invoke recursive multiply */ -#if IMATH_TEST -mp_size multiply_threshold = MP_MULT_THRESH; -#else -STATIC const mp_size multiply_threshold = MP_MULT_THRESH; -#endif - -/* }}} */ - -/* Allocate a buffer of (at least) num digits, or return - NULL if that couldn't be done. */ -STATIC mp_digit *s_alloc(mp_size num); - -/* Release a buffer of digits allocated by s_alloc(). */ -STATIC void s_free(void *ptr); - -/* Insure that z has at least min digits allocated, resizing if - necessary. Returns true if successful, false if out of memory. */ -STATIC int s_pad(mp_int z, mp_size min); - -/* Fill in a "fake" mp_int on the stack with a given value */ -STATIC void s_fake(mp_int z, mp_small value, mp_digit vbuf[]); - -/* Compare two runs of digits of given length, returns <0, 0, >0 */ -STATIC int s_cdig(mp_digit *da, mp_digit *db, mp_size len); - -/* Pack the unsigned digits of v into array t */ -STATIC int s_vpack(mp_small v, mp_digit t[]); - -/* Compare magnitudes of a and b, returns <0, 0, >0 */ -STATIC int s_ucmp(mp_int a, mp_int b); - -/* Compare magnitudes of a and v, returns <0, 0, >0 */ -STATIC int s_vcmp(mp_int a, mp_small v); - -/* Unsigned magnitude addition; assumes dc is big enough. - Carry out is returned (no memory allocated). */ -STATIC mp_digit s_uadd(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b); - -/* Unsigned magnitude subtraction. Assumes dc is big enough. */ -STATIC void s_usub(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b); - -/* Unsigned recursive multiplication. Assumes dc is big enough. */ -STATIC int s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b); - -/* Unsigned magnitude multiplication. Assumes dc is big enough. */ -STATIC void s_umul(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b); - -/* Unsigned recursive squaring. Assumes dc is big enough. */ -STATIC int s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a); - -/* Unsigned magnitude squaring. Assumes dc is big enough. */ -STATIC void s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a); - -/* Single digit addition. Assumes a is big enough. */ -STATIC void s_dadd(mp_int a, mp_digit b); - -/* Single digit multiplication. Assumes a is big enough. */ -STATIC void s_dmul(mp_int a, mp_digit b); - -/* Single digit multiplication on buffers; assumes dc is big enough. */ -STATIC void s_dbmul(mp_digit *da, mp_digit b, mp_digit *dc, - mp_size size_a); - -/* Single digit division. Replaces a with the quotient, - returns the remainder. */ -STATIC mp_digit s_ddiv(mp_int a, mp_digit b); - -/* Quick division by a power of 2, replaces z (no allocation) */ -STATIC void s_qdiv(mp_int z, mp_size p2); - -/* Quick remainder by a power of 2, replaces z (no allocation) */ -STATIC void s_qmod(mp_int z, mp_size p2); - -/* Quick multiplication by a power of 2, replaces z. - Allocates if necessary; returns false in case this fails. */ -STATIC int s_qmul(mp_int z, mp_size p2); - -/* Quick subtraction from a power of 2, replaces z. - Allocates if necessary; returns false in case this fails. */ -STATIC int s_qsub(mp_int z, mp_size p2); - -/* Return maximum k such that 2^k divides z. */ -STATIC int s_dp2k(mp_int z); - -/* Return k >= 0 such that z = 2^k, or -1 if there is no such k. */ -STATIC int s_isp2(mp_int z); - -/* Set z to 2^k. May allocate; returns false in case this fails. */ -STATIC int s_2expt(mp_int z, mp_small k); - -/* Normalize a and b for division, returns normalization constant */ -STATIC int s_norm(mp_int a, mp_int b); - -/* Compute constant mu for Barrett reduction, given modulus m, result - replaces z, m is untouched. */ -STATIC mp_result s_brmu(mp_int z, mp_int m); - -/* Reduce a modulo m, using Barrett's algorithm. */ -STATIC int s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2); - -/* Modular exponentiation, using Barrett reduction */ -STATIC mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c); - -/* Unsigned magnitude division. Assumes |a| > |b|. Allocates - temporaries; overwrites a with quotient, b with remainder. */ -STATIC mp_result s_udiv(mp_int a, mp_int b); - -/* Compute the number of digits in radix r required to represent the - given value. Does not account for sign flags, terminators, etc. */ -STATIC int s_outlen(mp_int z, mp_size r); - -/* Guess how many digits of precision will be needed to represent a - radix r value of the specified number of digits. Returns a value - guaranteed to be no smaller than the actual number required. */ -STATIC mp_size s_inlen(int len, mp_size r); - -/* Convert a character to a digit value in radix r, or - -1 if out of range */ -STATIC int s_ch2val(char c, int r); - -/* Convert a digit value to a character */ -STATIC char s_val2ch(int v, int caps); - -/* Take 2's complement of a buffer in place */ -STATIC void s_2comp(unsigned char *buf, int len); - -/* Convert a value to binary, ignoring sign. On input, *limpos is the - bound on how many bytes should be written to buf; on output, *limpos - is set to the number of bytes actually written. */ -STATIC mp_result s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad); - -#if DEBUG -/* Dump a representation of the mp_int to standard output */ -void s_print(char *tag, mp_int z); -void s_print_buf(char *tag, mp_digit *buf, mp_size num); -#endif - -/* {{{ mp_int_init(z) */ - -mp_result mp_int_init(mp_int z) -{ - if(z == NULL) - return MP_BADARG; - - z->single = 0; - z->digits = &(z->single); - z->alloc = 1; - z->used = 1; - z->sign = MP_ZPOS; - - return MP_OK; -} - -/* }}} */ - -/* {{{ mp_int_alloc() */ - -mp_int mp_int_alloc(void) -{ - mp_int out = malloc(sizeof(mpz_t)); - - if(out != NULL) - mp_int_init(out); - - return out; -} - -/* }}} */ - -/* {{{ mp_int_init_size(z, prec) */ - -mp_result mp_int_init_size(mp_int z, mp_size prec) -{ - CHECK(z != NULL); - - if(prec == 0) - prec = default_precision; - else if(prec == 1) - return mp_int_init(z); - else - prec = (mp_size) ROUND_PREC(prec); - - 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_int_init_copy(z, old) */ - -mp_result mp_int_init_copy(mp_int z, mp_int old) -{ - mp_result res; - mp_size uold; - - CHECK(z != NULL && old != NULL); - - uold = MP_USED(old); - if(uold == 1) { - mp_int_init(z); - } - else { - mp_size 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_int_init_value(z, value) */ - -mp_result mp_int_init_value(mp_int z, mp_small value) -{ - mpz_t vtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - - s_fake(&vtmp, value, vbuf); - return mp_int_init_copy(z, &vtmp); -} - -/* }}} */ - -/* {{{ mp_int_set_value(z, value) */ - -mp_result mp_int_set_value(mp_int z, mp_small value) -{ - mpz_t vtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - - s_fake(&vtmp, value, vbuf); - return mp_int_copy(&vtmp, z); -} - -/* }}} */ - -/* {{{ mp_int_clear(z) */ - -void mp_int_clear(mp_int z) -{ - if(z == NULL) - return; - - if(MP_DIGITS(z) != NULL) { - if((void *) MP_DIGITS(z) != (void *) z) - s_free(MP_DIGITS(z)); - - MP_DIGITS(z) = NULL; - } -} - -/* }}} */ - -/* {{{ mp_int_free(z) */ - -void mp_int_free(mp_int z) -{ - NRCHECK(z != NULL); - - mp_int_clear(z); - free(z); /* note: NOT s_free() */ -} - -/* }}} */ - -/* {{{ mp_int_copy(a, c) */ - -mp_result mp_int_copy(mp_int a, mp_int c) -{ - 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_int_swap(a, c) */ - -void mp_int_swap(mp_int a, mp_int c) -{ - if(a != c) { - mpz_t tmp = *a; - - *a = *c; - *c = tmp; - } -} - -/* }}} */ - -/* {{{ mp_int_zero(z) */ - -void mp_int_zero(mp_int z) -{ - NRCHECK(z != NULL); - - z->digits[0] = 0; - MP_USED(z) = 1; - MP_SIGN(z) = MP_ZPOS; -} - -/* }}} */ - -/* {{{ mp_int_abs(a, c) */ - -mp_result mp_int_abs(mp_int a, mp_int c) -{ - 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_int_neg(a, c) */ - -mp_result mp_int_neg(mp_int a, mp_int c) -{ - 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_int_add(a, b, c) */ - -mp_result mp_int_add(mp_int a, mp_int b, mp_int c) -{ - mp_size ua, ub, max; - - CHECK(a != NULL && b != NULL && c != NULL); - - ua = MP_USED(a); ub = MP_USED(b); - max = MAX(ua, ub); - - if(MP_SIGN(a) == MP_SIGN(b)) { - /* Same sign -- add magnitudes, preserve sign of addends */ - mp_digit carry; - mp_size uc; - - 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 comparision, sign ignored */ - - /* Set x to max(a, b), y to min(a, b) to simplify later code. - A special case yields zero for equal magnitudes. - */ - if(cmp == 0) { - mp_int_zero(c); - return MP_OK; - } - else if(cmp < 0) { - x = b; y = a; - } - else { - x = a; y = b; - } - - 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_int_add_value(a, value, c) */ - -mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c) -{ - mpz_t vtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - - s_fake(&vtmp, value, vbuf); - - return mp_int_add(a, &vtmp, c); -} - -/* }}} */ - -/* {{{ mp_int_sub(a, b, c) */ - -mp_result mp_int_sub(mp_int a, mp_int b, mp_int c) -{ - mp_size ua, ub, max; - - CHECK(a != NULL && b != NULL && c != NULL); - - ua = MP_USED(a); ub = MP_USED(b); - max = MAX(ua, ub); - - if(MP_SIGN(a) != MP_SIGN(b)) { - /* Different signs -- add magnitudes and keep sign of a */ - mp_digit carry; - mp_size uc; - - 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_int_sub_value(a, value, c) */ - -mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c) -{ - mpz_t vtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - - s_fake(&vtmp, value, vbuf); - - return mp_int_sub(a, &vtmp, c); -} - -/* }}} */ - -/* {{{ mp_int_mul(a, b, c) */ - -mp_result mp_int_mul(mp_int a, mp_int b, mp_int c) -{ - 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 identical to any of the inputs, we'll write - the results 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)) { - if((void *) MP_DIGITS(c) != (void *) 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_int_mul_value(a, value, c) */ - -mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c) -{ - mpz_t vtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - - s_fake(&vtmp, value, vbuf); - - return mp_int_mul(a, &vtmp, c); -} - -/* }}} */ - -/* {{{ mp_int_mul_pow2(a, p2, c) */ - -mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c) -{ - 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_int_sqr(a, c) */ - -mp_result mp_int_sqr(mp_int a, mp_int c) -{ - 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)) { - if((void *) MP_DIGITS(c) != (void *) 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_int_div(a, b, q, r) */ - -mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r) -{ - 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) { - if((res = mp_int_copy(a, q)) != MP_OK) - goto CLEANUP; - else - qout = q; - } - else { - qout = TEMP(last); - SETUP(mp_int_init_copy(TEMP(last), a), last); - } - - if(r && a != r) { - if((res = mp_int_copy(b, r)) != MP_OK) - goto CLEANUP; - else - 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_int_mod(a, m, c) */ - -mp_result mp_int_mod(mp_int a, mp_int m, mp_int c) -{ - mp_result res; - mpz_t tmp; - mp_int out; - - if(m == c) { - mp_int_init(&tmp); - 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_int_div_value(a, value, q, r) */ - -mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small *r) -{ - mpz_t vtmp, rtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - mp_result res; - - mp_int_init(&rtmp); - 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; -} - -/* }}} */ - -/* {{{ mp_int_div_pow2(a, p2, q, r) */ - -mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r) -{ - 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_int_expt(a, b, c) */ - -mp_result mp_int_expt(mp_int a, mp_small b, mp_int c) -{ - 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_int_expt_value(a, b, c) */ - -mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c) -{ - 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_int_compare(a, b) */ - -int mp_int_compare(mp_int a, mp_int b) -{ - 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; - } -} - -/* }}} */ - -/* {{{ mp_int_compare_unsigned(a, b) */ - -int mp_int_compare_unsigned(mp_int a, mp_int b) -{ - NRCHECK(a != NULL && b != NULL); - - return s_ucmp(a, b); -} - -/* }}} */ - -/* {{{ mp_int_compare_zero(z) */ - -int mp_int_compare_zero(mp_int z) -{ - 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_int_compare_value(z, value) */ - -int mp_int_compare_value(mp_int z, mp_small value) -{ - 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; - } -} - -/* }}} */ - -/* {{{ mp_int_exptmod(a, b, m, c) */ - -mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c) -{ - 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_int_exptmod_evalue(a, value, m, c) */ - -mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c) -{ - mpz_t vtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - - s_fake(&vtmp, value, vbuf); - - return mp_int_exptmod(a, &vtmp, m, c); -} - -/* }}} */ - -/* {{{ mp_int_exptmod_bvalue(v, b, m, c) */ - -mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, - mp_int m, mp_int c) -{ - mpz_t vtmp; - mp_digit vbuf[MP_VALUE_DIGITS(value)]; - - s_fake(&vtmp, value, vbuf); - - return mp_int_exptmod(&vtmp, b, m, c); -} - -/* }}} */ - -/* {{{ mp_int_exptmod_known(a, b, m, mu, c) */ - -mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c) -{ - 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; -} - -/* }}} */ - -/* {{{ mp_int_redux_const(m, c) */ - -mp_result mp_int_redux_const(mp_int m, mp_int c) -{ - CHECK(m != NULL && c != NULL && m != c); - - return s_brmu(c, m); -} - -/* }}} */ - -/* {{{ mp_int_invmod(a, m, c) */ - -mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c) -{ - 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) - mp_int_init(TEMP(last)); - - 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; -} - -/* }}} */ - -/* {{{ mp_int_gcd(a, b, c) */ - -/* Binary GCD algorithm due to Josef Stein, 1961 */ -mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c) -{ - 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); - - mp_int_init(&t); - 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_int_egcd(a, b, c, x, y) */ - -/* This is the binary GCD algorithm again, but this time we keep track - of the elementary matrix operations as we go, so we can get values - x and y satisfying c = ax + by. - */ -mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, - mp_int x, mp_int y) -{ - 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) - mp_int_init(TEMP(last)); - 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_int_lcm(a, b, c) */ - -mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c) -{ - mpz_t lcm; - mp_result res; - - CHECK(a != NULL && b != NULL && c != NULL); - - /* Since a * b = gcd(a, b) * lcm(a, b), we can compute - lcm(a, b) = (a / gcd(a, b)) * b. - - This formulation insures everything works even if the input - variables share space. - */ - if((res = mp_int_init(&lcm)) != MP_OK) - return res; - if((res = mp_int_gcd(a, b, &lcm)) != MP_OK) - goto CLEANUP; - if((res = mp_int_div(a, &lcm, &lcm, NULL)) != MP_OK) - goto CLEANUP; - if((res = mp_int_mul(&lcm, b, &lcm)) != MP_OK) - goto CLEANUP; - - res = mp_int_copy(&lcm, c); - - CLEANUP: - mp_int_clear(&lcm); - - return res; -} - -/* }}} */ - -/* {{{ mp_int_divisible_value(a, v) */ - -int mp_int_divisible_value(mp_int a, mp_small v) -{ - mp_small rem = 0; - - if(mp_int_div_value(a, v, NULL, &rem) != MP_OK) - return 0; - - return rem == 0; -} - -/* }}} */ - -/* {{{ mp_int_is_pow2(z) */ - -int mp_int_is_pow2(mp_int z) -{ - CHECK(z != NULL); - - return s_isp2(z); -} - -/* }}} */ - -/* {{{ mp_int_root(a, b, c) */ - -/* Implementation of Newton's root finding method, based loosely on a - patch contributed by Hal Finkel <half@halssoftware.com> - modified by M. J. Fromberger. - */ -mp_result mp_int_root(mp_int a, mp_small b, mp_int c) -{ - mp_result res = MP_OK; - mpz_t temp[5]; - int last = 0; - int flips = 0; - - CHECK(a != NULL && c != NULL && b > 0); - - if(b == 1) { - return mp_int_copy(a, c); - } - if(MP_SIGN(a) == MP_NEG) { - if(b % 2 == 0) - return MP_UNDEF; /* root does not exist for negative a with even b */ - else - flips = 1; - } - - SETUP(mp_int_init_copy(TEMP(last), a), last); - SETUP(mp_int_init_copy(TEMP(last), a), last); - SETUP(mp_int_init(TEMP(last)), last); - SETUP(mp_int_init(TEMP(last)), last); - SETUP(mp_int_init(TEMP(last)), last); - - (void) mp_int_abs(TEMP(0), TEMP(0)); - (void) mp_int_abs(TEMP(1), TEMP(1)); - - for(;;) { - if((res = mp_int_expt(TEMP(1), b, TEMP(2))) != MP_OK) - goto CLEANUP; - - if(mp_int_compare_unsigned(TEMP(2), TEMP(0)) <= 0) - break; - - if((res = mp_int_sub(TEMP(2), TEMP(0), TEMP(2))) != MP_OK) - goto CLEANUP; - if((res = mp_int_expt(TEMP(1), b - 1, TEMP(3))) != MP_OK) - goto CLEANUP; - if((res = mp_int_mul_value(TEMP(3), b, TEMP(3))) != MP_OK) - goto CLEANUP; - if((res = mp_int_div(TEMP(2), TEMP(3), TEMP(4), NULL)) != MP_OK) - goto CLEANUP; - if((res = mp_int_sub(TEMP(1), TEMP(4), TEMP(4))) != MP_OK) - goto CLEANUP; - - if(mp_int_compare_unsigned(TEMP(1), TEMP(4)) == 0) { - if((res = mp_int_sub_value(TEMP(4), 1, TEMP(4))) != MP_OK) - goto CLEANUP; - } - if((res = mp_int_copy(TEMP(4), TEMP(1))) != MP_OK) - goto CLEANUP; - } - - if((res = mp_int_copy(TEMP(1), c)) != MP_OK) - goto CLEANUP; - - /* If the original value of a was negative, flip the output sign. */ - if(flips) - (void) mp_int_neg(c, c); /* cannot fail */ - - CLEANUP: - while(--last >= 0) - mp_int_clear(TEMP(last)); - - return res; -} - -/* }}} */ - -/* {{{ mp_int_to_int(z, out) */ - -mp_result mp_int_to_int(mp_int z, mp_small *out) -{ - mp_usmall 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, MP_SMALL_MAX) > 0) || - mp_int_compare_value(z, MP_SMALL_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) ? -(mp_small)uv : (mp_small)uv; - - return MP_OK; -} - -/* }}} */ - -/* {{{ mp_int_to_uint(z, *out) */ - -mp_result mp_int_to_uint(mp_int z, mp_usmall *out) -{ - mp_usmall 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, UINT_MAX) <= 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 = uv; - - return MP_OK; -} - -/* }}} */ - -/* {{{ mp_int_to_string(z, radix, str, limit) */ - -mp_result mp_int_to_string(mp_int z, mp_size radix, - char *str, int limit) -{ - 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, 1); - } - 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, 1); - } - 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_int_string_len(z, radix) */ - -mp_result mp_int_string_len(mp_int z, mp_size radix) -{ - 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_int_read_string(z, radix, *str) */ - -/* Read zero-terminated string into z */ -mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str) -{ - return mp_int_read_cstring(z, radix, str, NULL); - -} - -/* }}} */ - -/* {{{ mp_int_read_cstring(z, radix, *str, **end) */ - -mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end) -{ - int ch; - - CHECK(z != NULL && str != NULL); - - if(radix < MP_MIN_RADIX || radix > MP_MAX_RADIX) - return MP_RANGE; - - /* Skip leading whitespace */ - while(isspace((int)*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_int_count_bits(z) */ - -mp_result mp_int_count_bits(mp_int z) -{ - 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_int_to_binary(z, buf, limit) */ - -mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit) -{ - 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_int_read_binary(z, buf, len) */ - -mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len) -{ - 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_int_binary_len(z) */ - -mp_result mp_int_binary_len(mp_int z) -{ - mp_result res = mp_int_count_bits(z); - int bytes; - - 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; -} - -/* }}} */ - -/* {{{ mp_int_to_unsigned(z, buf, limit) */ - -mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit) -{ - static const int NO_PADDING = 0; - - CHECK(z != NULL && buf != NULL); - - return s_tobin(z, buf, &limit, NO_PADDING); -} - -/* }}} */ - -/* {{{ mp_int_read_unsigned(z, buf, len) */ - -mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len) -{ - 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_int_unsigned_len(z) */ - -mp_result mp_int_unsigned_len(mp_int z) -{ - mp_result res = mp_int_count_bits(z); - int bytes; - - if(res <= 0) - return res; - - bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT; - - return bytes; -} - -/* }}} */ - -/* {{{ mp_error_string(res) */ - -const char *mp_error_string(mp_result res) -{ - 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; -} - -/* }}} */ - -/*------------------------------------------------------------------------*/ -/* Private functions for internal use. These make assumptions. */ - -/* {{{ s_alloc(num) */ - -STATIC mp_digit *s_alloc(mp_size num) -{ - mp_digit *out = malloc(num * sizeof(mp_digit)); - - assert(out != NULL); /* for debugging */ -#if DEBUG > 1 - { - mp_digit v = (mp_digit) 0xdeadbeef; - int ix; - - for(ix = 0; ix < num; ++ix) - out[ix] = v; - } -#endif - - return out; -} - -/* }}} */ - -/* {{{ s_realloc(old, osize, nsize) */ - -STATIC mp_digit *s_realloc(mp_digit *old, mp_size osize, mp_size nsize) -{ -#if DEBUG > 1 - mp_digit *new = s_alloc(nsize); - int ix; - - for(ix = 0; ix < nsize; ++ix) - new[ix] = (mp_digit) 0xdeadbeef; - - memcpy(new, old, osize * sizeof(mp_digit)); -#else - mp_digit *new = realloc(old, nsize * sizeof(mp_digit)); - - assert(new != NULL); /* for debugging */ -#endif - return new; -} - -/* }}} */ - -/* {{{ s_free(ptr) */ - -STATIC void s_free(void *ptr) -{ - free(ptr); -} - -/* }}} */ - -/* {{{ s_pad(z, min) */ - -STATIC int s_pad(mp_int z, mp_size min) -{ - if(MP_ALLOC(z) < min) { - mp_size nsize = ROUND_PREC(min); - mp_digit *tmp; - - if((void *)z->digits == (void *)z) { - if((tmp = s_alloc(nsize)) == NULL) - return 0; - - COPY(MP_DIGITS(z), tmp, MP_USED(z)); - } - else if((tmp = s_realloc(MP_DIGITS(z), MP_ALLOC(z), nsize)) == NULL) - return 0; - - MP_DIGITS(z) = tmp; - MP_ALLOC(z) = nsize; - } - - return 1; -} - -/* }}} */ - -/* {{{ s_fake(z, value, vbuf) */ - -STATIC void s_fake(mp_int z, mp_small value, mp_digit vbuf[]) -{ - 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; -} - -/* }}} */ - -/* {{{ s_cdig(da, db, len) */ - -STATIC int s_cdig(mp_digit *da, mp_digit *db, mp_size len) -{ - 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; -} - -/* }}} */ - -/* {{{ s_vpack(v, t[]) */ - -STATIC int s_vpack(mp_small v, mp_digit t[]) -{ - mp_usmall uv = (mp_usmall) ((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; -} - -/* }}} */ - -/* {{{ s_ucmp(a, b) */ - -STATIC int s_ucmp(mp_int a, mp_int b) -{ - 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); -} - -/* }}} */ - -/* {{{ s_vcmp(a, v) */ - -STATIC int s_vcmp(mp_int a, mp_small v) -{ - 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); -} - -/* }}} */ - -/* {{{ s_uadd(da, db, dc, size_a, size_b) */ - -STATIC mp_digit s_uadd(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b) -{ - 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; -} - -/* }}} */ - -/* {{{ s_usub(da, db, dc, size_a, size_b) */ - -STATIC void s_usub(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b) -{ - 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); -} - -/* }}} */ - -/* {{{ s_kmul(da, db, dc, size_a, size_b) */ - -STATIC int s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b) -{ - 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; -} - -/* }}} */ - -/* {{{ s_umul(da, db, dc, size_a, size_b) */ - -STATIC void s_umul(mp_digit *da, mp_digit *db, mp_digit *dc, - mp_size size_a, mp_size size_b) -{ - 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; - } -} - -/* }}} */ - -/* {{{ s_ksqr(da, dc, size_a) */ - -STATIC int s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a) -{ - 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, carry; - 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); - 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 that t2 and t2 are internal pointers only */ - - } - else { - s_usqr(da, dc, size_a); - } - - return 1; -} - -/* }}} */ - -/* {{{ s_usqr(da, dc, size_a) */ - -STATIC void s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a) -{ - 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); - } -} - -/* }}} */ - -/* {{{ s_dadd(a, b) */ - -STATIC void s_dadd(mp_int a, mp_digit b) -{ - 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; - } -} - -/* }}} */ - -/* {{{ s_dmul(a, b) */ - -STATIC void s_dmul(mp_int a, mp_digit b) -{ - 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; - } -} - -/* }}} */ - -/* {{{ s_dbmul(da, b, dc, size_a) */ - -STATIC void s_dbmul(mp_digit *da, mp_digit b, mp_digit *dc, mp_size size_a) -{ - 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); -} - -/* }}} */ - -/* {{{ s_ddiv(da, d, dc, size_a) */ - -STATIC mp_digit s_ddiv(mp_int a, mp_digit b) -{ - 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; -} - -/* }}} */ - -/* {{{ s_qdiv(z, p2) */ - -STATIC void s_qdiv(mp_int z, mp_size p2) -{ - 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; -} - -/* }}} */ - -/* {{{ s_qmod(z, p2) */ - -STATIC void s_qmod(mp_int z, mp_size p2) -{ - 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); - } -} - -/* }}} */ - -/* {{{ s_qmul(z, p2) */ - -STATIC int s_qmul(mp_int z, mp_size p2) -{ - 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; -} - -/* }}} */ - -/* {{{ s_qsub(z, p2) */ - -/* Compute z = 2^p2 - |z|; requires that 2^p2 >= |z| - The sign of the result is always zero/positive. - */ -STATIC int s_qsub(mp_int z, mp_size p2) -{ - 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; -} - -/* }}} */ - -/* {{{ s_dp2k(z) */ - -STATIC int s_dp2k(mp_int z) -{ - 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; -} - -/* }}} */ - -/* {{{ s_isp2(z) */ - -STATIC int s_isp2(mp_int z) -{ - 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; -} - -/* }}} */ - -/* {{{ s_2expt(z, k) */ - -STATIC int s_2expt(mp_int z, mp_small k) -{ - 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; -} - -/* }}} */ - -/* {{{ s_norm(a, b) */ - -STATIC int s_norm(mp_int a, mp_int b) -{ - mp_digit d = b->digits[MP_USED(b) - 1]; - int k = 0; - - while(d < (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; -} - -/* }}} */ - -/* {{{ s_brmu(z, m) */ - -STATIC mp_result s_brmu(mp_int z, mp_int m) -{ - 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); -} - -/* }}} */ - -/* {{{ s_reduce(x, m, mu, q1, q2) */ - -STATIC int s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2) -{ - 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; -} - -/* }}} */ - -/* {{{ s_embar(a, b, m, mu, c) */ - -/* Perform modular exponentiation using Barrett's method, where mu is - the reduction constant for m. Assumes a < m, b > 0. */ -STATIC mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c) -{ - mp_digit *db, *dbt, umu, d; - mpz_t temp[3]; - mp_result res = 0; - 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; -} - -/* }}} */ - -/* {{{ s_udiv(a, b) */ - -/* Precondition: a >= b and b > 0 - Postcondition: a' = a / b, b' = a % b - */ -STATIC mp_result s_udiv(mp_int a, mp_int b) -{ - 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 && qpos > 0) - q.digits[qpos++] = 0; - - CLAMP(&r); - } - else { - mp_word pfx = r.digits[r.used - 1]; - mp_word qdigit; - - if(r.used > 1 && pfx <= btop) { - 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 = MP_DIGIT_MAX; - } - - 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; -} - -/* }}} */ - -/* {{{ s_outlen(z, r) */ - -STATIC int s_outlen(mp_int z, mp_size r) -{ - mp_result bits; - double raw; - - assert(r >= MP_MIN_RADIX && r <= MP_MAX_RADIX); - - bits = mp_int_count_bits(z); - raw = (double)bits * s_log2[r]; - - return (int)(raw + 0.999999); -} - -/* }}} */ - -/* {{{ s_inlen(len, r) */ - -STATIC mp_size s_inlen(int len, mp_size r) -{ - 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); -} - -/* }}} */ - -/* {{{ s_ch2val(c, r) */ - -STATIC int s_ch2val(char c, int r) -{ - int out; - - if(isdigit((unsigned char) c)) - out = c - '0'; - else if(r > 10 && isalpha((unsigned char) c)) - out = toupper(c) - 'A' + 10; - else - return -1; - - return (out >= r) ? -1 : out; -} - -/* }}} */ - -/* {{{ s_val2ch(v, caps) */ - -STATIC char s_val2ch(int v, int caps) -{ - assert(v >= 0); - - if(v < 10) - return v + '0'; - else { - char out = (v - 10) + 'a'; - - if(caps) - return toupper(out); - else - return out; - } -} - -/* }}} */ - -/* {{{ s_2comp(buf, len) */ - -STATIC void s_2comp(unsigned char *buf, int len) -{ - 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 */ -} - -/* }}} */ - -/* {{{ s_tobin(z, buf, *limpos) */ - -STATIC mp_result s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad) -{ - 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; -} - -/* }}} */ - -/* {{{ s_print(tag, z) */ - -#if DEBUG -void s_print(char *tag, mp_int z) -{ - int i; - - fprintf(stderr, "%s: %c ", tag, - (MP_SIGN(z) == MP_NEG) ? '-' : '+'); - - for(i = MP_USED(z) - 1; i >= 0; --i) - fprintf(stderr, "%0*X", (int)(MP_DIGIT_BIT / 4), z->digits[i]); - - fputc('\n', stderr); - -} - -void s_print_buf(char *tag, mp_digit *buf, mp_size num) -{ - int i; - - fprintf(stderr, "%s: ", tag); - - for(i = num - 1; i >= 0; --i) - fprintf(stderr, "%0*X", (int)(MP_DIGIT_BIT / 4), buf[i]); - - fputc('\n', stderr); -} -#endif - -/* }}} */ - -/* HERE THERE BE DRAGONS */ |