http://git-wip-us.apache.org/repos/asf/incubator-hawq/blob/801100ed/contrib/pgcrypto/imath.c ---------------------------------------------------------------------- diff --git a/contrib/pgcrypto/imath.c b/contrib/pgcrypto/imath.c new file mode 100644 index 0000000..3286cd9 --- /dev/null +++ b/contrib/pgcrypto/imath.c @@ -0,0 +1,3681 @@ +/* imath version 1.3 */ +/* + Name: imath.c + Purpose: Arbitrary precision integer arithmetic routines. + Author: M. J. Fromberger <http://spinning-yarns.org/michael/sw/> + Info: Id: imath.c 21 2006-04-02 18:58:36Z sting + + Copyright (C) 2002 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. + */ +/* contrib/pgcrypto/imath.c */ + +#include "postgres.h" +#include "px.h" +#include "imath.h" + +#undef assert +#define assert(TEST) Assert(TEST) +#define TRACEABLE_CLAMP 0 +#define TRACEABLE_FREE 0 + +/* {{{ 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_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 null argument", + NULL +}; + +/* }}} */ + +/* Optional library flags */ +#define MP_CAP_DIGITS 1 /* flag bit to capitalize letter digits */ + +/* 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). + */ +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, 0.191958720, 0.190551412, 0.189200360, /* 36 37 38 39 */ + 0.187901825, 0.186652411, 0.185449023, 0.184288833, /* 40 41 42 43 */ + 0.183169251, 0.182087900, 0.181042597, 0.180031327, /* 44 45 46 47 */ + 0.179052232, 0.178103594, 0.177183820, 0.176291434, /* 48 49 50 51 */ + 0.175425064, 0.174583430, 0.173765343, 0.172969690, /* 52 53 54 55 */ + 0.172195434, 0.171441601, 0.170707280, 0.169991616, /* 56 57 58 59 */ + 0.169293808, 0.168613099, 0.167948779, 0.167300179, /* 60 61 62 63 */ + 0.166666667 +}; + +/* }}} */ +/* {{{ 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) + +#if TRACEABLE_CLAMP +#define CLAMP(Z) s_clamp(Z) +#else +#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) +#endif + +#undef MIN +#undef MAX +#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) \ +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) + +#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 number of digits allocated to a new mp_int */ +static mp_size default_precision = 64; + +/* Minimum number of digits to invoke recursive multiply */ +static mp_size multiply_threshold = 32; + +/* Default library configuration flags */ +static mp_word mp_flags = MP_CAP_DIGITS; + +/* 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); + +#if TRACEABLE_FREE +static void s_free(void *ptr); +#else +#define s_free(P) px_free(P) +#endif + +/* 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); + +/* Normalize by removing leading zeroes (except when z = 0) */ +#if TRACEABLE_CLAMP +static void s_clamp(mp_int z); +#endif + +/* Fill in a "fake" mp_int on the stack with a given value */ +static void s_fake(mp_int z, int 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(int 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, int 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, int 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 0 +/* 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 + +/* {{{ get_default_precision() */ + +mp_size +mp_get_default_precision(void) +{ + return default_precision; +} + +/* }}} */ + +/* {{{ mp_set_default_precision(s) */ + +void +mp_set_default_precision(mp_size s) +{ + NRCHECK(s > 0); + + default_precision = (mp_size) ROUND_PREC(s); +} + +/* }}} */ + +/* {{{ mp_get_multiply_threshold() */ + +mp_size +mp_get_multiply_threshold(void) +{ + return multiply_threshold; +} + +/* }}} */ + +/* {{{ mp_set_multiply_threshold(s) */ + +void +mp_set_multiply_threshold(mp_size s) +{ + multiply_threshold = s; +} + +/* }}} */ + +/* {{{ mp_int_init(z) */ + +mp_result +mp_int_init(mp_int z) +{ + return mp_int_init_size(z, default_precision); +} + +/* }}} */ + +/* {{{ mp_int_alloc() */ + +mp_int +mp_int_alloc(void) +{ + 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_int_init_size(z, prec) */ + +mp_result +mp_int_init_size(mp_int z, mp_size prec) +{ + 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_int_init_copy(z, old) */ + +mp_result +mp_int_init_copy(mp_int z, mp_int old) +{ + 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_int_init_value(z, value) */ + +mp_result +mp_int_init_value(mp_int z, int 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_int_set_value(z, value) */ + +mp_result +mp_int_set_value(mp_int z, int value) +{ + 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_int_clear(z) */ + +void +mp_int_clear(mp_int z) +{ + if (z == NULL) + return; + + if (MP_DIGITS(z) != NULL) + { + s_free(MP_DIGITS(z)); + MP_DIGITS(z) = NULL; + } +} + +/* }}} */ + +/* {{{ mp_int_free(z) */ + +void +mp_int_free(mp_int z) +{ + NRCHECK(z != NULL); + + if (z->digits != NULL) + mp_int_clear(z); + + px_free(z); +} + +/* }}} */ + +/* {{{ 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, + 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_int_add_value(a, value, c) */ + +mp_result +mp_int_add_value(mp_int a, int 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, + 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_int_sub_value(a, value, c) */ + +mp_result +mp_int_sub_value(mp_int a, int 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 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 = ua + ub; + + 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_int_mul_value(a, value, c) */ + +mp_result +mp_int_mul_value(mp_int a, int 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, int 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) 2 *MP_USED(a); + + 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_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 && (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_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) + { + 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_int_div_value(a, value, q, r) */ + +mp_result +mp_int_div_value(mp_int a, int value, mp_int q, int *r) +{ + 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; +} + +/* }}} */ + +/* {{{ mp_int_div_pow2(a, p2, q, r) */ + +mp_result +mp_int_div_pow2(mp_int a, int 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, int 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(int a, int 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, int 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, int 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(int 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) + 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; +} + +/* }}} */ + +/* {{{ 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); + + 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_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) + { + 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_int_divisible_value(a, v) */ + +int +mp_int_divisible_value(mp_int a, int v) +{ + int 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_sqrt(a, c) */ + +mp_result +mp_int_sqrt(mp_int a, mp_int c) +{ + 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_int_to_int(z, out) */ + +mp_result +mp_int_to_int(mp_int z, int *out) +{ + 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_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, 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_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((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_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 = 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; +} + +/* }}} */ + +/* {{{ 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 = px_alloc(num * sizeof(mp_digit)); + + assert(out != NULL); /* for debugging */ + + return out; +} + +/* }}} */ + +/* {{{ s_realloc(old, num) */ + +static mp_digit * +s_realloc(mp_digit *old, mp_size num) +{ + mp_digit *new = px_realloc(old, num * sizeof(mp_digit)); + + assert(new != NULL); /* for debugging */ + + return new; +} + +/* }}} */ + +/* {{{ s_free(ptr) */ + +#if TRACEABLE_FREE +static void +s_free(void *ptr) +{ + px_free(ptr); +} +#endif + +/* }}} */ + +/* {{{ 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 = s_realloc(MP_DIGITS(z), nsize); + + if (tmp == NULL) + return 0; + + MP_DIGITS(z) = tmp; + MP_ALLOC(z) = nsize; + } + + return 1; +} + +/* }}} */ + +/* {{{ s_clamp(z) */ + +#if TRACEABLE_CLAMP +static void +s_clamp(mp_int z) +{ + mp_size uz = MP_USED(z); + mp_digit *zd = MP_DIGITS(z) + uz - 1; + + while (uz > 1 && (*zd-- == 0)) + --uz; + + MP_USED(z) = uz; +} +#endif + +/* }}} */ + +/* {{{ s_fake(z, value, vbuf) */ + +static void +s_fake(mp_int z, int 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(int v, mp_digit t[]) +{ + 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; +} + +/* }}} */ + +/* {{{ 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, int 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, bot_size + 1); + ZERO(t2, bot_size + 1); + (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); + (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); + + 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; + 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; +} + +/* }}} */ + +/* {{{ 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) */ + +/* Subtract |z| from 2^p2, assuming 2^p2 > |z|, and set z to be 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, int 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) ((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; + 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), 2 * umu), last); + + (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) + 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; +} + +/* }}} */ + +/* {{{ s_outlen(z, r) */ + +/* Precondition: 2 <= r < 64 */ +static int +s_outlen(mp_int z, mp_size r) +{ + mp_result bits; + double raw; + + 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((unsigned char) 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((unsigned char) 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 0 +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 */
http://git-wip-us.apache.org/repos/asf/incubator-hawq/blob/801100ed/contrib/pgcrypto/imath.h ---------------------------------------------------------------------- diff --git a/contrib/pgcrypto/imath.h b/contrib/pgcrypto/imath.h new file mode 100644 index 0000000..f2b02d0 --- /dev/null +++ b/contrib/pgcrypto/imath.h @@ -0,0 +1,217 @@ +/* + Name: imath.h + Purpose: Arbitrary precision integer arithmetic routines. + Author: M. J. Fromberger <http://spinning-yarns.org/michael/sw/> + Info: Id: imath.h 21 2006-04-02 18:58:36Z sting + + Copyright (C) 2002 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. + */ +/* contrib/pgcrypto/imath.h */ + +#ifndef IMATH_H_ +#define IMATH_H_ + +/* use always 32bit digits - should some arch use 16bit digits? */ +#define USE_LONG_LONG + +#include <limits.h> + +typedef unsigned char mp_sign; +typedef unsigned int mp_size; +typedef int mp_result; + +#ifdef USE_LONG_LONG +typedef uint32 mp_digit; +typedef uint64 mp_word; + +#define MP_DIGIT_MAX 0xFFFFFFFFULL +#define MP_WORD_MAX 0xFFFFFFFFFFFFFFFFULL +#else +typedef uint16 mp_digit; +typedef uint32 mp_word; + +#define MP_DIGIT_MAX 0xFFFFUL +#define MP_WORD_MAX 0xFFFFFFFFUL +#endif + +typedef struct mpz +{ + mp_digit *digits; + mp_size alloc; + mp_size used; + mp_sign sign; +} mpz_t , + *mp_int; + +#define MP_DIGITS(Z) ((Z)->digits) +#define MP_ALLOC(Z) ((Z)->alloc) +#define MP_USED(Z) ((Z)->used) +#define MP_SIGN(Z) ((Z)->sign) + +extern const mp_result MP_OK; +extern const mp_result MP_FALSE; +extern const mp_result MP_TRUE; +extern const mp_result MP_MEMORY; +extern const mp_result MP_RANGE; +extern const mp_result MP_UNDEF; +extern const mp_result MP_TRUNC; +extern const mp_result MP_BADARG; + +#define MP_DIGIT_BIT (sizeof(mp_digit) * CHAR_BIT) +#define MP_WORD_BIT (sizeof(mp_word) * CHAR_BIT) + +#define MP_MIN_RADIX 2 +#define MP_MAX_RADIX 36 + +extern const mp_sign MP_NEG; +extern const mp_sign MP_ZPOS; + +#define mp_int_is_odd(Z) ((Z)->digits[0] & 1) +#define mp_int_is_even(Z) !((Z)->digits[0] & 1) + +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); /* c = a */ +void mp_int_swap(mp_int a, mp_int c); /* swap a, c */ +void mp_int_zero(mp_int z); /* z = 0 */ +mp_result mp_int_abs(mp_int a, mp_int c); /* c = |a| */ +mp_result mp_int_neg(mp_int a, mp_int c); /* c = -a */ +mp_result mp_int_add(mp_int a, mp_int b, mp_int c); /* c = a + b */ +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); /* c = a - b */ +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); /* c = a * b */ +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); /* c = a * a */ + +mp_result +mp_int_div(mp_int a, mp_int b, /* q = a / b */ + mp_int q, mp_int r); /* r = a % b */ +mp_result +mp_int_div_value(mp_int a, int value, /* q = a / value */ + mp_int q, int *r); /* r = a % value */ +mp_result +mp_int_div_pow2(mp_int a, int p2, /* q = a / 2^p2 */ + mp_int q, mp_int r); /* r = q % 2^p2 */ +mp_result mp_int_mod(mp_int a, mp_int m, mp_int c); /* c = a % m */ + +#define mp_int_mod_value(A, V, R) mp_int_div_value((A), (V), 0, (R)) +mp_result mp_int_expt(mp_int a, int b, mp_int c); /* c = a^b */ +mp_result mp_int_expt_value(int a, int b, mp_int c); /* c = a^b */ + +int mp_int_compare(mp_int a, mp_int b); /* a <=> b */ +int mp_int_compare_unsigned(mp_int a, mp_int b); /* |a| <=> |b| */ +int mp_int_compare_zero(mp_int z); /* a <=> 0 */ +int mp_int_compare_value(mp_int z, int value); /* a <=> v */ + +/* Returns true if v|a, false otherwise (including errors) */ +int mp_int_divisible_value(mp_int a, int v); + +/* Returns k >= 0 such that z = 2^k, if one exists; otherwise < 0 */ +int mp_int_is_pow2(mp_int z); + +mp_result +mp_int_exptmod(mp_int a, mp_int b, mp_int m, + mp_int c); /* c = a^b (mod m) */ +mp_result +mp_int_exptmod_evalue(mp_int a, int value, + mp_int m, mp_int c); /* c = a^v (mod m) */ +mp_result +mp_int_exptmod_bvalue(int value, mp_int b, + mp_int m, mp_int c); /* c = v^b (mod m) */ +mp_result +mp_int_exptmod_known(mp_int a, mp_int b, + mp_int m, mp_int mu, + mp_int c); /* c = a^b (mod m) */ +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); /* c = 1/a (mod m) */ + +mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c); /* c = gcd(a, b) */ + +mp_result +mp_int_egcd(mp_int a, mp_int b, mp_int c, /* c = gcd(a, b) */ + mp_int x, mp_int y); /* c = ax + by */ + +mp_result mp_int_sqrt(mp_int a, mp_int c); /* c = floor(sqrt(q)) */ + +/* Convert to an int, if representable (returns MP_RANGE if not). */ +mp_result mp_int_to_int(mp_int z, int *out); + +/* Convert to nul-terminated string with the specified radix, writing at + most limit characters including the nul terminator */ +mp_result mp_int_to_string(mp_int z, mp_size radix, + char *str, int limit); + +/* Return the number of characters required to represent + z in the given radix. May over-estimate. */ +mp_result mp_int_string_len(mp_int z, mp_size radix); + +/* Read zero-terminated string into z */ +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); + +/* Return the number of significant bits in z */ +mp_result mp_int_count_bits(mp_int z); + +/* Convert z to two's complement binary, writing at most limit bytes */ +mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit); + +/* Read a two's complement binary value into z from the given buffer */ +mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len); + +/* Return the number of bytes required to represent z in binary. */ +mp_result mp_int_binary_len(mp_int z); + +/* Convert z to unsigned binary, writing at most limit bytes */ +mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit); + +/* Read an unsigned binary value into z from the given buffer */ +mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len); + +/* Return the number of bytes required to represent z as unsigned output */ +mp_result mp_int_unsigned_len(mp_int z); + +/* Return a statically allocated string describing error code res */ +const char *mp_error_string(mp_result res); + +#if 0 +void s_print(char *tag, mp_int z); +void s_print_buf(char *tag, mp_digit *buf, mp_size num); +#endif + +#endif /* end IMATH_H_ */ http://git-wip-us.apache.org/repos/asf/incubator-hawq/blob/801100ed/contrib/pgcrypto/internal-sha2.c ---------------------------------------------------------------------- diff --git a/contrib/pgcrypto/internal-sha2.c b/contrib/pgcrypto/internal-sha2.c new file mode 100644 index 0000000..f86b478 --- /dev/null +++ b/contrib/pgcrypto/internal-sha2.c @@ -0,0 +1,316 @@ +/* + * internal.c + * Wrapper for builtin functions + * + * Copyright (c) 2001 Marko Kreen + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * contrib/pgcrypto/internal-sha2.c + */ + +#include "postgres.h" + +#include <time.h> + +#include "px.h" +#include "sha2.h" + +void init_sha224(PX_MD *h); +void init_sha256(PX_MD *h); +void init_sha384(PX_MD *h); +void init_sha512(PX_MD *h); + +/* SHA224 */ + +static unsigned +int_sha224_len(PX_MD *h) +{ + return SHA224_DIGEST_LENGTH; +} + +static unsigned +int_sha224_block_len(PX_MD *h) +{ + return SHA224_BLOCK_LENGTH; +} + +static void +int_sha224_update(PX_MD *h, const uint8 *data, unsigned dlen) +{ + SHA224_CTX *ctx = (SHA224_CTX *) h->p.ptr; + + SHA224_Update(ctx, data, dlen); +} + +static void +int_sha224_reset(PX_MD *h) +{ + SHA224_CTX *ctx = (SHA224_CTX *) h->p.ptr; + + SHA224_Init(ctx); +} + +static void +int_sha224_finish(PX_MD *h, uint8 *dst) +{ + SHA224_CTX *ctx = (SHA224_CTX *) h->p.ptr; + + SHA224_Final(dst, ctx); +} + +static void +int_sha224_free(PX_MD *h) +{ + SHA224_CTX *ctx = (SHA224_CTX *) h->p.ptr; + + memset(ctx, 0, sizeof(*ctx)); + px_free(ctx); + px_free(h); +} + +/* SHA256 */ + +static unsigned +int_sha256_len(PX_MD *h) +{ + return SHA256_DIGEST_LENGTH; +} + +static unsigned +int_sha256_block_len(PX_MD *h) +{ + return SHA256_BLOCK_LENGTH; +} + +static void +int_sha256_update(PX_MD *h, const uint8 *data, unsigned dlen) +{ + SHA256_CTX *ctx = (SHA256_CTX *) h->p.ptr; + + SHA256_Update(ctx, data, dlen); +} + +static void +int_sha256_reset(PX_MD *h) +{ + SHA256_CTX *ctx = (SHA256_CTX *) h->p.ptr; + + SHA256_Init(ctx); +} + +static void +int_sha256_finish(PX_MD *h, uint8 *dst) +{ + SHA256_CTX *ctx = (SHA256_CTX *) h->p.ptr; + + SHA256_Final(dst, ctx); +} + +static void +int_sha256_free(PX_MD *h) +{ + SHA256_CTX *ctx = (SHA256_CTX *) h->p.ptr; + + memset(ctx, 0, sizeof(*ctx)); + px_free(ctx); + px_free(h); +} + +/* SHA384 */ + +static unsigned +int_sha384_len(PX_MD *h) +{ + return SHA384_DIGEST_LENGTH; +} + +static unsigned +int_sha384_block_len(PX_MD *h) +{ + return SHA384_BLOCK_LENGTH; +} + +static void +int_sha384_update(PX_MD *h, const uint8 *data, unsigned dlen) +{ + SHA384_CTX *ctx = (SHA384_CTX *) h->p.ptr; + + SHA384_Update(ctx, data, dlen); +} + +static void +int_sha384_reset(PX_MD *h) +{ + SHA384_CTX *ctx = (SHA384_CTX *) h->p.ptr; + + SHA384_Init(ctx); +} + +static void +int_sha384_finish(PX_MD *h, uint8 *dst) +{ + SHA384_CTX *ctx = (SHA384_CTX *) h->p.ptr; + + SHA384_Final(dst, ctx); +} + +static void +int_sha384_free(PX_MD *h) +{ + SHA384_CTX *ctx = (SHA384_CTX *) h->p.ptr; + + memset(ctx, 0, sizeof(*ctx)); + px_free(ctx); + px_free(h); +} + +/* SHA512 */ + +static unsigned +int_sha512_len(PX_MD *h) +{ + return SHA512_DIGEST_LENGTH; +} + +static unsigned +int_sha512_block_len(PX_MD *h) +{ + return SHA512_BLOCK_LENGTH; +} + +static void +int_sha512_update(PX_MD *h, const uint8 *data, unsigned dlen) +{ + SHA512_CTX *ctx = (SHA512_CTX *) h->p.ptr; + + SHA512_Update(ctx, data, dlen); +} + +static void +int_sha512_reset(PX_MD *h) +{ + SHA512_CTX *ctx = (SHA512_CTX *) h->p.ptr; + + SHA512_Init(ctx); +} + +static void +int_sha512_finish(PX_MD *h, uint8 *dst) +{ + SHA512_CTX *ctx = (SHA512_CTX *) h->p.ptr; + + SHA512_Final(dst, ctx); +} + +static void +int_sha512_free(PX_MD *h) +{ + SHA512_CTX *ctx = (SHA512_CTX *) h->p.ptr; + + memset(ctx, 0, sizeof(*ctx)); + px_free(ctx); + px_free(h); +} + +/* init functions */ + +void +init_sha224(PX_MD *md) +{ + SHA224_CTX *ctx; + + ctx = px_alloc(sizeof(*ctx)); + memset(ctx, 0, sizeof(*ctx)); + + md->p.ptr = ctx; + + md->result_size = int_sha224_len; + md->block_size = int_sha224_block_len; + md->reset = int_sha224_reset; + md->update = int_sha224_update; + md->finish = int_sha224_finish; + md->free = int_sha224_free; + + md->reset(md); +} + +void +init_sha256(PX_MD *md) +{ + SHA256_CTX *ctx; + + ctx = px_alloc(sizeof(*ctx)); + memset(ctx, 0, sizeof(*ctx)); + + md->p.ptr = ctx; + + md->result_size = int_sha256_len; + md->block_size = int_sha256_block_len; + md->reset = int_sha256_reset; + md->update = int_sha256_update; + md->finish = int_sha256_finish; + md->free = int_sha256_free; + + md->reset(md); +} + +void +init_sha384(PX_MD *md) +{ + SHA384_CTX *ctx; + + ctx = px_alloc(sizeof(*ctx)); + memset(ctx, 0, sizeof(*ctx)); + + md->p.ptr = ctx; + + md->result_size = int_sha384_len; + md->block_size = int_sha384_block_len; + md->reset = int_sha384_reset; + md->update = int_sha384_update; + md->finish = int_sha384_finish; + md->free = int_sha384_free; + + md->reset(md); +} + +void +init_sha512(PX_MD *md) +{ + SHA512_CTX *ctx; + + ctx = px_alloc(sizeof(*ctx)); + memset(ctx, 0, sizeof(*ctx)); + + md->p.ptr = ctx; + + md->result_size = int_sha512_len; + md->block_size = int_sha512_block_len; + md->reset = int_sha512_reset; + md->update = int_sha512_update; + md->finish = int_sha512_finish; + md->free = int_sha512_free; + + md->reset(md); +}
