| /* |
| Name: imath.c |
| Purpose: Arbitrary precision integer arithmetic routines. |
| Author: M. J. Fromberger |
| |
| 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" |
| |
| #include <assert.h> |
| #include <ctype.h> |
| #include <stdlib.h> |
| #include <string.h> |
| |
| 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}; |
| |
| /* 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. |
| |
| If MP_MAX_RADIX is increased, this table should be expanded too. |
| */ |
| static const double s_log2[] = { |
| 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* (D)(D) 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 */ |
| }; |
| |
| /* 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 */ |
| static inline mp_size s_round_prec(mp_size P) { return 2 * ((P + 1) / 2); } |
| |
| /* Set array P of S digits to zero */ |
| static inline void ZERO(mp_digit *P, mp_size S) { |
| mp_size i__ = S * sizeof(mp_digit); |
| mp_digit *p__ = P; |
| memset(p__, 0, i__); |
| } |
| |
| /* Copy S digits from array P to array Q */ |
| static inline void COPY(mp_digit *P, mp_digit *Q, mp_size S) { |
| mp_size i__ = S * sizeof(mp_digit); |
| mp_digit *p__ = P; |
| mp_digit *q__ = Q; |
| memcpy(q__, p__, i__); |
| } |
| |
| /* Reverse N elements of unsigned char in A. */ |
| static inline void REV(unsigned char *A, int N) { |
| unsigned char *u_ = A; |
| unsigned char *v_ = u_ + N - 1; |
| while (u_ < v_) { |
| unsigned char xch = *u_; |
| *u_++ = *v_; |
| *v_-- = xch; |
| } |
| } |
| |
| /* Strip leading zeroes from z_ in-place. */ |
| static inline void CLAMP(mp_int z_) { |
| mp_size uz_ = MP_USED(z_); |
| mp_digit *dz_ = MP_DIGITS(z_) + uz_ - 1; |
| while (uz_ > 1 && (*dz_-- == 0)) --uz_; |
| z_->used = uz_; |
| } |
| |
| /* Select min/max. */ |
| static inline int MIN(int A, int B) { return (B < A ? B : A); } |
| static inline mp_size MAX(mp_size A, mp_size B) { return (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) |
| |
| /* Declare a block of N temporary mpz_t values. |
| These values are initialized to zero. |
| You must add CLEANUP_TEMP() at the end of the function. |
| Use TEMP(i) to access a pointer to the ith value. |
| */ |
| #define DECLARE_TEMP(N) \ |
| struct { \ |
| mpz_t value[(N)]; \ |
| int len; \ |
| mp_result err; \ |
| } temp_ = { \ |
| .len = (N), \ |
| .err = MP_OK, \ |
| }; \ |
| do { \ |
| for (int i = 0; i < temp_.len; i++) { \ |
| mp_int_init(TEMP(i)); \ |
| } \ |
| } while (0) |
| |
| /* Clear all allocated temp values. */ |
| #define CLEANUP_TEMP() \ |
| CLEANUP: \ |
| do { \ |
| for (int i = 0; i < temp_.len; i++) { \ |
| mp_int_clear(TEMP(i)); \ |
| } \ |
| if (temp_.err != MP_OK) { \ |
| return temp_.err; \ |
| } \ |
| } while (0) |
| |
| /* A pointer to the kth temp value. */ |
| #define TEMP(K) (temp_.value + (K)) |
| |
| /* Evaluate E, an expression of type mp_result expected to return MP_OK. If |
| the value is not MP_OK, the error is cached and control resumes at the |
| cleanup handler, which returns it. |
| */ |
| #define REQUIRE(E) \ |
| do { \ |
| temp_.err = (E); \ |
| if (temp_.err != MP_OK) goto CLEANUP; \ |
| } while (0) |
| |
| /* Compare value to zero. */ |
| static inline int CMPZ(mp_int Z) { |
| if (Z->used == 1 && Z->digits[0] == 0) return 0; |
| return (Z->sign == MP_NEG) ? -1 : 1; |
| } |
| |
| static inline mp_word UPPER_HALF(mp_word W) { return (W >> MP_DIGIT_BIT); } |
| static inline mp_digit LOWER_HALF(mp_word W) { return (mp_digit)(W); } |
| |
| /* Report whether the highest-order bit of W is 1. */ |
| static inline bool HIGH_BIT_SET(mp_word W) { |
| return (W >> (MP_WORD_BIT - 1)) != 0; |
| } |
| |
| /* Report whether adding W + V will carry out. */ |
| static inline bool ADD_WILL_OVERFLOW(mp_word W, mp_word V) { |
| return ((MP_WORD_MAX - V) < W); |
| } |
| |
| /* Default number of digits allocated to a new mp_int */ |
| static mp_size default_precision = 8; |
| |
| void mp_int_default_precision(mp_size size) { |
| assert(size > 0); |
| default_precision = size; |
| } |
| |
| /* Minimum number of digits to invoke recursive multiply */ |
| static mp_size multiply_threshold = 32; |
| |
| void mp_int_multiply_threshold(mp_size thresh) { |
| assert(thresh >= sizeof(mp_word)); |
| multiply_threshold = thresh; |
| } |
| |
| /* 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 bool s_pad(mp_int z, mp_size min); |
| |
| /* Ensure Z has at least N digits allocated. */ |
| static inline mp_result GROW(mp_int Z, mp_size N) { |
| return s_pad(Z, N) ? MP_OK : MP_MEMORY; |
| } |
| |
| /* 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[]); |
| static void s_ufake(mp_int z, mp_usmall 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_uvpack(mp_usmall 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); |
| static int s_uvcmp(mp_int a, mp_usmall uv); |
| |
| /* 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_knuth(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); |
| |
| /* Multiply X by Y into Z, ignoring signs. Requires that Z have enough storage |
| preallocated to hold the result. */ |
| static inline void UMUL(mp_int X, mp_int Y, mp_int Z) { |
| mp_size ua_ = MP_USED(X); |
| mp_size 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_); |
| Z->used = o_; |
| CLAMP(Z); |
| } |
| |
| /* Square X into Z. Requires that Z have enough storage to hold the result. */ |
| static inline void USQR(mp_int X, mp_int Z) { |
| mp_size ua_ = MP_USED(X); |
| mp_size o_ = ua_ + ua_; |
| ZERO(MP_DIGITS(Z), o_); |
| (void)s_ksqr(MP_DIGITS(X), MP_DIGITS(Z), ua_); |
| Z->used = o_; |
| CLAMP(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 mp_int_alloc(void) { |
| mp_int out = malloc(sizeof(mpz_t)); |
| |
| if (out != NULL) mp_int_init(out); |
| |
| return out; |
| } |
| |
| mp_result mp_int_init_size(mp_int z, mp_size prec) { |
| assert(z != NULL); |
| |
| if (prec == 0) { |
| prec = default_precision; |
| } else if (prec == 1) { |
| return mp_int_init(z); |
| } else { |
| prec = s_round_prec(prec); |
| } |
| |
| z->digits = s_alloc(prec); |
| if (MP_DIGITS(z) == NULL) return MP_MEMORY; |
| |
| z->digits[0] = 0; |
| z->used = 1; |
| z->alloc = prec; |
| z->sign = MP_ZPOS; |
| |
| return MP_OK; |
| } |
| |
| mp_result mp_int_init_copy(mp_int z, mp_int old) { |
| assert(z != NULL && old != NULL); |
| |
| mp_size uold = MP_USED(old); |
| if (uold == 1) { |
| mp_int_init(z); |
| } else { |
| mp_size target = MAX(uold, default_precision); |
| mp_result res = mp_int_init_size(z, target); |
| if (res != MP_OK) return res; |
| } |
| |
| z->used = uold; |
| z->sign = old->sign; |
| COPY(MP_DIGITS(old), MP_DIGITS(z), uold); |
| |
| return MP_OK; |
| } |
| |
| 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_result mp_int_init_uvalue(mp_int z, mp_usmall uvalue) { |
| mpz_t vtmp; |
| mp_digit vbuf[MP_VALUE_DIGITS(uvalue)]; |
| |
| s_ufake(&vtmp, uvalue, vbuf); |
| return mp_int_init_copy(z, &vtmp); |
| } |
| |
| 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_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue) { |
| mpz_t vtmp; |
| mp_digit vbuf[MP_VALUE_DIGITS(uvalue)]; |
| |
| s_ufake(&vtmp, uvalue, vbuf); |
| return mp_int_copy(&vtmp, z); |
| } |
| |
| void mp_int_clear(mp_int z) { |
| if (z == NULL) return; |
| |
| if (MP_DIGITS(z) != NULL) { |
| if (MP_DIGITS(z) != &(z->single)) s_free(MP_DIGITS(z)); |
| |
| z->digits = NULL; |
| } |
| } |
| |
| void mp_int_free(mp_int z) { |
| assert(z != NULL); |
| |
| mp_int_clear(z); |
| free(z); /* note: NOT s_free() */ |
| } |
| |
| mp_result mp_int_copy(mp_int a, mp_int c) { |
| assert(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); |
| |
| c->used = ua; |
| c->sign = a->sign; |
| } |
| |
| return MP_OK; |
| } |
| |
| void mp_int_swap(mp_int a, mp_int c) { |
| if (a != c) { |
| mpz_t tmp = *a; |
| |
| *a = *c; |
| *c = tmp; |
| |
| if (MP_DIGITS(a) == &(c->single)) a->digits = &(a->single); |
| if (MP_DIGITS(c) == &(a->single)) c->digits = &(c->single); |
| } |
| } |
| |
| void mp_int_zero(mp_int z) { |
| assert(z != NULL); |
| |
| z->digits[0] = 0; |
| z->used = 1; |
| z->sign = MP_ZPOS; |
| } |
| |
| mp_result mp_int_abs(mp_int a, mp_int c) { |
| assert(a != NULL && c != NULL); |
| |
| mp_result res; |
| if ((res = mp_int_copy(a, c)) != MP_OK) return res; |
| |
| c->sign = MP_ZPOS; |
| return MP_OK; |
| } |
| |
| mp_result mp_int_neg(mp_int a, mp_int c) { |
| assert(a != NULL && c != NULL); |
| |
| mp_result res; |
| if ((res = mp_int_copy(a, c)) != MP_OK) return res; |
| |
| if (CMPZ(c) != 0) c->sign = 1 - MP_SIGN(a); |
| |
| return MP_OK; |
| } |
| |
| mp_result mp_int_add(mp_int a, mp_int b, mp_int c) { |
| assert(a != NULL && b != NULL && c != NULL); |
| |
| mp_size ua = MP_USED(a); |
| mp_size ub = MP_USED(b); |
| mp_size max = MAX(ua, ub); |
| |
| if (MP_SIGN(a) == MP_SIGN(b)) { |
| /* Same sign -- add magnitudes, preserve sign of addends */ |
| if (!s_pad(c, max)) return MP_MEMORY; |
| |
| mp_digit carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub); |
| mp_size uc = max; |
| |
| if (carry) { |
| if (!s_pad(c, max + 1)) return MP_MEMORY; |
| |
| c->digits[max] = carry; |
| ++uc; |
| } |
| |
| c->used = uc; |
| c->sign = a->sign; |
| |
| } else { |
| /* Different signs -- subtract magnitudes, preserve sign of greater */ |
| 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. |
| A special case yields zero for equal magnitudes. |
| */ |
| mp_int x, y; |
| 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)); |
| c->used = x->used; |
| CLAMP(c); |
| |
| /* Give result the sign of the larger */ |
| c->sign = x->sign; |
| } |
| |
| return MP_OK; |
| } |
| |
| 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_result mp_int_sub(mp_int a, mp_int b, mp_int c) { |
| assert(a != NULL && b != NULL && c != NULL); |
| |
| mp_size ua = MP_USED(a); |
| mp_size ub = MP_USED(b); |
| mp_size max = MAX(ua, ub); |
| |
| if (MP_SIGN(a) != MP_SIGN(b)) { |
| /* Different signs -- add magnitudes and keep sign of a */ |
| if (!s_pad(c, max)) return MP_MEMORY; |
| |
| mp_digit carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub); |
| mp_size uc = max; |
| |
| if (carry) { |
| if (!s_pad(c, max + 1)) return MP_MEMORY; |
| |
| c->digits[max] = carry; |
| ++uc; |
| } |
| |
| c->used = uc; |
| c->sign = a->sign; |
| |
| } else { |
| /* Same signs -- subtract magnitudes */ |
| if (!s_pad(c, max)) return MP_MEMORY; |
| mp_int x, y; |
| mp_sign osign; |
| |
| int cmp = s_ucmp(a, b); |
| 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)); |
| c->used = x->used; |
| CLAMP(c); |
| |
| c->sign = osign; |
| } |
| |
| return MP_OK; |
| } |
| |
| 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_result mp_int_mul(mp_int a, mp_int b, mp_int c) { |
| assert(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 */ |
| mp_sign 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. */ |
| mp_size ua = MP_USED(a); |
| mp_size ub = MP_USED(b); |
| mp_size osize = MAX(ua, ub); |
| osize = 4 * ((osize + 1) / 2); |
| |
| mp_digit *out; |
| mp_size p = 0; |
| if (c == a || c == b) { |
| p = MAX(s_round_prec(osize), 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)); |
| c->digits = out; |
| c->alloc = p; |
| } |
| |
| c->used = osize; /* might not be true, but we'll fix it ... */ |
| CLAMP(c); /* ... right here */ |
| c->sign = osign; |
| |
| return MP_OK; |
| } |
| |
| 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_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c) { |
| assert(a != NULL && c != NULL && p2 >= 0); |
| |
| mp_result res = mp_int_copy(a, c); |
| if (res != MP_OK) return res; |
| |
| if (s_qmul(c, (mp_size)p2)) { |
| return MP_OK; |
| } else { |
| return MP_MEMORY; |
| } |
| } |
| |
| mp_result mp_int_sqr(mp_int a, mp_int c) { |
| assert(a != NULL && c != NULL); |
| |
| /* Get a temporary buffer big enough to hold the result */ |
| mp_size osize = (mp_size)4 * ((MP_USED(a) + 1) / 2); |
| mp_size p = 0; |
| mp_digit *out; |
| if (a == c) { |
| p = s_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)); |
| c->digits = out; |
| c->alloc = p; |
| } |
| |
| c->used = osize; /* might not be true, but we'll fix it ... */ |
| CLAMP(c); /* ... right here */ |
| c->sign = MP_ZPOS; |
| |
| return MP_OK; |
| } |
| |
| mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r) { |
| assert(a != NULL && b != NULL && q != r); |
| |
| int cmp; |
| mp_result res = MP_OK; |
| mp_int qout, rout; |
| mp_sign sa = MP_SIGN(a); |
| mp_sign sb = MP_SIGN(b); |
| 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) q->sign = 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. |
| */ |
| DECLARE_TEMP(2); |
| int lg; |
| if ((lg = s_isp2(b)) < 0) { |
| if (q && b != q) { |
| REQUIRE(mp_int_copy(a, q)); |
| qout = q; |
| } else { |
| REQUIRE(mp_int_copy(a, TEMP(0))); |
| qout = TEMP(0); |
| } |
| |
| if (r && a != r) { |
| REQUIRE(mp_int_copy(b, r)); |
| rout = r; |
| } else { |
| REQUIRE(mp_int_copy(b, TEMP(1))); |
| rout = TEMP(1); |
| } |
| |
| REQUIRE(s_udiv_knuth(qout, rout)); |
| } else { |
| if (q) REQUIRE(mp_int_copy(a, q)); |
| if (r) REQUIRE(mp_int_copy(a, r)); |
| |
| 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) { |
| rout->sign = sa; |
| if (CMPZ(rout) == 0) rout->sign = MP_ZPOS; |
| } |
| if (qout) { |
| qout->sign = (sa == sb) ? MP_ZPOS : MP_NEG; |
| if (CMPZ(qout) == 0) qout->sign = MP_ZPOS; |
| } |
| |
| if (q) REQUIRE(mp_int_copy(qout, q)); |
| if (r) REQUIRE(mp_int_copy(rout, r)); |
| CLEANUP_TEMP(); |
| return res; |
| } |
| |
| mp_result mp_int_mod(mp_int a, mp_int m, mp_int c) { |
| DECLARE_TEMP(1); |
| mp_int out = (m == c) ? TEMP(0) : c; |
| REQUIRE(mp_int_div(a, m, NULL, out)); |
| if (CMPZ(out) < 0) { |
| REQUIRE(mp_int_add(out, m, c)); |
| } else { |
| REQUIRE(mp_int_copy(out, c)); |
| } |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small *r) { |
| mpz_t vtmp; |
| mp_digit vbuf[MP_VALUE_DIGITS(value)]; |
| s_fake(&vtmp, value, vbuf); |
| |
| DECLARE_TEMP(1); |
| REQUIRE(mp_int_div(a, &vtmp, q, TEMP(0))); |
| |
| if (r) (void)mp_int_to_int(TEMP(0), r); /* can't fail */ |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r) { |
| assert(a != NULL && p2 >= 0 && q != r); |
| |
| mp_result res = MP_OK; |
| if (q != NULL && (res = mp_int_copy(a, q)) == MP_OK) { |
| s_qdiv(q, (mp_size)p2); |
| } |
| |
| if (res == MP_OK && r != NULL && (res = mp_int_copy(a, r)) == MP_OK) { |
| s_qmod(r, (mp_size)p2); |
| } |
| |
| return res; |
| } |
| |
| mp_result mp_int_expt(mp_int a, mp_small b, mp_int c) { |
| assert(c != NULL); |
| if (b < 0) return MP_RANGE; |
| |
| DECLARE_TEMP(1); |
| REQUIRE(mp_int_copy(a, TEMP(0))); |
| |
| (void)mp_int_set_value(c, 1); |
| unsigned int v = labs(b); |
| while (v != 0) { |
| if (v & 1) { |
| REQUIRE(mp_int_mul(c, TEMP(0), c)); |
| } |
| |
| v >>= 1; |
| if (v == 0) break; |
| |
| REQUIRE(mp_int_sqr(TEMP(0), TEMP(0))); |
| } |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c) { |
| assert(c != NULL); |
| if (b < 0) return MP_RANGE; |
| |
| DECLARE_TEMP(1); |
| REQUIRE(mp_int_set_value(TEMP(0), a)); |
| |
| (void)mp_int_set_value(c, 1); |
| unsigned int v = labs(b); |
| while (v != 0) { |
| if (v & 1) { |
| REQUIRE(mp_int_mul(c, TEMP(0), c)); |
| } |
| |
| v >>= 1; |
| if (v == 0) break; |
| |
| REQUIRE(mp_int_sqr(TEMP(0), TEMP(0))); |
| } |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c) { |
| assert(a != NULL && b != NULL && c != NULL); |
| if (MP_SIGN(b) == MP_NEG) return MP_RANGE; |
| |
| DECLARE_TEMP(1); |
| REQUIRE(mp_int_copy(a, TEMP(0))); |
| |
| (void)mp_int_set_value(c, 1); |
| for (unsigned ix = 0; ix < MP_USED(b); ++ix) { |
| mp_digit d = b->digits[ix]; |
| |
| for (unsigned jx = 0; jx < MP_DIGIT_BIT; ++jx) { |
| if (d & 1) { |
| REQUIRE(mp_int_mul(c, TEMP(0), c)); |
| } |
| |
| d >>= 1; |
| if (d == 0 && ix + 1 == MP_USED(b)) break; |
| REQUIRE(mp_int_sqr(TEMP(0), TEMP(0))); |
| } |
| } |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| int mp_int_compare(mp_int a, mp_int b) { |
| assert(a != NULL && b != NULL); |
| |
| mp_sign sa = MP_SIGN(a); |
| if (sa == MP_SIGN(b)) { |
| int cmp = s_ucmp(a, b); |
| |
| /* If they're both zero or positive, the normal comparison applies; if both |
| negative, the sense is reversed. */ |
| if (sa == MP_ZPOS) { |
| return cmp; |
| } else { |
| return -cmp; |
| } |
| } else if (sa == MP_ZPOS) { |
| return 1; |
| } else { |
| return -1; |
| } |
| } |
| |
| int mp_int_compare_unsigned(mp_int a, mp_int b) { |
| assert(a != NULL && b != NULL); |
| |
| return s_ucmp(a, b); |
| } |
| |
| int mp_int_compare_zero(mp_int z) { |
| assert(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; |
| } |
| } |
| |
| int mp_int_compare_value(mp_int z, mp_small value) { |
| assert(z != NULL); |
| |
| mp_sign vsign = (value < 0) ? MP_NEG : MP_ZPOS; |
| if (vsign == MP_SIGN(z)) { |
| int cmp = s_vcmp(z, value); |
| |
| return (vsign == MP_ZPOS) ? cmp : -cmp; |
| } else { |
| return (value < 0) ? 1 : -1; |
| } |
| } |
| |
| int mp_int_compare_uvalue(mp_int z, mp_usmall uv) { |
| assert(z != NULL); |
| |
| if (MP_SIGN(z) == MP_NEG) { |
| return -1; |
| } else { |
| return s_uvcmp(z, uv); |
| } |
| } |
| |
| mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c) { |
| assert(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; |
| |
| mp_size um = MP_USED(m); |
| DECLARE_TEMP(3); |
| REQUIRE(GROW(TEMP(0), 2 * um)); |
| REQUIRE(GROW(TEMP(1), 2 * um)); |
| |
| mp_int s; |
| if (c == b || c == m) { |
| REQUIRE(GROW(TEMP(2), 2 * um)); |
| s = TEMP(2); |
| } else { |
| s = c; |
| } |
| |
| REQUIRE(mp_int_mod(a, m, TEMP(0))); |
| REQUIRE(s_brmu(TEMP(1), m)); |
| REQUIRE(s_embar(TEMP(0), b, m, TEMP(1), s)); |
| REQUIRE(mp_int_copy(s, c)); |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| 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_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_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, |
| mp_int c) { |
| assert(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; |
| |
| DECLARE_TEMP(2); |
| mp_size um = MP_USED(m); |
| REQUIRE(GROW(TEMP(0), 2 * um)); |
| |
| mp_int s; |
| if (c == b || c == m) { |
| REQUIRE(GROW(TEMP(1), 2 * um)); |
| s = TEMP(1); |
| } else { |
| s = c; |
| } |
| |
| REQUIRE(mp_int_mod(a, m, TEMP(0))); |
| REQUIRE(s_embar(TEMP(0), b, m, mu, s)); |
| REQUIRE(mp_int_copy(s, c)); |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| mp_result mp_int_redux_const(mp_int m, mp_int c) { |
| assert(m != NULL && c != NULL && m != c); |
| |
| return s_brmu(c, m); |
| } |
| |
| mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c) { |
| assert(a != NULL && m != NULL && c != NULL); |
| |
| if (CMPZ(a) == 0 || CMPZ(m) <= 0) return MP_RANGE; |
| |
| DECLARE_TEMP(2); |
| |
| REQUIRE(mp_int_egcd(a, m, TEMP(0), TEMP(1), NULL)); |
| |
| if (mp_int_compare_value(TEMP(0), 1) != 0) { |
| REQUIRE(MP_UNDEF); |
| } |
| |
| /* It is first necessary to constrain the value to the proper range */ |
| REQUIRE(mp_int_mod(TEMP(1), m, TEMP(1))); |
| |
| /* 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 (MP_SIGN(a) == MP_NEG) { |
| REQUIRE(mp_int_sub(m, TEMP(1), c)); |
| } else { |
| REQUIRE(mp_int_copy(TEMP(1), c)); |
| } |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| /* Binary GCD algorithm due to Josef Stein, 1961 */ |
| mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c) { |
| assert(a != NULL && b != NULL && c != NULL); |
| |
| int ca = CMPZ(a); |
| int 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); |
| } |
| |
| DECLARE_TEMP(3); |
| REQUIRE(mp_int_copy(a, TEMP(0))); |
| REQUIRE(mp_int_copy(b, TEMP(1))); |
| |
| TEMP(0)->sign = MP_ZPOS; |
| TEMP(1)->sign = MP_ZPOS; |
| |
| int k = 0; |
| { /* Divide out common factors of 2 from u and v */ |
| int div2_u = s_dp2k(TEMP(0)); |
| int div2_v = s_dp2k(TEMP(1)); |
| |
| k = MIN(div2_u, div2_v); |
| s_qdiv(TEMP(0), (mp_size)k); |
| s_qdiv(TEMP(1), (mp_size)k); |
| } |
| |
| if (mp_int_is_odd(TEMP(0))) { |
| REQUIRE(mp_int_neg(TEMP(1), TEMP(2))); |
| } else { |
| REQUIRE(mp_int_copy(TEMP(0), TEMP(2))); |
| } |
| |
| for (;;) { |
| s_qdiv(TEMP(2), s_dp2k(TEMP(2))); |
| |
| if (CMPZ(TEMP(2)) > 0) { |
| REQUIRE(mp_int_copy(TEMP(2), TEMP(0))); |
| } else { |
| REQUIRE(mp_int_neg(TEMP(2), TEMP(1))); |
| } |
| |
| REQUIRE(mp_int_sub(TEMP(0), TEMP(1), TEMP(2))); |
| |
| if (CMPZ(TEMP(2)) == 0) break; |
| } |
| |
| REQUIRE(mp_int_abs(TEMP(0), c)); |
| if (!s_qmul(c, (mp_size)k)) REQUIRE(MP_MEMORY); |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| /* 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) { |
| assert(a != NULL && b != NULL && c != NULL && (x != NULL || y != NULL)); |
| |
| mp_result res = MP_OK; |
| int ca = CMPZ(a); |
| int 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 */ |
| DECLARE_TEMP(8); |
| REQUIRE(mp_int_set_value(TEMP(0), 1)); |
| REQUIRE(mp_int_set_value(TEMP(3), 1)); |
| REQUIRE(mp_int_copy(a, TEMP(4))); |
| REQUIRE(mp_int_copy(b, TEMP(5))); |
| |
| /* We will work with absolute values here */ |
| TEMP(4)->sign = MP_ZPOS; |
| TEMP(5)->sign = MP_ZPOS; |
| |
| int k = 0; |
| { /* 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); |
| } |
| |
| REQUIRE(mp_int_copy(TEMP(4), TEMP(6))); |
| REQUIRE(mp_int_copy(TEMP(5), TEMP(7))); |
| |
| 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))) { |
| REQUIRE(mp_int_add(TEMP(0), TEMP(7), TEMP(0))); |
| REQUIRE(mp_int_sub(TEMP(1), TEMP(6), TEMP(1))); |
| } |
| |
| 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))) { |
| REQUIRE(mp_int_add(TEMP(2), TEMP(7), TEMP(2))); |
| REQUIRE(mp_int_sub(TEMP(3), TEMP(6), TEMP(3))); |
| } |
| |
| s_qdiv(TEMP(2), 1); |
| s_qdiv(TEMP(3), 1); |
| } |
| |
| if (mp_int_compare(TEMP(4), TEMP(5)) >= 0) { |
| REQUIRE(mp_int_sub(TEMP(4), TEMP(5), TEMP(4))); |
| REQUIRE(mp_int_sub(TEMP(0), TEMP(2), TEMP(0))); |
| REQUIRE(mp_int_sub(TEMP(1), TEMP(3), TEMP(1))); |
| } else { |
| REQUIRE(mp_int_sub(TEMP(5), TEMP(4), TEMP(5))); |
| REQUIRE(mp_int_sub(TEMP(2), TEMP(0), TEMP(2))); |
| REQUIRE(mp_int_sub(TEMP(3), TEMP(1), TEMP(3))); |
| } |
| |
| if (CMPZ(TEMP(4)) == 0) { |
| if (x) REQUIRE(mp_int_copy(TEMP(2), x)); |
| if (y) REQUIRE(mp_int_copy(TEMP(3), y)); |
| if (c) { |
| if (!s_qmul(TEMP(5), k)) { |
| REQUIRE(MP_MEMORY); |
| } |
| REQUIRE(mp_int_copy(TEMP(5), c)); |
| } |
| |
| break; |
| } |
| } |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c) { |
| assert(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. |
| */ |
| DECLARE_TEMP(1); |
| REQUIRE(mp_int_gcd(a, b, TEMP(0))); |
| REQUIRE(mp_int_div(a, TEMP(0), TEMP(0), NULL)); |
| REQUIRE(mp_int_mul(TEMP(0), b, TEMP(0))); |
| REQUIRE(mp_int_copy(TEMP(0), c)); |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| bool 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 false; |
| } |
| return rem == 0; |
| } |
| |
| int mp_int_is_pow2(mp_int z) { |
| assert(z != NULL); |
| |
| return s_isp2(z); |
| } |
| |
| /* 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) { |
| assert(a != NULL && c != NULL && b > 0); |
| |
| if (b == 1) { |
| return mp_int_copy(a, c); |
| } |
| bool flips = false; |
| 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 = true; |
| } |
| } |
| |
| DECLARE_TEMP(5); |
| REQUIRE(mp_int_copy(a, TEMP(0))); |
| REQUIRE(mp_int_copy(a, TEMP(1))); |
| TEMP(0)->sign = MP_ZPOS; |
| TEMP(1)->sign = MP_ZPOS; |
| |
| for (;;) { |
| REQUIRE(mp_int_expt(TEMP(1), b, TEMP(2))); |
| |
| if (mp_int_compare_unsigned(TEMP(2), TEMP(0)) <= 0) break; |
| |
| REQUIRE(mp_int_sub(TEMP(2), TEMP(0), TEMP(2))); |
| REQUIRE(mp_int_expt(TEMP(1), b - 1, TEMP(3))); |
| REQUIRE(mp_int_mul_value(TEMP(3), b, TEMP(3))); |
| REQUIRE(mp_int_div(TEMP(2), TEMP(3), TEMP(4), NULL)); |
| REQUIRE(mp_int_sub(TEMP(1), TEMP(4), TEMP(4))); |
| |
| if (mp_int_compare_unsigned(TEMP(1), TEMP(4)) == 0) { |
| REQUIRE(mp_int_sub_value(TEMP(4), 1, TEMP(4))); |
| } |
| REQUIRE(mp_int_copy(TEMP(4), TEMP(1))); |
| } |
| |
| REQUIRE(mp_int_copy(TEMP(1), c)); |
| |
| /* If the original value of a was negative, flip the output sign. */ |
| if (flips) (void)mp_int_neg(c, c); /* cannot fail */ |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| mp_result mp_int_to_int(mp_int z, mp_small *out) { |
| assert(z != NULL); |
| |
| /* Make sure the value is representable as a small integer */ |
| mp_sign 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; |
| } |
| |
| mp_usmall uz = MP_USED(z); |
| mp_digit *dz = MP_DIGITS(z) + uz - 1; |
| mp_small uv = 0; |
| while (uz > 0) { |
| uv <<= MP_DIGIT_BIT / 2; |
| uv = (uv << (MP_DIGIT_BIT / 2)) | *dz--; |
| --uz; |
| } |
| |
| if (out) *out = (mp_small)((sz == MP_NEG) ? -uv : uv); |
| |
| return MP_OK; |
| } |
| |
| mp_result mp_int_to_uint(mp_int z, mp_usmall *out) { |
| assert(z != NULL); |
| |
| /* Make sure the value is representable as an unsigned small integer */ |
| mp_size sz = MP_SIGN(z); |
| if (sz == MP_NEG || mp_int_compare_uvalue(z, MP_USMALL_MAX) > 0) { |
| return MP_RANGE; |
| } |
| |
| mp_size uz = MP_USED(z); |
| mp_digit *dz = MP_DIGITS(z) + uz - 1; |
| mp_usmall uv = 0; |
| |
| while (uz > 0) { |
| uv <<= MP_DIGIT_BIT / 2; |
| uv = (uv << (MP_DIGIT_BIT / 2)) | *dz--; |
| --uz; |
| } |
| |
| if (out) *out = uv; |
| |
| return MP_OK; |
| } |
| |
| mp_result mp_int_to_string(mp_int z, mp_size radix, char *str, int limit) { |
| assert(z != NULL && str != NULL && limit >= 2); |
| assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX); |
| |
| int cmp = 0; |
| if (CMPZ(z) == 0) { |
| *str++ = s_val2ch(0, 1); |
| } else { |
| mp_result res; |
| 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_result mp_int_string_len(mp_int z, mp_size radix) { |
| assert(z != NULL); |
| assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX); |
| |
| int len = s_outlen(z, radix) + 1; /* for terminator */ |
| |
| /* Allow for sign marker on negatives */ |
| if (MP_SIGN(z) == MP_NEG) len += 1; |
| |
| return len; |
| } |
| |
| /* 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_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, |
| char **end) { |
| assert(z != NULL && str != NULL); |
| assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX); |
| |
| /* Skip leading whitespace */ |
| while (isspace((unsigned char)*str)) ++str; |
| |
| /* Handle leading sign tag (+/-, positive default) */ |
| switch (*str) { |
| case '-': |
| z->sign = MP_NEG; |
| ++str; |
| break; |
| case '+': |
| ++str; /* fallthrough */ |
| default: |
| z->sign = MP_ZPOS; |
| break; |
| } |
| |
| /* Skip leading zeroes */ |
| int ch; |
| 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; |
| |
| z->used = 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) z->sign = MP_ZPOS; |
| |
| if (end != NULL) *end = (char *)str; |
| |
| /* Return a truncation error if the string has unprocessed characters |
| remaining, so the caller can tell if the whole string was done */ |
| if (*str != '\0') { |
| return MP_TRUNC; |
| } else { |
| return MP_OK; |
| } |
| } |
| |
| mp_result mp_int_count_bits(mp_int z) { |
| assert(z != NULL); |
| |
| mp_size uz = MP_USED(z); |
| if (uz == 1 && z->digits[0] == 0) return 1; |
| |
| --uz; |
| mp_size nbits = uz * MP_DIGIT_BIT; |
| mp_digit d = z->digits[uz]; |
| |
| while (d != 0) { |
| d >>= 1; |
| ++nbits; |
| } |
| |
| return nbits; |
| } |
| |
| mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit) { |
| static const int PAD_FOR_2C = 1; |
| |
| assert(z != NULL && buf != NULL); |
| |
| int limpos = limit; |
| mp_result res = s_tobin(z, buf, &limpos, PAD_FOR_2C); |
| |
| if (MP_SIGN(z) == MP_NEG) s_2comp(buf, limpos); |
| |
| return res; |
| } |
| |
| mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len) { |
| assert(z != NULL && buf != NULL && len > 0); |
| |
| /* Figure out how many digits are needed to represent this value */ |
| mp_size 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)) { |
| z->sign = MP_NEG; |
| s_2comp(buf, len); |
| } |
| |
| mp_digit *dz = MP_DIGITS(z); |
| unsigned char *tmp = buf; |
| for (int i = len; i > 0; --i, ++tmp) { |
| s_qmul(z, (mp_size)CHAR_BIT); |
| *dz |= *tmp; |
| } |
| |
| /* Restore 2's complement if we took it before */ |
| if (MP_SIGN(z) == MP_NEG) s_2comp(buf, len); |
| |
| return MP_OK; |
| } |
| |
| mp_result mp_int_binary_len(mp_int z) { |
| mp_result res = mp_int_count_bits(z); |
| if (res <= 0) return res; |
| |
| int bytes = mp_int_unsigned_len(z); |
| |
| /* 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_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit) { |
| static const int NO_PADDING = 0; |
| |
| assert(z != NULL && buf != NULL); |
| |
| return s_tobin(z, buf, &limit, NO_PADDING); |
| } |
| |
| mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len) { |
| assert(z != NULL && buf != NULL && len > 0); |
| |
| /* Figure out how many digits are needed to represent this value */ |
| mp_size need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT; |
| if (!s_pad(z, need)) return MP_MEMORY; |
| |
| mp_int_zero(z); |
| |
| unsigned char *tmp = buf; |
| for (int i = len; i > 0; --i, ++tmp) { |
| (void)s_qmul(z, CHAR_BIT); |
| *MP_DIGITS(z) |= *tmp; |
| } |
| |
| return MP_OK; |
| } |
| |
| mp_result mp_int_unsigned_len(mp_int z) { |
| mp_result res = mp_int_count_bits(z); |
| if (res <= 0) return res; |
| |
| int bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT; |
| return bytes; |
| } |
| |
| const char *mp_error_string(mp_result res) { |
| if (res > 0) return s_unknown_err; |
| |
| res = -res; |
| int ix; |
| 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. */ |
| |
| #if DEBUG |
| static const mp_digit fill = (mp_digit)0xdeadbeefabad1dea; |
| #endif |
| |
| static mp_digit *s_alloc(mp_size num) { |
| mp_digit *out = malloc(num * sizeof(mp_digit)); |
| assert(out != NULL); |
| |
| #if DEBUG |
| for (mp_size ix = 0; ix < num; ++ix) out[ix] = fill; |
| #endif |
| return out; |
| } |
| |
| static mp_digit *s_realloc(mp_digit *old, mp_size osize, mp_size nsize) { |
| #if DEBUG |
| mp_digit *new = s_alloc(nsize); |
| assert(new != NULL); |
| |
| for (mp_size ix = 0; ix < nsize; ++ix) new[ix] = fill; |
| memcpy(new, old, osize * sizeof(mp_digit)); |
| #else |
| mp_digit *new = realloc(old, nsize * sizeof(mp_digit)); |
| assert(new != NULL); |
| #endif |
| |
| return new; |
| } |
| |
| static void s_free(void *ptr) { free(ptr); } |
| |
| static bool s_pad(mp_int z, mp_size min) { |
| if (MP_ALLOC(z) < min) { |
| mp_size nsize = s_round_prec(min); |
| mp_digit *tmp; |
| |
| if (z->digits == &(z->single)) { |
| if ((tmp = s_alloc(nsize)) == NULL) return false; |
| tmp[0] = z->single; |
| } else if ((tmp = s_realloc(MP_DIGITS(z), MP_ALLOC(z), nsize)) == NULL) { |
| return false; |
| } |
| |
| z->digits = tmp; |
| z->alloc = nsize; |
| } |
| |
| return true; |
| } |
| |
| /* Note: This will not work correctly when value == MP_SMALL_MIN */ |
| static void s_fake(mp_int z, mp_small value, mp_digit vbuf[]) { |
| mp_usmall uv = (mp_usmall)(value < 0) ? -value : value; |
| s_ufake(z, uv, vbuf); |
| if (value < 0) z->sign = MP_NEG; |
| } |
| |
| static void s_ufake(mp_int z, mp_usmall value, mp_digit vbuf[]) { |
| mp_size ndig = (mp_size)s_uvpack(value, vbuf); |
| |
| z->used = ndig; |
| z->alloc = MP_VALUE_DIGITS(value); |
| z->sign = MP_ZPOS; |
| z->digits = vbuf; |
| } |
| |
| 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; |
| } |
| |
| static int s_uvpack(mp_usmall uv, mp_digit t[]) { |
| 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; |
| } |
| |
| 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); |
| } |
| } |
| |
| static int s_vcmp(mp_int a, mp_small v) { |
| mp_usmall uv = (v < 0) ? -(mp_usmall)v : (mp_usmall)v; |
| return s_uvcmp(a, uv); |
| } |
| |
| static int s_uvcmp(mp_int a, mp_usmall uv) { |
| mpz_t vtmp; |
| mp_digit vdig[MP_VALUE_DIGITS(uv)]; |
| |
| s_ufake(&vtmp, uv, vdig); |
| return s_ucmp(a, &vtmp); |
| } |
| |
| 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; |
| } |
| |
| 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); |
| } |
| |
| 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; |
| } |
| |
| 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; |
| } |
| } |
| |
| 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; |
| } |
| |
| 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); |
| } |
| } |
| |
| 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; |
| a->used += 1; |
| } |
| } |
| |
| 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; |
| a->used += 1; |
| } |
| } |
| |
| 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); |
| } |
| |
| 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; |
| } |
| |
| 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++; |
| } |
| |
| z->used = 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) z->sign = MP_ZPOS; |
| } |
| |
| 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 = (1u << rest) - 1; |
| |
| if (start <= uz) { |
| z->used = start; |
| z->digits[start - 1] &= mask; |
| CLAMP(z); |
| } |
| } |
| |
| 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; |
| } |
| } |
| |
| z->used = uz; |
| CLAMP(z); |
| |
| return 1; |
| } |
| |
| /* 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 = (1u << (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 */ |
| |
| z->sign = MP_ZPOS; |
| CLAMP(z); |
| |
| return 1; |
| } |
| |
| 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; |
| } |
| |
| 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; |
| } |
| |
| 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) = (1u << rest); |
| z->used = ndig; |
| |
| return 1; |
| } |
| |
| static int s_norm(mp_int a, mp_int b) { |
| mp_digit d = b->digits[MP_USED(b) - 1]; |
| int k = 0; |
| |
| while (d < (1u << (mp_digit)(MP_DIGIT_BIT - 1))) { /* d < (MP_RADIX / 2) */ |
| d <<= 1; |
| ++k; |
| } |
| |
| /* These multiplications can't fail */ |
| if (k != 0) { |
| (void)s_qmul(a, (mp_size)k); |
| (void)s_qmul(b, (mp_size)k); |
| } |
| |
| return k; |
| } |
| |
| static 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); |
| } |
| |
| 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; |
| } |
| |
| /* 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 umu = MP_USED(mu); |
| mp_digit *db = MP_DIGITS(b); |
| mp_digit *dbt = db + MP_USED(b) - 1; |
| |
| DECLARE_TEMP(3); |
| REQUIRE(GROW(TEMP(0), 4 * umu)); |
| REQUIRE(GROW(TEMP(1), 4 * umu)); |
| REQUIRE(GROW(TEMP(2), 4 * umu)); |
| ZERO(TEMP(0)->digits, TEMP(0)->alloc); |
| ZERO(TEMP(1)->digits, TEMP(1)->alloc); |
| ZERO(TEMP(2)->digits, TEMP(2)->alloc); |
| |
| (void)mp_int_set_value(c, 1); |
| |
| /* Take care of low-order digits */ |
| while (db < dbt) { |
| mp_digit d = *db; |
| |
| for (int 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))) { |
| REQUIRE(MP_MEMORY); |
| } |
| 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))) { |
| REQUIRE(MP_MEMORY); |
| } |
| assert(MP_SIGN(TEMP(0)) == MP_ZPOS); |
| mp_int_copy(TEMP(0), a); |
| } |
| |
| ++db; |
| } |
| |
| /* Take care of highest-order digit */ |
| mp_digit d = *dbt; |
| for (;;) { |
| if (d & 1) { |
| UMUL(c, a, TEMP(0)); |
| if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) { |
| REQUIRE(MP_MEMORY); |
| } |
| 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))) { |
| REQUIRE(MP_MEMORY); |
| } |
| (void)mp_int_copy(TEMP(0), a); |
| } |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| /* Division of nonnegative integers |
| |
| This function implements division algorithm for unsigned multi-precision |
| integers. The algorithm is based on Algorithm D from Knuth's "The Art of |
| Computer Programming", 3rd ed. 1998, pg 272-273. |
| |
| We diverge from Knuth's algorithm in that we do not perform the subtraction |
| from the remainder until we have determined that we have the correct |
| quotient digit. This makes our algorithm less efficient that Knuth because |
| we might have to perform multiple multiplication and comparison steps before |
| the subtraction. The advantage is that it is easy to implement and ensure |
| correctness without worrying about underflow from the subtraction. |
| |
| inputs: u a n+m digit integer in base b (b is 2^MP_DIGIT_BIT) |
| v a n digit integer in base b (b is 2^MP_DIGIT_BIT) |
| n >= 1 |
| m >= 0 |
| outputs: u / v stored in u |
| u % v stored in v |
| */ |
| static mp_result s_udiv_knuth(mp_int u, mp_int v) { |
| /* Force signs to positive */ |
| u->sign = MP_ZPOS; |
| v->sign = MP_ZPOS; |
| |
| /* Use simple division algorithm when v is only one digit long */ |
| if (MP_USED(v) == 1) { |
| mp_digit d, rem; |
| d = v->digits[0]; |
| rem = s_ddiv(u, d); |
| mp_int_set_value(v, rem); |
| return MP_OK; |
| } |
| |
| /* Algorithm D |
| |
| The n and m variables are defined as used by Knuth. |
| u is an n digit number with digits u_{n-1}..u_0. |
| v is an n+m digit number with digits from v_{m+n-1}..v_0. |
| We require that n > 1 and m >= 0 |
| */ |
| mp_size n = MP_USED(v); |
| mp_size m = MP_USED(u) - n; |
| assert(n > 1); |
| /* assert(m >= 0) follows because m is unsigned. */ |
| |
| /* D1: Normalize. |
| The normalization step provides the necessary condition for Theorem B, |
| which states that the quotient estimate for q_j, call it qhat |
| |
| qhat = u_{j+n}u_{j+n-1} / v_{n-1} |
| |
| is bounded by |
| |
| qhat - 2 <= q_j <= qhat. |
| |
| That is, qhat is always greater than the actual quotient digit q, |
| and it is never more than two larger than the actual quotient digit. |
| */ |
| int k = s_norm(u, v); |
| |
| /* Extend size of u by one if needed. |
| |
| The algorithm begins with a value of u that has one more digit of input. |
| The normalization step sets u_{m+n}..u_0 = 2^k * u_{m+n-1}..u_0. If the |
| multiplication did not increase the number of digits of u, we need to add |
| a leading zero here. |
| */ |
| if (k == 0 || MP_USED(u) != m + n + 1) { |
| if (!s_pad(u, m + n + 1)) return MP_MEMORY; |
| u->digits[m + n] = 0; |
| u->used = m + n + 1; |
| } |
| |
| /* Add a leading 0 to v. |
| |
| The multiplication in step D4 multiplies qhat * 0v_{n-1}..v_0. We need to |
| add the leading zero to v here to ensure that the multiplication will |
| produce the full n+1 digit result. |
| */ |
| if (!s_pad(v, n + 1)) return MP_MEMORY; |
| v->digits[n] = 0; |
| |
| /* Initialize temporary variables q and t. |
| q allocates space for m+1 digits to store the quotient digits |
| t allocates space for n+1 digits to hold the result of q_j*v |
| */ |
| DECLARE_TEMP(2); |
| REQUIRE(GROW(TEMP(0), m + 1)); |
| REQUIRE(GROW(TEMP(1), n + 1)); |
| |
| /* D2: Initialize j */ |
| int j = m; |
| mpz_t r; |
| r.digits = MP_DIGITS(u) + j; /* The contents of r are shared with u */ |
| r.used = n + 1; |
| r.sign = MP_ZPOS; |
| r.alloc = MP_ALLOC(u); |
| ZERO(TEMP(1)->digits, TEMP(1)->alloc); |
| |
| /* Calculate the m+1 digits of the quotient result */ |
| for (; j >= 0; j--) { |
| /* D3: Calculate q' */ |
| /* r->digits is aligned to position j of the number u */ |
| mp_word pfx, qhat; |
| pfx = r.digits[n]; |
| pfx <<= MP_DIGIT_BIT / 2; |
| pfx <<= MP_DIGIT_BIT / 2; |
| pfx |= r.digits[n - 1]; /* pfx = u_{j+n}{j+n-1} */ |
| |
| qhat = pfx / v->digits[n - 1]; |
| /* Check to see if qhat > b, and decrease qhat if so. |
| Theorem B guarantess that qhat is at most 2 larger than the |
| actual value, so it is possible that qhat is greater than |
| the maximum value that will fit in a digit */ |
| if (qhat > MP_DIGIT_MAX) qhat = MP_DIGIT_MAX; |
| |
| /* D4,D5,D6: Multiply qhat * v and test for a correct value of q |
| |
| We proceed a bit different than the way described by Knuth. This way is |
| simpler but less efficent. Instead of doing the multiply and subtract |
| then checking for underflow, we first do the multiply of qhat * v and |
| see if it is larger than the current remainder r. If it is larger, we |
| decrease qhat by one and try again. We may need to decrease qhat one |
| more time before we get a value that is smaller than r. |
| |
| This way is less efficent than Knuth because we do more multiplies, but |
| we do not need to worry about underflow this way. |
| */ |
| /* t = qhat * v */ |
| s_dbmul(MP_DIGITS(v), (mp_digit)qhat, TEMP(1)->digits, n + 1); |
| TEMP(1)->used = n + 1; |
| CLAMP(TEMP(1)); |
| |
| /* Clamp r for the comparison. Comparisons do not like leading zeros. */ |
| CLAMP(&r); |
| if (s_ucmp(TEMP(1), &r) > 0) { /* would the remainder be negative? */ |
| qhat -= 1; /* try a smaller q */ |
| s_dbmul(MP_DIGITS(v), (mp_digit)qhat, TEMP(1)->digits, n + 1); |
| TEMP(1)->used = n + 1; |
| CLAMP(TEMP(1)); |
| if (s_ucmp(TEMP(1), &r) > 0) { /* would the remainder be negative? */ |
| assert(qhat > 0); |
| qhat -= 1; /* try a smaller q */ |
| s_dbmul(MP_DIGITS(v), (mp_digit)qhat, TEMP(1)->digits, n + 1); |
| TEMP(1)->used = n + 1; |
| CLAMP(TEMP(1)); |
| } |
| assert(s_ucmp(TEMP(1), &r) <= 0 && "The mathematics failed us."); |
| } |
| /* Unclamp r. The D algorithm expects r = u_{j+n}..u_j to always be n+1 |
| digits long. */ |
| r.used = n + 1; |
| |
| /* D4: Multiply and subtract |
| |
| Note: The multiply was completed above so we only need to subtract here. |
| */ |
| s_usub(r.digits, TEMP(1)->digits, r.digits, r.used, TEMP(1)->used); |
| |
| /* D5: Test remainder |
| |
| Note: Not needed because we always check that qhat is the correct value |
| before performing the subtract. Value cast to mp_digit to prevent |
| warning, qhat has been clamped to MP_DIGIT_MAX |
| */ |
| TEMP(0)->digits[j] = (mp_digit)qhat; |
| |
| /* D6: Add back |
| Note: Not needed because we always check that qhat is the correct value |
| before performing the subtract. |
| */ |
| |
| /* D7: Loop on j */ |
| r.digits--; |
| ZERO(TEMP(1)->digits, TEMP(1)->alloc); |
| } |
| |
| /* Get rid of leading zeros in q */ |
| TEMP(0)->used = m + 1; |
| CLAMP(TEMP(0)); |
| |
| /* Denormalize the remainder */ |
| CLAMP(u); /* use u here because the r.digits pointer is off-by-one */ |
| if (k != 0) s_qdiv(u, k); |
| |
| mp_int_copy(u, v); /* ok: 0 <= r < v */ |
| mp_int_copy(TEMP(0), u); /* ok: q <= u */ |
| |
| CLEANUP_TEMP(); |
| return MP_OK; |
| } |
| |
| static int s_outlen(mp_int z, mp_size r) { |
| assert(r >= MP_MIN_RADIX && r <= MP_MAX_RADIX); |
| |
| mp_result bits = mp_int_count_bits(z); |
| double raw = (double)bits * s_log2[r]; |
| |
| return (int)(raw + 0.999999); |
| } |
| |
| 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) + 1; |
| } |
| |
| static int s_ch2val(char c, int r) { |
| int out; |
| |
| /* |
| * In some locales, isalpha() accepts characters outside the range A-Z, |
| * producing out<0 or out>=36. The "out >= r" check will always catch |
| * out>=36. Though nothing explicitly catches out<0, our caller reacts the |
| * same way to every negative return value. |
| */ |
| if (isdigit((unsigned char)c)) |
| out = c - '0'; |
| else if (r > 10 && isalpha((unsigned char)c)) |
| out = toupper((unsigned char)c) - 'A' + 10; |
| else |
| return -1; |
| |
| return (out >= r) ? -1 : out; |
| } |
| |
| static 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; |
| } |
| } |
| } |
| |
| static void s_2comp(unsigned char *buf, int len) { |
| unsigned short s = 1; |
| |
| for (int i = len - 1; i >= 0; --i) { |
| unsigned char c = ~buf[i]; |
| |
| s = c + s; |
| c = s & UCHAR_MAX; |
| s >>= CHAR_BIT; |
| |
| buf[i] = c; |
| } |
| |
| /* last carry out is ignored */ |
| } |
| |
| static mp_result s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad) { |
| int pos = 0, limit = *limpos; |
| mp_size uz = MP_USED(z); |
| mp_digit *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(buf, pos); |
| |
| /* Return the number of bytes actually written */ |
| *limpos = pos; |
| |
| return (uz == 0) ? MP_OK : MP_TRUNC; |
| } |
| |
| /* Here there be dragons */ |