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Postgres FD Implementation
Commit 48e24ba6 authored by Noah Misch's avatar Noah Misch
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Import changes from IMath versions (1.3, 1.29]. 

Upstream fixed bugs over the years, but none are confirmed to have
affected pgcrypto.  We're better off naively tracking upstream than
reactively maintaining a twelve-year-old snapshot of upstream.  Add a
header comment describing the synchronization procedure.  Discard use of
INVERT_COMPARE_RESULT(); the domain of the comparisons in question is
{-1,0,1}, controlled entirely by code in imath.c.

Andrew Gierth reviewed the Makefile change.  Tom Lane reviewed the
synchronization procedure description.

Discussion: https://postgr.es/m/20190203035704.GA6226@rfd.leadboat.com
parent d1299aab
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contrib/pgcrypto/Makefile
View file @ 48e24ba6
......@@ -59,6 +59,9 @@ SHLIB_LINK += $(filter -leay32, $(LIBS))
SHLIB_LINK += -lws2_32
endif
# Upstream uses a larger subset of C99.
imath.o: CFLAGS+=$(PERMIT_DECLARATION_AFTER_STATEMENT)
rijndael.o: rijndael.tbl
rijndael.tbl:
......
contrib/pgcrypto/imath.c
View file @ 48e24ba6
/* imath version 1.3 */
/*-------------------------------------------------------------------------
*
* imath.c
*
* Last synchronized from https://github.com/creachadair/imath/tree/v1.29,
* using the following procedure:
*
* 1. Download imath.c and imath.h of the last synchronized version. Remove
* "#ifdef __cplusplus" blocks, which upset pgindent. Run pgindent on the
* two files. Filter the two files through "unexpand -t4 --first-only".
* Diff the result against the PostgreSQL versions. As of the last
* synchronization, changes were as follows:
*
* - replace malloc(), realloc() and free() with px_ versions
* - redirect assert() to Assert()
* - #undef MIN, #undef MAX before defining them
* - remove includes covered by c.h
* - rename DEBUG to IMATH_DEBUG
*
* 2. Download a newer imath.c and imath.h. Transform them like in step 1.
* Apply to these files the diff you saved in step 1. Look for new lines
* requiring the same kind of change, such as new malloc() calls.
*
* 3. Configure PostgreSQL using --without-openssl. Run "make -C
* contrib/pgcrypto check".
*
* 4. Update this header comment.
*
* Portions Copyright (c) 1996-2019, PostgreSQL Global Development Group
*
* IDENTIFICATION
* contrib/pgcrypto/imath.c
*
* Upstream copyright terms follow.
*-------------------------------------------------------------------------
*/
/*
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
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.
*/
/* contrib/pgcrypto/imath.c */
#include "postgres.h"
#include "px.h"
#include "imath.h"
#include "px.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 */
......@@ -48,42 +77,30 @@ 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 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 */
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, /* 0 1 2 3 */
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 */
......@@ -92,136 +109,242 @@ static const double s_log2[] = {
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
0.193426404, /* 36 */
};
/* }}} */
/* {{{ Various macros */
/* Return the number of digits needed to represent a static value */
#define MP_VALUE_DIGITS(V) \
((sizeof(V)+(sizeof(mp_digit)-1))/sizeof(mp_digit))
((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)))
static inline mp_size
s_round_prec(mp_size P)
{
return 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)
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 */
#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)
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;
/* 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)
memcpy(q__, p__, i__);
}
#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
/* 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. */
#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)
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);
}
#define CMPZ(Z) \
(((Z)->used==1&&(Z)->digits[0]==0)?0:((Z)->sign==MP_NEG)?-1:1)
/* 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)
#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)
/* 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;
}
#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)
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);
}
#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))
/* 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 = 64;
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;
/* Default library configuration flags */
static mp_word mp_flags = MP_CAP_DIGITS;
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);
#if TRACEABLE_FREE
/* Release a buffer of digits allocated by s_alloc(). */
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);
static bool 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
/* 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, int value, mp_digit vbuf[]);
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_vpack(int v, mp_digit 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, int v);
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);
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);
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);
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);
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);
......@@ -236,8 +359,7 @@ static void s_dadd(mp_int a, mp_digit b);
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);
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. */
......@@ -264,7 +386,7 @@ static int s_dp2k(mp_int z);
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);
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);
......@@ -279,17 +401,17 @@ 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);
/* 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. */
/* 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. */
/* 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
......@@ -302,177 +424,161 @@ 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. */
/* 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)
/* 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)
{
return default_precision;
}
/* }}} */
/* {{{ mp_set_default_precision(s) */
void
mp_set_default_precision(mp_size s)
{
NRCHECK(s > 0);
mp_size ua_ = MP_USED(X);
mp_size ub_ = MP_USED(Y);
mp_size o_ = ua_ + ub_;
default_precision = (mp_size) ROUND_PREC(s);
ZERO(MP_DIGITS(Z), o_);
(void) s_kmul(MP_DIGITS(X), MP_DIGITS(Y), MP_DIGITS(Z), ua_, ub_);
Z->used = o_;
CLAMP(Z);
}
/* }}} */
/* {{{ mp_get_multiply_threshold() */
mp_size
mp_get_multiply_threshold(void)
/* Square X into Z. Requires that Z have enough storage to hold the result. */
static inline void
USQR(mp_int X, mp_int Z)
{
return multiply_threshold;
}
/* }}} */
mp_size ua_ = MP_USED(X);
mp_size o_ = ua_ + ua_;
/* {{{ mp_set_multiply_threshold(s) */
void
mp_set_multiply_threshold(mp_size s)
{
multiply_threshold = s;
ZERO(MP_DIGITS(Z), o_);
(void) s_ksqr(MP_DIGITS(X), MP_DIGITS(Z), ua_);
Z->used = o_;
CLAMP(Z);
}
/* }}} */
/* {{{ mp_int_init(z) */
mp_result
mp_int_init(mp_int z)
{
return mp_int_init_size(z, default_precision);
}
if (z == NULL)
return MP_BADARG;
/* }}} */
z->single = 0;
z->digits = &(z->single);
z->alloc = 1;
z->used = 1;
z->sign = MP_ZPOS;
/* {{{ mp_int_alloc() */
return MP_OK;
}
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;
if (out != NULL)
mp_int_init(out);
return out;
}
/* }}} */
/* {{{ mp_int_init_size(z, prec) */
mp_result
mp_int_init_size(mp_int z, mp_size prec)
{
CHECK(z != NULL);
assert(z != NULL);
prec = (mp_size) ROUND_PREC(prec);
prec = MAX(prec, default_precision);
if (prec == 0)
{
prec = default_precision;
}
else if (prec == 1)
{
return mp_int_init(z);
}
else
{
prec = s_round_prec(prec);
}
if ((MP_DIGITS(z) = s_alloc(prec)) == NULL)
z->digits = s_alloc(prec);
if (MP_DIGITS(z) == NULL)
return MP_MEMORY;
z->digits[0] = 0;
MP_USED(z) = 1;
MP_ALLOC(z) = prec;
MP_SIGN(z) = MP_ZPOS;
z->used = 1;
z->alloc = prec;
z->sign = 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;
assert(z != NULL && old != NULL);
CHECK(z != NULL && old != NULL);
mp_size uold = MP_USED(old);
uold = MP_USED(old);
target = MAX(uold, default_precision);
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_int_init_size(z, target)) != MP_OK)
if (res != MP_OK)
return res;
}
MP_USED(z) = uold;
MP_SIGN(z) = MP_SIGN(old);
z->used = uold;
z->sign = old->sign;
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_int_init_value(mp_int z, mp_small value)
{
mp_result res;
CHECK(z != NULL);
if ((res = mp_int_init(z)) != MP_OK)
return res;
mpz_t vtmp;
mp_digit vbuf[MP_VALUE_DIGITS(value)];
return mp_int_set_value(z, value);
s_fake(&vtmp, value, vbuf);
return mp_int_init_copy(z, &vtmp);
}
/* }}} */
/* {{{ mp_int_set_value(z, value) */
mp_result
mp_int_set_value(mp_int z, int value)
mp_int_init_uvalue(mp_int z, mp_usmall uvalue)
{
mp_size ndig;
CHECK(z != NULL);
/* How many digits to copy */
ndig = (mp_size) MP_VALUE_DIGITS(value);
mpz_t vtmp;
mp_digit vbuf[MP_VALUE_DIGITS(uvalue)];
if (!s_pad(z, ndig))
return MP_MEMORY;
s_ufake(&vtmp, uvalue, vbuf);
return mp_int_init_copy(z, &vtmp);
}
MP_USED(z) = (mp_size) s_vpack(value, MP_DIGITS(z));
MP_SIGN(z) = (value < 0) ? MP_NEG : MP_ZPOS;
mp_result
mp_int_set_value(mp_int z, mp_small value)
{
mpz_t vtmp;
mp_digit vbuf[MP_VALUE_DIGITS(value)];
return MP_OK;
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)];
/* {{{ mp_int_clear(z) */
s_ufake(&vtmp, uvalue, vbuf);
return mp_int_copy(&vtmp, z);
}
void
mp_int_clear(mp_int z)
......@@ -482,34 +588,26 @@ mp_int_clear(mp_int z)
if (MP_DIGITS(z) != NULL)
{
if (MP_DIGITS(z) != &(z->single))
s_free(MP_DIGITS(z));
MP_DIGITS(z) = NULL;
z->digits = NULL;
}
}
/* }}} */
/* {{{ mp_int_free(z) */
void
mp_int_free(mp_int z)
{
NRCHECK(z != NULL);
assert(z != NULL);
if (z->digits != NULL)
mp_int_clear(z);
px_free(z);
px_free(z); /* note: NOT s_free() */
}
/* }}} */
/* {{{ mp_int_copy(a, c) */
mp_result
mp_int_copy(mp_int a, mp_int c)
{
CHECK(a != NULL && c != NULL);
assert(a != NULL && c != NULL);
if (a != c)
{
......@@ -524,17 +622,13 @@ mp_int_copy(mp_int a, mp_int c)
dc = MP_DIGITS(c);
COPY(da, dc, ua);
MP_USED(c) = ua;
MP_SIGN(c) = MP_SIGN(a);
c->used = ua;
c->sign = a->sign;
}
return MP_OK;
}
/* }}} */
/* {{{ mp_int_swap(a, c) */
void
mp_int_swap(mp_int a, mp_int c)
{
......@@ -544,90 +638,71 @@ mp_int_swap(mp_int a, mp_int c)
*a = *c;
*c = tmp;
if (MP_DIGITS(a) == &(c->single))
a->digits = &(a->single);
if (MP_DIGITS(c) == &(a->single))
c->digits = &(c->single);
}
}
/* }}} */
/* {{{ mp_int_zero(z) */
void
mp_int_zero(mp_int z)
{
NRCHECK(z != NULL);
assert(z != NULL);
z->digits[0] = 0;
MP_USED(z) = 1;
MP_SIGN(z) = MP_ZPOS;
z->used = 1;
z->sign = MP_ZPOS;
}
/* }}} */
/* {{{ mp_int_abs(a, c) */
mp_result
mp_int_abs(mp_int a, mp_int c)
{
mp_result res;
assert(a != NULL && c != NULL);
CHECK(a != NULL && c != NULL);
mp_result res;
if ((res = mp_int_copy(a, c)) != MP_OK)
return res;
MP_SIGN(c) = MP_ZPOS;
c->sign = MP_ZPOS;
return MP_OK;
}
/* }}} */
/* {{{ mp_int_neg(a, c) */
mp_result
mp_int_neg(mp_int a, mp_int c)
{
mp_result res;
assert(a != NULL && c != NULL);
CHECK(a != NULL && c != NULL);
mp_result res;
if ((res = mp_int_copy(a, c)) != MP_OK)
return res;
if (CMPZ(c) != 0)
MP_SIGN(c) = 1 - MP_SIGN(a);
c->sign = 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);
assert(a != NULL && b != NULL && c != NULL);
ua = MP_USED(a);
ub = MP_USED(b);
uc = MP_USED(c);
max = MAX(ua, ub);
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 */
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;
mp_digit carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
mp_size uc = max;
if (carry)
{
......@@ -638,50 +713,55 @@ mp_int_add(mp_int a, mp_int b, mp_int c)
++uc;
}
MP_USED(c) = uc;
MP_SIGN(c) = MP_SIGN(a);
c->used = uc;
c->sign = a->sign;
}
else
{
/* Different signs -- subtract magnitudes, preserve sign of greater */
int cmp = s_ucmp(a, b); /* magnitude comparision, sign ignored */
/*
* Set x to max(a, b), y to min(a, b) to simplify later code. A
* special case yields zero for equal magnitudes.
*/
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)
if (cmp == 0)
{
x = a;
y = b;
mp_int_zero(c);
return MP_OK;
}
else
else if (cmp < 0)
{
x = b;
y = a;
}
else
{
x = a;
y = b;
}
if (!s_pad(c, MP_USED(x)))
return MP_MEMORY;
/* Subtract smaller from larger */
s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y));
MP_USED(c) = MP_USED(x);
c->used = x->used;
CLAMP(c);
/* Give result the sign of the larger */
MP_SIGN(c) = MP_SIGN(x);
c->sign = x->sign;
}
return MP_OK;
}
/* }}} */
/* {{{ mp_int_add_value(a, value, c) */
mp_result
mp_int_add_value(mp_int a, int value, mp_int c)
mp_int_add_value(mp_int a, mp_small value, mp_int c)
{
mpz_t vtmp;
mp_digit vbuf[MP_VALUE_DIGITS(value)];
......@@ -691,35 +771,23 @@ mp_int_add_value(mp_int a, int value, mp_int c)
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;
assert(a != NULL && b != NULL && c != NULL);
CHECK(a != NULL && b != NULL && c != NULL);
ua = MP_USED(a);
ub = MP_USED(b);
uc = MP_USED(c);
max = MAX(ua, ub);
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 */
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;
mp_digit carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
mp_size uc = max;
if (carry)
{
......@@ -730,20 +798,20 @@ mp_int_sub(mp_int a, mp_int b, mp_int c)
++uc;
}
MP_USED(c) = uc;
MP_SIGN(c) = MP_SIGN(a);
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 (!s_pad(c, max))
return MP_MEMORY;
int cmp = s_ucmp(a, b);
if (cmp >= 0)
{
......@@ -762,21 +830,17 @@ mp_int_sub(mp_int a, mp_int b, mp_int c)
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);
c->used = x->used;
CLAMP(c);
MP_SIGN(c) = osign;
c->sign = 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)
mp_int_sub_value(mp_int a, mp_small value, mp_int c)
{
mpz_t vtmp;
mp_digit vbuf[MP_VALUE_DIGITS(value)];
......@@ -786,21 +850,10 @@ mp_int_sub_value(mp_int a, int value, mp_int c)
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);
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)
......@@ -810,21 +863,24 @@ mp_int_mul(mp_int a, mp_int b, mp_int c)
}
/* Output is positive if inputs have same sign, otherwise negative */
osign = (MP_SIGN(a) == MP_SIGN(b)) ? MP_ZPOS : MP_NEG;
mp_sign 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.
* If the output is not identical to any of the inputs, we'll write the
* results directly; otherwise, allocate a temporary space.
*/
ua = MP_USED(a);
ub = MP_USED(b);
osize = MAX(ua, ub);
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 = ROUND_PREC(osize);
p = MAX(p, default_precision);
p = MAX(s_round_prec(osize), default_precision);
if ((out = s_alloc(p)) == NULL)
return MP_MEMORY;
......@@ -847,24 +903,21 @@ mp_int_mul(mp_int a, mp_int b, mp_int c)
*/
if (out != MP_DIGITS(c))
{
if ((void *) MP_DIGITS(c) != (void *) c)
s_free(MP_DIGITS(c));
MP_DIGITS(c) = out;
MP_ALLOC(c) = p;
c->digits = out;
c->alloc = p;
}
MP_USED(c) = osize; /* might not be true, but we'll fix it ... */
c->used = osize; /* might not be true, but we'll fix it ... */
CLAMP(c); /* ... right here */
MP_SIGN(c) = osign;
c->sign = 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)
mp_int_mul_value(mp_int a, mp_small value, mp_int c)
{
mpz_t vtmp;
mp_digit vbuf[MP_VALUE_DIGITS(value)];
......@@ -874,45 +927,39 @@ mp_int_mul_value(mp_int a, int value, mp_int c)
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_int_mul_pow2(mp_int a, mp_small p2, mp_int c)
{
mp_result res;
assert(a != NULL && c != NULL && p2 >= 0);
CHECK(a != NULL && c != NULL && p2 >= 0);
mp_result res = mp_int_copy(a, c);
if ((res = mp_int_copy(a, c)) != MP_OK)
if (res != 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);
assert(a != NULL && c != NULL);
/* Get a temporary buffer big enough to hold the result */
osize = (mp_size) 4 * ((MP_USED(a) + 1) / 2);
mp_size osize = (mp_size) 4 * ((MP_USED(a) + 1) / 2);
mp_size p = 0;
mp_digit *out;
if (a == c)
{
p = ROUND_PREC(osize);
p = s_round_prec(osize);
p = MAX(p, default_precision);
if ((out = s_alloc(p)) == NULL)
......@@ -935,39 +982,35 @@ mp_int_sqr(mp_int a, mp_int c)
*/
if (out != MP_DIGITS(c))
{
if ((void *) MP_DIGITS(c) != (void *) c)
s_free(MP_DIGITS(c));
MP_DIGITS(c) = out;
MP_ALLOC(c) = p;
c->digits = out;
c->alloc = p;
}
MP_USED(c) = osize; /* might not be true, but we'll fix it ... */
c->used = osize; /* might not be true, but we'll fix it ... */
CLAMP(c); /* ... right here */
MP_SIGN(c) = MP_ZPOS;
c->sign = 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;
assert(a != NULL && b != NULL && q != r);
int cmp;
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);
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)
{
/*
......@@ -995,7 +1038,7 @@ mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r)
q->digits[0] = 1;
if (sa != sb)
MP_SIGN(q) = MP_NEG;
q->sign = MP_NEG;
}
return MP_OK;
......@@ -1006,37 +1049,41 @@ mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r)
* 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 && (res = mp_int_copy(a, q)) == MP_OK)
if (q && b != q)
{
REQUIRE(mp_int_copy(a, q));
qout = q;
}
else
{
qout = TEMP(last);
SETUP(mp_int_init_copy(TEMP(last), a), last);
REQUIRE(mp_int_copy(a, TEMP(0)));
qout = TEMP(0);
}
if (r && a != r && (res = mp_int_copy(b, r)) == MP_OK)
if (r && a != r)
{
REQUIRE(mp_int_copy(b, r));
rout = r;
}
else
{
rout = TEMP(last);
SETUP(mp_int_init_copy(TEMP(last), b), last);
REQUIRE(mp_int_copy(b, TEMP(1)));
rout = TEMP(1);
}
if ((res = s_udiv(qout, rout)) != MP_OK)
goto CLEANUP;
REQUIRE(s_udiv_knuth(qout, rout));
}
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)
REQUIRE(mp_int_copy(a, q));
if (r)
REQUIRE(mp_int_copy(a, r));
if (q)
s_qdiv(q, (mp_size) lg);
......@@ -1049,203 +1096,184 @@ mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r)
/* Recompute signs for output */
if (rout)
{
MP_SIGN(rout) = sa;
rout->sign = sa;
if (CMPZ(rout) == 0)
MP_SIGN(rout) = MP_ZPOS;
rout->sign = MP_ZPOS;
}
if (qout)
{
MP_SIGN(qout) = (sa == sb) ? MP_ZPOS : MP_NEG;
qout->sign = (sa == sb) ? MP_ZPOS : MP_NEG;
if (CMPZ(qout) == 0)
MP_SIGN(qout) = MP_ZPOS;
qout->sign = 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));
if (q)
REQUIRE(mp_int_copy(qout, q));
if (r)
REQUIRE(mp_int_copy(rout, r));
CLEANUP_TEMP();
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;
DECLARE_TEMP(1);
mp_int out = (m == c) ? TEMP(0) : c;
if (m == c)
REQUIRE(mp_int_div(a, m, NULL, out));
if (CMPZ(out) < 0)
{
if ((res = mp_int_init(&tmp)) != MP_OK)
return res;
out = &tmp;
REQUIRE(mp_int_add(out, m, c));
}
else
{
out = c;
REQUIRE(mp_int_copy(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;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ mp_int_div_value(a, value, q, r) */
mp_result
mp_int_div_value(mp_int a, int value, mp_int q, int *r)
mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small * r)
{
mpz_t vtmp,
rtmp;
mpz_t vtmp;
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;
DECLARE_TEMP(1);
REQUIRE(mp_int_div(a, &vtmp, q, TEMP(0)));
if (r)
(void) mp_int_to_int(&rtmp, r); /* can't fail */
(void) mp_int_to_int(TEMP(0), r); /* can't fail */
CLEANUP:
mp_int_clear(&rtmp);
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ 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_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r)
{
mp_result res = MP_OK;
assert(a != NULL && p2 >= 0 && q != r);
CHECK(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_int_expt(a, b, c) */
mp_result
mp_int_expt(mp_int a, int b, mp_int c)
mp_int_expt(mp_int a, mp_small b, mp_int c)
{
mpz_t t;
mp_result res;
unsigned int v = abs(b);
CHECK(b >= 0 && c != NULL);
assert(c != NULL);
if (b < 0)
return MP_RANGE;
if ((res = mp_int_init_copy(&t, a)) != MP_OK)
return res;
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)
{
if ((res = mp_int_mul(c, &t, c)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_mul(c, TEMP(0), c));
}
v >>= 1;
if (v == 0)
break;
if ((res = mp_int_sqr(&t, &t)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_sqr(TEMP(0), TEMP(0)));
}
CLEANUP:
mp_int_clear(&t);
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ mp_int_expt_value(a, b, c) */
mp_result
mp_int_expt_value(int a, int b, mp_int c)
mp_int_expt_value(mp_small a, mp_small b, mp_int c)
{
mpz_t t;
mp_result res;
unsigned int v = abs(b);
CHECK(b >= 0 && c != NULL);
assert(c != NULL);
if (b < 0)
return MP_RANGE;
if ((res = mp_int_init_value(&t, a)) != MP_OK)
return res;
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)
{
if ((res = mp_int_mul(c, &t, c)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_mul(c, TEMP(0), c));
}
v >>= 1;
if (v == 0)
break;
if ((res = mp_int_sqr(&t, &t)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_sqr(TEMP(0), TEMP(0)));
}
CLEANUP:
mp_int_clear(&t);
return res;
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)));
}
}
/* {{{ mp_int_compare(a, b) */
CLEANUP_TEMP();
return MP_OK;
}
int
mp_int_compare(mp_int a, mp_int b)
{
mp_sign sa;
assert(a != NULL && b != NULL);
CHECK(a != NULL && b != NULL);
mp_sign sa = MP_SIGN(a);
sa = MP_SIGN(a);
if (sa == MP_SIGN(b))
{
int cmp = s_ucmp(a, b);
......@@ -1254,91 +1282,90 @@ mp_int_compare(mp_int a, mp_int b)
* If they're both zero or positive, the normal comparison applies; if
* both negative, the sense is reversed.
*/
if (sa != MP_ZPOS)
INVERT_COMPARE_RESULT(cmp);
if (sa == MP_ZPOS)
{
return cmp;
}
else
{
if (sa == MP_ZPOS)
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);
assert(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);
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;
}
}
/* }}} */
/* {{{ mp_int_compare_value(z, value) */
int
mp_int_compare_value(mp_int z, int value)
mp_int_compare_value(mp_int z, mp_small value)
{
mp_sign vsign = (value < 0) ? MP_NEG : MP_ZPOS;
int cmp;
assert(z != NULL);
CHECK(z != NULL);
mp_sign vsign = (value < 0) ? MP_NEG : MP_ZPOS;
if (vsign == MP_SIGN(z))
{
cmp = s_vcmp(z, value);
int cmp = s_vcmp(z, value);
if (vsign != MP_ZPOS)
INVERT_COMPARE_RESULT(cmp);
return cmp;
return (vsign == MP_ZPOS) ? cmp : -cmp;
}
else
{
if (value < 0)
return 1;
else
return -1;
return (value < 0) ? 1 : -1;
}
}
/* }}} */
int
mp_int_compare_uvalue(mp_int z, mp_usmall uv)
{
assert(z != NULL);
/* {{{ mp_int_exptmod(a, b, m, c) */
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)
{
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);
assert(a != NULL && b != NULL && c != NULL && m != NULL);
/* Zero moduli and negative exponents are not considered. */
if (CMPZ(m) == 0)
......@@ -1346,13 +1373,17 @@ mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c)
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);
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)
{
SETUP(mp_int_init_size(TEMP(2), 2 * um), last);
REQUIRE(GROW(TEMP(2), 2 * um));
s = TEMP(2);
}
else
......@@ -1360,30 +1391,17 @@ mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c)
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);
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:
while (--last >= 0)
mp_int_clear(TEMP(last));
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ 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)
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)];
......@@ -1393,13 +1411,8 @@ mp_int_exptmod_evalue(mp_int a, int value, mp_int m, mp_int c)
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)
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)];
......@@ -1409,20 +1422,11 @@ mp_int_exptmod_bvalue(int value, mp_int b,
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_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);
assert(a && b && m && c);
/* Zero moduli and negative exponents are not considered. */
if (CMPZ(m) == 0)
......@@ -1430,12 +1434,16 @@ mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
if (CMPZ(b) < 0)
return MP_RANGE;
um = MP_USED(m);
SETUP(mp_int_init_size(TEMP(0), 2 * um), last);
DECLARE_TEMP(2);
mp_size um = MP_USED(m);
REQUIRE(GROW(TEMP(0), 2 * um));
mp_int s;
if (c == b || c == m)
{
SETUP(mp_int_init_size(TEMP(1), 2 * um), last);
REQUIRE(GROW(TEMP(1), 2 * um));
s = TEMP(1);
}
else
......@@ -1443,68 +1451,41 @@ mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
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);
REQUIRE(mp_int_mod(a, m, TEMP(0)));
REQUIRE(s_embar(TEMP(0), b, m, mu, s));
REQUIRE(mp_int_copy(s, c));
CLEANUP:
while (--last >= 0)
mp_int_clear(TEMP(last));
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ 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);
assert(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);
assert(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 */
DECLARE_TEMP(2);
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;
REQUIRE(mp_int_egcd(a, m, TEMP(0), TEMP(1), NULL));
if (mp_int_compare_value(TEMP(0), 1) != 0)
{
res = MP_UNDEF;
goto CLEANUP;
REQUIRE(MP_UNDEF);
}
/* 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;
REQUIRE(mp_int_mod(TEMP(1), m, TEMP(1)));
/*
* Now, if 'a' was originally negative, the value we have is actually the
......@@ -1512,136 +1493,112 @@ mp_int_invmod(mp_int a, mp_int m, mp_int c)
* 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);
if (MP_SIGN(a) == MP_NEG)
{
REQUIRE(mp_int_sub(m, TEMP(1), c));
}
else
res = mp_int_copy(TEMP(1), c);
CLEANUP:
while (--last >= 0)
mp_int_clear(TEMP(last));
{
REQUIRE(mp_int_copy(TEMP(1), c));
}
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ 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;
assert(a != NULL && b != NULL && c != NULL);
CHECK(a != NULL && b != NULL && c != NULL);
int ca = CMPZ(a);
int cb = CMPZ(b);
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;
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;
MP_SIGN(&u) = MP_ZPOS;
MP_SIGN(&v) = MP_ZPOS;
int k = 0;
{ /* Divide out common factors of 2 from u and v */
int div2_u = s_dp2k(&u),
div2_v = s_dp2k(&v);
int div2_u = s_dp2k(TEMP(0));
int div2_v = s_dp2k(TEMP(1));
k = MIN(div2_u, div2_v);
s_qdiv(&u, (mp_size) k);
s_qdiv(&v, (mp_size) k);
s_qdiv(TEMP(0), (mp_size) k);
s_qdiv(TEMP(1), (mp_size) k);
}
if (mp_int_is_odd(&u))
if (mp_int_is_odd(TEMP(0)))
{
if ((res = mp_int_neg(&v, &t)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_neg(TEMP(1), TEMP(2)));
}
else
{
if ((res = mp_int_copy(&u, &t)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_copy(TEMP(0), TEMP(2)));
}
for (;;)
{
s_qdiv(&t, s_dp2k(&t));
s_qdiv(TEMP(2), s_dp2k(TEMP(2)));
if (CMPZ(&t) > 0)
if (CMPZ(TEMP(2)) > 0)
{
if ((res = mp_int_copy(&t, &u)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_copy(TEMP(2), TEMP(0)));
}
else
{
if ((res = mp_int_neg(&t, &v)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_neg(TEMP(2), TEMP(1)));
}
if ((res = mp_int_sub(&u, &v, &t)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_sub(TEMP(0), TEMP(1), TEMP(2)));
if (CMPZ(&t) == 0)
if (CMPZ(TEMP(2)) == 0)
break;
}
if ((res = mp_int_abs(&u, c)) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_abs(TEMP(0), c));
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);
REQUIRE(MP_MEMORY);
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ 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.
/* 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;
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));
CHECK(a != NULL && b != NULL && c != NULL &&
(x != NULL || y != NULL));
mp_result res = MP_OK;
int ca = CMPZ(a);
int cb = CMPZ(b);
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)
......@@ -1662,20 +1619,17 @@ mp_int_egcd(mp_int a, mp_int b, mp_int c,
/*
* 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);
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 */
MP_SIGN(TEMP(4)) = MP_ZPOS;
MP_SIGN(TEMP(5)) = MP_ZPOS;
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)),
......@@ -1686,8 +1640,8 @@ mp_int_egcd(mp_int a, mp_int b, mp_int c,
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);
REQUIRE(mp_int_copy(TEMP(4), TEMP(6)));
REQUIRE(mp_int_copy(TEMP(5), TEMP(7)));
for (;;)
{
......@@ -1697,10 +1651,8 @@ mp_int_egcd(mp_int a, mp_int b, mp_int c,
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;
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);
......@@ -1713,10 +1665,8 @@ mp_int_egcd(mp_int a, mp_int b, mp_int c,
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;
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);
......@@ -1725,157 +1675,163 @@ mp_int_egcd(mp_int a, mp_int b, mp_int c,
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;
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
{
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;
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 && (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 (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))
{
res = MP_MEMORY;
goto CLEANUP;
REQUIRE(MP_MEMORY);
}
res = mp_int_copy(TEMP(5), c);
REQUIRE(mp_int_copy(TEMP(5), c));
}
break;
}
}
CLEANUP:
while (--last >= 0)
mp_int_clear(TEMP(last));
return res;
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));
/* {{{ mp_int_divisible_value(a, v) */
CLEANUP_TEMP();
return MP_OK;
}
int
mp_int_divisible_value(mp_int a, int v)
bool
mp_int_divisible_value(mp_int a, mp_small v)
{
int rem = 0;
mp_small rem = 0;
if (mp_int_div_value(a, v, NULL, &rem) != MP_OK)
return 0;
{
return false;
}
return rem == 0;
}
/* }}} */
/* {{{ mp_int_is_pow2(z) */
int
mp_int_is_pow2(mp_int z)
{
CHECK(z != NULL);
assert(z != NULL);
return s_isp2(z);
}
/* }}} */
/* {{{ mp_int_sqrt(a, c) */
/* Implementation of Newton's root finding method, based loosely on a patch
contributed by Hal Finkel <half@halssoftware.com>
modified by M. J. Fromberger.
*/
mp_result
mp_int_sqrt(mp_int a, mp_int c)
mp_int_root(mp_int a, mp_small b, mp_int c)
{
mp_result res = MP_OK;
mpz_t temp[2];
int last = 0;
assert(a != NULL && c != NULL && b > 0);
CHECK(a != NULL && c != NULL);
if (b == 1)
{
return mp_int_copy(a, c);
}
bool flips = false;
/* The square root of a negative value does not exist in the integers. */
if (MP_SIGN(a) == MP_NEG)
return MP_UNDEF;
{
if (b % 2 == 0)
{
return MP_UNDEF; /* root does not exist for negative a with
* even b */
}
else
{
flips = true;
}
}
SETUP(mp_int_init_copy(TEMP(last), a), last);
SETUP(mp_int_init(TEMP(last)), last);
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 (;;)
{
if ((res = mp_int_sqr(TEMP(0), TEMP(1))) != MP_OK)
goto CLEANUP;
REQUIRE(mp_int_expt(TEMP(1), b, TEMP(2)));
if (mp_int_compare_unsigned(a, TEMP(1)) == 0)
if (mp_int_compare_unsigned(TEMP(2), TEMP(0)) <= 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;
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 ((res = mp_int_copy(TEMP(1), TEMP(0))) != MP_OK)
goto CLEANUP;
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)));
}
res = mp_int_copy(TEMP(0), c);
REQUIRE(mp_int_copy(TEMP(1), c));
CLEANUP:
while (--last >= 0)
mp_int_clear(TEMP(last));
/* If the original value of a was negative, flip the output sign. */
if (flips)
(void) mp_int_neg(c, c); /* cannot fail */
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ mp_int_to_int(z, out) */
mp_result
mp_int_to_int(mp_int z, int *out)
mp_int_to_int(mp_int z, mp_small * out)
{
unsigned int uv = 0;
mp_size uz;
mp_digit *dz;
mp_sign sz;
assert(z != NULL);
CHECK(z != NULL);
/* Make sure the value is representable as a small integer */
mp_sign sz = MP_SIGN(z);
/* 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)
if ((sz == MP_ZPOS && mp_int_compare_value(z, MP_SMALL_MAX) > 0) ||
mp_int_compare_value(z, MP_SMALL_MIN) < 0)
{
return MP_RANGE;
}
uz = MP_USED(z);
dz = MP_DIGITS(z) + uz - 1;
mp_usmall uz = MP_USED(z);
mp_digit *dz = MP_DIGITS(z) + uz - 1;
mp_small uv = 0;
while (uz > 0)
{
......@@ -1885,33 +1841,56 @@ mp_int_to_int(mp_int z, int *out)
}
if (out)
*out = (sz == MP_NEG) ? -(int) uv : (int) uv;
*out = (mp_small) ((sz == MP_NEG) ? -uv : 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_int_to_uint(mp_int z, mp_usmall * out)
{
mp_result res;
int cmp = 0;
assert(z != NULL);
CHECK(z != NULL && str != NULL && limit >= 2);
/* Make sure the value is representable as an unsigned small integer */
mp_size sz = MP_SIGN(z);
if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
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, mp_flags & MP_CAP_DIGITS);
*str++ = s_val2ch(0, 1);
}
else
{
mp_result res;
mpz_t tmp;
char *h,
*t;
......@@ -1935,7 +1914,7 @@ mp_int_to_string(mp_int z, mp_size radix,
break;
d = s_ddiv(&tmp, (mp_digit) radix);
*str++ = s_val2ch(d, mp_flags & MP_CAP_DIGITS);
*str++ = s_val2ch(d, 1);
}
t = str - 1;
......@@ -1953,26 +1932,22 @@ mp_int_to_string(mp_int z, mp_size radix,
*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;
assert(z != NULL);
assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX);
CHECK(z != NULL);
if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
return MP_RANGE;
len = s_outlen(z, radix) + 1; /* for terminator */
int len = s_outlen(z, radix) + 1; /* for terminator */
/* Allow for sign marker on negatives */
if (MP_SIGN(z) == MP_NEG)
......@@ -1981,31 +1956,19 @@ mp_int_string_len(mp_int z, mp_size radix)
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)
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;
assert(z != NULL && str != NULL);
assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX);
/* Skip leading whitespace */
while (isspace((unsigned char) *str))
......@@ -2015,17 +1978,19 @@ mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end)
switch (*str)
{
case '-':
MP_SIGN(z) = MP_NEG;
z->sign = MP_NEG;
++str;
break;
case '+':
++str; /* fallthrough */
default:
MP_SIGN(z) = MP_ZPOS;
z->sign = MP_ZPOS;
break;
}
/* Skip leading zeroes */
int ch;
while ((ch = s_ch2val(*str, radix)) == 0)
++str;
......@@ -2033,7 +1998,7 @@ mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end)
if (!s_pad(z, s_inlen(strlen(str), radix)))
return MP_MEMORY;
MP_USED(z) = 1;
z->used = 1;
z->digits[0] = 0;
while (*str != '\0' && ((ch = s_ch2val(*str, radix)) >= 0))
......@@ -2047,7 +2012,7 @@ mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end)
/* Override sign for zero, even if negative specified. */
if (CMPZ(z) == 0)
MP_SIGN(z) = MP_ZPOS;
z->sign = MP_ZPOS;
if (end != NULL)
*end = unconstify(char *, str);
......@@ -2057,31 +2022,28 @@ mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end)
* 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;
assert(z != NULL);
CHECK(z != NULL);
mp_size uz = MP_USED(z);
uz = MP_USED(z);
if (uz == 1 && z->digits[0] == 0)
return 1;
--uz;
nbits = uz * MP_DIGIT_BIT;
d = z->digits[uz];
mp_size nbits = uz * MP_DIGIT_BIT;
mp_digit d = z->digits[uz];
while (d != 0)
{
......@@ -2092,21 +2054,15 @@ mp_int_count_bits(mp_int z)
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);
assert(z != NULL && buf != NULL);
res = s_tobin(z, buf, &limpos, PAD_FOR_2C);
int limpos = limit;
mp_result res = s_tobin(z, buf, &limpos, PAD_FOR_2C);
if (MP_SIGN(z) == MP_NEG)
s_2comp(buf, limpos);
......@@ -2114,22 +2070,14 @@ mp_int_to_binary(mp_int z, unsigned char *buf, int limit)
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);
assert(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;
mp_size need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT;
if (!s_pad(z, need))
return MP_MEMORY;
......@@ -2141,12 +2089,14 @@ mp_int_read_binary(mp_int z, unsigned char *buf, int len)
*/
if (buf[0] >> (CHAR_BIT - 1))
{
MP_SIGN(z) = MP_NEG;
z->sign = MP_NEG;
s_2comp(buf, len);
}
dz = MP_DIGITS(z);
for (tmp = buf, i = len; i > 0; --i, ++tmp)
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;
......@@ -2159,20 +2109,15 @@ mp_int_read_binary(mp_int z, unsigned char *buf, int 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;
int bytes = mp_int_unsigned_len(z);
/*
* If the highest-order bit falls exactly on a byte boundary, we need to
......@@ -2183,195 +2128,172 @@ mp_int_binary_len(mp_int z)
++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);
assert(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);
assert(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;
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);
dz = MP_DIGITS(z);
for (tmp = buf, i = len; i > 0; --i, ++tmp)
unsigned char *tmp = buf;
for (int i = len; i > 0; --i, ++tmp)
{
(void) s_qmul(z, CHAR_BIT);
*dz |= *tmp;
*MP_DIGITS(z) |= *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;
int 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;
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. */
/* {{{ s_alloc(num) */
#if IMATH_DEBUG
static const mp_digit fill = (mp_digit) 0xdeadbeefabad1dea;
#endif
static mp_digit *
s_alloc(mp_size num)
{
mp_digit *out = px_alloc(num * sizeof(mp_digit));
assert(out != NULL); /* for debugging */
assert(out != NULL);
#if IMATH_DEBUG
for (mp_size ix = 0; ix < num; ++ix)
out[ix] = fill;
#endif
return out;
}
/* }}} */
/* {{{ s_realloc(old, num) */
static mp_digit *
s_realloc(mp_digit *old, mp_size num)
s_realloc(mp_digit *old, mp_size osize, mp_size nsize)
{
mp_digit *new = px_realloc(old, num * sizeof(mp_digit));
#if IMATH_DEBUG
mp_digit *new = s_alloc(nsize);
assert(new != NULL); /* for debugging */
assert(new != NULL);
return new;
}
for (mp_size ix = 0; ix < nsize; ++ix)
new[ix] = fill;
memcpy(new, old, osize * sizeof(mp_digit));
#else
mp_digit *new = px_realloc(old, nsize * sizeof(mp_digit));
/* }}} */
assert(new != NULL);
#endif
/* {{{ s_free(ptr) */
return new;
}
#if TRACEABLE_FREE
static void
s_free(void *ptr)
{
px_free(ptr);
}
#endif
/* }}} */
/* {{{ s_pad(z, min) */
static int
static bool
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);
mp_size nsize = s_round_prec(min);
mp_digit *tmp;
if (tmp == NULL)
return 0;
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;
}
MP_DIGITS(z) = tmp;
MP_ALLOC(z) = nsize;
z->digits = tmp;
z->alloc = nsize;
}
return 1;
return true;
}
/* }}} */
/* {{{ s_clamp(z) */
#if TRACEABLE_CLAMP
/* Note: This will not work correctly when value == MP_SMALL_MIN */
static void
s_clamp(mp_int z)
s_fake(mp_int z, mp_small value, mp_digit vbuf[])
{
mp_size uz = MP_USED(z);
mp_digit *zd = MP_DIGITS(z) + uz - 1;
while (uz > 1 && (*zd-- == 0))
--uz;
mp_usmall uv = (mp_usmall) (value < 0) ? -value : value;
MP_USED(z) = uz;
s_ufake(z, uv, vbuf);
if (value < 0)
z->sign = MP_NEG;
}
#endif
/* }}} */
/* {{{ s_fake(z, value, vbuf) */
static void
s_fake(mp_int z, int value, mp_digit vbuf[])
s_ufake(mp_int z, mp_usmall value, mp_digit vbuf[])
{
mp_size uv = (mp_size) s_vpack(value, vbuf);
mp_size ndig = (mp_size) s_uvpack(value, vbuf);
z->used = uv;
z->used = ndig;
z->alloc = MP_VALUE_DIGITS(value);
z->sign = (value < 0) ? MP_NEG : MP_ZPOS;
z->sign = MP_ZPOS;
z->digits = vbuf;
}
/* }}} */
/* {{{ s_cdig(da, db, len) */
static int
s_cdig(mp_digit *da, mp_digit *db, mp_size len)
{
......@@ -2381,22 +2303,21 @@ s_cdig(mp_digit *da, mp_digit *db, mp_size len)
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[])
s_uvpack(mp_usmall uv, mp_digit t[])
{
unsigned int uv = (unsigned int) ((v < 0) ? -v : v);
int ndig = 0;
if (uv == 0)
......@@ -2414,10 +2335,6 @@ s_vpack(int v, mp_digit t[])
return ndig;
}
/* }}} */
/* {{{ s_ucmp(a, b) */
static int
s_ucmp(mp_int a, mp_int b)
{
......@@ -2425,41 +2342,40 @@ s_ucmp(mp_int a, mp_int b)
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)
s_vcmp(mp_int a, mp_small v)
{
mp_digit vdig[MP_VALUE_DIGITS(v)];
int ndig = 0;
mp_size ua = MP_USED(a);
ndig = s_vpack(v, vdig);
mp_usmall uv = (v < 0) ? -(mp_usmall) v : (mp_usmall) v;
if (ua > ndig)
return 1;
else if (ua < ndig)
return -1;
else
return s_cdig(MP_DIGITS(a), vdig, ndig);
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_uadd(da, db, dc, size_a, size_b) */
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)
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;
......@@ -2492,13 +2408,9 @@ s_uadd(mp_digit *da, mp_digit *db, mp_digit *dc,
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)
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;
......@@ -2510,7 +2422,8 @@ s_usub(mp_digit *da, mp_digit *db, mp_digit *dc,
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;
(mp_word) *da) -
w - (mp_word) *db;
*dc = LOWER_HALF(w);
w = (UPPER_HALF(w) == 0);
......@@ -2520,7 +2433,8 @@ s_usub(mp_digit *da, mp_digit *db, mp_digit *dc,
for ( /* */ ; pos < size_a; ++pos, ++da, ++dc)
{
w = ((mp_word) MP_DIGIT_MAX + 1 + /* MP_RADIX */
(mp_word) *da) - w;
(mp_word) *da) -
w;
*dc = LOWER_HALF(w);
w = (UPPER_HALF(w) == 0);
......@@ -2530,13 +2444,9 @@ s_usub(mp_digit *da, mp_digit *db, mp_digit *dc,
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)
s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc, mp_size size_a,
mp_size size_b)
{
mp_size bot_size;
......@@ -2558,11 +2468,8 @@ s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc,
* Karatsuba algorithm to compute the product; otherwise use the normal
* multiplication algorithm
*/
if (multiply_threshold &&
size_a >= multiply_threshold &&
size_b > bot_size)
if (multiply_threshold && size_a >= multiply_threshold && size_b > bot_size)
{
mp_digit *t1,
*t2,
*t3,
......@@ -2614,12 +2521,11 @@ s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc,
/* Assemble the output value */
COPY(t1, dc, buf_size);
carry = s_uadd(t3, dc + bot_size, dc + bot_size,
buf_size + 1, 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);
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
......@@ -2633,13 +2539,9 @@ s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc,
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)
s_umul(mp_digit *da, mp_digit *db, mp_digit *dc, mp_size size_a,
mp_size size_b)
{
mp_size a,
b;
......@@ -2666,10 +2568,6 @@ s_umul(mp_digit *da, mp_digit *db, mp_digit *dc,
}
}
/* }}} */
/* {{{ s_ksqr(da, dc, size_a) */
static int
s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a)
{
......@@ -2679,7 +2577,8 @@ s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a)
mp_digit *a_top = da + bot_size;
mp_digit *t1,
*t2,
*t3;
*t3,
carry;
mp_size at_size = size_a - bot_size;
mp_size buf_size = 2 * bot_size;
......@@ -2713,13 +2612,14 @@ s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a)
/* 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);
carry = s_uadd(t3, dc + bot_size, dc + bot_size, buf_size + 1, buf_size);
assert(carry == 0);
(void) s_uadd(t2, dc + 2 * bot_size, dc + 2 * bot_size,
buf_size, buf_size);
carry =
s_uadd(t2, dc + 2 * bot_size, dc + 2 * bot_size, buf_size, buf_size);
assert(carry == 0);
px_free(t1); /* note that t2 and t2 are internal pointers
s_free(t1); /* note that t2 and t2 are internal pointers
* only */
}
......@@ -2731,10 +2631,6 @@ s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a)
return 1;
}
/* }}} */
/* {{{ s_usqr(da, dc, size_a) */
static void
s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a)
{
......@@ -2797,10 +2693,6 @@ s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a)
}
}
/* }}} */
/* {{{ s_dadd(a, b) */
static void
s_dadd(mp_int a, mp_digit b)
{
......@@ -2823,14 +2715,10 @@ s_dadd(mp_int a, mp_digit b)
if (w)
{
*da = (mp_digit) w;
MP_USED(a) += 1;
a->used += 1;
}
}
/* }}} */
/* {{{ s_dmul(a, b) */
static void
s_dmul(mp_int a, mp_digit b)
{
......@@ -2849,14 +2737,10 @@ s_dmul(mp_int a, mp_digit b)
if (w)
{
*da = (mp_digit) w;
MP_USED(a) += 1;
a->used += 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)
{
......@@ -2875,10 +2759,6 @@ s_dbmul(mp_digit *da, mp_digit b, mp_digit *dc, mp_size size_a)
*dc = LOWER_HALF(w);
}
/* }}} */
/* {{{ s_ddiv(da, d, dc, size_a) */
static mp_digit
s_ddiv(mp_int a, mp_digit b)
{
......@@ -2908,10 +2788,6 @@ s_ddiv(mp_int a, mp_digit b)
return (mp_digit) w;
}
/* }}} */
/* {{{ s_qdiv(z, p2) */
static void
s_qdiv(mp_int z, mp_size p2)
{
......@@ -2935,9 +2811,11 @@ s_qdiv(mp_int z, mp_size p2)
from = to + ndig;
for (mark = ndig; mark < uz; ++mark)
{
*to++ = *from++;
}
MP_USED(z) = uz - ndig;
z->used = uz - ndig;
}
if (nbits)
......@@ -2962,33 +2840,25 @@ s_qdiv(mp_int z, mp_size p2)
}
if (MP_USED(z) == 1 && z->digits[0] == 0)
MP_SIGN(z) = MP_ZPOS;
z->sign = 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;
mp_digit mask = (1u << rest) - 1;
if (start <= uz)
{
MP_USED(z) = start;
z->used = start;
z->digits[start - 1] &= mask;
CLAMP(z);
}
}
/* }}} */
/* {{{ s_qmul(z, p2) */
static int
s_qmul(mp_int z, mp_size p2)
{
......@@ -3060,21 +2930,19 @@ s_qmul(mp_int z, mp_size p2)
}
}
MP_USED(z) = uz;
z->used = uz;
CLAMP(z);
return 1;
}
/* }}} */
/* {{{ s_qsub(z, p2) */
/* Subtract |z| from 2^p2, assuming 2^p2 > |z|, and set z to be positive */
/* Compute z = 2^p2 - |z|; requires that 2^p2 >= |z|
The sign of the result is always zero/positive.
*/
static int
s_qsub(mp_int z, mp_size p2)
{
mp_digit hi = (1 << (p2 % MP_DIGIT_BIT)),
mp_digit hi = (1u << (p2 % MP_DIGIT_BIT)),
*zp;
mp_size tdig = (p2 / MP_DIGIT_BIT),
pos;
......@@ -3096,16 +2964,12 @@ s_qsub(mp_int z, mp_size p2)
assert(UPPER_HALF(w) != 0); /* no borrow out should be possible */
MP_SIGN(z) = MP_ZPOS;
z->sign = MP_ZPOS;
CLAMP(z);
return 1;
}
/* }}} */
/* {{{ s_dp2k(z) */
static int
s_dp2k(mp_int z)
{
......@@ -3132,10 +2996,6 @@ s_dp2k(mp_int z)
return k;
}
/* }}} */
/* {{{ s_isp2(z) */
static int
s_isp2(mp_int z)
{
......@@ -3164,12 +3024,8 @@ s_isp2(mp_int z)
return (int) k;
}
/* }}} */
/* {{{ s_2expt(z, k) */
static int
s_2expt(mp_int z, int k)
s_2expt(mp_int z, mp_small k)
{
mp_size ndig,
rest;
......@@ -3183,23 +3039,19 @@ s_2expt(mp_int z, int k)
dz = MP_DIGITS(z);
ZERO(dz, ndig);
*(dz + ndig - 1) = (1 << rest);
MP_USED(z) = ndig;
*(dz + ndig - 1) = (1u << rest);
z->used = 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)))
while (d < (1u << (mp_digit) (MP_DIGIT_BIT - 1)))
{ /* d < (MP_RADIX / 2) */
d <<= 1;
++k;
......@@ -3215,10 +3067,6 @@ s_norm(mp_int a, mp_int b)
return k;
}
/* }}} */
/* {{{ s_brmu(z, m) */
static mp_result
s_brmu(mp_int z, mp_int m)
{
......@@ -3231,10 +3079,6 @@ s_brmu(mp_int z, mp_int m)
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)
{
......@@ -3277,49 +3121,43 @@ s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2)
* 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. */
/* 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;
mp_digit umu = MP_USED(mu);
mp_digit *db = MP_DIGITS(b);
mp_digit *dbt = db + MP_USED(b) - 1;
while (last < 3)
{
SETUP(mp_int_init_size(TEMP(last), 4 * umu), last);
ZERO(MP_DIGITS(TEMP(last - 1)), MP_ALLOC(TEMP(last - 1)));
}
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)
{
int i;
mp_digit d = *db;
for (d = *db, i = MP_DIGIT_BIT; i > 0; --i, d >>= 1)
for (int i = MP_DIGIT_BIT; i > 0; --i, d >>= 1)
{
if (d & 1)
{
......@@ -3327,31 +3165,27 @@ s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
UMUL(c, a, TEMP(0));
if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2)))
{
res = MP_MEMORY;
goto CLEANUP;
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)))
{
res = MP_MEMORY;
goto CLEANUP;
REQUIRE(MP_MEMORY);
}
assert(MP_SIGN(TEMP(0)) == MP_ZPOS);
mp_int_copy(TEMP(0), a);
}
++db;
}
/* Take care of highest-order digit */
d = *dbt;
mp_digit d = *dbt;
for (;;)
{
if (d & 1)
......@@ -3359,8 +3193,7 @@ s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
UMUL(c, a, TEMP(0));
if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2)))
{
res = MP_MEMORY;
goto CLEANUP;
REQUIRE(MP_MEMORY);
}
mp_int_copy(TEMP(0), c);
}
......@@ -3372,170 +3205,272 @@ s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
USQR(a, TEMP(0));
if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2)))
{
res = MP_MEMORY;
goto CLEANUP;
REQUIRE(MP_MEMORY);
}
(void) mp_int_copy(TEMP(0), a);
}
CLEANUP:
while (--last >= 0)
mp_int_clear(TEMP(last));
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* Division of nonnegative integers
/* {{{ s_udiv(a, b) */
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.
/* Precondition: a >= b and b > 0
Postcondition: a' = a / b, b' = a % b
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(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;
s_udiv_knuth(mp_int u, mp_int v)
{
/* Force signs to positive */
MP_SIGN(a) = MP_ZPOS;
MP_SIGN(b) = MP_ZPOS;
u->sign = MP_ZPOS;
v->sign = MP_ZPOS;
/* Normalize, per Knuth */
k = s_norm(a, b);
/* Use simple division algorithm when v is only one digit long */
if (MP_USED(v) == 1)
{
mp_digit d,
rem;
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;
d = v->digits[0];
rem = s_ddiv(u, d);
mp_int_set_value(v, rem);
return MP_OK;
}
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);
/*
* 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;
/* Solve for quotient digits, store in q.digits in reverse order */
while (r.digits >= da)
{
assert(qpos <= q.alloc);
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);
if (s_ucmp(b, &r) > 0)
/*
* 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)
{
r.digits -= 1;
r.used += 1;
if (!s_pad(u, m + n + 1))
return MP_MEMORY;
u->digits[m + n] = 0;
u->used = m + n + 1;
}
if (++skip > 1)
q.digits[qpos++] = 0;
/*
* 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;
CLAMP(&r);
}
else
{
mp_word pfx = r.digits[r.used - 1];
mp_word qdigit;
/*
* 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);
if (r.used > 1 && (pfx < btop || r.digits[r.used - 2] == 0))
/* 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[r.used - 2];
}
pfx |= r.digits[n - 1]; /* pfx = u_{j+n}{j+n-1} */
qdigit = pfx / btop;
if (qdigit > MP_DIGIT_MAX)
qdigit = 1;
qhat = pfx / v->digits[n - 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 */
}
/*
* 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;
s_usub(r.digits, t.digits, r.digits, r.used, t.used);
CLAMP(&r);
/*
* 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 becuase 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));
q.digits[qpos++] = (mp_digit) qdigit;
ZERO(t.digits, t.used);
skip = 0;
/* 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);
}
/* Put quotient digits in the correct order, and discard extra zeroes */
q.used = qpos;
REV(mp_digit, q.digits, qpos);
CLAMP(&q);
/* Get rid of leading zeros in q */
TEMP(0)->used = m + 1;
CLAMP(TEMP(0));
/* Denormalize the remainder */
CLAMP(a);
CLAMP(u); /* use u here because the r.digits pointer is
* off-by-one */
if (k != 0)
s_qdiv(a, k);
s_qdiv(u, k);
mp_int_copy(a, b); /* ok: 0 <= r < b */
mp_int_copy(&q, a); /* ok: q <= a */
mp_int_copy(u, v); /* ok: 0 <= r < v */
mp_int_copy(TEMP(0), u); /* ok: q <= u */
mp_int_clear(&t);
CLEANUP:
mp_int_clear(&q);
return res;
CLEANUP_TEMP();
return MP_OK;
}
/* }}} */
/* {{{ s_outlen(z, r) */
/* Precondition: 2 <= r < 64 */
static int
s_outlen(mp_int z, mp_size r)
{
mp_result bits;
double raw;
assert(r >= MP_MIN_RADIX && r <= MP_MAX_RADIX);
bits = mp_int_count_bits(z);
raw = (double) bits * s_log2[r];
mp_result bits = mp_int_count_bits(z);
double 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);
return (mp_size) ((bits + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT) + 1;
}
/* }}} */
/* {{{ s_ch2val(c, r) */
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))
......@@ -3546,39 +3481,36 @@ s_ch2val(char c, int r)
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)
for (int i = len - 1; i >= 0; --i)
{
unsigned char c = ~buf[i];
......@@ -3592,20 +3524,14 @@ s_2comp(unsigned char *buf, int len)
/* 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;
mp_size uz = MP_USED(z);
mp_digit *dz = MP_DIGITS(z);
uz = MP_USED(z);
dz = MP_DIGITS(z);
while (uz > 0 && pos < limit)
{
mp_digit d = *dz++;
......@@ -3631,13 +3557,17 @@ s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad)
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);
REV(buf, pos);
/* Return the number of bytes actually written */
*limpos = pos;
......@@ -3645,40 +3575,4 @@ s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad)
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 */
/* Here there be dragons */
contrib/pgcrypto/imath.h
View file @ 48e24ba6
/*
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
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.
*/
/* 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;
typedef long mp_small; /* must be a signed type */
typedef unsigned long mp_usmall; /* must be an unsigned type */
#ifdef USE_LONG_LONG
typedef uint32 mp_digit;
typedef uint64 mp_word;
#define MP_DIGIT_MAX 0xFFFFFFFFULL
#define MP_WORD_MAX 0xFFFFFFFFFFFFFFFFULL
/* Build with words as uint64_t by default. */
#ifdef USE_32BIT_WORDS
typedef uint16_t mp_digit;
typedef uint32_t mp_word;
#define MP_DIGIT_MAX (UINT16_MAX * 1UL)
#define MP_WORD_MAX (UINT32_MAX * 1UL)
#else
typedef uint16 mp_digit;
typedef uint32 mp_word;
#define MP_DIGIT_MAX 0xFFFFUL
#define MP_WORD_MAX 0xFFFFFFFFUL
typedef uint32_t mp_digit;
typedef uint64_t mp_word;
#define MP_DIGIT_MAX (UINT32_MAX * UINT64_C(1))
#define MP_WORD_MAX (UINT64_MAX)
#endif
typedef struct mpz
typedef struct
{
mp_digit single;
mp_digit *digits;
mp_size alloc;
mp_size used;
......@@ -64,10 +60,26 @@ typedef struct mpz
*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)
static inline mp_digit *
MP_DIGITS(mp_int Z)
{
return Z->digits;
}
static inline mp_size
MP_ALLOC(mp_int Z)
{
return Z->alloc;
}
static inline mp_size
MP_USED(mp_int Z)
{
return Z->used;
}
static inline mp_sign
MP_SIGN(mp_int Z)
{
return Z->sign;
}
extern const mp_result MP_OK;
extern const mp_result MP_FALSE;
......@@ -77,134 +89,357 @@ extern const mp_result MP_RANGE;
extern const mp_result MP_UNDEF;
extern const mp_result MP_TRUNC;
extern const mp_result MP_BADARG;
extern const mp_result MP_MINERR;
#define MP_DIGIT_BIT (sizeof(mp_digit) * CHAR_BIT)
#define MP_WORD_BIT (sizeof(mp_word) * CHAR_BIT)
#define MP_SMALL_MIN LONG_MIN
#define MP_SMALL_MAX LONG_MAX
#define MP_USMALL_MAX ULONG_MAX
#define MP_MIN_RADIX 2
#define MP_MAX_RADIX 36
/** Sets the default number of digits allocated to an `mp_int` constructed by
`mp_int_init_size()` with `prec == 0`. Allocations are rounded up to
multiples of this value. `MP_DEFAULT_PREC` is the default value. Requires
`ndigits > 0`. */
void mp_int_default_precision(mp_size ndigits);
/** Sets the number of digits below which multiplication will use the standard
quadratic "schoolbook" multiplcation algorithm rather than Karatsuba-Ofman.
Requires `ndigits >= sizeof(mp_word)`. */
void mp_int_multiply_threshold(mp_size ndigits);
/** A sign indicating a (strictly) negative value. */
extern const mp_sign MP_NEG;
/** A sign indicating a zero or positive value. */
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)
/** Reports whether `z` is odd, having remainder 1 when divided by 2. */
static inline bool
mp_int_is_odd(mp_int z)
{
return (z->digits[0] & 1) != 0;
}
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);
/** Reports whether `z` is even, having remainder 0 when divided by 2. */
static inline bool
mp_int_is_even(mp_int z)
{
return (z->digits[0] & 1) == 0;
}
/** Initializes `z` with 1-digit precision and sets it to zero. This function
cannot fail unless `z == NULL`. */
mp_result mp_int_init(mp_int z);
/** Allocates a fresh zero-valued `mpz_t` on the heap, returning NULL in case
of error. The only possible error is out-of-memory. */
mp_int mp_int_alloc(void);
/** Initializes `z` with at least `prec` digits of storage, and sets it to
zero. If `prec` is zero, the default precision is used. In either case the
size is rounded up to the nearest multiple of the word size. */
mp_result mp_int_init_size(mp_int z, mp_size prec);
/** Initializes `z` to be a copy of an already-initialized value in `old`. The
new copy does not share storage with the original. */
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);
/** Initializes `z` to the specified signed `value` at default precision. */
mp_result mp_int_init_value(mp_int z, mp_small value);
/** Initializes `z` to the specified unsigned `value` at default precision. */
mp_result mp_int_init_uvalue(mp_int z, mp_usmall uvalue);
/** Sets `z` to the value of the specified signed `value`. */
mp_result mp_int_set_value(mp_int z, mp_small value);
/** Sets `z` to the value of the specified unsigned `value`. */
mp_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue);
/** Releases the storage used by `z`. */
void mp_int_clear(mp_int z);
/** Releases the storage used by `z` and also `z` itself.
This should only be used for `z` allocated by `mp_int_alloc()`. */
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 */
/** Replaces the value of `c` with a copy of the value of `a`. No new memory is
allocated unless `a` has more significant digits than `c` has allocated. */
mp_result mp_int_copy(mp_int a, mp_int c);
/** Swaps the values and storage between `a` and `c`. */
void mp_int_swap(mp_int a, mp_int c);
/** Sets `z` to zero. The allocated storage of `z` is not changed. */
void mp_int_zero(mp_int z);
/** Sets `c` to the absolute value of `a`. */
mp_result mp_int_abs(mp_int a, mp_int c);
/** Sets `c` to the additive inverse (negation) of `a`. */
mp_result mp_int_neg(mp_int a, mp_int c);
/** Sets `c` to the sum of `a` and `b`. */
mp_result mp_int_add(mp_int a, mp_int b, mp_int c);
/** Sets `c` to the sum of `a` and `value`. */
mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c);
/** Sets `c` to the difference of `a` less `b`. */
mp_result mp_int_sub(mp_int a, mp_int b, mp_int c);
/** Sets `c` to the difference of `a` less `value`. */
mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c);
/** Sets `c` to the product of `a` and `b`. */
mp_result mp_int_mul(mp_int a, mp_int b, mp_int c);
/** Sets `c` to the product of `a` and `value`. */
mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c);
/** Sets `c` to the product of `a` and `2^p2`. Requires `p2 >= 0`. */
mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c);
/** Sets `c` to the square of `a`. */
mp_result mp_int_sqr(mp_int a, mp_int c);
/** Sets `q` and `r` to the quotent and remainder of `a / b`. Division by
powers of 2 is detected and handled efficiently. The remainder is pinned
to `0 <= r < b`.
Either of `q` or `r` may be NULL, but not both, and `q` and `r` may not
point to the same value. */
mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r);
/** Sets `q` and `*r` to the quotent and remainder of `a / value`. Division by
powers of 2 is detected and handled efficiently. The remainder is pinned to
`0 <= *r < b`. Either of `q` or `r` may be NULL. */
mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small * r);
/** Sets `q` and `r` to the quotient and remainder of `a / 2^p2`. This is a
special case for division by powers of two that is more efficient than
using ordinary division. Note that `mp_int_div()` will automatically handle
this case, this function is for cases where you have only the exponent. */
mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r);
/** Sets `c` to the remainder of `a / m`.
The remainder is pinned to `0 <= c < m`. */
mp_result mp_int_mod(mp_int a, mp_int m, mp_int c);
/** Sets `c` to the value of `a` raised to the `b` power.
It returns `MP_RANGE` if `b < 0`. */
mp_result mp_int_expt(mp_int a, mp_small b, mp_int c);
/** Sets `c` to the value of `a` raised to the `b` power.
It returns `MP_RANGE` if `b < 0`. */
mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c);
/** Sets `c` to the value of `a` raised to the `b` power.
It returns `MP_RANGE`) if `b < 0`. */
mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c);
/** Sets `*r` to the remainder of `a / value`.
The remainder is pinned to `0 <= r < value`. */
static inline
mp_result
mp_int_mod_value(mp_int a, mp_small value, mp_small * r)
{
return mp_int_div_value(a, value, 0, r);
}
/** Returns the comparator of `a` and `b`. */
int mp_int_compare(mp_int a, mp_int b);
/** Returns the comparator of the magnitudes of `a` and `b`, disregarding their
signs. Neither `a` nor `b` is modified by the comparison. */
int mp_int_compare_unsigned(mp_int a, mp_int b);
/** Returns the comparator of `z` and zero. */
int mp_int_compare_zero(mp_int z);
/** Returns the comparator of `z` and the signed value `v`. */
int mp_int_compare_value(mp_int z, mp_small v);
/** Returns the comparator of `z` and the unsigned value `uv`. */
int mp_int_compare_uvalue(mp_int z, mp_usmall uv);
/** Reports whether `a` is divisible by `v`. */
bool mp_int_divisible_value(mp_int a, mp_small v);
/** Returns `k >= 0` such that `z` is `2^k`, if such a `k` exists. If no such
`k` exists, the function returns -1. */
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) */
/** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`.
It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */
mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c);
/** Sets `c` to the value of `a` raised to the `value` power, modulo `m`.
It returns `MP_RANGE` if `value < 0` or `MP_UNDEF` if `m == 0`. */
mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c);
/** Sets `c` to the value of `value` raised to the `b` power, modulo `m`.
It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */
mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, mp_int m, mp_int c);
/** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`,
given a precomputed reduction constant `mu` defined for Barrett's modular
reduction algorithm.
It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */
mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c);
/** Sets `c` to the reduction constant for Barrett reduction by modulus `m`.
Requires that `c` and `m` point to distinct locations. */
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) */
/** Sets `c` to the multiplicative inverse of `a` modulo `m`, if it exists.
The least non-negative representative of the congruence class is computed.
It returns `MP_UNDEF` if the inverse does not exist, or `MP_RANGE` if `a ==
0` or `m <= 0`. */
mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c);
/** Sets `c` to the greatest common divisor of `a` and `b`.
It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a`
and `b` are both zero. */
mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c);
mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c); /* c = gcd(a, b) */
/** Sets `c` to the greatest common divisor of `a` and `b`, and sets `x` and
`y` to values satisfying Bezout's identity `gcd(a, b) = ax + by`.
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 */
It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a`
and `b` are both zero. */
mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, mp_int x, mp_int y);
mp_result mp_int_sqrt(mp_int a, mp_int c); /* c = floor(sqrt(q)) */
/** Sets `c` to the least common multiple of `a` and `b`.
/* Convert to an int, if representable (returns MP_RANGE if not). */
mp_result mp_int_to_int(mp_int z, int *out);
It returns `MP_UNDEF` if the LCM is undefined, such as for example if `a`
and `b` are both zero. */
mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c);
/* 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);
/** Sets `c` to the greatest integer not less than the `b`th root of `a`,
using Newton's root-finding algorithm.
It returns `MP_UNDEF` if `a < 0` and `b` is even. */
mp_result mp_int_root(mp_int a, mp_small b, mp_int c);
/* Return the number of characters required to represent
z in the given radix. May over-estimate. */
/** Sets `c` to the greatest integer not less than the square root of `a`.
This is a special case of `mp_int_root()`. */
static inline
mp_result
mp_int_sqrt(mp_int a, mp_int c)
{
return mp_int_root(a, 2, c);
}
/** Returns `MP_OK` if `z` is representable as `mp_small`, else `MP_RANGE`.
If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */
mp_result mp_int_to_int(mp_int z, mp_small * out);
/** Returns `MP_OK` if `z` is representable as `mp_usmall`, or `MP_RANGE`.
If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */
mp_result mp_int_to_uint(mp_int z, mp_usmall * out);
/** Converts `z` to a zero-terminated string of characters in the specified
`radix`, writing at most `limit` characters to `str` including the
terminating NUL value. A leading `-` is used to indicate a negative value.
Returns `MP_TRUNC` if `limit` was to small to write all of `z`.
Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
mp_result mp_int_to_string(mp_int z, mp_size radix, char *str, int limit);
/** Reports the minimum number of characters required to represent `z` as a
zero-terminated string in the given `radix`.
Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
mp_result mp_int_string_len(mp_int z, mp_size radix);
/* Read zero-terminated string into z */
/** Reads a string of ASCII digits in the specified `radix` from the zero
terminated `str` provided into `z`. For values of `radix > 10`, the letters
`A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect
to case.
Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a
sign flag. Processing stops when a NUL or any other character out of range
for a digit in the given radix is encountered.
If the whole string was consumed, `MP_OK` is returned; otherwise
`MP_TRUNC`. is returned.
Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str);
mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str,
char **end);
/* Return the number of significant bits in z */
/** Reads a string of ASCII digits in the specified `radix` from the zero
terminated `str` provided into `z`. For values of `radix > 10`, the letters
`A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect
to case.
Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a
sign flag. Processing stops when a NUL or any other character out of range
for a digit in the given radix is encountered.
If the whole string was consumed, `MP_OK` is returned; otherwise
`MP_TRUNC`. is returned. If `end` is not NULL, `*end` is set to point to
the first unconsumed byte of the input string (the NUL byte if the whole
string was consumed). This emulates the behavior of the standard C
`strtol()` function.
Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end);
/** Returns 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 */
/** Converts `z` to 2's complement binary, writing at most `limit` bytes into
the given `buf`. Returns `MP_TRUNC` if the buffer limit was too small to
contain the whole value. If this occurs, the contents of buf will be
effectively garbage, as the function uses the buffer as scratch space.
The binary representation of `z` is in base-256 with digits ordered from
most significant to least significant (network byte ordering). The
high-order bit of the first byte is set for negative values, clear for
non-negative values.
As a result, non-negative values will be padded with a leading zero byte if
the high-order byte of the base-256 magnitude is set. This extra byte is
accounted for by the `mp_int_binary_len()` function. */
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 */
/** Reads a 2's complement binary value from `buf` into `z`, where `len` is the
length of the buffer. The contents of `buf` may be overwritten during
processing, although they will be restored when the function returns. */
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. */
/** Returns the number of bytes to represent `z` in 2's complement binary. */
mp_result mp_int_binary_len(mp_int z);
/* Convert z to unsigned binary, writing at most limit bytes */
/** Converts the magnitude of `z` to unsigned binary, writing at most `limit`
bytes into the given `buf`. The sign of `z` is ignored, but `z` is not
modified. Returns `MP_TRUNC` if the buffer limit was too small to contain
the whole value. If this occurs, the contents of `buf` will be effectively
garbage, as the function uses the buffer as scratch space during
conversion.
The binary representation of `z` is in base-256 with digits ordered from
most significant to least significant (network byte ordering). */
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 */
/** Reads an unsigned binary value from `buf` into `z`, where `len` is the
length of the buffer. The contents of `buf` are not modified during
processing. */
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 */
/** Returns the number of bytes required to represent `z` as an unsigned binary
value in base 256. */
mp_result mp_int_unsigned_len(mp_int z);
/* Return a statically allocated string describing error code res */
/** Returns a pointer to a brief, human-readable, zero-terminated string
describing `res`. The returned string is statically allocated and must not
be freed by the caller. */
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_ */
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