/* -*-c-*-
*
- * $Id: mp.h,v 1.12 2001/06/16 12:57:43 mdw Exp $
+ * $Id$
*
* Simple multiprecision arithmetic
*
* (c) 1999 Straylight/Edgeware
*/
-/*----- Licensing notice --------------------------------------------------*
+/*----- Licensing notice --------------------------------------------------*
*
* This file is part of Catacomb.
*
* it under the terms of the GNU Library General Public License as
* published by the Free Software Foundation; either version 2 of the
* License, or (at your option) any later version.
- *
+ *
* Catacomb is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Library General Public License for more details.
- *
+ *
* You should have received a copy of the GNU Library General Public
* License along with Catacomb; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: mp.h,v $
- * Revision 1.12 2001/06/16 12:57:43 mdw
- * Move the @mpmont_factor@ structure and rename it now that it's used for
- * Barrett simultaneous exponentiation too.
- *
- * Revision 1.11 2001/04/03 19:36:05 mdw
- * Add some simple bitwise operations so that Perl can use them.
- *
- * Revision 1.10 2000/10/08 12:03:16 mdw
- * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two
- * integers.
- *
- * Revision 1.9 2000/07/29 17:03:31 mdw
- * Add support for left-to-right bitscanning, for use in modular
- * exponentiation.
- *
- * Revision 1.8 2000/06/22 19:02:01 mdw
- * Add new functions.
- *
- * Revision 1.7 2000/06/17 11:45:09 mdw
- * Major memory management overhaul. Added arena support. Use the secure
- * arena for secret integers. Replace and improve the MP management macros
- * (e.g., replace MP_MODIFY by MP_DEST).
- *
- * Revision 1.6 1999/12/10 23:19:46 mdw
- * Minor bugfixes. New interface for suggested destinations.
- *
- * Revision 1.5 1999/11/22 20:50:37 mdw
- * Add support for computing Jacobi symbols.
- *
- * Revision 1.4 1999/11/21 22:13:02 mdw
- * Add mp version of MPX_BITS.
- *
- * Revision 1.3 1999/11/19 13:19:14 mdw
- * Fix const annotation.
- *
- * Revision 1.2 1999/11/17 18:02:16 mdw
- * New multiprecision integer arithmetic suite.
- *
- */
-
#ifndef CATACOMB_MP_H
#define CATACOMB_MP_H
extern mp mp_const[];
#define MP_ZERO (&mp_const[0])
-#define MP_ONE (&mp_const[1])
-#define MP_TWO (&mp_const[2])
+#define MP_ONE (&mp_const[1])
+#define MP_TWO (&mp_const[2])
#define MP_THREE (&mp_const[3])
-#define MP_FOUR (&mp_const[4])
-#define MP_FIVE (&mp_const[5])
-#define MP_TEN (&mp_const[6])
+#define MP_FOUR (&mp_const[4])
+#define MP_FIVE (&mp_const[5])
+#define MP_TEN (&mp_const[6])
#define MP_256 (&mp_const[7])
-#define MP_MONE (&mp_const[8])
+#define MP_MONE (&mp_const[8])
#define MP_NEW ((mp *)0)
#define MP_NEWSEC (&mp_const[9])
if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \
mp_destroy(_mm); \
} while (0)
-
+
/* --- @mp_split@ --- *
*
* Arguments: @mp *m@ = pointer to a multiprecision integer
#define MP_SHRINK(m) do { \
mp *_mm = (m); \
MPX_SHRINK(_mm->v, _mm->vl); \
- if (!MP_LEN(_mm)) \
+ if (MP_ZEROP(_mm)) \
_mm->f &= ~MP_NEG; \
} while (0)
extern size_t mp_octets(const mp */*m*/);
+/* --- @mp_octets2c@ --- *
+ *
+ * Arguments: @const mp *m@ = a multiprecision integer
+ *
+ * Returns: The number of octets required to represent @m@.
+ *
+ * Use: Calculates the external storage required for a multiprecision
+ * integer represented as two's complement.
+ */
+
+extern size_t mp_octets2c(const mp */*m*/);
+
/* --- @mp_bits@ --- *
*
* Arguments: @const mp *m@ = a multiprecision integer
extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/);
-/*----- Simple arithmetic -------------------------------------------------*/
+/* --- @mp_loadl2c@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @const void *pv@ = pointer to source data
+ * @size_t sz@ = size of the source data
+ *
+ * Returns: Resulting multiprecision number.
+ *
+ * Use: Loads a multiprecision number from an array of octets as
+ * two's complement. The first byte in the array is the least
+ * significant.
+ */
+
+extern mp *mp_loadl2c(mp */*d*/, const void */*pv*/, size_t /*sz*/);
-/* --- @mp_2c@ --- *
+/* --- @mp_storel2c@ --- *
+ *
+ * Arguments: @const mp *m@ = source
+ * @void *pv@ = pointer to output array
+ * @size_t sz@ = size of the output array
+ *
+ * Returns: ---
+ *
+ * Use: Stores a multiprecision number in an array of octets as two's
+ * complement. The first byte in the array is the least
+ * significant. If the array is too small to represent the
+ * number, high-order bits are truncated; if the array is too
+ * large, high order bytes are sign-extended.
+ */
+
+extern void mp_storel2c(const mp */*m*/, void */*pv*/, size_t /*sz*/);
+
+/* --- @mp_loadb2c@ --- *
*
* Arguments: @mp *d@ = destination
- * @mp *a@ = source
+ * @const void *pv@ = pointer to source data
+ * @size_t sz@ = size of the source data
+ *
+ * Returns: Resulting multiprecision number.
+ *
+ * Use: Loads a multiprecision number from an array of octets as
+ * two's complement. The last byte in the array is the least
+ * significant.
+ */
+
+extern mp *mp_loadb2c(mp */*d*/, const void */*pv*/, size_t /*sz*/);
+
+/* --- @mp_storeb2c@ --- *
+ *
+ * Arguments: @const mp *m@ = source
+ * @void *pv@ = pointer to output array
+ * @size_t sz@ = size of the output array
+ *
+ * Returns: ---
*
- * Returns: Result, @a@ converted to two's complement notation.
+ * Use: Stores a multiprecision number in an array of octets, as
+ * two's complement. The last byte in the array is the least
+ * significant. If the array is too small to represent the
+ * number, high-order bits are truncated; if the array is too
+ * large, high order bytes are sign-extended.
*/
-extern mp *mp_2c(mp */*d*/, mp */*a*/);
+extern void mp_storeb2c(const mp */*m*/, void */*pv*/, size_t /*sz*/);
-/* --- @mp_sm@ --- *
+/*----- Bit operations ----------------------------------------------------*/
+
+/* --- @mp_not@ --- *
*
* Arguments: @mp *d@ = destination
* @mp *a@ = source
*
- * Returns: Result, @a@ converted to the native signed-magnitude
- * notation.
+ * Returns: The bitwise complement of the source.
+ */
+
+extern mp *mp_not(mp */*d*/, mp */*a*/);
+
+/* --- @mp_bitop@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @mp *a, *b@ = sources
+ *
+ * Returns: The result of the given bitwise operation. These functions
+ * don't handle negative numbers at all sensibly. For that, use
+ * the @...2c@ variants. The functions are named after the
+ * truth tables they generate:
+ *
+ * a: 0011
+ * b: 0101
+ * @mpx_bitXXXX@
+ */
+
+#define MP_BITDECL(string) \
+ extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/);
+MPX_DOBIN(MP_BITDECL)
+
+/* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
+ *
+ * Synonyms for the commonly-used functions.
+ */
+
+#define mp_and mp_bit0001
+#define mp_or mp_bit0111
+#define mp_nand mp_bit1110
+#define mp_nor mp_bit1000
+#define mp_xor mp_bit0110
+
+/* --- @mp_testbit@ --- *
+ *
+ * Arguments: @mp *x@ = a large integer
+ * @unsigned long n@ = which bit to test
+ *
+ * Returns: Nonzero if the bit is set, zero if not.
*/
-extern mp *mp_sm(mp */*d*/, mp */*a*/);
+extern int mp_testbit(mp */*x*/, unsigned long /*n*/);
-/* --- @mp_lsl@ --- *
+/* --- @mp_setbit@, @mp_clearbit@ --- *
+ *
+ * Arguments: @mp *d@ = a destination
+ * @mp *x@ = a large integer
+ * @unsigned long n@ = which bit to modify
+ *
+ * Returns: The argument @x@, with the appropriate bit set or cleared.
+ */
+
+extern mp *mp_setbit(mp */*d*/, mp */*x*/, unsigned long /*n*/);
+extern mp *mp_clearbit(mp */*d*/, mp */*x*/, unsigned long /*n*/);
+
+/* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- *
*
* Arguments: @mp *d@ = destination
* @mp *a@ = source
* @size_t n@ = number of bits to move
*
- * Returns: Result, @a@ shifted left by @n@.
+ * Returns: Result, @a@ shifted left or right by @n@.
+ *
+ * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced
+ * on the right with ones instead of zeroes: it's used
+ * internally by @mp_lsl2c@, though it may be useful on its
+ * own.
*/
extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/);
+extern mp *mp_lslc(mp */*d*/, mp */*a*/, size_t /*n*/);
+extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/);
-/* --- @mp_lsr@ --- *
+/* --- @mp_not2c@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @mp *a@ = source
+ *
+ * Returns: The sign-extended complement of the argument.
+ */
+
+extern mp *mp_not2c(mp */*d*/, mp */*a*/);
+
+/* --- @mp_bitop2c@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @mp *a, *b@ = sources
+ *
+ * Returns: The result of the given bitwise operation. Negative numbers
+ * are treated as two's complement, sign-extended infinitely to
+ * the left. The functions are named after the truth tables
+ * they generate:
+ *
+ * a: 0011
+ * b: 0101
+ * @mpx_bitXXXX@
+ */
+
+#define MP_BIT2CDECL(string) \
+ extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/);
+MPX_DOBIN(MP_BIT2CDECL)
+
+/* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
+ *
+ * Synonyms for the commonly-used functions.
+ */
+
+#define mp_and2c mp_bit00012c
+#define mp_or2c mp_bit01112c
+#define mp_nand2c mp_bit11102c
+#define mp_nor2c mp_bit10002c
+#define mp_xor2c mp_bit01102c
+
+/* --- @mp_lsl2c@, @mp_lsr2c@ --- *
*
* Arguments: @mp *d@ = destination
* @mp *a@ = source
* @size_t n@ = number of bits to move
*
- * Returns: Result, @a@ shifted left by @n@.
+ * Returns: Result, @a@ shifted left or right by @n@. Handles the
+ * pretence of sign-extension for negative numbers.
*/
-extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/);
+extern mp *mp_lsl2c(mp */*d*/, mp */*a*/, size_t /*n*/);
+extern mp *mp_lsr2c(mp */*d*/, mp */*a*/, size_t /*n*/);
+
+/* --- @mp_testbit2c@ --- *
+ *
+ * Arguments: @mp *x@ = a large integer
+ * @unsigned long n@ = which bit to test
+ *
+ * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
+ * complement representation.
+ */
+
+extern int mp_testbit2c(mp */*x*/, unsigned long /*n*/);
+
+/* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
+ *
+ * Arguments: @mp *d@ = a destination
+ * @mp *x@ = a large integer
+ * @unsigned long n@ = which bit to modify
+ *
+ * Returns: The argument @x@, with the appropriate bit set or cleared.
+ * Fakes up two's complement representation.
+ */
+
+extern mp *mp_setbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/);
+extern mp *mp_clearbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/);
+
+/*----- Comparisons -------------------------------------------------------*/
/* --- @mp_eq@ --- *
*
#define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0)
-/* --- @mpx_and@, @mpx_or@, @mpx_xor@, @mpx_not@ --- *
+/* --- Other handy macros --- */
+
+#define MP_NEGP(x) ((x)->f & MP_NEG)
+#define MP_ZEROP(x) (!MP_LEN(x))
+#define MP_POSP(x) (!MP_NEGP(x) && !MP_ZEROP(x))
+#define MP_ODDP(x) (!MP_ZEROP(x) && ((x)->v[0] & 1u))
+#define MP_EVENP(x) (!MP_ODDP(x))
+
+/*----- Arithmetic operations ---------------------------------------------*/
+
+/* --- @mp_neg@ --- *
*
* Arguments: @mp *d@ = destination
- * @mp *a, *b@ = sources
+ * @mp *a@ = argument
+ *
+ * Returns: The negation of the argument.
*
- * Returns: The result of the obvious bitwise operation.
+ * Use: Negates its argument.
*/
-extern mp *mp_and(mp */*d*/, mp */*a*/, mp */*b*/);
-extern mp *mp_or(mp */*d*/, mp */*a*/, mp */*b*/);
-extern mp *mp_xor(mp */*d*/, mp */*a*/, mp */*b*/);
-extern mp *mp_not(mp */*d*/, mp */*a*/);
+extern mp *mp_neg(mp */*d*/, mp */*a*/);
/* --- @mp_add@ --- *
*
extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/);
+/* --- @mp_exp@ --- *
+ *
+ * Arguments: @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
+ *
+ * Returns: Result, %$a^e$%.
+ */
+
+extern mp *mp_exp(mp */*d*/, mp */*a*/, mp */*e*/);
+
/* --- @mp_odd@ --- *
*
* Arguments: @mp *d@ = pointer to destination integer
extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/,
mp */*a*/, mp */*b*/);
+/* -- @mp_modinv@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @mp *x@ = argument
+ * @mp *p@ = modulus
+ *
+ * Returns: The inverse %$x^{-1} \bmod p$%.
+ *
+ * Use: Computes a modular inverse. An assertion fails if %$p$%
+ * has no inverse.
+ */
+
+extern mp *mp_modinv(mp */*d*/, mp */*x*/, mp */*p*/);
+
/* --- @mp_jacobi@ --- *
*
- * Arguments: @mp *a@ = an integer less than @n@
- * @mp *n@ = an odd integer
+ * Arguments: @mp *a@ = an integer
+ * @mp *n@ = another integer
*
* Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
*
- * Use: Computes the Jacobi symbol. If @n@ is prime, this is the
- * Legendre symbol and is equal to 1 if and only if @a@ is a
- * quadratic residue mod @n@. The result is zero if and only if
- * @a@ and @n@ have a common factor greater than one.
+ * Use: Computes the Kronecker symbol %$\jacobi{a}{n}$%. If @n@ is
+ * prime, this is the Legendre symbol and is equal to 1 if and
+ * only if @a@ is a quadratic residue mod @n@. The result is
+ * zero if and only if @a@ and @n@ have a common factor greater
+ * than one.
+ *
+ * If @n@ is composite, then this computes the Kronecker symbol
+ *
+ * %$\jacobi{a}{n}=\jacobi{a}{u}\prod_i\jacobi{a}{p_i}^{e_i}$%
+ *
+ * where %$n = u p_0^{e_0} \ldots p_{n-1}^{e_{n-1}}$% is the
+ * prime factorization of %$n$%. The missing bits are:
+ *
+ * * %$\jacobi{a}{1} = 1$%;
+ * * %$\jacobi{a}{-1} = 1$% if @a@ is negative, or 1 if
+ * positive;
+ * * %$\jacobi{a}{0} = 0$%;
+ * * %$\jacobi{a}{2}$ is 0 if @a@ is even, 1 if @a@ is
+ * congruent to 1 or 7 (mod 8), or %$-1$% otherwise.
+ *
+ * If %$n$% is positive and odd, then this is the Jacobi
+ * symbol. (The Kronecker symbol is a consistant domain
+ * extension; the Jacobi symbol was implemented first, and the
+ * name stuck.)
*/
extern int mp_jacobi(mp */*a*/, mp */*n*/);
* work if %$p$% is composite: you must factor the modulus, take
* a square root mod each factor, and recombine the results
* using the Chinese Remainder Theorem.
+ *
+ * We guarantee that the square root returned is the smallest
+ * one (i.e., the `positive' square root).
*/
extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/);
+/* --- @mp_modexp@ --- *
+ *
+ * Arguments: @mp *d@ = fake destination
+ * @mp *x@ = base of exponentiation
+ * @mp *e@ = exponent
+ * @mp *n@ = modulus (must be positive)
+ *
+ * Returns: The value %$x^e \bmod n$%.
+ */
+
+extern mp *mp_modexp(mp */*d*/, mp */*x*/, mp */*e*/, mp */*n*/);
+
/*----- Test harness support ----------------------------------------------*/
#include <mLib/testrig.h>
projects / u / mdw / catacomb / blobdiff