/* -*-c-*-
*
- * $Id: mp.h,v 1.19 2004/04/08 01:36:15 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,
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)
* @mp *a@ = source
*
* Returns: The bitwise complement of the source.
- */
+ */
extern mp *mp_not(mp */*d*/, mp */*a*/);
* Synonyms for the commonly-used functions.
*/
-#define mp_and mp_bit0001
-#define mp_or mp_bit0111
+#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
+#define mp_nor mp_bit1000
+#define mp_xor mp_bit0110
/* --- @mp_testbit@ --- *
*
*/
#define mp_and2c mp_bit00012c
-#define mp_or2c mp_bit01112c
+#define mp_or2c mp_bit01112c
#define mp_nand2c mp_bit11102c
#define mp_nor2c mp_bit10002c
#define mp_xor2c mp_bit01102c
/* --- Other handy macros --- */
-#define MP_ISNEG(x) ((x)->f & MP_NEG)
-#define MP_ISZERO(x) (!MP_LEN(x))
-#define MP_ISPOS(x) (!MP_ISNEG(x) && !MP_ISZERO(x))
-#define MP_ISODD(x) (!MP_ISZERO(x) && ((x)->v[0] & 1u))
-#define MP_ISEVEN(x) (!MP_ISODD(x))
+#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 ---------------------------------------------*/
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
/* --- @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