/* -*-c-*-
*
- * $Id: mp.h,v 1.9 2000/07/29 17:03:31 mdw Exp $
+ * $Id: mp.h,v 1.18 2004/04/03 03:32:05 mdw Exp $
*
* Simple multiprecision arithmetic
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mp.h,v $
+ * Revision 1.18 2004/04/03 03:32:05 mdw
+ * General robustification.
+ *
+ * Revision 1.17 2003/05/16 09:09:24 mdw
+ * Fix @mp_lsl2c@. Turns out to be surprisingly tricky.
+ *
+ * Revision 1.16 2002/10/15 22:57:22 mdw
+ * Handy new comparison macros.
+ *
+ * Revision 1.15 2002/10/15 19:18:31 mdw
+ * New operation to negate numbers.
+ *
+ * Revision 1.14 2002/10/15 00:19:40 mdw
+ * Bit setting and clearing functions.
+ *
+ * Revision 1.13 2002/10/06 22:52:50 mdw
+ * Pile of changes for supporting two's complement properly.
+ *
+ * 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.
/*----- Data structures ---------------------------------------------------*/
+/* --- A multiprecision integer --- */
+
typedef struct mp {
- mpw *v, *vl;
- size_t sz;
- mparena *a;
- unsigned f;
- unsigned ref;
+ mpw *v, *vl; /* Vector of digits, current limit */
+ size_t sz; /* Size of digit buffer in words */
+ mparena *a; /* Arena for buffer allocation */
+ unsigned f; /* Flags (see below) */
+ unsigned ref; /* Reference counter */
} mp;
-#define MP_NEG 1u
-#define MP_BURN 2u
-#define MP_CONST 4u
-#define MP_UNDEF 8u
-#define MP_DESTROYED 16u
+#define MP_NEG 1u /* Negative (signed magnitude) */
+#define MP_BURN 2u /* Secret (viral flag) */
+#define MP_CONST 4u /* Uses strange memory allocation */
+#define MP_UNDEF 8u /* Contains nothing interesting */
+#define MP_DESTROYED 16u /* Has been destroyed */
+
+/* --- A factor for simultaneous exponentation --- *
+ *
+ * Used by the Montgomery and Barrett exponentiators.
+ */
+
+typedef struct mp_expfactor {
+ mp *base;
+ mp *exp;
+} mp_expfactor;
/*----- Useful constants --------------------------------------------------*/
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@
*/
-extern mp *mp_sm(mp */*d*/, mp */*a*/);
+#define MP_BITDECL(string) \
+ extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/);
+MPX_DOBIN(MP_BITDECL)
-/* --- @mp_lsl@ --- *
+/* --- @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 int mp_testbit(mp */*x*/, unsigned long /*n*/);
+
+/* --- @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_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.
+ */
-/* --- @mp_lsr@ --- *
+#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@ --- *
+ *
+ * Arguments: @const mp *a, *b@ = two numbers
+ *
+ * Returns: Nonzero if the numbers are equal.
+ */
+
+extern int mp_eq(const mp */*a*/, const mp */*b*/);
+
+#define MP_EQ(a, b) \
+ ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \
+ mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl))
/* --- @mp_cmp@ --- *
*
#define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0)
+/* --- 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))
+
+/*----- Arithmetic operations ---------------------------------------------*/
+
+/* --- @mp_neg@ --- *
+ *
+ * Arguments: @mp *d@ = destination
+ * @mp *a@ = argument
+ *
+ * Returns: The negation of the argument.
+ *
+ * Use: Negates its argument.
+ */
+
+extern mp *mp_neg(mp */*d*/, mp */*a*/);
+
/* --- @mp_add@ --- *
*
* Arguments: @mp *d@ = destination
projects / u / mdw / catacomb / blobdiff