/* -*-c-*-
*
- * $Id: mp.h,v 1.7 2000/06/17 11:45:09 mdw Exp $
+ * $Id: mp.h,v 1.8 2000/06/22 19:02:01 mdw Exp $
*
* Simple multiprecision arithmetic
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mp.h,v $
+ * 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
extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/);
+/* --- @mp_odd@ --- *
+ *
+ * Arguments: @mp *d@ = pointer to destination integer
+ * @mp *m@ = pointer to source integer
+ * @size_t *s@ = where to store the power of 2
+ *
+ * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
+ *
+ * Use: Computes a power of two and an odd integer which, when
+ * multiplied, give a specified result. This sort of thing is
+ * useful in number theory quite often.
+ */
+
+extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/);
+
/*----- More advanced algorithms ------------------------------------------*/
+/* --- @mp_sqrt@ --- *
+ *
+ * Arguments: @mp *d@ = pointer to destination integer
+ * @mp *a@ = (nonnegative) integer to take square root of
+ *
+ * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
+ *
+ * Use: Computes integer square roots.
+ *
+ * The current implementation isn't very good: it uses the
+ * Newton-Raphson method to find an approximation to %$a$%. If
+ * there's any demand for a better version, I'll write one.
+ */
+
+extern mp *mp_sqrt(mp */*d*/, mp */*a*/);
+
/* --- @mp_gcd@ --- *
*
* Arguments: @mp **gcd, **xx, **yy@ = where to write the results
* @a@ and @n@ have a common factor greater than one.
*/
-int mp_jacobi(mp */*a*/, mp */*n*/);
+extern int mp_jacobi(mp */*a*/, mp */*n*/);
+
+/* --- @mp_modsqrt@ --- *
+ *
+ * Arguments: @mp *d@ = destination integer
+ * @mp *a@ = source integer
+ * @mp *p@ = modulus (must be prime)
+ *
+ * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else
+ * a null pointer.
+ *
+ * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%,
+ * if one exists; else a null pointer. This function will not
+ * 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.
+ */
+
+extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/);
/*----- Test harness support ----------------------------------------------*/