X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/27b1fbee28915abdf10c4dac4a9027583314c623..HEAD:/math/mp.h

diff --git a/math/mp.h b/math/mp.h
index bb109b53..23e71e36 100644
--- a/math/mp.h
+++ b/math/mp.h
@@ -37,6 +37,7 @@
 #include <assert.h>
 #include <string.h>
 
+#include <mLib/macros.h>
 #include <mLib/sub.h>
 
 #ifndef CATACOMB_MPW_H
@@ -196,7 +197,8 @@ extern void mp_destroy(mp */*m*/);
 
 extern mp *mp_copy(mp */*m*/);
 
-#define MP_COPY(m) ((m)->ref++, (m))
+#define MP_COPY(m) MUFFLE_WARNINGS_EXPR(GCC_WARNING("-Wunused-value"),	\
+					((m)->ref++, (m)))
 
 /* --- @mp_drop@ --- *
  *
@@ -890,6 +892,19 @@ extern mp *mp_exp(mp */*d*/, mp */*a*/, mp */*e*/);
 
 extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/);
 
+/* --- @mp_leastcongruent@ --- *
+ *
+ * Arguments:	@mp *d@ = pointer to destination
+ *		@mp *b@ = lower bound
+ *		@mp *r@ = representative
+ *		@mp *m@ = modulus
+ *
+ * Returns:	The smallest integer %$x \equiv r \pmod{m}$% such that
+ *		%$x \ge b$%.
+ */
+
+extern mp *mp_leastcongruent(mp */*d*/, mp */*b*/, mp */*r*/, mp */*m*/);
+
 /*----- More advanced algorithms ------------------------------------------*/
 
 /* --- @mp_sqrt@ --- *
@@ -908,6 +923,54 @@ extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/);
 
 extern mp *mp_sqrt(mp */*d*/, mp */*a*/);
 
+/* --- @mp_nthrt@ --- *
+ *
+ * Arguments:	@mp *d@ = fake destination
+ *		@mp *a@ = an integer
+ *		@mp *n@ = a strictly positive integer
+ *		@int *exectp_out@ = set nonzero if an exact solution is found
+ *
+ * Returns:	The integer %$\bigl\lfloor \sqrt[n]{a} \bigr\rfloor$%.
+ *
+ * Use:		Return an approximation to the %$n$%th root of %$a$%.
+ *		Specifically, it returns the largest integer %$x$% such that
+ *		%$x^n \le a$%.  If %$x^n = a$% then @*exactp_out@ is set
+ *		nonzero; otherwise it is set zero.  (If @exactp_out@ is null
+ *		then this information is discarded.)
+ *
+ *		The exponent %$n$% must be strictly positive: it's not clear
+ *		to me what the right answer is for %$n \le 0$%.  If %$a$% is
+ *		negative then %$n$% must be odd; otherwise there is no real
+ *		solution.
+ */
+
+extern mp *mp_nthrt(mp */*d*/, mp */*a*/, mp */*n*/, int */*exactp_out*/);
+
+/* --- @mp_perfect_power_p@ --- *
+ *
+ * Arguments:	@mp **x@ = where to write the base
+ *		@mp **n@ = where to write the exponent
+ *		@mp *a@ = an integer
+ *
+ * Returns:	Nonzero if %$a$% is a perfect power.
+ *
+ * Use:		Returns whether an integer %$a$% is a perfect power, i.e.,
+ *		whether it can be written in the form %$a = x^n$% where
+ *		%$|x| > 1$% and %$n > 1$% are integers.  If this is possible,
+ *		then (a) store %$x$% and the largest such %$n$% in @*x@ and
+ *		@*n@, and return nonzero; otherwise, store %$x = a$% and
+ *		%$n = 1$% and return zero.  (Either @x@ or @n@, or both, may
+ *		be null to discard these outputs.)
+ *
+ *		Note that %$-1$%, %$0$% and %$1$% are not considered perfect
+ *		powers by this definition.  (The exponent is not well-defined
+ *		in these cases, but it seemed better to implement a function
+ *		which worked for all integers.)  Note also that %$-4$% is not
+ *		a perfect power since it has no real square root.
+ */
+
+extern int mp_perfect_power_p(mp **/*x*/, mp **/*n*/, mp */*a*/);
+
 /* --- @mp_gcd@ --- *
  *
  * Arguments:	@mp **gcd, **xx, **yy@ = where to write the results