New divides function.

* arith.c (divides): New function.
(arith_init): Intrinsic registered.

* arith.h (divides): Declared.

* txr.1: Documented.

3 files changed, 53 insertions, 0 deletions

diff --git a/arith.c b/arith.c
index 80405e85..7700ea07 100644
--- a/arith.c
+++ b/arith.c
@@ -2021,6 +2021,28 @@ val lcm(val anum, val bnum)
   }
 }
 
+val divides(val d, val n)
+{
+  if (n == zero) {
+    if (!integerp(d))
+      uw_throwf(error_s, lit("divides: ~s isn't an integer"),
+                d, nao);
+    return tnil(!zerop(d));
+  }
+
+  if (d == one) {
+    if (!integerp(n))
+      uw_throwf(error_s, lit("divides: ~s isn't an integer"),
+                n, nao);
+    return t;
+  }
+
+  if (minusp(d))
+    d = neg(d);
+
+  return eql(gcd(d, n), d);
+}
+
 val floorf(val num)
 {
   switch (type(num)) {
@@ -2929,6 +2951,7 @@ void arith_init(void)
   reg_varl(intern(lit("*e*"), user_package), flo(M_E));
   reg_varl(intern(lit("%e%"), user_package), flo(M_E));
 
+  reg_fun(intern(lit("divides"), user_package), func_n2(divides));
   reg_fun(intern(lit("bits"), system_package), func_n1(bits));
   reg_fun(intern(lit("digpow"), user_package), func_n2o(digpow, 1));
   reg_fun(intern(lit("digits"), user_package), func_n2o(digits, 1));
diff --git a/arith.h b/arith.h
index 29e65706..235d4ba1 100644
--- a/arith.h
+++ b/arith.h
@@ -39,6 +39,7 @@ val unum(ucnum u);
 val cum_norm_dist(val x);
 val n_choose_k(val n, val k);
 val n_perm_k(val n, val k);
+val divides(val d, val n);
 val tofloat(val obj);
 val toint(val obj, val base);
 val tofloatz(val obj);
diff --git a/txr.1 b/txr.1
index cec90274..e005a34b 100644
--- a/txr.1
+++ b/txr.1
@@ -33713,6 +33713,35 @@ If
 .code lcm
 has any argument which is zero, it yields zero.
 
+.coNP Function @ divides
+.synb
+.mets (divides < d << n )
+.syne
+.desc
+The
+.code divides
+function tests whether integer
+.meta d
+divides integer
+.metn n .
+If this is true,
+.code t
+is returned, otherwise
+.codn nil .
+
+The integers 1 and -1 divide every other integer and themselves.
+By established convention, every integer, except zero, divides zero.
+
+For other values,
+.meta d
+divides
+.meta n
+if division of
+.meta n
+by
+.meta d
+leaves no remainder.
+
 .coNP Function @ abs
 .synb
 .mets (abs << number )