diff --git a/math.c b/math.c
index 51a9eac8b4..1e2af7aa75 100644
--- a/math.c
+++ b/math.c
@@ -474,7 +474,6 @@ math_exp(VALUE unused_obj, VALUE x)
 # define M_LN10 2.30258509299404568401799145468436421
 #endif
 
-static double math_log1(VALUE x);
 FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE));
 
 /*
@@ -509,20 +508,6 @@ math_log(int argc, const VALUE *argv, VALUE unused_obj)
     return rb_math_log(argc, argv);
 }
 
-VALUE
-rb_math_log(int argc, const VALUE *argv)
-{
-    VALUE x, base;
-    double d;
-
-    rb_scan_args(argc, argv, "11", &x, &base);
-    d = math_log1(x);
-    if (argc == 2) {
-        d /= math_log1(base);
-    }
-    return DBL2NUM(d);
-}
-
 static double
 get_double_rshift(VALUE x, size_t *pnumbits)
 {
@@ -541,16 +526,51 @@ get_double_rshift(VALUE x, size_t *pnumbits)
 }
 
 static double
-math_log1(VALUE x)
+math_log_split(VALUE x, size_t *numbits)
 {
-    size_t numbits;
-    double d = get_double_rshift(x, &numbits);
+    double d = get_double_rshift(x, numbits);
 
     domain_check_min(d, 0.0, "log");
-    /* check for pole error */
-    if (d == 0.0) return -HUGE_VAL;
+    return d;
+}
 
-    return log(d) + numbits * M_LN2; /* log(d * 2 ** numbits) */
+#if defined(log2) || defined(HAVE_LOG2)
+# define log_intermediate log2
+#else
+# define log_intermediate log10
+#endif
+
+VALUE
+rb_math_log(int argc, const VALUE *argv)
+{
+    VALUE x, base;
+    double d;
+    size_t numbits;
+
+    argc = rb_scan_args(argc, argv, "11", &x, &base);
+    d = math_log_split(x, &numbits);
+    if (argc == 2) {
+        size_t numbits_2;
+        double b = math_log_split(base, &numbits_2);
+        /* check for pole error */
+        if (d == 0.0) {
+            if (b > 0.0) return DBL2NUM(HUGE_VAL);
+            if (b < 0.0) return DBL2NUM(-HUGE_VAL);
+            return DBL2NUM(nan(""));
+        }
+        else if (b == 0.0) {
+            return DBL2NUM(-0.0);
+        }
+        d = log_intermediate(d) / log_intermediate(b);
+        numbits -= numbits_2;
+    }
+    else {
+        /* check for pole error */
+        if (d == 0.0) return DBL2NUM(-HUGE_VAL);
+        d = log(d);
+    }
+    d += numbits * M_LN2;
+    return DBL2NUM(d);
 }
 
 #ifndef log2