ircd::math: Add modular inversion utility.

include/ircd/math/inv.h

@@ -0,0 +1,38 @@
+// Matrix Construct
+//
+// Copyright (C) Matrix Construct Developers, Authors & Contributors
+// Copyright (C) 2016-2021 Jason Volk <jason@zemos.net>
+//
+// Permission to use, copy, modify, and/or distribute this software for any
+// purpose with or without fee is hereby granted, provided that the above
+// copyright notice and this permission notice is present in all copies. The
+// full license for this software is available in the LICENSE file.
+
+#pragma once
+#define HAVE_IRCD_MATH_INV_H
+
+namespace ircd::math
+{
+	template<class Z> constexpr Z inv(Z a, const Z m);
+}
+
+/// Modular Inverse
+template<class Z>
+inline constexpr Z
+ircd::math::inv(Z a,
+                const Z m)
+{
+	auto b{m}, x0{0}, x1{1};
+	if(likely(m != 1)) while(a > 1)
+	{
+		auto t{b}, q{a / b};
+		b = a % b;
+		a = t;
+		t = x0;
+		x0 = x1 - q * x0;
+		x1 = t;
+	}
+
+	x1 += boolmask<Z>(x1 < 0) & m;
+	return x1;
+}

include/ircd/math/math.h

@@ -12,3 +12,4 @@
 #define HAVE_IRCD_MATH_MATH_H
 
 #include "log2.h"
+#include "inv.h"