xmath: Addon math routines

So far only one of them: CeilPow2 to return min(y) >= x: y = 2^i - i.e.
next power of two >= x. This is handy to have in reallocation routines
to allocate buffers from 2^i classes.

Two implementations:

- fast for go19
- slower fallback for go18

xmath/math18.go

+// Copyright (C) 2017  Nexedi SA and Contributors.
+//                     Kirill Smelkov <kirr@nexedi.com>
+//
+// This program is free software: you can Use, Study, Modify and Redistribute
+// it under the terms of the GNU General Public License version 3, or (at your
+// option) any later version, as published by the Free Software Foundation.
+//
+// You can also Link and Combine this program with other software covered by
+// the terms of any of the Open Source Initiative approved licenses and Convey
+// the resulting work. Corresponding source of such a combination shall include
+// the source code for all other software used.
+//
+// This program is distributed WITHOUT ANY WARRANTY; without even the implied
+// warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+//
+// See COPYING file for full licensing terms.
+
+// +build !go1.9
+
+package xmath
+
+// CeilPow2 returns minimal y >= x, such that y = 2^i
+func CeilPow2(x uint64) uint64 {
+	if x == 0 {
+		return x
+	}
+
+	l := uint(0)
+	h := uint(63)
+	for l < h {
+		i := (l + h) / 2
+		y := uint64(1) << i
+
+		switch {
+		case y < x:
+			l = i + 1
+		case y > x:
+			h = i
+		default:
+			// y == x
+			return y
+		}
+	}
+
+	return 1 << h
+}

xmath/math19.go

+// Copyright (C) 2017  Nexedi SA and Contributors.
+//                     Kirill Smelkov <kirr@nexedi.com>
+//
+// This program is free software: you can Use, Study, Modify and Redistribute
+// it under the terms of the GNU General Public License version 3, or (at your
+// option) any later version, as published by the Free Software Foundation.
+//
+// You can also Link and Combine this program with other software covered by
+// the terms of any of the Open Source Initiative approved licenses and Convey
+// the resulting work. Corresponding source of such a combination shall include
+// the source code for all other software used.
+//
+// This program is distributed WITHOUT ANY WARRANTY; without even the implied
+// warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+//
+// See COPYING file for full licensing terms.
+
+// +build go1.9
+
+// Package xmath provides addons to std math package
+package xmath
+
+import (
+	"math/bits"
+)
+
+// CeilPow2 returns minimal y >= x, such that y = 2^i
+func CeilPow2(x uint64) uint64 {
+	switch bits.OnesCount64(x) {
+	case 0, 1:
+		return x // either 0 or 2^i already
+	default:
+		return 1 << uint(bits.Len64(x))
+	}
+}
+
+// XXX if needed: NextPow2 (y > x, such that y = 2^i) is
+//	1 << bits.Len64(x)

xmath/math_test.go

+// Copyright (C) 2017  Nexedi SA and Contributors.
+//                     Kirill Smelkov <kirr@nexedi.com>
+//
+// This program is free software: you can Use, Study, Modify and Redistribute
+// it under the terms of the GNU General Public License version 3, or (at your
+// option) any later version, as published by the Free Software Foundation.
+//
+// You can also Link and Combine this program with other software covered by
+// the terms of any of the Open Source Initiative approved licenses and Convey
+// the resulting work. Corresponding source of such a combination shall include
+// the source code for all other software used.
+//
+// This program is distributed WITHOUT ANY WARRANTY; without even the implied
+// warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+//
+// See COPYING file for full licensing terms.
+
+package xmath
+
+import (
+	"testing"
+)
+
+func TestCeilPow2(t *testing.T) {
+	testv := []struct {in, out uint64} {
+		{0, 0},
+		{1, 1},
+		{2, 2},
+		{3, 4},
+		{4, 4},
+		{5, 8},
+		{5, 8},
+		{6, 8},
+		{7, 8},
+		{8, 8},
+		{9, 16},
+		{10, 16},
+		{11, 16},
+		{12, 16},
+		{13, 16},
+		{14, 16},
+		{15, 16},
+		{16, 16},
+		{1<<62 - 1, 1<<62},
+		{1<<62, 1<<62},
+		{1<<62+1, 1<<63},
+		{1<<63 - 1, 1<<63},
+		{1<<63, 1<<63},
+	}
+
+	for _, tt := range testv {
+		out := CeilPow2(tt.in)
+		if out != tt.out {
+			t.Errorf("CeilPow2(%v) -> %v  ; want %v", tt.in, out, tt.out)
+		}
+	}
+
+}