math/fixed: new package.

Fixes golang/go#11906

Change-Id: I2b43311ff145e8453cd255f085c82add6da7de5b
Reviewed-on: https://go-review.googlesource.com/12863
Reviewed-by: Rob Pike <r@golang.org>

 math/fixed/fixed.go      | 59 ++++++++++++++++++++++++++++++++++++++++++++++++
 math/fixed/fixed_test.go | 25 ++++++++++++++++++++
 2 files changed, 84 insertions(+)

diff --git a/math/fixed/fixed.go b/math/fixed/fixed.go
new file mode 100644
index 0000000..e3dca01
--- /dev/null
+++ b/math/fixed/fixed.go
@@ -0,0 +1,59 @@
+// Copyright 2015 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package fixed implements fixed-point integer types.
+package fixed // import "golang.org/x/image/math/fixed"
+
+import (
+	"fmt"
+)
+
+// TODO: implement fmt.Formatter for %f and %g.
+
+// Int26_6 is a signed 26.6 fixed-point number.
+//
+// The integer part ranges from -33554432 to 33554431, inclusive. The
+// fractional part has 6 bits of precision.
+//
+// For example, the number one-and-a-quarter is Int26_6(1<<6 + 1<<4).
+type Int26_6 int32
+
+// String returns a human-readable representation of a 26.6 fixed-point number.
+//
+// For example, the number one-and-a-quarter becomes "1:16".
+func (x Int26_6) String() string {
+	const shift, mask = 6, 1<<6 - 1
+	if x >= 0 {
+		return fmt.Sprintf("%d:%02d", int32(x>>shift), int32(x&mask))
+	}
+	x = -x
+	if x >= 0 {
+		return fmt.Sprintf("-%d:%02d", int32(x>>shift), int32(x&mask))
+	}
+	return "-33554432:00" // The minimum value is -(1<<25).
+}
+
+// Int52_12 is a signed 52.12 fixed-point number.
+//
+// The integer part ranges from -2251799813685248 to 2251799813685247,
+// inclusive. The fractional part has 12 bits of precision.
+//
+// For example, the number one-and-a-quarter is Int52_12(1<<12 + 1<<10).
+type Int52_12 int64
+
+// String returns a human-readable representation of a 52.12 fixed-point
+// number.
+//
+// For example, the number one-and-a-quarter becomes "1:1024".
+func (x Int52_12) String() string {
+	const shift, mask = 12, 1<<12 - 1
+	if x >= 0 {
+		return fmt.Sprintf("%d:%04d", int64(x>>shift), int64(x&mask))
+	}
+	x = -x
+	if x >= 0 {
+		return fmt.Sprintf("-%d:%04d", int64(x>>shift), int64(x&mask))
+	}
+	return "-2251799813685248:0000" // The minimum value is -(1<<51).
+}
diff --git a/math/fixed/fixed_test.go b/math/fixed/fixed_test.go
new file mode 100644
index 0000000..e252de7
--- /dev/null
+++ b/math/fixed/fixed_test.go
@@ -0,0 +1,25 @@
+// Copyright 2015 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package fixed
+
+import (
+	"testing"
+)
+
+func TestInt26_6(t *testing.T) {
+	got := Int26_6(1<<6 + 1<<4).String()
+	want := "1:16"
+	if got != want {
+		t.Fatalf("got %q, want %q", got, want)
+	}
+}
+
+func TestInt52_12(t *testing.T) {
+	got := Int52_12(1<<12 + 1<<10).String()
+	want := "1:1024"
+	if got != want {
+		t.Fatalf("got %q, want %q", got, want)
+	}
+}