Add pure XOR for 1 parity (#138)

WithFastOneParityMatrix will switch the matrix to a simple xor if there is only one parity shard.
The PAR1 matrix already has this property so it has little effect there.

README.md

@@ -29,6 +29,7 @@ go get -u github.com/klauspost/reedsolomon
 
 Numerous updates:
 
+* Added WithFastOneParityMatrix for faster operation with 1 parity shard.
 * Much better performance when using a limited number of goroutines.
 * AVX512 is now using multiple cores.
 * Stream processing overhaul, big speedups in most cases.

options.go

@@ -10,13 +10,15 @@ import (
 type Option func(*options)
 
 type options struct {
-	maxGoroutines                         int
-	minSplitSize                          int
+	maxGoroutines int
+	minSplitSize  int
+	shardSize     int
+	perRound      int
+
 	useAVX512, useAVX2, useSSSE3, useSSE2 bool
 	usePAR1Matrix                         bool
 	useCauchy                             bool
-	shardSize                             int
-	perRound                              int
+	fastOneParity                         bool
 
 	// stream options
 	concReads  bool
@@ -27,6 +29,7 @@ type options struct {
 var defaultOptions = options{
 	maxGoroutines: 384,
 	minSplitSize:  -1,
+	fastOneParity: false,
 
 	// Detect CPU capabilities.
 	useSSSE3:  cpuid.CPU.SSSE3(),
@@ -161,3 +164,12 @@ func WithCauchyMatrix() Option {
 		o.usePAR1Matrix = false
 	}
 }
+
+// WithFastOneParityMatrix will switch the matrix to a simple xor
+// if there is only one parity shard.
+// The PAR1 matrix already has this property so it has little effect there.
+func WithFastOneParityMatrix() Option {
+	return func(o *options) {
+		o.fastOneParity = true
+	}
+}

reedsolomon.go

@@ -206,6 +206,32 @@ func buildMatrixCauchy(dataShards, totalShards int) (matrix, error) {
 	return result, nil
 }
 
+// buildXorMatrix can be used to build a matrix with pure XOR
+// operations if there is only one parity shard.
+func buildXorMatrix(dataShards, totalShards int) (matrix, error) {
+	if dataShards+1 != totalShards {
+		return nil, errors.New("internal error")
+	}
+	result, err := newMatrix(totalShards, dataShards)
+	if err != nil {
+		return nil, err
+	}
+
+	for r, row := range result {
+		// The top portion of the matrix is the identity
+		// matrix.
+		if r < dataShards {
+			result[r][r] = 1
+		} else {
+			// Set all values to 1 (XOR)
+			for c := range row {
+				result[r][c] = 1
+			}
+		}
+	}
+	return result, nil
+}
+
 // New creates a new encoder and initializes it to
 // the number of data shards and parity shards that
 // you want to use. You can reuse this encoder.
@@ -232,6 +258,8 @@ func New(dataShards, parityShards int, opts ...Option) (Encoder, error) {
 
 	var err error
 	switch {
+	case r.o.fastOneParity && parityShards == 1:
+		r.m, err = buildXorMatrix(dataShards, r.Shards)
 	case r.o.useCauchy:
 		r.m, err = buildMatrixCauchy(dataShards, r.Shards)
 	case r.o.usePAR1Matrix:

reedsolomon_test.go

@@ -137,6 +137,7 @@ func testOpts() [][]Option {
 	}
 	opts := [][]Option{
 		{WithPAR1Matrix()}, {WithCauchyMatrix()},
+		{WithFastOneParityMatrix()}, {WithPAR1Matrix(), WithFastOneParityMatrix()}, {WithCauchyMatrix(), WithFastOneParityMatrix()},
 		{WithMaxGoroutines(1), WithMinSplitSize(500), withSSSE3(false), withAVX2(false), withAVX512(false)},
 		{WithMaxGoroutines(5000), WithMinSplitSize(50), withSSSE3(false), withAVX2(false), withAVX512(false)},
 		{WithMaxGoroutines(5000), WithMinSplitSize(500000), withSSSE3(false), withAVX2(false), withAVX512(false)},
@@ -179,7 +180,7 @@ func TestEncoding(t *testing.T) {
 
 // matrix sizes to test.
 // note that par1 matric will fail on some combinations.
-var testSizes = [][2]int{{1, 1}, {1, 2}, {3, 3}, {3, 1}, {5, 3}, {8, 4}, {10, 30}, {14, 7}, {41, 17}}
+var testSizes = [][2]int{{1, 1}, {1, 2}, {3, 3}, {3, 1}, {5, 3}, {8, 4}, {10, 30}, {14, 7}, {41, 17}, {49, 1}}
 var testDataSizes = []int{10, 100, 1000, 10001, 100003, 1000055}
 var testDataSizesShort = []int{10, 10001, 100003}
 
@@ -1257,7 +1258,7 @@ func TestStandardMatrices(t *testing.T) {
 					continue
 				}
 				sh := shards[:i+j]
-				r, err := New(i, j, testOptions()...)
+				r, err := New(i, j, testOptions(WithFastOneParityMatrix())...)
 				if err != nil {
 					// We are not supposed to write to t from goroutines.
 					t.Fatal("creating matrix size", i, j, ":", err)
@@ -1320,7 +1321,7 @@ func TestCauchyMatrices(t *testing.T) {
 					continue
 				}
 				sh := shards[:i+j]
-				r, err := New(i, j, WithCauchyMatrix())
+				r, err := New(i, j, testOptions(WithCauchyMatrix(), WithFastOneParityMatrix())...)
 				if err != nil {
 					// We are not supposed to write to t from goroutines.
 					t.Fatal("creating matrix size", i, j, ":", err)