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 // Copyright 2016 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 vector import ( "bytes" "fmt" "math/rand" "testing" ) // TestDivideByFFFF tests that dividing by 0xffff is equivalent to multiplying // and then shifting by magic constants. The Go compiler itself issues this // multiply-and-shift for a division by the constant value 0xffff. This trick // is used in the asm code as the GOARCH=amd64 SIMD instructions have parallel // multiply but not parallel divide. // // There's undoubtedly a justification somewhere in Hacker's Delight chapter 10 // "Integer Division by Constants", but I don't have a more specific link. // // http://www.hackersdelight.org/divcMore.pdf and // http://www.hackersdelight.org/magic.htm func TestDivideByFFFF(t *testing.T) { const mul, shift = 0x80008001, 47 rng := rand.New(rand.NewSource(1)) for i := 0; i < 20000; i++ { u := rng.Uint32() got := uint32((uint64(u) * mul) >> shift) want := u / 0xffff if got != want { t.Fatalf("i=%d, u=%#08x: got %#08x, want %#08x", i, u, got, want) } } } // TestXxxSIMDUnaligned tests that unaligned SIMD loads/stores don't crash. func TestFixedAccumulateSIMDUnaligned(t *testing.T) { if !haveFixedAccumulateSIMD { t.Skip("No SIMD implemention") } dst := make([]uint8, 64) src := make([]uint32, 64) for d := 0; d < 16; d++ { for s := 0; s < 16; s++ { fixedAccumulateOpSrcSIMD(dst[d:d+32], src[s:s+32]) } } } func TestFloatingAccumulateSIMDUnaligned(t *testing.T) { if !haveFloatingAccumulateSIMD { t.Skip("No SIMD implemention") } dst := make([]uint8, 64) src := make([]float32, 64) for d := 0; d < 16; d++ { for s := 0; s < 16; s++ { floatingAccumulateOpSrcSIMD(dst[d:d+32], src[s:s+32]) } } } // TestXxxSIMDShortDst tests that the SIMD implementations don't write past the // end of the dst buffer. func TestFixedAccumulateSIMDShortDst(t *testing.T) { if !haveFixedAccumulateSIMD { t.Skip("No SIMD implemention") } const oneQuarter = uint32(int2ϕ(fxOne*fxOne)) / 4 src := []uint32{oneQuarter, oneQuarter, oneQuarter, oneQuarter} for i := 0; i < 4; i++ { dst := make([]uint8, 4) fixedAccumulateOpSrcSIMD(dst[:i], src[:i]) for j := range dst { if j < i { if got := dst[j]; got == 0 { t.Errorf("i=%d, j=%d: got %#02x, want non-zero", i, j, got) } } else { if got := dst[j]; got != 0 { t.Errorf("i=%d, j=%d: got %#02x, want zero", i, j, got) } } } } } func TestFloatingAccumulateSIMDShortDst(t *testing.T) { if !haveFloatingAccumulateSIMD { t.Skip("No SIMD implemention") } const oneQuarter = 0.25 src := []float32{oneQuarter, oneQuarter, oneQuarter, oneQuarter} for i := 0; i < 4; i++ { dst := make([]uint8, 4) floatingAccumulateOpSrcSIMD(dst[:i], src[:i]) for j := range dst { if j < i { if got := dst[j]; got == 0 { t.Errorf("i=%d, j=%d: got %#02x, want non-zero", i, j, got) } } else { if got := dst[j]; got != 0 { t.Errorf("i=%d, j=%d: got %#02x, want zero", i, j, got) } } } } } func TestFixedAccumulateOpOverShort(t *testing.T) { testAcc(t, fxInShort, fxMaskShort, "over") } func TestFixedAccumulateOpSrcShort(t *testing.T) { testAcc(t, fxInShort, fxMaskShort, "src") } func TestFixedAccumulateMaskShort(t *testing.T) { testAcc(t, fxInShort, fxMaskShort, "mask") } func TestFloatingAccumulateOpOverShort(t *testing.T) { testAcc(t, flInShort, flMaskShort, "over") } func TestFloatingAccumulateOpSrcShort(t *testing.T) { testAcc(t, flInShort, flMaskShort, "src") } func TestFloatingAccumulateMaskShort(t *testing.T) { testAcc(t, flInShort, flMaskShort, "mask") } func TestFixedAccumulateOpOver16(t *testing.T) { testAcc(t, fxIn16, fxMask16, "over") } func TestFixedAccumulateOpSrc16(t *testing.T) { testAcc(t, fxIn16, fxMask16, "src") } func TestFixedAccumulateMask16(t *testing.T) { testAcc(t, fxIn16, fxMask16, "mask") } func TestFloatingAccumulateOpOver16(t *testing.T) { testAcc(t, flIn16, flMask16, "over") } func TestFloatingAccumulateOpSrc16(t *testing.T) { testAcc(t, flIn16, flMask16, "src") } func TestFloatingAccumulateMask16(t *testing.T) { testAcc(t, flIn16, flMask16, "mask") } func testAcc(t *testing.T, in interface{}, mask []uint32, op string) { for _, simd := range []bool{false, true} { maxN := 0 switch in := in.(type) { case []uint32: if simd && !haveFixedAccumulateSIMD { continue } maxN = len(in) case []float32: if simd && !haveFloatingAccumulateSIMD { continue } maxN = len(in) } for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 33, 55, 79, 96, 120, 165, 256, maxN} { if n > maxN { continue } var ( got8, want8 []uint8 got32, want32 []uint32 ) switch op { case "over": const background = 0x40 got8 = make([]uint8, n) for i := range got8 { got8[i] = background } want8 = make([]uint8, n) for i := range want8 { dstA := uint32(background * 0x101) maskA := mask[i] outA := dstA*(0xffff-maskA)/0xffff + maskA want8[i] = uint8(outA >> 8) } case "src": got8 = make([]uint8, n) want8 = make([]uint8, n) for i := range want8 { want8[i] = uint8(mask[i] >> 8) } case "mask": got32 = make([]uint32, n) want32 = mask[:n] } switch in := in.(type) { case []uint32: switch op { case "over": if simd { fixedAccumulateOpOverSIMD(got8, in[:n]) } else { fixedAccumulateOpOver(got8, in[:n]) } case "src": if simd { fixedAccumulateOpSrcSIMD(got8, in[:n]) } else { fixedAccumulateOpSrc(got8, in[:n]) } case "mask": copy(got32, in[:n]) if simd { fixedAccumulateMaskSIMD(got32) } else { fixedAccumulateMask(got32) } } case []float32: switch op { case "over": if simd { floatingAccumulateOpOverSIMD(got8, in[:n]) } else { floatingAccumulateOpOver(got8, in[:n]) } case "src": if simd { floatingAccumulateOpSrcSIMD(got8, in[:n]) } else { floatingAccumulateOpSrc(got8, in[:n]) } case "mask": if simd { floatingAccumulateMaskSIMD(got32, in[:n]) } else { floatingAccumulateMask(got32, in[:n]) } } } if op != "mask" { if !bytes.Equal(got8, want8) { t.Errorf("simd=%t, n=%d:\ngot: % x\nwant: % x", simd, n, got8, want8) } } else { if !uint32sEqual(got32, want32) { t.Errorf("simd=%t, n=%d:\ngot: % x\nwant: % x", simd, n, got32, want32) } } } } } func uint32sEqual(xs, ys []uint32) bool { if len(xs) != len(ys) { return false } for i := range xs { if xs[i] != ys[i] { return false } } return true } func float32sEqual(xs, ys []float32) bool { if len(xs) != len(ys) { return false } for i := range xs { if xs[i] != ys[i] { return false } } return true } func BenchmarkFixedAccumulateOpOver16(b *testing.B) { benchAcc(b, fxIn16, "over", false) } func BenchmarkFixedAccumulateOpOverSIMD16(b *testing.B) { benchAcc(b, fxIn16, "over", true) } func BenchmarkFixedAccumulateOpSrc16(b *testing.B) { benchAcc(b, fxIn16, "src", false) } func BenchmarkFixedAccumulateOpSrcSIMD16(b *testing.B) { benchAcc(b, fxIn16, "src", true) } func BenchmarkFixedAccumulateMask16(b *testing.B) { benchAcc(b, fxIn16, "mask", false) } func BenchmarkFixedAccumulateMaskSIMD16(b *testing.B) { benchAcc(b, fxIn16, "mask", true) } func BenchmarkFloatingAccumulateOpOver16(b *testing.B) { benchAcc(b, flIn16, "over", false) } func BenchmarkFloatingAccumulateOpOverSIMD16(b *testing.B) { benchAcc(b, flIn16, "over", true) } func BenchmarkFloatingAccumulateOpSrc16(b *testing.B) { benchAcc(b, flIn16, "src", false) } func BenchmarkFloatingAccumulateOpSrcSIMD16(b *testing.B) { benchAcc(b, flIn16, "src", true) } func BenchmarkFloatingAccumulateMask16(b *testing.B) { benchAcc(b, flIn16, "mask", false) } func BenchmarkFloatingAccumulateMaskSIMD16(b *testing.B) { benchAcc(b, flIn16, "mask", true) } func BenchmarkFixedAccumulateOpOver64(b *testing.B) { benchAcc(b, fxIn64, "over", false) } func BenchmarkFixedAccumulateOpOverSIMD64(b *testing.B) { benchAcc(b, fxIn64, "over", true) } func BenchmarkFixedAccumulateOpSrc64(b *testing.B) { benchAcc(b, fxIn64, "src", false) } func BenchmarkFixedAccumulateOpSrcSIMD64(b *testing.B) { benchAcc(b, fxIn64, "src", true) } func BenchmarkFixedAccumulateMask64(b *testing.B) { benchAcc(b, fxIn64, "mask", false) } func BenchmarkFixedAccumulateMaskSIMD64(b *testing.B) { benchAcc(b, fxIn64, "mask", true) } func BenchmarkFloatingAccumulateOpOver64(b *testing.B) { benchAcc(b, flIn64, "over", false) } func BenchmarkFloatingAccumulateOpOverSIMD64(b *testing.B) { benchAcc(b, flIn64, "over", true) } func BenchmarkFloatingAccumulateOpSrc64(b *testing.B) { benchAcc(b, flIn64, "src", false) } func BenchmarkFloatingAccumulateOpSrcSIMD64(b *testing.B) { benchAcc(b, flIn64, "src", true) } func BenchmarkFloatingAccumulateMask64(b *testing.B) { benchAcc(b, flIn64, "mask", false) } func BenchmarkFloatingAccumulateMaskSIMD64(b *testing.B) { benchAcc(b, flIn64, "mask", true) } func benchAcc(b *testing.B, in interface{}, op string, simd bool) { var f func() switch in := in.(type) { case []uint32: if simd && !haveFixedAccumulateSIMD { b.Skip("No SIMD implemention") } switch op { case "over": dst := make([]uint8, len(in)) if simd { f = func() { fixedAccumulateOpOverSIMD(dst, in) } } else { f = func() { fixedAccumulateOpOver(dst, in) } } case "src": dst := make([]uint8, len(in)) if simd { f = func() { fixedAccumulateOpSrcSIMD(dst, in) } } else { f = func() { fixedAccumulateOpSrc(dst, in) } } case "mask": buf := make([]uint32, len(in)) copy(buf, in) if simd { f = func() { fixedAccumulateMaskSIMD(buf) } } else { f = func() { fixedAccumulateMask(buf) } } } case []float32: if simd && !haveFloatingAccumulateSIMD { b.Skip("No SIMD implemention") } switch op { case "over": dst := make([]uint8, len(in)) if simd { f = func() { floatingAccumulateOpOverSIMD(dst, in) } } else { f = func() { floatingAccumulateOpOver(dst, in) } } case "src": dst := make([]uint8, len(in)) if simd { f = func() { floatingAccumulateOpSrcSIMD(dst, in) } } else { f = func() { floatingAccumulateOpSrc(dst, in) } } case "mask": dst := make([]uint32, len(in)) if simd { f = func() { floatingAccumulateMaskSIMD(dst, in) } } else { f = func() { floatingAccumulateMask(dst, in) } } } } b.ResetTimer() for i := 0; i < b.N; i++ { f() } } // itou exists because "uint32(int2ϕ(-1))" doesn't compile: constant -1 // overflows uint32. func itou(i int2ϕ) uint32 { return uint32(i) } var fxInShort = []uint32{ itou(+0x08000), // +0.125, // Running sum: +0.125 itou(-0x20000), // -0.500, // Running sum: -0.375 itou(+0x10000), // +0.250, // Running sum: -0.125 itou(+0x18000), // +0.375, // Running sum: +0.250 itou(+0x08000), // +0.125, // Running sum: +0.375 itou(+0x00000), // +0.000, // Running sum: +0.375 itou(-0x40000), // -1.000, // Running sum: -0.625 itou(-0x20000), // -0.500, // Running sum: -1.125 itou(+0x10000), // +0.250, // Running sum: -0.875 itou(+0x38000), // +0.875, // Running sum: +0.000 itou(+0x10000), // +0.250, // Running sum: +0.250 itou(+0x30000), // +0.750, // Running sum: +1.000 } var flInShort = []float32{ +0.125, // Running sum: +0.125 -0.500, // Running sum: -0.375 +0.250, // Running sum: -0.125 +0.375, // Running sum: +0.250 +0.125, // Running sum: +0.375 +0.000, // Running sum: +0.375 -1.000, // Running sum: -0.625 -0.500, // Running sum: -1.125 +0.250, // Running sum: -0.875 +0.875, // Running sum: +0.000 +0.250, // Running sum: +0.250 +0.750, // Running sum: +1.000 } // It's OK for fxMaskShort and flMaskShort to have slightly different values. // Both the fixed and floating point implementations already have (different) // rounding errors in the xxxLineTo methods before we get to accumulation. It's // OK for 50% coverage (in ideal math) to be approximated by either 0x7fff or // 0x8000. Both slices do contain checks that 0% and 100% map to 0x0000 and // 0xffff, as does checkCornersCenter in vector_test.go. // // It is important, though, for the SIMD and non-SIMD fixed point // implementations to give the exact same output, and likewise for the floating // point implementations. var fxMaskShort = []uint32{ 0x2000, 0x6000, 0x2000, 0x4000, 0x6000, 0x6000, 0xa000, 0xffff, 0xe000, 0x0000, 0x4000, 0xffff, } var flMaskShort = []uint32{ 0x1fff, 0x5fff, 0x1fff, 0x3fff, 0x5fff, 0x5fff, 0x9fff, 0xffff, 0xdfff, 0x0000, 0x3fff, 0xffff, } func TestMakeFxInXxx(t *testing.T) { dump := func(us []uint32) string { var b bytes.Buffer for i, u := range us { if i%8 == 0 { b.WriteByte('\n') } fmt.Fprintf(&b, "%#08x, ", u) } return b.String() } if !uint32sEqual(fxIn16, hardCodedFxIn16) { t.Errorf("height 16: got:%v\nwant:%v", dump(fxIn16), dump(hardCodedFxIn16)) } } func TestMakeFlInXxx(t *testing.T) { dump := func(fs []float32) string { var b bytes.Buffer for i, f := range fs { if i%8 == 0 { b.WriteByte('\n') } fmt.Fprintf(&b, "%v, ", f) } return b.String() } if !float32sEqual(flIn16, hardCodedFlIn16) { t.Errorf("height 16: got:%v\nwant:%v", dump(flIn16), dump(hardCodedFlIn16)) } } func makeInXxx(height int, useFloatingPointMath bool) *Rasterizer { width, data := scaledBenchmarkGlyphData(height) z := NewRasterizer(width, height) z.setUseFloatingPointMath(useFloatingPointMath) for _, d := range data { switch d.n { case 0: z.MoveTo(d.px, d.py) case 1: z.LineTo(d.px, d.py) case 2: z.QuadTo(d.px, d.py, d.qx, d.qy) } } return z } func makeFxInXxx(height int) []uint32 { z := makeInXxx(height, false) return z.bufU32 } func makeFlInXxx(height int) []float32 { z := makeInXxx(height, true) return z.bufF32 } // fxInXxx and flInXxx are the z.bufU32 and z.bufF32 inputs to the accumulate // functions when rasterizing benchmarkGlyphData at a height of Xxx pixels. // // fxMaskXxx and flMaskXxx are the corresponding golden outputs of those // accumulateMask functions. // // The hardCodedEtc versions are a sanity check for unexpected changes in the // rasterization implementations up to but not including accumulation. var ( fxIn16 = makeFxInXxx(16) fxIn64 = makeFxInXxx(64) flIn16 = makeFlInXxx(16) flIn64 = makeFlInXxx(64) ) var hardCodedFxIn16 = []uint32{ 0x00000000, 0x00000000, 0xffffe91d, 0xfffe7c4a, 0xfffeaa9f, 0xffff4e33, 0xffffc1c5, 0x00007782, 0x00009619, 0x0001a857, 0x000129e9, 0x00000028, 0x00000000, 0x00000000, 0xffff6e70, 0xfffd3199, 0xffff5ff8, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00014b29, 0x0002acf3, 0x000007e2, 0xffffca5a, 0xfffcab73, 0xffff8a34, 0x00001b55, 0x0001b334, 0x0001449e, 0x0000434d, 0xffff62ec, 0xfffe1443, 0xffff325d, 0x00000000, 0x0002234a, 0x0001dcb6, 0xfffe2948, 0xfffdd6b8, 0x00000000, 0x00028cc0, 0x00017340, 0x00000000, 0x00000000, 0x00000000, 0xffffd2d6, 0xfffcadd0, 0xffff7f5c, 0x00007400, 0x00038c00, 0xfffe9260, 0xffff2da0, 0x0000023a, 0x0002259b, 0x0000182a, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xfffdc600, 0xfffe3a00, 0x00000059, 0x0003a44d, 0x00005b59, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xfffe33f3, 0xfffdcc0d, 0x00000000, 0x00033c02, 0x0000c3fe, 0x00000000, 0x00000000, 0xffffa13d, 0xfffeeec8, 0xffff8c02, 0xffff8c48, 0xffffc7b5, 0x00000000, 0xffff5b68, 0xffff3498, 0x00000000, 0x00033c00, 0x0000c400, 0xffff9bc4, 0xfffdf4a3, 0xfffe8df3, 0xffffe1a8, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00033c00, 0x000092c7, 0xfffcf373, 0xffff3dc7, 0x00000fcc, 0x00011ae7, 0x000130c3, 0x0000680d, 0x00004a59, 0x00000a20, 0xfffe9dc4, 0xfffe4a3c, 0x00000000, 0x00033c00, 0xfffe87ef, 0xfffe3c11, 0x0000105e, 0x0002b9c4, 0x000135dc, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xfffe3600, 0xfffdca00, 0x00000000, 0x00033c00, 0xfffd9000, 0xffff3400, 0x0000e400, 0x00031c00, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xfffe3600, 0xfffdca00, 0x00000000, 0x00033c00, 0xfffcf9a5, 0xffffca5b, 0x000120e6, 0x0002df1a, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xfffdb195, 0xfffe4e6b, 0x00000000, 0x00033c00, 0xfffd9e00, 0xffff2600, 0x00002f0e, 0x00033ea3, 0x0000924d, 0x00000000, 0x00000000, 0x00000000, 0xfffe83b3, 0xfffd881d, 0xfffff431, 0x00000000, 0x00031f60, 0xffff297a, 0xfffdb726, 0x00000000, 0x000053a7, 0x0001b506, 0x0000a24b, 0xffffa32d, 0xfffead9b, 0xffff0479, 0xffffffc9, 0x00000000, 0x00000000, 0x0002d800, 0x0001249d, 0xfffd67bb, 0xfffe9baa, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x0000ac03, 0x0001448b, 0xfffe0f70, 0x00000000, 0x000229ea, 0x0001d616, 0xffffff8c, 0xfffebf76, 0xfffe54d9, 0xffff5d9e, 0xffffd3eb, 0x0000c65e, 0x0000fc15, 0x0001d491, 0xffffb566, 0xfffd9433, 0x00000000, 0x0000e4ec, } var hardCodedFlIn16 = []float32{ 0, 0, -0.022306755, -0.3782405, -0.33334962, -0.1741521, -0.0607556, 0.11660573, 0.14664596, 0.41462868, 0.2907673, 0.0001568835, 0, 0, -0.14239307, -0.7012868, -0.15632017, 0, 0, 0, 0, 0, 0, 0.3230303, 0.6690931, 0.007876594, -0.05189419, -0.832786, -0.11531975, 0.026225802, 0.42518616, 0.3154636, 0.06598757, -0.15304244, -0.47969276, -0.20012794, 0, 0.5327272, 0.46727282, -0.45950258, -0.5404974, 0, 0.63484025, 0.36515975, 0, 0, 0, -0.04351709, -0.8293345, -0.12714837, 0.11087036, 0.88912964, -0.35792422, -0.2053554, 0.0022513224, 0.5374398, 0.023588525, 0, 0, 0, 0, -0.55346966, -0.44653034, 0.0002531938, 0.9088273, 0.090919495, 0, 0, 0, 0, 0, 0, 0, 0, -0.44745448, -0.5525455, 0, 0.80748945, 0.19251058, 0, 0, -0.092476256, -0.2661464, -0.11322958, -0.11298219, -0.055094406, 0, -0.16045958, -0.1996116, 0, 0.80748653, 0.19251347, -0.09804727, -0.51129663, -0.3610403, -0.029615778, 0, 0, 0, 0, 0, 0, 0, 0.80748653, 0.14411622, -0.76251525, -0.1890875, 0.01527351, 0.27528667, 0.29730347, 0.101477206, 0.07259522, 0.009900213, -0.34395567, -0.42788061, 0, 0.80748653, -0.3648737, -0.44261283, 0.015778137, 0.6826565, 0.30156538, 0, 0, 0, 0, -0.44563293, -0.55436707, 0, 0.80748653, -0.60703933, -0.20044717, 0.22371745, 0.77628255, 0, 0, 0, 0, 0, -0.44563293, -0.55436707, 0, 0.80748653, -0.7550391, -0.05244744, 0.2797074, 0.72029257, 0, 0, 0, 0, 0, -0.57440215, -0.42559785, 0, 0.80748653, -0.59273535, -0.21475118, 0.04544862, 0.81148535, 0.14306602, 0, 0, 0, -0.369642, -0.61841226, -0.011945802, 0, 0.7791623, -0.20691396, -0.57224834, 0, 0.08218567, 0.42637306, 0.1586175, -0.089709565, -0.32935485, -0.24788953, -0.00022224105, 0, 0, 0.7085409, 0.28821066, -0.64765793, -0.34909368, 0, 0, 0, 0, 0, 0.16679136, 0.31914657, -0.48593786, 0, 0.537915, 0.462085, -0.00041967133, -0.3120329, -0.41914812, -0.15886839, -0.042683028, 0.19370951, 0.24624406, 0.45803425, -0.07049577, -0.6091341, 0, 0.22253075, } var fxMask16 = []uint32{ 0x0000, 0x0000, 0x05b8, 0x66a6, 0xbbfe, 0xe871, 0xf800, 0xda20, 0xb499, 0x4a84, 0x0009, 0x0000, 0x0000, 0x0000, 0x2463, 0xd7fd, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xad35, 0x01f8, 0x0000, 0x0d69, 0xe28c, 0xffff, 0xf92a, 0x8c5d, 0x3b36, 0x2a62, 0x51a7, 0xcc97, 0xffff, 0xffff, 0x772d, 0x0000, 0x75ad, 0xffff, 0xffff, 0x5ccf, 0x0000, 0x0000, 0x0000, 0x0000, 0x0b4a, 0xdfd6, 0xffff, 0xe2ff, 0x0000, 0x5b67, 0x8fff, 0x8f70, 0x060a, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8e7f, 0xffff, 0xffe9, 0x16d6, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x7303, 0xffff, 0xffff, 0x30ff, 0x0000, 0x0000, 0x0000, 0x17b0, 0x5bfe, 0x78fe, 0x95ec, 0xa3fe, 0xa3fe, 0xcd24, 0xfffe, 0xfffe, 0x30fe, 0x0001, 0x190d, 0x9be5, 0xf868, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0x30fe, 0x0c4c, 0xcf6f, 0xfffe, 0xfc0b, 0xb551, 0x6920, 0x4f1d, 0x3c87, 0x39ff, 0x928e, 0xffff, 0xffff, 0x30ff, 0x8f03, 0xffff, 0xfbe7, 0x4d76, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x727f, 0xffff, 0xffff, 0x30ff, 0xccff, 0xffff, 0xc6ff, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x727f, 0xffff, 0xffff, 0x30ff, 0xf296, 0xffff, 0xb7c6, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x939a, 0xffff, 0xffff, 0x30ff, 0xc97f, 0xffff, 0xf43c, 0x2493, 0x0000, 0x0000, 0x0000, 0x0000, 0x5f13, 0xfd0c, 0xffff, 0xffff, 0x3827, 0x6dc9, 0xffff, 0xffff, 0xeb16, 0x7dd4, 0x5541, 0x6c76, 0xc10f, 0xfff1, 0xffff, 0xffff, 0xffff, 0x49ff, 0x00d8, 0xa6e9, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0xfffe, 0xd4fe, 0x83db, 0xffff, 0xffff, 0x7584, 0x0000, 0x001c, 0x503e, 0xbb08, 0xe3a1, 0xeea6, 0xbd0e, 0x7e09, 0x08e5, 0x1b8b, 0xb67f, 0xb67f, 0x7d44, } var flMask16 = []uint32{ 0x0000, 0x0000, 0x05b5, 0x668a, 0xbbe0, 0xe875, 0xf803, 0xda29, 0xb49f, 0x4a7a, 0x000a, 0x0000, 0x0000, 0x0000, 0x2473, 0xd7fb, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xad4d, 0x0204, 0x0000, 0x0d48, 0xe27a, 0xffff, 0xf949, 0x8c70, 0x3bae, 0x2ac9, 0x51f7, 0xccc4, 0xffff, 0xffff, 0x779f, 0x0000, 0x75a1, 0xffff, 0xffff, 0x5d7b, 0x0000, 0x0000, 0x0000, 0x0000, 0x0b23, 0xdf73, 0xffff, 0xe39d, 0x0000, 0x5ba0, 0x9033, 0x8f9f, 0x0609, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8db0, 0xffff, 0xffef, 0x1746, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x728c, 0xffff, 0xffff, 0x3148, 0x0000, 0x0000, 0x0000, 0x17ac, 0x5bce, 0x78cb, 0x95b7, 0xa3d2, 0xa3d2, 0xcce6, 0xffff, 0xffff, 0x3148, 0x0000, 0x1919, 0x9bfd, 0xf86b, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x3148, 0x0c63, 0xcf97, 0xffff, 0xfc17, 0xb59d, 0x6981, 0x4f87, 0x3cf1, 0x3a68, 0x9276, 0xffff, 0xffff, 0x3148, 0x8eb0, 0xffff, 0xfbf5, 0x4d33, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x7214, 0xffff, 0xffff, 0x3148, 0xccaf, 0xffff, 0xc6ba, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x7214, 0xffff, 0xffff, 0x3148, 0xf292, 0xffff, 0xb865, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x930c, 0xffff, 0xffff, 0x3148, 0xc906, 0xffff, 0xf45d, 0x249f, 0x0000, 0x0000, 0x0000, 0x0000, 0x5ea0, 0xfcf1, 0xffff, 0xffff, 0x3888, 0x6d81, 0xffff, 0xffff, 0xeaf5, 0x7dcf, 0x5533, 0x6c2b, 0xc07b, 0xfff1, 0xffff, 0xffff, 0xffff, 0x4a9d, 0x00d4, 0xa6a1, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xd54d, 0x8399, 0xffff, 0xffff, 0x764b, 0x0000, 0x001b, 0x4ffc, 0xbb4a, 0xe3f5, 0xeee3, 0xbd4c, 0x7e42, 0x0900, 0x1b0c, 0xb6fc, 0xb6fc, 0x7e04, } // TestFixedFloatingCloseness compares the closeness of the fixed point and // floating point rasterizer. func TestFixedFloatingCloseness(t *testing.T) { if len(fxMask16) != len(flMask16) { t.Fatalf("len(fxMask16) != len(flMask16)") } total := uint32(0) for i := range fxMask16 { a := fxMask16[i] b := flMask16[i] if a > b { total += a - b } else { total += b - a } } n := len(fxMask16) // This log message is useful when changing the fixed point rasterizer // implementation, such as by changing ϕ. Assuming that the floating point // rasterizer is accurate, the average difference is a measure of how // inaccurate the (faster) fixed point rasterizer is. // // Smaller is better. percent := float64(total*100) / float64(n*65535) t.Logf("Comparing closeness of the fixed point and floating point rasterizer.\n"+ "Specifically, the elements of fxMask16 and flMask16.\n"+ "Total diff = %d, n = %d, avg = %.5f out of 65535, or %.5f%%.\n", total, n, float64(total)/float64(n), percent) const thresholdPercent = 1.0 if percent > thresholdPercent { t.Errorf("average difference: got %.5f%%, want <= %.5f%%", percent, thresholdPercent) } }