diff options
Diffstat (limited to 'vendor/golang.org/x/image/math')
-rw-r--r-- | vendor/golang.org/x/image/math/f32/f32.go | 37 | ||||
-rw-r--r-- | vendor/golang.org/x/image/math/f64/f64.go | 37 | ||||
-rw-r--r-- | vendor/golang.org/x/image/math/fixed/fixed_test.go | 439 |
3 files changed, 0 insertions, 513 deletions
diff --git a/vendor/golang.org/x/image/math/f32/f32.go b/vendor/golang.org/x/image/math/f32/f32.go deleted file mode 100644 index 4ca1eb47d..000000000 --- a/vendor/golang.org/x/image/math/f32/f32.go +++ /dev/null @@ -1,37 +0,0 @@ -// 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 f32 implements float32 vector and matrix types. -package f32 // import "golang.org/x/image/math/f32" - -// Vec2 is a 2-element vector. -type Vec2 [2]float32 - -// Vec3 is a 3-element vector. -type Vec3 [3]float32 - -// Vec4 is a 4-element vector. -type Vec4 [4]float32 - -// Mat3 is a 3x3 matrix in row major order. -// -// m[3*r + c] is the element in the r'th row and c'th column. -type Mat3 [9]float32 - -// Mat4 is a 4x4 matrix in row major order. -// -// m[4*r + c] is the element in the r'th row and c'th column. -type Mat4 [16]float32 - -// Aff3 is a 3x3 affine transformation matrix in row major order, where the -// bottom row is implicitly [0 0 1]. -// -// m[3*r + c] is the element in the r'th row and c'th column. -type Aff3 [6]float32 - -// Aff4 is a 4x4 affine transformation matrix in row major order, where the -// bottom row is implicitly [0 0 0 1]. -// -// m[4*r + c] is the element in the r'th row and c'th column. -type Aff4 [12]float32 diff --git a/vendor/golang.org/x/image/math/f64/f64.go b/vendor/golang.org/x/image/math/f64/f64.go deleted file mode 100644 index a1f7fc0ef..000000000 --- a/vendor/golang.org/x/image/math/f64/f64.go +++ /dev/null @@ -1,37 +0,0 @@ -// 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 f64 implements float64 vector and matrix types. -package f64 // import "golang.org/x/image/math/f64" - -// Vec2 is a 2-element vector. -type Vec2 [2]float64 - -// Vec3 is a 3-element vector. -type Vec3 [3]float64 - -// Vec4 is a 4-element vector. -type Vec4 [4]float64 - -// Mat3 is a 3x3 matrix in row major order. -// -// m[3*r + c] is the element in the r'th row and c'th column. -type Mat3 [9]float64 - -// Mat4 is a 4x4 matrix in row major order. -// -// m[4*r + c] is the element in the r'th row and c'th column. -type Mat4 [16]float64 - -// Aff3 is a 3x3 affine transformation matrix in row major order, where the -// bottom row is implicitly [0 0 1]. -// -// m[3*r + c] is the element in the r'th row and c'th column. -type Aff3 [6]float64 - -// Aff4 is a 4x4 affine transformation matrix in row major order, where the -// bottom row is implicitly [0 0 0 1]. -// -// m[4*r + c] is the element in the r'th row and c'th column. -type Aff4 [12]float64 diff --git a/vendor/golang.org/x/image/math/fixed/fixed_test.go b/vendor/golang.org/x/image/math/fixed/fixed_test.go deleted file mode 100644 index c81fb7205..000000000 --- a/vendor/golang.org/x/image/math/fixed/fixed_test.go +++ /dev/null @@ -1,439 +0,0 @@ -// 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 ( - "math" - "math/rand" - "testing" -) - -var testCases = []struct { - x float64 - s26_6 string - s52_12 string - floor int - round int - ceil int -}{{ - x: 0, - s26_6: "0:00", - s52_12: "0:0000", - floor: 0, - round: 0, - ceil: 0, -}, { - x: 1, - s26_6: "1:00", - s52_12: "1:0000", - floor: 1, - round: 1, - ceil: 1, -}, { - x: 1.25, - s26_6: "1:16", - s52_12: "1:1024", - floor: 1, - round: 1, - ceil: 2, -}, { - x: 2.5, - s26_6: "2:32", - s52_12: "2:2048", - floor: 2, - round: 3, - ceil: 3, -}, { - x: 63 / 64.0, - s26_6: "0:63", - s52_12: "0:4032", - floor: 0, - round: 1, - ceil: 1, -}, { - x: -0.5, - s26_6: "-0:32", - s52_12: "-0:2048", - floor: -1, - round: +0, - ceil: +0, -}, { - x: -4.125, - s26_6: "-4:08", - s52_12: "-4:0512", - floor: -5, - round: -4, - ceil: -4, -}, { - x: -7.75, - s26_6: "-7:48", - s52_12: "-7:3072", - floor: -8, - round: -8, - ceil: -7, -}} - -func TestInt26_6(t *testing.T) { - const one = Int26_6(1 << 6) - for _, tc := range testCases { - x := Int26_6(tc.x * (1 << 6)) - if got, want := x.String(), tc.s26_6; got != want { - t.Errorf("tc.x=%v: String: got %q, want %q", tc.x, got, want) - } - if got, want := x.Floor(), tc.floor; got != want { - t.Errorf("tc.x=%v: Floor: got %v, want %v", tc.x, got, want) - } - if got, want := x.Round(), tc.round; got != want { - t.Errorf("tc.x=%v: Round: got %v, want %v", tc.x, got, want) - } - if got, want := x.Ceil(), tc.ceil; got != want { - t.Errorf("tc.x=%v: Ceil: got %v, want %v", tc.x, got, want) - } - if got, want := x.Mul(one), x; got != want { - t.Errorf("tc.x=%v: Mul by one: got %v, want %v", tc.x, got, want) - } - if got, want := x.mul(one), x; got != want { - t.Errorf("tc.x=%v: mul by one: got %v, want %v", tc.x, got, want) - } - } -} - -func TestInt52_12(t *testing.T) { - const one = Int52_12(1 << 12) - for _, tc := range testCases { - x := Int52_12(tc.x * (1 << 12)) - if got, want := x.String(), tc.s52_12; got != want { - t.Errorf("tc.x=%v: String: got %q, want %q", tc.x, got, want) - } - if got, want := x.Floor(), tc.floor; got != want { - t.Errorf("tc.x=%v: Floor: got %v, want %v", tc.x, got, want) - } - if got, want := x.Round(), tc.round; got != want { - t.Errorf("tc.x=%v: Round: got %v, want %v", tc.x, got, want) - } - if got, want := x.Ceil(), tc.ceil; got != want { - t.Errorf("tc.x=%v: Ceil: got %v, want %v", tc.x, got, want) - } - if got, want := x.Mul(one), x; got != want { - t.Errorf("tc.x=%v: Mul by one: got %v, want %v", tc.x, got, want) - } - } -} - -var mulTestCases = []struct { - x float64 - y float64 - z26_6 float64 // Equals truncate26_6(x)*truncate26_6(y). - z52_12 float64 // Equals truncate52_12(x)*truncate52_12(y). - s26_6 string - s52_12 string -}{{ - x: 0, - y: 1.5, - z26_6: 0, - z52_12: 0, - s26_6: "0:00", - s52_12: "0:0000", -}, { - x: +1.25, - y: +4, - z26_6: +5, - z52_12: +5, - s26_6: "5:00", - s52_12: "5:0000", -}, { - x: +1.25, - y: -4, - z26_6: -5, - z52_12: -5, - s26_6: "-5:00", - s52_12: "-5:0000", -}, { - x: -1.25, - y: +4, - z26_6: -5, - z52_12: -5, - s26_6: "-5:00", - s52_12: "-5:0000", -}, { - x: -1.25, - y: -4, - z26_6: +5, - z52_12: +5, - s26_6: "5:00", - s52_12: "5:0000", -}, { - x: 1.25, - y: 1.5, - z26_6: 1.875, - z52_12: 1.875, - s26_6: "1:56", - s52_12: "1:3584", -}, { - x: 1234.5, - y: -8888.875, - z26_6: -10973316.1875, - z52_12: -10973316.1875, - s26_6: "-10973316:12", - s52_12: "-10973316:0768", -}, { - x: 1.515625, // 1 + 33/64 = 97/64 - y: 1.531250, // 1 + 34/64 = 98/64 - z26_6: 2.32080078125, // 2 + 1314/4096 = 9506/4096 - z52_12: 2.32080078125, // 2 + 1314/4096 = 9506/4096 - s26_6: "2:21", // 2.32812500000, which is closer than 2:20 (in decimal, 2.3125) - s52_12: "2:1314", // 2.32080078125 -}, { - x: 0.500244140625, // 2049/4096, approximately 32/64 - y: 0.500732421875, // 2051/4096, approximately 32/64 - z26_6: 0.25, // 4194304/16777216, or 1024/4096 - z52_12: 0.2504884600639343, // 4202499/16777216 - s26_6: "0:16", // 0.25000000000 - s52_12: "0:1026", // 0.25048828125, which is closer than 0:1027 (in decimal, 0.250732421875) -}, { - x: 0.015625, // 1/64 - y: 0.000244140625, // 1/4096, approximately 0/64 - z26_6: 0.0, // 0 - z52_12: 0.000003814697265625, // 1/262144 - s26_6: "0:00", // 0 - s52_12: "0:0000", // 0, which is closer than 0:0001 (in decimal, 0.000244140625) -}, { - // Round the Int52_12 calculation down. - x: 1.44140625, // 1 + 1808/4096 = 5904/4096, approximately 92/64 - y: 1.44140625, // 1 + 1808/4096 = 5904/4096, approximately 92/64 - z26_6: 2.06640625, // 2 + 272/4096 = 8464/4096 - z52_12: 2.0776519775390625, // 2 + 318/4096 + 256/16777216 = 34857216/16777216 - s26_6: "2:04", // 2.06250000000, which is closer than 2:05 (in decimal, 2.078125000000) - s52_12: "2:0318", // 2.07763671875, which is closer than 2:0319 (in decimal, 2.077880859375) -}, { - // Round the Int52_12 calculation up. - x: 1.44140625, // 1 + 1808/4096 = 5904/4096, approximately 92/64 - y: 1.441650390625, // 1 + 1809/4096 = 5905/4096, approximately 92/64 - z26_6: 2.06640625, // 2 + 272/4096 = 8464/4096 - z52_12: 2.0780038833618164, // 2 + 319/4096 + 2064/16777216 = 34863120/16777216 - s26_6: "2:04", // 2.06250000000, which is closer than 2:05 (in decimal, 2.078125000000) - s52_12: "2:0320", // 2.07812500000, which is closer than 2:0319 (in decimal, 2.077880859375) -}} - -func TestInt26_6Mul(t *testing.T) { - for _, tc := range mulTestCases { - x := Int26_6(tc.x * (1 << 6)) - y := Int26_6(tc.y * (1 << 6)) - if z := float64(x) * float64(y) / (1 << 12); z != tc.z26_6 { - t.Errorf("tc.x=%v, tc.y=%v: z: got %v, want %v", tc.x, tc.y, z, tc.z26_6) - continue - } - if got, want := x.Mul(y).String(), tc.s26_6; got != want { - t.Errorf("tc.x=%v: Mul: got %q, want %q", tc.x, got, want) - } - } -} - -func TestInt52_12Mul(t *testing.T) { - for _, tc := range mulTestCases { - x := Int52_12(tc.x * (1 << 12)) - y := Int52_12(tc.y * (1 << 12)) - if z := float64(x) * float64(y) / (1 << 24); z != tc.z52_12 { - t.Errorf("tc.x=%v, tc.y=%v: z: got %v, want %v", tc.x, tc.y, z, tc.z52_12) - continue - } - if got, want := x.Mul(y).String(), tc.s52_12; got != want { - t.Errorf("tc.x=%v: Mul: got %q, want %q", tc.x, got, want) - } - } -} - -func TestInt26_6MulByOneMinusIota(t *testing.T) { - const ( - totalBits = 32 - fracBits = 6 - - oneMinusIota = Int26_6(1<<fracBits) - 1 - oneMinusIotaF = float64(oneMinusIota) / (1 << fracBits) - ) - - for _, neg := range []bool{false, true} { - for i := uint(0); i < totalBits; i++ { - x := Int26_6(1 << i) - if neg { - x = -x - } else if i == totalBits-1 { - // A signed int32 can't represent 1<<31. - continue - } - - // want equals x * oneMinusIota, rounded to nearest. - want := Int26_6(0) - if -1<<fracBits < x && x < 1<<fracBits { - // (x * oneMinusIota) isn't exactly representable as an - // Int26_6. Calculate the rounded value using float64 math. - xF := float64(x) / (1 << fracBits) - wantF := xF * oneMinusIotaF * (1 << fracBits) - want = Int26_6(math.Floor(wantF + 0.5)) - } else { - // (x * oneMinusIota) is exactly representable. - want = oneMinusIota << (i - fracBits) - if neg { - want = -want - } - } - - if got := x.Mul(oneMinusIota); got != want { - t.Errorf("neg=%t, i=%d, x=%v, Mul: got %v, want %v", neg, i, x, got, want) - } - if got := x.mul(oneMinusIota); got != want { - t.Errorf("neg=%t, i=%d, x=%v, mul: got %v, want %v", neg, i, x, got, want) - } - } - } -} - -func TestInt52_12MulByOneMinusIota(t *testing.T) { - const ( - totalBits = 64 - fracBits = 12 - - oneMinusIota = Int52_12(1<<fracBits) - 1 - oneMinusIotaF = float64(oneMinusIota) / (1 << fracBits) - ) - - for _, neg := range []bool{false, true} { - for i := uint(0); i < totalBits; i++ { - x := Int52_12(1 << i) - if neg { - x = -x - } else if i == totalBits-1 { - // A signed int64 can't represent 1<<63. - continue - } - - // want equals x * oneMinusIota, rounded to nearest. - want := Int52_12(0) - if -1<<fracBits < x && x < 1<<fracBits { - // (x * oneMinusIota) isn't exactly representable as an - // Int52_12. Calculate the rounded value using float64 math. - xF := float64(x) / (1 << fracBits) - wantF := xF * oneMinusIotaF * (1 << fracBits) - want = Int52_12(math.Floor(wantF + 0.5)) - } else { - // (x * oneMinusIota) is exactly representable. - want = oneMinusIota << (i - fracBits) - if neg { - want = -want - } - } - - if got := x.Mul(oneMinusIota); got != want { - t.Errorf("neg=%t, i=%d, x=%v, Mul: got %v, want %v", neg, i, x, got, want) - } - } - } -} - -func TestInt26_6MulVsMul(t *testing.T) { - rng := rand.New(rand.NewSource(1)) - for i := 0; i < 10000; i++ { - u := Int26_6(rng.Uint32()) - v := Int26_6(rng.Uint32()) - Mul := u.Mul(v) - mul := u.mul(v) - if Mul != mul { - t.Errorf("u=%#08x, v=%#08x: Mul=%#08x and mul=%#08x differ", - uint32(u), uint32(v), uint32(Mul), uint32(mul)) - } - } -} - -func TestMuli32(t *testing.T) { - rng := rand.New(rand.NewSource(2)) - for i := 0; i < 10000; i++ { - u := int32(rng.Uint32()) - v := int32(rng.Uint32()) - lo, hi := muli32(u, v) - got := uint64(lo) | uint64(hi)<<32 - want := uint64(int64(u) * int64(v)) - if got != want { - t.Errorf("u=%#08x, v=%#08x: got %#016x, want %#016x", uint32(u), uint32(v), got, want) - } - } -} - -func TestMulu32(t *testing.T) { - rng := rand.New(rand.NewSource(3)) - for i := 0; i < 10000; i++ { - u := rng.Uint32() - v := rng.Uint32() - lo, hi := mulu32(u, v) - got := uint64(lo) | uint64(hi)<<32 - want := uint64(u) * uint64(v) - if got != want { - t.Errorf("u=%#08x, v=%#08x: got %#016x, want %#016x", u, v, got, want) - } - } -} - -// mul (with a lower case 'm') is an alternative implementation of Int26_6.Mul -// (with an upper case 'M'). It has the same structure as the Int52_12.Mul -// implementation, but Int26_6.mul is easier to test since Go has built-in -// 64-bit integers. -func (x Int26_6) mul(y Int26_6) Int26_6 { - const M, N = 26, 6 - lo, hi := muli32(int32(x), int32(y)) - ret := Int26_6(hi<<M | lo>>N) - ret += Int26_6((lo >> (N - 1)) & 1) // Round to nearest, instead of rounding down. - return ret -} - -// muli32 multiplies two int32 values, returning the 64-bit signed integer -// result as two uint32 values. -// -// muli32 isn't used directly by this package, but it has the same structure as -// muli64, and muli32 is easier to test since Go has built-in 64-bit integers. -func muli32(u, v int32) (lo, hi uint32) { - const ( - s = 16 - mask = 1<<s - 1 - ) - - u1 := uint32(u >> s) - u0 := uint32(u & mask) - v1 := uint32(v >> s) - v0 := uint32(v & mask) - - w0 := u0 * v0 - t := u1*v0 + w0>>s - w1 := t & mask - w2 := uint32(int32(t) >> s) - w1 += u0 * v1 - return uint32(u) * uint32(v), u1*v1 + w2 + uint32(int32(w1)>>s) -} - -// mulu32 is like muli32, except that it multiplies unsigned instead of signed -// values. -// -// This implementation comes from $GOROOT/src/runtime/softfloat64.go's mullu -// function, which is in turn adapted from Hacker's Delight. -// -// mulu32 (and its corresponding test, TestMulu32) isn't used directly by this -// package. It is provided in this test file as a reference point to compare -// the muli32 (and TestMuli32) implementations against. -func mulu32(u, v uint32) (lo, hi uint32) { - const ( - s = 16 - mask = 1<<s - 1 - ) - - u0 := u & mask - u1 := u >> s - v0 := v & mask - v1 := v >> s - - w0 := u0 * v0 - t := u1*v0 + w0>>s - w1 := t & mask - w2 := t >> s - w1 += u0 * v1 - return u * v, u1*v1 + w2 + w1>>s -} |