| // 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 |
| } |
