golang-image/math/fixed/fixed_test.go
Nigel Tao 112f996332 math/fixed: add Mul methods.
Change-Id: Id6f9f5825527b311b5b1aa4ae0923c9551fa076b
Reviewed-on: https://go-review.googlesource.com/27413
Reviewed-by: David Crawshaw <crawshaw@golang.org>
Run-TryBot: David Crawshaw <crawshaw@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
2016-08-25 00:04:48 +00:00

440 lines
12 KiB
Go

// 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
}